decimal.py revision b7e835b820fc7d17a02dc4cdf3b745bb993952ad
17c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Copyright (c) 2004 Python Software Foundation. 27c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# All rights reserved. 37c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Written by Eric Price <eprice at tjhsst.edu> 57c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Facundo Batista <facundo at taniquetil.com.ar> 67c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Raymond Hettinger <python at rcn.com> 71f34eb17b501687c1251678bcffab9accd432591Fred Drake# and Aahz <aahz at pobox.com> 87c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Tim Peters 97c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1027dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# This module is currently Py2.3 compatible and should be kept that way 1127dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# unless a major compelling advantage arises. IOW, 2.3 compatibility is 1227dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# strongly preferred, but not guaranteed. 1327dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger 1427dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# Also, this module should be kept in sync with the latest updates of 1527dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# the IBM specification as it evolves. Those updates will be treated 1627dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# as bug fixes (deviation from the spec is a compatibility, usability 1727dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# bug) and will be backported. At this point the spec is stabilizing 1827dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# and the updates are becoming fewer, smaller, and less significant. 197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerThis is a Py2.3 implementation of decimal floating point arithmetic based on 227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerthe General Decimal Arithmetic Specification: 237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www2.hursley.ibm.com/decimal/decarith.html 257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 260ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerand IEEE standard 854-1987: 277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html 297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal floating point has finite precision with arbitrarily large bounds. 317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo BatistaThe purpose of this module is to support arithmetic using familiar 3359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista"schoolhouse" rules and to avoid some of the tricky representation 347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerissues associated with binary floating point. The package is especially 357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingeruseful for financial applications or for contexts where users have 367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerexpectations that are at odds with binary floating point (for instance, 377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerin binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead 38abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettingerof the expected Decimal('0.00') returned by decimal floating point). 397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerHere are some examples of using the decimal module: 417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> from decimal import * 43bd7f76dd04780304c397323ae994092ce759d5a2Raymond Hettinger>>> setcontext(ExtendedContext) 447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(0) 45abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('0') 46abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger>>> Decimal('1') 47abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('1') 48abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger>>> Decimal('-.0123') 49abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('-0.0123') 507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(123456) 51abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('123456') 52abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger>>> Decimal('123.45e12345678901234567890') 53abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('1.2345E+12345678901234567892') 54abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger>>> Decimal('1.33') + Decimal('1.27') 55abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('2.60') 56abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41') 57abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('-2.20') 587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> dig = Decimal(1) 597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333 617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> getcontext().prec = 18 627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333333333333 647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig.sqrt() 657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3).sqrt() 677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1.73205080756887729 687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3) ** 123 697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger4.85192780976896427E+58 707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> inf = Decimal(1) / Decimal(0) 717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print inf 727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> neginf = Decimal(-1) / Decimal(0) 747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf 757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf + inf 777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf * inf 797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 82bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> getcontext().traps[DivisionByZero] = 1 837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDivisionByZero: x / 0 897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c = Context() 90bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 915aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c.divide(Decimal(0), Decimal(0)) 94abe32371878dcaea31c835e10144fdaa2eca6492Raymond HettingerDecimal('NaN') 95bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 1 965aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 985aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 995aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 1017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 1027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 1037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1065aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond HettingerInvalidOperation: 0 / 0 1075aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1095aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 110bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 1117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 1127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 1135aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> 1167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 1177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger__all__ = [ 1197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Two major classes 1207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'Decimal', 'Context', 1217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Contexts 1239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 'DefaultContext', 'BasicContext', 'ExtendedContext', 1247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Exceptions 126d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', 127d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', 1287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Constants for use in setting up contexts 1307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', 131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP', 1327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Functions for manipulating contexts 1348b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 'setcontext', 'getcontext', 'localcontext' 1357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger] 1367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 137eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettingerimport copy as _copy 138f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettingerimport math as _math 1397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 140097a1903035f9ee2efb1953306123f183124125dRaymond Hettingertry: 141097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger from collections import namedtuple as _namedtuple 142097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') 143097a1903035f9ee2efb1953306123f183124125dRaymond Hettingerexcept ImportError: 144097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger DecimalTuple = lambda *args: args 145097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger 14659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Rounding 1470ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1480ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1490ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1500ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1510ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1520ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1530ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo BatistaROUND_05UP = 'ROUND_05UP' 1557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Errors 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1595aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 167cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis handle -- Called when context._raise_error is called and the 168cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis trap_enabler is set. First argument is self, second is the 169cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context. More arguments can be given, those being after 170cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis the explanation in _raise_error (For example, 171cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context._raise_error(NewError, '(-x)!', self._sign) would 172cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis call NewError().handle(context, self._sign).) 173cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 18659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista representation. This may occur when the exponent of a zero result would 18759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be outside the bounds of a representation, or when a large normal 18859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista number would have an encoded exponent that cannot be represented. In 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 20059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 0 * (+-)INF 20159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista (+-)INF / (+-)INF 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of the operation after these is a quiet positive NaN, 212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista except when the cause is a signaling NaN, in which case the result is 213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista also a quiet NaN, but with the original sign, and an optional 214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista diagnostic information. 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 2180f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) 2190f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return ans._fix_nan(context) 220c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson return _NaN 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 22759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista syntax. The result is [0,qNaN]. 2287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 229cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis def handle(self, context, *args): 230c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson return _NaN 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 244cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 245cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, sign, *args): 246b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[sign] 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 25359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista longer than precision). The result is [0,qNaN]. 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 255cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 257c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson return _NaN 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 26459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the dividend is also zero. The result is [0,qNaN]. 2657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 266cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 267cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, *args): 268c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson return _NaN 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 27559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista were non-zero), or if an overflow or underflow condition occurs. The 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 28659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista detected during an operation. This can occur if contexts are not checked 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 28959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista was specified. These aspects of the context need only be checked when 29059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the values are required to be used. The result is [0,qNaN]. 2917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 292cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 294c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson return _NaN 2957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 2987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 3007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 30159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista coefficient), or if an overflow or underflow condition occurs. The 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 3057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 31359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin, before any rounding). The result in all cases is unchanged. 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 33159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista where sign is the sign of the intermediate result. For round-down, the 3327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 33359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista current precision, with the sign of the intermediate result. For 3347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 33559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 33759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 3390f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista """ 340cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ROUND_HALF_DOWN, ROUND_UP): 344b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[sign] 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 347b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[sign] 34872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 34972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 352b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[sign] 35372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 36359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin). That is, the result is both inexact and subnormal. 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 36659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista necessary, so that its exponent is not less than Etiny. This may result 3677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3725aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 373fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 374cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Underflow, InvalidOperation, Subnormal] 3757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3765aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context Functions ################################################## 3837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 384ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 385ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 386ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 3877e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# work for older Pythons. If threads are not part of the build, create a 388cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# mock threading object with threading.local() returning the module namespace. 3897e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger 3907e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingertry: 3917e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import threading 3927e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingerexcept ImportError: 3937e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger # Python was compiled without threads; create a mock object instead 3947e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import sys 39559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista class MockThreading(object): 3967e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger def local(self, sys=sys): 3977e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger return sys.modules[__name__] 3987e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger threading = MockThreading() 3997e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger del sys, MockThreading 400ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 404ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 405ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 40659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # To fix reloading, force it to create a new context 40759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Old contexts have different exceptions in their dicts, making problems. 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4149fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 41561992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 417ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4359fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4369fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 437ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 441ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 445ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 446ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 450ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 451ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 452ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 453ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 454ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4559fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 45661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 457ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 458ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 459cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis del threading, local # Don't contaminate the namespace 4607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4618b6999b4c5fab174090be263ba90f193bdede141Nick Coghlandef localcontext(ctx=None): 4628b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Return a context manager for a copy of the supplied context 4638b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4648b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan Uses a copy of the current context if no context is specified 4658b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan The returned context manager creates a local decimal context 4668b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan in a with statement: 4678b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4688b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext() as ctx: 4698b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ctx.prec += 2 4708b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4718b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses a precision 2 greater than normal 47259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal precision 4738b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4748b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4758b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext(ExtendedContext): 4768b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4778b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses the Extended Context from the 4788b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # General Decimal Arithmetic Specification 47959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal context 4808b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 481ee340e501d2a59d70a91748ebd948787bfac8044Facundo Batista >>> setcontext(DefaultContext) 4828b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4838b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4848b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(): 4858b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... ctx = getcontext() 486495df4716fce4156c1eb110f9342297164eecbb6Raymond Hettinger ... ctx.prec += 2 4878b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print ctx.prec 4888b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4898b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 30 4908b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(ExtendedContext): 4918b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print getcontext().prec 4928b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4938b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 9 4948b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4958b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4968b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 497ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan if ctx is None: ctx = getcontext() 498ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan return _ContextManager(ctx) 4998b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 5007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Decimal class ####################################################### 5027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 5047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 5057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 506636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger __slots__ = ('_exp','_int','_sign', '_is_special') 507636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Generally, the value of the Decimal instance is given by 508636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (-1)**_sign * _int * 10**_exp 509636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special values are signified by _is_special == True 5107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 511dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger # We're immutable, so use __new__ not __init__ 512636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger def __new__(cls, value="0", context=None): 5137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 5147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 516abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 51759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) 518abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 5197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 520abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('314') 5217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 522abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('314') 52359bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay 524abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 5257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Note that the coefficient, self._int, is actually stored as 52872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # a string rather than as a tuple of digits. This speeds up 52972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # the "digits to integer" and "integer to digits" conversions 53072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # that are used in almost every arithmetic operation on 53172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Decimals. This is an internal detail: the as_tuple function 53272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # and the Decimal constructor still deal with tuples of 53372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # digits. 53472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 535636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self = object.__new__(cls) 536636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5370d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From a string 5380d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # REs insist on real strings, so we can too. 5390d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, basestring): 54059bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson m = _parser(value.strip()) 5410d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m is None: 5420d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if context is None: 5430d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista context = getcontext() 5440d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return context._raise_error(ConversionSyntax, 5450d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista "Invalid literal for Decimal: %r" % value) 546636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5470d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('sign') == "-": 5480d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 1 5490d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5500d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 0 5510d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista intpart = m.group('int') 5520d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if intpart is not None: 5530d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # finite number 5540d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista fracpart = m.group('frac') 5550d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista exp = int(m.group('exp') or '0') 5560d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if fracpart is not None: 5578e85ffa4b213be809109180142a107a1ac66f4d5Mark Dickinson self._int = str((intpart+fracpart).lstrip('0') or '0') 5580d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp - len(fracpart) 5590d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5608e85ffa4b213be809109180142a107a1ac66f4d5Mark Dickinson self._int = str(intpart.lstrip('0') or '0') 5610d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp 5620d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5630d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5640d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista diag = m.group('diag') 5650d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if diag is not None: 5660d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # NaN 5678e85ffa4b213be809109180142a107a1ac66f4d5Mark Dickinson self._int = str(diag.lstrip('0')) 5680d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('signal'): 5690d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'N' 5700d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5710d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'n' 5720d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5730d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # infinity 5740d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = '0' 5750d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'F' 5760d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = True 577636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 578636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 579636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From an integer 5807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 581636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if value >= 0: 582636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 0 583636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 584636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 1 585636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = 0 58672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = str(abs(value)) 5870d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5880d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 5890d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 5900d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From another decimal 5910d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, Decimal): 5920d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = value._exp 5930d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value._sign 5940d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = value._int 5950d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = value._is_special 5960d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 5970d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 5980d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From an internal working value 5990d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, _WorkRep): 6000d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value.sign 6010d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = str(value.int) 6020d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = int(value.exp) 6030d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 604636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 605636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 606636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 607636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, (list,tuple)): 608636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if len(value) != 3: 6099b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError('Invalid tuple size in creation of Decimal ' 6109b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'from list or tuple. The list or tuple ' 6119b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'should have exactly three elements.') 6129b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process sign. The isinstance test rejects floats 6139b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if not (isinstance(value[0], (int, long)) and value[0] in (0,1)): 6149b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("Invalid sign. The first value in the tuple " 6159b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "should be an integer; either 0 for a " 6169b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "positive number or 1 for a negative number.") 617636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = value[0] 6189b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] == 'F': 6199b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # infinity: value[1] is ignored 62072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = '0' 621636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = value[2] 622636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 623636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 6249b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process and validate the digits in value[1] 6259b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits = [] 6269b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista for digit in value[1]: 6279b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if isinstance(digit, (int, long)) and 0 <= digit <= 9: 6289b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # skip leading zeros 6299b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if digits or digit != 0: 6309b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits.append(digit) 6319b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6329b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The second value in the tuple must " 6339b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be composed of integers in the range " 6349b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "0 through 9.") 6359b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] in ('n', 'N'): 6369b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # NaN: digits form the diagnostic 63772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits)) 6389b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6399b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = True 6409b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista elif isinstance(value[2], (int, long)): 6419b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # finite number: digits give the coefficient 64272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits or [0])) 6439b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6449b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = False 6459b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6469b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The third value in the tuple must " 6479b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be an integer, or one of the " 6489b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "strings 'F', 'n', 'N'.") 649636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 650636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 651636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, float): 652636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 653636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger "First convert the float to a string") 6547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 655636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert %r to Decimal" % value) 6567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 657f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger @classmethod 658f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger def from_float(cls, f): 659f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger """Converts a float to a decimal number, exactly. 660f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 661f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). 662f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Since 0.1 is not exactly representable in binary floating point, the 663f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger value is stored as the nearest representable value which is 664f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 0x1.999999999999ap-4. The exact equivalent of the value in decimal 665f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger is 0.1000000000000000055511151231257827021181583404541015625. 666f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 667f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> Decimal.from_float(0.1) 668f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('0.1000000000000000055511151231257827021181583404541015625') 669f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> Decimal.from_float(float('nan')) 670f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('NaN') 671f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> Decimal.from_float(float('inf')) 672f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('Infinity') 673f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> Decimal.from_float(-float('inf')) 674f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('-Infinity') 675f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> Decimal.from_float(-0.0) 676f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('-0') 677f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 678f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger """ 679f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger if isinstance(f, (int, long)): # handle integer inputs 680f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger return cls(f) 681f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger if _math.isinf(f) or _math.isnan(f): # raises TypeError if not a float 682f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger return cls(repr(f)) 683f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger sign = 0 if _math.copysign(1.0, f) == 1.0 else 1 684f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger n, d = abs(f).as_integer_ratio() 685f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger k = d.bit_length() - 1 686f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger result = _dec_from_triple(sign, str(n*5**k), -k) 687f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger return result if cls is Decimal else cls(result) 688f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 6930f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista 1 if NaN 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 696636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 697636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = self._exp 698636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp == 'n': 699636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 1 700636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif exp == 'N': 701636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 2 7027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 7057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 7067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 7087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 7097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 7107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 7127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 7137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 7147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 7157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _check_nans(self, other=None, context=None): 7187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 7197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 7217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 7257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 727636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_is_nan = self._isnan() 728636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other is None: 729636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = False 730636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 731636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = other._isnan() 732636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 733636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan or other_is_nan: 734636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 735636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 736636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 737636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan == 2: 738636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 7390f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista self) 740636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other_is_nan == 2: 741636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 7420f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista other) 743636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan: 744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 745636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other._fix_nan(context) 7477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7492fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def _compare_check_nans(self, other, context): 7502fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """Version of _check_nans used for the signaling comparisons 7512fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson compare_signal, __le__, __lt__, __ge__, __gt__. 7522fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7532fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Signal InvalidOperation if either self or other is a (quiet 7542fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson or signaling) NaN. Signaling NaNs take precedence over quiet 7552fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson NaNs. 7562fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7572fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Return 0 if neither operand is a NaN. 7582fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7592fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """ 7602fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if context is None: 7612fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson context = getcontext() 7622fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7632fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self._is_special or other._is_special: 7642fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_snan(): 7652fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7662fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving sNaN', 7672fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson self) 7682fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif other.is_snan(): 7692fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7702fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving sNaN', 7712fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other) 7722fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif self.is_qnan(): 7732fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7742fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving NaN', 7752fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson self) 7762fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif other.is_qnan(): 7772fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7782fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving NaN', 7792fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other) 7802fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return 0 7812fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 7831a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is nonzero; otherwise return False. 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7851a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista NaNs and infinities are considered nonzero. 7867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 78772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._is_special or self._int != '0' 7887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7892fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def _cmp(self, other): 7902fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """Compare the two non-NaN decimal instances self and other. 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7922fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Returns -1 if self < other, 0 if self == other and 1 7932fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self > other. This routine is for internal use only.""" 794636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 7952fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self._is_special or other._is_special: 796636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return cmp(self._isinfinity(), other._isinfinity()) 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for zeros; note that cmp(0, -0) should return 0 799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 0 802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return -((-1)**other._sign) 804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return (-1)**self._sign 8067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 80759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If different signs, neg one is less 8087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 8097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 8107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 8117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 8127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 813636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_adjusted = self.adjusted() 814636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_adjusted = other.adjusted() 815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted == other_adjusted: 81672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - other._exp) 81772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista other_padded = other._int + '0'*(other._exp - self._exp) 818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return cmp(self_padded, other_padded) * (-1)**self._sign 819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self_adjusted > other_adjusted: 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # self_adjusted < other_adjusted 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 8237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8242fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # Note: The Decimal standard doesn't cover rich comparisons for 8252fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # Decimals. In particular, the specification is silent on the 8262fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # subject of what should happen for a comparison involving a NaN. 8272fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # We take the following approach: 8282fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # 8292fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # == comparisons involving a NaN always return False 8302fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # != comparisons involving a NaN always return True 8312fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # <, >, <= and >= comparisons involving a (quiet or signaling) 8322fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # NaN signal InvalidOperation, and return False if the 8333a94ee05f77d0200cfb7988d02f3fdf292932a94Mark Dickinson # InvalidOperation is not trapped. 8342fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # 8352fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # This behavior is designed to conform as closely as possible to 8362fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # that specified by IEEE 754. 8372fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8380aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 8392fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8402fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8412fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8422fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_nan() or other.is_nan(): 8432fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8442fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) == 0 8450aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 8460aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 8472fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8482fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8492fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8502fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_nan() or other.is_nan(): 8512fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return True 8522fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) != 0 8532fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8542fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __lt__(self, other, context=None): 8552fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8562fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8572fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8582fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8592fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8602fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8612fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) < 0 8622fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8632fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __le__(self, other, context=None): 8642fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8652fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8662fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8672fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8682fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8692fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8702fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) <= 0 8712fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8722fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __gt__(self, other, context=None): 8732fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8742fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8752fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8762fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8772fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8782fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8792fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) > 0 8802fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8812fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __ge__(self, other, context=None): 8822fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8832fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8842fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8852fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8862fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8872fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8882fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) >= 0 8890aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 8907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 8927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 8947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 8977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 8987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 9007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 90159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Compare(NaN, NaN) = NaN 902636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if (self._is_special or other and other._is_special): 903636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 904636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 905636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9072fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return Decimal(self._cmp(other)) 9087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 9107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 9117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 91252b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # 91352b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # The hash of a nonspecial noninteger Decimal must depend only 91452b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # on the value of that Decimal, and not on its representation. 915abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger # For example: hash(Decimal('100E-1')) == hash(Decimal('10')). 916bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._is_special: 917bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._isnan(): 918bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger raise TypeError('Cannot hash a NaN value.') 919bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger return hash(str(self)) 9208c202440699cef19602acc24822366d0d7c32083Facundo Batista if not self: 9218c202440699cef19602acc24822366d0d7c32083Facundo Batista return 0 9228c202440699cef19602acc24822366d0d7c32083Facundo Batista if self._isinteger(): 9238c202440699cef19602acc24822366d0d7c32083Facundo Batista op = _WorkRep(self.to_integral_value()) 9248c202440699cef19602acc24822366d0d7c32083Facundo Batista # to make computation feasible for Decimals with large 9258c202440699cef19602acc24822366d0d7c32083Facundo Batista # exponent, we use the fact that hash(n) == hash(m) for 9268c202440699cef19602acc24822366d0d7c32083Facundo Batista # any two nonzero integers n and m such that (i) n and m 9278c202440699cef19602acc24822366d0d7c32083Facundo Batista # have the same sign, and (ii) n is congruent to m modulo 9288c202440699cef19602acc24822366d0d7c32083Facundo Batista # 2**64-1. So we can replace hash((-1)**s*c*10**e) with 9298c202440699cef19602acc24822366d0d7c32083Facundo Batista # hash((-1)**s*c*pow(10, e, 2**64-1). 9308c202440699cef19602acc24822366d0d7c32083Facundo Batista return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) 93152b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # The value of a nonzero nonspecial Decimal instance is 93252b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # faithfully represented by the triple consisting of its sign, 93352b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # its adjusted exponent, and its coefficient with trailing 93452b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # zeros removed. 93552b25795c02442fc40f8932d05e5d728266339a4Facundo Batista return hash((self._sign, 93652b25795c02442fc40f8932d05e5d728266339a4Facundo Batista self._exp+len(self._int), 93752b25795c02442fc40f8932d05e5d728266339a4Facundo Batista self._int.rstrip('0'))) 9387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 9407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 9417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 9437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 944097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp) 9457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 9477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 949abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger return "Decimal('%s')" % str(self) 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __str__(self, eng=False, context=None): 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 9537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 95762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista sign = ['', '-'][self._sign] 958e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._is_special: 95962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp == 'F': 96062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'Infinity' 96162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._exp == 'n': 96262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'NaN' + self._int 96362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: # self._exp == 'N' 96462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'sNaN' + self._int 96562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 96662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # number of digits of self._int to left of decimal point 96762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista leftdigits = self._exp + len(self._int) 96862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 96962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # dotplace is number of digits of self._int to the left of the 97062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # decimal point in the mantissa of the output string (that is, 97162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # after adjusting the exponent) 97262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp <= 0 and leftdigits > -6: 97362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # no exponent required 97462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = leftdigits 97562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif not eng: 97662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # usual scientific notation: 1 digit on left of the point 9777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 97862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._int == '0': 97962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, zero 98062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits + 1) % 3 - 1 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 98262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, nonzero 98362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits - 1) % 3 + 1 98462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 98562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if dotplace <= 0: 98662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = '0' 98762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + '0'*(-dotplace) + self._int 98862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif dotplace >= len(self._int): 98962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int+'0'*(dotplace-len(self._int)) 99062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '' 99162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 99262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int[:dotplace] 99362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + self._int[dotplace:] 99462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if leftdigits == dotplace: 99562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = '' 99662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 99762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if context is None: 99862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista context = getcontext() 99962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) 100062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 100162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + intpart + fracpart + exp 10027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 10057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 10087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 10107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__str__(eng=True, context=context) 10127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 10147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 10177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1018636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1019636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1020636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1021636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 10247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 10250f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = self.copy_abs() 10267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_negate() 1028636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1029636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1030636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1031e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 10327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 10347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 10357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 10377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1038636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1039636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1040636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1041636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 10450f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = self.copy_abs() 1046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 10487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1049636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1050636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1051e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 10527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1053e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista def __abs__(self, round=True, context=None): 10547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1056e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista If the keyword argument 'round' is false, do not round. The 1057e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista expression self.__abs__(round=False) is equivalent to 1058e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.copy_abs(). 10597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1060e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if not round: 1061e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return self.copy_abs() 1062e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista 1063636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1064636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1065636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1066636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 10697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 10707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 10717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 10767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1080636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1081267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1082267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1083636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 10847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1087636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1088636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1089636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1090636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1092636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 109359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both INF, same sign => same as both, opposite => error. 1094636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 1095636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 1096636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 1097636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 109859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return Decimal(other) # Can't both be infinity here 10997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 11017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 11027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 110359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the answer is 0, the sign should be negative, in this case. 11047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 11057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 11077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 11087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 11097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 111072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, '0', exp) 1111e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 1112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 11137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 111499b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, other._exp - context.prec-1) 1115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other._rescale(exp, context.rounding) 1116e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 111999b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, self._exp - context.prec-1) 1120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp, context.rounding) 1121e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 11257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 1126e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista op1, op2 = _normalize(op1, op2, context.prec) 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 11297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 11307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 113117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int == op2.int: 113272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(negativezero, '0', exp) 1133e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 1134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 113517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int < op2.int: 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 113759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # OK, now abs(op1) > abs(op2) 113817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.sign == 1: 113917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 1 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 11417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 114217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 114359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # So we know the sign, and op1 > 0. 114417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif op1.sign == 1: 11457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 114617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger op1.sign, op2.sign = (0, 0) 114717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 114817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 114959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Now, op1 > abs(op2) > 0 11507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 115117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op2.sign == 0: 1152636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int + op2.int 11537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1154636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int - op2.int 11557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 11577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 1158e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 11627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 1164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self - other""" 1165636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1166267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1167267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 11687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1169636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1170636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context=context) 1171636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1172636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 11737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self - other is computed as self + other.copy_negate() 1175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__add__(other.copy_negate(), context=context) 11767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 1178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return other - self""" 1179636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1180267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1181267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 11827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__sub__(self, context=context) 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 11867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 11877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 11897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1190636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1191267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1192267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1193636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 11947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1197d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 11987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1199636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1200636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1201636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1202636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1203636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1204636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1205636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1206636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 1207b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[resultsign] 1208636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1209636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1210636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1211636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 1212b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[resultsign] 12137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 12157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 12177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 121872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, '0', resultexp) 1219e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista # Fixing in case the exponent is out of bounds 1220e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 122472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int == '1': 122572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, other._int, resultexp) 1226e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 122872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if other._int == '1': 122972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, self._int, resultexp) 1230e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1233636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1 = _WorkRep(self) 1234636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2 = _WorkRep(other) 1235636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 123672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) 1237e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 12417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12428aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson def __truediv__(self, other, context=None): 12437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 1244636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1245267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1246cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NotImplemented 1247636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 12487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 12497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 12507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1251636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sign = self._sign ^ other._sign 1252636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1253636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1254636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1255636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 12567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1258636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and other._isinfinity(): 12597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 12607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 1262b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[sign] 1263636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1264636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1265636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 126672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '0', context.Etiny()) 1267636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1268636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special cases for zeroes 1269636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1270cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1271cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 / 0') 1272636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1274cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1275cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp 1276cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff = 0 1277cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1278cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # OK, so neither = 0, INF or NaN 1279cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista shift = len(other._int) - len(self._int) + context.prec + 1 1280cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp - shift 1281cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1282cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1283cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if shift >= 0: 1284cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int * 10**shift, op2.int) 1285cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1286cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int, op2.int * 10**-shift) 1287cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if remainder: 1288cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is not exact; adjust to ensure correct rounding 1289cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if coeff % 5 == 0: 1290cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff += 1 1291cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1292cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is exact; get as close to ideal exponent as possible 1293cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp - other._exp 1294cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista while exp < ideal_exp and coeff % 10 == 0: 1295cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff //= 10 1296cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp += 1 12977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 129872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(coeff), exp) 1299cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans._fix(context) 13007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1301cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def _divide(self, other, context): 1302cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """Return (self // other, self % other), to context.prec precision. 13037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1304cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Assumes that neither self nor other is a NaN, that self is not 1305cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista infinite and that other is nonzero. 1306cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """ 1307cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1308cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1309cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp 1310cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1311cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = min(self._exp, other._exp) 13127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1313cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista expdiff = self.adjusted() - other.adjusted() 1314cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self or other._isinfinity() or expdiff <= -2: 131572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, '0', 0), 1316cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._rescale(ideal_exp, context.rounding)) 1317cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if expdiff <= context.prec: 1318cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1319cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1320cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if op1.exp >= op2.exp: 1321cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 1322cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1323cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1324cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista q, r = divmod(op1.int, op2.int) 1325cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if q < 10**context.prec: 132672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, str(q), 0), 132772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista _dec_from_triple(self._sign, str(r), ideal_exp)) 13287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1329cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # Here the quotient is too large to be representable 1330cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionImpossible, 1331cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 'quotient too large in //, % or divmod') 1332cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 13337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13348aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson def __rtruediv__(self, other, context=None): 13358aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson """Swaps self/other and returns __truediv__.""" 1336636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1337267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1338267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13398aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson return other.__truediv__(self, context=context) 13408aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson 13418aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson __div__ = __truediv__ 13428aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson __rdiv__ = __rtruediv__ 13437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 13457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1346cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Return (self // other, self % other) 13477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1348cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1349cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1350cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1351cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1352cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1353cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1354cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1355cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1356cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1357cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (ans, ans) 1358cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1359cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1360cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1361cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1362cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') 1363cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1364cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1365b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return (_SignedInfinity[sign], 1366cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'INF % x')) 1367cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1368cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1369cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1370cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') 1371cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1372cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1373cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (context._raise_error(DivisionByZero, 'x // 0', sign), 1374cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'x % 0')) 1375cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1376cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista quotient, remainder = self._divide(other, context) 1377e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1378cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return quotient, remainder 13797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 13817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 1382636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1383267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1384267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 13867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 13887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 13907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1391636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1392267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1393267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1395cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1396cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 13977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1398cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1399cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1400cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 14017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1402cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1403cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF % x') 1404cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista elif not other: 1405cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1406cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'x % 0') 1407cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1408cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 % 0') 1409cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1410cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = self._divide(other, context)[1] 1411e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1412cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return remainder 14137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 14157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 1416636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1417267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1418267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 14197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 14207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 14227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 14247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1425636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1426636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1434353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self == +/-infinity -> InvalidOperation 1435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 1436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(infinity, x)') 14387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other == 0 -> either InvalidOperation or DivisionUndefined 1440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 1442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(x, 0)') 1444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1445353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(DivisionUndefined, 1446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(0, 0)') 14477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1448353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other = +/-infinity -> remainder = self 1449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 1450353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 1451353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self = 0 -> remainder = self, with ideal exponent 1454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = min(self._exp, other._exp) 1455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 145672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', ideal_exponent) 1457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # catch most cases of large or small quotient 1460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = self.adjusted() - other.adjusted() 1461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff >= context.prec + 1: 1462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff >= prec+1 => abs(self/other) > 10**prec 1463cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff <= -2: 1465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff <= -2 => abs(self/other) < 0.1 1466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(ideal_exponent, context.rounding) 1467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust both arguments to have the same exponent, then divide 1470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1 = _WorkRep(self) 1471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2 = _WorkRep(other) 1472353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp >= op2.exp: 1473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 14747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1476353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(op1.int, op2.int) 1477353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # remainder is r*10**ideal_exponent; other is +/-op2.int * 1478353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**ideal_exponent. Apply correction to ensure that 1479353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # abs(remainder) <= abs(other)/2 1480353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if 2*r + (q&1) > op2.int: 1481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r -= op2.int 1482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q += 1 1483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if q >= 10**context.prec: 1485cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has same sign as self unless r is negative 1488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if r < 0: 1490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 1-sign 1491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r = -r 14927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 149372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(r), ideal_exponent) 1494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 14977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 1498cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1499cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1500cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1501cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1502cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1503cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1504cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1505cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1506cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1507cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 1508cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1509cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1510cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1511cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF // INF') 1512cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1513b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[self._sign ^ other._sign] 1514cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1515cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1516cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1517cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'x // 0', 1518cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._sign ^ other._sign) 1519cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1520cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 // 0') 1521cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1522cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return self._divide(other, context)[0] 15237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 15257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 1526636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1527267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1528267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 15297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 15307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 15327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 15337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 15347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 153646b0802ccd9a9c47b27a285526fbb2a8bee5b8cbBrett Cannon """Converts self to an int, truncating if necessary.""" 1537636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1538636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan(): 1539636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1540636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidContext) 1541636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self._isinfinity(): 15428aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson raise OverflowError("Cannot convert infinity to int") 1543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = (-1)**self._sign 15447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 154572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int)*10**self._exp 1546605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger else: 154772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int[:self._exp] or '0') 15487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15495a05364049a7b0c3eeee94fb7b77e6b41036b3aeRaymond Hettinger __trunc__ = __int__ 15505a05364049a7b0c3eeee94fb7b77e6b41036b3aeRaymond Hettinger 1551116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger @property 1552116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def real(self): 1553116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return self 1554116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1555116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger @property 1556116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def imag(self): 1557116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return Decimal(0) 1558116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1559116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def conjugate(self): 1560116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return self 1561116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1562116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def __complex__(self): 1563116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return complex(float(self)) 1564116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 15657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 15667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 15677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 15697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 15707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 15717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fix_nan(self, context): 1573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Decapitate the payload of a NaN to fit the context""" 1574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista payload = self._int 1575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # maximum length of payload is precision if _clamp=0, 1577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision-1 if _clamp=1. 1578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista max_payload_len = context.prec - context._clamp 1579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(payload) > max_payload_len: 158072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista payload = payload[len(payload)-max_payload_len:].lstrip('0') 158172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, payload, self._exp, True) 15826c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 1583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1584dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _fix(self, context): 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 15867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 15887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 15907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 15917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1593636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1594353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 1595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan(): 1596353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decapitate payload if necessary 1597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 1598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is +/-Infinity; return unaltered 16006c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 16017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1602353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if self is zero then exponent should be between Etiny and 1603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. 1604353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 1605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etop = context.Etop() 16067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 1607353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, Etop][context._clamp] 1608353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_exp = min(max(self._exp, Etiny), exp_max) 1609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_exp != self._exp: 1610353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 161172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', new_exp) 16127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16136c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 16147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp_min is the smallest allowable exponent of the result, 1616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equal to max(self.adjusted()-context.prec+1, Etiny) 1617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = len(self._int) + self._exp - context.prec 1618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp_min > Etop: 1619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow: exp_min > Etop iff self.adjusted() > Emax 1620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 1622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(Overflow, 'above Emax', self._sign) 1623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_subnormal = exp_min < Etiny 1624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 1626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = Etiny 16277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round if self has too many digits 1629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < exp_min: 16307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16312ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = len(self._int) + self._exp - exp_min 16322ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if digits < 0: 16332ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista self = _dec_from_triple(self._sign, '1', exp_min-1) 16342ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = 0 16352ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista this_function = getattr(self, self._pick_rounding_function[context.rounding]) 16362ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 16372ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 16382ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 16392ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 16402ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista ans = _dec_from_triple(self._sign, coeff, exp_min) 16412ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista 16422ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed: 1643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 1646353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 1647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Clamped on underflow to 0 1648353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 1649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif len(ans._int) == context.prec+1: 1650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we get here only if rescaling rounds the 1651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # cofficient up to exactly 10**context.prec 1652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp < Etop: 165372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, 165472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._int[:-1], ans._exp+1) 1655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inexact and Rounded have already been raised 1657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = context._raise_error(Overflow, 'above Emax', 1658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self._sign) 16597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fold down if _clamp == 1 and self has too few digits 1662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._clamp == 1 and self._exp > Etop: 1663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 166472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - Etop) 166572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, self_padded, Etop) 16667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # here self was representable to begin with; return unchanged 16686c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 16697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 16717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for each of the rounding functions below: 1673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is a finite, nonzero Decimal 1674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # prec is an integer satisfying 0 <= prec < len(self._int) 16752ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 16762ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # each function returns either -1, 0, or 1, as follows: 16772ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 1 indicates that self should be rounded up (away from zero) 16782ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 0 indicates that self should be truncated, and that all the 16792ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # digits to be truncated are zeros (so the value is unchanged) 16802ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # -1 indicates that there are nonzero digits to be truncated 16817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_down(self, prec): 1683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Also known as round-towards-0, truncate.""" 16842ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _all_zeros(self._int, prec): 16852ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 16862ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 16872ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 16887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_up(self, prec): 1690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds away from 0.""" 16912ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 16927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_up(self, prec): 1694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds 5 up (away from 0)""" 169572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[prec] in '56789': 16962ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 1 16972ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista elif _all_zeros(self._int, prec): 16982ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 1699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 17002ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 17017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_down(self, prec): 17037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 17042ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec): 17052ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 17062ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 17072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 17087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_even(self, prec): 1710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round 5 to even, rest to nearest.""" 17112ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec) and \ 17122ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista (prec == 0 or self._int[prec-1] in '02468'): 17132ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 1714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 17152ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 17167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_ceiling(self, prec): 17187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 17197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 1720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 17217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 17222ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 17237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_floor(self, prec): 17257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 17267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 1727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 17287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 17292ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 17307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_05up(self, prec): 1732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round down unless digit prec-1 is 0 or 5.""" 17332ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if prec and self._int[prec-1] not in '05': 1734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 17352ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 17362ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 1737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, other, third, context=None): 1739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Fused multiply-add. 17407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Returns self*other+third with no rounding of the intermediate 1742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista product self*other. 1743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self and other are multiplied together, with no rounding of 1745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the result. The third operand is then added to the result, 1746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista and a single final rounding is performed. 17477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 17507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 175158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # compute product; raise InvalidOperation if either operand is 175258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # a signaling NaN or if the product is zero times infinity. 175358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._is_special or other._is_special: 175458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if context is None: 175558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista context = getcontext() 175658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'N': 17570f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return context._raise_error(InvalidOperation, 'sNaN', self) 175858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if other._exp == 'N': 17590f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return context._raise_error(InvalidOperation, 'sNaN', other) 176058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'n': 176158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = self 176258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'n': 176358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = other 176458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif self._exp == 'F': 176558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not other: 176658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 176758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista 'INF * 0 in fma') 1768b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger product = _SignedInfinity[self._sign ^ other._sign] 176958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'F': 177058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not self: 177158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 177258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista '0 * INF in fma') 1773b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger product = _SignedInfinity[self._sign ^ other._sign] 177458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista else: 177558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = _dec_from_triple(self._sign ^ other._sign, 177658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista str(int(self._int) * int(other._int)), 177758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista self._exp + other._exp) 17787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 177958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista third = _convert_other(third, raiseit=True) 178058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return product.__add__(third, context) 17817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_modulo(self, other, modulo, context=None): 1783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Three argument version of __pow__""" 17847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if can't convert other and modulo to Decimal, raise 1786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # TypeError; there's no point returning NotImplemented (no 1787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equivalent of __rpow__ for three argument pow) 1788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 1789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = _convert_other(modulo, raiseit=True) 17907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 17937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # deal with NaNs: if there are any sNaNs then first one wins, 1795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (i.e. behaviour for NaNs is identical to that of fma) 1796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 1797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 1798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo_is_nan = modulo._isnan() 1799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan or other_is_nan or modulo_is_nan: 1800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 1801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 18020f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista self) 1803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 1804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 18050f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista other) 1806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo_is_nan == 2: 1807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 18080f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista modulo) 1809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 18106c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 1811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 18126c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 18136c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return modulo._fix_nan(context) 1814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check inputs: we apply same restrictions as Python's pow() 1816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (self._isinteger() and 1817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other._isinteger() and 1818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo._isinteger()): 1819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument not allowed ' 1821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'unless all arguments are integers') 1822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other < 0: 1823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 2nd argument cannot be ' 1825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'negative when 3rd argument specified') 1826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not modulo: 1827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument cannot be 0') 1829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # additional restriction for decimal: the modulus must be less 1831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # than 10**prec in absolute value 1832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo.adjusted() >= context.prec: 1833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'insufficient precision: pow() 3rd ' 1835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'argument must not have more than ' 1836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'precision digits') 1837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # define 0**0 == NaN, for consistency with two-argument pow 1839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (even though it hurts!) 1840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other and not self: 1841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'at least one of pow() 1st argument ' 1843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'and 2nd argument must be nonzero ;' 1844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0**0 is not defined') 1845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute sign of result 1847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._iseven(): 1848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 0 1849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # convert modulo to a Python integer, and self and other to 1853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal integers (i.e. force their exponents to be >= 0) 1854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = abs(int(modulo)) 1855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = _WorkRep(self.to_integral_value()) 1856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = _WorkRep(other.to_integral_value()) 1857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute result using integer pow() 1859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo 1860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(exponent.exp): 1861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, 10, modulo) 1862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, exponent.int, modulo) 1863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 186472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, str(base), 0) 1865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_exact(self, other, p): 1867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Attempt to compute self**other exactly. 1868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given Decimals self and other and an integer p, attempt to 1870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista compute an exact result for the power self**other, with p 1871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision. Return None if self**other is not 1872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exactly representable in p digits. 1873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that elimination of special cases has already been 1875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista performed: self and other must both be nonspecial; self must 1876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista be positive and not numerically equal to 1; other must be 1877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista nonzero. For efficiency, other._exp should not be too large, 1878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista so that 10**abs(other._exp) is a feasible calculation.""" 1879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # In the comments below, we write x for the value of self and 1881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # y for the value of other. Write x = xc*10**xe and y = 1882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # yc*10**ye. 1883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The main purpose of this method is to identify the *failure* 1885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of x**y to be exactly representable with as little effort as 1886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possible. So we look for cheap and easy tests that 1887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # eliminate the possibility of x**y being exact. Only if all 1888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # these tests are passed do we go on to actually compute x**y. 1889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Here's the main idea. First normalize both x and y. We 1891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # express y as a rational m/n, with m and n relatively prime 1892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # and n>0. Then for x**y to be exactly representable (at 1893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # *any* precision), xc must be the nth power of a positive 1894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # integer and xe must be divisible by n. If m is negative 1895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then additionally xc must be a power of either 2 or 5, hence 1896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a power of 2**n or 5**n. 1897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's a limit to how small |y| can be: if y=m/n as above 1899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then: 1900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1) if xc != 1 then for the result to be representable we 1902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So 1903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= 1904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2**(1/|y|), hence xc**|y| < 2 and the result is not 1905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # representable. 1906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if 1908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # |y| < 1/|xe| then the result is not representable. 1909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Note that since x is not equal to 1, at least one of (1) and 1911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < 1912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. 1913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's also a limit to how large y can be, at least if it's 1915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive: the normalized result will have coefficient xc**y, 1916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so if it's representable then xc**y < 10**p, and y < 1917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p/log10(xc). Hence if y*log10(xc) >= p then the result is 1918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # not exactly representable. 1919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, 1921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so |y| < 1/xe and the result is not representable. 1922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| 1923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # < 1/nbits(xc). 1924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 1926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 1927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 10 == 0: 1928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 10 1929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe += 1 1930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 1932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 1933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while yc % 10 == 0: 1934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc //= 10 1935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ye += 1 1936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where xc == 1: result is 10**(xe*y), with xe*y 1938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # required to be an integer 1939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc == 1: 1940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = xe*yc*10**ye 1942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent, remainder = divmod(xe*yc, 10**-ye) 1944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = -exponent 1948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if other is a nonnegative integer, use ideal exponent 1949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(exponent-ideal_exponent, p-1) 1952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 195472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) 1955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where y is negative: xc must be either a power 1957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of 2 or a power of 5. 1958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista last_digit = xc % 10 1960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if last_digit in (2,4,6,8): 1961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # quick test for power of 2 1962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc & -xc != xc: 1963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc is a power of 2; e is its exponent 1965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)-1 1966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find e*y and xe*y; both must be integers 1967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_int = yc*10**ye 1969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_int 1970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_int 1971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*65 >= p*93: # 93/65 > log(10)/log(5) 1981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 5**e 1983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif last_digit == 5: 1985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # e >= log_5(xc) if xc is a power of 5; we have 1986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equality all the way up to xc=5**2658 1987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)*28//65 1988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, remainder = divmod(5**e, xc) 1989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 5 == 0: 1992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 5 1993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= 1 1994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_integer = yc*10**ye 1996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_integer 1997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_integer 1998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 2000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 2001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 2002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 2004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 2005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*3 >= p*10: # 10/3 > log(10)/log(2) 2007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 2**e 2009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 20117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc >= 10**p: 2013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = -e-xe 201572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str(xc), xe) 20167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now y is positive; find m and n such that y = m/n 2018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 2019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc*10**ye, 1 2020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xe != 0 and len(str(abs(yc*xe))) <= -ye: 2022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc_bits = _nbits(xc) 2024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: 2025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc, 10**(-ye) 2027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 2 == n % 2 == 0: 2028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 2 2029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 2 2030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 5 == n % 5 == 0: 2031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 5 2032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 5 2033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc*10**xe 2035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n > 1: 2036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if 1 < xc < 2**n then xc isn't an nth power 2037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and xc_bits <= n: 2038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, rem = divmod(xe, n) 2041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rem != 0: 2042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc using Newton's method 2045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = 1L << -(-_nbits(xc)//n) # initial estimate 2046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(xc, a**(n-1)) 2048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if a <= q: 2049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = (a*(n-1) + q)//n 2052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (a == q and r == 0): 2053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = a 2055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc*10**xe is the nth root of the original xc*10**xe 2057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute mth power of xc*10**xe 2058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > 2060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**p and the result is not representable. 2061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 1 and m > p*100//_log10_lb(xc): 2062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = xc**m 2064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe *= m 2065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 10**p: 2066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by this point the result *is* exactly representable 2069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust the exponent to get as close as possible to the ideal 2070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent, if necessary 2071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_xc = str(xc) 2072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 2073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 2074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(xe-ideal_exponent, p-len(str_xc)) 2075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 207772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) 2078cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __pow__(self, other, modulo=None, context=None): 2080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self ** other [ % modulo]. 20817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute self**other. 20837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (self**other) % modulo. For the 2085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 2086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 20877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 2089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - other must be nonnegative 2090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - either self or other (or both) must be nonzero 2091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and must have at most p digits, 2092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista where p is the context precision. 20937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If any of these restrictions is violated the InvalidOperation 2095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista flag is raised. 2096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(self, other, modulo) is identical to the 2098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result that would be obtained by computing (self**other) % 2099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo with unbounded precision, but is computed more 2100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista efficiently. It is always exact. 2101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo is not None: 2104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._power_modulo(other, modulo, context) 21057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2106636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 2107267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 2108267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 21097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 21127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # either argument is a NaN => result is NaN 2114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 2115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 21177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) 2119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 2120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, '0 ** 0') 2122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2123b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 21247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has sign 1 iff self._sign is 1 and other is an odd integer 2126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 0 2127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._iseven(): 2130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 1 2131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # -ve**noninteger = NaN 2133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (-0)**noninteger = 0**noninteger 2134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 2135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'x ** y with x negative and y not an integer') 2137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # negate self, without doing any unwanted rounding 213872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = self.copy_negate() 2139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity 2141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 214372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2145b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[result_sign] 2146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 2148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 2150b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[result_sign] 2151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 215272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1**other = 1, but the choice of exponent and the flags 2155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # depend on the exponent of self, and on whether other is a 2156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive integer, a negative integer, or neither 2157b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger if self == _One: 2158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp = max(self._exp*max(int(other), 0), 2160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-context.prec) but evaluating int(other) directly 2161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is dangerous until we know other is small (other 2162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # could be 1e999999999) 2163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 1: 2164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = 0 2165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif other > context.prec: 2166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = context.prec 2167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = int(other) 2169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = self._exp * multiplier 2171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp < 1-context.prec: 2172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 217972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) 2180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute adjusted exponent of self 2182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adj = self.adjusted() 2183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** infinity is infinity if self > 1, 0 if self < 1 2185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** -infinity is infinity if self < 1, 0 if self > 1 2186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 2187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (other._sign == 0) == (self_adj < 0): 218872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2190b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _SignedInfinity[result_sign] 2191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # from here on, the result always goes through the call 2193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # to _fix at the end of this function. 2194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = None 2195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # crude test to catch cases of extreme overflow/underflow. If 2197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(self)*other >= 10**bound and bound >= len(str(Emax)) 2198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence 2199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self**other >= 10**(Emax+1), so overflow occurs. The test 2200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for underflow is similar. 2201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista bound = self._log10_exp_bound() + other.adjusted() 2202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (self_adj >= 0) == (other._sign == 0): 2203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other +ve, or self < 1 and other -ve 2204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of overflow 2205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(context.Emax)): 220672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', context.Emax+1) 2207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other -ve, or self < 1 and other +ve 2209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of underflow to 0 2210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 2211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(-Etiny)): 221272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', Etiny-1) 2213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # try for an exact result with precision +1 2215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._power_exact(other, context.prec + 1) 2217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is not None and result_sign == 1: 221872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(1, ans._int, ans._exp) 2219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # usual case: inexact result, x**y computed directly as exp(y*log(x)) 2221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 2224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 2225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 2226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 2227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 2228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc = -yc 2229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: start with precision +3, 2231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then increase precision until result is unambiguously roundable 2232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dpower(xc, xe, yc, ye, p+extra) 2235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 223972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, str(coeff), exp) 2240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the specification says that for non-integer other we need to 2242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Inexact, even when the result is actually exact. In 2243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the same way, we need to raise Underflow here if the result 2244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is subnormal. (The call to _fix will take care of raising 2245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Rounded and Subnormal, as usual.) 2246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._isinteger(): 2247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad with zeros up to length context.prec+1 if necessary 2249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) <= context.prec: 2250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = context.prec+1 - len(ans._int) 225172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, 225272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._exp-expdiff) 2253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() < context.Emin: 2254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 2255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # unlike exp, ln and log10, the power function respects the 2257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode; no need to use ROUND_HALF_EVEN here 2258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __rpow__(self, other, context=None): 2262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Swaps self/other and returns __pow__.""" 2263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other) 2264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other is NotImplemented: 2265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other 2266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__pow__(self, context=context) 2267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def normalize(self, context=None): 2269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 2270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dup = self._fix(context) 2280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dup._isinfinity(): 2281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return dup 2282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not dup: 228472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, '0', 0) 2285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, context.Etop()][context._clamp] 2286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista end = len(dup._int) 22877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 228872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista while dup._int[end-1] == '0' and exp < exp_max: 22897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 22907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 229172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, dup._int[:end], exp) 22927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2293bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista def quantize(self, exp, rounding=None, context=None, watchexp=True): 22947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 22957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 22977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2298bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista exp = _convert_other(exp, raiseit=True) 2299bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2305636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or exp._is_special: 2306636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(exp, context) 2307636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2308636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 23097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2310636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 2311636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 23126c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) # if both are inf, it is OK 2313636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 2314636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 'quantize with one INF') 2315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2316bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # if we're not watching exponents, do a simple rescale 2317bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if not watchexp: 2318bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista ans = self._rescale(exp._exp, rounding) 2319bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # raise Inexact and Rounded where appropriate 2320bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans._exp > self._exp: 2321bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Rounded) 2322bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans != self: 2323bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Inexact) 2324bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista return ans 2325bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp._exp should be between Etiny and Emax 2327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (context.Etiny() <= exp._exp <= context.Emax): 2328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'target exponent out of bounds in quantize') 2330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 233272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', exp._exp) 2333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 2334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adjusted = self.adjusted() 2336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted > context.Emax: 2337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted - exp._exp + 1 > context.prec: 2340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp._exp, rounding) 2344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() > context.Emax: 2345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) > context.prec: 2348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise appropriate flags 2352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp > self._exp: 2353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans and ans.adjusted() < context.Emin: 2357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 2358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # call to fix takes care of any necessary folddown 2360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 23627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 23641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self and other have the same exponent; otherwise 23651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False. 23667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23671a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista If either operand is a special value, the following rules are used: 23681a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are infinities 23691a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are NaNs 23701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * otherwise, return False. 23717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista other = _convert_other(other, raiseit=True) 2373636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 23741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return (self.is_nan() and other.is_nan() or 23751a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista self.is_infinite() and other.is_infinite()) 23767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 23777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _rescale(self, exp, rounding): 2379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rescale self so that the exponent is exp, either by padding with zeros 2380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or by truncating digits, using the given rounding mode. 2381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Specials are returned without change. This operation is 2383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista quiet: it raises no flags, and uses no information from the 2384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 23857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 2387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = rounding mode 23887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2389636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 23906c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 23917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 239272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', exp) 23937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2394353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= exp: 2395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad answer with zeros if necessary 239672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 239772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int + '0'*(self._exp - exp), exp) 23987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # too many digits; round and lose data. If self.adjusted() < 2400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp-1, replace self by 10**(exp-1) before rounding 2401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = len(self._int) + self._exp - exp 24027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 240372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = _dec_from_triple(self._sign, '1', exp-1) 2404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = 0 2405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this_function = getattr(self, self._pick_rounding_function[rounding]) 24062ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 24072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 24082ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 24092ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 24102ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return _dec_from_triple(self._sign, coeff, exp) 24117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson def _round(self, places, rounding): 24131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Round a nonzero, nonspecial Decimal to a fixed number of 24141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson significant figures, using the given rounding mode. 24151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 24161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Infinities, NaNs and zeros are returned unaltered. 24171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 24181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson This operation is quiet: it raises no flags, and uses no 24191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson information from the context. 24201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 24211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 24221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if places <= 0: 24231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("argument should be at least 1 in _round") 24241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._is_special or not self: 24251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return Decimal(self) 24261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson ans = self._rescale(self.adjusted()+1-places, rounding) 24271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # it can happen that the rescale alters the adjusted exponent; 24281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # for example when rounding 99.97 to 3 significant figures. 24291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # When this happens we end up with an extra 0 at the end of 24301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # the number; a second rescale fixes this. 24311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if ans.adjusted() != self.adjusted(): 24321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson ans = ans._rescale(ans.adjusted()+1-places, rounding) 24331ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return ans 24341ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 2435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, rounding=None, context=None): 2436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to a nearby integer. 24377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If no rounding mode is specified, take the rounding mode from 2439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the context. This method raises the Rounded and Inexact flags 2440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista when appropriate. 24417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista See also: to_integral_value, which does exactly the same as 2443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this method except that it doesn't raise Inexact or Rounded. 2444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2445636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2446636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2447636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2448636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 24496c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 24507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 24516c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 245372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', 0) 2454636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2455636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2456353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(0, rounding) 2460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 24627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 24637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, rounding=None, context=None): 2465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to the nearest integer, without raising inexact, rounded.""" 2466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2472353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 24746c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= 0: 24766c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2477353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2478353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._rescale(0, rounding) 24797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2480353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 2481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 2482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def sqrt(self, context=None): 2484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return the square root of self.""" 24853b24ccbe7e2b43c4373e4b1e988df55978b819e7Mark Dickinson if context is None: 24863b24ccbe7e2b43c4373e4b1e988df55978b819e7Mark Dickinson context = getcontext() 24873b24ccbe7e2b43c4373e4b1e988df55978b819e7Mark Dickinson 2488636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2489636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2490636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2491636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 24927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2493636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 2494636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 24957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 2497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent = self._exp // 2. sqrt(-0) = -0 249872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', self._exp // 2) 2499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 25007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 25037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # At this point self represents a positive number. Let p be 2505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the desired precision and express self in the form c*100**e 2506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with c a positive real number and e an integer, c and e 2507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # being chosen so that 100**(p-1) <= c < 100**p. Then the 2508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) 2509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # <= sqrt(c) < 10**p, so the closest representable Decimal at 2510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision p is n*10**e where n = round_half_even(sqrt(c)), 2511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the closest integer to sqrt(c) with the even integer chosen 2512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # in the case of a tie. 2513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # To ensure correct rounding in all cases, we use the 2515353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # following trick: we compute the square root to an extra 2516353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # place (precision p+1 instead of precision p), rounding down. 2517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then, if the result is inexact and its last digit is 0 or 5, 2518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we increase the last digit to 1 or 6 respectively; if it's 2519353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exact we leave the last digit alone. Now the final round to 2520353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p places (or fewer in the case of underflow) will round 2521353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly and raise the appropriate flags. 2522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # use an extra digit of precision 2524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista prec = context.prec+1 2525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write argument in the form c*100**e where e = self._exp//2 2527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is the 'ideal' exponent, to be used if the square root is 2528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exactly representable. l is the number of 'digits' of c in 2529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # base 100, so that 100**(l-1) <= c < 100**l. 2530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = op.exp >> 1 2532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.exp & 1: 2533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int * 10 2534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = (len(self._int) >> 1) + 1 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int 2537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(self._int)+1 >> 1 2538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rescale so that c has exactly prec base 100 'digits' 2540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = prec-l 2541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 100**shift 2543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = True 25447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, remainder = divmod(c, 100**-shift) 2546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = not remainder 2547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= shift 2548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find n = floor(sqrt(c)) using Newton's method 2550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = 10**prec 2551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2552353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = c//n 2553353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= q: 25547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 2555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = n + q >> 1 2557353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = exact and n*n == c 2558353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exact: 2560353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is exact; rescale to use ideal exponent e 2561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert n % 10**shift == 0 2563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 10**shift 2564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n *= 10**-shift 2566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e += shift 25677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is not exact; fix last digit as described above 2569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n % 5 == 0: 2570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n += 1 25717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 257272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(n), e) 25737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round, and fit to current context 2575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2577dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 2578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 25797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 25817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 25837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 25847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like max(self, other) except if one is not a number, returns 25867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 25877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2589636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 25906c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 25916c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 25926c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2593636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 259459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2595636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2596636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2597636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2598636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2599e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if on == 1 and sn == 0: 2600e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return self._fix(context) 2601e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if sn == 1 and on == 0: 2602e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return other._fix(context) 2603636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 26047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26052fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2606d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 260759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both operands are finite and equal in numerical value 2608d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2609d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 261059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs differ then max returns the operand with the 2611d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2612d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 261359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs are the same then the exponent is used to select 2614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result. This is exactly the ordering used in compare_total. 2615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 26187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2621636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2622e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 26237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 26257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 26267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 262759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Like min(self, other) except if one is not a number, returns 26287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 26297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2631636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 26326c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 26336c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 26346c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2635636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 263659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2637636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2638636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2639636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2640636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2641e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if on == 1 and sn == 0: 2642e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return self._fix(context) 2643e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if sn == 1 and on == 0: 2644e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return other._fix(context) 2645636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 26467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26472fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2648d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 2652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 26547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2655636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2656e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 26577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 26597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 2660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 26627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 26637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 26647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 266572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return rest == '0'*len(rest) 26667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 2668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns True if self is even. Assumes self is an integer.""" 2669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self or self._exp > 0: 2670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 267172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._int[-1+self._exp] in '02468' 26727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 26747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 26757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 26767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 267759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If NaN or Infinity, self._exp is string 26787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 26797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 26807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, context=None): 2682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 2683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 2685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 2686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self 2688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, other, context=None): 2690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to the other operand numerically. 2691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 2693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 2694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 26952fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other, raiseit = True) 26962fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 26972fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 26982fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return ans 2699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.compare(other, context=context) 2700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, other): 2702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using the abstract representations. 2703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 2705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 2706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 2707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if one is negative and the other is positive, it's easy 2709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign and not other._sign: 2710b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._sign and other._sign: 2712b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 2714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's handle both NaN types 2716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_nan = self._isnan() 2717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_nan = other._isnan() 2718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan or other_nan: 2719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == other_nan: 2720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int < other._int: 2721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2722b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2724b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int > other._int: 2726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2727b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2728353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2729b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2730b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Zero 2731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2734b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2736b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2738b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2740b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2743b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2745b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2747b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2749b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self < other: 2752b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self > other: 2754b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < other._exp: 2757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2758b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2760b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp > other._exp: 2762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2763b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeOne 2764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2765b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2766b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Zero 2767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, other): 2770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using abstract repr., ignoring sign. 2771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 2773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = self.copy_abs() 2775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista o = other.copy_abs() 2776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return s.compare_total(o) 2777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self): 2779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign set to 0. """ 278072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self): 2783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign inverted.""" 2784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 278572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 278772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, self._int, self._exp, self._is_special) 2788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, other): 2790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self with the sign of other.""" 279172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(other._sign, self._int, 279272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp, self._is_special) 2793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, context=None): 2795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** self.""" 2796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(NaN) = NaN 2801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(-Infinity) = 0 2806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 2807b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Zero 2808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(0) = 1 2810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2811b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _One 2812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(Infinity) = Infinity 2814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self) 2816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result is now guaranteed to be inexact (the true 2818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # mathematical result is transcendental). There's no need to 2819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Rounded and Inexact here---they'll always be raised as 2820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a result of the call to _fix. 2821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self.adjusted() 2823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we only need to do any computation for quite a small range 2825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of adjusted exponents---for example, -29 <= adj <= 10 for 2826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the default context. For smaller exponent the result is 2827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # indistinguishable from 1 at the given precision, while for 2828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # larger exponent the result either overflows or underflows. 2829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 0 and adj > len(str((context.Emax+1)*3)): 2830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow 283172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Emax+1) 2832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): 2833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # underflow to 0 283472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Etiny()-1) 2835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 0 and adj < -p: 2836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 283772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) 2838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj < -p-1: 2839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 284072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '9'*(p+1), -p-1) 2841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # general case 2842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.sign == 1: 2846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = -c 2847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: increase precision by 2849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 3 digits at a time until we get an unambiguously 2850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # roundable result 2851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(c, e, p+extra) 2854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 285872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(coeff), exp) 2859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # at this stage, ans should round correctly with *any* 2861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode, not just with ROUND_HALF_EVEN 2862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self): 28701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is canonical; otherwise return False. 28711a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 28721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 28731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 28741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """ 28751a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return True 2876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self): 28781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is finite; otherwise return False. 2879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 28801a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 28811a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 2882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 28831a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return not self._is_special 2884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self): 28861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is infinite; otherwise return False.""" 28871a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'F' 2888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self): 28901a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a qNaN or sNaN; otherwise return False.""" 28911a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp in ('n', 'N') 2892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, context=None): 28941a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a normal number; otherwise return False.""" 28951a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 28961a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 28991a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return context.Emin <= self.adjusted() <= context.Emax 2900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self): 29021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a quiet NaN; otherwise return False.""" 29031a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'n' 2904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self): 29061a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is negative; otherwise return False.""" 29071a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._sign == 1 2908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self): 29101a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a signaling NaN; otherwise return False.""" 29111a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'N' 2912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, context=None): 29141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is subnormal; otherwise return False.""" 29151a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 29161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 29191a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self.adjusted() < context.Emin 2920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self): 29221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a zero; otherwise return False.""" 292372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return not self._is_special and self._int == '0' 2924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _ln_exp_bound(self): 2926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.ln(). 2927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, compute r such that self.ln() >= 10**r. Assumes 2928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that self is finite and positive and that self != 1. 2929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 2932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) 2935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj*23//10)) - 1 2936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument <= 0.1 2938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str((-1-adj)*23//10)) - 1 2939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(c) 2945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) 2946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return e + len(str(10**-e - c)) - 1 2948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, context=None): 2951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of self.""" 2952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(NaN) = NaN 2957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(0.0) == -Infinity 2962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2963b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeInfinity 2964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(Infinity) = Infinity 2966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2967b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Infinity 2968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(1.0) == 0.0 2970b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger if self == _One: 2971b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Zero 2972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(negative) raises InvalidOperation 2974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ln of a negative value') 2977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision by 3 2984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until we get an unambiguously roundable result 2985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p - self._ln_exp_bound() + 2 # at least p+3 places 2986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog(c, e, places) 2988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 299272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _log10_exp_bound(self): 3001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.log10(). 3002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, find r such that self.log10() >= 10**r. 3003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that self is finite and positive and that self != 1. 3004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # For x >= 10 or x < 0.1 we only need a bound on the integer 3007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # part of log10(self), and this comes directly from the 3008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent of x. For 0.1 <= x <= 10 we use the inequalities 3009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > 3010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 3011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 3013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 3014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self >= 10 3015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj))-1 3016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 3017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self < 0.1 3018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(-1-adj))-1 3019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 3020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 3021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 3022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 3023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 3024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(231*c) 3025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) + 2 3026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 3027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(10**-e-c) 3028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) + e - (num < "231") - 1 3029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, context=None): 3031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of self.""" 3032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(NaN) = NaN 3037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(0.0) == -Infinity 3042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 3043b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeInfinity 3044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(Infinity) = Infinity 3046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3047b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Infinity 3048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(negative or -Infinity) raises InvalidOperation 3050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 3051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 3052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'log10 of a negative value') 3053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(10**n) = n 305572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): 3056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # answer may need rounding 3057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self._exp + len(self._int) - 1) 3058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 3060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 3061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 3062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 3063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision 3065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until result is unambiguously roundable 3066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p-self._log10_exp_bound()+2 3067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 3068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog10(c, e, places) 3069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 3070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 3071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 3072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 307372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 3074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 3076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 3077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 3078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 3079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, context=None): 3082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of self's MSD. 3083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 3085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of self (as though it were truncated 3086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to a single digit while maintaining the value of that digit and 3087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista without limiting the resulting exponent). 3088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(NaN) = NaN 3090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(+/-Inf) = +Inf 3098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 3099b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Infinity 3100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(0) = -Inf, DivisionByZero 3102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 3103cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'logb(0)', 1) 3104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # otherwise, simply return the adjusted exponent of self, as a 3106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal. Note that no attempt is made to fit the result 3107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # into the current context. 3108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.adjusted()) 3109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _islogical(self): 3111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return True if self is a logical operand. 3112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3113c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling For being logical, it must be a finite number with a sign of 0, 3114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an exponent of 0, and a coefficient whose digits must all be 3115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista either 0 or 1. 3116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign != 0 or self._exp != 0: 3118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for dig in self._int: 312072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if dig not in '01': 3121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 3123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fill_logical(self, context, opa, opb): 3125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opa) 3126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 312772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opa = '0'*dif + opa 3128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opa = opa[-context.prec:] 3130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opb) 3131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 313272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opb = '0'*dif + opb 3133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opb = opb[-context.prec:] 3135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return opa, opb 3136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, other, context=None): 3138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'and' operation between self and other's digits.""" 3139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 314872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) 314972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, context=None): 3152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all its digits.""" 3153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 315572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), 315672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, other, context=None): 3159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'or' operation between self and other's digits.""" 3160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 316972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb)) 317072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, other, context=None): 3173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'xor' operation between self and other's digits.""" 3174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 318372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb)) 318472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, other, context=None): 3187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31906c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 31916c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 31926c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3199e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if on == 1 and sn == 0: 3200e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return self._fix(context) 3201e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if sn == 1 and on == 0: 3202e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return other._fix(context) 3203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32052fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3214e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, other, context=None): 3217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32206c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 32216c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 32226c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3229e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if on == 1 and sn == 0: 3230e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return self._fix(context) 3231e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista if sn == 1 and on == 0: 3232e29d435e0cefb3e1772f6de0844e628aac3cf98eFacundo Batista return other._fix(context) 3233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32352fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3244e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, context=None): 3247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than itself.""" 3248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 3256b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _NegativeInfinity 3257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 325872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '9'*context.prec, context.Etop()) 3259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_FLOOR) 3262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 326672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), 326772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, context=None): 3270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than itself.""" 3271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3279b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger return _Infinity 3280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 328172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, '9'*context.prec, context.Etop()) 3282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_CEILING) 3285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 328972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), 329072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, other, context=None): 3293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to self, in the direction towards other. 3294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number to self 3296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (excluding self) that is in the direction towards other, 3297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unless both have the same value. If the two operands are 3298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista numerically equal, then the result is a copy of self with the 3299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign set to be the same as the sign of other. 3300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 33102fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson comparison = self._cmp(other) 3311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == 0: 331272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.copy_sign(other) 3313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == -1: 3315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_plus(context) 3316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # comparison == 1 3317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_minus(context) 3318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decide which flags to raise using value of ans 3320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._isinfinity(): 3321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Overflow, 3322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'Infinite result from next_toward', 3323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans._sign) 3324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif ans.adjusted() < context.Emin: 3327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 3328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 3329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if precision == 1 then we don't raise Clamped for a 3332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result 0E-Etiny. 3333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 3334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 3335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, context=None): 3339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of self. 3340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 33420f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista sNaN 33430f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista NaN 3344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 3345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 3346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 3347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 3348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 3349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 3350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 3351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 3352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_snan(): 3354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "sNaN" 3355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_qnan(): 3356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "NaN" 3357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista inf = self._isinfinity() 3358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == 1: 3359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Infinity" 3360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == -1: 3361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Infinity" 3362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_zero(): 3363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Zero" 3365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Zero" 3367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_subnormal(context=context): 3370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Subnormal" 3372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Subnormal" 3374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # just a normal, regular, boring number, :) 3375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Normal" 3377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Normal" 3379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 3381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :)""" 3382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 3383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, other, context=None): 3385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of self, value-of-other times.""" 3386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3388353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3389353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3394353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3397353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3398353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33996c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 340672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's rotate! 3409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[torot:] + rotdig[:torot] 341072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 341172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, other, context=None): 3414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self operand after adding the second value to its exp.""" 3415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista liminf = -2 * (context.Emax + context.prec) 3425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista limsup = 2 * (context.Emax + context.prec) 3426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (liminf <= int(other) <= limsup): 3427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 34306c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 343272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) 3433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista d = d._fix(context) 3434353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return d 3435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, other, context=None): 3437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of self, value-of-other times.""" 3438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3445353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3447353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3448353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3450353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 34516c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not torot: 34566c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 346072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's shift! 3463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if torot < 0: 3464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[:torot] 3465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 346672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated = rotdig + '0'*torot 3467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotated[-context.prec:] 3468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 346972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 347072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 347259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Support for pickling, copy, and deepcopy 34737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 34747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 34757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 34777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3478cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # I'm immutable; therefore I am my own clone 34797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 34827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3483cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # My components are also immutable 34847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # PEP 3101 support. See also _parse_format_specifier and _format_align 34871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson def __format__(self, specifier, context=None): 3488f4da77765f8581e31620e9f49c68028e57b0ae85Mark Dickinson """Format a Decimal instance according to the given specifier. 34891ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34901ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson The specifier should be a standard format specifier, with the 34911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson form described in PEP 3101. Formatting types 'e', 'E', 'f', 34921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 'F', 'g', 'G', and '%' are supported. If the formatting type 34931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson is omitted it defaults to 'g' or 'G', depending on the value 34941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson of context.capitals. 34951ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34961ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson At this time the 'n' format specifier type (which is supposed 34971ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson to use the current locale) is not supported. 34981ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 34991ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35001ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # Note: PEP 3101 says that if the type is not present then 35011ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # there should be at least one digit after the decimal point. 35021ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # We take the liberty of ignoring this requirement for 35031ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # Decimal---it's presumably there to make sure that 35041ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # format(float, '') behaves similarly to str(float). 35051ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if context is None: 35061ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson context = getcontext() 35071ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35081ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson spec = _parse_format_specifier(specifier) 35091ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35101ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # special values don't care about the type or precision... 35111ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._is_special: 35121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return _format_align(str(self), spec) 35131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # a type of None defaults to 'g' or 'G', depending on context 35151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # if type is '%', adjust exponent of self accordingly 35161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] is None: 35171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson spec['type'] = ['g', 'G'][context.capitals] 35181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] == '%': 35191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = _dec_from_triple(self._sign, self._int, self._exp+2) 35201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # round if necessary, taking rounding mode from the context 35221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson rounding = context.rounding 35231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson precision = spec['precision'] 35241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if precision is not None: 35251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] in 'eE': 35261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._round(precision+1, rounding) 35271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'gG': 35281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if len(self._int) > precision: 35291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._round(precision, rounding) 35301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'fF%': 35311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._rescale(-precision, rounding) 35321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # special case: zeros with a positive exponent can't be 35331ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # represented in fixed point; rescale them to 0e0. 35341ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif not self and self._exp > 0 and spec['type'] in 'fF%': 35351ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._rescale(0, rounding) 35361ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35371ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out placement of the decimal point 35381ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson leftdigits = self._exp + len(self._int) 35391ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] in 'fF%': 35401ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = leftdigits 35411ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'eE': 35421ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if not self and precision is not None: 35431ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 - precision 35441ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35451ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 35461ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'gG': 35471ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._exp <= 0 and leftdigits > -6: 35481ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = leftdigits 35491ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35501ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 35511ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35521ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out main part of numeric string... 35531ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if dotplace <= 0: 35541ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = '0.' + '0'*(-dotplace) + self._int 35551ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif dotplace >= len(self._int): 35561ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # make sure we're not padding a '0' with extra zeros on the right 35571ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson assert dotplace==len(self._int) or self._int != '0' 35581ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = self._int + '0'*(dotplace-len(self._int)) 35591ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35601ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = self._int[:dotplace] + '.' + self._int[dotplace:] 35611ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35621ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # ...then the trailing exponent, or trailing '%' 35631ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if leftdigits != dotplace or spec['type'] in 'eE': 35641ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] 35651ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = num + "{0}{1:+}".format(echar, leftdigits-dotplace) 35661ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] == '%': 35671ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = num + '%' 35681ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35691ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # add sign 35701ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._sign == 1: 35711ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = '-' + num 35721ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return _format_align(num, spec) 35731ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35741ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 357572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistadef _dec_from_triple(sign, coefficient, exponent, special=False): 357672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """Create a decimal instance directly, without any validation, 357772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista normalization (e.g. removal of leading zeros) or argument 357872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista conversion. 357972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 358072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista This function is for *internal use only*. 358172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """ 358272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 358372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = object.__new__(Decimal) 358472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._sign = sign 358572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = coefficient 358672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp = exponent 358772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._is_special = special 358872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 358972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self 359072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 359159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context class ####################################################### 3592cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 35937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3594cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# get rounding method function: 359559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batistarounding_functions = [name for name in Decimal.__dict__.keys() 359659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if name.startswith('_round_')] 35977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 359859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 35997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 36007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 36017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 36027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 36047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3605ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlanclass _ContextManager(object): 36068b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Context manager class to support localcontext(). 36071a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 3608ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan Sets a copy of the supplied context in __enter__() and restores 36098b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan the previous decimal context in __exit__() 36108b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 36111a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 3612ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan self.new_context = new_context.copy() 36131a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 36141a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 36151a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 36161a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 36171a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 36181a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 36191a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 36207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 36217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 36227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 36247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 362559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista rounding - rounding type (how you round) 3626bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 36277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 36287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 36291840c1abcade9215faf91b701ab4525ba948d9dcMark Dickinson flags - When an exception is caused, flags[exception] is set. 36307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 36317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 36320ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 36330ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 36347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 36357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 3636e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 36377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 36397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 3640abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 36410ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 3642e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 3643abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 3644abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 3645abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 3646abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 3647abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 3648bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 364971f3b85497f25bad3b00555173c51378f64edbb5Mark Dickinson flags = dict([(s, int(s in flags)) for s in _signals]) 3650b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 3651bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 365271f3b85497f25bad3b00555173c51378f64edbb5Mark Dickinson traps = dict([(s, int(s in traps)) for s in _signals]) 3653b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 36547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 36557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 3656eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 36577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 36587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 36597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 36607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3661b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 3662bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 3663b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 366459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' 366559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' 366659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista % vars(self)) 366759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [f.__name__ for f, v in self.flags.items() if v] 366859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('flags=[' + ', '.join(names) + ']') 366959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [t.__name__ for t, v in self.traps.items() if v] 367059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('traps=[' + ', '.join(names) + ']') 3671b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 3672b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 3673d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 3674d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 3675d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 3676b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 3677d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 36789fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 36799fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 3680e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista nc = Context(self.prec, self.rounding, self.traps, 3681e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags, self.Emin, self.Emax, 3682e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 36837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 36849fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 36859fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 36869fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 368759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista nc = Context(self.prec, self.rounding, self.traps.copy(), 3688e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags.copy(), self.Emin, self.Emax, 3689e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 36909fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 36919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 36927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36935aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 36947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 36957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 36971840c1abcade9215faf91b701ab4525ba948d9dcMark Dickinson Otherwise, it sets the flag, then, if the corresponding 36987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 36991840c1abcade9215faf91b701ab4525ba948d9dcMark Dickinson the default value after setting the flag. 37007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37015aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 37027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 370359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Don't touch the flag 37047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 37057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37061840c1abcade9215faf91b701ab4525ba948d9dcMark Dickinson self.flags[error] = 1 3707bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 370859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # The errors define how to handle themselves. 37095aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 37107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 371259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # self._ignored_flags = [] 37138aca9d032e7813da9a23fd0771c008aff5a5e62fMark Dickinson raise error(explanation) 37147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 37167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 3717fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 37187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 37207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 37217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 37227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 37237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 37247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 37257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 37277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 37287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 37297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 37307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 37317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 37327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 373353663a695ef2bb96ac0252cd4cc4aa40d4f953beNick Coghlan # We inherit object.__hash__, so we must deny this explicitly 373453663a695ef2bb96ac0252cd4cc4aa40d4f953beNick Coghlan __hash__ = None 37355aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 37367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 37377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 37387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 37397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 3741e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 37427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 37437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 37457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 37467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 37487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 37497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 37517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 37527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 37537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 37547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 37557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 37567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 37587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 37607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 37617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 37627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3763fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 376459bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson """Creates a new Decimal instance but using self as context. 376559bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 376659bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson This method implements the to-number operation of the 376759bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson IBM Decimal specification.""" 376859bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 376959bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson if isinstance(num, basestring) and num != num.strip(): 377059bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson return self._raise_error(ConversionSyntax, 377159bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "no trailing or leading whitespace is " 377259bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "permitted.") 377359bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 37747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 3775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if d._isnan() and len(d._int) > self.prec - self._clamp: 3776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._raise_error(ConversionSyntax, 3777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista "diagnostic info too long in NaN") 3778dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 37797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3780f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger def create_decimal_from_float(self, f): 3781f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger """Creates a new Decimal instance from a float but rounding using self 3782f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger as the context. 3783f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 3784f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> context = Context(prec=5, rounding=ROUND_DOWN) 3785f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> context.create_decimal_from_float(3.1415926535897932) 3786f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Decimal('3.1415') 3787f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> context = Context(prec=5, traps=[Inexact]) 3788f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger >>> context.create_decimal_from_float(3.1415926535897932) 3789f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Traceback (most recent call last): 3790f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger ... 3791f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger Inexact: None 3792f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 3793f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger """ 3794f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger d = Decimal.from_float(f) # An exact conversion 3795f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger return d._fix(self) # Apply the context rounding 3796f4d8597a59990c41bc9cc8d499d8bc919d7ebf2dRaymond Hettinger 379759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Methods 37987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 37997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 38007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 380259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation on the operand. Otherwise, the result is the same as using 38037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 38047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 3806abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 38079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 3808abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 38099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 3810abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 38119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 3812abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 38137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 38157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 38177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 38187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 3820abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('19.00') 38219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 3822abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.02E+4') 38237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 38257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 3827dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 38287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, a): 3830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 3831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 3833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 3834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.canonical(Decimal('2.50')) 3836abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.50') 3837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.canonical(context=self) 3839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 38407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 38417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 38427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 38447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 38457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 38467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 38477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 38487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 38507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 38517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 38527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 38537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 3855abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 38569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 3857abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 38589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 3859abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 38609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 3861abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 38629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 3863abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 38649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 3865abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 38667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 38687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, a, b): 3870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values of the two operands numerically. 3871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 3873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 3874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext 3876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('3')) 3877abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) 3879abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) 3884abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) 3891abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_signal(b, context=self) 3896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, a, b): 3898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation. 3899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 3901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 3902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 3903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) 3905abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) 3907abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) 3909abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) 3911abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) 3913abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 3914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) 3915abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total(b) 3918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, a, b): 3920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation ignoring sign. 3921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 3923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total_mag(b) 3925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self, a): 3927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign set to 0. 3928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('2.1')) 3930abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('-100')) 3932abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 3933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_abs() 3935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_decimal(self, a): 3937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the decimal objet. 3938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('2.1')) 3940abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('-1.00')) 3942abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00') 3943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 39446c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(a) 3945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self, a): 3947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign inverted. 3948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('101.5')) 3950abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-101.5') 3951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('-101.5')) 3952abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 3953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_negate() 3955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, a, b): 3957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Copies the second operand's sign to the first one. 3958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In detail, it returns a copy of the first operand with the sign 3960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista equal to the sign of the second operand. 3961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) 3963abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) 3965abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) 3967abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) 3969abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_sign(b) 3972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 39737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 39747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 39757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 3977abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.333333333') 39789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 3979abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.666666667') 39809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 3981abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.5') 39829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 3983abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 39849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 3985abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 39869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 3987abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.00') 39889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 3989abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20') 39909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 3991abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 39929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 3993abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 39949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 3995abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20E+6') 39967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 39977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 39987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 40007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 40017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 40029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 4003abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 40049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 4005abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 40069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 4007abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 40087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 40097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 40107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 40117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 40127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 40137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, a): 4015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** a. 4016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-Infinity')) 4021abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-1')) 4023abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.367879441') 4024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0')) 4025abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('1')) 4027abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.71828183') 4028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0.693147181')) 4029abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 4030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('+Infinity')) 4031abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.exp(context=self) 4034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, a, b, c): 4036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a multiplied by b, plus c. 4037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The first two operands are multiplied together, using multiply, 4039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the third operand is then added to the result of that 4040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplication, using add, all with only one final rounding. 4041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) 4043abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('22') 4044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) 4045abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 4046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) 4047abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.38435736E+12') 4048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.fma(b, c, context=self) 4050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self, a): 40521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is canonical; otherwise return False. 40531a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 40541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 40551a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 4056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_canonical(Decimal('2.50')) 40581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 40601a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return a.is_canonical() 4061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self, a): 40631a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is finite; otherwise return False. 4064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 40651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 40661a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 4067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('2.50')) 40691a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('-0.3')) 40711a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('0')) 40731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('Inf')) 40751a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('NaN')) 40771a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_finite() 4080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self, a): 40821a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is infinite; otherwise return False. 4083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('2.50')) 40851a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('-Inf')) 40871a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('NaN')) 40891a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_infinite() 4092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self, a): 40941a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a qNaN or sNaN; 40951a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('2.50')) 40981a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('NaN')) 41001a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('-sNaN')) 41021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_nan() 4105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, a): 41071a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a normal number; 41081a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('2.50')) 41141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.1E-999')) 41161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.00')) 41181a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('-Inf')) 41201a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('NaN')) 41221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_normal(context=self) 4125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self, a): 41271a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a quiet NaN; otherwise return False. 4128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('2.50')) 41301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('NaN')) 41321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('sNaN')) 41341a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_qnan() 4137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self, a): 41391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is negative; otherwise return False. 4140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('2.50')) 41421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-12')) 41441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-0')) 41461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_signed() 4149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self, a): 41511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a signaling NaN; 41521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('2.50')) 41551a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('NaN')) 41571a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('sNaN')) 41591a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_snan() 4162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, a): 41641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is subnormal; otherwise return False. 4165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('2.50')) 41701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.1E-999')) 41721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.00')) 41741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('-Inf')) 41761a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('NaN')) 41781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_subnormal(context=self) 4181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self, a): 41831a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a zero; otherwise return False. 4184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('0')) 41861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('2.50')) 41881a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('-0E+2')) 41901a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_zero() 4193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, a): 4195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of the operand. 4196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('0')) 4201abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('1.000')) 4203abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('2.71828183')) 4205abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000000') 4206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('10')) 4207abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.30258509') 4208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('+Infinity')) 4209abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.ln(context=self) 4212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, a): 4214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of the operand. 4215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0')) 4220abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0.001')) 4222abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-3') 4223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('1.000')) 4224abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('2')) 4226abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.301029996') 4227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('10')) 4228abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('70')) 4230abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.84509804') 4231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('+Infinity')) 4232abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.log10(context=self) 4235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, a): 4237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of the operand's MSD. 4238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 4240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of the operand (as though the 4241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand were truncated to a single digit while maintaining the 4242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value of that digit and without limiting the resulting exponent). 4243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('250')) 4245abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('2.50')) 4247abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0.03')) 4249abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 4250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0')) 4251abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logb(context=self) 4254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, a, b): 4256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'and' between each operand's digits. 4257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) 4261abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) 4263abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) 4265abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) 4267abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) 4269abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 4270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) 4271abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_and(b, context=self) 4274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, a): 4276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all the digits in the operand. 4277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operand must be a logical number. 4279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('0')) 4281abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111111') 4282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('1')) 4283abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111110') 4284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('111111111')) 4285abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('101010101')) 4287abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10101010') 4288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_invert(context=self) 4290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, a, b): 4292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'or' between each operand's digits. 4293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) 4297abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) 4299abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) 4301abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) 4303abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) 4305abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) 4307abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_or(b, context=self) 4310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, a, b): 4312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'xor' between each operand's digits. 4313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) 4317abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) 4319abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) 4321abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) 4323abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) 4325abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('110') 4326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) 4327abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1101') 4328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_xor(b, context=self) 4330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 43327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 43337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4335c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 433659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 433759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the maximum (closer to positive 43387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 43397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 4341abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 43429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 4343abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 43449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 4345abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4346d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 4347abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 43487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 43507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, a, b): 4352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.max_mag(b, context=self) 4354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 43567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 43577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4359c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 436059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 436159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the minimum (closer to negative 43627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 43637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 4365abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 43669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 4367abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-10') 43689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 4369abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 4370d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 4371abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 43727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 43747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, a, b): 4376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.min_mag(b, context=self) 4378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 43807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 43817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 43837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 43847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 43857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 4387abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 43889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 4389abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 43907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 43927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 43947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 43957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4396cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis If either operand is a special value then the general rules apply. 4397cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Otherwise, the operands are multiplied together ('long multiplication'), 4398cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis resulting in a number which may be as long as the sum of the lengths 4399cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis of the two operands. 44007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 4402abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.60') 44039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 4404abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('21') 44059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 4406abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.72') 44079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 4408abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.0') 44099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 4410abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.28135971E+11') 44117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 44137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, a): 4415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than a. 4416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('1')) 4421abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('1E-1007')) 4423abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('-1.00000003')) 4425abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('Infinity')) 4427abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('9.99999999E+999') 4428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_minus(context=self) 4430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, a): 4432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than a. 4433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4434353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('1')) 4438abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-1E-1007')) 4440abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('-1.00000003')) 4442abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-Infinity')) 4444abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-9.99999999E+999') 4445353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_plus(context=self) 4447353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4448353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, a, b): 4449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to a, in direction towards b. 4450353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4451353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number from the first 4452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand (but not the first operand) that is in the direction 4453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista towards the second operand, unless the operands have the same 4454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. 4455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4456353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('2')) 4460abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) 4462abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) 4464abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('0')) 4466abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) 4468abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) 4470abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) 4472abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.00') 4473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4474353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_toward(b, context=self) 4475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 44767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 4477e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 44787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 44807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 44817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 4483abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 44849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 4485abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 44869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 4487abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2') 44889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 4489abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.2E+2') 44909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 4491abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2E+2') 44929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 4493abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 44947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 44967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, a): 4498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of the operand. 4499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4500353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 4501353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 4502353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 4503353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 4504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 4505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 4506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 4507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 4508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 4509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 4510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 4511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = Context(ExtendedContext) 4513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4515353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('Infinity')) 4516353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Infinity' 4517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('1E-10')) 4518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4519353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('2.50')) 4520353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4521353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0.1E-999')) 4522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Subnormal' 4523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0')) 4524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Zero' 4525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0')) 4526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Zero' 4527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0.1E-999')) 4528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Subnormal' 4529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-1E-10')) 4530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-2.50')) 4532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-Infinity')) 4534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Infinity' 4535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('NaN')) 4536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-NaN')) 4538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('sNaN')) 4540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'sNaN' 4541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.number_class(context=self) 4543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 45457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 45467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 45487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 45497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 45507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 4552abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 45539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 4554abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 45557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 45577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 45597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 45607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute a**b. If a is negative then b 4562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista must be integral. The result will be inexact unless b is 4563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integral and the result is finite and can be expressed exactly 4564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in 'precision' digits. 4565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (a**b) % modulo. For the 4567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 4568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 4569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 4571353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - b must be nonnegative 4572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - at least one of a or b must be nonzero 4573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and have at most 'precision' digits 4574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(a, b, modulo) is identical to the result 4576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that would be obtained by computing (a**b) % modulo with 4577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unbounded precision, but is computed more efficiently. It is 4578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista always exact. 4579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('3')) 4584abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('8') 4585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-2'), Decimal('3')) 4586abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 4587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('-3')) 4588abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.125') 4589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('1.7'), Decimal('8')) 4590abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('69.7575744') 4591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('10'), Decimal('0.301029996')) 4592abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 4593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('-1')) 4594abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('0')) 4596abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('1')) 4598abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('-1')) 4600abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('0')) 4602abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('1')) 4604abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('2')) 4606abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4607353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('0'), Decimal('0')) 4608abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 4609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4610353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) 4611abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4612353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) 4613abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-11') 4614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) 4615abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) 4617abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) 4619abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11729830') 4620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) 4621abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) 4623abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 46247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 46267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 462859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Returns a value equal to 'a' (rounded), having the exponent of 'b'. 46297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 463159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operand. It may be rounded using the current rounding setting (if the 46327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 46337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 46347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 46357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 46377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 463859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation condition is raised. This guarantees that, unless there is 463959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista an error condition, the exponent of the result of a quantize is always 46407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 46417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 46437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 46447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 4646abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.170') 46479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 4648abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.17') 46499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 4650abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2') 46519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 4652abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 46539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 4654abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E+1') 46559ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 4656abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 46579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 4658abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 4660abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 46619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 4662abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E+5') 46639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 4664abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 4666abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 4668abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217.0') 46699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 4670abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217') 46719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 4672abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2E+2') 46739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 4674abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2E+2') 46757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 46777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 4679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :) 4680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.radix() 4682abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 4685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 46867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 46877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 46887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 469059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista calculating integer division as described for divide-integer, rounded 46910d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz to precision digits if necessary. The sign of the result, if 469259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista non-zero, is the same as that of the original dividend. 46937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 46957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 46967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 46977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 4699abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 47009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 4701abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 47029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 4703abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 47049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 4705abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 47069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 4707abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 47089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 4709abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 47107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 47127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 47147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 47157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 471659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen). If the result is equal to 0 then its sign will be the 47177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 47187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 47207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 47217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 47227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 4724abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.9') 47259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 4726abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 47279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 4728abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 47299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 4730abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 47319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 4732abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 47339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 4734abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 47359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 4736abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.3') 47377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 47397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, a, b): 4741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of a, b times. 4742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a rotated copy of the digits in 4744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the coefficient of the first operand. The number of places of 4745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotation is taken from the absolute value of the second operand, 4746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the rotation being to the left if the second operand is 4747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. 4748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) 4750abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000003') 4751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) 4752abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('12') 4753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) 4754abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('891234567') 4755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) 4756abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) 4758abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678912') 4759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.rotate(b, context=self) 4761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 47627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 47637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 47647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 47667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 47677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 47697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 47709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 47717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 47729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 47737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 47749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 47757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 47767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 47787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, a, b): 4780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the first operand after adding the second value its exp. 4781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) 4783abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.0750') 4784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) 4785abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50') 4786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) 4787abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50E+3') 4788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.scaleb (b, context=self) 4790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, a, b): 4792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of a, b times. 4793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a shifted copy of the digits 4795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the coefficient of the first operand. The number of places 4796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to shift is taken from the absolute value of the second operand, 4797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the shift being to the left if the second operand is 4798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. Digits shifted into the 4799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coefficient are zeros. 4800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) 4802abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000000') 4803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) 4804abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) 4806abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1234567') 4807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) 4808abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) 4810abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678900') 4811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.shift(b, context=self) 4813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 48147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 481559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Square root of a non-negative number to context precision. 48167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 48187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 48197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 4821abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 48229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 4823abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 48249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 4825abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.624499800') 48269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 4827abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 48289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 4829abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 48309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 4831abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 48329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 4833abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 48349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 4835abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.64575131') 48369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 4837abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.16227766') 48389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 48396ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 48407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 48427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 4844f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 48457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 4847abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.23') 48489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 4849abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.00') 48509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 4851abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.77') 48527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 48547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 48567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 48577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 48597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 48617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 48637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 48647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 48667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 48687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, a): 4870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to an integer. 4871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista When the operand has a negative exponent, the result is the same 4873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista as using the quantize() operation using the given operand as the 4874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista left-hand-operand, 1E+0 as the right-hand-operand, and the precision 4875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the operand as the precision setting; Inexact and Rounded flags 4876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista are allowed in this operation. The rounding mode is taken from the 4877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 4878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('2.1')) 4880abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100')) 4882abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100.0')) 4884abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('101.5')) 4886abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) 4888abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) 4890abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) 4892abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) 4894abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_exact(context=self) 4897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, a): 48997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 49007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 49027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 49037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 49047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 490559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be set. The rounding mode is taken from the context. 49067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('2.1')) 4908abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100')) 4910abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100.0')) 4912abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('101.5')) 4914abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-101.5')) 4916abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('10E+5')) 4918abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) 4920abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-Inf')) 4922abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 49237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_value(context=self) 4925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 4927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 49287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 49307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 493117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 4932636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 49337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 49347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 49367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 49377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 4938636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 49397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 494017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 494117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 494272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self.int = int(value._int) 49437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 494417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 494517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 49467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 49477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 49487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 49497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 49517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 49527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 49547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4957e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batistadef _normalize(op1, op2, prec = 0): 49587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 49597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 49617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp < op2.exp: 49637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 49647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 49657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 49667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 49677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 49687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). 4970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then adding 10**exp to tmp has the same effect (after rounding) 4971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as adding any positive quantity smaller than 10**exp; similarly 4972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for subtraction. So if other is smaller than 10**exp we replace 4973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # it with 10**exp. This avoids tmp.exp - other.exp getting too large. 4974e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista tmp_len = len(str(tmp.int)) 4975e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other_len = len(str(other.int)) 4976e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista exp = tmp.exp + min(-1, tmp_len - prec - 2) 4977e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if other_len + other.exp - 1 < exp: 4978e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.int = 1 4979e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.exp = exp 4980636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 4981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.int *= 10 ** (tmp.exp - other.exp) 4982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.exp = other.exp 49837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 49847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### 4986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# This function from Tim Peters was taken from here: 4988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# http://mail.python.org/pipermail/python-list/1999-July/007758.html 4989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# The correction being in the function definition is for speed, and 4990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the whole function is not resolved with math.log because of avoiding 4991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the use of floats. 4992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _nbits(n, correction = { 4993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0': 4, '1': 3, '2': 2, '3': 2, 4994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '4': 1, '5': 1, '6': 1, '7': 1, 4995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '8': 0, '9': 0, 'a': 0, 'b': 0, 4996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'c': 0, 'd': 0, 'e': 0, 'f': 0}): 4997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Number of bits in binary representation of the positive integer n, 4998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or 0 if n == 0. 4999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n < 0: 5001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _nbits should be nonnegative.") 5002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista hex_n = "%x" % n 5003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 4*len(hex_n) - correction[hex_n[0]] 5004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _sqrt_nearest(n, a): 5006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to the square root of the positive integer n. a is 5007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an initial approximation to the square root. Any positive integer 5008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista will do for a, but the closer a is to the square root of n the 5009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista faster convergence will be. 5010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= 0 or a <= 0: 5013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("Both arguments to _sqrt_nearest should be positive.") 5014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b=0 5016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while a != b: 5017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, a = a, a--n//a>>1 5018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a 5019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _rshift_nearest(x, shift): 5021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given an integer x and a nonnegative integer shift, return closest 5022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integer to x / 2**shift; use round-to-even in case of a tie. 5023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, q = 1L << shift, x >> shift 5026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*(x & (b-1)) + (q&1) > b) 5027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _div_nearest(a, b): 5029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to a/b, a and b positive integers; rounds to even 5030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the case of a tie. 5031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(a, b) 5034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*r + (q&1) > b) 5035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _ilog(x, M, L = 8): 5037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Integer approximation to M*log(x/M), with absolute error boundable 5038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in terms only of x/M. 5039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given positive integers x and M, return an integer approximation to 5041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference 5042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista between the approximation and the exact result is at most 22. For 5043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In 5044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista both cases these are upper bounds on the error; it will usually be 5045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista much smaller.""" 5046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The basic algorithm is the following: let log1p be the function 5048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use 5049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the reduction 5050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) 5052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # repeatedly until the argument to log1p is small (< 2**-L in 5054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # absolute value). For small y we can use the Taylor series 5055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expansion 5056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T 5058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # truncating at T such that y**T is small enough. The whole 5060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # computation is carried out in a form of fixed-point arithmetic, 5061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with a real number z being represented by an integer 5062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # approximation to z*M. To avoid loss of precision, the y below 5063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is actually an integer approximation to 2**R*y*M, where R is the 5064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number of reductions performed so far. 5065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = x-M 5067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument reduction; R = number of reductions performed 5068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = 0 5069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while (R <= L and long(abs(y)) << L-R >= M or 5070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R > L and abs(y) >> R-L >= M): 5071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(long(M*y) << 1, 5072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) 5073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R += 1 5074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series with T terms 5076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yshift = _rshift_nearest(y, R) 5078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, T) 5079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(T-1, 0, -1): 5080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, k) - _div_nearest(yshift*w, M) 5081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(w*y, M) 5083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog10(c, e, p): 5085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, p >= 0, compute an integer 5086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log10(c*10**e), with an absolute error of 5087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 5088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # increase precision by 2; compensate for this by dividing 5090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # final result by 100 5091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write c*10**e as d*10**f with either: 5094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f >= 0 and 1 <= d <= 10, or 5095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f <= 0 and 0.1 <= d <= 1. 5096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Thus for c*10**e close to 1, f = 0 5097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 5098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 5099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 5101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M = 10**p 5102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 5103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 5104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 5105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) 5107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, M) # error < 5 + 22 = 27 5109be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista log_10 = _log10_digits(p) # error < 1 5110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _div_nearest(log_d*M, log_10) 5111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = f*M # exact 5112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 # error < 2.31 511418aa388ca084e1d40aa48c8c8f1b4f730c6fe059Neal Norwitz log_tenpower = _div_nearest(f, 10**-p) # error < 0.5 5115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(log_tenpower+log_d, 100) 5117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog(c, e, p): 5119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, compute an integer 5120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log(c*10**e), with an absolute error of 5121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 5122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Increase precision by 2. The precision increase is compensated 5124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for at the end with a division by 100. 5125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, 5128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) 5129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as 10**p * log(d) + 10**p*f * log(10). 5130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 5131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 5132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute approximation to 10**p*log(d), with error < 27 5134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 5135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 5136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 5137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 5138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) # error of <= 0.5 in c 5140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # _ilog magnifies existing error in c by a factor of at most 10 5142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 5143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p <= 0: just approximate the whole thing by 0; error < 2.31 5145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 5146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5147be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute approximation to f*10**p*log(10), with error < 11. 5148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if f: 5149be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = len(str(abs(f)))-1 5150be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p + extra >= 0: 5151be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in f * _log10_digits(p+extra) < |f| * 1 = |f| 5152be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 5153be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) 5154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5159be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 5160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(f_log_ten + log_d, 100) 5161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5162be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batistaclass _Log10Memoize(object): 5163be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Class to compute, store, and allow retrieval of, digits of the 5164be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista constant log(10) = 2.302585.... This constant is needed by 5165be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" 5166be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def __init__(self): 5167be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = "23025850929940456840179914546843642076011014886" 5168be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5169be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def getdigits(self, p): 5170be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Given an integer p >= 0, return floor(10**p)*log(10). 5171be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5172be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista For example, self.getdigits(3) returns 2302. 5173be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """ 5174be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits are stored as a string, for quick conversion to 5175be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # integer in the case that we've already computed enough 5176be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits; the stored digits should always be correct 5177be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # (truncated, not rounded to nearest). 5178be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p < 0: 5179be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista raise ValueError("p should be nonnegative") 5180be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5181be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p >= len(self.digits): 5182be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+3, p+6, p+9, ... digits; continue until at 5183be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # least one of the extra digits is nonzero 5184be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = 3 5185be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista while True: 5186be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+extra digits, correct to within 1ulp 5187be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista M = 10**(p+extra+2) 5188be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista digits = str(_div_nearest(_ilog(10*M, M), 100)) 5189be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if digits[-extra:] != '0'*extra: 5190be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista break 5191be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra += 3 5192be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # keep all reliable digits so far; remove trailing zeros 5193be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # and next nonzero digit 5194be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = digits.rstrip('0')[:-1] 5195be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista return int(self.digits[:p+1]) 5196be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5197be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista_log10_digits = _Log10Memoize().getdigits 5198be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _iexp(x, M, L=8): 5200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers x and M, M > 0, such that x/M is small in absolute 5201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value, compute an integer approximation to M*exp(x/M). For 0 <= 5202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x/M <= 2.4, the absolute error in the result is bounded by 60 (and 5203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista is usually much smaller).""" 5204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Algorithm: to compute exp(z) for a real number z, first divide z 5206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then 5207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor 5208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # series 5209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(x) = x + x**2/2! + x**3/3! + ... 5211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Now use the identity 5213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(2x) = expm1(x)*(expm1(x)+2) 5215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # R times to compute the sequence expm1(z/2**R), 5217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). 5218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find R such that x/2**R/M <= 2**-L 5220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = _nbits((long(x)<<L)//M) 5221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series. (2**L)**T > M 5223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x, T) 5225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<R 5226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(T-1, 0, -1): 5227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x*(Mshift + y), Mshift * i) 5228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Expansion 5230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(R-1, -1, -1): 5231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<(k+2) 5232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(y*(y+Mshift), Mshift) 5233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return M+y 5235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dexp(c, e, p): 5237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute an approximation to exp(c*10**e), with p decimal places of 5238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista precision. 5239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5240be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Returns integers d, f such that: 5241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= d <= 10**p, and 5243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (d-1)*10**f < exp(c*10**e) < (d+1)*10**f 5244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, d*10**f is an approximation to exp(c*10**e) with p 5246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision, and with an error in d of at most 1. This is 5247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when d 5248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista = 10**(p-1) the error could be up to 10 ulp.""" 5249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision 5251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5253be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute log(10) with extra precision = adjusted exponent of c*10**e 5254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = max(0, e + len(str(c)) - 1) 5255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = p + extra 5256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5257be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), 5258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding down 5259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = e+q 5260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c*10**shift 5262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c//10**-shift 5264be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista quot, rem = divmod(cshift, _log10_digits(q)) 5265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reduce remainder back to original precision 5267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rem = _div_nearest(rem, 10**extra) 5268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # error in result of _iexp < 120; error after division < 0.62 5270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 5271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dpower(xc, xe, yc, ye, p): 5273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and 5274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 5275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= c <= 10**p, and 5277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (c-1)*10**e < x**y < (c+1)*10**e 5278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in other words, c*10**e is an approximation to x**y with p digits 5280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of precision, and with an error in c of at most 1. (This is 5281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when c 5282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista == 10**(p-1) we can only guarantee error < 10ulp.) 5283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista We assume that: x is positive and not equal to 1, and y is nonzero. 5285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find b such that 10**(b-1) <= |y| <= 10**b 5288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b = len(str(abs(yc))) + ye 5289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point 5291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista lxc = _dlog(xc, xe, p+b+1) 5292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) 5294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = ye-b 5295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = lxc*yc*10**shift 5297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = _div_nearest(lxc*yc, 10**-shift) 5299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if pc == 0: 5301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we prefer a result that isn't exactly 1; this makes it 5302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # easier to compute a correctly rounded result in __pow__ 5303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: 5304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**(p-1)+1, 1-p 5305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**p-1, -p 5307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(pc, -(p+1), p+1) 5309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _div_nearest(coeff, 10) 5310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp += 1 5311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return coeff, exp 5313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _log10_lb(c, correction = { 5315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, 5316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '6': 23, '7': 16, '8': 10, '9': 5}): 5317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for 100*log10(c) for a positive integer c.""" 5318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c <= 0: 5319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _log10_lb should be nonnegative.") 5320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_c = str(c) 5321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 100*len(str_c) - correction[str_c[0]] 5322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 532359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Helper Functions #################################################### 53247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _convert_other(other, raiseit=False): 5326636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 5327636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5328636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5329636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 5330636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 5331636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 5332636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 5333636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 5334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if raiseit: 5335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise TypeError("Unable to convert %s to Decimal" % other) 5336267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 5337636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 533859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Setup Specific Contexts ############################################ 53397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 5341fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 53427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 53446ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 5345bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 5346bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 534799148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 534899148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 5349e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 53507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 53537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 53547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 53557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 53567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 53587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 5359bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 5360bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 53617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 53646ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 5365bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 5366bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 53677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 537059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### crud for parsing strings ############################################# 53716a123cb7827859748a0096570dfbb5ceba0e59dcMark Dickinson# 537272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Regular expression used for parsing numeric strings. Additional 537372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# comments: 537472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 537572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 1. Uncomment the two '\s*' lines to allow leading and/or trailing 537672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# whitespace. But note that the specification disallows whitespace in 537772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# a numeric string. 537872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 537972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 2. For finite numbers (not infinities and NaNs) the body of the 538072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# number between the optional sign and the optional exponent must have 538172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# at least one decimal digit, possibly after the decimal point. The 538272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# lookahead expression '(?=\d|\.\d)' checks this. 538372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 538472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# As the flag UNICODE is not enabled here, we're explicitly avoiding any 538572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# other meaning for \d than the numbers [0-9]. 53867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 538772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistaimport re 538870c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson_parser = re.compile(r""" # A numeric string consists of: 53897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 539070c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (?P<sign>[-+])? # an optional sign, followed by either... 53917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 539270c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (?=[0-9]|\.[0-9]) # ...a number (with at least one digit) 539370c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (?P<int>[0-9]*) # having a (possibly empty) integer part 539470c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (\.(?P<frac>[0-9]*))? # followed by an optional fractional part 539570c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (E(?P<exp>[-+]?[0-9]+))? # followed by an optional exponent, or... 53967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 539770c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson Inf(inity)? # ...an infinity, or... 539872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista | 539970c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (?P<signal>s)? # ...an (optionally signaling) 540070c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson NaN # NaN 540170c3289085d08d97edbfaa626efc2d2c2ac21859Mark Dickinson (?P<diag>[0-9]*) # with (possibly empty) diagnostic info. 54027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 54037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 540459bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson \Z 540572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista""", re.VERBOSE | re.IGNORECASE).match 54067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 54072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_all_zeros = re.compile('0*$').match 54082ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_exact_half = re.compile('50*$').match 54091ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54101ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson##### PEP3101 support functions ############################################## 54111ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# The functions parse_format_specifier and format_align have little to do 54121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# with the Decimal class, and could potentially be reused for other pure 54131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# Python numeric classes that want to implement __format__ 54141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 54151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# A format specifier for Decimal looks like: 54161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 54171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# [[fill]align][sign][0][minimumwidth][.precision][type] 54181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 54191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson_parse_format_specifier_regex = re.compile(r"""\A 54211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?: 54221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson (?P<fill>.)? 54231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson (?P<align>[<>=^]) 54241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson)? 54251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<sign>[-+ ])? 54261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<zeropad>0)? 54271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<minimumwidth>(?!0)\d+)? 54281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?:\.(?P<precision>0|(?!0)\d+))? 54291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<type>[eEfFgG%])? 54301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson\Z 54311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson""", re.VERBOSE) 54321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 54347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 54351ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinsondef _parse_format_specifier(format_spec): 54361ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Parse and validate a format specifier. 54371ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54381ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Turns a standard numeric format specifier into a dict, with the 54391ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson following entries: 54401ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54411ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill: fill character to pad field to minimum width 54421ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align: alignment type, either '<', '>', '=' or '^' 54431ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign: either '+', '-' or ' ' 54441ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson minimumwidth: nonnegative integer giving minimum width 54451ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson precision: nonnegative integer giving precision, or None 54461ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson type: one of the characters 'eEfFgG%', or None 54471ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson unicode: either True or False (always True for Python 3.x) 54481ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54491ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 54501ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson m = _parse_format_specifier_regex.match(format_spec) 54511ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if m is None: 54521ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Invalid format specifier: " + format_spec) 54531ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54541ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # get the dictionary 54551ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict = m.groupdict() 54561ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54571ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # defaults for fill and alignment 54581ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = format_dict['fill'] 54591ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = format_dict['align'] 54601ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict.pop('zeropad') is not None: 54611ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # in the face of conflict, refuse the temptation to guess 54621ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if fill is not None and fill != '0': 54631ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Fill character conflicts with '0'" 54641ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson " in format specifier: " + format_spec) 54651ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if align is not None and align != '=': 54661ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Alignment conflicts with '0' in " 54671ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson "format specifier: " + format_spec) 54681ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = '0' 54691ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = '=' 54701ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['fill'] = fill or ' ' 54711ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['align'] = align or '<' 54721ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54731ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['sign'] is None: 54741ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['sign'] = '-' 54751ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54761ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # turn minimumwidth and precision entries into integers. 54771ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # minimumwidth defaults to 0; precision remains None if not given 54781ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') 54791ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['precision'] is not None: 54801ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['precision'] = int(format_dict['precision']) 54811ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54821ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # if format type is 'g' or 'G' then a precision of 0 makes little 54831ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # sense; convert it to 1. Same if format type is unspecified. 54841ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['precision'] == 0: 54851ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['type'] in 'gG' or format_dict['type'] is None: 54861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['precision'] = 1 54871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54881ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # record whether return type should be str or unicode 54891ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['unicode'] = isinstance(format_spec, unicode) 54901ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return format_dict 54921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinsondef _format_align(body, spec_dict): 54941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Given an unpadded, non-aligned numeric string, add padding and 54951ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson aligment to conform with the given format specifier dictionary (as 54961ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson output from parse_format_specifier). 54971ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54981ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson It's assumed that if body is negative then it starts with '-'. 54991ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Any leading sign ('-' or '+') is stripped from the body before 55001ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson applying the alignment and padding rules, and replaced in the 55011ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson appropriate position. 55021ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55031ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 55041ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out the sign; we only examine the first character, so if 55051ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # body has leading whitespace the results may be surprising. 55061ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if len(body) > 0 and body[0] in '-+': 55071ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = body[0] 55081ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson body = body[1:] 55091ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 55101ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = '' 55111ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if sign != '-': 55131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec_dict['sign'] in ' +': 55141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = spec_dict['sign'] 55151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 55161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = '' 55171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # how much extra space do we have to play with? 55191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson minimumwidth = spec_dict['minimumwidth'] 55201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = spec_dict['fill'] 55211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson padding = fill*(max(minimumwidth - (len(sign+body)), 0)) 55221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = spec_dict['align'] 55241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if align == '<': 55251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = padding + sign + body 55261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif align == '>': 55271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = sign + body + padding 55281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif align == '=': 55291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = sign + padding + body 55301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: #align == '^' 55311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson half = len(padding)//2 55321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = padding[:half] + sign + body + padding[half:] 55331ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55341ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # make sure that result is unicode if necessary 55351ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec_dict['unicode']: 55361ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = unicode(result) 55371ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 55381ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return result 55390d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz 554072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista##### Useful Constants (internal use only) ################################ 55417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 554272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Reusable defaults 5543b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_Infinity = Decimal('Inf') 5544b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_NegativeInfinity = Decimal('-Inf') 5545c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson_NaN = Decimal('NaN') 5546b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_Zero = Decimal(0) 5547b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_One = Decimal(1) 5548b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_NegativeOne = Decimal(-1) 5549c5de0969ca2a82c66efd30bb675f03c2324a3b27Mark Dickinson 5550b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger# _SignedInfinity[sign] is infinity w/ that sign 5551b7e835b820fc7d17a02dc4cdf3b745bb993952adRaymond Hettinger_SignedInfinity = (_Infinity, _NegativeInfinity) 55527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 55567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 55577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 5558