decimal.py revision f4da77765f8581e31620e9f49c68028e57b0ae85
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 23831ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson def _round(self, places, rounding): 23841ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Round a nonzero, nonspecial Decimal to a fixed number of 23851ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson significant figures, using the given rounding mode. 23861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 23871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Infinities, NaNs and zeros are returned unaltered. 23881ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 23891ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson This operation is quiet: it raises no flags, and uses no 23901ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson information from the context. 23911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 23921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 23931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if places <= 0: 23941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("argument should be at least 1 in _round") 23951ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._is_special or not self: 23961ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return Decimal(self) 23971ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson ans = self._rescale(self.adjusted()+1-places, rounding) 23981ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # it can happen that the rescale alters the adjusted exponent; 23991ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # for example when rounding 99.97 to 3 significant figures. 24001ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # When this happens we end up with an extra 0 at the end of 24011ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # the number; a second rescale fixes this. 24021ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if ans.adjusted() != self.adjusted(): 24031ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson ans = ans._rescale(ans.adjusted()+1-places, rounding) 24041ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return ans 24051ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 2406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, rounding=None, context=None): 2407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to a nearby integer. 24087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If no rounding mode is specified, take the rounding mode from 2410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the context. This method raises the Rounded and Inexact flags 2411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista when appropriate. 24127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista See also: to_integral_value, which does exactly the same as 2414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this method except that it doesn't raise Inexact or Rounded. 2415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2416636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2417636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2418636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2419636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 24206c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 24217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 24226c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 242472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', 0) 2425636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2426636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(0, rounding) 2431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 24337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 24347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, rounding=None, context=None): 2436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to the nearest integer, without raising inexact, rounded.""" 2437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2443353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2444353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 24456c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= 0: 24476c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2448353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2449353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._rescale(0, rounding) 24507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2451353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 2452353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 2453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def sqrt(self, context=None): 2455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return the square root of self.""" 2456636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2457636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2458636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2459636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 24607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2461636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 2462636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 24637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 2465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent = self._exp // 2. sqrt(-0) = -0 246672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', self._exp // 2) 2467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 24687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2469636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2470636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2471636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 24737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 24747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # At this point self represents a positive number. Let p be 2476353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the desired precision and express self in the form c*100**e 2477353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with c a positive real number and e an integer, c and e 2478353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # being chosen so that 100**(p-1) <= c < 100**p. Then the 2479353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) 2480353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # <= sqrt(c) < 10**p, so the closest representable Decimal at 2481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision p is n*10**e where n = round_half_even(sqrt(c)), 2482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the closest integer to sqrt(c) with the even integer chosen 2483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # in the case of a tie. 2484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # To ensure correct rounding in all cases, we use the 2486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # following trick: we compute the square root to an extra 2487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # place (precision p+1 instead of precision p), rounding down. 2488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then, if the result is inexact and its last digit is 0 or 5, 2489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we increase the last digit to 1 or 6 respectively; if it's 2490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exact we leave the last digit alone. Now the final round to 2491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p places (or fewer in the case of underflow) will round 2492353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly and raise the appropriate flags. 2493353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # use an extra digit of precision 2495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista prec = context.prec+1 2496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write argument in the form c*100**e where e = self._exp//2 2498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is the 'ideal' exponent, to be used if the square root is 2499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exactly representable. l is the number of 'digits' of c in 2500353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # base 100, so that 100**(l-1) <= c < 100**l. 2501353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2502353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = op.exp >> 1 2503353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.exp & 1: 2504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int * 10 2505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = (len(self._int) >> 1) + 1 25067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int 2508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(self._int)+1 >> 1 2509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rescale so that c has exactly prec base 100 'digits' 2511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = prec-l 2512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 100**shift 2514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = True 25157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2516353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, remainder = divmod(c, 100**-shift) 2517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = not remainder 2518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= shift 2519353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2520353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find n = floor(sqrt(c)) using Newton's method 2521353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = 10**prec 2522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = c//n 2524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= q: 25257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 2526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = n + q >> 1 2528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = exact and n*n == c 2529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exact: 2531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is exact; rescale to use ideal exponent e 2532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert n % 10**shift == 0 2534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 10**shift 2535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n *= 10**-shift 2537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e += shift 25387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is not exact; fix last digit as described above 2540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n % 5 == 0: 2541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n += 1 25427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 254372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(n), e) 25447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round, and fit to current context 2546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2548dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 2549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 25507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 25527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 25547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 25557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like max(self, other) except if one is not a number, returns 25577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 25587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2560636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 25616c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 25626c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 25636c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2564636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 256559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2566636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2567636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2568636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2569636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2570636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 25716c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2572636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 25736c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2574636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 25757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25762fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2577d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 257859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both operands are finite and equal in numerical value 2579d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2580d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 258159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs differ then max returns the operand with the 2582d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2583d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 258459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs are the same then the exponent is used to select 2585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result. This is exactly the ordering used in compare_total. 2586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 25897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2592636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2593e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 25947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 25967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 25977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 259859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Like min(self, other) except if one is not a number, returns 25997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 26007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2602636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 26036c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 26046c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 26056c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2606636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 260759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2608636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2609636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2610636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2611636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2612636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 26136c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2614636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 26156c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2616636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 26177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26182fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self._cmp(other) 2619d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 2623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 26257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2626636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2627e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 26287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 26307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 2631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 26337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 26347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 26357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 263672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return rest == '0'*len(rest) 26377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 2639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns True if self is even. Assumes self is an integer.""" 2640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self or self._exp > 0: 2641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 264272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._int[-1+self._exp] in '02468' 26437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 26457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 26467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 26477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 264859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If NaN or Infinity, self._exp is string 26497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 26507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 26517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, context=None): 2653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 2654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 2656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 2657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self 2659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, other, context=None): 2661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to the other operand numerically. 2662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 2664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 2665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 26662fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson other = _convert_other(other, raiseit = True) 26672fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson ans = self._compare_check_nans(other, context) 26682fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson if ans: 26692fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson return ans 2670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.compare(other, context=context) 2671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, other): 2673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using the abstract representations. 2674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 2676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 2677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 2678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if one is negative and the other is positive, it's easy 2680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign and not other._sign: 2681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._sign and other._sign: 2683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 2685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's handle both NaN types 2687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_nan = self._isnan() 2688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_nan = other._isnan() 2689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan or other_nan: 2690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == other_nan: 2691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int < other._int: 2692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int > other._int: 2697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self < other: 2723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self > other: 2725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < other._exp: 2728353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp > other._exp: 2733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, other): 2741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using abstract repr., ignoring sign. 2742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 2744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = self.copy_abs() 2746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista o = other.copy_abs() 2747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return s.compare_total(o) 2748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self): 2750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign set to 0. """ 275172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self): 2754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign inverted.""" 2755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 275672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 275872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, self._int, self._exp, self._is_special) 2759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, other): 2761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self with the sign of other.""" 276272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(other._sign, self._int, 276372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp, self._is_special) 2764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, context=None): 2766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** self.""" 2767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(NaN) = NaN 2772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(-Infinity) = 0 2777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 2778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(0) = 1 2781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(Infinity) = Infinity 2785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self) 2787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result is now guaranteed to be inexact (the true 2789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # mathematical result is transcendental). There's no need to 2790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Rounded and Inexact here---they'll always be raised as 2791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a result of the call to _fix. 2792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self.adjusted() 2794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we only need to do any computation for quite a small range 2796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of adjusted exponents---for example, -29 <= adj <= 10 for 2797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the default context. For smaller exponent the result is 2798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # indistinguishable from 1 at the given precision, while for 2799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # larger exponent the result either overflows or underflows. 2800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 0 and adj > len(str((context.Emax+1)*3)): 2801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow 280272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Emax+1) 2803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): 2804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # underflow to 0 280572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Etiny()-1) 2806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 0 and adj < -p: 2807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 280872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) 2809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj < -p-1: 2810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 281172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '9'*(p+1), -p-1) 2812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # general case 2813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.sign == 1: 2817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = -c 2818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: increase precision by 2820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 3 digits at a time until we get an unambiguously 2821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # roundable result 2822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(c, e, p+extra) 2825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 282972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(coeff), exp) 2830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # at this stage, ans should round correctly with *any* 2832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode, not just with ROUND_HALF_EVEN 2833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self): 28411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is canonical; otherwise return False. 28421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 28431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 28441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 28451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """ 28461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return True 2847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self): 28491a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is finite; otherwise return False. 2850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 28511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 28521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 2853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 28541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return not self._is_special 2855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self): 28571a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is infinite; otherwise return False.""" 28581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'F' 2859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self): 28611a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a qNaN or sNaN; otherwise return False.""" 28621a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp in ('n', 'N') 2863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, context=None): 28651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a normal number; otherwise return False.""" 28661a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 28671a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 28701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return context.Emin <= self.adjusted() <= context.Emax 2871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self): 28731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a quiet NaN; otherwise return False.""" 28741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'n' 2875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self): 28771a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is negative; otherwise return False.""" 28781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._sign == 1 2879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self): 28811a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a signaling NaN; otherwise return False.""" 28821a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'N' 2883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, context=None): 28851a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is subnormal; otherwise return False.""" 28861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 28871a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 28901a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self.adjusted() < context.Emin 2891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self): 28931a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a zero; otherwise return False.""" 289472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return not self._is_special and self._int == '0' 2895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _ln_exp_bound(self): 2897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.ln(). 2898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, compute r such that self.ln() >= 10**r. Assumes 2899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that self is finite and positive and that self != 1. 2900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 2903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) 2906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj*23//10)) - 1 2907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument <= 0.1 2909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str((-1-adj)*23//10)) - 1 2910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(c) 2916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) 2917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return e + len(str(10**-e - c)) - 1 2919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, context=None): 2922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of self.""" 2923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(NaN) = NaN 2928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(0.0) == -Infinity 2933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(Infinity) = Infinity 2937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(1.0) == 0.0 2941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(negative) raises InvalidOperation 2945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ln of a negative value') 2948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision by 3 2955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until we get an unambiguously roundable result 2956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p - self._ln_exp_bound() + 2 # at least p+3 places 2957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog(c, e, places) 2959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 296372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _log10_exp_bound(self): 2972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.log10(). 2973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, find r such that self.log10() >= 10**r. 2974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that self is finite and positive and that self != 1. 2975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # For x >= 10 or x < 0.1 we only need a bound on the integer 2978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # part of log10(self), and this comes directly from the 2979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent of x. For 0.1 <= x <= 10 we use the inequalities 2980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > 2981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 2982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self >= 10 2986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj))-1 2987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self < 0.1 2989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(-1-adj))-1 2990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(231*c) 2996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) + 2 2997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(10**-e-c) 2999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) + e - (num < "231") - 1 3000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, context=None): 3002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of self.""" 3003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(NaN) = NaN 3008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(0.0) == -Infinity 3013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 3014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 3015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(Infinity) = Infinity 3017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(negative or -Infinity) raises InvalidOperation 3021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 3022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 3023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'log10 of a negative value') 3024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(10**n) = n 302672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): 3027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # answer may need rounding 3028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self._exp + len(self._int) - 1) 3029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 3031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 3032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 3033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 3034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision 3036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until result is unambiguously roundable 3037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p-self._log10_exp_bound()+2 3038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 3039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog10(c, e, places) 3040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 3041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 3042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 3043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 304472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 3045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 3047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 3048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 3049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 3050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, context=None): 3053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of self's MSD. 3054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 3056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of self (as though it were truncated 3057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to a single digit while maintaining the value of that digit and 3058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista without limiting the resulting exponent). 3059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(NaN) = NaN 3061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(+/-Inf) = +Inf 3069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 3070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(0) = -Inf, DivisionByZero 3073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 3074cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'logb(0)', 1) 3075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # otherwise, simply return the adjusted exponent of self, as a 3077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal. Note that no attempt is made to fit the result 3078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # into the current context. 3079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.adjusted()) 3080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _islogical(self): 3082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return True if self is a logical operand. 3083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3084c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling For being logical, it must be a finite number with a sign of 0, 3085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an exponent of 0, and a coefficient whose digits must all be 3086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista either 0 or 1. 3087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign != 0 or self._exp != 0: 3089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for dig in self._int: 309172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if dig not in '01': 3092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 3093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 3094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fill_logical(self, context, opa, opb): 3096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opa) 3097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 309872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opa = '0'*dif + opa 3099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opa = opa[-context.prec:] 3101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opb) 3102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 310372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opb = '0'*dif + opb 3104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opb = opb[-context.prec:] 3106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return opa, opb 3107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, other, context=None): 3109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'and' operation between self and other's digits.""" 3110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 311972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) 312072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, context=None): 3123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all its digits.""" 3124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 312672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), 312772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, other, context=None): 3130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'or' operation between self and other's digits.""" 3131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 314072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb)) 314172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, other, context=None): 3144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'xor' operation between self and other's digits.""" 3145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 315472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb)) 315572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, other, context=None): 3158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31616c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 31626c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 31636c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 31716c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 31736c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31762fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3185e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, other, context=None): 3188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 31916c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 31926c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 31936c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 32016c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 32036c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32062fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson c = self.copy_abs()._cmp(other.copy_abs()) 3207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3215e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, context=None): 3218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller 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 negInf 3228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 322972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '9'*context.prec, context.Etop()) 3230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_FLOOR) 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.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), 323872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, context=None): 3241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than itself.""" 3242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 325272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, '9'*context.prec, context.Etop()) 3253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_CEILING) 3256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 326072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), 326172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, other, context=None): 3264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to self, in the direction towards other. 3265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number to self 3267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (excluding self) that is in the direction towards other, 3268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unless both have the same value. If the two operands are 3269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista numerically equal, then the result is a copy of self with the 3270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign set to be the same as the sign of other. 3271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 32812fc9263df56d28a6c1def6c8a0517bbddfa899afMark Dickinson comparison = self._cmp(other) 3282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == 0: 328372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.copy_sign(other) 3284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == -1: 3286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_plus(context) 3287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # comparison == 1 3288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_minus(context) 3289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decide which flags to raise using value of ans 3291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._isinfinity(): 3292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Overflow, 3293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'Infinite result from next_toward', 3294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans._sign) 3295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif ans.adjusted() < context.Emin: 3298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 3299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 3300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if precision == 1 then we don't raise Clamped for a 3303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result 0E-Etiny. 3304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 3305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 3306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, context=None): 3310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of self. 3311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 33130f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista sNaN 33140f5e7bf3049408d6f4c1855807204c9f13ae98f9Facundo Batista NaN 3315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 3316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 3317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 3318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 3319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 3320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 3321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 3322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 3323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_snan(): 3325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "sNaN" 3326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_qnan(): 3327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "NaN" 3328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista inf = self._isinfinity() 3329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == 1: 3330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Infinity" 3331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == -1: 3332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Infinity" 3333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_zero(): 3334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Zero" 3336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Zero" 3338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_subnormal(context=context): 3341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Subnormal" 3343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Subnormal" 3345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # just a normal, regular, boring number, :) 3346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Normal" 3348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Normal" 3350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 3352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :)""" 3353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 3354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, other, context=None): 3356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of self, value-of-other times.""" 3357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33706c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 337772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's rotate! 3380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[torot:] + rotdig[:torot] 338172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 338272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, other, context=None): 3385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self operand after adding the second value to its exp.""" 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 liminf = -2 * (context.Emax + context.prec) 3396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista limsup = 2 * (context.Emax + context.prec) 3397353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (liminf <= int(other) <= limsup): 3398353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 34016c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 340372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) 3404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista d = d._fix(context) 3405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return d 3406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, other, context=None): 3408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of self, value-of-other times.""" 3409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 34226c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not torot: 34276c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 343172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3432353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's shift! 3434353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if torot < 0: 3435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[:torot] 3436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 343772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated = rotdig + '0'*torot 3438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotated[-context.prec:] 3439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 344072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 344172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 344359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Support for pickling, copy, and deepcopy 34447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 34457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 34467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 34487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3449cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # I'm immutable; therefore I am my own clone 34507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 34537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3454cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # My components are also immutable 34557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 34567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34571ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # PEP 3101 support. See also _parse_format_specifier and _format_align 34581ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson def __format__(self, specifier, context=None): 3459f4da77765f8581e31620e9f49c68028e57b0ae85Mark Dickinson """Format a Decimal instance according to the given specifier. 34601ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34611ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson The specifier should be a standard format specifier, with the 34621ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson form described in PEP 3101. Formatting types 'e', 'E', 'f', 34631ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 'F', 'g', 'G', and '%' are supported. If the formatting type 34641ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson is omitted it defaults to 'g' or 'G', depending on the value 34651ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson of context.capitals. 34661ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34671ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson At this time the 'n' format specifier type (which is supposed 34681ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson to use the current locale) is not supported. 34691ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 34701ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34711ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # Note: PEP 3101 says that if the type is not present then 34721ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # there should be at least one digit after the decimal point. 34731ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # We take the liberty of ignoring this requirement for 34741ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # Decimal---it's presumably there to make sure that 34751ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # format(float, '') behaves similarly to str(float). 34761ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if context is None: 34771ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson context = getcontext() 34781ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34791ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson spec = _parse_format_specifier(specifier) 34801ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34811ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # special values don't care about the type or precision... 34821ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._is_special: 34831ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return _format_align(str(self), spec) 34841ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34851ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # a type of None defaults to 'g' or 'G', depending on context 34861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # if type is '%', adjust exponent of self accordingly 34871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] is None: 34881ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson spec['type'] = ['g', 'G'][context.capitals] 34891ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] == '%': 34901ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = _dec_from_triple(self._sign, self._int, self._exp+2) 34911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 34921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # round if necessary, taking rounding mode from the context 34931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson rounding = context.rounding 34941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson precision = spec['precision'] 34951ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if precision is not None: 34961ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] in 'eE': 34971ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._round(precision+1, rounding) 34981ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'gG': 34991ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if len(self._int) > precision: 35001ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._round(precision, rounding) 35011ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'fF%': 35021ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._rescale(-precision, rounding) 35031ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # special case: zeros with a positive exponent can't be 35041ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # represented in fixed point; rescale them to 0e0. 35051ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif not self and self._exp > 0 and spec['type'] in 'fF%': 35061ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson self = self._rescale(0, rounding) 35071ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35081ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out placement of the decimal point 35091ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson leftdigits = self._exp + len(self._int) 35101ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec['type'] in 'fF%': 35111ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = leftdigits 35121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'eE': 35131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if not self and precision is not None: 35141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 - precision 35151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 35171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] in 'gG': 35181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._exp <= 0 and leftdigits > -6: 35191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = leftdigits 35201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson dotplace = 1 35221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out main part of numeric string... 35241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if dotplace <= 0: 35251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = '0.' + '0'*(-dotplace) + self._int 35261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif dotplace >= len(self._int): 35271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # make sure we're not padding a '0' with extra zeros on the right 35281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson assert dotplace==len(self._int) or self._int != '0' 35291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = self._int + '0'*(dotplace-len(self._int)) 35301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 35311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = self._int[:dotplace] + '.' + self._int[dotplace:] 35321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35331ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # ...then the trailing exponent, or trailing '%' 35341ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if leftdigits != dotplace or spec['type'] in 'eE': 35351ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] 35361ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = num + "{0}{1:+}".format(echar, leftdigits-dotplace) 35371ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif spec['type'] == '%': 35381ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = num + '%' 35391ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35401ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # add sign 35411ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if self._sign == 1: 35421ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson num = '-' + num 35431ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return _format_align(num, spec) 35441ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 35451ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 354672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistadef _dec_from_triple(sign, coefficient, exponent, special=False): 354772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """Create a decimal instance directly, without any validation, 354872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista normalization (e.g. removal of leading zeros) or argument 354972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista conversion. 355072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 355172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista This function is for *internal use only*. 355272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """ 355372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 355472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = object.__new__(Decimal) 355572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._sign = sign 355672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = coefficient 355772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp = exponent 355872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._is_special = special 355972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 356072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self 356172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 356259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context class ####################################################### 3563cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 35647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3565cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# get rounding method function: 356659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batistarounding_functions = [name for name in Decimal.__dict__.keys() 356759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if name.startswith('_round_')] 35687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 356959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 35707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 35717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 35727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 35737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 35757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3576ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlanclass _ContextManager(object): 35778b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Context manager class to support localcontext(). 35781a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 3579ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan Sets a copy of the supplied context in __enter__() and restores 35808b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan the previous decimal context in __exit__() 35818b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 35821a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 3583ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan self.new_context = new_context.copy() 35841a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 35851a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 35861a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 35871a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 35881a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 35891a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 35901a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 35917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 35927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 35937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 35957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 359659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista rounding - rounding type (how you round) 3597bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 35987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 35997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 36007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 36017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 36027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 36030ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 36040ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 36057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 36067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 3607e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 36087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 36107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 3611abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 36120ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 3613e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 3614abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 3615abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 3616abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 3617abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 3618abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 3619bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 3620fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 3621b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 3622bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 3623fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 3624b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 36257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 36267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 3627eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 36287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 36297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 36307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 36317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3632b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 3633bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 3634b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 363559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' 363659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' 363759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista % vars(self)) 363859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [f.__name__ for f, v in self.flags.items() if v] 363959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('flags=[' + ', '.join(names) + ']') 364059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [t.__name__ for t, v in self.traps.items() if v] 364159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('traps=[' + ', '.join(names) + ']') 3642b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 3643b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 3644d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 3645d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 3646d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 3647b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 3648d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 36499fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 36509fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 3651e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista nc = Context(self.prec, self.rounding, self.traps, 3652e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags, self.Emin, self.Emax, 3653e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 36547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 36559fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 36569fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 36579fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 365859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista nc = Context(self.prec, self.rounding, self.traps.copy(), 3659e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags.copy(), self.Emin, self.Emax, 3660e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 36619fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 36629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 36637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36645aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 36657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 36667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 36687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 36697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 36707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 36717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36725aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 36737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 367459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Don't touch the flag 36757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 36767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 3678bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 367959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # The errors define how to handle themselves. 36805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 36817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 368359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # self._ignored_flags = [] 36847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 36857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 36877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 3688fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 36897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 36917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 36927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 36937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 36947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 36957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 36967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 36987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 36997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 37007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 37017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 37027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 37037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37045aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 37055aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 37065aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 370759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise TypeError("Cannot hash a Context.") 37085aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 37097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 37107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 37117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 37127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 3714e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 37157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 37167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 37187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 37197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 37217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 37227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 37247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 37257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 37267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 37277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 37287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 37297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 37317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 37337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 37347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 37357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3736fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 373759bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson """Creates a new Decimal instance but using self as context. 373859bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 373959bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson This method implements the to-number operation of the 374059bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson IBM Decimal specification.""" 374159bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 374259bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson if isinstance(num, basestring) and num != num.strip(): 374359bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson return self._raise_error(ConversionSyntax, 374459bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "no trailing or leading whitespace is " 374559bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson "permitted.") 374659bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson 37477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 3748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if d._isnan() and len(d._int) > self.prec - self._clamp: 3749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._raise_error(ConversionSyntax, 3750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista "diagnostic info too long in NaN") 3751dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 37527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 375359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Methods 37547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 37557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 37567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 375859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation on the operand. Otherwise, the result is the same as using 37597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 37607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 3762abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 37639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 3764abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 37659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 3766abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 37679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 3768abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 37697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 37717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 37737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 37747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 3776abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('19.00') 37779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 3778abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.02E+4') 37797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 37817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 3783dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 37847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, a): 3786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 3787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 3789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 3790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.canonical(Decimal('2.50')) 3792abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.50') 3793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.canonical(context=self) 3795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 37967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 37977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 37987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 38007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 38017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 38027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 38037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 38047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 38067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 38077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 38087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 38097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 3811abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 38129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 3813abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 38149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 3815abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 38169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 3817abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 38189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 3819abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 38209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 3821abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 38227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 38237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 38247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, a, b): 3826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values of the two operands numerically. 3827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 3829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 3830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext 3832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('3')) 3833abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) 3835abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) 3840abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) 3847abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 3848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_signal(b, context=self) 3852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, a, b): 3854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation. 3855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 3857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 3858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 3859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) 3861abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) 3863abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) 3865abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) 3867abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) 3869abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 3870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) 3871abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 3872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total(b) 3874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, a, b): 3876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation ignoring sign. 3877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 3879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total_mag(b) 3881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self, a): 3883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign set to 0. 3884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('2.1')) 3886abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('-100')) 3888abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 3889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_abs() 3891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_decimal(self, a): 3893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the decimal objet. 3894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('2.1')) 3896abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 3897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('-1.00')) 3898abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00') 3899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 39006c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(a) 3901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self, a): 3903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign inverted. 3904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('101.5')) 3906abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-101.5') 3907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('-101.5')) 3908abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('101.5') 3909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_negate() 3911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, a, b): 3913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Copies the second operand's sign to the first one. 3914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In detail, it returns a copy of the first operand with the sign 3916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista equal to the sign of the second operand. 3917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) 3919abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) 3921abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.50') 3922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) 3923abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) 3925abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.50') 3926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_sign(b) 3928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 39297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 39307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 39317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 3933abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.333333333') 39349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 3935abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.666666667') 39369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 3937abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.5') 39389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 3939abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 39409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 3941abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 39429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 3943abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.00') 39449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 3945abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20') 39469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 3947abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 39489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 3949abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 39509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 3951abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.20E+6') 39527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 39537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 39547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 39567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 39577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 3959abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 39609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 3961abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 39629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 3963abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 39647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 39657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 39667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 39677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 39687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 39697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, a): 3971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** a. 3972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-Infinity')) 3977abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 3978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-1')) 3979abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.367879441') 3980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0')) 3981abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 3982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('1')) 3983abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.71828183') 3984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0.693147181')) 3985abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 3986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('+Infinity')) 3987abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 3988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.exp(context=self) 3990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, a, b, c): 3992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a multiplied by b, plus c. 3993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The first two operands are multiplied together, using multiply, 3995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the third operand is then added to the result of that 3996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplication, using add, all with only one final rounding. 3997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) 3999abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('22') 4000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) 4001abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 4002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) 4003abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.38435736E+12') 4004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.fma(b, c, context=self) 4006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self, a): 40081a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is canonical; otherwise return False. 40091a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 40101a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 40111a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 4012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_canonical(Decimal('2.50')) 40141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 40161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return a.is_canonical() 4017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self, a): 40191a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is finite; otherwise return False. 4020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 40211a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 40221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 4023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('2.50')) 40251a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('-0.3')) 40271a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('0')) 40291a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('Inf')) 40311a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('NaN')) 40331a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_finite() 4036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self, a): 40381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is infinite; otherwise return False. 4039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('2.50')) 40411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('-Inf')) 40431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('NaN')) 40451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_infinite() 4048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self, a): 40501a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a qNaN or sNaN; 40511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('2.50')) 40541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('NaN')) 40561a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('-sNaN')) 40581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_nan() 4061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, a): 40631a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a normal number; 40641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('2.50')) 40701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.1E-999')) 40721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.00')) 40741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('-Inf')) 40761a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('NaN')) 40781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_normal(context=self) 4081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self, a): 40831a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a quiet NaN; otherwise return False. 4084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('2.50')) 40861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('NaN')) 40881a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('sNaN')) 40901a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_qnan() 4093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self, a): 40951a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is negative; otherwise return False. 4096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('2.50')) 40981a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-12')) 41001a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-0')) 41021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_signed() 4105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self, a): 41071a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a signaling NaN; 41081a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 4109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('2.50')) 41111a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('NaN')) 41131a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('sNaN')) 41151a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_snan() 4118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, a): 41201a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is subnormal; otherwise return False. 4121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('2.50')) 41261a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.1E-999')) 41281a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.00')) 41301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('-Inf')) 41321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('NaN')) 41341a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_subnormal(context=self) 4137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self, a): 41391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a zero; otherwise return False. 4140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('0')) 41421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('2.50')) 41441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 4145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('-0E+2')) 41461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 4147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_zero() 4149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, a): 4151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of the operand. 4152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('0')) 4157abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('1.000')) 4159abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('2.71828183')) 4161abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000000') 4162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('10')) 4163abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.30258509') 4164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('+Infinity')) 4165abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.ln(context=self) 4168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, a): 4170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of the operand. 4171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0')) 4176abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0.001')) 4178abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-3') 4179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('1.000')) 4180abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('2')) 4182abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.301029996') 4183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('10')) 4184abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('70')) 4186abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.84509804') 4187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('+Infinity')) 4188abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.log10(context=self) 4191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, a): 4193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of the operand's MSD. 4194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 4196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of the operand (as though the 4197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand were truncated to a single digit while maintaining the 4198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value of that digit and without limiting the resulting exponent). 4199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('250')) 4201abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('2.50')) 4203abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0.03')) 4205abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 4206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0')) 4207abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logb(context=self) 4210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, a, b): 4212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'and' between each operand's digits. 4213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) 4217abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) 4219abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) 4221abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) 4223abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) 4225abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1000') 4226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) 4227abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_and(b, context=self) 4230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, a): 4232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all the digits in the operand. 4233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operand must be a logical number. 4235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('0')) 4237abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111111') 4238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('1')) 4239abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('111111110') 4240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('111111111')) 4241abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('101010101')) 4243abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10101010') 4244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_invert(context=self) 4246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, a, b): 4248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'or' between each operand's digits. 4249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) 4253abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) 4255abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) 4257abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) 4259abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) 4261abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) 4263abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1110') 4264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_or(b, context=self) 4266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, a, b): 4268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'xor' between each operand's digits. 4269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) 4273abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) 4275abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) 4277abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) 4279abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) 4281abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('110') 4282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) 4283abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1101') 4284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_xor(b, context=self) 4286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 42877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 42887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 42897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4291c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 429259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 429359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the maximum (closer to positive 42947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 42957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 4297abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 42989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 4299abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3') 43009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 4301abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4302d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 4303abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 43047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 43067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, a, b): 4308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.max_mag(b, context=self) 4310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 43127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 43137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 4315c8acc882a92c1fe5df95ae73b7b8004737ed9222Andrew M. Kuchling Otherwise, the operands are compared as though by the compare 431659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 431759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the minimum (closer to negative 43187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 43197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 4321abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 43229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 4323abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-10') 43249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 4325abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 4326d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 4327abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7') 43287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 43307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, a, b): 4332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.min_mag(b, context=self) 4334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 43367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 43377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 43397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 43407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 43417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 4343abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 43449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 4345abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 43467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 43487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 43507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 43517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4352cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis If either operand is a special value then the general rules apply. 4353cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Otherwise, the operands are multiplied together ('long multiplication'), 4354cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis resulting in a number which may be as long as the sum of the lengths 4355cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis of the two operands. 43567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 4358abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.60') 43599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 4360abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('21') 43619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 4362abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.72') 43639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 4364abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.0') 43659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 4366abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('4.28135971E+11') 43677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 43697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, a): 4371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than a. 4372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('1')) 4377abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('1E-1007')) 4379abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('-1.00000003')) 4381abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('Infinity')) 4383abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('9.99999999E+999') 4384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_minus(context=self) 4386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, a): 4388353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than a. 4389353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('1')) 4394abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-1E-1007')) 4396abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4397353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('-1.00000003')) 4398abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-Infinity')) 4400abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-9.99999999E+999') 4401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_plus(context=self) 4403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, a, b): 4405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to a, in direction towards b. 4406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number from the first 4408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand (but not the first operand) that is in the direction 4409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista towards the second operand, unless the operands have the same 4410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. 4411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('2')) 4416abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.00000001') 4417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) 4418abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E-1007') 4419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) 4420abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000002') 4421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('0')) 4422abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.999999999') 4423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) 4424abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E-1007') 4425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) 4426abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.00000004') 4427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) 4428abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.00') 4429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_toward(b, context=self) 4431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 44327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 4433e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 44347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 44367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 44377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 4439abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 44409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 4441abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 44429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 4443abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2') 44449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 4445abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.2E+2') 44469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 4447abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.2E+2') 44489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 4449abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 44507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 44527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4453353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, a): 4454353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of the operand. 4455353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4456353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 4457353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 4458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 4459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 4460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 4461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 4462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 4463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 4464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 4465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 4466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 4467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = Context(ExtendedContext) 4469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('Infinity')) 4472353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Infinity' 4473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('1E-10')) 4474353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('2.50')) 4476353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4477353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0.1E-999')) 4478353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Subnormal' 4479353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0')) 4480353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Zero' 4481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0')) 4482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Zero' 4483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0.1E-999')) 4484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Subnormal' 4485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-1E-10')) 4486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-2.50')) 4488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-Infinity')) 4490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Infinity' 4491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('NaN')) 4492353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4493353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-NaN')) 4494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('sNaN')) 4496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'sNaN' 4497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.number_class(context=self) 4499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 45017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 45027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 45047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 45057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 45067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 4508abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.3') 45099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 4510abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1.3') 45117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 45137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 45157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 45167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute a**b. If a is negative then b 4518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista must be integral. The result will be inexact unless b is 4519353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integral and the result is finite and can be expressed exactly 4520353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in 'precision' digits. 4521353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (a**b) % modulo. For the 4523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 4524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 4525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 4527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - b must be nonnegative 4528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - at least one of a or b must be nonzero 4529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and have at most 'precision' digits 4530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(a, b, modulo) is identical to the result 4532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that would be obtained by computing (a**b) % modulo with 4533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unbounded precision, but is computed more efficiently. It is 4534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista always exact. 4535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('3')) 4540abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('8') 4541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-2'), Decimal('3')) 4542abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-8') 4543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('-3')) 4544abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.125') 4545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('1.7'), Decimal('8')) 4546abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('69.7575744') 4547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('10'), Decimal('0.301029996')) 4548abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.00000000') 4549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('-1')) 4550abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('0')) 4552abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4553353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('1')) 4554abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('-1')) 4556abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4557353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('0')) 4558abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('1')) 4560abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('2')) 4562abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('Infinity') 4563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('0'), Decimal('0')) 4564abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 4565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) 4567abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) 4569abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-11') 4570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) 4571abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 4572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) 4573abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11') 4574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) 4575abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('11729830') 4576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) 4577abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 4578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) 4579abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 45807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 45827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 458459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Returns a value equal to 'a' (rounded), having the exponent of 'b'. 45857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 458759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operand. It may be rounded using the current rounding setting (if the 45887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 45897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 45907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 45917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 45937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 459459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation condition is raised. This guarantees that, unless there is 459559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista an error condition, the exponent of the result of a quantize is always 45967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 45977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 45997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 46007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 4602abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.170') 46039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 4604abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.17') 46059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 4606abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2') 46079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 4608abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 46099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 4610abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0E+1') 46119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 4612abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 46139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 4614abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 4616abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 46179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 4618abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0E+5') 46199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 4620abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 4622abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('NaN') 46239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 4624abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217.0') 46259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 4626abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('217') 46279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 4628abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.2E+2') 46299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 4630abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2E+2') 46317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 46337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 4635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :) 4636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.radix() 4638abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 4639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 4641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 46427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 46437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 46447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 464659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista calculating integer division as described for divide-integer, rounded 46470d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz to precision digits if necessary. The sign of the result, if 464859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista non-zero, is the same as that of the original dividend. 46497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 46517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 46527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 46537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 4655abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.1') 46569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 4657abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 46589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 4659abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 46609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 4661abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 46629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 4663abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 46649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 4665abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 46667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 46687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 46707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 46717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 467259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen). If the result is equal to 0 then its sign will be the 46737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 46747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 46767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 46777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 46787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 4680abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.9') 46819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 4682abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-2') 46839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 4684abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 46859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 4686abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-1') 46879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 4688abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.2') 46899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 4690abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.1') 46919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 4692abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.3') 46937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 46957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, a, b): 4697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of a, b times. 4698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a rotated copy of the digits in 4700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the coefficient of the first operand. The number of places of 4701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotation is taken from the absolute value of the second operand, 4702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the rotation being to the left if the second operand is 4703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. 4704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) 4706abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000003') 4707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) 4708abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('12') 4709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) 4710abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('891234567') 4711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) 4712abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) 4714abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678912') 4715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.rotate(b, context=self) 4717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 47187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 47197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 47207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 47227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 47237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 47257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 47269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 47277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 47289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 47297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 47309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 47317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 47327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 47347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, a, b): 4736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the first operand after adding the second value its exp. 4737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) 4739abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.0750') 4740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) 4741abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50') 4742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) 4743abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.50E+3') 4744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.scaleb (b, context=self) 4746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, a, b): 4748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of a, b times. 4749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a shifted copy of the digits 4751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the coefficient of the first operand. The number of places 4752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to shift is taken from the absolute value of the second operand, 4753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the shift being to the left if the second operand is 4754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. Digits shifted into the 4755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coefficient are zeros. 4756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) 4758abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('400000000') 4759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) 4760abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 4761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) 4762abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1234567') 4763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) 4764abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('123456789') 4765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) 4766abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('345678900') 4767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.shift(b, context=self) 4769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 47707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 477159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Square root of a non-negative number to context precision. 47727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 47747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 47757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 4777abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0') 47789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 4779abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0') 47809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 4781abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.624499800') 47829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 4783abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('10') 47849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 4785abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1') 47869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 4787abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 47889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 4789abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0') 47909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 4791abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2.64575131') 47929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 4793abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('3.16227766') 47949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 47956ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 47967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 47977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 47987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 4800f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 48017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 4803abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.23') 48049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 4805abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('0.00') 48069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 4807abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-0.77') 48087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 48107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 48127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 48137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 48157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 48177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 48197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 48207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 48227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 48237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 48247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, a): 4826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to an integer. 4827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista When the operand has a negative exponent, the result is the same 4829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista as using the quantize() operation using the given operand as the 4830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista left-hand-operand, 1E+0 as the right-hand-operand, and the precision 4831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the operand as the precision setting; Inexact and Rounded flags 4832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista are allowed in this operation. The rounding mode is taken from the 4833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 4834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('2.1')) 4836abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100')) 4838abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100.0')) 4840abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('101.5')) 4842abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) 4844abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) 4846abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) 4848abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) 4850abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 4851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_exact(context=self) 4853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, a): 48557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 48567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 48587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 48597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 48607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 486159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be set. The rounding mode is taken from the context. 48627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('2.1')) 4864abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('2') 4865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100')) 4866abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100.0')) 4868abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('100') 4869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('101.5')) 4870abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('102') 4871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-101.5')) 4872abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-102') 4873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('10E+5')) 4874abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('1.0E+6') 4875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) 4876abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('7.89E+77') 4877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-Inf')) 4878abe32371878dcaea31c835e10144fdaa2eca6492Raymond Hettinger Decimal('-Infinity') 48797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_value(context=self) 4881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 4883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 48847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 48867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 488717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 4888636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 48897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 48907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 48917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 48927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 48937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 4894636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 48957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 489617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 489717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 489872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self.int = int(value._int) 48997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 490017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 490117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 49027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 49037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 49047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 49057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 49077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 49087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 49107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4913e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batistadef _normalize(op1, op2, prec = 0): 49147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 49157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 49167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 49177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp < op2.exp: 49197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 49207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 49217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 49227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 49237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 49247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). 4926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then adding 10**exp to tmp has the same effect (after rounding) 4927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as adding any positive quantity smaller than 10**exp; similarly 4928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for subtraction. So if other is smaller than 10**exp we replace 4929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # it with 10**exp. This avoids tmp.exp - other.exp getting too large. 4930e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista tmp_len = len(str(tmp.int)) 4931e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other_len = len(str(other.int)) 4932e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista exp = tmp.exp + min(-1, tmp_len - prec - 2) 4933e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if other_len + other.exp - 1 < exp: 4934e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.int = 1 4935e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.exp = exp 4936636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 4937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.int *= 10 ** (tmp.exp - other.exp) 4938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.exp = other.exp 49397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 49407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### 4942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# This function from Tim Peters was taken from here: 4944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# http://mail.python.org/pipermail/python-list/1999-July/007758.html 4945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# The correction being in the function definition is for speed, and 4946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the whole function is not resolved with math.log because of avoiding 4947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the use of floats. 4948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _nbits(n, correction = { 4949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0': 4, '1': 3, '2': 2, '3': 2, 4950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '4': 1, '5': 1, '6': 1, '7': 1, 4951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '8': 0, '9': 0, 'a': 0, 'b': 0, 4952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'c': 0, 'd': 0, 'e': 0, 'f': 0}): 4953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Number of bits in binary representation of the positive integer n, 4954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or 0 if n == 0. 4955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n < 0: 4957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _nbits should be nonnegative.") 4958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista hex_n = "%x" % n 4959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 4*len(hex_n) - correction[hex_n[0]] 4960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _sqrt_nearest(n, a): 4962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to the square root of the positive integer n. a is 4963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an initial approximation to the square root. Any positive integer 4964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista will do for a, but the closer a is to the square root of n the 4965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista faster convergence will be. 4966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= 0 or a <= 0: 4969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("Both arguments to _sqrt_nearest should be positive.") 4970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b=0 4972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while a != b: 4973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, a = a, a--n//a>>1 4974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a 4975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _rshift_nearest(x, shift): 4977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given an integer x and a nonnegative integer shift, return closest 4978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integer to x / 2**shift; use round-to-even in case of a tie. 4979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, q = 1L << shift, x >> shift 4982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*(x & (b-1)) + (q&1) > b) 4983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _div_nearest(a, b): 4985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to a/b, a and b positive integers; rounds to even 4986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the case of a tie. 4987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(a, b) 4990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*r + (q&1) > b) 4991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _ilog(x, M, L = 8): 4993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Integer approximation to M*log(x/M), with absolute error boundable 4994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in terms only of x/M. 4995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given positive integers x and M, return an integer approximation to 4997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference 4998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista between the approximation and the exact result is at most 22. For 4999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In 5000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista both cases these are upper bounds on the error; it will usually be 5001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista much smaller.""" 5002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The basic algorithm is the following: let log1p be the function 5004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use 5005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the reduction 5006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) 5008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # repeatedly until the argument to log1p is small (< 2**-L in 5010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # absolute value). For small y we can use the Taylor series 5011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expansion 5012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T 5014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # truncating at T such that y**T is small enough. The whole 5016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # computation is carried out in a form of fixed-point arithmetic, 5017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with a real number z being represented by an integer 5018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # approximation to z*M. To avoid loss of precision, the y below 5019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is actually an integer approximation to 2**R*y*M, where R is the 5020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number of reductions performed so far. 5021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = x-M 5023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument reduction; R = number of reductions performed 5024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = 0 5025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while (R <= L and long(abs(y)) << L-R >= M or 5026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R > L and abs(y) >> R-L >= M): 5027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(long(M*y) << 1, 5028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) 5029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R += 1 5030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series with T terms 5032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yshift = _rshift_nearest(y, R) 5034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, T) 5035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(T-1, 0, -1): 5036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, k) - _div_nearest(yshift*w, M) 5037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(w*y, M) 5039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog10(c, e, p): 5041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, p >= 0, compute an integer 5042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log10(c*10**e), with an absolute error of 5043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 5044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # increase precision by 2; compensate for this by dividing 5046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # final result by 100 5047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write c*10**e as d*10**f with either: 5050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f >= 0 and 1 <= d <= 10, or 5051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f <= 0 and 0.1 <= d <= 1. 5052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Thus for c*10**e close to 1, f = 0 5053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 5054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 5055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 5057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M = 10**p 5058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 5059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 5060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 5061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) 5063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, M) # error < 5 + 22 = 27 5065be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista log_10 = _log10_digits(p) # error < 1 5066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _div_nearest(log_d*M, log_10) 5067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = f*M # exact 5068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 # error < 2.31 5070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = div_nearest(f, 10**-p) # error < 0.5 5071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(log_tenpower+log_d, 100) 5073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog(c, e, p): 5075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, compute an integer 5076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log(c*10**e), with an absolute error of 5077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 5078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Increase precision by 2. The precision increase is compensated 5080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for at the end with a division by 100. 5081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, 5084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) 5085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as 10**p * log(d) + 10**p*f * log(10). 5086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 5087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 5088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute approximation to 10**p*log(d), with error < 27 5090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 5091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 5092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 5093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 5094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) # error of <= 0.5 in c 5096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # _ilog magnifies existing error in c by a factor of at most 10 5098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 5099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p <= 0: just approximate the whole thing by 0; error < 2.31 5101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 5102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5103be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute approximation to f*10**p*log(10), with error < 11. 5104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if f: 5105be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = len(str(abs(f)))-1 5106be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p + extra >= 0: 5107be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in f * _log10_digits(p+extra) < |f| * 1 = |f| 5108be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 5109be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) 5110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 5114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5115be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 5116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(f_log_ten + log_d, 100) 5117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5118be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batistaclass _Log10Memoize(object): 5119be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Class to compute, store, and allow retrieval of, digits of the 5120be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista constant log(10) = 2.302585.... This constant is needed by 5121be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" 5122be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def __init__(self): 5123be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = "23025850929940456840179914546843642076011014886" 5124be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5125be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def getdigits(self, p): 5126be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Given an integer p >= 0, return floor(10**p)*log(10). 5127be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5128be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista For example, self.getdigits(3) returns 2302. 5129be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """ 5130be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits are stored as a string, for quick conversion to 5131be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # integer in the case that we've already computed enough 5132be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits; the stored digits should always be correct 5133be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # (truncated, not rounded to nearest). 5134be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p < 0: 5135be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista raise ValueError("p should be nonnegative") 5136be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5137be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p >= len(self.digits): 5138be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+3, p+6, p+9, ... digits; continue until at 5139be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # least one of the extra digits is nonzero 5140be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = 3 5141be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista while True: 5142be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+extra digits, correct to within 1ulp 5143be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista M = 10**(p+extra+2) 5144be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista digits = str(_div_nearest(_ilog(10*M, M), 100)) 5145be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if digits[-extra:] != '0'*extra: 5146be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista break 5147be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra += 3 5148be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # keep all reliable digits so far; remove trailing zeros 5149be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # and next nonzero digit 5150be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = digits.rstrip('0')[:-1] 5151be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista return int(self.digits[:p+1]) 5152be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5153be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista_log10_digits = _Log10Memoize().getdigits 5154be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 5155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _iexp(x, M, L=8): 5156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers x and M, M > 0, such that x/M is small in absolute 5157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value, compute an integer approximation to M*exp(x/M). For 0 <= 5158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x/M <= 2.4, the absolute error in the result is bounded by 60 (and 5159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista is usually much smaller).""" 5160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Algorithm: to compute exp(z) for a real number z, first divide z 5162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then 5163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor 5164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # series 5165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(x) = x + x**2/2! + x**3/3! + ... 5167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Now use the identity 5169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(2x) = expm1(x)*(expm1(x)+2) 5171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # R times to compute the sequence expm1(z/2**R), 5173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). 5174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find R such that x/2**R/M <= 2**-L 5176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = _nbits((long(x)<<L)//M) 5177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series. (2**L)**T > M 5179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x, T) 5181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<R 5182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(T-1, 0, -1): 5183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x*(Mshift + y), Mshift * i) 5184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Expansion 5186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(R-1, -1, -1): 5187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<(k+2) 5188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(y*(y+Mshift), Mshift) 5189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return M+y 5191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dexp(c, e, p): 5193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute an approximation to exp(c*10**e), with p decimal places of 5194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista precision. 5195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5196be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Returns integers d, f such that: 5197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= d <= 10**p, and 5199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (d-1)*10**f < exp(c*10**e) < (d+1)*10**f 5200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, d*10**f is an approximation to exp(c*10**e) with p 5202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision, and with an error in d of at most 1. This is 5203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when d 5204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista = 10**(p-1) the error could be up to 10 ulp.""" 5205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision 5207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5209be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute log(10) with extra precision = adjusted exponent of c*10**e 5210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = max(0, e + len(str(c)) - 1) 5211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = p + extra 5212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5213be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), 5214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding down 5215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = e+q 5216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c*10**shift 5218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c//10**-shift 5220be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista quot, rem = divmod(cshift, _log10_digits(q)) 5221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reduce remainder back to original precision 5223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rem = _div_nearest(rem, 10**extra) 5224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # error in result of _iexp < 120; error after division < 0.62 5226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 5227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dpower(xc, xe, yc, ye, p): 5229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and 5230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 5231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= c <= 10**p, and 5233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (c-1)*10**e < x**y < (c+1)*10**e 5234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in other words, c*10**e is an approximation to x**y with p digits 5236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of precision, and with an error in c of at most 1. (This is 5237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when c 5238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista == 10**(p-1) we can only guarantee error < 10ulp.) 5239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista We assume that: x is positive and not equal to 1, and y is nonzero. 5241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find b such that 10**(b-1) <= |y| <= 10**b 5244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b = len(str(abs(yc))) + ye 5245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point 5247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista lxc = _dlog(xc, xe, p+b+1) 5248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) 5250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = ye-b 5251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = lxc*yc*10**shift 5253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = _div_nearest(lxc*yc, 10**-shift) 5255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if pc == 0: 5257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we prefer a result that isn't exactly 1; this makes it 5258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # easier to compute a correctly rounded result in __pow__ 5259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: 5260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**(p-1)+1, 1-p 5261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**p-1, -p 5263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(pc, -(p+1), p+1) 5265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _div_nearest(coeff, 10) 5266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp += 1 5267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return coeff, exp 5269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _log10_lb(c, correction = { 5271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, 5272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '6': 23, '7': 16, '8': 10, '9': 5}): 5273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for 100*log10(c) for a positive integer c.""" 5274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c <= 0: 5275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _log10_lb should be nonnegative.") 5276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_c = str(c) 5277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 100*len(str_c) - correction[str_c[0]] 5278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 527959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Helper Functions #################################################### 52807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _convert_other(other, raiseit=False): 5282636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 5283636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5284636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5285636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 5286636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 5287636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 5288636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 5289636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 5290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if raiseit: 5291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise TypeError("Unable to convert %s to Decimal" % other) 5292267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 5293636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 529459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Setup Specific Contexts ############################################ 52957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 5297fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 52987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 53006ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 5301bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 5302bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 530399148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 530499148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 5305e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 53067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 53097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 53107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 53117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 53127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 53147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 5315bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 5316bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 53177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 53206ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 5321bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 5322bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 53237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 53247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 532659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### crud for parsing strings ############################################# 53276a123cb7827859748a0096570dfbb5ceba0e59dcMark Dickinson# 532872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Regular expression used for parsing numeric strings. Additional 532972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# comments: 533072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 533172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 1. Uncomment the two '\s*' lines to allow leading and/or trailing 533272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# whitespace. But note that the specification disallows whitespace in 533372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# a numeric string. 533472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 533572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 2. For finite numbers (not infinities and NaNs) the body of the 533672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# number between the optional sign and the optional exponent must have 533772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# at least one decimal digit, possibly after the decimal point. The 533872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# lookahead expression '(?=\d|\.\d)' checks this. 533972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 534072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# As the flag UNICODE is not enabled here, we're explicitly avoiding any 534172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# other meaning for \d than the numbers [0-9]. 53427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 534372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistaimport re 534472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista_parser = re.compile(r""" # A numeric string consists of: 53457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 534672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<sign>[-+])? # an optional sign, followed by either... 53477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 534872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?=\d|\.\d) # ...a number (with at least one digit) 534972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<int>\d*) # consisting of a (possibly empty) integer part 535072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (\.(?P<frac>\d*))? # followed by an optional fractional part 535172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... 53527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 535372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista Inf(inity)? # ...an infinity, or... 535472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista | 535572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<signal>s)? # ...an (optionally signaling) 535672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista NaN # NaN 535772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<diag>\d*) # with (possibly empty) diagnostic information. 53587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 53597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 536059bc20bb273055e2cd48a467524d21340c1771ccMark Dickinson \Z 536172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista""", re.VERBOSE | re.IGNORECASE).match 53627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53632ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_all_zeros = re.compile('0*$').match 53642ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_exact_half = re.compile('50*$').match 53651ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 53661ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson##### PEP3101 support functions ############################################## 53671ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# The functions parse_format_specifier and format_align have little to do 53681ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# with the Decimal class, and could potentially be reused for other pure 53691ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# Python numeric classes that want to implement __format__ 53701ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 53711ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# A format specifier for Decimal looks like: 53721ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 53731ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# [[fill]align][sign][0][minimumwidth][.precision][type] 53741ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson# 53751ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 53761ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson_parse_format_specifier_regex = re.compile(r"""\A 53771ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?: 53781ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson (?P<fill>.)? 53791ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson (?P<align>[<>=^]) 53801ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson)? 53811ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<sign>[-+ ])? 53821ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<zeropad>0)? 53831ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<minimumwidth>(?!0)\d+)? 53841ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?:\.(?P<precision>0|(?!0)\d+))? 53851ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson(?P<type>[eEfFgG%])? 53861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson\Z 53871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson""", re.VERBOSE) 53881ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 53897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 53907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinsondef _parse_format_specifier(format_spec): 53921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Parse and validate a format specifier. 53931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 53941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Turns a standard numeric format specifier into a dict, with the 53951ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson following entries: 53961ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 53971ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill: fill character to pad field to minimum width 53981ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align: alignment type, either '<', '>', '=' or '^' 53991ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign: either '+', '-' or ' ' 54001ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson minimumwidth: nonnegative integer giving minimum width 54011ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson precision: nonnegative integer giving precision, or None 54021ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson type: one of the characters 'eEfFgG%', or None 54031ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson unicode: either True or False (always True for Python 3.x) 54041ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54051ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 54061ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson m = _parse_format_specifier_regex.match(format_spec) 54071ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if m is None: 54081ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Invalid format specifier: " + format_spec) 54091ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54101ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # get the dictionary 54111ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict = m.groupdict() 54121ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54131ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # defaults for fill and alignment 54141ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = format_dict['fill'] 54151ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = format_dict['align'] 54161ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict.pop('zeropad') is not None: 54171ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # in the face of conflict, refuse the temptation to guess 54181ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if fill is not None and fill != '0': 54191ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Fill character conflicts with '0'" 54201ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson " in format specifier: " + format_spec) 54211ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if align is not None and align != '=': 54221ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson raise ValueError("Alignment conflicts with '0' in " 54231ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson "format specifier: " + format_spec) 54241ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = '0' 54251ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = '=' 54261ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['fill'] = fill or ' ' 54271ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['align'] = align or '<' 54281ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54291ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['sign'] is None: 54301ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['sign'] = '-' 54311ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54321ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # turn minimumwidth and precision entries into integers. 54331ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # minimumwidth defaults to 0; precision remains None if not given 54341ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') 54351ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['precision'] is not None: 54361ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['precision'] = int(format_dict['precision']) 54371ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54381ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # if format type is 'g' or 'G' then a precision of 0 makes little 54391ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # sense; convert it to 1. Same if format type is unspecified. 54401ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['precision'] == 0: 54411ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if format_dict['type'] in 'gG' or format_dict['type'] is None: 54421ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['precision'] = 1 54431ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54441ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # record whether return type should be str or unicode 54451ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson format_dict['unicode'] = isinstance(format_spec, unicode) 54461ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54471ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return format_dict 54481ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54491ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinsondef _format_align(body, spec_dict): 54501ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """Given an unpadded, non-aligned numeric string, add padding and 54511ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson aligment to conform with the given format specifier dictionary (as 54521ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson output from parse_format_specifier). 54531ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54541ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson It's assumed that if body is negative then it starts with '-'. 54551ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson Any leading sign ('-' or '+') is stripped from the body before 54561ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson applying the alignment and padding rules, and replaced in the 54571ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson appropriate position. 54581ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54591ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson """ 54601ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # figure out the sign; we only examine the first character, so if 54611ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # body has leading whitespace the results may be surprising. 54621ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if len(body) > 0 and body[0] in '-+': 54631ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = body[0] 54641ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson body = body[1:] 54651ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 54661ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = '' 54671ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54681ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if sign != '-': 54691ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec_dict['sign'] in ' +': 54701ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = spec_dict['sign'] 54711ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: 54721ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson sign = '' 54731ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54741ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # how much extra space do we have to play with? 54751ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson minimumwidth = spec_dict['minimumwidth'] 54761ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson fill = spec_dict['fill'] 54771ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson padding = fill*(max(minimumwidth - (len(sign+body)), 0)) 54781ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54791ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson align = spec_dict['align'] 54801ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if align == '<': 54811ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = padding + sign + body 54821ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif align == '>': 54831ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = sign + body + padding 54841ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson elif align == '=': 54851ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = sign + padding + body 54861ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson else: #align == '^' 54871ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson half = len(padding)//2 54881ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = padding[:half] + sign + body + padding[half:] 54891ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54901ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson # make sure that result is unicode if necessary 54911ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson if spec_dict['unicode']: 54921ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson result = unicode(result) 54931ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson 54941ddf1d8482f4fd8ae034bfd0221696ee2068c144Mark Dickinson return result 54950d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz 549672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista##### Useful Constants (internal use only) ################################ 54977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 549872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Reusable defaults 549972bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInf = Decimal('Inf') 550072bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistanegInf = Decimal('-Inf') 550172bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaNaN = Decimal('NaN') 550272bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_0 = Decimal(0) 550372bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p1 = Decimal(1) 550472bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n1 = Decimal(-1) 55057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 550672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Infsign[sign] is infinity w/ that sign 550772bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInfsign = (Inf, negInf) 55087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 55117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 55127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 55137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 5514