decimal.py revision 2ec7415db5ad63c4e4b27ee793214071454f6fe5
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# Rounding decision (not part of the public API) 1500ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerNEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY 1510ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. 1527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista# Errors 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1565aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 164cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis handle -- Called when context._raise_error is called and the 165cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis trap_enabler is set. First argument is self, second is the 166cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context. More arguments can be given, those being after 167cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis the explanation in _raise_error (For example, 168cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis context._raise_error(NewError, '(-x)!', self._sign) would 169cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis call NewError().handle(context, self._sign).) 170cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 18359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista representation. This may occur when the exponent of a zero result would 18459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be outside the bounds of a representation, or when a large normal 18559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista number would have an encoded exponent that cannot be represented. In 1867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 19859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 0 * (+-)INF 19959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista (+-)INF / (+-)INF 2007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of the operation after these is a quiet positive NaN, 210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista except when the cause is a signaling NaN, in which case the result is 211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista also a quiet NaN, but with the original sign, and an optional 212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista diagnostic information. 2137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 21659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if args[0] == 1: # sNaN, must drop 's' but keep diagnostics 21772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(args[1]._sign, args[1]._int, 'n', True) 218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix_nan(context) 219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif args[0] == 2: 22072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(args[1], args[2], 'n', True) 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 22959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista syntax. The result is [0,qNaN]. 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 231cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis def handle(self, context, *args): 232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return NaN 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 246cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 247cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, sign, *args): 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 25559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista longer than precision). The result is [0,qNaN]. 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 257cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 259cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NaN 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 26659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the dividend is also zero. The result is [0,qNaN]. 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 268cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 269cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def handle(self, context, *args): 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 27759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista were non-zero), or if an overflow or underflow condition occurs. The 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2835aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 28959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista detected during an operation. This can occur if contexts are not checked 2907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 29259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista was specified. These aspects of the context need only be checked when 29359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the values are required to be used. The result is [0,qNaN]. 2947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 295cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 3007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 3017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 30459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista coefficient), or if an overflow or underflow condition occurs. The 3057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3105aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 31759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin, before any rounding). The result in all cases is unchanged. 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 33659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista where sign is the sign of the intermediate result. For round-down, the 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 33859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista current precision, with the sign of the intermediate result. For 3397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 34059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 34259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 344cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis """ 345cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ROUND_HALF_DOWN, ROUND_UP): 3497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 35372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 35872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '9'*context.prec, 35972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context.Emax-context.prec+1) 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 36859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Emin). That is, the result is both inexact and subnormal. 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 37159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista necessary, so that its exponent is not less than Etiny. This may result 3727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 378fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 379cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Underflow, InvalidOperation, Subnormal] 3807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3815aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3825aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3835aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3845aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3855aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 38759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context Functions ################################################## 3887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 389ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 390ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 391ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 3927e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# work for older Pythons. If threads are not part of the build, create a 393cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# mock threading object with threading.local() returning the module namespace. 3947e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger 3957e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingertry: 3967e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import threading 3977e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingerexcept ImportError: 3987e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger # Python was compiled without threads; create a mock object instead 3997e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import sys 40059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista class MockThreading(object): 4017e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger def local(self, sys=sys): 4027e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger return sys.modules[__name__] 4037e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger threading = MockThreading() 4047e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger del sys, MockThreading 405ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 406ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 407ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 41159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # To fix reloading, force it to create a new context 41259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Old contexts have different exceptions in their dicts, making problems. 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 414ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 415ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 416ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 417ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4199fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 42061992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 435ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 436ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 437ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4409fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4419fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 445ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 446ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 450ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 451ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 452ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 453ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 454ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 455ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 456ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 457ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 458ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 459ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4609fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 46161992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 462ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 463ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 464cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis del threading, local # Don't contaminate the namespace 4657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4668b6999b4c5fab174090be263ba90f193bdede141Nick Coghlandef localcontext(ctx=None): 4678b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Return a context manager for a copy of the supplied context 4688b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4698b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan Uses a copy of the current context if no context is specified 4708b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan The returned context manager creates a local decimal context 4718b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan in a with statement: 4728b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4738b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext() as ctx: 4748b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ctx.prec += 2 4758b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4768b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses a precision 2 greater than normal 47759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal precision 4788b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4798b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan def sin(x): 4808b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan with localcontext(ExtendedContext): 4818b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # Rest of sin calculation algorithm 4828b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # uses the Extended Context from the 4838b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # General Decimal Arithmetic Specification 48459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return +s # Convert result to normal context 4858b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 4868b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 487681d86743c21773bb00508dbacb05ed9012388d8Neal Norwitz # The string below can't be included in the docstring until Python 2.6 4888b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan # as the doctest module doesn't understand __future__ statements 4898b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 4908b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> from __future__ import with_statement 4918b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 4928b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 4938b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(): 4948b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... ctx = getcontext() 495495df4716fce4156c1eb110f9342297164eecbb6Raymond Hettinger ... ctx.prec += 2 4968b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print ctx.prec 4978b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 4988b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 30 4998b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> with localcontext(ExtendedContext): 5008b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... print getcontext().prec 5018b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan ... 5028b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 9 5038b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan >>> print getcontext().prec 5048b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 28 5058b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 506ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan if ctx is None: ctx = getcontext() 507ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan return _ContextManager(ctx) 5088b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan 5097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Decimal class ####################################################### 5117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 5137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 5147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 515636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger __slots__ = ('_exp','_int','_sign', '_is_special') 516636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Generally, the value of the Decimal instance is given by 517636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (-1)**_sign * _int * 10**_exp 518636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special values are signified by _is_special == True 5197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 520dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger # We're immutable, so use __new__ not __init__ 521636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger def __new__(cls, value="0", context=None): 5227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 5237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 5257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 52659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) 5277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 5287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 5297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 5307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 5317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 5327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 53472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Note that the coefficient, self._int, is actually stored as 53572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # a string rather than as a tuple of digits. This speeds up 53672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # the "digits to integer" and "integer to digits" conversions 53772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # that are used in almost every arithmetic operation on 53872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # Decimals. This is an internal detail: the as_tuple function 53972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # and the Decimal constructor still deal with tuples of 54072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista # digits. 54172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 542636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self = object.__new__(cls) 543636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5440d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From a string 5450d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # REs insist on real strings, so we can too. 5460d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, basestring): 5470d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista m = _parser(value) 5480d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m is None: 5490d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if context is None: 5500d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista context = getcontext() 5510d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return context._raise_error(ConversionSyntax, 5520d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista "Invalid literal for Decimal: %r" % value) 553636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5540d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('sign') == "-": 5550d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 1 5560d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5570d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = 0 5580d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista intpart = m.group('int') 5590d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if intpart is not None: 5600d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # finite number 5610d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista fracpart = m.group('frac') 5620d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista exp = int(m.group('exp') or '0') 5630d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if fracpart is not None: 5640d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = (intpart+fracpart).lstrip('0') or '0' 5650d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp - len(fracpart) 5660d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5670d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = intpart.lstrip('0') or '0' 5680d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = exp 5690d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5700d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5710d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista diag = m.group('diag') 5720d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if diag is not None: 5730d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # NaN 5740d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = diag.lstrip('0') 5750d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if m.group('signal'): 5760d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'N' 5770d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5780d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'n' 5790d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista else: 5800d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # infinity 5810d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = '0' 5820d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = 'F' 5830d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = True 584636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 585636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 586636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From an integer 5877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 588636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if value >= 0: 589636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 0 590636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 591636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 1 592636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = 0 59372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = str(abs(value)) 5940d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 5950d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 5960d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 5970d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From another decimal 5980d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, Decimal): 5990d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = value._exp 6000d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value._sign 6010d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = value._int 6020d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = value._is_special 6030d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista return self 6040d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista 6050d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista # From an internal working value 6060d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista if isinstance(value, _WorkRep): 6070d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._sign = value.sign 6080d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._int = str(value.int) 6090d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._exp = int(value.exp) 6100d157a0154140dc6dcd491d62df3a2b66367be15Facundo Batista self._is_special = False 611636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 612636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 613636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 614636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, (list,tuple)): 615636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if len(value) != 3: 6169b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError('Invalid tuple size in creation of Decimal ' 6179b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'from list or tuple. The list or tuple ' 6189b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista 'should have exactly three elements.') 6199b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process sign. The isinstance test rejects floats 6209b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if not (isinstance(value[0], (int, long)) and value[0] in (0,1)): 6219b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("Invalid sign. The first value in the tuple " 6229b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "should be an integer; either 0 for a " 6239b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "positive number or 1 for a negative number.") 624636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = value[0] 6259b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] == 'F': 6269b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # infinity: value[1] is ignored 62772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = '0' 628636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = value[2] 629636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 630636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 6319b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # process and validate the digits in value[1] 6329b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits = [] 6339b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista for digit in value[1]: 6349b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if isinstance(digit, (int, long)) and 0 <= digit <= 9: 6359b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # skip leading zeros 6369b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if digits or digit != 0: 6379b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista digits.append(digit) 6389b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6399b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The second value in the tuple must " 6409b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be composed of integers in the range " 6419b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "0 through 9.") 6429b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista if value[2] in ('n', 'N'): 6439b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # NaN: digits form the diagnostic 64472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits)) 6459b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6469b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = True 6479b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista elif isinstance(value[2], (int, long)): 6489b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista # finite number: digits give the coefficient 64972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = ''.join(map(str, digits or [0])) 6509b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._exp = value[2] 6519b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista self._is_special = False 6529b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista else: 6539b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista raise ValueError("The third value in the tuple must " 6549b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "be an integer, or one of the " 6559b5e23148badbb0d11fffd05cf9d432f35631a4aFacundo Batista "strings 'F', 'n', 'N'.") 656636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 657636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 658636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, float): 659636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 660636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger "First convert the float to a string") 6617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 662636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert %r to Decimal" % value) 6637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 6657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 if NaN (it could be a normal quiet NaN or a phantom one) 6697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 6707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 671636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 672636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = self._exp 673636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp == 'n': 674636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 1 675636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif exp == 'N': 676636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 2 6777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 6807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 6817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 6837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 6847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 6857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 6877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 6887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _check_nans(self, other=None, context=None): 6937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 6967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 6977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 7007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 702636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_is_nan = self._isnan() 703636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other is None: 704636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = False 705636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 706636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = other._isnan() 707636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 708636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan or other_is_nan: 709636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 710636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 711636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 712636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan == 2: 713636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 714636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, self) 715636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other_is_nan == 2: 716636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 717636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, other) 718636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan: 719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 720636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other._fix_nan(context) 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 7237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 7251a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is nonzero; otherwise return False. 7267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7271a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista NaNs and infinities are considered nonzero. 7287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 72972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._is_special or self._int != '0' 7307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __cmp__(self, other): 732636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 733267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Never return NotImplemented 735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 1 7367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 737636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for nans, without raising on a signaling nan 739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan() or other._isnan(): 74059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return 1 # Comparison involving NaN's always reports self > other 741636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 742636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # INF = INF 743636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return cmp(self._isinfinity(), other._isinfinity()) 7447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check for zeros; note that cmp(0, -0) should return 0 746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 0 749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return -((-1)**other._sign) 751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return (-1)**self._sign 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 75459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If different signs, neg one is less 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 7567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 7577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 7587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 7597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 760636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_adjusted = self.adjusted() 761636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_adjusted = other.adjusted() 762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted == other_adjusted: 76372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - other._exp) 76472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista other_padded = other._int + '0'*(other._exp - self._exp) 765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return cmp(self_padded, other_padded) * (-1)**self._sign 766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self_adjusted > other_adjusted: 7677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # self_adjusted < other_adjusted 7697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 7707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7710aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 7720aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 773267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7740aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) == 0 7750aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7760aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 7770aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 778267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7790aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) != 0 7800aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 7857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 7867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 7877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 7887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 7897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 79259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Compare(NaN, NaN) = NaN 793636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if (self._is_special or other and other._is_special): 794636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 795636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 796636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.__cmp__(other)) 7997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 8017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 8027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 8037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Non-integer decimals are normalized and hashed as strings 8041fb9f528bd69efa135bacda917ec7bb166068d5dGeorg Brandl # Normalization assures that hash(100E-1) == hash(10) 805bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._is_special: 806bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._isnan(): 807bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger raise TypeError('Cannot hash a NaN value.') 808bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger return hash(str(self)) 8098c202440699cef19602acc24822366d0d7c32083Facundo Batista if not self: 8108c202440699cef19602acc24822366d0d7c32083Facundo Batista return 0 8118c202440699cef19602acc24822366d0d7c32083Facundo Batista if self._isinteger(): 8128c202440699cef19602acc24822366d0d7c32083Facundo Batista op = _WorkRep(self.to_integral_value()) 8138c202440699cef19602acc24822366d0d7c32083Facundo Batista # to make computation feasible for Decimals with large 8148c202440699cef19602acc24822366d0d7c32083Facundo Batista # exponent, we use the fact that hash(n) == hash(m) for 8158c202440699cef19602acc24822366d0d7c32083Facundo Batista # any two nonzero integers n and m such that (i) n and m 8168c202440699cef19602acc24822366d0d7c32083Facundo Batista # have the same sign, and (ii) n is congruent to m modulo 8178c202440699cef19602acc24822366d0d7c32083Facundo Batista # 2**64-1. So we can replace hash((-1)**s*c*10**e) with 8188c202440699cef19602acc24822366d0d7c32083Facundo Batista # hash((-1)**s*c*pow(10, e, 2**64-1). 8198c202440699cef19602acc24822366d0d7c32083Facundo Batista return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(str(self.normalize())) 8217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 8237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 8247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 8267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 82772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (self._sign, tuple(map(int, self._int)), self._exp) 8287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 8307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 8317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 8327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 'Decimal("%s")' % str(self) 8337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __str__(self, eng=False, context=None): 8357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 8367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 8387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 84062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista sign = ['', '-'][self._sign] 841e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._is_special: 84262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp == 'F': 84362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'Infinity' 84462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._exp == 'n': 84562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'NaN' + self._int 84662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: # self._exp == 'N' 84762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + 'sNaN' + self._int 84862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 84962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # number of digits of self._int to left of decimal point 85062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista leftdigits = self._exp + len(self._int) 85162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 85262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # dotplace is number of digits of self._int to the left of the 85362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # decimal point in the mantissa of the output string (that is, 85462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # after adjusting the exponent) 85562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if self._exp <= 0 and leftdigits > -6: 85662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # no exponent required 85762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = leftdigits 85862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif not eng: 85962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # usual scientific notation: 1 digit on left of the point 8607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 86162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif self._int == '0': 86262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, zero 86362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits + 1) % 3 - 1 8647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 86562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista # engineering notation, nonzero 86662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista dotplace = (leftdigits - 1) % 3 + 1 86762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 86862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if dotplace <= 0: 86962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = '0' 87062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + '0'*(-dotplace) + self._int 87162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista elif dotplace >= len(self._int): 87262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int+'0'*(dotplace-len(self._int)) 87362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '' 87462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 87562edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista intpart = self._int[:dotplace] 87662edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista fracpart = '.' + self._int[dotplace:] 87762edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if leftdigits == dotplace: 87862edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = '' 87962edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista else: 88062edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista if context is None: 88162edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista context = getcontext() 88262edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) 88362edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista 88462edb71556d26f924a0e2e949af9cd3c211dea23Facundo Batista return sign + intpart + fracpart + exp 8857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 8877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 8887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 8907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__str__(eng=True, context=context) 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 8977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 8987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 9007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 901636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 902636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 903636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 904636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_sign(Dec_0) 9097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_negate() 911636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 912636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 913636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 9177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 9197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 9207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 9227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 923636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 924636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 925636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 926636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.copy_sign(Dec_0) 931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 9337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 934636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 935636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 9367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 9387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self, round=1, context=None): 9417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 9427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the second argument is 0, do not round. 9447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 945636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 946636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 947636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 948636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not round: 951636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 952636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 9539fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(NEVER_ROUND) 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 9577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 9587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 9607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 9647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 9657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 9677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 968636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 969267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 970267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 971636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 9727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 9737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 9747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 975636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 976636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 977636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 978636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 980636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 98159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both INF, same sign => same as both, opposite => error. 982636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 983636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 984636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 985636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 98659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista return Decimal(other) # Can't both be infinity here 9877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 9897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 9917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 9927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 99359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the answer is 0, the sign should be negative, in this case. 9947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 9957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 9977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 9987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 9997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 100072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, '0', exp) 1001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shouldround: 1002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 1003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 100599b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, other._exp - context.prec-1) 1006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other._rescale(exp, context.rounding) 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1008dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 101199b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, self._exp - context.prec-1) 1012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp, context.rounding) 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1014dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 10187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 10197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = _normalize(op1, op2, shouldround, context.prec) 10207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 10227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 102417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int == op2.int: 102572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(negativezero, '0', exp) 1026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shouldround: 1027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 1028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 102917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int < op2.int: 10307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 103159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # OK, now abs(op1) > abs(op2) 103217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.sign == 1: 103317931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 1 10347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 10357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 103617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 103759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # So we know the sign, and op1 > 0. 103817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif op1.sign == 1: 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 104017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger op1.sign, op2.sign = (0, 0) 104117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 104217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 104359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Now, op1 > abs(op2) > 0 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 104517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op2.sign == 0: 1046636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int + op2.int 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1048636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int - op2.int 10497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 10517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 10527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1053dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 10547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 10577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 1059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self - other""" 1060636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1061267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1062267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1064636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1065636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context=context) 1066636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1067636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self - other is computed as self + other.copy_negate() 1070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.__add__(other.copy_negate(), context=context) 10717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 1073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return other - self""" 1074636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1075267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1076267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__sub__(self, context=context) 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 10817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 10827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 10847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1085636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1086267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1087267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1088636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 10897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1092d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 10937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1094636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1095636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1096636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1097636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1098636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1099636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1100636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1101636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 1102636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 1103636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1104636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1105636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1106636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 1107636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 11087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 11107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 11137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 111472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, '0', resultexp) 11157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 111659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Fixing in case the exponent is out of bounds 1117dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 112172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int == '1': 112272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, other._int, resultexp) 11237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1124dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 112672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if other._int == '1': 112772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, self._int, resultexp) 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1129dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1132636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1 = _WorkRep(self) 1133636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2 = _WorkRep(other) 1134636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 113572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1137dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 11417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 11437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 1144636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1145267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1146cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return NotImplemented 1147636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 11487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1151636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sign = self._sign ^ other._sign 1152636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1153636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1154636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1155636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 11567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1158636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and other._isinfinity(): 11597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 11607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 1162636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[sign] 1163636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1164636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1165636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 116672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, '0', context.Etiny()) 1167636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1168636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special cases for zeroes 1169636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1170cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1171cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 / 0') 1172636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 11737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1174cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1175cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp 1176cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff = 0 1177cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1178cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # OK, so neither = 0, INF or NaN 1179cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista shift = len(other._int) - len(self._int) + context.prec + 1 1180cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp = self._exp - other._exp - shift 1181cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1182cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1183cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if shift >= 0: 1184cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int * 10**shift, op2.int) 1185cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1186cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff, remainder = divmod(op1.int, op2.int * 10**-shift) 1187cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if remainder: 1188cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is not exact; adjust to ensure correct rounding 1189cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if coeff % 5 == 0: 1190cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff += 1 1191cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1192cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # result is exact; get as close to ideal exponent as possible 1193cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp - other._exp 1194cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista while exp < ideal_exp and coeff % 10 == 0: 1195cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista coeff //= 10 1196cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista exp += 1 11977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 119872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(coeff), exp) 1199cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans._fix(context) 12007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1201cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista __truediv__ = __div__ 12027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1203cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista def _divide(self, other, context): 1204cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """Return (self // other, self % other), to context.prec precision. 12057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1206cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Assumes that neither self nor other is a NaN, that self is not 1207cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista infinite and that other is nonzero. 1208cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista """ 1209cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1210cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1211cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = self._exp 1212cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1213cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ideal_exp = min(self._exp, other._exp) 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1215cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista expdiff = self.adjusted() - other.adjusted() 1216cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self or other._isinfinity() or expdiff <= -2: 121772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, '0', 0), 1218cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._rescale(ideal_exp, context.rounding)) 1219cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if expdiff <= context.prec: 1220cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1 = _WorkRep(self) 1221cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2 = _WorkRep(other) 1222cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if op1.exp >= op2.exp: 1223cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 1224cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1225cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1226cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista q, r = divmod(op1.int, op2.int) 1227cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if q < 10**context.prec: 122872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return (_dec_from_triple(sign, str(q), 0), 122972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista _dec_from_triple(self._sign, str(r), ideal_exp)) 12307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1231cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista # Here the quotient is too large to be representable 1232cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionImpossible, 1233cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 'quotient too large in //, % or divmod') 1234cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 12357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 12377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 1238636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1239267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1240267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 12427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 12437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 12457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1246cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista Return (self // other, self % other) 12477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1248cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1249cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1250cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1251cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1252cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1253cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1254cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1255cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1256cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1257cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (ans, ans) 1258cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1259cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista sign = self._sign ^ other._sign 1260cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1261cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1262cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') 1263cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1264cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1265cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (Infsign[sign], 1266cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'INF % x')) 1267cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1268cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1269cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not self: 1270cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') 1271cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans, ans 1272cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1273cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return (context._raise_error(DivisionByZero, 'x // 0', sign), 1274cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context._raise_error(InvalidOperation, 'x % 0')) 1275cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1276cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista quotient, remainder = self._divide(other, context) 1277cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context._rounding_decision == ALWAYS_ROUND: 1278cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = remainder._fix(context) 1279cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return quotient, remainder 12807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 12827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 1283636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1284267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1285267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 12877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 12897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 12907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 12917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1292636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1293267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1294267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 12957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1296cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1297cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 12987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1299cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1300cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1301cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 13027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1303cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1304cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF % x') 1305cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista elif not other: 1306cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1307cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'x % 0') 1308cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1309cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 % 0') 1310cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1311cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = self._divide(other, context)[1] 1312cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context._rounding_decision == ALWAYS_ROUND: 1313cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista remainder = remainder._fix(context) 1314cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return remainder 13157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 13177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 1318636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1319267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1320267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 13227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1327636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1328636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 13297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 13317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 13357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self == +/-infinity -> InvalidOperation 1337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 1338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(infinity, x)') 13407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other == 0 -> either InvalidOperation or DivisionUndefined 1342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1343353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 1344353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(x, 0)') 1346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(DivisionUndefined, 1348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'remainder_near(0, 0)') 13497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # other = +/-infinity -> remainder = self 1351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 1352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self) 1353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self = 0 -> remainder = self, with ideal exponent 1356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = min(self._exp, other._exp) 1357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 135872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', ideal_exponent) 1359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # catch most cases of large or small quotient 1362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = self.adjusted() - other.adjusted() 1363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff >= context.prec + 1: 1364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff >= prec+1 => abs(self/other) > 10**prec 1365cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if expdiff <= -2: 1367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expdiff <= -2 => abs(self/other) < 0.1 1368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(ideal_exponent, context.rounding) 1369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust both arguments to have the same exponent, then divide 1372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1 = _WorkRep(self) 1373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2 = _WorkRep(other) 1374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp >= op2.exp: 1375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op1.int *= 10**(op1.exp - op2.exp) 13767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op2.int *= 10**(op2.exp - op1.exp) 1378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(op1.int, op2.int) 1379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # remainder is r*10**ideal_exponent; other is +/-op2.int * 1380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**ideal_exponent. Apply correction to ensure that 1381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # abs(remainder) <= abs(other)/2 1382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if 2*r + (q&1) > op2.int: 1383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r -= op2.int 1384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q += 1 1385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if q >= 10**context.prec: 1387cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionImpossible) 1388353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1389353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has same sign as self unless r is negative 1390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if r < 0: 1392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 1-sign 1393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista r = -r 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 139572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(sign, str(r), ideal_exponent) 1396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 13977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 13997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 1400cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista other = _convert_other(other) 1401cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other is NotImplemented: 1402cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return other 1403cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1404cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if context is None: 1405cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista context = getcontext() 1406cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1407cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista ans = self._check_nans(other, context) 1408cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if ans: 1409cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return ans 1410cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1411cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self._isinfinity(): 1412cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if other._isinfinity(): 1413cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(InvalidOperation, 'INF // INF') 1414cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1415cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return Infsign[self._sign ^ other._sign] 1416cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1417cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if not other: 1418cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista if self: 1419cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'x // 0', 1420cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista self._sign ^ other._sign) 1421cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista else: 1422cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionUndefined, '0 // 0') 1423cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista 1424cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return self._divide(other, context)[0] 14257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 1428636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1429267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1430267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 14317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 14327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 14347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 14357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 14367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 143846b0802ccd9a9c47b27a285526fbb2a8bee5b8cbBrett Cannon """Converts self to an int, truncating if necessary.""" 1439636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1440636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan(): 1441636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1442636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidContext) 1443636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self._isinfinity(): 144459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise OverflowError("Cannot convert infinity to long") 1445353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = (-1)**self._sign 14467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 144772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int)*10**self._exp 1448605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger else: 144972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return s*int(self._int[:self._exp] or '0') 14507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 14527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 14537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 14557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 14577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1458353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fix_nan(self, context): 1459353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Decapitate the payload of a NaN to fit the context""" 1460353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista payload = self._int 1461353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # maximum length of payload is precision if _clamp=0, 1463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision-1 if _clamp=1. 1464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista max_payload_len = context.prec - context._clamp 1465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(payload) > max_payload_len: 146672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista payload = payload[len(payload)-max_payload_len:].lstrip('0') 146772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, payload, self._exp, True) 14686c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 1469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1470dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _fix(self, context): 14717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 14727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 14747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 14767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 14777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 14787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1479636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 14807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1483353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 1484353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isnan(): 1485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decapitate payload if necessary 1486353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._fix_nan(context) 1487353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1488353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is +/-Infinity; return unaltered 14896c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 14907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1491353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if self is zero then exponent should be between Etiny and 1492353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. 1493353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 1494353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etop = context.Etop() 14957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 1496353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, Etop][context._clamp] 1497353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_exp = min(max(self._exp, Etiny), exp_max) 1498353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_exp != self._exp: 1499353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 150072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', new_exp) 15017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15026c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 15037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp_min is the smallest allowable exponent of the result, 1505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equal to max(self.adjusted()-context.prec+1, Etiny) 1506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = len(self._int) + self._exp - context.prec 1507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp_min > Etop: 1508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow: exp_min > Etop iff self.adjusted() > Emax 1509353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1510353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 1511353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(Overflow, 'above Emax', self._sign) 1512353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_subnormal = exp_min < Etiny 1513353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1514353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 1515353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_min = Etiny 15167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round if self has too many digits 1518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < exp_min: 15197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15202ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = len(self._int) + self._exp - exp_min 15212ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if digits < 0: 15222ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista self = _dec_from_triple(self._sign, '1', exp_min-1) 15232ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista digits = 0 15242ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista this_function = getattr(self, self._pick_rounding_function[context.rounding]) 15252ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 15262ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 15272ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 15282ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 15292ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista ans = _dec_from_triple(self._sign, coeff, exp_min) 15302ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista 15312ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed: 1532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 1533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_subnormal: 1534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 1535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 1536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Clamped on underflow to 0 1537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 1538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif len(ans._int) == context.prec+1: 1539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we get here only if rescaling rounds the 1540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # cofficient up to exactly 10**context.prec 1541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp < Etop: 154272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, 154372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._int[:-1], ans._exp+1) 1544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inexact and Rounded have already been raised 1546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = context._raise_error(Overflow, 'above Emax', 1547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self._sign) 15487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fold down if _clamp == 1 and self has too few digits 1551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._clamp == 1 and self._exp > Etop: 1552353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 155372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self_padded = self._int + '0'*(self._exp - Etop) 155472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, self_padded, Etop) 15557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # here self was representable to begin with; return unchanged 15576c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 15607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for each of the rounding functions below: 1562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self is a finite, nonzero Decimal 1563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # prec is an integer satisfying 0 <= prec < len(self._int) 15642ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 15652ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # each function returns either -1, 0, or 1, as follows: 15662ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 1 indicates that self should be rounded up (away from zero) 15672ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # 0 indicates that self should be truncated, and that all the 15682ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # digits to be truncated are zeros (so the value is unchanged) 15692ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista # -1 indicates that there are nonzero digits to be truncated 15707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1571353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_down(self, prec): 1572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Also known as round-towards-0, truncate.""" 15732ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _all_zeros(self._int, prec): 15742ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 15752ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 15762ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_up(self, prec): 1579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds away from 0.""" 15802ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 15817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_up(self, prec): 1583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds 5 up (away from 0)""" 158472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[prec] in '56789': 15852ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 1 15862ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista elif _all_zeros(self._int, prec): 15872ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return 0 1588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 15892ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_down(self, prec): 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 15932ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec): 15942ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 15952ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 15962ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 15977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_half_even(self, prec): 1599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round 5 to even, rest to nearest.""" 16002ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if _exact_half(self._int, prec) and \ 16012ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista (prec == 0 or self._int[prec-1] in '02468'): 16022ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -1 1603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 16042ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return self._round_half_up(prec) 16057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1606353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_ceiling(self, prec): 16077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 16087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 1609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16112ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 16127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1613353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_floor(self, prec): 16147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 16157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 1616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16182ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 16197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _round_05up(self, prec): 1621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Round down unless digit prec-1 is 0 or 5.""" 16222ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if prec and self._int[prec-1] not in '05': 1623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._round_down(prec) 16242ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista else: 16252ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return -self._round_down(prec) 1626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, other, third, context=None): 1628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Fused multiply-add. 16297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Returns self*other+third with no rounding of the intermediate 1631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista product self*other. 1632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self and other are multiplied together, with no rounding of 1634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the result. The third operand is then added to the result, 1635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista and a single final rounding is performed. 16367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 1639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista third = _convert_other(third, raiseit=True) 1640636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 16417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 16427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 16437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # do self*other in fresh context with no traps and no rounding 1645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista mul_context = Context(traps=[], flags=[], 1646353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista _rounding_decision=NEVER_ROUND) 1647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista product = self.__mul__(other, mul_context) 16487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if mul_context.flags[InvalidOperation]: 1650353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reraise in current context 1651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'invalid multiplication in fma', 1653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, product) 16547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = product.__add__(third, context) 1656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 16577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_modulo(self, other, modulo, context=None): 1659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Three argument version of __pow__""" 16607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if can't convert other and modulo to Decimal, raise 1662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # TypeError; there's no point returning NotImplemented (no 1663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equivalent of __rpow__ for three argument pow) 1664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 1665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = _convert_other(modulo, raiseit=True) 16667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 16697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # deal with NaNs: if there are any sNaNs then first one wins, 1671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (i.e. behaviour for NaNs is identical to that of fma) 1672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 1673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 1674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo_is_nan = modulo._isnan() 1675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan or other_is_nan or modulo_is_nan: 1676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 1677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 1679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 1680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 1682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo_is_nan == 2: 1683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 1684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, modulo) 1685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 16866c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 1687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 16886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 16896c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return modulo._fix_nan(context) 1690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # check inputs: we apply same restrictions as Python's pow() 1692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (self._isinteger() and 1693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other._isinteger() and 1694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo._isinteger()): 1695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument not allowed ' 1697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'unless all arguments are integers') 1698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other < 0: 1699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 2nd argument cannot be ' 1701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'negative when 3rd argument specified') 1702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not modulo: 1703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'pow() 3rd argument cannot be 0') 1705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # additional restriction for decimal: the modulus must be less 1707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # than 10**prec in absolute value 1708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo.adjusted() >= context.prec: 1709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'insufficient precision: pow() 3rd ' 1711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'argument must not have more than ' 1712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'precision digits') 1713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # define 0**0 == NaN, for consistency with two-argument pow 1715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (even though it hurts!) 1716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other and not self: 1717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 1718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'at least one of pow() 1st argument ' 1719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'and 2nd argument must be nonzero ;' 1720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0**0 is not defined') 1721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute sign of result 1723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._iseven(): 1724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = 0 1725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 1727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1728353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # convert modulo to a Python integer, and self and other to 1729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal integers (i.e. force their exponents to be >= 0) 1730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo = abs(int(modulo)) 1731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = _WorkRep(self.to_integral_value()) 1732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = _WorkRep(other.to_integral_value()) 1733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute result using integer pow() 1735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo 1736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(exponent.exp): 1737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, 10, modulo) 1738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista base = pow(base, exponent.int, modulo) 1739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 174072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(sign, str(base), 0) 1741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _power_exact(self, other, p): 1743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Attempt to compute self**other exactly. 1744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given Decimals self and other and an integer p, attempt to 1746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista compute an exact result for the power self**other, with p 1747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision. Return None if self**other is not 1748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exactly representable in p digits. 1749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that elimination of special cases has already been 1751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista performed: self and other must both be nonspecial; self must 1752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista be positive and not numerically equal to 1; other must be 1753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista nonzero. For efficiency, other._exp should not be too large, 1754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista so that 10**abs(other._exp) is a feasible calculation.""" 1755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # In the comments below, we write x for the value of self and 1757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # y for the value of other. Write x = xc*10**xe and y = 1758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # yc*10**ye. 1759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1760353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The main purpose of this method is to identify the *failure* 1761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of x**y to be exactly representable with as little effort as 1762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possible. So we look for cheap and easy tests that 1763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # eliminate the possibility of x**y being exact. Only if all 1764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # these tests are passed do we go on to actually compute x**y. 1765353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Here's the main idea. First normalize both x and y. We 1767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # express y as a rational m/n, with m and n relatively prime 1768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # and n>0. Then for x**y to be exactly representable (at 1769353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # *any* precision), xc must be the nth power of a positive 1770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # integer and xe must be divisible by n. If m is negative 1771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then additionally xc must be a power of either 2 or 5, hence 1772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a power of 2**n or 5**n. 1773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's a limit to how small |y| can be: if y=m/n as above 1775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then: 1776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1) if xc != 1 then for the result to be representable we 1778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So 1779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= 1780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2**(1/|y|), hence xc**|y| < 2 and the result is not 1781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # representable. 1782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if 1784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # |y| < 1/|xe| then the result is not representable. 1785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Note that since x is not equal to 1, at least one of (1) and 1787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < 1788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. 1789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # There's also a limit to how large y can be, at least if it's 1791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive: the normalized result will have coefficient xc**y, 1792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so if it's representable then xc**y < 10**p, and y < 1793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p/log10(xc). Hence if y*log10(xc) >= p then the result is 1794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # not exactly representable. 1795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, 1797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # so |y| < 1/xe and the result is not representable. 1798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| 1799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # < 1/nbits(xc). 1800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 1802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 1803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 10 == 0: 1804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 10 1805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe += 1 1806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 1808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 1809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while yc % 10 == 0: 1810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc //= 10 1811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ye += 1 1812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where xc == 1: result is 10**(xe*y), with xe*y 1814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # required to be an integer 1815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc == 1: 1816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = xe*yc*10**ye 1818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent, remainder = divmod(xe*yc, 10**-ye) 1820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exponent = -exponent 1824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if other is a nonnegative integer, use ideal exponent 1825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(exponent-ideal_exponent, p-1) 1828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 183072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) 1831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # case where y is negative: xc must be either a power 1833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of 2 or a power of 5. 1834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 1835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista last_digit = xc % 10 1836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if last_digit in (2,4,6,8): 1837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # quick test for power of 2 1838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc & -xc != xc: 1839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc is a power of 2; e is its exponent 1841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)-1 1842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find e*y and xe*y; both must be integers 1843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_int = yc*10**ye 1845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_int 1846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_int 1847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*65 >= p*93: # 93/65 > log(10)/log(5) 1857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 5**e 1859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif last_digit == 5: 1861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # e >= log_5(xc) if xc is a power of 5; we have 1862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # equality all the way up to xc=5**2658 1863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = _nbits(xc)*28//65 1864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, remainder = divmod(5**e, xc) 1865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while xc % 5 == 0: 1868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc //= 5 1869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= 1 1870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y_as_integer = yc*10**ye 1872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = e*y_as_integer 1873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = xe*y_as_integer 1874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ten_pow = 10**-ye 1876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e, remainder = divmod(e*yc, ten_pow) 1877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, remainder = divmod(xe*yc, ten_pow) 1880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if remainder: 1881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if e*3 >= p*10: # 10/3 > log(10)/log(2) 1883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = 2**e 1885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 18877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc >= 10**p: 1889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe = -e-xe 189172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str(xc), xe) 18927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now y is positive; find m and n such that y = m/n 1894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ye >= 0: 1895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc*10**ye, 1 1896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xe != 0 and len(str(abs(yc*xe))) <= -ye: 1898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc_bits = _nbits(xc) 1900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: 1901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m, n = yc, 10**(-ye) 1903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 2 == n % 2 == 0: 1904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 2 1905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 2 1906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while m % 5 == n % 5 == 0: 1907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista m //= 5 1908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 5 1909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc*10**xe 1911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n > 1: 1912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if 1 < xc < 2**n then xc isn't an nth power 1913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc != 1 and xc_bits <= n: 1914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe, rem = divmod(xe, n) 1917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rem != 0: 1918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute nth root of xc using Newton's method 1921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = 1L << -(-_nbits(xc)//n) # initial estimate 1922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 1923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(xc, a**(n-1)) 1924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if a <= q: 1925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 1926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista a = (a*(n-1) + q)//n 1928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (a == q and r == 0): 1929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = a 1931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # now xc*10**xe is the nth root of the original xc*10**xe 1933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute mth power of xc*10**xe 1934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > 1936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 10**p and the result is not representable. 1937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 1 and m > p*100//_log10_lb(xc): 1938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc = xc**m 1940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xe *= m 1941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if xc > 10**p: 1942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return None 1943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by this point the result *is* exactly representable 1945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adjust the exponent to get as close as possible to the ideal 1946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent, if necessary 1947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_xc = str(xc) 1948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger() and other._sign == 0: 1949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ideal_exponent = self._exp*int(other) 1950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = min(xe-ideal_exponent, p-len(str_xc)) 1951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista zeros = 0 195372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) 1954cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 1955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __pow__(self, other, modulo=None, context=None): 1956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return self ** other [ % modulo]. 19577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute self**other. 19597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (self**other) % modulo. For the 1961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 1962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 19637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 1965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - other must be nonnegative 1966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - either self or other (or both) must be nonzero 1967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and must have at most p digits, 1968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista where p is the context precision. 19697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If any of these restrictions is violated the InvalidOperation 1971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista flag is raised. 1972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(self, other, modulo) is identical to the 1974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result that would be obtained by computing (self**other) % 1975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista modulo with unbounded precision, but is computed more 1976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista efficiently. It is always exact. 1977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 1978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if modulo is not None: 1980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._power_modulo(other, modulo, context) 19817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1982636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1983267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1984267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 19857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 1987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 19887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # either argument is a NaN => result is NaN 1990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 1991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 1992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 19937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) 1995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other: 1996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 1997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, '0 ** 0') 1998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 1999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 20007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result has sign 1 iff self._sign is 1 and other is an odd integer 2002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 0 2003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._iseven(): 2006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista result_sign = 1 2007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # -ve**noninteger = NaN 2009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (-0)**noninteger = 0**noninteger 2010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self: 2011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'x ** y with x negative and y not an integer') 2013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # negate self, without doing any unwanted rounding 201472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = self.copy_negate() 2015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity 2017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 201972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 2024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 0: 2026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 202872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1**other = 1, but the choice of exponent and the flags 2031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # depend on the exponent of self, and on whether other is a 2032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # positive integer, a negative integer, or neither 2033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinteger(): 2035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp = max(self._exp*max(int(other), 0), 2036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-context.prec) but evaluating int(other) directly 2037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is dangerous until we know other is small (other 2038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # could be 1e999999999) 2039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._sign == 1: 2040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = 0 2041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif other > context.prec: 2042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = context.prec 2043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplier = int(other) 2045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = self._exp * multiplier 2047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exp < 1-context.prec: 2048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = 1-context.prec 2054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 205572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) 2056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute adjusted exponent of self 2058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adj = self.adjusted() 2059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** infinity is infinity if self > 1, 0 if self < 1 2061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self ** -infinity is infinity if self < 1, 0 if self > 1 2062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._isinfinity(): 2063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (other._sign == 0) == (self_adj < 0): 206472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(result_sign, '0', 0) 2065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Infsign[result_sign] 2067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # from here on, the result always goes through the call 2069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # to _fix at the end of this function. 2070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = None 2071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # crude test to catch cases of extreme overflow/underflow. If 2073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(self)*other >= 10**bound and bound >= len(str(Emax)) 2074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence 2075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self**other >= 10**(Emax+1), so overflow occurs. The test 2076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for underflow is similar. 2077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista bound = self._log10_exp_bound() + other.adjusted() 2078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if (self_adj >= 0) == (other._sign == 0): 2079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other +ve, or self < 1 and other -ve 2080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of overflow 2081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(context.Emax)): 208272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', context.Emax+1) 2083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self > 1 and other -ve, or self < 1 and other +ve 2085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # possibility of underflow to 0 2086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Etiny = context.Etiny() 2087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if bound >= len(str(-Etiny)): 208872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, '1', Etiny-1) 2089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # try for an exact result with precision +1 2091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._power_exact(other, context.prec + 1) 2093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is not None and result_sign == 1: 209472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(1, ans._int, ans._exp) 2095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # usual case: inexact result, x**y computed directly as exp(y*log(x)) 2097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans is None: 2098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x = _WorkRep(self) 2100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista xc, xe = x.int, x.exp 2101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _WorkRep(other) 2102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc, ye = y.int, y.exp 2103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if y.sign == 1: 2104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yc = -yc 2105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: start with precision +3, 2107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # then increase precision until result is unambiguously roundable 2108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dpower(xc, xe, yc, ye, p+extra) 2111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 211572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(result_sign, str(coeff), exp) 2116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the specification says that for non-integer other we need to 2118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Inexact, even when the result is actually exact. In 2119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the same way, we need to raise Underflow here if the result 2120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is subnormal. (The call to _fix will take care of raising 2121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Rounded and Subnormal, as usual.) 2122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not other._isinteger(): 2123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad with zeros up to length context.prec+1 if necessary 2125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) <= context.prec: 2126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista expdiff = context.prec+1 - len(ans._int) 212772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, 212872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans._exp-expdiff) 2129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() < context.Emin: 2130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 2131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2132353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # unlike exp, ln and log10, the power function respects the 2133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode; no need to use ROUND_HALF_EVEN here 2134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def __rpow__(self, other, context=None): 2138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Swaps self/other and returns __pow__.""" 2139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other) 2140353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other is NotImplemented: 2141353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other 2142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return other.__pow__(self, context=context) 2143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def normalize(self, context=None): 2145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 2146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2155353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dup = self._fix(context) 2156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dup._isinfinity(): 2157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return dup 2158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not dup: 216072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, '0', 0) 2161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp_max = [context.Emax, context.Etop()][context._clamp] 2162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista end = len(dup._int) 21637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 216472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista while dup._int[end-1] == '0' and exp < exp_max: 21657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 21667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 216772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(dup._sign, dup._int[:end], exp) 21687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2169bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista def quantize(self, exp, rounding=None, context=None, watchexp=True): 21707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 21717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 21737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2174bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista exp = _convert_other(exp, raiseit=True) 2175bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2181636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or exp._is_special: 2182636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(exp, context) 2183636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2184636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 21857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2186636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 2187636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 21886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) # if both are inf, it is OK 2189636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 2190636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 'quantize with one INF') 2191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2192bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # if we're not watching exponents, do a simple rescale 2193bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if not watchexp: 2194bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista ans = self._rescale(exp._exp, rounding) 2195bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista # raise Inexact and Rounded where appropriate 2196bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans._exp > self._exp: 2197bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Rounded) 2198bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista if ans != self: 2199bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista context._raise_error(Inexact) 2200bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista return ans 2201bd2fe839db886de6ce9631acd8aa9796b413a565Facundo Batista 2202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp._exp should be between Etiny and Emax 2203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (context.Etiny() <= exp._exp <= context.Emax): 2204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'target exponent out of bounds in quantize') 2206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 220872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', exp._exp) 2209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 2210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_adjusted = self.adjusted() 2212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted > context.Emax: 2213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_adjusted - exp._exp + 1 > context.prec: 2216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(exp._exp, rounding) 2220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans.adjusted() > context.Emax: 2221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'exponent of quantize result too large for current context') 2223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if len(ans._int) > context.prec: 2224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'quantize result has too many digits for current context') 2226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise appropriate flags 2228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._exp > self._exp: 2229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 2232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans and ans.adjusted() < context.Emin: 2233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 2234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # call to fix takes care of any necessary folddown 2236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 22387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 22401a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self and other have the same exponent; otherwise 22411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False. 22427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista If either operand is a special value, the following rules are used: 22441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are infinities 22451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * return True if both operands are NaNs 22461a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista * otherwise, return False. 22477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22481a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista other = _convert_other(other, raiseit=True) 2249636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 22501a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return (self.is_nan() and other.is_nan() or 22511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista self.is_infinite() and other.is_infinite()) 22527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 22537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _rescale(self, exp, rounding): 2255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rescale self so that the exponent is exp, either by padding with zeros 2256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or by truncating digits, using the given rounding mode. 2257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Specials are returned without change. This operation is 2259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista quiet: it raises no flags, and uses no information from the 2260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 22617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 2263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = rounding mode 22647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2265636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 22666c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 22677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 226872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', exp) 22697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= exp: 2271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # pad answer with zeros if necessary 227272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 227372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int + '0'*(self._exp - exp), exp) 22747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # too many digits; round and lose data. If self.adjusted() < 2276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp-1, replace self by 10**(exp-1) before rounding 2277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = len(self._int) + self._exp - exp 22787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 227972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = _dec_from_triple(self._sign, '1', exp-1) 2280353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits = 0 2281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this_function = getattr(self, self._pick_rounding_function[rounding]) 22822ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista changed = this_function(digits) 22832ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = self._int[:digits] or '0' 22842ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista if changed == 1: 22852ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista coeff = str(int(coeff)+1) 22862ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista return _dec_from_triple(self._sign, coeff, exp) 22877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, rounding=None, context=None): 2289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to a nearby integer. 22907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista If no rounding mode is specified, take the rounding mode from 2292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the context. This method raises the Rounded and Inexact flags 2293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista when appropriate. 22947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista See also: to_integral_value, which does exactly the same as 2296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista this method except that it doesn't raise Inexact or Rounded. 2297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2298636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2299636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2300636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2301636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 23026c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 23037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 23046c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 230672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, '0', 0) 2307636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2308636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 2312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._rescale(0, rounding) 2313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans != self: 2314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 23157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 23167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, rounding=None, context=None): 2318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to the nearest integer, without raising inexact, rounded.""" 2319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if rounding is None: 2322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context.rounding 2323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 23276c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp >= 0: 23296c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 2330353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._rescale(0, rounding) 23327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 2334353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 2335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def sqrt(self, context=None): 2337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return the square root of self.""" 2338636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 2339636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 2340636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 2341636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2343636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 2344636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 23457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 2347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent = self._exp // 2. sqrt(-0) = -0 234872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(self._sign, '0', self._exp // 2) 2349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 23507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2351636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2352636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 2353636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 23547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 23557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 23567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # At this point self represents a positive number. Let p be 2358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the desired precision and express self in the form c*100**e 2359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with c a positive real number and e an integer, c and e 2360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # being chosen so that 100**(p-1) <= c < 100**p. Then the 2361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) 2362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # <= sqrt(c) < 10**p, so the closest representable Decimal at 2363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # precision p is n*10**e where n = round_half_even(sqrt(c)), 2364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the closest integer to sqrt(c) with the even integer chosen 2365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # in the case of a tie. 2366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 2367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # To ensure correct rounding in all cases, we use the 2368353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # following trick: we compute the square root to an extra 2369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # place (precision p+1 instead of precision p), rounding down. 2370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then, if the result is inexact and its last digit is 0 or 5, 2371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we increase the last digit to 1 or 6 respectively; if it's 2372353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exact we leave the last digit alone. Now the final round to 2373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p places (or fewer in the case of underflow) will round 2374353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly and raise the appropriate flags. 2375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # use an extra digit of precision 2377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista prec = context.prec+1 2378353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write argument in the form c*100**e where e = self._exp//2 2380353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is the 'ideal' exponent, to be used if the square root is 2381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exactly representable. l is the number of 'digits' of c in 2382353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # base 100, so that 100**(l-1) <= c < 100**l. 2383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2384353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e = op.exp >> 1 2385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.exp & 1: 2386353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int * 10 2387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = (len(self._int) >> 1) + 1 23887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2389353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = op.int 2390353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(self._int)+1 >> 1 2391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2392353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rescale so that c has exactly prec base 100 'digits' 2393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = prec-l 2394353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 100**shift 2396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = True 23977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2398353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, remainder = divmod(c, 100**-shift) 2399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = not remainder 2400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e -= shift 2401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # find n = floor(sqrt(c)) using Newton's method 2403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = 10**prec 2404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = c//n 2406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= q: 24077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 2408353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2409353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n = n + q >> 1 2410353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exact = exact and n*n == c 2411353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2412353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if exact: 2413353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is exact; rescale to use ideal exponent e 2414353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 2415353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert n % 10**shift == 0 2416353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n //= 10**shift 2417353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2418353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n *= 10**-shift 2419353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista e += shift 24207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 2421353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is not exact; fix last digit as described above 2422353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n % 5 == 0: 2423353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista n += 1 24247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 242572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(n), e) 24267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2427353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # round, and fit to current context 2428353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2429353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2430dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 2431353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 24327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2433353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 24347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 24367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 24377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2438353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like max(self, other) except if one is not a number, returns 24397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 24407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2441353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2442636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24436c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 24446c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 24456c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2446636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 244759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2448636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2449636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2450636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2451636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2452636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 24536c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2454636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 24556c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2456636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 24577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2458d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2459d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 246059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If both operands are finite and equal in numerical value 2461d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2462d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 246359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs differ then max returns the operand with the 2464d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2465d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 246659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If the signs are the same then the exponent is used to select 2467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result. This is exactly the ordering used in compare_total. 2468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2470353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 24717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2472353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2473353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2474636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 247576e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 247676e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans._fix(context) 247776e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans 24787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 24807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 24817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 248259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista Like min(self, other) except if one is not a number, returns 24837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 24847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2485353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 2486636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 24876c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 24886c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 24896c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 2490636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 249159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If one operand is a quiet NaN and the other is number, then the 2492636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2493636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2494636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2495636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2496636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 24976c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 2498636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 24996c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 2500636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 25017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2502d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2503d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2504353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 2505353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2506353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 2507353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 2508353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 25097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2510636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 251176e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 251276e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans._fix(context) 251376e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans 25147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 25167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 2517353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special: 2518353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 25197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 25207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 25217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 252272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return rest == '0'*len(rest) 25237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 2525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns True if self is even. Assumes self is an integer.""" 2526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self or self._exp > 0: 2527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 252872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self._int[-1+self._exp] in '02468' 25297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 25317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 25327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 25337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 253459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # If NaN or Infinity, self._exp is string 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 25367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 25377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, context=None): 2539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 2540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 2542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 2543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self 2545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2546353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, other, context=None): 2547353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to the other operand numerically. 2548353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2549353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 2550353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 2551353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2552353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2553353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2554353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2555353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_is_nan = self._isnan() 2556353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_is_nan = other._isnan() 2557353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan == 2: 2558353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 2559353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 2560353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan == 2: 2561353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'sNaN', 2562353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 2563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_is_nan: 2564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'NaN in compare_signal', 2565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, self) 2566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_is_nan: 2567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 'NaN in compare_signal', 2568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1, other) 2569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self.compare(other, context=context) 2570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2571353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, other): 2572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using the abstract representations. 2573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 2575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 2576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 2577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if one is negative and the other is positive, it's easy 2579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign and not other._sign: 2580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._sign and other._sign: 2582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign = self._sign 2584353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's handle both NaN types 2586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista self_nan = self._isnan() 2587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other_nan = other._isnan() 2588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan or other_nan: 2589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == other_nan: 2590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int < other._int: 2591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2592353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2594353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._int > other._int: 2596353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2598353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2599353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2600353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2601353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2602353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2603353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2604353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2605353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2606353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2607353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2608353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2609353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2610353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2611353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2612353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 1: 2613353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 1: 2615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self_nan == 2: 2617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_nan == 2: 2619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self < other: 2622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self > other: 2624353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2625353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2626353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp < other._exp: 2627353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2628353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2629353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2630353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2631353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._exp > other._exp: 2632353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sign: 2633353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_n1 2634353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2635353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2636353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2637353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2638353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2639353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, other): 2640353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares self to other using abstract repr., ignoring sign. 2641353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2642353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 2643353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2644353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista s = self.copy_abs() 2645353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista o = other.copy_abs() 2646353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return s.compare_total(o) 2647353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2648353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self): 2649353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign set to 0. """ 265072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2651353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2652353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self): 2653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy with the sign inverted.""" 2654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 265572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, self._int, self._exp, self._is_special) 2656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 265772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, self._int, self._exp, self._is_special) 2658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, other): 2660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self with the sign of other.""" 266172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(other._sign, self._int, 266272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp, self._is_special) 2663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, context=None): 2665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** self.""" 2666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(NaN) = NaN 2671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(-Infinity) = 0 2676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 2677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(0) = 1 2680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_p1 2682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exp(Infinity) = Infinity 2684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self) 2686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the result is now guaranteed to be inexact (the true 2688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # mathematical result is transcendental). There's no need to 2689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # raise Rounded and Inexact here---they'll always be raised as 2690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # a result of the call to _fix. 2691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self.adjusted() 2693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we only need to do any computation for quite a small range 2695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # of adjusted exponents---for example, -29 <= adj <= 10 for 2696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the default context. For smaller exponent the result is 2697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # indistinguishable from 1 at the given precision, while for 2698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # larger exponent the result either overflows or underflows. 2699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 0 and adj > len(str((context.Emax+1)*3)): 2700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # overflow 270172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Emax+1) 2702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): 2703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # underflow to 0 270472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1', context.Etiny()-1) 2705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 0 and adj < -p: 2706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 270772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) 2708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif self._sign == 1 and adj < -p-1: 2709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p+1 digits; final round will raise correct flags 271072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, '9'*(p+1), -p-1) 2711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # general case 2712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op.sign == 1: 2716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = -c 2717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute correctly rounded result: increase precision by 2719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 3 digits at a time until we get an unambiguously 2720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # roundable result 2721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = 3 2722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(c, e, p+extra) 2724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(coeff))-p-1)): 2725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra += 3 2727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 272872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(0, str(coeff), exp) 2729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # at this stage, ans should round correctly with *any* 2731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding mode, not just with ROUND_HALF_EVEN 2732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self): 27401a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is canonical; otherwise return False. 27411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 27421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 27431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 27441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """ 27451a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return True 2746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self): 27481a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is finite; otherwise return False. 2749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 27501a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 27511a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 2752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 27531a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return not self._is_special 2754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self): 27561a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is infinite; otherwise return False.""" 27571a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'F' 2758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2759353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self): 27601a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a qNaN or sNaN; otherwise return False.""" 27611a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp in ('n', 'N') 2762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2763353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, context=None): 27641a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a normal number; otherwise return False.""" 27651a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 27661a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2768353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 27691a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return context.Emin <= self.adjusted() <= context.Emax 2770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self): 27721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a quiet NaN; otherwise return False.""" 27731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'n' 2774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self): 27761a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is negative; otherwise return False.""" 27771a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._sign == 1 2778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self): 27801a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a signaling NaN; otherwise return False.""" 27811a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self._exp == 'N' 2782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, context=None): 27841a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is subnormal; otherwise return False.""" 27851a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista if self._is_special or not self: 27861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return False 2787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 27891a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return self.adjusted() < context.Emin 2790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self): 27921a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if self is a zero; otherwise return False.""" 279372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return not self._is_special and self._int == '0' 2794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _ln_exp_bound(self): 2796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.ln(). 2797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, compute r such that self.ln() >= 10**r. Assumes 2798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that self is finite and positive and that self != 1. 2799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 2802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) 2805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj*23//10)) - 1 2806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument <= 0.1 2808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str((-1-adj)*23//10)) - 1 2809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(c) 2815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) 2816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return e + len(str(10**-e - c)) - 1 2818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, context=None): 2821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of self.""" 2822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(NaN) = NaN 2827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(0.0) == -Infinity 2832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(Infinity) = Infinity 2836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(1.0) == 0.0 2840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self == Dec_p1: 2841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Dec_0 2842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # ln(negative) raises InvalidOperation 2844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'ln of a negative value') 2847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision by 3 2854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until we get an unambiguously roundable result 2855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p - self._ln_exp_bound() + 2 # at least p+3 places 2856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog(c, e, places) 2858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 286272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _log10_exp_bound(self): 2871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for the adjusted exponent of self.log10(). 2872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, find r such that self.log10() >= 10**r. 2873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Assumes that self is finite and positive and that self != 1. 2874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # For x >= 10 or x < 0.1 we only need a bound on the integer 2877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # part of log10(self), and this comes directly from the 2878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # exponent of x. For 0.1 <= x <= 10 we use the inequalities 2879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > 2880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 2881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista adj = self._exp + len(self._int) - 1 2883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj >= 1: 2884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self >= 10 2885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(adj))-1 2886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj <= -2: 2887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # self < 0.1 2888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(str(-1-adj))-1 2889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if adj == 0: 2892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 1 < self < 10 2893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(c-10**-e) 2894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista den = str(231*c) 2895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) - len(den) - (num < den) + 2 2896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # adj == -1, 0.1 <= self < 1 2897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista num = str(10**-e-c) 2898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return len(num) + e - (num < "231") - 1 2899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, context=None): 2901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of self.""" 2902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(NaN) = NaN 2907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(0.0) == -Infinity 2912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 2914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(Infinity) = Infinity 2916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 2917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(negative or -Infinity) raises InvalidOperation 2920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign == 1: 2921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation, 2922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'log10 of a negative value') 2923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log10(10**n) = n 292572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): 2926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # answer may need rounding 2927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = Decimal(self._exp + len(self._int) - 1) 2928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 2929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result is irrational, so necessarily inexact 2930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista op = _WorkRep(self) 2931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c, e = op.int, op.exp 2932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p = context.prec 2933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # correctly rounded result: repeatedly increase precision 2935353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # until result is unambiguously roundable 2936353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places = p-self._log10_exp_bound()+2 2937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while True: 2938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _dlog10(c, e, places) 2939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # assert len(str(abs(coeff)))-p >= 1 2940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if coeff % (5*10**(len(str(abs(coeff)))-p-1)): 2941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista break 2942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista places += 3 294372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) 2944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context._shallow_copy() 2946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rounding = context._set_rounding(ROUND_HALF_EVEN) 2947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = ans._fix(context) 2948353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context.rounding = rounding 2949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, context=None): 2952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of self's MSD. 2953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2954353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 2955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of self (as though it were truncated 2956353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to a single digit while maintaining the value of that digit and 2957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista without limiting the resulting exponent). 2958353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(NaN) = NaN 2960353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 2961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 2962353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 2963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 2965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 2966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2967353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(+/-Inf) = +Inf 2968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 2969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 2970353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # logb(0) = -Inf, DivisionByZero 2972353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self: 2973cce8df2f678b1e1ec11c86cf2fabf12c2077577dFacundo Batista return context._raise_error(DivisionByZero, 'logb(0)', 1) 2974353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # otherwise, simply return the adjusted exponent of self, as a 2976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Decimal. Note that no attempt is made to fit the result 2977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # into the current context. 2978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(self.adjusted()) 2979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _islogical(self): 2981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Return True if self is a logical operand. 2982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista For being logical, it must be a finite numbers with a sign of 0, 2984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an exponent of 0, and a coefficient whose digits must all be 2985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista either 0 or 1. 2986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 2987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign != 0 or self._exp != 0: 2988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 2989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for dig in self._int: 299072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista if dig not in '01': 2991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return False 2992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return True 2993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 2994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def _fill_logical(self, context, opa, opb): 2995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opa) 2996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 299772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opa = '0'*dif + opa 2998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 2999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opa = opa[-context.prec:] 3000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista dif = context.prec - len(opb) 3001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if dif > 0: 300272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista opb = '0'*dif + opb 3003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif dif < 0: 3004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista opb = opb[-context.prec:] 3005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return opa, opb 3006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, other, context=None): 3008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'and' operation between self and other's digits.""" 3009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 301872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) 301972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, context=None): 3022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all its digits.""" 3023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 302572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), 302672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, other, context=None): 3029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'or' operation between self and other's digits.""" 3030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 303972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb)) 304072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, other, context=None): 3043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies an 'xor' operation between self and other's digits.""" 3044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not self._islogical() or not other._islogical(): 3047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # fill to context.prec 3050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (opa, opb) = self._fill_logical(context, self._int, other._int) 3051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # make the operation, and clean starting zeroes 305372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb)) 305472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, result.lstrip('0') or '0', 0) 3055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, other, context=None): 3057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 30606c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 30616c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 30626c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 30706c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 30726c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.copy_abs().__cmp__(other.copy_abs()) 3076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._rounding_decision == ALWAYS_ROUND: 3085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 3086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, other, context=None): 3089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 3090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 30926c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista if context is None: 30936c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista context = getcontext() 30946c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista 3095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._is_special or other._is_special: 3096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # If one operand is a quiet NaN and the other is number, then the 3097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number is always returned 3098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sn = self._isnan() 3099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista on = other._isnan() 3100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn or on: 3101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if on == 1 and sn != 2: 31026c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return self._fix_nan(context) 3103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if sn == 1 and on != 2: 31046c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return other._fix_nan(context) 3105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._check_nans(other, context) 3106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.copy_abs().__cmp__(other.copy_abs()) 3108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == 0: 3109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = self.compare_total(other) 3110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c == -1: 3112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self 3113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = other 3115353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3116353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context._rounding_decision == ALWAYS_ROUND: 3117353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans._fix(context) 3118353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, context=None): 3121353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than itself.""" 3122353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3123353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3124353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3125353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3126353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3127353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3128353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3129353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 3130353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return negInf 3131353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 313272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(0, '9'*context.prec, context.Etop()) 3133353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3134353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_FLOOR) 3136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3139353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 314072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), 314172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3142353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3143353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, context=None): 3144353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than itself.""" 3145353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3146353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3147353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3148353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(context=context) 3149353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3150353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3151353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3152353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == 1: 3153353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Inf 3154353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity() == -1: 315572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(1, '9'*context.prec, context.Etop()) 3156353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3157353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = context.copy() 3158353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._set_rounding(ROUND_CEILING) 3159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._ignore_all_flags() 3160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista new_self = self._fix(context) 3161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if new_self != self: 3162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return new_self 316372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), 316472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista context) 3165353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3166353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, other, context=None): 3167353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to self, in the direction towards other. 3168353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3169353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number to self 3170353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (excluding self) that is in the direction towards other, 3171353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unless both have the same value. If the two operands are 3172353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista numerically equal, then the result is a copy of self with the 3173353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista sign set to be the same as the sign of other. 3174353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3175353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other = _convert_other(other, raiseit=True) 3176353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3177353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3178353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3179353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3180353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3181353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3182353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3183353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3184353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista comparison = self.__cmp__(other) 3185353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == 0: 318672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self.copy_sign(other) 3187353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3188353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if comparison == -1: 3189353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_plus(context) 3190353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: # comparison == 1 3191353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self.next_minus(context) 3192353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3193353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # decide which flags to raise using value of ans 3194353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans._isinfinity(): 3195353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Overflow, 3196353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'Infinite result from next_toward', 3197353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans._sign) 3198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista elif ans.adjusted() < context.Emin: 3201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Underflow) 3202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Subnormal) 3203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Rounded) 3204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Inexact) 3205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # if precision == 1 then we don't raise Clamped for a 3206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # result 0E-Etiny. 3207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not ans: 3208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context._raise_error(Clamped) 3209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, context=None): 3213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of self. 3214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 3216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 3217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 3218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 3219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 3220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 3221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 3222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 3223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 3224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 3225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 3226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_snan(): 3228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "sNaN" 3229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_qnan(): 3230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "NaN" 3231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista inf = self._isinfinity() 3232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == 1: 3233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Infinity" 3234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if inf == -1: 3235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Infinity" 3236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_zero(): 3237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Zero" 3239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Zero" 3241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self.is_subnormal(context=context): 3244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Subnormal" 3246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Subnormal" 3248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # just a normal, regular, boring number, :) 3249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._sign: 3250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "-Normal" 3251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 3252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return "+Normal" 3253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 3255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :)""" 3256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 3257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, other, context=None): 3259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of self, value-of-other times.""" 3260353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3261353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3262353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3263353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3264353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3265353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3266353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3267353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3268353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3269353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3270353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3271353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3272353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 32736c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3274353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3275353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3276353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3277353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3278353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3279353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 328072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's rotate! 3283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[torot:] + rotdig[:torot] 328472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 328572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, other, context=None): 3288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns self operand after adding the second value to its exp.""" 3289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista liminf = -2 * (context.Emax + context.prec) 3299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista limsup = 2 * (context.Emax + context.prec) 3300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (liminf <= int(other) <= limsup): 3301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33046c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 330672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) 3307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista d = d._fix(context) 3308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return d 3309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, other, context=None): 3311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of self, value-of-other times.""" 3312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if context is None: 3313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context = getcontext() 3314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista ans = self._check_nans(other, context) 3316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ans: 3317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return ans 3318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other._exp != 0: 3320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not (-context.prec <= int(other) <= context.prec): 3322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return context._raise_error(InvalidOperation) 3323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if self._isinfinity(): 33256c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # get values, pad if necessary 3328353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista torot = int(other) 3329353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if not torot: 33306c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(self) 3331353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotdig = self._int 3332353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista topad = context.prec - len(rotdig) 3333353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if topad: 333472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotdig = '0'*topad + rotdig 3335353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3336353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # let's shift! 3337353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if torot < 0: 3338353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotdig[:torot] 3339353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 334072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated = rotdig + '0'*torot 3341353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotated = rotated[-context.prec:] 3342353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 334372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return _dec_from_triple(self._sign, 334472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista rotated.lstrip('0') or '0', self._exp) 3345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 334659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Support for pickling, copy, and deepcopy 33477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 33487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 33497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 33517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3352cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # I'm immutable; therefore I am my own clone 33537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 33547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 33567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 3357cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis return self # My components are also immutable 33587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 33597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 336072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistadef _dec_from_triple(sign, coefficient, exponent, special=False): 336172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """Create a decimal instance directly, without any validation, 336272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista normalization (e.g. removal of leading zeros) or argument 336372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista conversion. 336472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 336572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista This function is for *internal use only*. 336672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista """ 336772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 336872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self = object.__new__(Decimal) 336972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._sign = sign 337072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._int = coefficient 337172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._exp = exponent 337272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self._is_special = special 337372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 337472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista return self 337572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista 337659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Context class ####################################################### 3377cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 33787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3379cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis# get rounding method function: 338059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batistarounding_functions = [name for name in Decimal.__dict__.keys() 338159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista if name.startswith('_round_')] 33827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 338359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 33847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 33857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 33867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 33877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 33889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 33897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3390ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlanclass _ContextManager(object): 33918b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """Context manager class to support localcontext(). 33921a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 3393ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan Sets a copy of the supplied context in __enter__() and restores 33948b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan the previous decimal context in __exit__() 33958b6999b4c5fab174090be263ba90f193bdede141Nick Coghlan """ 33961a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 3397ced1218dd1b69ac848f8c79d1afaada5669af33cNick Coghlan self.new_context = new_context.copy() 33981a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 33991a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 34001a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 34011a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 34021a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 34031a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 34041a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 34057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 34067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 34077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 34097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 341059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista rounding - rounding type (how you round) 34117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round? 3412bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 34137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 34147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 34157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 34167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 34177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 34180ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 34190ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 34207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 34217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 3422e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 34237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 34249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 34257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 3426abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 34277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=None, 34280ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 3429e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 3430abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 3431abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 3432abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 3433abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 3434abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 3435bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 3436fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 3437b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 3438bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 3439fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 3440b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 34417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 34427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 3443eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 34447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 34457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 34467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 34477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3448b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 3449bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 3450b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 345159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' 345259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' 345359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista % vars(self)) 345459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [f.__name__ for f, v in self.flags.items() if v] 345559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('flags=[' + ', '.join(names) + ']') 345659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista names = [t.__name__ for t, v in self.traps.items() if v] 345759c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista s.append('traps=[' + ', '.join(names) + ']') 3458b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 3459b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 3460d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 3461d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 3462d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 3463b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 3464d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 34659fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 34669fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 3467bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger nc = Context(self.prec, self.rounding, self.traps, self.flags, 34687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 34697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 34707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 34719fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 34729fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 34739fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 347459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista nc = Context(self.prec, self.rounding, self.traps.copy(), 347559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista self.flags.copy(), self._rounding_decision, self.Emin, 347659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista self.Emax, self.capitals, self._clamp, self._ignored_flags) 34779fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 34789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 34797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 34817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 34827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 34847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 34857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 34867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 34877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 34885aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 34897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 349059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Don't touch the flag 34917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 34927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 3494bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 349559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # The errors define how to handle themselves. 34965aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 34977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 34987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 349959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # self._ignored_flags = [] 35007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 35017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 35037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 3504fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 35057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 35077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 35087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 35097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 35107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 35117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 35127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 35147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 35157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 35167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 35177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 35187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 35197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35205aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 35215aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 35225aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 352359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista raise TypeError("Cannot hash a Context.") 35245aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 35257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 35267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 35277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 35287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 3530e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 35317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 35327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding_decision(self, type): 35347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding decision. 35357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding decision, and returns the current (previous) 35377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding decision. Often used like: 35387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35399fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 35407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # That so you don't change the calling context 35417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle (say DivisionImpossible is raised). 35427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 35447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger instance = instance / Decimal(2) 35457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 35467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it not round for that operation. 35487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3549cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis 35507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self._rounding_decision 35517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision = type 35527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 35537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 35557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 35567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 35587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 35597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 35617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 35627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 35637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 35647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 35657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 35667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 35687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 35707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 35717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 35727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3573fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 35747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Creates a new Decimal instance but using self as context.""" 35757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 3576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if d._isnan() and len(d._int) > self.prec - self._clamp: 3577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return self._raise_error(ConversionSyntax, 3578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista "diagnostic info too long in NaN") 3579dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 35807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 358159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista # Methods 35827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 35837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 35847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 358659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation on the operand. Otherwise, the result is the same as using 35877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 35887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 35899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 35907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 35919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 35927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 35939ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 35947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 35959ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 35967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 35977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 35987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 35997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 36017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 36027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 36047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("19.00") 36059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 36067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.02E+4") 36077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 36097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 3611dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 36127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3613353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def canonical(self, a): 3614353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the same Decimal object. 3615353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3616353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista As we do not have different encodings for the same number, the 3617353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista received object already is in its canonical form. 3618353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3619353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.canonical(Decimal('2.50')) 3620353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.50") 3621353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3622353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.canonical(context=self) 3623353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 36247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 36257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 36267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 36287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 36297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 36307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 36317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 36327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 36347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 36357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 36367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 36377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 36389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 36397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 36409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 36417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 36429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 36437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 36449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 36457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 36469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 36477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 36489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 36497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 36507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 36517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 36527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_signal(self, a, b): 3654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values of the two operands numerically. 3655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista It's pretty much like compare(), but all NaNs signal, with signaling 3657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista NaNs taking precedence over quiet NaNs. 3658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext 3660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('3')) 3661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) 3663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) 3668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("NaN") 3669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.flags[InvalidOperation] = 0 3672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 0 3674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) 3675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("NaN") 3676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> print c.flags[InvalidOperation] 3677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 1 3678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_signal(b, context=self) 3680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total(self, a, b): 3682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation. 3683353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3684353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista This is not like the standard compare, which use their numerical 3685353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. Note that a total ordering is defined for all possible abstract 3686353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista representations. 3687353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3688353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) 3689353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3690353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) 3691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3692353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) 3693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3694353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) 3695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3696353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) 3697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 3698353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) 3699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1") 3700353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total(b) 3702353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def compare_total_mag(self, a, b): 3704353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares two operands using their abstract representation ignoring sign. 3705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3706353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Like compare_total, but with operand's sign ignored and assumed to be 0. 3707353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.compare_total_mag(b) 3709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_abs(self, a): 3711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign set to 0. 3712353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3713353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('2.1')) 3714353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.1") 3715353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_abs(Decimal('-100')) 3716353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 3717353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3718353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_abs() 3719353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3720353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_decimal(self, a): 3721353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the decimal objet. 3722353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3723353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('2.1')) 3724353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.1") 3725353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_decimal(Decimal('-1.00')) 3726353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00") 3727353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 37286c398da0e79cbd68ec4625f00f37a8f2a0a26e5cFacundo Batista return Decimal(a) 3729353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3730353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_negate(self, a): 3731353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a copy of the operand with the sign inverted. 3732353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3733353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('101.5')) 3734353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-101.5") 3735353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_negate(Decimal('-101.5')) 3736353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("101.5") 3737353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3738353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_negate() 3739353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3740353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def copy_sign(self, a, b): 3741353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Copies the second operand's sign to the first one. 3742353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3743353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In detail, it returns a copy of the first operand with the sign 3744353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista equal to the sign of the second operand. 3745353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) 3747353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.50") 3748353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) 3749353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.50") 3750353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) 3751353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.50") 3752353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) 3753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.50") 3754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.copy_sign(b) 3756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 37577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 37587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 37597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 37617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.333333333") 37629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 37637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.666666667") 37649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 37657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.5") 37669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 37677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 37689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 37697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 37709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 37717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.00") 37729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 37737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20") 37749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 37757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 37769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 37777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1000") 37789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 37797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20E+6") 37807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 37827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 37847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 37857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 37877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 37889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 37897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 37909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 37917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 37927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 37937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 37947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 37957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 37967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 37977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def exp(self, a): 3799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns e ** a. 3800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-Infinity')) 3805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('-1')) 3807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.367879441") 3808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0')) 3809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 3810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('1')) 3811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.71828183") 3812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('0.693147181')) 3813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.00000000") 3814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.exp(Decimal('+Infinity')) 3815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 3816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.exp(context=self) 3818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def fma(self, a, b, c): 3820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a multiplied by b, plus c. 3821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The first two operands are multiplied together, using multiply, 3823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the third operand is then added to the result of that 3824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista multiplication, using add, all with only one final rounding. 3825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) 3827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("22") 3828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) 3829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-8") 3830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) 3831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.38435736E+12") 3832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.fma(b, c, context=self) 3834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_canonical(self, a): 38361a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is canonical; otherwise return False. 38371a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista 38381a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista Currently, the encoding of a Decimal instance is always 38391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista canonical, so this method returns True for any Decimal. 3840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_canonical(Decimal('2.50')) 38421a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 38441a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista return a.is_canonical() 3845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_finite(self, a): 38471a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is finite; otherwise return False. 3848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 38491a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista A Decimal instance is considered finite if it is neither 38501a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista infinite nor a NaN. 3851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('2.50')) 38531a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('-0.3')) 38551a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('0')) 38571a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('Inf')) 38591a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_finite(Decimal('NaN')) 38611a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_finite() 3864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_infinite(self, a): 38661a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is infinite; otherwise return False. 3867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('2.50')) 38691a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('-Inf')) 38711a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_infinite(Decimal('NaN')) 38731a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_infinite() 3876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_nan(self, a): 38781a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a qNaN or sNaN; 38791a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('2.50')) 38821a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('NaN')) 38841a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_nan(Decimal('-sNaN')) 38861a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_nan() 3889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_normal(self, a): 38911a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a normal number; 38921a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3894353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('2.50')) 38981a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.1E-999')) 39001a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('0.00')) 39021a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('-Inf')) 39041a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_normal(Decimal('NaN')) 39061a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_normal(context=self) 3909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_qnan(self, a): 39111a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a quiet NaN; otherwise return False. 3912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('2.50')) 39141a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('NaN')) 39161a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_qnan(Decimal('sNaN')) 39181a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_qnan() 3921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_signed(self, a): 39231a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is negative; otherwise return False. 3924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('2.50')) 39261a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-12')) 39281a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_signed(Decimal('-0')) 39301a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3932353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_signed() 3933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3934353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_snan(self, a): 39351a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a signaling NaN; 39361a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista otherwise return False. 3937353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3938353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('2.50')) 39391a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('NaN')) 39411a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_snan(Decimal('sNaN')) 39431a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3944353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_snan() 3946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3947353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_subnormal(self, a): 39481a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is subnormal; otherwise return False. 3949353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3950353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3951353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3952353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3953353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('2.50')) 39541a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3955353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.1E-999')) 39561a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3957353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('0.00')) 39581a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3959353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('-Inf')) 39601a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3961353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.is_subnormal(Decimal('NaN')) 39621a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3963353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3964353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_subnormal(context=self) 3965353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3966353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def is_zero(self, a): 39671a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista """Return True if the operand is a zero; otherwise return False. 3968353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3969353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('0')) 39701a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3971353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('2.50')) 39721a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista False 3973353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.is_zero(Decimal('-0E+2')) 39741a191df14dc2f37933ef32f553fcaa7a5ac77cf7Facundo Batista True 3975353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3976353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.is_zero() 3977353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3978353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def ln(self, a): 3979353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the natural (base e) logarithm of the operand. 3980353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3981353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 3982353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 3983353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 3984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('0')) 3985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 3986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('1.000')) 3987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 3988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('2.71828183')) 3989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000000") 3990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('10')) 3991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.30258509") 3992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.ln(Decimal('+Infinity')) 3993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 3994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 3995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.ln(context=self) 3996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 3997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def log10(self, a): 3998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the base 10 logarithm of the operand. 3999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0')) 4004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 4005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('0.001')) 4006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-3") 4007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('1.000')) 4008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('2')) 4010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.301029996") 4011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('10')) 4012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('70')) 4014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.84509804") 4015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.log10(Decimal('+Infinity')) 4016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("Infinity") 4017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.log10(context=self) 4019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logb(self, a): 4021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ Returns the exponent of the magnitude of the operand's MSD. 4022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the integer which is the exponent of the magnitude 4024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the most significant digit of the operand (as though the 4025353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand were truncated to a single digit while maintaining the 4026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value of that digit and without limiting the resulting exponent). 4027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('250')) 4029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2") 4030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('2.50')) 4031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0.03')) 4033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-2") 4034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logb(Decimal('0')) 4035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 4036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logb(context=self) 4038353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_and(self, a, b): 4040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'and' between each operand's digits. 4041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4042353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) 4045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) 4047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) 4049353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) 4051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) 4053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1000") 4054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) 4055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10") 4056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_and(b, context=self) 4058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_invert(self, a): 4060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Invert all the digits in the operand. 4061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operand must be a logical number. 4063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('0')) 4065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("111111111") 4066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('1')) 4067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("111111110") 4068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('111111111')) 4069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_invert(Decimal('101010101')) 4071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10101010") 4072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_invert(context=self) 4074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_or(self, a, b): 4076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'or' between each operand's digits. 4077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) 4081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) 4083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) 4085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) 4087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) 4089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1110") 4090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) 4091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1110") 4092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_or(b, context=self) 4094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def logical_xor(self, a, b): 4096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Applies the logical operation 'xor' between each operand's digits. 4097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The operands must be both logical numbers. 4099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) 4101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) 4103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) 4105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) 4107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4108353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) 4109353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("110") 4110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) 4111353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1101") 4112353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4113353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.logical_xor(b, context=self) 4114353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 41167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 41177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 41197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 412059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 412159c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the maximum (closer to positive 41227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 41237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 41257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 41269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 41277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 41289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 4129d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("1") 4130d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 4131d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 41327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 41347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4135353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def max_mag(self, a, b): 4136353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4137353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.max_mag(b, context=self) 4138353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 41407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 41417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 41437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 414459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation. If they are numerically equal then the left-hand operand 414559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen as the result. Otherwise the minimum (closer to negative 41467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 41477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 41497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 41509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 41517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-10") 41529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 41537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 4154d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 4155d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 41567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 41587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4159353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def min_mag(self, a, b): 4160353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compares the values numerically with their sign ignored.""" 4161353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.min_mag(b, context=self) 4162353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 41637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 41647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 41657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 41677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 41687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 41697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 41717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 41729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 41737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 41747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 41767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 41787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 41797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4180cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis If either operand is a special value then the general rules apply. 4181cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis Otherwise, the operands are multiplied together ('long multiplication'), 4182cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis resulting in a number which may be as long as the sum of the lengths 4183cfe3128cd58c4a59d236527184b40352ae35e44aMartin v. Löwis of the two operands. 41847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 41859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 41867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.60") 41879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 41887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("21") 41899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 41907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.72") 41919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 41927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.0") 41939ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 41947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.28135971E+11") 41957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 41967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 41977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4198353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_minus(self, a): 4199353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the largest representable number smaller than a. 4200353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4201353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4202353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4203353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4204353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('1')) 4205353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.999999999") 4206353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('1E-1007')) 4207353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0E-1007") 4208353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_minus(Decimal('-1.00000003')) 4209353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000004") 4210353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_minus(Decimal('Infinity')) 4211353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("9.99999999E+999") 4212353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4213353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_minus(context=self) 4214353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4215353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_plus(self, a): 4216353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the smallest representable number larger than a. 4217353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4218353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4219353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4220353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4221353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('1')) 4222353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000001") 4223353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-1E-1007')) 4224353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0E-1007") 4225353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.next_plus(Decimal('-1.00000003')) 4226353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000002") 4227353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_plus(Decimal('-Infinity')) 4228353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-9.99999999E+999") 4229353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4230353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_plus(context=self) 4231353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4232353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def next_toward(self, a, b): 4233353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the number closest to a, in direction towards b. 4234353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4235353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result is the closest representable number from the first 4236353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista operand (but not the first operand) that is in the direction 4237353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista towards the second operand, unless the operands have the same 4238353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value. 4239353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4240353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4241353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4242353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4243353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('2')) 4244353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.00000001") 4245353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) 4246353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0E-1007") 4247353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) 4248353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000002") 4249353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1'), Decimal('0')) 4250353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.999999999") 4251353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) 4252353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0E-1007") 4253353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) 4254353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-1.00000004") 4255353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) 4256353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0.00") 4257353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4258353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.next_toward(b, context=self) 4259353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 42607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 4261e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 42627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 42647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 42657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 42669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 42677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 42689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 42697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 42709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 42717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2") 42729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 42737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.2E+2") 42749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 42757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2E+2") 42769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 42777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 42787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 42797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 42807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4281353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def number_class(self, a): 4282353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns an indication of the class of the operand. 4283353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4284353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The class is one of the following strings: 4285353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -sNaN 4286353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -NaN 4287353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Infinity 4288353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Normal 4289353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Subnormal 4290353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista -Zero 4291353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Zero 4292353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Subnormal 4293353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Normal 4294353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista +Infinity 4295353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4296353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = Context(ExtendedContext) 4297353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4298353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4299353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('Infinity')) 4300353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Infinity' 4301353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('1E-10')) 4302353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4303353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('2.50')) 4304353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Normal' 4305353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0.1E-999')) 4306353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Subnormal' 4307353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('0')) 4308353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '+Zero' 4309353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0')) 4310353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Zero' 4311353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-0.1E-999')) 4312353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Subnormal' 4313353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-1E-10')) 4314353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4315353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-2.50')) 4316353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Normal' 4317353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-Infinity')) 4318353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '-Infinity' 4319353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('NaN')) 4320353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4321353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('-NaN')) 4322353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'NaN' 4323353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.number_class(Decimal('sNaN')) 4324353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'sNaN' 4325353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4326353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.number_class(context=self) 4327353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 43287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 43297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 43307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 43327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 43337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 43347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 43367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 43379ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 43387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 43397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 43407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 43417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 43427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 43437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 43447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4345353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With two arguments, compute a**b. If a is negative then b 4346353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista must be integral. The result will be inexact unless b is 4347353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integral and the result is finite and can be expressed exactly 4348353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in 'precision' digits. 4349353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4350353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista With three arguments, compute (a**b) % modulo. For the 4351353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista three argument form, the following restrictions on the 4352353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista arguments hold: 4353353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4354353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - all three arguments must be integral 4355353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - b must be nonnegative 4356353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - at least one of a or b must be nonzero 4357353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista - modulo must be nonzero and have at most 'precision' digits 4358353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4359353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The result of pow(a, b, modulo) is identical to the result 4360353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista that would be obtained by computing (a**b) % modulo with 4361353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista unbounded precision, but is computed more efficiently. It is 4362353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista always exact. 4363353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4364353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c = ExtendedContext.copy() 4365353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emin = -999 4366353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.Emax = 999 4367353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('3')) 43687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("8") 4369353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-2'), Decimal('3')) 4370353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-8") 4371353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('2'), Decimal('-3')) 43727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.125") 4373353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('1.7'), Decimal('8')) 43747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("69.7575744") 4375353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('10'), Decimal('0.301029996')) 4376353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2.00000000") 4377353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('-1')) 43787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 4379353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('0')) 43807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 4381353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('Infinity'), Decimal('1')) 43827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 4383353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('-1')) 43847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 4385353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('0')) 43867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 4387353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('1')) 43887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 4389353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-Infinity'), Decimal('2')) 43907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 4391353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('0'), Decimal('0')) 43927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 4393353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4394353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) 4395353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11") 4396353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) 4397353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-11") 4398353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) 4399353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 4400353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) 4401353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11") 4402353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) 4403353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("11729830") 4404353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) 4405353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-0") 4406353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) 4407353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1") 44087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 44107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 441259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Returns a value equal to 'a' (rounded), having the exponent of 'b'. 44137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 441559c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operand. It may be rounded using the current rounding setting (if the 44167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 44177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 44187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 44197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 44217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 442259c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista operation condition is raised. This guarantees that, unless there is 442359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista an error condition, the exponent of the result of a quantize is always 44247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 44257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 44277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 44287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 44307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.170") 44319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 44327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.17") 44339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 44347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2") 44359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 44367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 44379ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 44387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0E+1") 44399ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 44407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 44419ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 44427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44439ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 44447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 44459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 44467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0E+5") 44479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 44487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 44507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 44519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 44527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217.0") 44539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 44547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217") 44559ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 44567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2E+2") 44579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 44587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2E+2") 44597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 44617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4462353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def radix(self): 4463353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Just returns 10, as this is Decimal, :) 4464353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4465353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.radix() 4466353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("10") 4467353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4468353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return Decimal(10) 4469353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 44707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 44717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 44727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 447459c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista calculating integer division as described for divide-integer, rounded 44750d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz to precision digits if necessary. The sign of the result, if 447659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista non-zero, is the same as that of the original dividend. 44777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 44797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 44807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 44817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 44837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 44849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 44857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 44869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 44877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 44889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 44897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 44909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 44917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 44929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 44937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 44947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 44957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 44967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 44977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 44987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 44997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 450059c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista is chosen). If the result is equal to 0 then its sign will be the 45017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 45027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 45047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 45057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 45067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 45087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.9") 45099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 45107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 45119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 45127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 45139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 45147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 45159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 45167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 45179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 45187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 45199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 45207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.3") 45217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 45237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4524353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def rotate(self, a, b): 4525353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a rotated copy of a, b times. 4526353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4527353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a rotated copy of the digits in 4528353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista the coefficient of the first operand. The number of places of 4529353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rotation is taken from the absolute value of the second operand, 4530353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the rotation being to the left if the second operand is 4531353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. 4532353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4533353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) 4534353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("400000003") 4535353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) 4536353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("12") 4537353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) 4538353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("891234567") 4539353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) 4540353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("123456789") 4541353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) 4542353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("345678912") 4543353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4544353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.rotate(b, context=self) 4545353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 45477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 45487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 45507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 45517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 45529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 45537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 45549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 45557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 45569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 45577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 45589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 45597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 45607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 45617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 45627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4563353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def scaleb (self, a, b): 4564353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns the first operand after adding the second value its exp. 4565353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4566353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) 4567353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0.0750") 4568353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) 4569353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.50") 4570353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) 4571353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.50E+3") 4572353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4573353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.scaleb (b, context=self) 4574353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4575353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def shift(self, a, b): 4576353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Returns a shifted copy of a, b times. 4577353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4578353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista The coefficient of the result is a shifted copy of the digits 4579353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the coefficient of the first operand. The number of places 4580353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to shift is taken from the absolute value of the second operand, 4581353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista with the shift being to the left if the second operand is 4582353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista positive or to the right otherwise. Digits shifted into the 4583353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coefficient are zeros. 4584353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4585353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) 4586353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("400000000") 4587353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) 4588353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("0") 4589353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) 4590353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1234567") 4591353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) 4592353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("123456789") 4593353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) 4594353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("345678900") 4595353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4596353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.shift(b, context=self) 4597353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 45987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 459959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista """Square root of a non-negative number to context precision. 46007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 46027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 46037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 46057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 46069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 46077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 46089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 46097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.624499800") 46109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 46117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 46129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 46137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 46149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 46157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 46169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 46177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 46189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 46197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.64575131") 46209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 46217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.16227766") 46229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 46236ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 46247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 46267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 4628f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 46297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 46317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.23") 46329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 46337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.00") 46349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 46357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.77") 46367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 46387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 46407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 46417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 46437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 46457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 46477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 46487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 46507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 46517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 46527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4653353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_exact(self, a): 4654353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Rounds to an integer. 4655353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4656353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista When the operand has a negative exponent, the result is the same 4657353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista as using the quantize() operation using the given operand as the 4658353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista left-hand-operand, 1E+0 as the right-hand-operand, and the precision 4659353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of the operand as the precision setting; Inexact and Rounded flags 4660353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista are allowed in this operation. The rounding mode is taken from the 4661353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista context. 4662353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4663353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('2.1')) 4664353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("2") 4665353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100')) 4666353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 4667353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('100.0')) 4668353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("100") 4669353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('101.5')) 4670353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("102") 4671353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) 4672353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-102") 4673353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) 4674353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("1.0E+6") 4675353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) 4676353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("7.89E+77") 4677353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) 4678353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Decimal("-Infinity") 4679353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4680353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_exact(context=self) 4681353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4682353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista def to_integral_value(self, a): 46837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 46847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 46857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 46867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 46877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 46887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 468959c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista be set. The rounding mode is taken from the context. 46907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4691353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('2.1')) 46927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 4693353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100')) 46947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 4695353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('100.0')) 46967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 4697353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('101.5')) 46987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("102") 4699353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-101.5')) 47007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-102") 4701353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('10E+5')) 47027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0E+6") 4703353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) 47047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("7.89E+77") 4705353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista >>> ExtendedContext.to_integral_value(Decimal('-Inf')) 47067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 47077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4708353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a.to_integral_value(context=self) 4709353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4710353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the method name changed, but we provide also the old one, for compatibility 4711353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista to_integral = to_integral_value 47127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 47147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 471517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 4716636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 47177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 47187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 47207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 47217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 4722636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 47237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 472417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 472517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 472672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista self.int = int(value._int) 47277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 472817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 472917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 47307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 47317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 47327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 47337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 47357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 47367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 47387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _normalize(op1, op2, shouldround = 0, prec = 0): 47427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 47437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 47457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4746353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if op1.exp < op2.exp: 47477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 47487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 47497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 47507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 47517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 47527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4753353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). 4754353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Then adding 10**exp to tmp has the same effect (after rounding) 4755353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as adding any positive quantity smaller than 10**exp; similarly 4756353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for subtraction. So if other is smaller than 10**exp we replace 4757353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # it with 10**exp. This avoids tmp.exp - other.exp getting too large. 4758353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shouldround: 4759636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp_len = len(str(tmp.int)) 4760636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_len = len(str(other.int)) 4761353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp = tmp.exp + min(-1, tmp_len - prec - 2) 4762353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if other_len + other.exp - 1 < exp: 4763636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other.int = 1 4764353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista other.exp = exp 4765636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 4766353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.int *= 10 ** (tmp.exp - other.exp) 4767353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista tmp.exp = other.exp 47687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 47697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4770353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### 4771353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4772353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# This function from Tim Peters was taken from here: 4773353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# http://mail.python.org/pipermail/python-list/1999-July/007758.html 4774353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# The correction being in the function definition is for speed, and 4775353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the whole function is not resolved with math.log because of avoiding 4776353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista# the use of floats. 4777353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _nbits(n, correction = { 4778353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '0': 4, '1': 3, '2': 2, '3': 2, 4779353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '4': 1, '5': 1, '6': 1, '7': 1, 4780353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '8': 0, '9': 0, 'a': 0, 'b': 0, 4781353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 'c': 0, 'd': 0, 'e': 0, 'f': 0}): 4782353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Number of bits in binary representation of the positive integer n, 4783353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista or 0 if n == 0. 4784353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4785353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n < 0: 4786353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _nbits should be nonnegative.") 4787353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista hex_n = "%x" % n 4788353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 4*len(hex_n) - correction[hex_n[0]] 4789353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4790353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _sqrt_nearest(n, a): 4791353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to the square root of the positive integer n. a is 4792353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista an initial approximation to the square root. Any positive integer 4793353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista will do for a, but the closer a is to the square root of n the 4794353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista faster convergence will be. 4795353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4796353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4797353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if n <= 0 or a <= 0: 4798353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("Both arguments to _sqrt_nearest should be positive.") 4799353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4800353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b=0 4801353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while a != b: 4802353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, a = a, a--n//a>>1 4803353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return a 4804353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4805353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _rshift_nearest(x, shift): 4806353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given an integer x and a nonnegative integer shift, return closest 4807353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista integer to x / 2**shift; use round-to-even in case of a tie. 4808353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4809353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4810353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b, q = 1L << shift, x >> shift 4811353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*(x & (b-1)) + (q&1) > b) 4812353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4813353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _div_nearest(a, b): 4814353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Closest integer to a/b, a and b positive integers; rounds to even 4815353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in the case of a tie. 4816353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4817353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 4818353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q, r = divmod(a, b) 4819353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return q + (2*r + (q&1) > b) 4820353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4821353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _ilog(x, M, L = 8): 4822353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Integer approximation to M*log(x/M), with absolute error boundable 4823353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in terms only of x/M. 4824353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4825353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Given positive integers x and M, return an integer approximation to 4826353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference 4827353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista between the approximation and the exact result is at most 22. For 4828353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In 4829353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista both cases these are upper bounds on the error; it will usually be 4830353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista much smaller.""" 4831353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4832353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # The basic algorithm is the following: let log1p be the function 4833353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use 4834353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # the reduction 4835353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4836353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) 4837353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4838353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # repeatedly until the argument to log1p is small (< 2**-L in 4839353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # absolute value). For small y we can use the Taylor series 4840353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expansion 4841353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4842353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T 4843353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4844353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # truncating at T such that y**T is small enough. The whole 4845353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # computation is carried out in a form of fixed-point arithmetic, 4846353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # with a real number z being represented by an integer 4847353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # approximation to z*M. To avoid loss of precision, the y below 4848353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # is actually an integer approximation to 2**R*y*M, where R is the 4849353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # number of reductions performed so far. 4850353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4851353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = x-M 4852353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # argument reduction; R = number of reductions performed 4853353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = 0 4854353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista while (R <= L and long(abs(y)) << L-R >= M or 4855353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R > L and abs(y) >> R-L >= M): 4856353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(long(M*y) << 1, 4857353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) 4858353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R += 1 4859353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4860353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series with T terms 4861353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 4862353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista yshift = _rshift_nearest(y, R) 4863353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, T) 4864353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(T-1, 0, -1): 4865353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista w = _div_nearest(M, k) - _div_nearest(yshift*w, M) 4866353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4867353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(w*y, M) 4868353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4869353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog10(c, e, p): 4870353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, p >= 0, compute an integer 4871353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log10(c*10**e), with an absolute error of 4872353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4873353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4874353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # increase precision by 2; compensate for this by dividing 4875353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # final result by 100 4876353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4877353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4878353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # write c*10**e as d*10**f with either: 4879353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f >= 0 and 1 <= d <= 10, or 4880353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # f <= 0 and 0.1 <= d <= 1. 4881353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Thus for c*10**e close to 1, f = 0 4882353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4883353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4884353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4885353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4886353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista M = 10**p 4887353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4888353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4889353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4890353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4891353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) 4892353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4893353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, M) # error < 5 + 22 = 27 4894be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista log_10 = _log10_digits(p) # error < 1 4895353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _div_nearest(log_d*M, log_10) 4896353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = f*M # exact 4897353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4898353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 # error < 2.31 4899353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_tenpower = div_nearest(f, 10**-p) # error < 0.5 4900353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4901353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(log_tenpower+log_d, 100) 4902353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4903353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dlog(c, e, p): 4904353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers c, e and p with c > 0, compute an integer 4905353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista approximation to 10**p * log(c*10**e), with an absolute error of 4906353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista at most 1. Assumes that c*10**e is not exactly 1.""" 4907353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4908353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Increase precision by 2. The precision increase is compensated 4909353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # for at the end with a division by 100. 4910353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 4911353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4912353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, 4913353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) 4914353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # as 10**p * log(d) + 10**p*f * log(10). 4915353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista l = len(str(c)) 4916353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f = e+l - (e+l >= 1) 4917353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4918353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute approximation to 10**p*log(d), with error < 27 4919353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if p > 0: 4920353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista k = e+p-f 4921353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if k >= 0: 4922353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c *= 10**k 4923353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4924353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista c = _div_nearest(c, 10**-k) # error of <= 0.5 in c 4925353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4926353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # _ilog magnifies existing error in c by a factor of at most 10 4927353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 4928353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4929353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # p <= 0: just approximate the whole thing by 0; error < 2.31 4930353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista log_d = 0 4931353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4932be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute approximation to f*10**p*log(10), with error < 11. 4933353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if f: 4934be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = len(str(abs(f)))-1 4935be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p + extra >= 0: 4936be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in f * _log10_digits(p+extra) < |f| * 1 = |f| 4937be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 4938be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) 4939353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4940353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 4941353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 4942353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista f_log_ten = 0 4943353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4944be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 4945353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(f_log_ten + log_d, 100) 4946353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4947be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batistaclass _Log10Memoize(object): 4948be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Class to compute, store, and allow retrieval of, digits of the 4949be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista constant log(10) = 2.302585.... This constant is needed by 4950be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" 4951be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def __init__(self): 4952be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = "23025850929940456840179914546843642076011014886" 4953be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4954be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista def getdigits(self, p): 4955be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """Given an integer p >= 0, return floor(10**p)*log(10). 4956be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4957be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista For example, self.getdigits(3) returns 2302. 4958be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista """ 4959be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits are stored as a string, for quick conversion to 4960be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # integer in the case that we've already computed enough 4961be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # digits; the stored digits should always be correct 4962be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # (truncated, not rounded to nearest). 4963be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p < 0: 4964be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista raise ValueError("p should be nonnegative") 4965be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4966be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if p >= len(self.digits): 4967be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+3, p+6, p+9, ... digits; continue until at 4968be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # least one of the extra digits is nonzero 4969be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra = 3 4970be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista while True: 4971be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute p+extra digits, correct to within 1ulp 4972be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista M = 10**(p+extra+2) 4973be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista digits = str(_div_nearest(_ilog(10*M, M), 100)) 4974be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista if digits[-extra:] != '0'*extra: 4975be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista break 4976be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista extra += 3 4977be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # keep all reliable digits so far; remove trailing zeros 4978be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # and next nonzero digit 4979be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista self.digits = digits.rstrip('0')[:-1] 4980be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista return int(self.digits[:p+1]) 4981be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4982be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista_log10_digits = _Log10Memoize().getdigits 4983be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista 4984353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _iexp(x, M, L=8): 4985353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers x and M, M > 0, such that x/M is small in absolute 4986353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista value, compute an integer approximation to M*exp(x/M). For 0 <= 4987353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista x/M <= 2.4, the absolute error in the result is bounded by 60 (and 4988353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista is usually much smaller).""" 4989353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 4990353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Algorithm: to compute exp(z) for a real number z, first divide z 4991353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then 4992353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor 4993353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # series 4994353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4995353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(x) = x + x**2/2! + x**3/3! + ... 4996353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4997353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Now use the identity 4998353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 4999353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(2x) = expm1(x)*(expm1(x)+2) 5000353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # 5001353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # R times to compute the sequence expm1(z/2**R), 5002353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). 5003353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5004353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find R such that x/2**R/M <= 2**-L 5005353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista R = _nbits((long(x)<<L)//M) 5006353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5007353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Taylor series. (2**L)**T > M 5008353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista T = -int(-10*len(str(M))//(3*L)) 5009353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x, T) 5010353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<R 5011353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for i in xrange(T-1, 0, -1): 5012353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(x*(Mshift + y), Mshift * i) 5013353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5014353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Expansion 5015353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista for k in xrange(R-1, -1, -1): 5016353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista Mshift = long(M)<<(k+2) 5017353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = _div_nearest(y*(y+Mshift), Mshift) 5018353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5019353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return M+y 5020353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5021353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dexp(c, e, p): 5022353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute an approximation to exp(c*10**e), with p decimal places of 5023353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista precision. 5024353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5025be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista Returns integers d, f such that: 5026353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5027353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= d <= 10**p, and 5028353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (d-1)*10**f < exp(c*10**e) < (d+1)*10**f 5029353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5030353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista In other words, d*10**f is an approximation to exp(c*10**e) with p 5031353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista digits of precision, and with an error in d of at most 1. This is 5032353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when d 5033353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista = 10**(p-1) the error could be up to 10 ulp.""" 5034353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5035353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision 5036353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista p += 2 5037353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5038be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute log(10) with extra precision = adjusted exponent of c*10**e 5039353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista extra = max(0, e + len(str(c)) - 1) 5040353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista q = p + extra 5041353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5042be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), 5043353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # rounding down 5044353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = e+q 5045353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5046353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c*10**shift 5047353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5048353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista cshift = c//10**-shift 5049be6c7ba72ad2bc3087a7df20871387b11756e140Facundo Batista quot, rem = divmod(cshift, _log10_digits(q)) 5050353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5051353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # reduce remainder back to original precision 5052353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista rem = _div_nearest(rem, 10**extra) 5053353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5054353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # error in result of _iexp < 120; error after division < 0.62 5055353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 5056353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5057353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _dpower(xc, xe, yc, ye, p): 5058353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and 5059353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 5060353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5061353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 10**(p-1) <= c <= 10**p, and 5062353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista (c-1)*10**e < x**y < (c+1)*10**e 5063353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5064353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista in other words, c*10**e is an approximation to x**y with p digits 5065353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista of precision, and with an error in c of at most 1. (This is 5066353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista almost, but not quite, the same as the error being < 1ulp: when c 5067353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista == 10**(p-1) we can only guarantee error < 10ulp.) 5068353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5069353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista We assume that: x is positive and not equal to 1, and y is nonzero. 5070353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """ 5071353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5072353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # Find b such that 10**(b-1) <= |y| <= 10**b 5073353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista b = len(str(abs(yc))) + ye 5074353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5075353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point 5076353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista lxc = _dlog(xc, xe, p+b+1) 5077353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5078353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) 5079353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista shift = ye-b 5080353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if shift >= 0: 5081353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = lxc*yc*10**shift 5082353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5083353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista pc = _div_nearest(lxc*yc, 10**-shift) 5084353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5085353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if pc == 0: 5086353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # we prefer a result that isn't exactly 1; this makes it 5087353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista # easier to compute a correctly rounded result in __pow__ 5088353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: 5089353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**(p-1)+1, 1-p 5090353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5091353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = 10**p-1, -p 5092353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista else: 5093353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff, exp = _dexp(pc, -(p+1), p+1) 5094353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista coeff = _div_nearest(coeff, 10) 5095353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista exp += 1 5096353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5097353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return coeff, exp 5098353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 5099353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _log10_lb(c, correction = { 5100353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, 5101353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista '6': 23, '7': 16, '8': 10, '9': 5}): 5102353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista """Compute a lower bound for 100*log10(c) for a positive integer c.""" 5103353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if c <= 0: 5104353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise ValueError("The argument to _log10_lb should be nonnegative.") 5105353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista str_c = str(c) 5106353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista return 100*len(str_c) - correction[str_c[0]] 5107353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista 510859c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Helper Functions #################################################### 51097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5110353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batistadef _convert_other(other, raiseit=False): 5111636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 5112636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 5113636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5114636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 5115636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 5116636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 5117636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 5118636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 5119353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista if raiseit: 5120353750c405c9099d0be69c6af1d17037b38c4ddfFacundo Batista raise TypeError("Unable to convert %s to Decimal" % other) 5121267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 5122636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 512359c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### Setup Specific Contexts ############################################ 51247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 5126fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 51277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 51296ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 5130bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 5131bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 51327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=ALWAYS_ROUND, 513399148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 513499148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 5135e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 51367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 51397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 51407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 51417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 51427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51439ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 51447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 5145bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 5146bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 51477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 51506ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 5151bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 5152bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 51537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 51547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 515659c5884b4c37b6288911ff2aed218cfbb41f06abFacundo Batista##### crud for parsing strings ############################################# 51577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport re 51587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 515972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Regular expression used for parsing numeric strings. Additional 516072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# comments: 516172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 516272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 1. Uncomment the two '\s*' lines to allow leading and/or trailing 516372bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# whitespace. But note that the specification disallows whitespace in 516472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# a numeric string. 516572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 516672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 2. For finite numbers (not infinities and NaNs) the body of the 516772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# number between the optional sign and the optional exponent must have 516872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# at least one decimal digit, possibly after the decimal point. The 516972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# lookahead expression '(?=\d|\.\d)' checks this. 517072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# 517172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# As the flag UNICODE is not enabled here, we're explicitly avoiding any 517272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# other meaning for \d than the numbers [0-9]. 51737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 517472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batistaimport re 517572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista_parser = re.compile(r""" # A numeric string consists of: 51767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 517772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<sign>[-+])? # an optional sign, followed by either... 51787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 517972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?=\d|\.\d) # ...a number (with at least one digit) 518072bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<int>\d*) # consisting of a (possibly empty) integer part 518172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (\.(?P<frac>\d*))? # followed by an optional fractional part 518272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... 51837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 518472bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista Inf(inity)? # ...an infinity, or... 518572bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista | 518672bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<signal>s)? # ...an (optionally signaling) 518772bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista NaN # NaN 518872bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista (?P<diag>\d*) # with (possibly empty) diagnostic information. 51897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 51907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 51917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger $ 519272bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista""", re.VERBOSE | re.IGNORECASE).match 51937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51942ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_all_zeros = re.compile('0*$').match 51952ec7415db5ad63c4e4b27ee793214071454f6fe5Facundo Batista_exact_half = re.compile('50*$').match 51967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 51977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 51980d4c06e06e5ee1f3bb1fa8068114bd700d74864aNeal Norwitz 519972bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista##### Useful Constants (internal use only) ################################ 52007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 520172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Reusable defaults 520272bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInf = Decimal('Inf') 520372bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistanegInf = Decimal('-Inf') 520472bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaNaN = Decimal('NaN') 520572bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_0 = Decimal(0) 520672bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p1 = Decimal(1) 520772bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n1 = Decimal(-1) 520872bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_p2 = Decimal(2) 520972bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaDec_n2 = Decimal(-2) 52107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 521172bc54faed8f12dc89ecc989fc7921002db3427fFacundo Batista# Infsign[sign] is infinity w/ that sign 521272bc54faed8f12dc89ecc989fc7921002db3427fFacundo BatistaInfsign = (Inf, negInf) 52137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 52167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 52177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 52187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 5219