decimal.py revision 6a123cb7827859748a0096570dfbb5ceba0e59dc
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 1387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 139097a1903035f9ee2efb1953306123f183124125dRaymond Hettingertry: 140097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger from collections import namedtuple as _namedtuple 141097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') 142097a1903035f9ee2efb1953306123f183124125dRaymond Hettingerexcept ImportError: 143097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger DecimalTuple = lambda *args: args 144097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger 14559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Rounding 1460ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1470ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1480ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1490ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1500ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1510ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1520ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo BatistaROUND_05UP = 'ROUND_05UP' 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Errors 1567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1585aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 166cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis handle -- Called when context._raise_error is called and the 167cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis trap_enabler is set. First argument is self, second is the 168cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context. More arguments can be given, those being after 169cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis the explanation in _raise_error (For example, 170cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context._raise_error(NewError, '(-x)!', self._sign) would 171cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis call NewError().handle(context, self._sign).) 172cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 18559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista representation. This may occur when the exponent of a zero result would 18659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be outside the bounds of a representation, or when a large normal 18759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista number would have an encoded exponent that cannot be represented. In 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 19959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 0 * (+-)INF 20059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista (+-)INF / (+-)INF 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of the operation after these is a quiet positive NaN, 211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista except when the cause is a signaling NaN, in which case the result is 212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista also a quiet NaN, but with the original sign, and an optional 213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista diagnostic information. 2147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 2170f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) 2180f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return ans._fix_nan(context) 2197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 22659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista syntax. The result is [0,qNaN]. 2277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 228cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis def handle(self, context, *args): 229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return NaN 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 243cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 244cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, sign, *args): 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 25259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista longer than precision). The result is [0,qNaN]. 2537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 254cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 256cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NaN 2577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 26359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the dividend is also zero. The result is [0,qNaN]. 2647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 265cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 266cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, *args): 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 27459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista were non-zero), or if an overflow or underflow condition occurs. The 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 28559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista detected during an operation. This can occur if contexts are not checked 2867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 28859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista was specified. These aspects of the context need only be checked when 28959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the values are required to be used. The result is [0,qNaN]. 2907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 291cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 30059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista coefficient), or if an overflow or underflow condition occurs. The 3017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 3047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 3057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 31259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin, before any rounding). The result in all cases is unchanged. 3137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 33059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista where sign is the sign of the intermediate result. For round-down, the 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 33259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista current precision, with the sign of the intermediate result. For 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 33459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 33659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 3380f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista """ 339cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 3407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ROUND_HALF_DOWN, ROUND_UP): 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 34772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 34872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 35272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 36259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin). That is, the result is both inexact and subnormal. 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 36559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista necessary, so that its exponent is not less than Etiny. This may result 3667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3715aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 372fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 373cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Underflow, InvalidOperation, Subnormal] 3747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3755aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3765aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context Functions ################################################## 3827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 383ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 384ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 385ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 3867e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# work for older Pythons. If threads are not part of the build, create a 387cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# mock threading object with threading.local() returning the module namespace. 3887e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger 3897e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingertry: 3907e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import threading 3917e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingerexcept ImportError: 3927e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger # Python was compiled without threads; create a mock object instead 3937e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import sys 39459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista class MockThreading(object): 3957e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger def local(self, sys=sys): 3967e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger return sys.modules[__name__] 3977e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger threading = MockThreading() 3987e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger del sys, MockThreading 399ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 400ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 404ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 40559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # To fix reloading, force it to create a new context 40659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Old contexts have different exceptions in their dicts, making problems. 407ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4139fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 41461992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 416ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 417ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4349fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4359fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 436ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 437ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 441ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 445ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 446ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 450ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 451ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 452ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 453ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4549fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 45561992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 456ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 457ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 458cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis del threading, local # Don't contaminate the namespace 4597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4608b6999b4c5fab174090be263ba90f193bdede141Nick Coghlandef localcontext(ctx=None): 4618b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Return a context manager for a copy of the supplied context 4628b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4638b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan Uses a copy of the current context if no context is specified 4648b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan The returned context manager creates a local decimal context 4658b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan in a with statement: 4668b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4678b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext() as ctx: 4688b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ctx.prec += 2 4698b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4708b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses a precision 2 greater than normal 47159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal precision 4728b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4738b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4748b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext(ExtendedContext): 4758b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4768b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses the Extended Context from the 4778b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # General Decimal Arithmetic Specification 47859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal context 4798b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4808b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 481681d86743c21773bb00508dbacb05ed9012388d8Neal Norwitz # The string below can't be included in the docstring until Python 2.6 4828b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # as the doctest module doesn't understand __future__ statements 4838b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 4848b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> from __future__ import with_statement 4858b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4868b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4878b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(): 4888b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... ctx = getcontext() 489495df4716fce4156c1eb110f9342297164eecbb6Raymond Hettinger ... ctx.prec += 2 4908b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print ctx.prec 4918b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4928b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 30 4938b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(ExtendedContext): 4948b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print getcontext().prec 4958b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4968b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 9 4978b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4988b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4998b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 500ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan if ctx is None: ctx = getcontext() 501ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan return _ContextManager(ctx) 5028b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 5037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Decimal class ####################################################### 5057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 5077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 5087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 509636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger __slots__ = ('_exp','_int','_sign', '_is_special') 510636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Generally, the value of the Decimal instance is given by 511636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (-1)**_sign * _int * 10**_exp 512636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special values are signified by _is_special == True 5137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 514dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger # We're immutable, so use __new__ not __init__ 515636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger def __new__(cls, value="0", context=None): 5167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 5177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 519abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 52059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) 521abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 5227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 523abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('314') 5247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 525abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('314') 52659bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay 527abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.14') 5287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Note that the coefficient, self._int, is actually stored as 53172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # a string rather than as a tuple of digits. This speeds up 53272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # the "digits to integer" and "integer to digits" conversions 53372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # that are used in almost every arithmetic operation on 53472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Decimals. This is an internal detail: the as_tuple function 53572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # and the Decimal constructor still deal with tuples of 53672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # digits. 53772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 538636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self = object.__new__(cls) 539636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5400d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From a string 5410d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # REs insist on real strings, so we can too. 5420d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, basestring): 54359bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson m = _parser(value.strip()) 5440d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m is None: 5450d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if context is None: 5460d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista context = getcontext() 5470d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return context._raise_error(ConversionSyntax, 5480d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista "Invalid literal for Decimal: %r" % value) 549636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5500d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('sign') == "-": 5510d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 1 5520d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5530d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 0 5540d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista intpart = m.group('int') 5550d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if intpart is not None: 5560d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # finite number 5570d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista fracpart = m.group('frac') 5580d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista exp = int(m.group('exp') or '0') 5590d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if fracpart is not None: 5600d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = (intpart+fracpart).lstrip('0') or '0' 5610d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp - len(fracpart) 5620d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5630d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = intpart.lstrip('0') or '0' 5640d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp 5650d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5660d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5670d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista diag = m.group('diag') 5680d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if diag is not None: 5690d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # NaN 5700d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = diag.lstrip('0') 5710d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('signal'): 5720d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'N' 5730d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5740d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'n' 5750d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5760d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # infinity 5770d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = '0' 5780d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'F' 5790d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = True 580636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 581636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 582636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From an integer 5837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 584636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if value >= 0: 585636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 0 586636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 587636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 1 588636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = 0 58972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = str(abs(value)) 5900d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5910d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 5920d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 5930d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From another decimal 5940d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, Decimal): 5950d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = value._exp 5960d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value._sign 5970d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = value._int 5980d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = value._is_special 5990d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 6000d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 6010d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From an internal working value 6020d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, _WorkRep): 6030d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value.sign 6040d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = str(value.int) 6050d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = int(value.exp) 6060d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 607636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 608636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 609636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 610636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, (list,tuple)): 611636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if len(value) != 3: 6129b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError('Invalid tuple size in creation of Decimal ' 6139b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'from list or tuple. The list or tuple ' 6149b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'should have exactly three elements.') 6159b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process sign. The isinstance test rejects floats 6169b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if not (isinstance(value[0], (int, long)) and value[0] in (0,1)): 6179b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("Invalid sign. The first value in the tuple " 6189b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "should be an integer; either 0 for a " 6199b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "positive number or 1 for a negative number.") 620636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = value[0] 6219b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] == 'F': 6229b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # infinity: value[1] is ignored 62372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = '0' 624636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = value[2] 625636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 626636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 6279b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process and validate the digits in value[1] 6289b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits = [] 6299b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista for digit in value[1]: 6309b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if isinstance(digit, (int, long)) and 0 <= digit <= 9: 6319b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # skip leading zeros 6329b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if digits or digit != 0: 6339b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits.append(digit) 6349b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6359b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The second value in the tuple must " 6369b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be composed of integers in the range " 6379b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "0 through 9.") 6389b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] in ('n', 'N'): 6399b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # NaN: digits form the diagnostic 64072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits)) 6419b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6429b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = True 6439b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista elif isinstance(value[2], (int, long)): 6449b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # finite number: digits give the coefficient 64572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits or [0])) 6469b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6479b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = False 6489b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6499b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The third value in the tuple must " 6509b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be an integer, or one of the " 6519b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "strings 'F', 'n', 'N'.") 652636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 653636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 654636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, float): 655636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 656636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger "First convert the float to a string") 6577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 658636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert %r to Decimal" % value) 6597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 6617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 6640f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista 1 if NaN 6657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 6667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 667636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 668636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = self._exp 669636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp == 'n': 670636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 1 671636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif exp == 'N': 672636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 2 6737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 6767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 6777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 6797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 6807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 6817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 6837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 6847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _check_nans(self, other=None, context=None): 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 6927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 6937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 6967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 698636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_is_nan = self._isnan() 699636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other is None: 700636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = False 701636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 702636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = other._isnan() 703636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 704636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan or other_is_nan: 705636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 706636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 707636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 708636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan == 2: 709636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 7100f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista self) 711636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other_is_nan == 2: 712636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 7130f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista other) 714636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan: 715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 716636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other._fix_nan(context) 7187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7202fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def _compare_check_nans(self, other, context): 7212fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """Version of _check_nans used for the signaling comparisons 7222fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson compare_signal, __le__, __lt__, __ge__, __gt__. 7232fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7242fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Signal InvalidOperation if either self or other is a (quiet 7252fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson or signaling) NaN. Signaling NaNs take precedence over quiet 7262fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson NaNs. 7272fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7282fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Return 0 if neither operand is a NaN. 7292fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7302fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """ 7312fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if context is None: 7322fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson context = getcontext() 7332fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7342fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self._is_special or other._is_special: 7352fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_snan(): 7362fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7372fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving sNaN', 7382fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson self) 7392fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif other.is_snan(): 7402fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7412fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving sNaN', 7422fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other) 7432fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif self.is_qnan(): 7442fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7452fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving NaN', 7462fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson self) 7472fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson elif other.is_qnan(): 7482fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return context._raise_error(InvalidOperation, 7492fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 'comparison involving NaN', 7502fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other) 7512fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return 0 7522fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 7541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is nonzero; otherwise return False. 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7561a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista NaNs and infinities are considered nonzero. 7577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 75872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._is_special or self._int != '0' 7597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7602fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def _cmp(self, other): 7612fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson """Compare the two non-NaN decimal instances self and other. 7627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7632fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson Returns -1 if self < other, 0 if self == other and 1 7642fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self > other. This routine is for internal use only.""" 765636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 7662fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self._is_special or other._is_special: 767636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return cmp(self._isinfinity(), other._isinfinity()) 7687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for zeros; note that cmp(0, -0) should return 0 770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 0 773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return -((-1)**other._sign) 775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return (-1)**self._sign 7777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 77859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If different signs, neg one is less 7797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 7807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 784636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_adjusted = self.adjusted() 785636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_adjusted = other.adjusted() 786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted == other_adjusted: 78772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - other._exp) 78872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista other_padded = other._int + '0'*(other._exp - self._exp) 789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return cmp(self_padded, other_padded) * (-1)**self._sign 790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self_adjusted > other_adjusted: 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # self_adjusted < other_adjusted 7937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 7947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7952fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # Note: The Decimal standard doesn't cover rich comparisons for 7962fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # Decimals. In particular, the specification is silent on the 7972fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # subject of what should happen for a comparison involving a NaN. 7982fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # We take the following approach: 7992fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # 8002fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # == comparisons involving a NaN always return False 8012fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # != comparisons involving a NaN always return True 8022fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # <, >, <= and >= comparisons involving a (quiet or signaling) 8032fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # NaN signal InvalidOperation, and return False if the 8043a94ee05f77d0200cfb7988d02f3fdf292932a94Mark Dickinson # InvalidOperation is not trapped. 8052fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # 8062fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # This behavior is designed to conform as closely as possible to 8072fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson # that specified by IEEE 754. 8082fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8090aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 8102fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8112fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8122fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8132fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_nan() or other.is_nan(): 8142fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8152fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) == 0 8160aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 8170aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 8182fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8192fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8202fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8212fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if self.is_nan() or other.is_nan(): 8222fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return True 8232fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) != 0 8242fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8252fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __lt__(self, other, context=None): 8262fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8272fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8282fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8292fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8302fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8312fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8322fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) < 0 8332fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8342fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __le__(self, other, context=None): 8352fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8362fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8372fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8382fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8392fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8402fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8412fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) <= 0 8422fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8432fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __gt__(self, other, context=None): 8442fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8452fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8462fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8472fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8482fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8492fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8502fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) > 0 8512fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson 8522fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson def __ge__(self, other, context=None): 8532fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other) 8542fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if other is NotImplemented: 8552fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return other 8562fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 8572fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 8582fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return False 8592fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return self._cmp(other) >= 0 8600aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 8617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 8627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 8637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 8657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 8667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 8677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 8687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 8697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 8717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 87259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Compare(NaN, NaN) = NaN 873636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if (self._is_special or other and other._is_special): 874636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 875636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 876636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 8777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8782fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return Decimal(self._cmp(other)) 8797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 8817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 8827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 88352b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # 88452b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # The hash of a nonspecial noninteger Decimal must depend only 88552b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # on the value of that Decimal, and not on its representation. 886abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger # For example: hash(Decimal('100E-1')) == hash(Decimal('10')). 887bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._is_special: 888bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._isnan(): 889bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger raise TypeError('Cannot hash a NaN value.') 890bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger return hash(str(self)) 8918c202440699cef19602acc24822366d0d7c32083Facundo Batista if not self: 8928c202440699cef19602acc24822366d0d7c32083Facundo Batista return 0 8938c202440699cef19602acc24822366d0d7c32083Facundo Batista if self._isinteger(): 8948c202440699cef19602acc24822366d0d7c32083Facundo Batista op = _WorkRep(self.to_integral_value()) 8958c202440699cef19602acc24822366d0d7c32083Facundo Batista # to make computation feasible for Decimals with large 8968c202440699cef19602acc24822366d0d7c32083Facundo Batista # exponent, we use the fact that hash(n) == hash(m) for 8978c202440699cef19602acc24822366d0d7c32083Facundo Batista # any two nonzero integers n and m such that (i) n and m 8988c202440699cef19602acc24822366d0d7c32083Facundo Batista # have the same sign, and (ii) n is congruent to m modulo 8998c202440699cef19602acc24822366d0d7c32083Facundo Batista # 2**64-1. So we can replace hash((-1)**s*c*10**e) with 9008c202440699cef19602acc24822366d0d7c32083Facundo Batista # hash((-1)**s*c*pow(10, e, 2**64-1). 9018c202440699cef19602acc24822366d0d7c32083Facundo Batista return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) 90252b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # The value of a nonzero nonspecial Decimal instance is 90352b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # faithfully represented by the triple consisting of its sign, 90452b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # its adjusted exponent, and its coefficient with trailing 90552b25795c02442fc40f8932d05e5d728266339a4Facundo Batista # zeros removed. 90652b25795c02442fc40f8932d05e5d728266339a4Facundo Batista return hash((self._sign, 90752b25795c02442fc40f8932d05e5d728266339a4Facundo Batista self._exp+len(self._int), 90852b25795c02442fc40f8932d05e5d728266339a4Facundo Batista self._int.rstrip('0'))) 9097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 9117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 9127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 915097a1903035f9ee2efb1953306123f183124125dRaymond Hettinger return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp) 9167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 9187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 9197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 920abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger return "Decimal('%s')" % str(self) 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __str__(self, eng=False, context=None): 9237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 9247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 9267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 9277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 92862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista sign = ['', '-'][self._sign] 929e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._is_special: 93062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp == 'F': 93162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'Infinity' 93262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._exp == 'n': 93362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'NaN' + self._int 93462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: # self._exp == 'N' 93562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'sNaN' + self._int 93662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 93762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # number of digits of self._int to left of decimal point 93862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista leftdigits = self._exp + len(self._int) 93962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 94062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # dotplace is number of digits of self._int to the left of the 94162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # decimal point in the mantissa of the output string (that is, 94262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # after adjusting the exponent) 94362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp <= 0 and leftdigits > -6: 94462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # no exponent required 94562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = leftdigits 94662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif not eng: 94762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # usual scientific notation: 1 digit on left of the point 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 94962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._int == '0': 95062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, zero 95162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits + 1) % 3 - 1 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 95362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, nonzero 95462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits - 1) % 3 + 1 95562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 95662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if dotplace <= 0: 95762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = '0' 95862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + '0'*(-dotplace) + self._int 95962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif dotplace >= len(self._int): 96062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int+'0'*(dotplace-len(self._int)) 96162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '' 96262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 96362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int[:dotplace] 96462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + self._int[dotplace:] 96562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if leftdigits == dotplace: 96662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = '' 96762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 96862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if context is None: 96962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista context = getcontext() 97062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) 97162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 97262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + intpart + fracpart + exp 9737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 9757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 9767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 9787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 9797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__str__(eng=True, context=context) 9837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 9857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 9867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 9887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 989636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 990636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 991636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 992636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 9960f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = self.copy_abs() 9977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_negate() 999636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1000636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1001636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1002e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 10037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 10057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 10087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1009636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1010636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1011636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1012636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 10160f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista ans = self.copy_abs() 1017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 10197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1020636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1021636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1022e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1024e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista def __abs__(self, round=True, context=None): 10257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 10267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1027e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista If the keyword argument 'round' is false, do not round. The 1028e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista expression self.__abs__(round=False) is equivalent to 1029e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.copy_abs(). 10307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1031e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if not round: 1032e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return self.copy_abs() 1033e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista 1034636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1035636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1036636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1037636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 10407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 10417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 10437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 10487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 10507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1051636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1052267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1053267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1054636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1058636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1059636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1060636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1061636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1063636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 106459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both INF, same sign => same as both, opposite => error. 1065636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 1066636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 1067636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 1068636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 106959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return Decimal(other) # Can't both be infinity here 10707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 10737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 107459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the answer is 0, the sign should be negative, in this case. 10757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 10767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 10787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 10807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 108172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, '0', exp) 1082e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 1083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 10847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 108599b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, other._exp - context.prec-1) 1086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other._rescale(exp, context.rounding) 1087e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 10887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 109099b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, self._exp - context.prec-1) 1091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp, context.rounding) 1092e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 10937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 10967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 1097e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista op1, op2 = _normalize(op1, op2, context.prec) 10987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 11007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 11017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 110217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int == op2.int: 110372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(negativezero, '0', exp) 1104e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 1105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 110617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int < op2.int: 11077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 110859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # OK, now abs(op1) > abs(op2) 110917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.sign == 1: 111017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 1 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 11127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 111317931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 111459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # So we know the sign, and op1 > 0. 111517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif op1.sign == 1: 11167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 111717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger op1.sign, op2.sign = (0, 0) 111817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 111917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 112059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Now, op1 > abs(op2) > 0 11217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 112217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op2.sign == 0: 1123636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int + op2.int 11247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1125636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int - op2.int 11267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 1129e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 11337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 1135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self - other""" 1136636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1137267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1138267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1140636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1141636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context=context) 1142636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1143636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 11447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self - other is computed as self + other.copy_negate() 1146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__add__(other.copy_negate(), context=context) 11477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 1149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return other - self""" 1150636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1151267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1152267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 11537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__sub__(self, context=context) 11557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 11577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 11587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 11607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1161636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1162267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1163267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1164636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 11657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1168d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 11697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1170636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1171636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1172636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1173636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1174636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1175636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1176636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1177636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 1178636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 1179636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1180636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1181636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1182636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 1183636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 11867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 11887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 118972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, '0', resultexp) 1190e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista # Fixing in case the exponent is out of bounds 1191e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 119572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int == '1': 119672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, other._int, resultexp) 1197e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 119972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if other._int == '1': 120072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, self._int, resultexp) 1201e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1204636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1 = _WorkRep(self) 1205636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2 = _WorkRep(other) 1206636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 120772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) 1208e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 12097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 12127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 1215636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1216267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1217cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NotImplemented 1218636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 12197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 12207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1222636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sign = self._sign ^ other._sign 1223636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1224636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1225636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1226636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 12277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 12287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1229636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and other._isinfinity(): 12307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 12317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 1233636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[sign] 1234636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1235636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1236636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 123772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '0', context.Etiny()) 1238636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1239636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special cases for zeroes 1240636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1241cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1242cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 / 0') 1243636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 12447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1245cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1246cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp 1247cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff = 0 1248cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1249cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # OK, so neither = 0, INF or NaN 1250cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista shift = len(other._int) - len(self._int) + context.prec + 1 1251cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp - shift 1252cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1253cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1254cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if shift >= 0: 1255cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int * 10**shift, op2.int) 1256cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1257cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int, op2.int * 10**-shift) 1258cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if remainder: 1259cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is not exact; adjust to ensure correct rounding 1260cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if coeff % 5 == 0: 1261cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff += 1 1262cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1263cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is exact; get as close to ideal exponent as possible 1264cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp - other._exp 1265cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista while exp < ideal_exp and coeff % 10 == 0: 1266cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff //= 10 1267cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp += 1 12687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 126972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(coeff), exp) 1270cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans._fix(context) 12717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1272cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista __truediv__ = __div__ 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1274cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def _divide(self, other, context): 1275cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """Return (self // other, self % other), to context.prec precision. 12767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1277cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Assumes that neither self nor other is a NaN, that self is not 1278cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista infinite and that other is nonzero. 1279cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """ 1280cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1281cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1282cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp 1283cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1284cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = min(self._exp, other._exp) 12857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1286cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista expdiff = self.adjusted() - other.adjusted() 1287cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self or other._isinfinity() or expdiff <= -2: 128872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, '0', 0), 1289cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._rescale(ideal_exp, context.rounding)) 1290cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if expdiff <= context.prec: 1291cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1292cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1293cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if op1.exp >= op2.exp: 1294cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 1295cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1296cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1297cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista q, r = divmod(op1.int, op2.int) 1298cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if q < 10**context.prec: 129972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, str(q), 0), 130072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista _dec_from_triple(self._sign, str(r), ideal_exp)) 13017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1302cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # Here the quotient is too large to be representable 1303cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionImpossible, 1304cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 'quotient too large in //, % or divmod') 1305cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 13067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 13087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 1309636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1310267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1311267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 13137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 13147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 13167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1317cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Return (self // other, self % other) 13187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1319cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1320cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1321cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1322cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1323cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1324cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1325cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1326cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1327cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1328cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (ans, ans) 1329cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1330cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1331cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1332cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1333cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') 1334cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1335cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1336cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (Infsign[sign], 1337cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'INF % x')) 1338cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1339cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1340cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1341cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') 1342cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1343cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1344cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (context._raise_error(DivisionByZero, 'x // 0', sign), 1345cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'x % 0')) 1346cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1347cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista quotient, remainder = self._divide(other, context) 1348e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1349cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return quotient, remainder 13507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 13527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 1353636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1354267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1355267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 13577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 13597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 13617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1362636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1363267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1364267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1366cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1367cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 13687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1369cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1370cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1371cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 13727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1373cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1374cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF % x') 1375cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista elif not other: 1376cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1377cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'x % 0') 1378cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1379cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 % 0') 1380cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1381cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = self._divide(other, context)[1] 1382e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1383cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return remainder 13847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 13867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 1387636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1388267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1389267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 13917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1396636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1397636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 13987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 14007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 14047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self == +/-infinity -> InvalidOperation 1406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 1407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(infinity, x)') 14097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other == 0 -> either InvalidOperation or DivisionUndefined 1411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 1413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(x, 0)') 1415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(DivisionUndefined, 1417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(0, 0)') 14187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other = +/-infinity -> remainder = self 1420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 1421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 1422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self = 0 -> remainder = self, with ideal exponent 1425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = min(self._exp, other._exp) 1426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 142772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', ideal_exponent) 1428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # catch most cases of large or small quotient 1431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = self.adjusted() - other.adjusted() 1432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff >= context.prec + 1: 1433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff >= prec+1 => abs(self/other) > 10**prec 1434cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff <= -2: 1436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff <= -2 => abs(self/other) < 0.1 1437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(ideal_exponent, context.rounding) 1438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust both arguments to have the same exponent, then divide 1441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1 = _WorkRep(self) 1442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2 = _WorkRep(other) 1443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp >= op2.exp: 1444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 14457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1447353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(op1.int, op2.int) 1448353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # remainder is r*10**ideal_exponent; other is +/-op2.int * 1449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**ideal_exponent. Apply correction to ensure that 1450353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # abs(remainder) <= abs(other)/2 1451353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if 2*r + (q&1) > op2.int: 1452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r -= op2.int 1453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q += 1 1454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if q >= 10**context.prec: 1456cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has same sign as self unless r is negative 1459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if r < 0: 1461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 1-sign 1462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r = -r 14637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 146472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(r), ideal_exponent) 1465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 14667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 14687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 1469cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1470cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1471cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1472cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1473cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1474cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1475cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1476cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1477cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1478cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 1479cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1480cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1481cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1482cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF // INF') 1483cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1484cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return Infsign[self._sign ^ other._sign] 1485cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1486cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1487cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1488cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'x // 0', 1489cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._sign ^ other._sign) 1490cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1491cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 // 0') 1492cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1493cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return self._divide(other, context)[0] 14947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 1497636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1498267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1499267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 15007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 15017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 15037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 15047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 15057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 150746b0802ccd9a9c47b27a285526fbb2a8bee5b8cbBrett Cannon """Converts self to an int, truncating if necessary.""" 1508636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1509636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan(): 1510636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1511636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidContext) 1512636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self._isinfinity(): 151359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise OverflowError("Cannot convert infinity to long") 1514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = (-1)**self._sign 15157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 151672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int)*10**self._exp 1517605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger else: 151872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int[:self._exp] or '0') 15197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15205a05364049a7b0c3eeee94fb7b77e6b41036b3aeRaymond Hettinger __trunc__ = __int__ 15215a05364049a7b0c3eeee94fb7b77e6b41036b3aeRaymond Hettinger 1522116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger @property 1523116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def real(self): 1524116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return self 1525116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1526116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger @property 1527116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def imag(self): 1528116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return Decimal(0) 1529116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1530116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def conjugate(self): 1531116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return self 1532116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 1533116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger def __complex__(self): 1534116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger return complex(float(self)) 1535116f72fa5ceb864efcc47da2f8c437fd29c7e8b3Raymond Hettinger 15367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 15377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 15387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 15407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 15417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 15427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fix_nan(self, context): 1544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Decapitate the payload of a NaN to fit the context""" 1545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista payload = self._int 1546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # maximum length of payload is precision if _clamp=0, 1548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision-1 if _clamp=1. 1549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista max_payload_len = context.prec - context._clamp 1550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(payload) > max_payload_len: 155172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista payload = payload[len(payload)-max_payload_len:].lstrip('0') 155272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, payload, self._exp, True) 15536c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 1554353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1555dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _fix(self, context): 15567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 15577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 15597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 15617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 15627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 15637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1564636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 1566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan(): 1567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decapitate payload if necessary 1568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 1569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is +/-Infinity; return unaltered 15716c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 15727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if self is zero then exponent should be between Etiny and 1574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. 1575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 1576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etop = context.Etop() 15777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 1578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, Etop][context._clamp] 1579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_exp = min(max(self._exp, Etiny), exp_max) 1580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_exp != self._exp: 1581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 158272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', new_exp) 15837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15846c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp_min is the smallest allowable exponent of the result, 1587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equal to max(self.adjusted()-context.prec+1, Etiny) 1588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = len(self._int) + self._exp - context.prec 1589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp_min > Etop: 1590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow: exp_min > Etop iff self.adjusted() > Emax 1591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1592353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 1593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(Overflow, 'above Emax', self._sign) 1594353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_subnormal = exp_min < Etiny 1595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1596353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 1597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = Etiny 15987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round if self has too many digits 1600353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < exp_min: 16017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16022ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = len(self._int) + self._exp - exp_min 16032ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if digits < 0: 16042ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista self = _dec_from_triple(self._sign, '1', exp_min-1) 16052ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = 0 16062ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista this_function = getattr(self, self._pick_rounding_function[context.rounding]) 16072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 16082ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 16092ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 16102ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 16112ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista ans = _dec_from_triple(self._sign, coeff, exp_min) 16122ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista 16132ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed: 1614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 1617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 1618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Clamped on underflow to 0 1619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 1620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif len(ans._int) == context.prec+1: 1621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we get here only if rescaling rounds the 1622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # cofficient up to exactly 10**context.prec 1623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp < Etop: 162472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, 162572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._int[:-1], ans._exp+1) 1626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inexact and Rounded have already been raised 1628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = context._raise_error(Overflow, 'above Emax', 1629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self._sign) 16307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fold down if _clamp == 1 and self has too few digits 1633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._clamp == 1 and self._exp > Etop: 1634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 163572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - Etop) 163672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, self_padded, Etop) 16377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # here self was representable to begin with; return unchanged 16396c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 16407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 16427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for each of the rounding functions below: 1644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is a finite, nonzero Decimal 1645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # prec is an integer satisfying 0 <= prec < len(self._int) 16462ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 16472ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # each function returns either -1, 0, or 1, as follows: 16482ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 1 indicates that self should be rounded up (away from zero) 16492ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 0 indicates that self should be truncated, and that all the 16502ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # digits to be truncated are zeros (so the value is unchanged) 16512ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # -1 indicates that there are nonzero digits to be truncated 16527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_down(self, prec): 1654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Also known as round-towards-0, truncate.""" 16552ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _all_zeros(self._int, prec): 16562ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 16572ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 16582ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 16597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_up(self, prec): 1661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds away from 0.""" 16622ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 16637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_up(self, prec): 1665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds 5 up (away from 0)""" 166672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[prec] in '56789': 16672ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 1 16682ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista elif _all_zeros(self._int, prec): 16692ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 1670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 16712ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 16727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_down(self, prec): 16747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 16752ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec): 16762ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 16772ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 16782ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 16797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_even(self, prec): 1681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round 5 to even, rest to nearest.""" 16822ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec) and \ 16832ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista (prec == 0 or self._int[prec-1] in '02468'): 16842ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 1685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 16862ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 16877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_ceiling(self, prec): 16897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 16907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 1691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16932ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 16947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_floor(self, prec): 16967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 16977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 1698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 17002ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 17017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_05up(self, prec): 1703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round down unless digit prec-1 is 0 or 5.""" 17042ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if prec and self._int[prec-1] not in '05': 1705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 17062ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 17072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 1708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, other, third, context=None): 1710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Fused multiply-add. 17117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Returns self*other+third with no rounding of the intermediate 1713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista product self*other. 1714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self and other are multiplied together, with no rounding of 1716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the result. The third operand is then added to the result, 1717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista and a single final rounding is performed. 17187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 17217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 172258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # compute product; raise InvalidOperation if either operand is 172358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # a signaling NaN or if the product is zero times infinity. 172458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._is_special or other._is_special: 172558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if context is None: 172658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista context = getcontext() 172758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'N': 17280f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return context._raise_error(InvalidOperation, 'sNaN', self) 172958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if other._exp == 'N': 17300f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista return context._raise_error(InvalidOperation, 'sNaN', other) 173158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'n': 173258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = self 173358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'n': 173458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = other 173558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif self._exp == 'F': 173658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not other: 173758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 173858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista 'INF * 0 in fma') 173958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = Infsign[self._sign ^ other._sign] 174058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'F': 174158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not self: 174258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 174358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista '0 * INF in fma') 174458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = Infsign[self._sign ^ other._sign] 174558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista else: 174658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = _dec_from_triple(self._sign ^ other._sign, 174758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista str(int(self._int) * int(other._int)), 174858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista self._exp + other._exp) 17497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 175058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista third = _convert_other(third, raiseit=True) 175158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return product.__add__(third, context) 17527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_modulo(self, other, modulo, context=None): 1754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Three argument version of __pow__""" 17557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if can't convert other and modulo to Decimal, raise 1757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # TypeError; there's no point returning NotImplemented (no 1758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equivalent of __rpow__ for three argument pow) 1759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 1760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = _convert_other(modulo, raiseit=True) 17617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 17647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # deal with NaNs: if there are any sNaNs then first one wins, 1766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (i.e. behaviour for NaNs is identical to that of fma) 1767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 1768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 1769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo_is_nan = modulo._isnan() 1770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan or other_is_nan or modulo_is_nan: 1771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 1772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 17730f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista self) 1774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 1775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 17760f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista other) 1777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo_is_nan == 2: 1778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 17790f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista modulo) 1780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 17816c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 1782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 17836c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 17846c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return modulo._fix_nan(context) 1785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check inputs: we apply same restrictions as Python's pow() 1787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (self._isinteger() and 1788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other._isinteger() and 1789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo._isinteger()): 1790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument not allowed ' 1792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'unless all arguments are integers') 1793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other < 0: 1794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 2nd argument cannot be ' 1796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'negative when 3rd argument specified') 1797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not modulo: 1798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument cannot be 0') 1800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # additional restriction for decimal: the modulus must be less 1802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # than 10**prec in absolute value 1803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo.adjusted() >= context.prec: 1804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'insufficient precision: pow() 3rd ' 1806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'argument must not have more than ' 1807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'precision digits') 1808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # define 0**0 == NaN, for consistency with two-argument pow 1810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (even though it hurts!) 1811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other and not self: 1812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'at least one of pow() 1st argument ' 1814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'and 2nd argument must be nonzero ;' 1815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0**0 is not defined') 1816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute sign of result 1818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._iseven(): 1819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 0 1820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # convert modulo to a Python integer, and self and other to 1824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal integers (i.e. force their exponents to be >= 0) 1825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = abs(int(modulo)) 1826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = _WorkRep(self.to_integral_value()) 1827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = _WorkRep(other.to_integral_value()) 1828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute result using integer pow() 1830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo 1831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(exponent.exp): 1832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, 10, modulo) 1833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, exponent.int, modulo) 1834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 183572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, str(base), 0) 1836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_exact(self, other, p): 1838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Attempt to compute self**other exactly. 1839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given Decimals self and other and an integer p, attempt to 1841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista compute an exact result for the power self**other, with p 1842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision. Return None if self**other is not 1843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exactly representable in p digits. 1844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that elimination of special cases has already been 1846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista performed: self and other must both be nonspecial; self must 1847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista be positive and not numerically equal to 1; other must be 1848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista nonzero. For efficiency, other._exp should not be too large, 1849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista so that 10**abs(other._exp) is a feasible calculation.""" 1850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # In the comments below, we write x for the value of self and 1852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # y for the value of other. Write x = xc*10**xe and y = 1853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # yc*10**ye. 1854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The main purpose of this method is to identify the *failure* 1856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of x**y to be exactly representable with as little effort as 1857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possible. So we look for cheap and easy tests that 1858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # eliminate the possibility of x**y being exact. Only if all 1859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # these tests are passed do we go on to actually compute x**y. 1860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Here's the main idea. First normalize both x and y. We 1862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # express y as a rational m/n, with m and n relatively prime 1863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # and n>0. Then for x**y to be exactly representable (at 1864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # *any* precision), xc must be the nth power of a positive 1865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # integer and xe must be divisible by n. If m is negative 1866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then additionally xc must be a power of either 2 or 5, hence 1867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a power of 2**n or 5**n. 1868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's a limit to how small |y| can be: if y=m/n as above 1870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then: 1871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1) if xc != 1 then for the result to be representable we 1873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So 1874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= 1875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2**(1/|y|), hence xc**|y| < 2 and the result is not 1876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # representable. 1877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if 1879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # |y| < 1/|xe| then the result is not representable. 1880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Note that since x is not equal to 1, at least one of (1) and 1882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < 1883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. 1884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's also a limit to how large y can be, at least if it's 1886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive: the normalized result will have coefficient xc**y, 1887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so if it's representable then xc**y < 10**p, and y < 1888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p/log10(xc). Hence if y*log10(xc) >= p then the result is 1889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # not exactly representable. 1890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, 1892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so |y| < 1/xe and the result is not representable. 1893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| 1894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # < 1/nbits(xc). 1895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 1897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 1898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 10 == 0: 1899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 10 1900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe += 1 1901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 1903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 1904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while yc % 10 == 0: 1905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc //= 10 1906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ye += 1 1907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where xc == 1: result is 10**(xe*y), with xe*y 1909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # required to be an integer 1910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc == 1: 1911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = xe*yc*10**ye 1913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent, remainder = divmod(xe*yc, 10**-ye) 1915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = -exponent 1919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if other is a nonnegative integer, use ideal exponent 1920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(exponent-ideal_exponent, p-1) 1923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 192572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) 1926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where y is negative: xc must be either a power 1928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of 2 or a power of 5. 1929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista last_digit = xc % 10 1931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if last_digit in (2,4,6,8): 1932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # quick test for power of 2 1933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc & -xc != xc: 1934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc is a power of 2; e is its exponent 1936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)-1 1937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find e*y and xe*y; both must be integers 1938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_int = yc*10**ye 1940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_int 1941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_int 1942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*65 >= p*93: # 93/65 > log(10)/log(5) 1952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 5**e 1954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif last_digit == 5: 1956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # e >= log_5(xc) if xc is a power of 5; we have 1957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equality all the way up to xc=5**2658 1958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)*28//65 1959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, remainder = divmod(5**e, xc) 1960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 5 == 0: 1963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 5 1964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= 1 1965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_integer = yc*10**ye 1967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_integer 1968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_integer 1969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*3 >= p*10: # 10/3 > log(10)/log(2) 1978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 2**e 1980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 19827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc >= 10**p: 1984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = -e-xe 198672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str(xc), xe) 19877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now y is positive; find m and n such that y = m/n 1989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc*10**ye, 1 1991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xe != 0 and len(str(abs(yc*xe))) <= -ye: 1993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc_bits = _nbits(xc) 1995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: 1996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc, 10**(-ye) 1998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 2 == n % 2 == 0: 1999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 2 2000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 2 2001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 5 == n % 5 == 0: 2002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 5 2003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 5 2004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc*10**xe 2006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n > 1: 2007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if 1 < xc < 2**n then xc isn't an nth power 2008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and xc_bits <= n: 2009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, rem = divmod(xe, n) 2012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rem != 0: 2013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc using Newton's method 2016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = 1L << -(-_nbits(xc)//n) # initial estimate 2017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(xc, a**(n-1)) 2019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if a <= q: 2020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = (a*(n-1) + q)//n 2023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (a == q and r == 0): 2024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = a 2026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc*10**xe is the nth root of the original xc*10**xe 2028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute mth power of xc*10**xe 2029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > 2031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**p and the result is not representable. 2032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 1 and m > p*100//_log10_lb(xc): 2033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = xc**m 2035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe *= m 2036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 10**p: 2037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 2038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by this point the result *is* exactly representable 2040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust the exponent to get as close as possible to the ideal 2041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent, if necessary 2042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_xc = str(xc) 2043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 2044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 2045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(xe-ideal_exponent, p-len(str_xc)) 2046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 204872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) 2049cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __pow__(self, other, modulo=None, context=None): 2051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self ** other [ % modulo]. 20527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute self**other. 20547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (self**other) % modulo. For the 2056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 2057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 20587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 2060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - other must be nonnegative 2061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - either self or other (or both) must be nonzero 2062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and must have at most p digits, 2063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista where p is the context precision. 20647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If any of these restrictions is violated the InvalidOperation 2066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista flag is raised. 2067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(self, other, modulo) is identical to the 2069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result that would be obtained by computing (self**other) % 2070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo with unbounded precision, but is computed more 2071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista efficiently. It is always exact. 2072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo is not None: 2075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._power_modulo(other, modulo, context) 20767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2077636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 2078267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 2079267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 20807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 20837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # either argument is a NaN => result is NaN 2085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 2086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 20887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) 2090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 2091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, '0 ** 0') 2093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 20957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has sign 1 iff self._sign is 1 and other is an odd integer 2097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 0 2098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._iseven(): 2101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 1 2102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # -ve**noninteger = NaN 2104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (-0)**noninteger = 0**noninteger 2105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 2106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'x ** y with x negative and y not an integer') 2108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # negate self, without doing any unwanted rounding 210972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = self.copy_negate() 2110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity 2112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 211472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 2119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 2121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 212372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1**other = 1, but the choice of exponent and the flags 2126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # depend on the exponent of self, and on whether other is a 2127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive integer, a negative integer, or neither 2128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp = max(self._exp*max(int(other), 0), 2131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-context.prec) but evaluating int(other) directly 2132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is dangerous until we know other is small (other 2133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # could be 1e999999999) 2134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 1: 2135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = 0 2136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif other > context.prec: 2137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = context.prec 2138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = int(other) 2140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = self._exp * multiplier 2142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp < 1-context.prec: 2143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 215072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) 2151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute adjusted exponent of self 2153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adj = self.adjusted() 2154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** infinity is infinity if self > 1, 0 if self < 1 2156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** -infinity is infinity if self < 1, 0 if self > 1 2157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 2158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (other._sign == 0) == (self_adj < 0): 215972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # from here on, the result always goes through the call 2164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # to _fix at the end of this function. 2165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = None 2166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # crude test to catch cases of extreme overflow/underflow. If 2168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(self)*other >= 10**bound and bound >= len(str(Emax)) 2169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence 2170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self**other >= 10**(Emax+1), so overflow occurs. The test 2171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for underflow is similar. 2172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista bound = self._log10_exp_bound() + other.adjusted() 2173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (self_adj >= 0) == (other._sign == 0): 2174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other +ve, or self < 1 and other -ve 2175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of overflow 2176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(context.Emax)): 217772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', context.Emax+1) 2178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other -ve, or self < 1 and other +ve 2180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of underflow to 0 2181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 2182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(-Etiny)): 218372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', Etiny-1) 2184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # try for an exact result with precision +1 2186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._power_exact(other, context.prec + 1) 2188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is not None and result_sign == 1: 218972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(1, ans._int, ans._exp) 2190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # usual case: inexact result, x**y computed directly as exp(y*log(x)) 2192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 2195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 2196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 2197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 2198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 2199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc = -yc 2200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: start with precision +3, 2202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then increase precision until result is unambiguously roundable 2203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dpower(xc, xe, yc, ye, p+extra) 2206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 221072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, str(coeff), exp) 2211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the specification says that for non-integer other we need to 2213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Inexact, even when the result is actually exact. In 2214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the same way, we need to raise Underflow here if the result 2215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is subnormal. (The call to _fix will take care of raising 2216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Rounded and Subnormal, as usual.) 2217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._isinteger(): 2218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad with zeros up to length context.prec+1 if necessary 2220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) <= context.prec: 2221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = context.prec+1 - len(ans._int) 222272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, 222372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._exp-expdiff) 2224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() < context.Emin: 2225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 2226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # unlike exp, ln and log10, the power function respects the 2228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode; no need to use ROUND_HALF_EVEN here 2229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __rpow__(self, other, context=None): 2233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Swaps self/other and returns __pow__.""" 2234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other) 2235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other is NotImplemented: 2236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other 2237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__pow__(self, context=context) 2238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def normalize(self, context=None): 2240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 2241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dup = self._fix(context) 2251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dup._isinfinity(): 2252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return dup 2253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not dup: 225572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, '0', 0) 2256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, context.Etop()][context._clamp] 2257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista end = len(dup._int) 22587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 225972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista while dup._int[end-1] == '0' and exp < exp_max: 22607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 22617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 226272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, dup._int[:end], exp) 22637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2264bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista def quantize(self, exp, rounding=None, context=None, watchexp=True): 22657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 22667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 22687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2269bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista exp = _convert_other(exp, raiseit=True) 2270bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2276636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or exp._is_special: 2277636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(exp, context) 2278636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2279636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 22807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2281636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 2282636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 22836c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) # if both are inf, it is OK 2284636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 2285636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 'quantize with one INF') 2286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2287bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # if we're not watching exponents, do a simple rescale 2288bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if not watchexp: 2289bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista ans = self._rescale(exp._exp, rounding) 2290bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # raise Inexact and Rounded where appropriate 2291bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans._exp > self._exp: 2292bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Rounded) 2293bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans != self: 2294bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Inexact) 2295bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista return ans 2296bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp._exp should be between Etiny and Emax 2298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (context.Etiny() <= exp._exp <= context.Emax): 2299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'target exponent out of bounds in quantize') 2301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 230372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', exp._exp) 2304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 2305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adjusted = self.adjusted() 2307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted > context.Emax: 2308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted - exp._exp + 1 > context.prec: 2311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp._exp, rounding) 2315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() > context.Emax: 2316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) > context.prec: 2319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise appropriate flags 2323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp > self._exp: 2324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans and ans.adjusted() < context.Emin: 2328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 2329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # call to fix takes care of any necessary folddown 2331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 23337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 23351a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self and other have the same exponent; otherwise 23361a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False. 23377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista If either operand is a special value, the following rules are used: 23391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are infinities 23401a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are NaNs 23411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * otherwise, return False. 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista other = _convert_other(other, raiseit=True) 2344636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 23451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return (self.is_nan() and other.is_nan() or 23461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista self.is_infinite() and other.is_infinite()) 23477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 23487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _rescale(self, exp, rounding): 2350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rescale self so that the exponent is exp, either by padding with zeros 2351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or by truncating digits, using the given rounding mode. 2352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Specials are returned without change. This operation is 2354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista quiet: it raises no flags, and uses no information from the 2355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 23567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 2358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = rounding mode 23597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2360636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 23616c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 23627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 236372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', exp) 23647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= exp: 2366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad answer with zeros if necessary 236772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 236872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int + '0'*(self._exp - exp), exp) 23697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # too many digits; round and lose data. If self.adjusted() < 2371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp-1, replace self by 10**(exp-1) before rounding 2372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = len(self._int) + self._exp - exp 23737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 237472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = _dec_from_triple(self._sign, '1', exp-1) 2375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = 0 2376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this_function = getattr(self, self._pick_rounding_function[rounding]) 23772ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 23782ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 23792ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 23802ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 23812ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return _dec_from_triple(self._sign, coeff, exp) 23827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, rounding=None, context=None): 2384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to a nearby integer. 23857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If no rounding mode is specified, take the rounding mode from 2387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the context. This method raises the Rounded and Inexact flags 2388353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista when appropriate. 23897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista See also: to_integral_value, which does exactly the same as 2391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this method except that it doesn't raise Inexact or Rounded. 2392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2393636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2394636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2395636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2396636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 23976c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 23987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 23996c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 240172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', 0) 2402636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2403636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(0, rounding) 2408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 24107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 24117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, rounding=None, context=None): 2413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to the nearest integer, without raising inexact, rounded.""" 2414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 24226c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= 0: 24246c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._rescale(0, rounding) 24277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 2429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 2430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def sqrt(self, context=None): 2432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return the square root of self.""" 2433636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2434636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2435636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2436636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 24377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2438636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 2439636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 24407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 2442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent = self._exp // 2. sqrt(-0) = -0 244372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', self._exp // 2) 2444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 24457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2446636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2447636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2448636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 24507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 24517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # At this point self represents a positive number. Let p be 2453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the desired precision and express self in the form c*100**e 2454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with c a positive real number and e an integer, c and e 2455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # being chosen so that 100**(p-1) <= c < 100**p. Then the 2456353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) 2457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # <= sqrt(c) < 10**p, so the closest representable Decimal at 2458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision p is n*10**e where n = round_half_even(sqrt(c)), 2459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the closest integer to sqrt(c) with the even integer chosen 2460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # in the case of a tie. 2461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # To ensure correct rounding in all cases, we use the 2463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # following trick: we compute the square root to an extra 2464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # place (precision p+1 instead of precision p), rounding down. 2465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then, if the result is inexact and its last digit is 0 or 5, 2466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we increase the last digit to 1 or 6 respectively; if it's 2467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exact we leave the last digit alone. Now the final round to 2468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p places (or fewer in the case of underflow) will round 2469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly and raise the appropriate flags. 2470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # use an extra digit of precision 2472353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista prec = context.prec+1 2473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2474353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write argument in the form c*100**e where e = self._exp//2 2475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is the 'ideal' exponent, to be used if the square root is 2476353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exactly representable. l is the number of 'digits' of c in 2477353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # base 100, so that 100**(l-1) <= c < 100**l. 2478353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2479353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = op.exp >> 1 2480353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.exp & 1: 2481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int * 10 2482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = (len(self._int) >> 1) + 1 24837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int 2485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(self._int)+1 >> 1 2486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rescale so that c has exactly prec base 100 'digits' 2488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = prec-l 2489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 100**shift 2491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = True 24927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2493353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, remainder = divmod(c, 100**-shift) 2494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = not remainder 2495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= shift 2496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find n = floor(sqrt(c)) using Newton's method 2498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = 10**prec 2499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2500353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = c//n 2501353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= q: 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 2503353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = n + q >> 1 2505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = exact and n*n == c 2506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exact: 2508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is exact; rescale to use ideal exponent e 2509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert n % 10**shift == 0 2511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 10**shift 2512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n *= 10**-shift 2514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e += shift 25157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2516353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is not exact; fix last digit as described above 2517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n % 5 == 0: 2518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n += 1 25197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 252072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(n), e) 25217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round, and fit to current context 2523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2525dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 2526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 25277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 25297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 25317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 25327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like max(self, other) except if one is not a number, returns 25347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2537636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 25386c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 25396c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 25406c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2541636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 254259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2543636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2544636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2545636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2546636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2547636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 25486c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2549636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 25506c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2551636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 25527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25532fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2554d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 255559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both operands are finite and equal in numerical value 2556d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2557d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 255859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs differ then max returns the operand with the 2559d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2560d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 256159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs are the same then the exponent is used to select 2562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result. This is exactly the ordering used in compare_total. 2563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 25667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2569636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2570e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 25717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 25737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 25747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 257559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Like min(self, other) except if one is not a number, returns 25767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 25777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2579636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 25806c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 25816c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 25826c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2583636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 258459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2585636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2586636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2587636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2588636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2589636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 25906c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2591636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 25926c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2593636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 25947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25952fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2596d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 2600353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 26027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2603636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2604e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 26057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 26077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 2608353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 26107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 26117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 26127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 261372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return rest == '0'*len(rest) 26147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 2616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns True if self is even. Assumes self is an integer.""" 2617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self or self._exp > 0: 2618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 261972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._int[-1+self._exp] in '02468' 26207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 26227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 26237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 26247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 262559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If NaN or Infinity, self._exp is string 26267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 26277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 26287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, context=None): 2630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 2631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 2633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 2634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self 2636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, other, context=None): 2638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to the other operand numerically. 2639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 2641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 2642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 26432fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other, raiseit = True) 26442fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 26452fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 26462fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return ans 2647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.compare(other, context=context) 2648353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, other): 2650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using the abstract representations. 2651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 2653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 2654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 2655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if one is negative and the other is positive, it's easy 2657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign and not other._sign: 2658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._sign and other._sign: 2660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 2662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's handle both NaN types 2664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_nan = self._isnan() 2665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_nan = other._isnan() 2666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan or other_nan: 2667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == other_nan: 2668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int < other._int: 2669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int > other._int: 2674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self < other: 2700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self > other: 2702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < other._exp: 2705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp > other._exp: 2710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, other): 2718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using abstract repr., ignoring sign. 2719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 2721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = self.copy_abs() 2723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista o = other.copy_abs() 2724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return s.compare_total(o) 2725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self): 2727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign set to 0. """ 272872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self): 2731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign inverted.""" 2732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 273372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 273572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, self._int, self._exp, self._is_special) 2736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, other): 2738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self with the sign of other.""" 273972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(other._sign, self._int, 274072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp, self._is_special) 2741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, context=None): 2743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** self.""" 2744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(NaN) = NaN 2749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(-Infinity) = 0 2754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 2755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(0) = 1 2758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(Infinity) = Infinity 2762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self) 2764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result is now guaranteed to be inexact (the true 2766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # mathematical result is transcendental). There's no need to 2767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Rounded and Inexact here---they'll always be raised as 2768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a result of the call to _fix. 2769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self.adjusted() 2771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we only need to do any computation for quite a small range 2773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of adjusted exponents---for example, -29 <= adj <= 10 for 2774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the default context. For smaller exponent the result is 2775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # indistinguishable from 1 at the given precision, while for 2776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # larger exponent the result either overflows or underflows. 2777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 0 and adj > len(str((context.Emax+1)*3)): 2778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow 277972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Emax+1) 2780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): 2781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # underflow to 0 278272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Etiny()-1) 2783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 0 and adj < -p: 2784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 278572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) 2786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj < -p-1: 2787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 278872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '9'*(p+1), -p-1) 2789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # general case 2790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.sign == 1: 2794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = -c 2795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: increase precision by 2797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 3 digits at a time until we get an unambiguously 2798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # roundable result 2799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(c, e, p+extra) 2802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 280672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(coeff), exp) 2807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # at this stage, ans should round correctly with *any* 2809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode, not just with ROUND_HALF_EVEN 2810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self): 28181a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is canonical; otherwise return False. 28191a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 28201a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 28211a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 28221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """ 28231a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return True 2824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self): 28261a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is finite; otherwise return False. 2827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 28281a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 28291a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 2830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 28311a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return not self._is_special 2832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self): 28341a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is infinite; otherwise return False.""" 28351a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'F' 2836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self): 28381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a qNaN or sNaN; otherwise return False.""" 28391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp in ('n', 'N') 2840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, context=None): 28421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a normal number; otherwise return False.""" 28431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 28441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 28471a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return context.Emin <= self.adjusted() <= context.Emax 2848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self): 28501a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a quiet NaN; otherwise return False.""" 28511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'n' 2852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self): 28541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is negative; otherwise return False.""" 28551a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._sign == 1 2856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self): 28581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a signaling NaN; otherwise return False.""" 28591a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'N' 2860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, context=None): 28621a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is subnormal; otherwise return False.""" 28631a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 28641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 28671a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self.adjusted() < context.Emin 2868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self): 28701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a zero; otherwise return False.""" 287172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return not self._is_special and self._int == '0' 2872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _ln_exp_bound(self): 2874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.ln(). 2875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, compute r such that self.ln() >= 10**r. Assumes 2876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that self is finite and positive and that self != 1. 2877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 2880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) 2883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj*23//10)) - 1 2884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument <= 0.1 2886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str((-1-adj)*23//10)) - 1 2887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(c) 2893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) 2894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return e + len(str(10**-e - c)) - 1 2896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, context=None): 2899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of self.""" 2900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(NaN) = NaN 2905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(0.0) == -Infinity 2910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(Infinity) = Infinity 2914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(1.0) == 0.0 2918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(negative) raises InvalidOperation 2922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ln of a negative value') 2925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision by 3 2932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until we get an unambiguously roundable result 2933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p - self._ln_exp_bound() + 2 # at least p+3 places 2934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog(c, e, places) 2936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 294072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _log10_exp_bound(self): 2949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.log10(). 2950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, find r such that self.log10() >= 10**r. 2951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that self is finite and positive and that self != 1. 2952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # For x >= 10 or x < 0.1 we only need a bound on the integer 2955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # part of log10(self), and this comes directly from the 2956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent of x. For 0.1 <= x <= 10 we use the inequalities 2957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > 2958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 2959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self >= 10 2963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj))-1 2964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self < 0.1 2966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(-1-adj))-1 2967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(231*c) 2973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) + 2 2974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(10**-e-c) 2976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) + e - (num < "231") - 1 2977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, context=None): 2979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of self.""" 2980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(NaN) = NaN 2985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(0.0) == -Infinity 2990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(Infinity) = Infinity 2994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(negative or -Infinity) raises InvalidOperation 2998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 3000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'log10 of a negative value') 3001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(10**n) = n 300372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): 3004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # answer may need rounding 3005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self._exp + len(self._int) - 1) 3006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 3008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 3009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 3010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 3011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision 3013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until result is unambiguously roundable 3014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p-self._log10_exp_bound()+2 3015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 3016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog10(c, e, places) 3017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 3018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 3019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 3020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 302172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 3022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 3024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 3025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 3026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 3027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, context=None): 3030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of self's MSD. 3031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 3033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of self (as though it were truncated 3034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to a single digit while maintaining the value of that digit and 3035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista without limiting the resulting exponent). 3036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(NaN) = NaN 3038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(+/-Inf) = +Inf 3046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 3047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(0) = -Inf, DivisionByZero 3050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 3051cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'logb(0)', 1) 3052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # otherwise, simply return the adjusted exponent of self, as a 3054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal. Note that no attempt is made to fit the result 3055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # into the current context. 3056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.adjusted()) 3057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _islogical(self): 3059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return True if self is a logical operand. 3060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3061c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling For being logical, it must be a finite number with a sign of 0, 3062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an exponent of 0, and a coefficient whose digits must all be 3063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista either 0 or 1. 3064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign != 0 or self._exp != 0: 3066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for dig in self._int: 306872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if dig not in '01': 3069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 3071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fill_logical(self, context, opa, opb): 3073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opa) 3074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 307572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opa = '0'*dif + opa 3076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opa = opa[-context.prec:] 3078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opb) 3079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 308072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opb = '0'*dif + opb 3081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opb = opb[-context.prec:] 3083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return opa, opb 3084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, other, context=None): 3086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'and' operation between self and other's digits.""" 3087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 309672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) 309772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, context=None): 3100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all its digits.""" 3101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 310372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), 310472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, other, context=None): 3107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'or' operation between self and other's digits.""" 3108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 311772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb)) 311872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, other, context=None): 3121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'xor' operation between self and other's digits.""" 3122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 313172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb)) 313272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, other, context=None): 3135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31386c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 31396c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 31406c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 31486c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 31506c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31532fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3162e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, other, context=None): 3165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31686c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 31696c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 31706c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 31786c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 31806c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31832fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3192e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, context=None): 3195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than itself.""" 3196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 3204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 3205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 320672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '9'*context.prec, context.Etop()) 3207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_FLOOR) 3210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 321472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), 321572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, context=None): 3218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than itself.""" 3219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 322972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, '9'*context.prec, context.Etop()) 3230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_CEILING) 3233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 323772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), 323872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, other, context=None): 3241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to self, in the direction towards other. 3242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number to self 3244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (excluding self) that is in the direction towards other, 3245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unless both have the same value. If the two operands are 3246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista numerically equal, then the result is a copy of self with the 3247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign set to be the same as the sign of other. 3248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32582fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson comparison = self._cmp(other) 3259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == 0: 326072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.copy_sign(other) 3261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == -1: 3263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_plus(context) 3264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # comparison == 1 3265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_minus(context) 3266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decide which flags to raise using value of ans 3268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._isinfinity(): 3269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Overflow, 3270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'Infinite result from next_toward', 3271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans._sign) 3272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif ans.adjusted() < context.Emin: 3275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 3276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 3277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if precision == 1 then we don't raise Clamped for a 3280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result 0E-Etiny. 3281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 3282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 3283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, context=None): 3287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of self. 3288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 32900f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista sNaN 32910f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista NaN 3292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 3293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 3294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 3295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 3296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 3297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 3298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 3299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 3300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_snan(): 3302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "sNaN" 3303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_qnan(): 3304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "NaN" 3305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista inf = self._isinfinity() 3306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == 1: 3307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Infinity" 3308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == -1: 3309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Infinity" 3310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_zero(): 3311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Zero" 3313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Zero" 3315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_subnormal(context=context): 3318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Subnormal" 3320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Subnormal" 3322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # just a normal, regular, boring number, :) 3323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Normal" 3325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Normal" 3327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 3329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :)""" 3330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 3331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, other, context=None): 3333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of self, value-of-other times.""" 3334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33476c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 335472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's rotate! 3357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[torot:] + rotdig[:torot] 335872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 335972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, other, context=None): 3362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self operand after adding the second value to its exp.""" 3363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista liminf = -2 * (context.Emax + context.prec) 3373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista limsup = 2 * (context.Emax + context.prec) 3374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (liminf <= int(other) <= limsup): 3375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33786c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 338072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) 3381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista d = d._fix(context) 3382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return d 3383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, other, context=None): 3385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted 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 if not torot: 34046c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 340872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's shift! 3411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if torot < 0: 3412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[:torot] 3413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 341472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated = rotdig + '0'*torot 3415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotated[-context.prec:] 3416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 341772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 341872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 342059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Support for pickling, copy, and deepcopy 34217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 34227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 34237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 34257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3426cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # I'm immutable; therefore I am my own clone 34277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 34307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3431cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # My components are also immutable 34327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 343472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistadef _dec_from_triple(sign, coefficient, exponent, special=False): 343572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """Create a decimal instance directly, without any validation, 343672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista normalization (e.g. removal of leading zeros) or argument 343772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista conversion. 343872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 343972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista This function is for *internal use only*. 344072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """ 344172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 344272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = object.__new__(Decimal) 344372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._sign = sign 344472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = coefficient 344572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp = exponent 344672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._is_special = special 344772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 344872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self 344972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 345059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context class ####################################################### 3451cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 34527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3453cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# get rounding method function: 345459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batistarounding_functions = [name for name in Decimal.__dict__.keys() 345559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if name.startswith('_round_')] 34567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 345759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 34587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 34597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 34607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 34617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 34637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3464ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlanclass _ContextManager(object): 34658b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Context manager class to support localcontext(). 34661a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 3467ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan Sets a copy of the supplied context in __enter__() and restores 34688b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan the previous decimal context in __exit__() 34698b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 34701a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 3471ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan self.new_context = new_context.copy() 34721a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 34731a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 34741a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 34751a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 34761a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 34771a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 34781a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 34797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 34807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 34817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 34837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 348459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista rounding - rounding type (how you round) 3485bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 34867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 34877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 34887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 34897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 34907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 34910ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 34920ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 34937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 34947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 3495e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 34967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 34979ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 34987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 3499abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 35000ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 3501e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 3502abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 3503abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 3504abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 3505abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 3506abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 3507bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 3508fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 3509b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 3510bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 3511fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 3512b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 35137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 35147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 3515eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 35167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 35177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 35187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 35197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3520b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 3521bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 3522b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 352359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' 352459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' 352559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista % vars(self)) 352659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [f.__name__ for f, v in self.flags.items() if v] 352759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('flags=[' + ', '.join(names) + ']') 352859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [t.__name__ for t, v in self.traps.items() if v] 352959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('traps=[' + ', '.join(names) + ']') 3530b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 3531b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 3532d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 3533d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 3534d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 3535b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 3536d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 35379fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 35389fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 3539e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista nc = Context(self.prec, self.rounding, self.traps, 3540e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags, self.Emin, self.Emax, 3541e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 35427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 35439fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 35449fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 35459fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 354659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista nc = Context(self.prec, self.rounding, self.traps.copy(), 3547e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags.copy(), self.Emin, self.Emax, 3548e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 35499fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 35509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 35517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35525aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 35537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 35547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 35567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 35577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 35587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 35597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35605aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 35617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 356259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Don't touch the flag 35637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 35647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 3566bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 356759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # The errors define how to handle themselves. 35685aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 35697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 357159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # self._ignored_flags = [] 35727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 35737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 35757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 3576fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 35777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 35797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 35807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 35817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 35827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 35837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 35847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 35867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 35877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 35887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 35897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 35907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 35917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35925aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 35935aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 35945aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 359559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise TypeError("Cannot hash a Context.") 35965aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 35977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 35987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 35997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 36007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 3602e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 36037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 36047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 36067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 36077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 36097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 36107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 36127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 36137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 36147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 36157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 36167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 36177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 36197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 36217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 36227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 36237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3624fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 362559bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson """Creates a new Decimal instance but using self as context. 362659bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 362759bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson This method implements the to-number operation of the 362859bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson IBM Decimal specification.""" 362959bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 363059bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson if isinstance(num, basestring) and num != num.strip(): 363159bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson return self._raise_error(ConversionSyntax, 363259bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "no trailing or leading whitespace is " 363359bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "permitted.") 363459bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 36357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 3636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if d._isnan() and len(d._int) > self.prec - self._clamp: 3637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._raise_error(ConversionSyntax, 3638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista "diagnostic info too long in NaN") 3639dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 36407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 364159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Methods 36427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 36437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 36447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 364659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation on the operand. Otherwise, the result is the same as using 36477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 36487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 3650abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 36519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 3652abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 36539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 3654abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 36559ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 3656abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 36577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 36597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 36617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 36627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 3664abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('19.00') 36659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 3666abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.02E+4') 36677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 36697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 3671dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 36727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, a): 3674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 3675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 3677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 3678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.canonical(Decimal('2.50')) 3680abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.50') 3681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.canonical(context=self) 3683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 36847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 36857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 36867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 36887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 36897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 36907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 36917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 36927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 36947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 36957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 36967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 36977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 3699abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 37009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 3701abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 37029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 3703abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 37049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 3705abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 37069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 3707abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 37089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 3709abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 37107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 37127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, a, b): 3714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values of the two operands numerically. 3715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 3717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 3718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext 3720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('3')) 3721abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) 3723abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) 3728abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) 3735abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_signal(b, context=self) 3740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, a, b): 3742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation. 3743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 3745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 3746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 3747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) 3749abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) 3751abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) 3753abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) 3755abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) 3757abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 3758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) 3759abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total(b) 3762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, a, b): 3764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation ignoring sign. 3765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 3767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total_mag(b) 3769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self, a): 3771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign set to 0. 3772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('2.1')) 3774abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('-100')) 3776abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 3777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_abs() 3779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_decimal(self, a): 3781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the decimal objet. 3782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('2.1')) 3784abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('-1.00')) 3786abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00') 3787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 37886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(a) 3789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self, a): 3791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign inverted. 3792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('101.5')) 3794abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-101.5') 3795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('-101.5')) 3796abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 3797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_negate() 3799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, a, b): 3801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Copies the second operand's sign to the first one. 3802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In detail, it returns a copy of the first operand with the sign 3804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista equal to the sign of the second operand. 3805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) 3807abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) 3809abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) 3811abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) 3813abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_sign(b) 3816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 38177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 38187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 38197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 3821abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.333333333') 38229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 3823abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.666666667') 38249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 3825abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.5') 38269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 3827abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 38289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 3829abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 38309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 3831abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.00') 38329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 3833abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20') 38349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 3835abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 38369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 3837abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 38389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 3839abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20E+6') 38407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 38427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 38447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 38457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 3847abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 38489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 3849abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 38509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 3851abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 38527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 38547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 38567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 38577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, a): 3859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** a. 3860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-Infinity')) 3865abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-1')) 3867abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.367879441') 3868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0')) 3869abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 3870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('1')) 3871abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.71828183') 3872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0.693147181')) 3873abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 3874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('+Infinity')) 3875abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 3876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.exp(context=self) 3878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, a, b, c): 3880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a multiplied by b, plus c. 3881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The first two operands are multiplied together, using multiply, 3883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the third operand is then added to the result of that 3884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplication, using add, all with only one final rounding. 3885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) 3887abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('22') 3888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) 3889abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 3890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) 3891abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.38435736E+12') 3892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.fma(b, c, context=self) 3894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self, a): 38961a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is canonical; otherwise return False. 38971a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 38981a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 38991a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 3900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_canonical(Decimal('2.50')) 39021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 39041a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return a.is_canonical() 3905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self, a): 39071a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is finite; otherwise return False. 3908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 39091a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 39101a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 3911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('2.50')) 39131a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('-0.3')) 39151a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('0')) 39171a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('Inf')) 39191a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('NaN')) 39211a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_finite() 3924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self, a): 39261a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is infinite; otherwise return False. 3927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('2.50')) 39291a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('-Inf')) 39311a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('NaN')) 39331a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_infinite() 3936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self, a): 39381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a qNaN or sNaN; 39391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('2.50')) 39421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('NaN')) 39441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('-sNaN')) 39461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_nan() 3949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, a): 39511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a normal number; 39521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('2.50')) 39581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.1E-999')) 39601a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.00')) 39621a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('-Inf')) 39641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('NaN')) 39661a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_normal(context=self) 3969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self, a): 39711a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a quiet NaN; otherwise return False. 3972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('2.50')) 39741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('NaN')) 39761a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('sNaN')) 39781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_qnan() 3981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self, a): 39831a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is negative; otherwise return False. 3984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('2.50')) 39861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-12')) 39881a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-0')) 39901a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_signed() 3993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self, a): 39951a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a signaling NaN; 39961a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('2.50')) 39991a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('NaN')) 40011a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('sNaN')) 40031a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_snan() 4006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, a): 40081a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is subnormal; otherwise return False. 4009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('2.50')) 40141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.1E-999')) 40161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.00')) 40181a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('-Inf')) 40201a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('NaN')) 40221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_subnormal(context=self) 4025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self, a): 40271a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a zero; otherwise return False. 4028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('0')) 40301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('2.50')) 40321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('-0E+2')) 40341a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_zero() 4037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, a): 4039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of the operand. 4040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('0')) 4045abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('1.000')) 4047abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('2.71828183')) 4049abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000000') 4050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('10')) 4051abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.30258509') 4052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('+Infinity')) 4053abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.ln(context=self) 4056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, a): 4058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of the operand. 4059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0')) 4064abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0.001')) 4066abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-3') 4067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('1.000')) 4068abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('2')) 4070abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.301029996') 4071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('10')) 4072abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('70')) 4074abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.84509804') 4075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('+Infinity')) 4076abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.log10(context=self) 4079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, a): 4081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of the operand's MSD. 4082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 4084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of the operand (as though the 4085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand were truncated to a single digit while maintaining the 4086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value of that digit and without limiting the resulting exponent). 4087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('250')) 4089abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('2.50')) 4091abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0.03')) 4093abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 4094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0')) 4095abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logb(context=self) 4098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, a, b): 4100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'and' between each operand's digits. 4101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) 4105abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) 4107abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) 4109abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) 4111abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) 4113abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 4114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) 4115abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_and(b, context=self) 4118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, a): 4120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all the digits in the operand. 4121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operand must be a logical number. 4123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('0')) 4125abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111111') 4126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('1')) 4127abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111110') 4128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('111111111')) 4129abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('101010101')) 4131abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10101010') 4132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_invert(context=self) 4134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, a, b): 4136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'or' between each operand's digits. 4137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) 4141abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) 4143abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) 4145abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) 4147abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) 4149abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) 4151abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_or(b, context=self) 4154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, a, b): 4156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'xor' between each operand's digits. 4157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) 4161abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) 4163abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) 4165abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) 4167abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) 4169abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('110') 4170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) 4171abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1101') 4172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_xor(b, context=self) 4174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 41767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 41777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4179c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 418059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 418159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the maximum (closer to positive 41827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 41837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 4185abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 41869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 4187abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 41889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 4189abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4190d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 4191abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 41927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 41947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, a, b): 4196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.max_mag(b, context=self) 4198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 42007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 42017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4203c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 420459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 420559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the minimum (closer to negative 42067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 42077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 4209abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 42109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 4211abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-10') 42129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 4213abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 4214d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 4215abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 42167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 42177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 42187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, a, b): 4220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.min_mag(b, context=self) 4222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 42237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 42247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 42257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 42277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 42287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 42297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 4231abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 42329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 4233abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 42347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 42357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 42367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 42387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 42397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4240cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis If either operand is a special value then the general rules apply. 4241cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Otherwise, the operands are multiplied together ('long multiplication'), 4242cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis resulting in a number which may be as long as the sum of the lengths 4243cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis of the two operands. 42447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 4246abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.60') 42479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 4248abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('21') 42499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 4250abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.72') 42519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 4252abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.0') 42539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 4254abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.28135971E+11') 42557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 42567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 42577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, a): 4259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than a. 4260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('1')) 4265abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('1E-1007')) 4267abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('-1.00000003')) 4269abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('Infinity')) 4271abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('9.99999999E+999') 4272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_minus(context=self) 4274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, a): 4276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than a. 4277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('1')) 4282abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-1E-1007')) 4284abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('-1.00000003')) 4286abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-Infinity')) 4288abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-9.99999999E+999') 4289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_plus(context=self) 4291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, a, b): 4293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to a, in direction towards b. 4294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number from the first 4296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand (but not the first operand) that is in the direction 4297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista towards the second operand, unless the operands have the same 4298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. 4299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('2')) 4304abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) 4306abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) 4308abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('0')) 4310abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) 4312abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) 4314abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) 4316abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.00') 4317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_toward(b, context=self) 4319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 4321e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 43227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 43247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 43257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 4327abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 43289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 4329abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 43309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 4331abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2') 43329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 4333abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.2E+2') 43349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 4335abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2E+2') 43369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 4337abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 43387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 43407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, a): 4342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of the operand. 4343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 4345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 4346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 4347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 4348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 4349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 4350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 4351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 4352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 4353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 4354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 4355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = Context(ExtendedContext) 4357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('Infinity')) 4360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Infinity' 4361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('1E-10')) 4362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('2.50')) 4364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0.1E-999')) 4366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Subnormal' 4367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0')) 4368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Zero' 4369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0')) 4370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Zero' 4371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0.1E-999')) 4372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Subnormal' 4373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-1E-10')) 4374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-2.50')) 4376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-Infinity')) 4378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Infinity' 4379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('NaN')) 4380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-NaN')) 4382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('sNaN')) 4384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'sNaN' 4385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.number_class(context=self) 4387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 43897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 43907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 43927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 43937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 43947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43959ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 4396abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 43979ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 4398abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 43997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 44017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 44037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 44047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute a**b. If a is negative then b 4406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista must be integral. The result will be inexact unless b is 4407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integral and the result is finite and can be expressed exactly 4408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in 'precision' digits. 4409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (a**b) % modulo. For the 4411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 4412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 4413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 4415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - b must be nonnegative 4416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - at least one of a or b must be nonzero 4417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and have at most 'precision' digits 4418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(a, b, modulo) is identical to the result 4420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that would be obtained by computing (a**b) % modulo with 4421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unbounded precision, but is computed more efficiently. It is 4422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista always exact. 4423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('3')) 4428abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('8') 4429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-2'), Decimal('3')) 4430abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 4431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('-3')) 4432abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.125') 4433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('1.7'), Decimal('8')) 4434abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('69.7575744') 4435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('10'), Decimal('0.301029996')) 4436abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 4437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('-1')) 4438abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('0')) 4440abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('1')) 4442abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('-1')) 4444abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4445353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('0')) 4446abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4447353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('1')) 4448abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('2')) 4450abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4451353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('0'), Decimal('0')) 4452abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 4453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) 4455abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4456353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) 4457abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-11') 4458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) 4459abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) 4461abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) 4463abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11729830') 4464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) 4465abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) 4467abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 44687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 44707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 447259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Returns a value equal to 'a' (rounded), having the exponent of 'b'. 44737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 447559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operand. It may be rounded using the current rounding setting (if the 44767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 44777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 44787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 44797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 44817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 448259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation condition is raised. This guarantees that, unless there is 448359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista an error condition, the exponent of the result of a quantize is always 44847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 44857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 44877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 44887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 4490abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.170') 44919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 4492abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.17') 44939ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 4494abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2') 44959ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 4496abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 44979ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 4498abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E+1') 44999ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 4500abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 45019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 4502abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 45039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 4504abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 45059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 4506abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E+5') 45079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 4508abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 45099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 4510abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 45119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 4512abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217.0') 45139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 4514abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217') 45159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 4516abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2E+2') 45179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 4518abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2E+2') 45197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 45217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 4523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :) 4524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.radix() 4526abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 4529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 45317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 45327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 453459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista calculating integer division as described for divide-integer, rounded 45350d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz to precision digits if necessary. The sign of the result, if 453659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista non-zero, is the same as that of the original dividend. 45377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 45397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 45407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 45417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 4543abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 45449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 4545abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 45469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 4547abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 45489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 4549abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 45509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 4551abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 45529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 4553abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 45547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 45567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 45587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 45597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 456059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen). If the result is equal to 0 then its sign will be the 45617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 45627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 45647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 45657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 45667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 4568abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.9') 45699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 4570abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 45719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 4572abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 45739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 4574abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 45759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 4576abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 45779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 4578abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 45799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 4580abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.3') 45817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 45837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4584353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, a, b): 4585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of a, b times. 4586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a rotated copy of the digits in 4588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the coefficient of the first operand. The number of places of 4589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotation is taken from the absolute value of the second operand, 4590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the rotation being to the left if the second operand is 4591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. 4592353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) 4594abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000003') 4595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) 4596abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('12') 4597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) 4598abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('891234567') 4599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) 4600abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) 4602abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678912') 4603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4604353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.rotate(b, context=self) 4605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 46067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 46077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 46087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 46107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 46117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 46137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 46149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 46157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 46169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 46177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 46189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 46197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 46207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 46227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, a, b): 4624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the first operand after adding the second value its exp. 4625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) 4627abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.0750') 4628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) 4629abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50') 4630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) 4631abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50E+3') 4632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.scaleb (b, context=self) 4634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, a, b): 4636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of a, b times. 4637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a shifted copy of the digits 4639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the coefficient of the first operand. The number of places 4640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to shift is taken from the absolute value of the second operand, 4641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the shift being to the left if the second operand is 4642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. Digits shifted into the 4643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coefficient are zeros. 4644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) 4646abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000000') 4647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) 4648abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) 4650abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1234567') 4651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) 4652abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) 4654abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678900') 4655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.shift(b, context=self) 4657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 46587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 465959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Square root of a non-negative number to context precision. 46607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 46627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 46637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 4665abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 46669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 4667abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 46689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 4669abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.624499800') 46709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 4671abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 46729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 4673abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 46749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 4675abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 46769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 4677abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 46789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 4679abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.64575131') 46809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 4681abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.16227766') 46829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 46836ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 46847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 46867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 4688f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 46897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 4691abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.23') 46929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 4693abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.00') 46949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 4695abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.77') 46967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 46987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 47007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 47017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 47037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 47057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 47077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 47087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 47107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 47127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, a): 4714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to an integer. 4715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista When the operand has a negative exponent, the result is the same 4717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista as using the quantize() operation using the given operand as the 4718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista left-hand-operand, 1E+0 as the right-hand-operand, and the precision 4719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the operand as the precision setting; Inexact and Rounded flags 4720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista are allowed in this operation. The rounding mode is taken from the 4721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 4722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('2.1')) 4724abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100')) 4726abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100.0')) 4728abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('101.5')) 4730abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) 4732abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) 4734abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) 4736abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) 4738abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_exact(context=self) 4741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, a): 47437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 47447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 47467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 47477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 47487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 474959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be set. The rounding mode is taken from the context. 47507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('2.1')) 4752abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100')) 4754abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100.0')) 4756abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('101.5')) 4758abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-101.5')) 4760abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('10E+5')) 4762abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) 4764abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-Inf')) 4766abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 47677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_value(context=self) 4769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 4771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 47727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 47747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 477517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 4776636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 47777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 47787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 47807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 47817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 4782636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 47837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 478417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 478517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 478672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self.int = int(value._int) 47877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 478817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 478917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 47907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 47917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 47927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 47937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 47957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 47967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 47987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4801e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batistadef _normalize(op1, op2, prec = 0): 48027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 48037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 48057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp < op2.exp: 48077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 48087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 48097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 48107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 48117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 48127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). 4814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then adding 10**exp to tmp has the same effect (after rounding) 4815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as adding any positive quantity smaller than 10**exp; similarly 4816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for subtraction. So if other is smaller than 10**exp we replace 4817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # it with 10**exp. This avoids tmp.exp - other.exp getting too large. 4818e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista tmp_len = len(str(tmp.int)) 4819e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other_len = len(str(other.int)) 4820e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista exp = tmp.exp + min(-1, tmp_len - prec - 2) 4821e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if other_len + other.exp - 1 < exp: 4822e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.int = 1 4823e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.exp = exp 4824636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 4825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.int *= 10 ** (tmp.exp - other.exp) 4826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.exp = other.exp 48277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 48287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### 4830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# This function from Tim Peters was taken from here: 4832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# http://mail.python.org/pipermail/python-list/1999-July/007758.html 4833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# The correction being in the function definition is for speed, and 4834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the whole function is not resolved with math.log because of avoiding 4835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the use of floats. 4836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _nbits(n, correction = { 4837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0': 4, '1': 3, '2': 2, '3': 2, 4838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '4': 1, '5': 1, '6': 1, '7': 1, 4839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '8': 0, '9': 0, 'a': 0, 'b': 0, 4840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'c': 0, 'd': 0, 'e': 0, 'f': 0}): 4841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Number of bits in binary representation of the positive integer n, 4842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or 0 if n == 0. 4843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n < 0: 4845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _nbits should be nonnegative.") 4846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista hex_n = "%x" % n 4847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 4*len(hex_n) - correction[hex_n[0]] 4848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _sqrt_nearest(n, a): 4850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to the square root of the positive integer n. a is 4851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an initial approximation to the square root. Any positive integer 4852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista will do for a, but the closer a is to the square root of n the 4853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista faster convergence will be. 4854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= 0 or a <= 0: 4857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("Both arguments to _sqrt_nearest should be positive.") 4858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b=0 4860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while a != b: 4861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, a = a, a--n//a>>1 4862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a 4863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _rshift_nearest(x, shift): 4865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given an integer x and a nonnegative integer shift, return closest 4866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integer to x / 2**shift; use round-to-even in case of a tie. 4867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, q = 1L << shift, x >> shift 4870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*(x & (b-1)) + (q&1) > b) 4871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _div_nearest(a, b): 4873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to a/b, a and b positive integers; rounds to even 4874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the case of a tie. 4875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(a, b) 4878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*r + (q&1) > b) 4879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _ilog(x, M, L = 8): 4881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Integer approximation to M*log(x/M), with absolute error boundable 4882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in terms only of x/M. 4883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given positive integers x and M, return an integer approximation to 4885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference 4886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista between the approximation and the exact result is at most 22. For 4887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In 4888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista both cases these are upper bounds on the error; it will usually be 4889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista much smaller.""" 4890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The basic algorithm is the following: let log1p be the function 4892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use 4893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the reduction 4894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) 4896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # repeatedly until the argument to log1p is small (< 2**-L in 4898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # absolute value). For small y we can use the Taylor series 4899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expansion 4900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T 4902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # truncating at T such that y**T is small enough. The whole 4904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # computation is carried out in a form of fixed-point arithmetic, 4905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with a real number z being represented by an integer 4906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # approximation to z*M. To avoid loss of precision, the y below 4907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is actually an integer approximation to 2**R*y*M, where R is the 4908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number of reductions performed so far. 4909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = x-M 4911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument reduction; R = number of reductions performed 4912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = 0 4913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while (R <= L and long(abs(y)) << L-R >= M or 4914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R > L and abs(y) >> R-L >= M): 4915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(long(M*y) << 1, 4916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) 4917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R += 1 4918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series with T terms 4920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 4921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yshift = _rshift_nearest(y, R) 4922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, T) 4923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(T-1, 0, -1): 4924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, k) - _div_nearest(yshift*w, M) 4925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(w*y, M) 4927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog10(c, e, p): 4929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, p >= 0, compute an integer 4930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log10(c*10**e), with an absolute error of 4931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # increase precision by 2; compensate for this by dividing 4934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # final result by 100 4935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write c*10**e as d*10**f with either: 4938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f >= 0 and 1 <= d <= 10, or 4939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f <= 0 and 0.1 <= d <= 1. 4940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Thus for c*10**e close to 1, f = 0 4941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M = 10**p 4946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) 4951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, M) # error < 5 + 22 = 27 4953be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista log_10 = _log10_digits(p) # error < 1 4954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _div_nearest(log_d*M, log_10) 4955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = f*M # exact 4956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 # error < 2.31 4958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = div_nearest(f, 10**-p) # error < 0.5 4959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(log_tenpower+log_d, 100) 4961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog(c, e, p): 4963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, compute an integer 4964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log(c*10**e), with an absolute error of 4965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Increase precision by 2. The precision increase is compensated 4968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for at the end with a division by 100. 4969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, 4972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) 4973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as 10**p * log(d) + 10**p*f * log(10). 4974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute approximation to 10**p*log(d), with error < 27 4978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) # error of <= 0.5 in c 4984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # _ilog magnifies existing error in c by a factor of at most 10 4986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 4987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p <= 0: just approximate the whole thing by 0; error < 2.31 4989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 4990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4991be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute approximation to f*10**p*log(10), with error < 11. 4992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if f: 4993be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = len(str(abs(f)))-1 4994be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p + extra >= 0: 4995be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in f * _log10_digits(p+extra) < |f| * 1 = |f| 4996be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 4997be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) 4998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5003be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 5004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(f_log_ten + log_d, 100) 5005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5006be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batistaclass _Log10Memoize(object): 5007be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Class to compute, store, and allow retrieval of, digits of the 5008be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista constant log(10) = 2.302585.... This constant is needed by 5009be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" 5010be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def __init__(self): 5011be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = "23025850929940456840179914546843642076011014886" 5012be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5013be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def getdigits(self, p): 5014be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Given an integer p >= 0, return floor(10**p)*log(10). 5015be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5016be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista For example, self.getdigits(3) returns 2302. 5017be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """ 5018be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits are stored as a string, for quick conversion to 5019be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # integer in the case that we've already computed enough 5020be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits; the stored digits should always be correct 5021be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # (truncated, not rounded to nearest). 5022be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p < 0: 5023be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista raise ValueError("p should be nonnegative") 5024be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5025be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p >= len(self.digits): 5026be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+3, p+6, p+9, ... digits; continue until at 5027be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # least one of the extra digits is nonzero 5028be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = 3 5029be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista while True: 5030be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+extra digits, correct to within 1ulp 5031be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista M = 10**(p+extra+2) 5032be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista digits = str(_div_nearest(_ilog(10*M, M), 100)) 5033be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if digits[-extra:] != '0'*extra: 5034be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista break 5035be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra += 3 5036be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # keep all reliable digits so far; remove trailing zeros 5037be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # and next nonzero digit 5038be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = digits.rstrip('0')[:-1] 5039be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista return int(self.digits[:p+1]) 5040be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5041be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista_log10_digits = _Log10Memoize().getdigits 5042be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _iexp(x, M, L=8): 5044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers x and M, M > 0, such that x/M is small in absolute 5045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value, compute an integer approximation to M*exp(x/M). For 0 <= 5046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x/M <= 2.4, the absolute error in the result is bounded by 60 (and 5047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista is usually much smaller).""" 5048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Algorithm: to compute exp(z) for a real number z, first divide z 5050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then 5051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor 5052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # series 5053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(x) = x + x**2/2! + x**3/3! + ... 5055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Now use the identity 5057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(2x) = expm1(x)*(expm1(x)+2) 5059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # R times to compute the sequence expm1(z/2**R), 5061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). 5062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find R such that x/2**R/M <= 2**-L 5064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = _nbits((long(x)<<L)//M) 5065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series. (2**L)**T > M 5067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x, T) 5069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<R 5070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(T-1, 0, -1): 5071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x*(Mshift + y), Mshift * i) 5072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Expansion 5074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(R-1, -1, -1): 5075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<(k+2) 5076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(y*(y+Mshift), Mshift) 5077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return M+y 5079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dexp(c, e, p): 5081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute an approximation to exp(c*10**e), with p decimal places of 5082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista precision. 5083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5084be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Returns integers d, f such that: 5085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= d <= 10**p, and 5087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (d-1)*10**f < exp(c*10**e) < (d+1)*10**f 5088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, d*10**f is an approximation to exp(c*10**e) with p 5090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision, and with an error in d of at most 1. This is 5091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when d 5092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista = 10**(p-1) the error could be up to 10 ulp.""" 5093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision 5095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5097be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute log(10) with extra precision = adjusted exponent of c*10**e 5098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = max(0, e + len(str(c)) - 1) 5099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = p + extra 5100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5101be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), 5102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding down 5103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = e+q 5104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c*10**shift 5106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c//10**-shift 5108be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista quot, rem = divmod(cshift, _log10_digits(q)) 5109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reduce remainder back to original precision 5111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rem = _div_nearest(rem, 10**extra) 5112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # error in result of _iexp < 120; error after division < 0.62 5114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 5115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dpower(xc, xe, yc, ye, p): 5117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and 5118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 5119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= c <= 10**p, and 5121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (c-1)*10**e < x**y < (c+1)*10**e 5122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in other words, c*10**e is an approximation to x**y with p digits 5124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of precision, and with an error in c of at most 1. (This is 5125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when c 5126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista == 10**(p-1) we can only guarantee error < 10ulp.) 5127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista We assume that: x is positive and not equal to 1, and y is nonzero. 5129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find b such that 10**(b-1) <= |y| <= 10**b 5132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b = len(str(abs(yc))) + ye 5133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point 5135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista lxc = _dlog(xc, xe, p+b+1) 5136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) 5138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = ye-b 5139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = lxc*yc*10**shift 5141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = _div_nearest(lxc*yc, 10**-shift) 5143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if pc == 0: 5145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we prefer a result that isn't exactly 1; this makes it 5146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # easier to compute a correctly rounded result in __pow__ 5147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: 5148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**(p-1)+1, 1-p 5149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**p-1, -p 5151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(pc, -(p+1), p+1) 5153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _div_nearest(coeff, 10) 5154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp += 1 5155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return coeff, exp 5157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _log10_lb(c, correction = { 5159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, 5160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '6': 23, '7': 16, '8': 10, '9': 5}): 5161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for 100*log10(c) for a positive integer c.""" 5162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c <= 0: 5163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _log10_lb should be nonnegative.") 5164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_c = str(c) 5165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 100*len(str_c) - correction[str_c[0]] 5166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 516759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Helper Functions #################################################### 51687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _convert_other(other, raiseit=False): 5170636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 5171636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5172636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5173636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 5174636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 5175636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 5176636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 5177636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 5178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if raiseit: 5179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise TypeError("Unable to convert %s to Decimal" % other) 5180267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 5181636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 518259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Setup Specific Contexts ############################################ 51837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 5185fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 51867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 51886ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 5189bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 5190bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 519199148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 519299148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 5193e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 51947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 51977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 51987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 51997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 52007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 52027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 5203bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 5204bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 52057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 52067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 52086ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 5209bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 5210bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 52117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 52127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 521459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### crud for parsing strings ############################################# 52156a123cb7827859748a0096570dfbb5ceba0e59dcMark Dickinson# 521672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Regular expression used for parsing numeric strings. Additional 521772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# comments: 521872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 521972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 1. Uncomment the two '\s*' lines to allow leading and/or trailing 522072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# whitespace. But note that the specification disallows whitespace in 522172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# a numeric string. 522272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 522372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 2. For finite numbers (not infinities and NaNs) the body of the 522472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# number between the optional sign and the optional exponent must have 522572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# at least one decimal digit, possibly after the decimal point. The 522672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# lookahead expression '(?=\d|\.\d)' checks this. 522772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 522872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# As the flag UNICODE is not enabled here, we're explicitly avoiding any 522972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# other meaning for \d than the numbers [0-9]. 52307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 523172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistaimport re 523272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista_parser = re.compile(r""" # A numeric string consists of: 52337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 523472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<sign>[-+])? # an optional sign, followed by either... 52357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 523672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?=\d|\.\d) # ...a number (with at least one digit) 523772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<int>\d*) # consisting of a (possibly empty) integer part 523872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (\.(?P<frac>\d*))? # followed by an optional fractional part 523972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... 52407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 524172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista Inf(inity)? # ...an infinity, or... 524272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista | 524372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<signal>s)? # ...an (optionally signaling) 524472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista NaN # NaN 524572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<diag>\d*) # with (possibly empty) diagnostic information. 52467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 52477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 524859bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson \Z 524972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista""", re.VERBOSE | re.IGNORECASE).match 52507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52512ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_all_zeros = re.compile('0*$').match 52522ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_exact_half = re.compile('50*$').match 52537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 52547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52550d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz 525672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista##### Useful Constants (internal use only) ################################ 52577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 525872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Reusable defaults 525972bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInf = Decimal('Inf') 526072bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistanegInf = Decimal('-Inf') 526172bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaNaN = Decimal('NaN') 526272bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_0 = Decimal(0) 526372bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p1 = Decimal(1) 526472bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n1 = Decimal(-1) 52657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 526672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Infsign[sign] is infinity w/ that sign 526772bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInfsign = (Inf, negInf) 52687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 52727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 52737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 5274