decimal.py revision e64acfad3dd13809943eecf50f11c40c510dedbe
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 387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond 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) 457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("0") 467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1") 477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1") 487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("-.0123") 497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("-0.0123") 507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(123456) 517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("123456") 527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("123.45e12345678901234567890") 537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1.2345E+12345678901234567892") 547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1.33") + Decimal("1.27") 557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("2.60") 567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41") 577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond 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)) 947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond 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 13959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Rounding 1400ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1410ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1420ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1430ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1440ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1450ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1460ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo BatistaROUND_05UP = 'ROUND_05UP' 1487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Errors 1507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1525aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 160cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis handle -- Called when context._raise_error is called and the 161cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis trap_enabler is set. First argument is self, second is the 162cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context. More arguments can be given, those being after 163cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis the explanation in _raise_error (For example, 164cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context._raise_error(NewError, '(-x)!', self._sign) would 165cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis call NewError().handle(context, self._sign).) 166cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 17959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista representation. This may occur when the exponent of a zero result would 18059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be outside the bounds of a representation, or when a large normal 18159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista number would have an encoded exponent that cannot be represented. In 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 19459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 0 * (+-)INF 19559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista (+-)INF / (+-)INF 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 1997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of the operation after these is a quiet positive NaN, 206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista except when the cause is a signaling NaN, in which case the result is 207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista also a quiet NaN, but with the original sign, and an optional 208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista diagnostic information. 2097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 21259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if args[0] == 1: # sNaN, must drop 's' but keep diagnostics 21372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(args[1]._sign, args[1]._int, 'n', True) 214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix_nan(context) 215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif args[0] == 2: 21672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(args[1], args[2], 'n', True) 2177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 22559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista syntax. The result is [0,qNaN]. 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 227cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis def handle(self, context, *args): 228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return NaN 2297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 242cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 243cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, sign, *args): 2447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 25159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista longer than precision). The result is [0,qNaN]. 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 253cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 255cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NaN 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 26259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the dividend is also zero. The result is [0,qNaN]. 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 264cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 265cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, *args): 2667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 27359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista were non-zero), or if an overflow or underflow condition occurs. The 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 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 """ 3065aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 31359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin, before any rounding). The result in all cases is unchanged. 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 33259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista where sign is the sign of the intermediate result. For round-down, the 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 33459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista current precision, with the sign of the intermediate result. For 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 33659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 33859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 340cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis """ 341cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 3427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ROUND_HALF_DOWN, ROUND_UP): 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 34972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 35472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 36459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin). That is, the result is both inexact and subnormal. 3657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 36759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista necessary, so that its exponent is not less than Etiny. This may result 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3735aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 374fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 375cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Underflow, InvalidOperation, Subnormal] 3767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3815aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context Functions ################################################## 3847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 385ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 386ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 387ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 3887e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# work for older Pythons. If threads are not part of the build, create a 389cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# mock threading object with threading.local() returning the module namespace. 3907e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger 3917e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingertry: 3927e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import threading 3937e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingerexcept ImportError: 3947e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger # Python was compiled without threads; create a mock object instead 3957e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import sys 39659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista class MockThreading(object): 3977e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger def local(self, sys=sys): 3987e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger return sys.modules[__name__] 3997e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger threading = MockThreading() 4007e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger del sys, MockThreading 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 404ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 405ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 406ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 40759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # To fix reloading, force it to create a new context 40859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Old contexts have different exceptions in their dicts, making problems. 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 414ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4159fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 41661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 435ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4369fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4379fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 441ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 445ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 446ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 450ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 451ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 452ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 453ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 454ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 455ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4569fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 45761992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 458ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 459ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 460cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis del threading, local # Don't contaminate the namespace 4617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4628b6999b4c5fab174090be263ba90f193bdede141Nick Coghlandef localcontext(ctx=None): 4638b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Return a context manager for a copy of the supplied context 4648b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4658b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan Uses a copy of the current context if no context is specified 4668b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan The returned context manager creates a local decimal context 4678b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan in a with statement: 4688b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4698b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext() as ctx: 4708b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ctx.prec += 2 4718b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4728b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses a precision 2 greater than normal 47359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal precision 4748b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4758b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4768b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext(ExtendedContext): 4778b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4788b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses the Extended Context from the 4798b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # General Decimal Arithmetic Specification 48059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal context 4818b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4828b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 483681d86743c21773bb00508dbacb05ed9012388d8Neal Norwitz # The string below can't be included in the docstring until Python 2.6 4848b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # as the doctest module doesn't understand __future__ statements 4858b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 4868b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> from __future__ import with_statement 4878b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4888b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4898b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(): 4908b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... ctx = getcontext() 491495df4716fce4156c1eb110f9342297164eecbb6Raymond Hettinger ... ctx.prec += 2 4928b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print ctx.prec 4938b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4948b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 30 4958b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(ExtendedContext): 4968b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print getcontext().prec 4978b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4988b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 9 4998b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 5008b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 5018b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 502ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan if ctx is None: ctx = getcontext() 503ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan return _ContextManager(ctx) 5048b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 5057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Decimal class ####################################################### 5077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 5097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 5107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 511636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger __slots__ = ('_exp','_int','_sign', '_is_special') 512636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Generally, the value of the Decimal instance is given by 513636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (-1)**_sign * _int * 10**_exp 514636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special values are signified by _is_special == True 5157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 516dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger # We're immutable, so use __new__ not __init__ 517636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger def __new__(cls, value="0", context=None): 5187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 5197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 5217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 52259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) 5237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 5247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 5257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 5267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 5277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 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): 5430d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista m = _parser(value) 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 664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 if NaN (it could be a normal quiet NaN or a phantom one) 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', 710636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, self) 711636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other_is_nan == 2: 712636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 713636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, 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 7207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 7211a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is nonzero; otherwise return False. 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7231a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista NaNs and infinities are considered nonzero. 7247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 72572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._is_special or self._int != '0' 7267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __cmp__(self, other): 728636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 729267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Never return NotImplemented 731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 1 7327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 733636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for nans, without raising on a signaling nan 735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan() or other._isnan(): 73659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return 1 # Comparison involving NaN's always reports self > other 737636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 738636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # INF = INF 739636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return cmp(self._isinfinity(), other._isinfinity()) 7407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for zeros; note that cmp(0, -0) should return 0 742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 0 745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return -((-1)**other._sign) 747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return (-1)**self._sign 7497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 75059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If different signs, neg one is less 7517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 7527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 7547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 756636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_adjusted = self.adjusted() 757636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_adjusted = other.adjusted() 758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted == other_adjusted: 75972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - other._exp) 76072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista other_padded = other._int + '0'*(other._exp - self._exp) 761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return cmp(self_padded, other_padded) * (-1)**self._sign 762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self_adjusted > other_adjusted: 7637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # self_adjusted < other_adjusted 7657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 7667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7670aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 7680aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 769267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7700aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) == 0 7710aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7720aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 7730aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 774267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7750aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) != 0 7760aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 7787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 7797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 7857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 7877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 78859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Compare(NaN, NaN) = NaN 789636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if (self._is_special or other and other._is_special): 790636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 791636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 792636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 7937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.__cmp__(other)) 7957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 7987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 7997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Non-integer decimals are normalized and hashed as strings 8001fb9f528bd69efa135bacda917ec7bb166068d5dGeorg Brandl # Normalization assures that hash(100E-1) == hash(10) 801bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._is_special: 802bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._isnan(): 803bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger raise TypeError('Cannot hash a NaN value.') 804bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger return hash(str(self)) 8058c202440699cef19602acc24822366d0d7c32083Facundo Batista if not self: 8068c202440699cef19602acc24822366d0d7c32083Facundo Batista return 0 8078c202440699cef19602acc24822366d0d7c32083Facundo Batista if self._isinteger(): 8088c202440699cef19602acc24822366d0d7c32083Facundo Batista op = _WorkRep(self.to_integral_value()) 8098c202440699cef19602acc24822366d0d7c32083Facundo Batista # to make computation feasible for Decimals with large 8108c202440699cef19602acc24822366d0d7c32083Facundo Batista # exponent, we use the fact that hash(n) == hash(m) for 8118c202440699cef19602acc24822366d0d7c32083Facundo Batista # any two nonzero integers n and m such that (i) n and m 8128c202440699cef19602acc24822366d0d7c32083Facundo Batista # have the same sign, and (ii) n is congruent to m modulo 8138c202440699cef19602acc24822366d0d7c32083Facundo Batista # 2**64-1. So we can replace hash((-1)**s*c*10**e) with 8148c202440699cef19602acc24822366d0d7c32083Facundo Batista # hash((-1)**s*c*pow(10, e, 2**64-1). 8158c202440699cef19602acc24822366d0d7c32083Facundo Batista return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) 8167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(str(self.normalize())) 8177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 8197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 82372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (self._sign, tuple(map(int, self._int)), self._exp) 8247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 8267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 8277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 8287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 'Decimal("%s")' % str(self) 8297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __str__(self, eng=False, context=None): 8317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 8327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 8347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 83662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista sign = ['', '-'][self._sign] 837e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._is_special: 83862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp == 'F': 83962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'Infinity' 84062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._exp == 'n': 84162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'NaN' + self._int 84262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: # self._exp == 'N' 84362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'sNaN' + self._int 84462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 84562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # number of digits of self._int to left of decimal point 84662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista leftdigits = self._exp + len(self._int) 84762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 84862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # dotplace is number of digits of self._int to the left of the 84962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # decimal point in the mantissa of the output string (that is, 85062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # after adjusting the exponent) 85162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp <= 0 and leftdigits > -6: 85262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # no exponent required 85362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = leftdigits 85462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif not eng: 85562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # usual scientific notation: 1 digit on left of the point 8567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 85762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._int == '0': 85862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, zero 85962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits + 1) % 3 - 1 8607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 86162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, nonzero 86262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits - 1) % 3 + 1 86362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 86462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if dotplace <= 0: 86562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = '0' 86662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + '0'*(-dotplace) + self._int 86762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif dotplace >= len(self._int): 86862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int+'0'*(dotplace-len(self._int)) 86962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '' 87062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 87162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int[:dotplace] 87262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + self._int[dotplace:] 87362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if leftdigits == dotplace: 87462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = '' 87562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 87662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if context is None: 87762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista context = getcontext() 87862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) 87962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 88062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + intpart + fracpart + exp 8817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 8837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 8847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 8867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 8877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 8897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__str__(eng=True, context=context) 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 8947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 897636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 898636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 899636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 900636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_sign(Dec_0) 9057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_negate() 907636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 908636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 909636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 910e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 9117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 9137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 9167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 917636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 918636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 919636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 920636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_sign(Dec_0) 925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 9277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 928636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 929636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 930e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 9317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 932e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista def __abs__(self, round=True, context=None): 9337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 9347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 935e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista If the keyword argument 'round' is false, do not round. The 936e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista expression self.__abs__(round=False) is equivalent to 937e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.copy_abs(). 9387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 939e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if not round: 940e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return self.copy_abs() 941e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista 942636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 943636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 944636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 945636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 9497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 9517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 9587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 959636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 960267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 961267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 962636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 9637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 9647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 9657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 966636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 967636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 968636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 969636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 971636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 97259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both INF, same sign => same as both, opposite => error. 973636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 974636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 975636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 976636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 97759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return Decimal(other) # Can't both be infinity here 9787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 9807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 98259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the answer is 0, the sign should be negative, in this case. 9837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 9847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 9867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 9877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 9887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 98972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, '0', exp) 990e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 9927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 99399b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, other._exp - context.prec-1) 994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other._rescale(exp, context.rounding) 995e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 9967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 99899b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, self._exp - context.prec-1) 999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp, context.rounding) 1000e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 10017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 1005e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista op1, op2 = _normalize(op1, op2, context.prec) 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 10087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 101017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int == op2.int: 101172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(negativezero, '0', exp) 1012e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 1013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 101417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int < op2.int: 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 101659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # OK, now abs(op1) > abs(op2) 101717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.sign == 1: 101817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 1 10197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 10207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 102117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 102259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # So we know the sign, and op1 > 0. 102317931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif op1.sign == 1: 10247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 102517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger op1.sign, op2.sign = (0, 0) 102617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 102717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 102859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Now, op1 > abs(op2) > 0 10297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 103017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op2.sign == 0: 1031636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int + op2.int 10327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1033636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int - op2.int 10347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 10367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 1037e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 10387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 10417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 1043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self - other""" 1044636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1045267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1046267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1048636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1049636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context=context) 1050636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1051636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self - other is computed as self + other.copy_negate() 1054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__add__(other.copy_negate(), context=context) 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 1057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return other - self""" 1058636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1059267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1060267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__sub__(self, context=context) 10637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 10657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 10667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1069636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1070267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1071267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1072636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 10737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1076d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1078636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1079636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1080636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1081636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1082636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1083636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1084636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1085636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 1086636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 1087636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1088636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1089636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1090636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 1091636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 10927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 10947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 10967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 109772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, '0', resultexp) 1098e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista # Fixing in case the exponent is out of bounds 1099e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 110372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int == '1': 110472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, other._int, resultexp) 1105e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 110772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if other._int == '1': 110872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, self._int, resultexp) 1109e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1112636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1 = _WorkRep(self) 1113636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2 = _WorkRep(other) 1114636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 111572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) 1116e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista ans = ans._fix(context) 11177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 11207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 11227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 1123636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1124267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1125cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NotImplemented 1126636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1130636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sign = self._sign ^ other._sign 1131636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1132636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1133636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1134636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 11357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1137636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and other._isinfinity(): 11387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 1141636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[sign] 1142636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1143636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1144636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 114572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '0', context.Etiny()) 1146636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1147636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special cases for zeroes 1148636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1149cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1150cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 / 0') 1151636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 11527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1153cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1154cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp 1155cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff = 0 1156cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1157cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # OK, so neither = 0, INF or NaN 1158cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista shift = len(other._int) - len(self._int) + context.prec + 1 1159cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp - shift 1160cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1161cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1162cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if shift >= 0: 1163cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int * 10**shift, op2.int) 1164cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1165cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int, op2.int * 10**-shift) 1166cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if remainder: 1167cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is not exact; adjust to ensure correct rounding 1168cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if coeff % 5 == 0: 1169cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff += 1 1170cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1171cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is exact; get as close to ideal exponent as possible 1172cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp - other._exp 1173cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista while exp < ideal_exp and coeff % 10 == 0: 1174cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff //= 10 1175cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp += 1 11767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 117772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(coeff), exp) 1178cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans._fix(context) 11797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1180cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista __truediv__ = __div__ 11817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1182cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def _divide(self, other, context): 1183cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """Return (self // other, self % other), to context.prec precision. 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1185cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Assumes that neither self nor other is a NaN, that self is not 1186cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista infinite and that other is nonzero. 1187cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """ 1188cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1189cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1190cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp 1191cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1192cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = min(self._exp, other._exp) 11937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1194cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista expdiff = self.adjusted() - other.adjusted() 1195cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self or other._isinfinity() or expdiff <= -2: 119672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, '0', 0), 1197cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._rescale(ideal_exp, context.rounding)) 1198cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if expdiff <= context.prec: 1199cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1200cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1201cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if op1.exp >= op2.exp: 1202cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 1203cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1204cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1205cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista q, r = divmod(op1.int, op2.int) 1206cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if q < 10**context.prec: 120772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, str(q), 0), 120872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista _dec_from_triple(self._sign, str(r), ideal_exp)) 12097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1210cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # Here the quotient is too large to be representable 1211cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionImpossible, 1212cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 'quotient too large in //, % or divmod') 1213cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 12167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 1217636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1218267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1219267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 12227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 12247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1225cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Return (self // other, self % other) 12267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1227cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1228cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1229cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1230cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1231cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1232cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1233cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1234cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1235cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1236cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (ans, ans) 1237cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1238cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1239cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1240cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1241cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') 1242cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1243cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1244cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (Infsign[sign], 1245cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'INF % x')) 1246cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1247cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1248cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1249cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') 1250cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1251cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1252cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (context._raise_error(DivisionByZero, 'x // 0', sign), 1253cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'x % 0')) 1254cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1255cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista quotient, remainder = self._divide(other, context) 1256e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1257cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return quotient, remainder 12587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 12607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 1261636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1262267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1263267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 12657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 12677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 12687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 12697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1270636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1271267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1272267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1274cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1275cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 12767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1277cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1278cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1279cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 12807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1281cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1282cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF % x') 1283cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista elif not other: 1284cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1285cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'x % 0') 1286cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1287cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 % 0') 1288cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1289cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = self._divide(other, context)[1] 1290e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista remainder = remainder._fix(context) 1291cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return remainder 12927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 12947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 1295636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1296267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1297267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 12997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1304636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1305636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 13067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 13087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 13127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self == +/-infinity -> InvalidOperation 1314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 1315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(infinity, x)') 13177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other == 0 -> either InvalidOperation or DivisionUndefined 1319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 1321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(x, 0)') 1323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(DivisionUndefined, 1325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(0, 0)') 13267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other = +/-infinity -> remainder = self 1328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 1329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 1330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self = 0 -> remainder = self, with ideal exponent 1333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = min(self._exp, other._exp) 1334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 133572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', ideal_exponent) 1336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # catch most cases of large or small quotient 1339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = self.adjusted() - other.adjusted() 1340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff >= context.prec + 1: 1341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff >= prec+1 => abs(self/other) > 10**prec 1342cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff <= -2: 1344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff <= -2 => abs(self/other) < 0.1 1345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(ideal_exponent, context.rounding) 1346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust both arguments to have the same exponent, then divide 1349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1 = _WorkRep(self) 1350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2 = _WorkRep(other) 1351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp >= op2.exp: 1352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 13537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(op1.int, op2.int) 1356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # remainder is r*10**ideal_exponent; other is +/-op2.int * 1357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**ideal_exponent. Apply correction to ensure that 1358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # abs(remainder) <= abs(other)/2 1359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if 2*r + (q&1) > op2.int: 1360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r -= op2.int 1361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q += 1 1362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if q >= 10**context.prec: 1364cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has same sign as self unless r is negative 1367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if r < 0: 1369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 1-sign 1370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r = -r 13717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 137272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(r), ideal_exponent) 1373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 13767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 1377cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1378cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1379cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1380cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1381cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1382cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1383cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1384cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1385cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1386cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 1387cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1388cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1389cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1390cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF // INF') 1391cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1392cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return Infsign[self._sign ^ other._sign] 1393cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1394cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1395cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1396cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'x // 0', 1397cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._sign ^ other._sign) 1398cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1399cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 // 0') 1400cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1401cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return self._divide(other, context)[0] 14027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 1405636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1406267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1407267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 14087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 14097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 14117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 14127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 14137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 141546b0802ccd9a9c47b27a285526fbb2a8bee5b8cbBrett Cannon """Converts self to an int, truncating if necessary.""" 1416636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1417636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan(): 1418636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1419636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidContext) 1420636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self._isinfinity(): 142159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise OverflowError("Cannot convert infinity to long") 1422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = (-1)**self._sign 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 142472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int)*10**self._exp 1425605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger else: 142672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int[:self._exp] or '0') 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 14307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 14327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 14347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1435353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fix_nan(self, context): 1436353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Decapitate the payload of a NaN to fit the context""" 1437353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista payload = self._int 1438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1439353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # maximum length of payload is precision if _clamp=0, 1440353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision-1 if _clamp=1. 1441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista max_payload_len = context.prec - context._clamp 1442353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(payload) > max_payload_len: 144372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista payload = payload[len(payload)-max_payload_len:].lstrip('0') 144472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, payload, self._exp, True) 14456c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 1446353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1447dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _fix(self, context): 14487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 14497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 14517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 14537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 14547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 14557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1456636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 14577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 1461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan(): 1462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decapitate payload if necessary 1463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 1464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is +/-Infinity; return unaltered 14666c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 14677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if self is zero then exponent should be between Etiny and 1469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. 1470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 1471353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etop = context.Etop() 14727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 1473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, Etop][context._clamp] 1474353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_exp = min(max(self._exp, Etiny), exp_max) 1475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_exp != self._exp: 1476353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 147772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', new_exp) 14787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14796c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 14807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1481353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp_min is the smallest allowable exponent of the result, 1482353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equal to max(self.adjusted()-context.prec+1, Etiny) 1483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = len(self._int) + self._exp - context.prec 1484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp_min > Etop: 1485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow: exp_min > Etop iff self.adjusted() > Emax 1486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 1488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(Overflow, 'above Emax', self._sign) 1489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_subnormal = exp_min < Etiny 1490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 1492353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = Etiny 14937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round if self has too many digits 1495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < exp_min: 14967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 14972ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = len(self._int) + self._exp - exp_min 14982ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if digits < 0: 14992ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista self = _dec_from_triple(self._sign, '1', exp_min-1) 15002ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = 0 15012ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista this_function = getattr(self, self._pick_rounding_function[context.rounding]) 15022ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 15032ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 15042ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 15052ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 15062ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista ans = _dec_from_triple(self._sign, coeff, exp_min) 15072ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista 15082ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed: 1509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 1512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 1513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Clamped on underflow to 0 1514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 1515353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif len(ans._int) == context.prec+1: 1516353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we get here only if rescaling rounds the 1517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # cofficient up to exactly 10**context.prec 1518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp < Etop: 151972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, 152072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._int[:-1], ans._exp+1) 1521353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1522353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inexact and Rounded have already been raised 1523353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = context._raise_error(Overflow, 'above Emax', 1524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self._sign) 15257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fold down if _clamp == 1 and self has too few digits 1528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._clamp == 1 and self._exp > Etop: 1529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 153072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - Etop) 153172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, self_padded, Etop) 15327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # here self was representable to begin with; return unchanged 15346c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 15357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 15377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for each of the rounding functions below: 1539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is a finite, nonzero Decimal 1540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # prec is an integer satisfying 0 <= prec < len(self._int) 15412ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 15422ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # each function returns either -1, 0, or 1, as follows: 15432ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 1 indicates that self should be rounded up (away from zero) 15442ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 0 indicates that self should be truncated, and that all the 15452ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # digits to be truncated are zeros (so the value is unchanged) 15462ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # -1 indicates that there are nonzero digits to be truncated 15477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_down(self, prec): 1549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Also known as round-towards-0, truncate.""" 15502ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _all_zeros(self._int, prec): 15512ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 15522ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 15532ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_up(self, prec): 1556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds away from 0.""" 15572ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_up(self, prec): 1560353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds 5 up (away from 0)""" 156172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[prec] in '56789': 15622ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 1 15632ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista elif _all_zeros(self._int, prec): 15642ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 1565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 15662ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_down(self, prec): 15697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 15702ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec): 15712ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15722ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 15732ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 15747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_even(self, prec): 1576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round 5 to even, rest to nearest.""" 15772ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec) and \ 15782ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista (prec == 0 or self._int[prec-1] in '02468'): 15792ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 1580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 15812ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 15827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_ceiling(self, prec): 15847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 1586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 15877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15882ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 15897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_floor(self, prec): 15917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 1593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 15947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15952ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 15967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_05up(self, prec): 1598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round down unless digit prec-1 is 0 or 5.""" 15992ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if prec and self._int[prec-1] not in '05': 1600353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16012ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 16022ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 1603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1604353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, other, third, context=None): 1605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Fused multiply-add. 16067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1607353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Returns self*other+third with no rounding of the intermediate 1608353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista product self*other. 1609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1610353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self and other are multiplied together, with no rounding of 1611353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the result. The third operand is then added to the result, 1612353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista and a single final rounding is performed. 16137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 16167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 161758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # compute product; raise InvalidOperation if either operand is 161858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista # a signaling NaN or if the product is zero times infinity. 161958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._is_special or other._is_special: 162058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if context is None: 162158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista context = getcontext() 162258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'N': 162358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 162458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista 1, self) 162558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if other._exp == 'N': 162658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 162758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista 1, other) 162858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if self._exp == 'n': 162958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = self 163058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'n': 163158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = other 163258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif self._exp == 'F': 163358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not other: 163458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 163558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista 'INF * 0 in fma') 163658f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = Infsign[self._sign ^ other._sign] 163758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista elif other._exp == 'F': 163858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista if not self: 163958f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return context._raise_error(InvalidOperation, 164058f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista '0 * INF in fma') 164158f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = Infsign[self._sign ^ other._sign] 164258f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista else: 164358f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista product = _dec_from_triple(self._sign ^ other._sign, 164458f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista str(int(self._int) * int(other._int)), 164558f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista self._exp + other._exp) 16467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 164758f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista third = _convert_other(third, raiseit=True) 164858f6f2e0c9fad1ef9ee921980888dc52da8100ceFacundo Batista return product.__add__(third, context) 16497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_modulo(self, other, modulo, context=None): 1651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Three argument version of __pow__""" 16527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if can't convert other and modulo to Decimal, raise 1654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # TypeError; there's no point returning NotImplemented (no 1655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equivalent of __rpow__ for three argument pow) 1656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 1657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = _convert_other(modulo, raiseit=True) 16587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 16617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # deal with NaNs: if there are any sNaNs then first one wins, 1663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (i.e. behaviour for NaNs is identical to that of fma) 1664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 1665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 1666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo_is_nan = modulo._isnan() 1667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan or other_is_nan or modulo_is_nan: 1668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 1669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 1671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 1672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 1674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo_is_nan == 2: 1675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, modulo) 1677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 16786c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 1679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 16806c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 16816c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return modulo._fix_nan(context) 1682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check inputs: we apply same restrictions as Python's pow() 1684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (self._isinteger() and 1685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other._isinteger() and 1686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo._isinteger()): 1687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument not allowed ' 1689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'unless all arguments are integers') 1690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other < 0: 1691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 2nd argument cannot be ' 1693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'negative when 3rd argument specified') 1694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not modulo: 1695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument cannot be 0') 1697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # additional restriction for decimal: the modulus must be less 1699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # than 10**prec in absolute value 1700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo.adjusted() >= context.prec: 1701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'insufficient precision: pow() 3rd ' 1703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'argument must not have more than ' 1704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'precision digits') 1705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # define 0**0 == NaN, for consistency with two-argument pow 1707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (even though it hurts!) 1708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other and not self: 1709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'at least one of pow() 1st argument ' 1711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'and 2nd argument must be nonzero ;' 1712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0**0 is not defined') 1713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute sign of result 1715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._iseven(): 1716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 0 1717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # convert modulo to a Python integer, and self and other to 1721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal integers (i.e. force their exponents to be >= 0) 1722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = abs(int(modulo)) 1723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = _WorkRep(self.to_integral_value()) 1724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = _WorkRep(other.to_integral_value()) 1725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute result using integer pow() 1727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo 1728353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(exponent.exp): 1729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, 10, modulo) 1730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, exponent.int, modulo) 1731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 173272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, str(base), 0) 1733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_exact(self, other, p): 1735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Attempt to compute self**other exactly. 1736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given Decimals self and other and an integer p, attempt to 1738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista compute an exact result for the power self**other, with p 1739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision. Return None if self**other is not 1740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exactly representable in p digits. 1741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that elimination of special cases has already been 1743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista performed: self and other must both be nonspecial; self must 1744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista be positive and not numerically equal to 1; other must be 1745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista nonzero. For efficiency, other._exp should not be too large, 1746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista so that 10**abs(other._exp) is a feasible calculation.""" 1747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # In the comments below, we write x for the value of self and 1749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # y for the value of other. Write x = xc*10**xe and y = 1750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # yc*10**ye. 1751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The main purpose of this method is to identify the *failure* 1753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of x**y to be exactly representable with as little effort as 1754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possible. So we look for cheap and easy tests that 1755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # eliminate the possibility of x**y being exact. Only if all 1756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # these tests are passed do we go on to actually compute x**y. 1757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Here's the main idea. First normalize both x and y. We 1759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # express y as a rational m/n, with m and n relatively prime 1760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # and n>0. Then for x**y to be exactly representable (at 1761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # *any* precision), xc must be the nth power of a positive 1762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # integer and xe must be divisible by n. If m is negative 1763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then additionally xc must be a power of either 2 or 5, hence 1764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a power of 2**n or 5**n. 1765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's a limit to how small |y| can be: if y=m/n as above 1767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then: 1768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1) if xc != 1 then for the result to be representable we 1770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So 1771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= 1772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2**(1/|y|), hence xc**|y| < 2 and the result is not 1773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # representable. 1774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if 1776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # |y| < 1/|xe| then the result is not representable. 1777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Note that since x is not equal to 1, at least one of (1) and 1779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < 1780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. 1781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's also a limit to how large y can be, at least if it's 1783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive: the normalized result will have coefficient xc**y, 1784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so if it's representable then xc**y < 10**p, and y < 1785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p/log10(xc). Hence if y*log10(xc) >= p then the result is 1786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # not exactly representable. 1787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, 1789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so |y| < 1/xe and the result is not representable. 1790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| 1791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # < 1/nbits(xc). 1792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 1794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 1795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 10 == 0: 1796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 10 1797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe += 1 1798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 1800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 1801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while yc % 10 == 0: 1802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc //= 10 1803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ye += 1 1804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where xc == 1: result is 10**(xe*y), with xe*y 1806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # required to be an integer 1807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc == 1: 1808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = xe*yc*10**ye 1810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent, remainder = divmod(xe*yc, 10**-ye) 1812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = -exponent 1816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if other is a nonnegative integer, use ideal exponent 1817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(exponent-ideal_exponent, p-1) 1820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 182272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) 1823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where y is negative: xc must be either a power 1825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of 2 or a power of 5. 1826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista last_digit = xc % 10 1828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if last_digit in (2,4,6,8): 1829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # quick test for power of 2 1830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc & -xc != xc: 1831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc is a power of 2; e is its exponent 1833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)-1 1834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find e*y and xe*y; both must be integers 1835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_int = yc*10**ye 1837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_int 1838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_int 1839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*65 >= p*93: # 93/65 > log(10)/log(5) 1849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 5**e 1851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif last_digit == 5: 1853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # e >= log_5(xc) if xc is a power of 5; we have 1854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equality all the way up to xc=5**2658 1855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)*28//65 1856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, remainder = divmod(5**e, xc) 1857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 5 == 0: 1860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 5 1861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= 1 1862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_integer = yc*10**ye 1864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_integer 1865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_integer 1866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*3 >= p*10: # 10/3 > log(10)/log(2) 1875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 2**e 1877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 18797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc >= 10**p: 1881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = -e-xe 188372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str(xc), xe) 18847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now y is positive; find m and n such that y = m/n 1886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc*10**ye, 1 1888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xe != 0 and len(str(abs(yc*xe))) <= -ye: 1890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc_bits = _nbits(xc) 1892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: 1893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc, 10**(-ye) 1895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 2 == n % 2 == 0: 1896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 2 1897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 2 1898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 5 == n % 5 == 0: 1899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 5 1900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 5 1901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc*10**xe 1903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n > 1: 1904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if 1 < xc < 2**n then xc isn't an nth power 1905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and xc_bits <= n: 1906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, rem = divmod(xe, n) 1909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rem != 0: 1910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc using Newton's method 1913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = 1L << -(-_nbits(xc)//n) # initial estimate 1914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 1915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(xc, a**(n-1)) 1916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if a <= q: 1917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 1918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = (a*(n-1) + q)//n 1920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (a == q and r == 0): 1921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = a 1923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc*10**xe is the nth root of the original xc*10**xe 1925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute mth power of xc*10**xe 1926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > 1928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**p and the result is not representable. 1929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 1 and m > p*100//_log10_lb(xc): 1930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = xc**m 1932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe *= m 1933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 10**p: 1934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by this point the result *is* exactly representable 1937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust the exponent to get as close as possible to the ideal 1938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent, if necessary 1939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_xc = str(xc) 1940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(xe-ideal_exponent, p-len(str_xc)) 1943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 194572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) 1946cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __pow__(self, other, modulo=None, context=None): 1948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self ** other [ % modulo]. 19497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute self**other. 19517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (self**other) % modulo. For the 1953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 1954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 19557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 1957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - other must be nonnegative 1958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - either self or other (or both) must be nonzero 1959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and must have at most p digits, 1960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista where p is the context precision. 19617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If any of these restrictions is violated the InvalidOperation 1963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista flag is raised. 1964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(self, other, modulo) is identical to the 1966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result that would be obtained by computing (self**other) % 1967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo with unbounded precision, but is computed more 1968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista efficiently. It is always exact. 1969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 1970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo is not None: 1972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._power_modulo(other, modulo, context) 19737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1974636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1975267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1976267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 19777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 19807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # either argument is a NaN => result is NaN 1982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 19857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) 1987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 1989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, '0 ** 0') 1990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 19927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has sign 1 iff self._sign is 1 and other is an odd integer 1994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 0 1995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 1996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 1997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._iseven(): 1998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 1 1999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # -ve**noninteger = NaN 2001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (-0)**noninteger = 0**noninteger 2002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 2003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'x ** y with x negative and y not an integer') 2005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # negate self, without doing any unwanted rounding 200672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = self.copy_negate() 2007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity 2009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 201172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 2016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 2018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 202072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1**other = 1, but the choice of exponent and the flags 2023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # depend on the exponent of self, and on whether other is a 2024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive integer, a negative integer, or neither 2025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp = max(self._exp*max(int(other), 0), 2028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-context.prec) but evaluating int(other) directly 2029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is dangerous until we know other is small (other 2030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # could be 1e999999999) 2031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 1: 2032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = 0 2033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif other > context.prec: 2034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = context.prec 2035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = int(other) 2037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = self._exp * multiplier 2039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp < 1-context.prec: 2040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 204772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) 2048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute adjusted exponent of self 2050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adj = self.adjusted() 2051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** infinity is infinity if self > 1, 0 if self < 1 2053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** -infinity is infinity if self < 1, 0 if self > 1 2054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 2055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (other._sign == 0) == (self_adj < 0): 205672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # from here on, the result always goes through the call 2061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # to _fix at the end of this function. 2062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = None 2063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # crude test to catch cases of extreme overflow/underflow. If 2065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(self)*other >= 10**bound and bound >= len(str(Emax)) 2066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence 2067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self**other >= 10**(Emax+1), so overflow occurs. The test 2068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for underflow is similar. 2069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista bound = self._log10_exp_bound() + other.adjusted() 2070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (self_adj >= 0) == (other._sign == 0): 2071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other +ve, or self < 1 and other -ve 2072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of overflow 2073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(context.Emax)): 207472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', context.Emax+1) 2075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other -ve, or self < 1 and other +ve 2077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of underflow to 0 2078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 2079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(-Etiny)): 208072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', Etiny-1) 2081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # try for an exact result with precision +1 2083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._power_exact(other, context.prec + 1) 2085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is not None and result_sign == 1: 208672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(1, ans._int, ans._exp) 2087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # usual case: inexact result, x**y computed directly as exp(y*log(x)) 2089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 2092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 2093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 2094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 2095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 2096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc = -yc 2097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: start with precision +3, 2099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then increase precision until result is unambiguously roundable 2100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dpower(xc, xe, yc, ye, p+extra) 2103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 210772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, str(coeff), exp) 2108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the specification says that for non-integer other we need to 2110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Inexact, even when the result is actually exact. In 2111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the same way, we need to raise Underflow here if the result 2112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is subnormal. (The call to _fix will take care of raising 2113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Rounded and Subnormal, as usual.) 2114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._isinteger(): 2115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad with zeros up to length context.prec+1 if necessary 2117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) <= context.prec: 2118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = context.prec+1 - len(ans._int) 211972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, 212072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._exp-expdiff) 2121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() < context.Emin: 2122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 2123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # unlike exp, ln and log10, the power function respects the 2125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode; no need to use ROUND_HALF_EVEN here 2126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __rpow__(self, other, context=None): 2130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Swaps self/other and returns __pow__.""" 2131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other) 2132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other is NotImplemented: 2133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other 2134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__pow__(self, context=context) 2135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def normalize(self, context=None): 2137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 2138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dup = self._fix(context) 2148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dup._isinfinity(): 2149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return dup 2150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not dup: 215272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, '0', 0) 2153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, context.Etop()][context._clamp] 2154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista end = len(dup._int) 21557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 215672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista while dup._int[end-1] == '0' and exp < exp_max: 21577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 21587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 215972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, dup._int[:end], exp) 21607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2161bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista def quantize(self, exp, rounding=None, context=None, watchexp=True): 21627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 21637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 21657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2166bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista exp = _convert_other(exp, raiseit=True) 2167bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2173636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or exp._is_special: 2174636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(exp, context) 2175636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2176636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 21777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2178636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 2179636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 21806c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) # if both are inf, it is OK 2181636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 2182636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 'quantize with one INF') 2183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2184bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # if we're not watching exponents, do a simple rescale 2185bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if not watchexp: 2186bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista ans = self._rescale(exp._exp, rounding) 2187bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # raise Inexact and Rounded where appropriate 2188bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans._exp > self._exp: 2189bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Rounded) 2190bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans != self: 2191bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Inexact) 2192bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista return ans 2193bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp._exp should be between Etiny and Emax 2195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (context.Etiny() <= exp._exp <= context.Emax): 2196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'target exponent out of bounds in quantize') 2198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 220072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', exp._exp) 2201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 2202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adjusted = self.adjusted() 2204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted > context.Emax: 2205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted - exp._exp + 1 > context.prec: 2208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp._exp, rounding) 2212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() > context.Emax: 2213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) > context.prec: 2216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise appropriate flags 2220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp > self._exp: 2221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans and ans.adjusted() < context.Emin: 2225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 2226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # call to fix takes care of any necessary folddown 2228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 22307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 22321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self and other have the same exponent; otherwise 22331a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False. 22347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22351a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista If either operand is a special value, the following rules are used: 22361a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are infinities 22371a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are NaNs 22381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * otherwise, return False. 22397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22401a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista other = _convert_other(other, raiseit=True) 2241636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 22421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return (self.is_nan() and other.is_nan() or 22431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista self.is_infinite() and other.is_infinite()) 22447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 22457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _rescale(self, exp, rounding): 2247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rescale self so that the exponent is exp, either by padding with zeros 2248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or by truncating digits, using the given rounding mode. 2249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Specials are returned without change. This operation is 2251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista quiet: it raises no flags, and uses no information from the 2252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 22537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 2255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = rounding mode 22567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2257636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 22586c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 22597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 226072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', exp) 22617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= exp: 2263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad answer with zeros if necessary 226472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 226572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int + '0'*(self._exp - exp), exp) 22667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # too many digits; round and lose data. If self.adjusted() < 2268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp-1, replace self by 10**(exp-1) before rounding 2269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = len(self._int) + self._exp - exp 22707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 227172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = _dec_from_triple(self._sign, '1', exp-1) 2272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = 0 2273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this_function = getattr(self, self._pick_rounding_function[rounding]) 22742ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 22752ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 22762ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 22772ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 22782ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return _dec_from_triple(self._sign, coeff, exp) 22797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, rounding=None, context=None): 2281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to a nearby integer. 22827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If no rounding mode is specified, take the rounding mode from 2284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the context. This method raises the Rounded and Inexact flags 2285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista when appropriate. 22867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista See also: to_integral_value, which does exactly the same as 2288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this method except that it doesn't raise Inexact or Rounded. 2289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2290636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2291636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2292636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2293636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 22946c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 22957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 22966c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 229872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', 0) 2299636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2300636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(0, rounding) 2305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 23077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 23087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, rounding=None, context=None): 2310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to the nearest integer, without raising inexact, rounded.""" 2311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 23196c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= 0: 23216c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._rescale(0, rounding) 23247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 2326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 2327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def sqrt(self, context=None): 2329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return the square root of self.""" 2330636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2331636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2332636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2333636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 23347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2335636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 2336636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 23377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 2339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent = self._exp // 2. sqrt(-0) = -0 234072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', self._exp // 2) 2341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2343636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2344636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2345636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 23467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 23477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 23487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # At this point self represents a positive number. Let p be 2350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the desired precision and express self in the form c*100**e 2351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with c a positive real number and e an integer, c and e 2352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # being chosen so that 100**(p-1) <= c < 100**p. Then the 2353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) 2354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # <= sqrt(c) < 10**p, so the closest representable Decimal at 2355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision p is n*10**e where n = round_half_even(sqrt(c)), 2356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the closest integer to sqrt(c) with the even integer chosen 2357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # in the case of a tie. 2358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # To ensure correct rounding in all cases, we use the 2360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # following trick: we compute the square root to an extra 2361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # place (precision p+1 instead of precision p), rounding down. 2362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then, if the result is inexact and its last digit is 0 or 5, 2363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we increase the last digit to 1 or 6 respectively; if it's 2364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exact we leave the last digit alone. Now the final round to 2365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p places (or fewer in the case of underflow) will round 2366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly and raise the appropriate flags. 2367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # use an extra digit of precision 2369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista prec = context.prec+1 2370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write argument in the form c*100**e where e = self._exp//2 2372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is the 'ideal' exponent, to be used if the square root is 2373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exactly representable. l is the number of 'digits' of c in 2374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # base 100, so that 100**(l-1) <= c < 100**l. 2375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = op.exp >> 1 2377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.exp & 1: 2378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int * 10 2379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = (len(self._int) >> 1) + 1 23807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int 2382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(self._int)+1 >> 1 2383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rescale so that c has exactly prec base 100 'digits' 2385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = prec-l 2386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 100**shift 2388353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = True 23897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, remainder = divmod(c, 100**-shift) 2391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = not remainder 2392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= shift 2393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2394353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find n = floor(sqrt(c)) using Newton's method 2395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = 10**prec 2396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2397353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = c//n 2398353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= q: 23997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 2400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = n + q >> 1 2402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = exact and n*n == c 2403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exact: 2405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is exact; rescale to use ideal exponent e 2406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert n % 10**shift == 0 2408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 10**shift 2409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n *= 10**-shift 2411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e += shift 24127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is not exact; fix last digit as described above 2414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n % 5 == 0: 2415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n += 1 24167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 241772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(n), e) 24187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round, and fit to current context 2420353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2422dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 2423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 24247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 24267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 24287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 24297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like max(self, other) except if one is not a number, returns 24317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 24327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2434636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24356c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 24366c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 24376c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2438636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 243959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2440636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2441636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2442636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2443636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2444636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 24456c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2446636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 24476c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2448636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 24497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2450d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2451d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 245259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both operands are finite and equal in numerical value 2453d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2454d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 245559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs differ then max returns the operand with the 2456d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2457d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 245859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs are the same then the exponent is used to select 2459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result. This is exactly the ordering used in compare_total. 2460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 24637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2466636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2467e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 24687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 24707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 24717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 247259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Like min(self, other) except if one is not a number, returns 24737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 24747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2475353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2476636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24776c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 24786c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 24796c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2480636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 248159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2482636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2483636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2484636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2485636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2486636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 24876c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2488636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 24896c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2490636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 24917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2492d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2493d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 2497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 24997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2500636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2501e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 25047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 2505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 25077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 25087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 25097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 251072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return rest == '0'*len(rest) 25117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 2513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns True if self is even. Assumes self is an integer.""" 2514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self or self._exp > 0: 2515353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 251672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._int[-1+self._exp] in '02468' 25177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 25197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 25207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 25217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 252259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If NaN or Infinity, self._exp is string 25237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 25247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 25257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, context=None): 2527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 2528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 2530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 2531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self 2533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, other, context=None): 2535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to the other operand numerically. 2536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 2538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 2539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 2544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 2545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 2546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 2547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 2548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 2549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 2550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 2551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 2552353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'NaN in compare_signal', 2553353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 2554353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 2555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'NaN in compare_signal', 2556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 2557353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.compare(other, context=context) 2558353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, other): 2560353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using the abstract representations. 2561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 2563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 2564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 2565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if one is negative and the other is positive, it's easy 2567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign and not other._sign: 2568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._sign and other._sign: 2570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2571353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 2572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's handle both NaN types 2574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_nan = self._isnan() 2575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_nan = other._isnan() 2576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan or other_nan: 2577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == other_nan: 2578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int < other._int: 2579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int > other._int: 2584353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2592353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2594353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2596353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2600353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2602353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2604353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2606353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2607353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2608353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self < other: 2610353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2611353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self > other: 2612353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2613353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < other._exp: 2615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp > other._exp: 2620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, other): 2628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using abstract repr., ignoring sign. 2629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 2631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = self.copy_abs() 2633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista o = other.copy_abs() 2634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return s.compare_total(o) 2635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self): 2637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign set to 0. """ 263872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self): 2641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign inverted.""" 2642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 264372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 264572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, self._int, self._exp, self._is_special) 2646353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, other): 2648353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self with the sign of other.""" 264972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(other._sign, self._int, 265072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp, self._is_special) 2651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, context=None): 2653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** self.""" 2654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(NaN) = NaN 2659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(-Infinity) = 0 2664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 2665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(0) = 1 2668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(Infinity) = Infinity 2672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self) 2674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result is now guaranteed to be inexact (the true 2676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # mathematical result is transcendental). There's no need to 2677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Rounded and Inexact here---they'll always be raised as 2678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a result of the call to _fix. 2679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self.adjusted() 2681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we only need to do any computation for quite a small range 2683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of adjusted exponents---for example, -29 <= adj <= 10 for 2684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the default context. For smaller exponent the result is 2685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # indistinguishable from 1 at the given precision, while for 2686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # larger exponent the result either overflows or underflows. 2687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 0 and adj > len(str((context.Emax+1)*3)): 2688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow 268972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Emax+1) 2690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): 2691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # underflow to 0 269272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Etiny()-1) 2693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 0 and adj < -p: 2694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 269572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) 2696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj < -p-1: 2697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 269872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '9'*(p+1), -p-1) 2699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # general case 2700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.sign == 1: 2704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = -c 2705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: increase precision by 2707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 3 digits at a time until we get an unambiguously 2708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # roundable result 2709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(c, e, p+extra) 2712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 271672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(coeff), exp) 2717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # at this stage, ans should round correctly with *any* 2719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode, not just with ROUND_HALF_EVEN 2720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self): 27281a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is canonical; otherwise return False. 27291a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 27301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 27311a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 27321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """ 27331a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return True 2734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self): 27361a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is finite; otherwise return False. 2737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 27381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 27391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 2740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 27411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return not self._is_special 2742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self): 27441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is infinite; otherwise return False.""" 27451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'F' 2746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self): 27481a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a qNaN or sNaN; otherwise return False.""" 27491a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp in ('n', 'N') 2750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, context=None): 27521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a normal number; otherwise return False.""" 27531a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 27541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 27571a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return context.Emin <= self.adjusted() <= context.Emax 2758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self): 27601a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a quiet NaN; otherwise return False.""" 27611a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'n' 2762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self): 27641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is negative; otherwise return False.""" 27651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._sign == 1 2766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self): 27681a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a signaling NaN; otherwise return False.""" 27691a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'N' 2770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, context=None): 27721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is subnormal; otherwise return False.""" 27731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 27741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 27771a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self.adjusted() < context.Emin 2778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self): 27801a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a zero; otherwise return False.""" 278172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return not self._is_special and self._int == '0' 2782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _ln_exp_bound(self): 2784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.ln(). 2785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, compute r such that self.ln() >= 10**r. Assumes 2786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that self is finite and positive and that self != 1. 2787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 2790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) 2793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj*23//10)) - 1 2794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument <= 0.1 2796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str((-1-adj)*23//10)) - 1 2797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(c) 2803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) 2804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return e + len(str(10**-e - c)) - 1 2806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, context=None): 2809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of self.""" 2810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(NaN) = NaN 2815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(0.0) == -Infinity 2820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(Infinity) = Infinity 2824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(1.0) == 0.0 2828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(negative) raises InvalidOperation 2832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ln of a negative value') 2835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision by 3 2842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until we get an unambiguously roundable result 2843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p - self._ln_exp_bound() + 2 # at least p+3 places 2844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog(c, e, places) 2846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 285072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _log10_exp_bound(self): 2859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.log10(). 2860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, find r such that self.log10() >= 10**r. 2861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that self is finite and positive and that self != 1. 2862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # For x >= 10 or x < 0.1 we only need a bound on the integer 2865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # part of log10(self), and this comes directly from the 2866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent of x. For 0.1 <= x <= 10 we use the inequalities 2867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > 2868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 2869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self >= 10 2873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj))-1 2874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self < 0.1 2876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(-1-adj))-1 2877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(231*c) 2883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) + 2 2884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(10**-e-c) 2886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) + e - (num < "231") - 1 2887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, context=None): 2889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of self.""" 2890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(NaN) = NaN 2895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(0.0) == -Infinity 2900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(Infinity) = Infinity 2904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(negative or -Infinity) raises InvalidOperation 2908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'log10 of a negative value') 2911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(10**n) = n 291372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): 2914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # answer may need rounding 2915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self._exp + len(self._int) - 1) 2916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision 2923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until result is unambiguously roundable 2924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p-self._log10_exp_bound()+2 2925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog10(c, e, places) 2927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 293172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, context=None): 2940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of self's MSD. 2941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 2943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of self (as though it were truncated 2944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to a single digit while maintaining the value of that digit and 2945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista without limiting the resulting exponent). 2946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(NaN) = NaN 2948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(+/-Inf) = +Inf 2956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(0) = -Inf, DivisionByZero 2960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2961cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'logb(0)', 1) 2962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # otherwise, simply return the adjusted exponent of self, as a 2964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal. Note that no attempt is made to fit the result 2965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # into the current context. 2966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.adjusted()) 2967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _islogical(self): 2969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return True if self is a logical operand. 2970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista For being logical, it must be a finite numbers with a sign of 0, 2972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an exponent of 0, and a coefficient whose digits must all be 2973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista either 0 or 1. 2974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign != 0 or self._exp != 0: 2976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 2977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for dig in self._int: 297872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if dig not in '01': 2979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 2980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 2981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fill_logical(self, context, opa, opb): 2983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opa) 2984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 298572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opa = '0'*dif + opa 2986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 2987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opa = opa[-context.prec:] 2988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opb) 2989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 299072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opb = '0'*dif + opb 2991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 2992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opb = opb[-context.prec:] 2993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return opa, opb 2994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, other, context=None): 2996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'and' operation between self and other's digits.""" 2997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 300672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) 300772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, context=None): 3010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all its digits.""" 3011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 301372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), 301472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, other, context=None): 3017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'or' operation between self and other's digits.""" 3018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 302772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb)) 302872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, other, context=None): 3031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'xor' operation between self and other's digits.""" 3032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 304172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb)) 304272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, other, context=None): 3045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 30486c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 30496c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 30506c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 30586c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 30606c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.copy_abs().__cmp__(other.copy_abs()) 3064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3072e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, other, context=None): 3075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 30786c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 30796c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 30806c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 30886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 30906c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.copy_abs().__cmp__(other.copy_abs()) 3094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3102e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista return ans._fix(context) 3103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, context=None): 3105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than itself.""" 3106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 3114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 3115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 311672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '9'*context.prec, context.Etop()) 3117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_FLOOR) 3120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 312472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), 312572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, context=None): 3128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than itself.""" 3129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 313972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, '9'*context.prec, context.Etop()) 3140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_CEILING) 3143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 314772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), 314872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, other, context=None): 3151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to self, in the direction towards other. 3152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number to self 3154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (excluding self) that is in the direction towards other, 3155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unless both have the same value. If the two operands are 3156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista numerically equal, then the result is a copy of self with the 3157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign set to be the same as the sign of other. 3158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista comparison = self.__cmp__(other) 3169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == 0: 317072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.copy_sign(other) 3171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == -1: 3173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_plus(context) 3174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # comparison == 1 3175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_minus(context) 3176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decide which flags to raise using value of ans 3178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._isinfinity(): 3179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Overflow, 3180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'Infinite result from next_toward', 3181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans._sign) 3182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif ans.adjusted() < context.Emin: 3185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 3186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 3187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if precision == 1 then we don't raise Clamped for a 3190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result 0E-Etiny. 3191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 3192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 3193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, context=None): 3197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of self. 3198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 3200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 3201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 3202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 3203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 3204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 3205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 3206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 3207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 3208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 3209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 3210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_snan(): 3212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "sNaN" 3213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_qnan(): 3214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "NaN" 3215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista inf = self._isinfinity() 3216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == 1: 3217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Infinity" 3218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == -1: 3219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Infinity" 3220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_zero(): 3221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Zero" 3223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Zero" 3225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_subnormal(context=context): 3228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Subnormal" 3230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Subnormal" 3232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # just a normal, regular, boring number, :) 3233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Normal" 3235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Normal" 3237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 3239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :)""" 3240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 3241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, other, context=None): 3243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of self, value-of-other times.""" 3244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 32576c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 326472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's rotate! 3267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[torot:] + rotdig[:torot] 326872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 326972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, other, context=None): 3272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self operand after adding the second value to its exp.""" 3273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista liminf = -2 * (context.Emax + context.prec) 3283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista limsup = 2 * (context.Emax + context.prec) 3284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (liminf <= int(other) <= limsup): 3285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 32886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 329072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) 3291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista d = d._fix(context) 3292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return d 3293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, other, context=None): 3295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of self, value-of-other times.""" 3296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33096c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not torot: 33146c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 331872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's shift! 3321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if torot < 0: 3322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[:torot] 3323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 332472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated = rotdig + '0'*torot 3325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotated[-context.prec:] 3326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 332772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 332872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 333059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Support for pickling, copy, and deepcopy 33317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 33327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 33337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 33357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3336cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # I'm immutable; therefore I am my own clone 33377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 33387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 33407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3341cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # My components are also immutable 33427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 33437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 334472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistadef _dec_from_triple(sign, coefficient, exponent, special=False): 334572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """Create a decimal instance directly, without any validation, 334672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista normalization (e.g. removal of leading zeros) or argument 334772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista conversion. 334872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 334972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista This function is for *internal use only*. 335072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """ 335172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 335272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = object.__new__(Decimal) 335372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._sign = sign 335472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = coefficient 335572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp = exponent 335672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._is_special = special 335772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 335872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self 335972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 336059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context class ####################################################### 3361cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 33627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3363cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# get rounding method function: 336459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batistarounding_functions = [name for name in Decimal.__dict__.keys() 336559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if name.startswith('_round_')] 33667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 336759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 33687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 33697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 33707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 33717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 33737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3374ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlanclass _ContextManager(object): 33758b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Context manager class to support localcontext(). 33761a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 3377ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan Sets a copy of the supplied context in __enter__() and restores 33788b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan the previous decimal context in __exit__() 33798b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 33801a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 3381ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan self.new_context = new_context.copy() 33821a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 33831a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 33841a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 33851a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 33861a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 33871a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 33881a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 33897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 33907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 33917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 33937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 339459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista rounding - rounding type (how you round) 3395bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 33967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 33977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 33987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 33997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 34007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 34010ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 34020ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 34037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 34047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 3405e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 34067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 34079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 34087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 3409abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 34100ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 3411e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 3412abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 3413abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 3414abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 3415abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 3416abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 3417bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 3418fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 3419b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 3420bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 3421fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 3422b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 34237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 34247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 3425eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 34267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 34277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 34287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 34297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3430b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 3431bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 3432b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 343359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' 343459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' 343559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista % vars(self)) 343659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [f.__name__ for f, v in self.flags.items() if v] 343759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('flags=[' + ', '.join(names) + ']') 343859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [t.__name__ for t, v in self.traps.items() if v] 343959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('traps=[' + ', '.join(names) + ']') 3440b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 3441b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 3442d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 3443d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 3444d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 3445b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 3446d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 34479fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 34489fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 3449e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista nc = Context(self.prec, self.rounding, self.traps, 3450e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags, self.Emin, self.Emax, 3451e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 34527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 34539fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 34549fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 34559fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 345659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista nc = Context(self.prec, self.rounding, self.traps.copy(), 3457e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.flags.copy(), self.Emin, self.Emax, 3458e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista self.capitals, self._clamp, self._ignored_flags) 34599fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 34609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 34617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34625aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 34637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 34647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 34667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 34677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 34687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 34697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 34705aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 34717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 347259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Don't touch the flag 34737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 34747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 3476bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 347759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # The errors define how to handle themselves. 34785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 34797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 348159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # self._ignored_flags = [] 34827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 34837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 34857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 3486fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 34877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 34897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 34907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 34917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 34927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 34937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 34947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 34967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 34977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 34987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 34997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 35007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 35017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35025aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 35035aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 35045aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 350559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise TypeError("Cannot hash a Context.") 35065aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 35077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 35087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 35097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 35107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 3512e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 35137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 35147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 35167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 35177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 35197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 35207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 35227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 35237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 35247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 35257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 35267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 35277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 35297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 35317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 35327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 35337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3534fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 35357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Creates a new Decimal instance but using self as context.""" 35367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 3537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if d._isnan() and len(d._int) > self.prec - self._clamp: 3538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._raise_error(ConversionSyntax, 3539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista "diagnostic info too long in NaN") 3540dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 35417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 354259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Methods 35437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 35447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 35457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 354759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation on the operand. Otherwise, the result is the same as using 35487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 35497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 35517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 35529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 35537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 35549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 35557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 35569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 35577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 35587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 35607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 35627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 35637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 35657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("19.00") 35669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 35677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.02E+4") 35687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 35707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 3572dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 35737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, a): 3575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 3576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 3578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 3579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.canonical(Decimal('2.50')) 3581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.50") 3582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.canonical(context=self) 3584353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 35857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 35867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 35877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 35897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 35907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 35917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 35927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 35937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 35957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 35967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 35977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 35987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35999ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 36007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 36019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 36027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 36039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 36047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 36059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 36067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 36079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 36087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 36099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 36107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 36117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 36137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, a, b): 3615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values of the two operands numerically. 3616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 3618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 3619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext 3621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('3')) 3622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) 3624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) 3629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("NaN") 3630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) 3636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("NaN") 3637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_signal(b, context=self) 3641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, a, b): 3643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation. 3644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 3646353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 3647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 3648353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) 3650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) 3652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) 3654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) 3656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) 3658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 3659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) 3660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total(b) 3663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, a, b): 3665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation ignoring sign. 3666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 3668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total_mag(b) 3670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self, a): 3672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign set to 0. 3673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('2.1')) 3675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.1") 3676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('-100')) 3677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 3678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_abs() 3680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_decimal(self, a): 3682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the decimal objet. 3683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('2.1')) 3685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.1") 3686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('-1.00')) 3687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00") 3688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 36896c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(a) 3690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self, a): 3692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign inverted. 3693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('101.5')) 3695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-101.5") 3696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('-101.5')) 3697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("101.5") 3698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_negate() 3700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, a, b): 3702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Copies the second operand's sign to the first one. 3703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In detail, it returns a copy of the first operand with the sign 3705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista equal to the sign of the second operand. 3706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) 3708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.50") 3709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) 3710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.50") 3711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) 3712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.50") 3713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) 3714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.50") 3715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_sign(b) 3717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 37187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 37197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 37207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 37227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.333333333") 37239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 37247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.666666667") 37259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 37267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.5") 37279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 37287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 37299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 37307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 37319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 37327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.00") 37339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 37347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20") 37359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 37367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 37379ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 37387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1000") 37399ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 37407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20E+6") 37417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 37437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 37457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 37467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 37487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 37499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 37507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 37519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 37527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 37537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 37557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 37577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 37587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, a): 3760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** a. 3761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-Infinity')) 3766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-1')) 3768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.367879441") 3769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0')) 3770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 3771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('1')) 3772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.71828183") 3773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0.693147181')) 3774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.00000000") 3775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('+Infinity')) 3776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 3777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.exp(context=self) 3779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, a, b, c): 3781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a multiplied by b, plus c. 3782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The first two operands are multiplied together, using multiply, 3784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the third operand is then added to the result of that 3785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplication, using add, all with only one final rounding. 3786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) 3788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("22") 3789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) 3790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-8") 3791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) 3792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.38435736E+12") 3793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.fma(b, c, context=self) 3795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self, a): 37971a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is canonical; otherwise return False. 37981a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 37991a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 38001a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 3801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_canonical(Decimal('2.50')) 38031a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 38051a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return a.is_canonical() 3806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self, a): 38081a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is finite; otherwise return False. 3809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 38101a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 38111a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 3812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('2.50')) 38141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('-0.3')) 38161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('0')) 38181a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('Inf')) 38201a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('NaN')) 38221a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_finite() 3825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self, a): 38271a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is infinite; otherwise return False. 3828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('2.50')) 38301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('-Inf')) 38321a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('NaN')) 38341a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_infinite() 3837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self, a): 38391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a qNaN or sNaN; 38401a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('2.50')) 38431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('NaN')) 38451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('-sNaN')) 38471a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_nan() 3850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, a): 38521a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a normal number; 38531a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('2.50')) 38591a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.1E-999')) 38611a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.00')) 38631a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('-Inf')) 38651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('NaN')) 38671a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_normal(context=self) 3870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self, a): 38721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a quiet NaN; otherwise return False. 3873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('2.50')) 38751a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('NaN')) 38771a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('sNaN')) 38791a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_qnan() 3882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self, a): 38841a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is negative; otherwise return False. 3885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('2.50')) 38871a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-12')) 38891a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-0')) 38911a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_signed() 3894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self, a): 38961a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a signaling NaN; 38971a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('2.50')) 39001a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('NaN')) 39021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('sNaN')) 39041a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_snan() 3907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, a): 39091a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is subnormal; otherwise return False. 3910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('2.50')) 39151a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.1E-999')) 39171a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.00')) 39191a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('-Inf')) 39211a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('NaN')) 39231a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_subnormal(context=self) 3926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self, a): 39281a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a zero; otherwise return False. 3929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('0')) 39311a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('2.50')) 39331a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('-0E+2')) 39351a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_zero() 3938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, a): 3940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of the operand. 3941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('0')) 3946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 3947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('1.000')) 3948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('2.71828183')) 3950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000000") 3951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('10')) 3952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.30258509") 3953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('+Infinity')) 3954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 3955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.ln(context=self) 3957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, a): 3959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of the operand. 3960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0')) 3965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 3966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0.001')) 3967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-3") 3968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('1.000')) 3969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('2')) 3971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.301029996") 3972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('10')) 3973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 3974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('70')) 3975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.84509804") 3976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('+Infinity')) 3977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 3978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.log10(context=self) 3980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, a): 3982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of the operand's MSD. 3983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 3985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of the operand (as though the 3986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand were truncated to a single digit while maintaining the 3987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value of that digit and without limiting the resulting exponent). 3988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('250')) 3990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2") 3991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('2.50')) 3992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0.03')) 3994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-2") 3995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0')) 3996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 3997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logb(context=self) 3999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, a, b): 4001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'and' between each operand's digits. 4002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) 4006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) 4008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) 4010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) 4012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) 4014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1000") 4015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) 4016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10") 4017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_and(b, context=self) 4019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, a): 4021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all the digits in the operand. 4022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operand must be a logical number. 4024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('0')) 4026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("111111111") 4027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('1')) 4028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("111111110") 4029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('111111111')) 4030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('101010101')) 4032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10101010") 4033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_invert(context=self) 4035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, a, b): 4037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'or' between each operand's digits. 4038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) 4042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) 4044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) 4046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) 4048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) 4050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1110") 4051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) 4052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1110") 4053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_or(b, context=self) 4055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, a, b): 4057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'xor' between each operand's digits. 4058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) 4062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) 4064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) 4066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) 4068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) 4070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("110") 4071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) 4072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1101") 4073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_xor(b, context=self) 4075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 40767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 40777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 40787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 40797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 40807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 408159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 408259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the maximum (closer to positive 40837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 40847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 40859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 40867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 40879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 40887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 40899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 4090d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("1") 4091d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 4092d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 40937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 40947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 40957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, a, b): 4097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.max_mag(b, context=self) 4099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 41017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 41027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 41047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 410559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 410659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the minimum (closer to negative 41077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 41087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 41107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 41119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 41127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-10") 41139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 41147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 4115d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 4116d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 41177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 41197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, a, b): 4121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.min_mag(b, context=self) 4123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 41257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 41267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 41287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 41297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 41307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 41327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 41339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 41347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 41357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 41377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 41397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 41407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4141cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis If either operand is a special value then the general rules apply. 4142cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Otherwise, the operands are multiplied together ('long multiplication'), 4143cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis resulting in a number which may be as long as the sum of the lengths 4144cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis of the two operands. 41457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 41477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.60") 41489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 41497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("21") 41509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 41517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.72") 41529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 41537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.0") 41549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 41557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.28135971E+11") 41567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 41587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, a): 4160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than a. 4161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4163353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4164353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('1')) 4166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.999999999") 4167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('1E-1007')) 4168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0E-1007") 4169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('-1.00000003')) 4170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000004") 4171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('Infinity')) 4172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("9.99999999E+999") 4173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_minus(context=self) 4175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, a): 4177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than a. 4178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('1')) 4183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000001") 4184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-1E-1007')) 4185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0E-1007") 4186353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('-1.00000003')) 4187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000002") 4188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-Infinity')) 4189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-9.99999999E+999") 4190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_plus(context=self) 4192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, a, b): 4194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to a, in direction towards b. 4195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number from the first 4197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand (but not the first operand) that is in the direction 4198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista towards the second operand, unless the operands have the same 4199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. 4200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('2')) 4205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000001") 4206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) 4207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0E-1007") 4208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) 4209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000002") 4210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('0')) 4211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.999999999") 4212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) 4213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0E-1007") 4214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) 4215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000004") 4216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) 4217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0.00") 4218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_toward(b, context=self) 4220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 42217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 4222e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 42237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 42257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 42267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 42287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 42299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 42307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 42319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 42327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2") 42339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 42347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.2E+2") 42359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 42367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2E+2") 42379ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 42387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 42397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 42407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 42417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, a): 4243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of the operand. 4244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 4246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 4247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 4248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 4249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 4250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 4251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 4252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 4253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 4254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 4255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 4256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = Context(ExtendedContext) 4258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('Infinity')) 4261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Infinity' 4262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('1E-10')) 4263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('2.50')) 4265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0.1E-999')) 4267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Subnormal' 4268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0')) 4269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Zero' 4270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0')) 4271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Zero' 4272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0.1E-999')) 4273353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Subnormal' 4274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-1E-10')) 4275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-2.50')) 4277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-Infinity')) 4279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Infinity' 4280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('NaN')) 4281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-NaN')) 4283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('sNaN')) 4285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'sNaN' 4286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.number_class(context=self) 4288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 42897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 42907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 42917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 42937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 42947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 42957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 42977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 42989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 42997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 43007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 43027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 43047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 43057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute a**b. If a is negative then b 4307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista must be integral. The result will be inexact unless b is 4308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integral and the result is finite and can be expressed exactly 4309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in 'precision' digits. 4310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (a**b) % modulo. For the 4312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 4313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 4314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 4316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - b must be nonnegative 4317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - at least one of a or b must be nonzero 4318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and have at most 'precision' digits 4319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(a, b, modulo) is identical to the result 4321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that would be obtained by computing (a**b) % modulo with 4322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unbounded precision, but is computed more efficiently. It is 4323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista always exact. 4324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('3')) 43297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("8") 4330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-2'), Decimal('3')) 4331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-8") 4332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('-3')) 43337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.125") 4334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('1.7'), Decimal('8')) 43357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("69.7575744") 4336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('10'), Decimal('0.301029996')) 4337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.00000000") 4338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('-1')) 43397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 4340353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('0')) 43417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 4342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('1')) 43437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 4344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('-1')) 43457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 4346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('0')) 43477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 4348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('1')) 43497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 4350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('2')) 43517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 4352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('0'), Decimal('0')) 43537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 4354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) 4356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11") 4357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) 4358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-11") 4359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) 4360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) 4362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11") 4363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) 4364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11729830") 4365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) 4366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0") 4367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) 4368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 43697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 43717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 437359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Returns a value equal to 'a' (rounded), having the exponent of 'b'. 43747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 437659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operand. It may be rounded using the current rounding setting (if the 43777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 43787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 43797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 43807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 43827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 438359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation condition is raised. This guarantees that, unless there is 438459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista an error condition, the exponent of the result of a quantize is always 43857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 43867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 43887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 43897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 43917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.170") 43929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 43937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.17") 43949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 43957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2") 43969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 43977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 43989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 43997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0E+1") 44009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 44017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 44029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 44037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 44057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 44069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 44077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0E+5") 44089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 44097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 44117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 44137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217.0") 44149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 44157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217") 44169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 44177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2E+2") 44189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 44197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2E+2") 44207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 44227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 4424353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :) 4425353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4426353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.radix() 4427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10") 4428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 4430353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 44317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 44327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 44337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 443559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista calculating integer division as described for divide-integer, rounded 44360d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz to precision digits if necessary. The sign of the result, if 443759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista non-zero, is the same as that of the original dividend. 44387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 44407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 44417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 44427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44439ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 44447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 44459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 44467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 44479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 44487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 44499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 44507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 44519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 44527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 44539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 44547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 44557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 44577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 44597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 44607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 446159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen). If the result is equal to 0 then its sign will be the 44627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 44637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 44657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 44667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 44677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 44697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.9") 44709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 44717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 44729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 44737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 44749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 44757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 44769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 44777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 44789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 44797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 44809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 44817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.3") 44827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 44847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, a, b): 4486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of a, b times. 4487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a rotated copy of the digits in 4489353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the coefficient of the first operand. The number of places of 4490353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotation is taken from the absolute value of the second operand, 4491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the rotation being to the left if the second operand is 4492353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. 4493353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) 4495353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("400000003") 4496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) 4497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("12") 4498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) 4499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("891234567") 4500353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) 4501353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("123456789") 4502353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) 4503353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("345678912") 4504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.rotate(b, context=self) 4506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 45087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 45097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 45117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 45127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 45147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 45159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 45167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 45179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 45187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 45199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 45207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 45217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 45237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, a, b): 4525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the first operand after adding the second value its exp. 4526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) 4528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.0750") 4529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) 4530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.50") 4531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) 4532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.50E+3") 4533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.scaleb (b, context=self) 4535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, a, b): 4537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of a, b times. 4538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a shifted copy of the digits 4540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the coefficient of the first operand. The number of places 4541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to shift is taken from the absolute value of the second operand, 4542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the shift being to the left if the second operand is 4543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. Digits shifted into the 4544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coefficient are zeros. 4545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) 4547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("400000000") 4548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) 4549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) 4551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1234567") 4552353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) 4553353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("123456789") 4554353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) 4555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("345678900") 4556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4557353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.shift(b, context=self) 4558353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 456059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Square root of a non-negative number to context precision. 45617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 45637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 45647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 45667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 45679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 45687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 45699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 45707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.624499800") 45719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 45727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 45739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 45747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 45759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 45767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 45779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 45787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 45799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 45807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.64575131") 45819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 45827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.16227766") 45839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 45846ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 45857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 45877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 4589f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 45907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 45927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.23") 45939ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 45947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.00") 45959ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 45967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.77") 45977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 45997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 46017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 46027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 46047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 46067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 46087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 46097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 46117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 46137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, a): 4615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to an integer. 4616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista When the operand has a negative exponent, the result is the same 4618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista as using the quantize() operation using the given operand as the 4619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista left-hand-operand, 1E+0 as the right-hand-operand, and the precision 4620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the operand as the precision setting; Inexact and Rounded flags 4621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista are allowed in this operation. The rounding mode is taken from the 4622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 4623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('2.1')) 4625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2") 4626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100')) 4627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 4628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100.0')) 4629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 4630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('101.5')) 4631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("102") 4632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) 4633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-102") 4634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) 4635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.0E+6") 4636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) 4637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.89E+77") 4638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) 4639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 4640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_exact(context=self) 4642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, a): 46447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 46457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 46477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 46487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 46497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 465059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be set. The rounding mode is taken from the context. 46517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('2.1')) 46537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 4654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100')) 46557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 4656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100.0')) 46577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 4658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('101.5')) 46597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("102") 4660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-101.5')) 46617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-102") 4662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('10E+5')) 46637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0E+6") 4664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) 46657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("7.89E+77") 4666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-Inf')) 46677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 46687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_value(context=self) 4670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 4672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 46737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 46757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 467617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 4677636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 46787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 46797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 46817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 46827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 4683636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 46847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 468517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 468617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 468772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self.int = int(value._int) 46887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 468917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 469017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 46917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 46927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 46937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 46947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 46967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 46977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 46997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4702e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batistadef _normalize(op1, op2, prec = 0): 47037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 47047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 47067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp < op2.exp: 47087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 47097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 47107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 47117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 47127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 47137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). 4715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then adding 10**exp to tmp has the same effect (after rounding) 4716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as adding any positive quantity smaller than 10**exp; similarly 4717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for subtraction. So if other is smaller than 10**exp we replace 4718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # it with 10**exp. This avoids tmp.exp - other.exp getting too large. 4719e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista tmp_len = len(str(tmp.int)) 4720e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other_len = len(str(other.int)) 4721e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista exp = tmp.exp + min(-1, tmp_len - prec - 2) 4722e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista if other_len + other.exp - 1 < exp: 4723e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.int = 1 4724e64acfad3dd13809943eecf50f11c40c510dedbeFacundo Batista other.exp = exp 4725636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 4726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.int *= 10 ** (tmp.exp - other.exp) 4727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.exp = other.exp 47287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 47297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### 4731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# This function from Tim Peters was taken from here: 4733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# http://mail.python.org/pipermail/python-list/1999-July/007758.html 4734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# The correction being in the function definition is for speed, and 4735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the whole function is not resolved with math.log because of avoiding 4736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the use of floats. 4737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _nbits(n, correction = { 4738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0': 4, '1': 3, '2': 2, '3': 2, 4739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '4': 1, '5': 1, '6': 1, '7': 1, 4740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '8': 0, '9': 0, 'a': 0, 'b': 0, 4741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'c': 0, 'd': 0, 'e': 0, 'f': 0}): 4742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Number of bits in binary representation of the positive integer n, 4743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or 0 if n == 0. 4744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n < 0: 4746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _nbits should be nonnegative.") 4747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista hex_n = "%x" % n 4748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 4*len(hex_n) - correction[hex_n[0]] 4749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _sqrt_nearest(n, a): 4751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to the square root of the positive integer n. a is 4752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an initial approximation to the square root. Any positive integer 4753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista will do for a, but the closer a is to the square root of n the 4754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista faster convergence will be. 4755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= 0 or a <= 0: 4758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("Both arguments to _sqrt_nearest should be positive.") 4759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b=0 4761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while a != b: 4762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, a = a, a--n//a>>1 4763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a 4764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _rshift_nearest(x, shift): 4766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given an integer x and a nonnegative integer shift, return closest 4767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integer to x / 2**shift; use round-to-even in case of a tie. 4768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, q = 1L << shift, x >> shift 4771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*(x & (b-1)) + (q&1) > b) 4772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _div_nearest(a, b): 4774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to a/b, a and b positive integers; rounds to even 4775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the case of a tie. 4776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(a, b) 4779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*r + (q&1) > b) 4780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _ilog(x, M, L = 8): 4782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Integer approximation to M*log(x/M), with absolute error boundable 4783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in terms only of x/M. 4784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given positive integers x and M, return an integer approximation to 4786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference 4787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista between the approximation and the exact result is at most 22. For 4788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In 4789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista both cases these are upper bounds on the error; it will usually be 4790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista much smaller.""" 4791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The basic algorithm is the following: let log1p be the function 4793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use 4794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the reduction 4795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) 4797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # repeatedly until the argument to log1p is small (< 2**-L in 4799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # absolute value). For small y we can use the Taylor series 4800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expansion 4801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T 4803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # truncating at T such that y**T is small enough. The whole 4805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # computation is carried out in a form of fixed-point arithmetic, 4806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with a real number z being represented by an integer 4807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # approximation to z*M. To avoid loss of precision, the y below 4808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is actually an integer approximation to 2**R*y*M, where R is the 4809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number of reductions performed so far. 4810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = x-M 4812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument reduction; R = number of reductions performed 4813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = 0 4814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while (R <= L and long(abs(y)) << L-R >= M or 4815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R > L and abs(y) >> R-L >= M): 4816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(long(M*y) << 1, 4817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) 4818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R += 1 4819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series with T terms 4821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 4822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yshift = _rshift_nearest(y, R) 4823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, T) 4824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(T-1, 0, -1): 4825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, k) - _div_nearest(yshift*w, M) 4826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(w*y, M) 4828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog10(c, e, p): 4830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, p >= 0, compute an integer 4831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log10(c*10**e), with an absolute error of 4832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # increase precision by 2; compensate for this by dividing 4835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # final result by 100 4836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write c*10**e as d*10**f with either: 4839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f >= 0 and 1 <= d <= 10, or 4840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f <= 0 and 0.1 <= d <= 1. 4841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Thus for c*10**e close to 1, f = 0 4842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M = 10**p 4847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) 4852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, M) # error < 5 + 22 = 27 4854be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista log_10 = _log10_digits(p) # error < 1 4855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _div_nearest(log_d*M, log_10) 4856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = f*M # exact 4857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 # error < 2.31 4859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = div_nearest(f, 10**-p) # error < 0.5 4860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(log_tenpower+log_d, 100) 4862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog(c, e, p): 4864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, compute an integer 4865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log(c*10**e), with an absolute error of 4866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Increase precision by 2. The precision increase is compensated 4869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for at the end with a division by 100. 4870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, 4873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) 4874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as 10**p * log(d) + 10**p*f * log(10). 4875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute approximation to 10**p*log(d), with error < 27 4879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) # error of <= 0.5 in c 4885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # _ilog magnifies existing error in c by a factor of at most 10 4887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 4888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p <= 0: just approximate the whole thing by 0; error < 2.31 4890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 4891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4892be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute approximation to f*10**p*log(10), with error < 11. 4893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if f: 4894be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = len(str(abs(f)))-1 4895be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p + extra >= 0: 4896be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in f * _log10_digits(p+extra) < |f| * 1 = |f| 4897be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 4898be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) 4899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 4901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 4903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4904be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 4905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(f_log_ten + log_d, 100) 4906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4907be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batistaclass _Log10Memoize(object): 4908be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Class to compute, store, and allow retrieval of, digits of the 4909be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista constant log(10) = 2.302585.... This constant is needed by 4910be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" 4911be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def __init__(self): 4912be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = "23025850929940456840179914546843642076011014886" 4913be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4914be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def getdigits(self, p): 4915be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Given an integer p >= 0, return floor(10**p)*log(10). 4916be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4917be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista For example, self.getdigits(3) returns 2302. 4918be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """ 4919be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits are stored as a string, for quick conversion to 4920be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # integer in the case that we've already computed enough 4921be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits; the stored digits should always be correct 4922be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # (truncated, not rounded to nearest). 4923be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p < 0: 4924be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista raise ValueError("p should be nonnegative") 4925be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4926be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p >= len(self.digits): 4927be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+3, p+6, p+9, ... digits; continue until at 4928be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # least one of the extra digits is nonzero 4929be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = 3 4930be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista while True: 4931be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+extra digits, correct to within 1ulp 4932be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista M = 10**(p+extra+2) 4933be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista digits = str(_div_nearest(_ilog(10*M, M), 100)) 4934be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if digits[-extra:] != '0'*extra: 4935be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista break 4936be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra += 3 4937be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # keep all reliable digits so far; remove trailing zeros 4938be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # and next nonzero digit 4939be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = digits.rstrip('0')[:-1] 4940be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista return int(self.digits[:p+1]) 4941be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4942be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista_log10_digits = _Log10Memoize().getdigits 4943be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _iexp(x, M, L=8): 4945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers x and M, M > 0, such that x/M is small in absolute 4946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value, compute an integer approximation to M*exp(x/M). For 0 <= 4947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x/M <= 2.4, the absolute error in the result is bounded by 60 (and 4948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista is usually much smaller).""" 4949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Algorithm: to compute exp(z) for a real number z, first divide z 4951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then 4952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor 4953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # series 4954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(x) = x + x**2/2! + x**3/3! + ... 4956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Now use the identity 4958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(2x) = expm1(x)*(expm1(x)+2) 4960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # R times to compute the sequence expm1(z/2**R), 4962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). 4963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find R such that x/2**R/M <= 2**-L 4965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = _nbits((long(x)<<L)//M) 4966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series. (2**L)**T > M 4968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 4969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x, T) 4970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<R 4971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(T-1, 0, -1): 4972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x*(Mshift + y), Mshift * i) 4973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Expansion 4975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(R-1, -1, -1): 4976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<(k+2) 4977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(y*(y+Mshift), Mshift) 4978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return M+y 4980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dexp(c, e, p): 4982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute an approximation to exp(c*10**e), with p decimal places of 4983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista precision. 4984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4985be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Returns integers d, f such that: 4986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= d <= 10**p, and 4988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (d-1)*10**f < exp(c*10**e) < (d+1)*10**f 4989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, d*10**f is an approximation to exp(c*10**e) with p 4991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision, and with an error in d of at most 1. This is 4992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when d 4993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista = 10**(p-1) the error could be up to 10 ulp.""" 4994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision 4996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4998be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute log(10) with extra precision = adjusted exponent of c*10**e 4999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = max(0, e + len(str(c)) - 1) 5000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = p + extra 5001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5002be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), 5003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding down 5004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = e+q 5005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c*10**shift 5007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c//10**-shift 5009be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista quot, rem = divmod(cshift, _log10_digits(q)) 5010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reduce remainder back to original precision 5012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rem = _div_nearest(rem, 10**extra) 5013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # error in result of _iexp < 120; error after division < 0.62 5015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 5016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dpower(xc, xe, yc, ye, p): 5018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and 5019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 5020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= c <= 10**p, and 5022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (c-1)*10**e < x**y < (c+1)*10**e 5023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in other words, c*10**e is an approximation to x**y with p digits 5025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of precision, and with an error in c of at most 1. (This is 5026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when c 5027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista == 10**(p-1) we can only guarantee error < 10ulp.) 5028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista We assume that: x is positive and not equal to 1, and y is nonzero. 5030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find b such that 10**(b-1) <= |y| <= 10**b 5033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b = len(str(abs(yc))) + ye 5034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point 5036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista lxc = _dlog(xc, xe, p+b+1) 5037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) 5039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = ye-b 5040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = lxc*yc*10**shift 5042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = _div_nearest(lxc*yc, 10**-shift) 5044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if pc == 0: 5046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we prefer a result that isn't exactly 1; this makes it 5047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # easier to compute a correctly rounded result in __pow__ 5048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: 5049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**(p-1)+1, 1-p 5050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**p-1, -p 5052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(pc, -(p+1), p+1) 5054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _div_nearest(coeff, 10) 5055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp += 1 5056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return coeff, exp 5058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _log10_lb(c, correction = { 5060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, 5061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '6': 23, '7': 16, '8': 10, '9': 5}): 5062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for 100*log10(c) for a positive integer c.""" 5063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c <= 0: 5064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _log10_lb should be nonnegative.") 5065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_c = str(c) 5066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 100*len(str_c) - correction[str_c[0]] 5067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 506859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Helper Functions #################################################### 50697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _convert_other(other, raiseit=False): 5071636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 5072636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5073636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5074636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 5075636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 5076636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 5077636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 5078636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 5079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if raiseit: 5080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise TypeError("Unable to convert %s to Decimal" % other) 5081267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 5082636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 508359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Setup Specific Contexts ############################################ 50847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 5086fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 50877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 50896ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 5090bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 5091bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 509299148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 509399148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 5094e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 50957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 50967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 50977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 50987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 50997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 51007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 51017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 51037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 5104bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 5105bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 51067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 51096ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 5110bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 5111bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 51127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 511559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### crud for parsing strings ############################################# 51167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport re 51177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 511872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Regular expression used for parsing numeric strings. Additional 511972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# comments: 512072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 512172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 1. Uncomment the two '\s*' lines to allow leading and/or trailing 512272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# whitespace. But note that the specification disallows whitespace in 512372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# a numeric string. 512472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 512572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 2. For finite numbers (not infinities and NaNs) the body of the 512672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# number between the optional sign and the optional exponent must have 512772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# at least one decimal digit, possibly after the decimal point. The 512872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# lookahead expression '(?=\d|\.\d)' checks this. 512972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 513072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# As the flag UNICODE is not enabled here, we're explicitly avoiding any 513172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# other meaning for \d than the numbers [0-9]. 51327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 513372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistaimport re 513472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista_parser = re.compile(r""" # A numeric string consists of: 51357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 513672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<sign>[-+])? # an optional sign, followed by either... 51377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 513872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?=\d|\.\d) # ...a number (with at least one digit) 513972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<int>\d*) # consisting of a (possibly empty) integer part 514072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (\.(?P<frac>\d*))? # followed by an optional fractional part 514172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... 51427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 514372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista Inf(inity)? # ...an infinity, or... 514472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista | 514572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<signal>s)? # ...an (optionally signaling) 514672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista NaN # NaN 514772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<diag>\d*) # with (possibly empty) diagnostic information. 51487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 51497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 51507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger $ 515172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista""", re.VERBOSE | re.IGNORECASE).match 51527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51532ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_all_zeros = re.compile('0*$').match 51542ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_exact_half = re.compile('50*$').match 51557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 51567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51570d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz 515872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista##### Useful Constants (internal use only) ################################ 51597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 516072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Reusable defaults 516172bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInf = Decimal('Inf') 516272bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistanegInf = Decimal('-Inf') 516372bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaNaN = Decimal('NaN') 516472bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_0 = Decimal(0) 516572bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p1 = Decimal(1) 516672bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n1 = Decimal(-1) 516772bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p2 = Decimal(2) 516872bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n2 = Decimal(-2) 51697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 517072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Infsign[sign] is infinity w/ that sign 517172bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInfsign = (Inf, negInf) 51727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 51767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 51777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 5178