decimal.py revision d6c700a320eacd6f04cbcc60996b84e765766890
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 107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerThis is a Py2.3 implementation of decimal floating point arithmetic based on 137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerthe General Decimal Arithmetic Specification: 147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www2.hursley.ibm.com/decimal/decarith.html 167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 170ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerand IEEE standard 854-1987: 187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html 207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal floating point has finite precision with arbitrarily large bounds. 227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerThe purpose of the module is to support arithmetic using familiar 247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger"schoolhouse" rules and to avoid the some of tricky representation 257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerissues associated with binary floating point. The package is especially 267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingeruseful for financial applications or for contexts where users have 277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerexpectations that are at odds with binary floating point (for instance, 287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerin binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead 297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerof the expected Decimal("0.00") returned by decimal floating point). 307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerHere are some examples of using the decimal module: 327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> from decimal import * 34bd7f76dd04780304c397323ae994092ce759d5a2Raymond Hettinger>>> setcontext(ExtendedContext) 357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(0) 367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("0") 377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1") 387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1") 397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("-.0123") 407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("-0.0123") 417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(123456) 427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("123456") 437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("123.45e12345678901234567890") 447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1.2345E+12345678901234567892") 457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1.33") + Decimal("1.27") 467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("2.60") 477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41") 487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("-2.20") 497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> dig = Decimal(1) 507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333 527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> getcontext().prec = 18 537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333333333333 557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig.sqrt() 567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3).sqrt() 587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1.73205080756887729 597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3) ** 123 607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger4.85192780976896427E+58 617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> inf = Decimal(1) / Decimal(0) 627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print inf 637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> neginf = Decimal(-1) / Decimal(0) 657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf 667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf + inf 687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf * inf 707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 73bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> getcontext().traps[DivisionByZero] = 1 747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDivisionByZero: x / 0 807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c = Context() 81bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 825aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c.divide(Decimal(0), Decimal(0)) 857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("NaN") 86bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 1 875aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 895aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 905aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 975aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond HettingerInvalidOperation: 0 / 0 985aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1005aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 101bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 1027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 1037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 1045aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> 1077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 1087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger__all__ = [ 1107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Two major classes 1117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'Decimal', 'Context', 1127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Contexts 1149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 'DefaultContext', 'BasicContext', 'ExtendedContext', 1157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Exceptions 117d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', 118d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', 1197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Constants for use in setting up contexts 1217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', 1227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 1237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Functions for manipulating contexts 1250ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger 'setcontext', 'getcontext' 1267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger] 1277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport threading 1297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport copy 1307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport operator 1317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Rounding 1330ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1340ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1350ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1360ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1370ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1380ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1390ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 1407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1419ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger#Rounding decision (not part of the public API) 1420ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerNEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY 1430ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. 1447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Errors 1467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1485aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger handle -- Called when context._raise_error is called and the 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set. First argument is self, second is the 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context. More arguments can be given, those being after 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the explanation in _raise_error (For example, 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(NewError, '(-x)!', self._sign) would 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger call NewError().handle(context, self._sign).) 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger representation. This may occur when the exponent of a zero result would 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be outside the bounds of a representation, or when a large normal 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number would have an encoded exponent that cannot be represented. In 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 * (+-)INF 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF / (+-)INF 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 1997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 2007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args[0] == 1: #sNaN, must drop 's' but keep diagnostics 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (args[1]._sign, args[1]._int, 'n') ) 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 2127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger syntax. The result is [0,qNaN]. 2137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (0, (0,), 'n') #Passed to something which uses a tuple. 2177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, double = None, *args): 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if double is not None: 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign],)*2 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger longer than precision). The result is [0,qNaN]. 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) 2467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the dividend is also zero. The result is [0,qNaN]. 2537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, tup=None, *args): 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tup is not None: 2577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) #for 0 %0, 0 // 0 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 2657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger were non-zero), or if an overflow or underflow condition occurs. The 2667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2715aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger detected during an operation. This can occur if contexts are not checked 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 2807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger was specified. These aspects of the context need only be checked when 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the values are required to be used. The result is [0,qNaN]. 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 2887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 2897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 2917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 2927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger coefficient), or if an overflow or underflow condition occurs. The 2937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2985aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 3057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin, before any rounding). The result in all cases is unchanged. 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger where sign is the sign of the intermediate result. For round-down, the 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger current precision, with the sign of the intermediate result. For 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 3327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 3367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ROUND_HALF_DOWN, ROUND_UP): 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, (9,)*context.prec, 3427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (9,)*context.prec, 3477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin). That is, the result is both inexact and subnormal. 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger necessary, so that its exponent is not less than Etiny. This may result 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3655aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 366fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 3675aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger Underflow, InvalidOperation, Subnormal] 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3695aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3705aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3715aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3725aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3735aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Context Functions ####################################### 3767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 377ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 378ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 379ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 380ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# work for older Pythons. 381ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 382ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 383ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 384ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 385ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 386ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 387ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #To fix reloading, force it to create a new context 388ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #Old contexts have different exceptions in their dicts, making problems. 389ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 390ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 391ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 392ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 393ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 394ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 3959fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 39661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 3977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 398ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 399ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 400ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 404ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 405ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 406ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 407ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 414ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 415ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4169fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4179fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 435ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4369fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 43761992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading, local # Don't contaminate the namespace 4417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Decimal class ########################################### 4447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 4467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 4477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('_exp','_int','_sign') 4497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value="0", context=None): 4517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 4527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 4547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent) 4567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 4587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 4607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 4637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 4647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 4667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value = str(value) 4677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # String? 4697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # REs insist on real strings, so we can too. 4707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, basestring): 4710ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isinfinity(value): 4727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'F' 4737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = (0,) 4740ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger sign = _isinfinity(value) 4757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 4767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 0 4777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 4787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 1 4797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 4800ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isnan(value): 4810ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger sig, sign, diag = _isnan(value) 4827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(diag) > context.prec: #Diagnostic info too long 4837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign, self._int, self._exp = \ 4847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(ConversionSyntax) 4857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 4867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sig == 1: 4877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'n' #qNaN 4887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: #sig == 2 4897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'N' #sNaN 4907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = sign 4917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(map(int, diag)) #Diagnostic info 4927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 493d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger try: 494d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = _string2exact(value) 495d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger except ValueError: 496d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = context._raise_error(ConversionSyntax) 4977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 4987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 5007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (list,tuple)): 5017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(value) != 3: 5027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, 'Invalid arguments' 5037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value[0] not in [0,1]: 5047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, 'Invalid sign' 5057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in value[1]: 5067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not isinstance(digit, (int,long)) or digit < 0: 5077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, "The second value in the tuple must be composed of non negative integer elements." 5087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = value[0] 5107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(value[1]) 5117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value[2] in ('F','n','N'): 5127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = value[2] 5137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 5147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = int(value[2]) 5157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 5167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Turn an intermediate value back to Decimal() 5187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, _WorkRep): 5197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value.sign == 1: 5207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 0 5217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 5227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 1 5237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(value.int) 5247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = int(value.exp) 5257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 5267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, Decimal): 5284e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._exp = value._exp 5294e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._sign = value._sign 5304e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._int = value._int 5314e0e1b6a540e664e89739456db4c706701bf062bTim Peters return 5327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 533bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if isinstance(value, float): 534bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 535bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger "First convert the float to a string") 536bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger 537bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger raise TypeError("Cannot convert %r" % value) 5387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _convert_other(self, other): 5407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert other to Decimal. 5417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(other, Decimal): 5457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 5467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(other, (int, long)): 5477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = Decimal(other) 5487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 5497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise TypeError, "You can interact Decimal only with int, long or Decimal data types." 5517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 5537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 5547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 5567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if NaN 5577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 5587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'n': 5607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 5617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp == 'N': 5627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 2 5637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 5667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 5677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 5697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 5707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 5717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 5737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 5747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 5757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 5767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _check_nans(self, other = None, context=None): 5797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 5807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 5827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 5837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 5867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 5887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 5897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() == 2: 5917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 5927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1, self) 5937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other is not None and other._isnan() == 2: 5947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 5957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1, other) 5967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 5977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 5987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other is not None and other._isnan(): 5997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 6007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 6037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Is the number non-zero? 6047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if self == 0 6067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if self != 0 6077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(self._exp, str): 6097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._int != (0,)*len(self._int) 6117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __cmp__(self, other, context=None): 6137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 6147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 6157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 6167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 6187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 6197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 6227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #If both 0, sign comparison isn't certain. 6237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If different signs, neg one is less 6257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 6267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 6287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # INF = INF 6317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() and other._isinfinity(): 6327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 6347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 6357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 6367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**other._sign) 6377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.adjusted() == other.adjusted() and \ 6397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int + (0,)*(self._exp - other._exp) == \ 6407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other._int + (0,)*(other._exp - self._exp): 6417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #equal, except in precision. ([0]*(-x) = []) 6427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self.adjusted() > other.adjusted() and self._int[0] != 0: 6437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 6447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self.adjusted < other.adjusted() and other._int[0] != 0: 6457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 6467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6479fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 6487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) #round away from 0 6497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 6517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res = self.__sub__(other, context=context) 6527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 6547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 6567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not res: 6587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif res._sign: 6607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6630aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 6640aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 6650aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return False 6660aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) == 0 6670aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 6680aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 6690aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 6700aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return True 6710aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) != 0 6720aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 6737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 6747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 6757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 6777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 6787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 6797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 6807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 6817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 6837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 6847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 6857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #compare(NaN, NaN) = NaN 6877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 6887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self.__cmp__(other, context)) 6927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 6967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Non-integer decimals are normalized and hashed as strings 6977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Normalization assures that hast(100E-1) == hash(10) 6987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger i = int(self) 6997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(i): 7007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(i) 7017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger assert self.__nonzero__() # '-0' handled by integer case 7027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(str(self.normalize())) 7037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 7057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 7067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 7087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self._sign, self._int, self._exp) 7107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 7127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 7137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 7147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 'Decimal("%s")' % str(self) 7157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __str__(self, eng = 0, context=None): 7177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 7187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 7207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 7237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger minus = '-'*self._sign 7247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int == (0,): 7257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger info = '' 7267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger info = ''.join(map(str, self._int)) 7287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() == 2: 7297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'sNaN' + info 7307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'NaN' + info 7317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 7327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger minus = '-'*self._sign 7337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'Infinity' 7347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 7367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 7377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(str, self._int) 7397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(self._int) 7407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger leftdigits = self._exp + numdigits 7417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY 7427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp < 0 and self._exp >= -6: #short, no need for e/E 7437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + '0.' + '0'*(abs(self._exp)) 7447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 7457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exp is closest mult. of 3 >= self._exp 7467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = ((self._exp - 1)// 3 + 1) * 3 7477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != self._exp: 7487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0.'+'0'*(exp - self._exp) 7497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0' 7517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != 0: 7527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.capitals: 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'E' 7547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'e' 7567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp > 0: 7577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += '+' #0.0e+3, not 0.0e3 7587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += str(exp) 7597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + s 7607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 7617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 7627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = (leftdigits-1)%3+1 7637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits -1 - (leftdigits-1)%3 7647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits-1 7667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 7677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 0: 7687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 7697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= 0: 7707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(leftdigits, '.') 7717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= -6: 7727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] * int(-leftdigits) 7737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '0.') 7747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits > dotplace: 7767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(dotplace, '.') 7777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif numdigits < dotplace: 7787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend(['0']*(dotplace-numdigits)) 7797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp: 7807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not context.capitals: 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('e') 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('E') 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp > 0: 7857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('+') 7867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append(str(adjexp)) 7877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 7887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp[0:1] == ['0']: 7897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:1] = [] 7907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e': 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] 7927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 7937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '-') 7947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ''.join(tmp) 7967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 7987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 7997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 8017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 8027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 8047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__str__(eng=1, context=context) 8087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 8107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 8117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 8137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._sign: 8247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 8277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 8287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, self._int, self._exp))._fix(context=context) 8297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, self._int, self._exp)) 8307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 8327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 8337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 8357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign 8437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 8457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 8487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._fix(context=context) 8497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 8517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._sign = sign 8527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self, round=1, context=None): 8557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 8567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the second argument is 0, do not round. 8587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not round: 8669fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 8677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(NEVER_ROUND) 8687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 8707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 8717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 8737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 8777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 8787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 8807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 8847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 8867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 8907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If both INF, same sign => same as both, opposite => error. 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 8927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 8947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(other) #Can't both be infinity here 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 8987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 9007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 9017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 9027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If the answer is 0, the sign should be negative, in this case. 9037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 9047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 9067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 9077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 9087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 9097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), exp)) 9107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < other._exp - context.prec-1: 9127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = other._exp - context.prec-1 9137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other._rescale(exp, watchexp=0, context=context) 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 9187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < self._exp - context.prec-1: 9197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp - context.prec-1 9207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(exp, watchexp=0, context=context) 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 9267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 9277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = _normalize(op1, op2, shouldround, context.prec) 9287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 9307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 9327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = cmp(abs(op1), abs(op2)) 9337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 9347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if diff == 0: 9357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < context.Etiny(): 9367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Etiny() 9377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 9387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((negativezero, (0,), exp)) 9397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if diff < 0: 9407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 9417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, now abs(op1) > abs(op2) 9427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign == -1: 9437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = -1 9447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 9457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 9477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #So we know the sign, and op1 > 0. 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif op1.sign == -1: 9497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = -1 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = (1, 1) 9517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 9537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, op1 > abs(op2) > 0 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.reverse() 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.reverse() 9577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op2.sign == 1: 9597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.int = resultint = map(operator.add, op1.int, op2.int) 9607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 9617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op1.int)): 9627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = resultint[i] + carry 9637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 9647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp > 9: 9657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 1 9667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp -= 10 9677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint[i] = tmp 9687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 9697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.append(1) 9707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.int = resultint = map(operator.sub, op1.int, op2.int) 9727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 0 9737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op1.int)): 9747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = resultint[i] - loan 9757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 0 9767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp < 0: 9777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 1 9787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp += 10 9797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint[i] = tmp 9807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger assert not loan 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while resultint[-1] == 0: 9837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.pop() 9847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.reverse() 9857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 9877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 9887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 9937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 9957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self + (-other)""" 9967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 9977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 9987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 9997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context=context) 10017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal(0) = Decimal(0), which we don't want since 10057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.) 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so we change the sign directly to a copy 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(other) 10087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1-tmp._sign 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__add__(tmp, context=context) 10117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return other + (-self)""" 10147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 10177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 10197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1 - tmp._sign 10207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__add__(tmp, context=context) 10217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _increment(self, round=1, context=None): 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Special case of add, adding 1eExponent 10247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Since it is common, (rounding, for example) this adds 10267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (sign)*one E self._exp to the number more efficiently than add. 10277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For example: 10297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal('5.624e10')._increment() == Decimal('5.625e10') 10307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 10317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 10347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L = list(self._int) 10387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[-1] += 1 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = len(L)-1 10407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while L[spot] == 10: 10417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot] = 0 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot == 0: 10437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[0:0] = [1] 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 10457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot-1] += 1 10467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot -= 1 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, L, self._exp)) 10487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if round and context._rounding_decision == ALWAYS_ROUND: 10507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 10547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 10577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 10587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 10617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 10637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1066d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 10677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 10697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 10707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[resultsign] 10717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 10737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 10747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 10757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[resultsign] 10767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 10787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 10817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 10827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, (0,), resultexp)) 10837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 10847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Fixing in case the exponent is out of bounds 10857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 10897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int == (1,): 10907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, other._int, resultexp)) 10917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 10927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._int == (1,): 10957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, self._int, resultexp)) 10967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 10977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = list(self._int) 11017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = list(other._int) 11027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.reverse() 11037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.reverse() 11047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Minimize Decimal additions 11057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op2) > len(op1): 11067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 11077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _divmod = divmod 11097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator = [0]*(len(self._int) + len(other._int)) 11107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op2)): 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op2[i] == 0: 11127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger continue 11137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mult = op2[i] 11147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 11157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for j in xrange(len(op1)): 11167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry, accumulator[i+j] = _divmod( mult * op1[j] + carry 11177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger + accumulator[i+j], 10) 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 11207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator[i + j + 1] += carry 11217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while not accumulator[-1]: 11227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator.pop() 11237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator.reverse() 11247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (resultsign, accumulator, resultexp)) 11267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 11317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 11337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 11347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, context=context) 11357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __truediv__ = __div__ 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _divide(self, other, divmod = 0, context=None): 11387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return a / b, to context.prec precision. 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divmod: 11417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => true division 11427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => (a //b, a%b) 11437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 => a //b 11447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3 => a%b 11457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Actually, if divmod is 2 or 3 a tuple is returned, but errors for 11477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger computing the other value are not raised. 11487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 11497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 11527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 11547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 11557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 11567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (ans, ans) 11577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 11587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1160d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger sign = self._sign ^ other._sign 11617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 11627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 11637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0', 1) 11647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0') 11657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() and other._isinfinity(): 11667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not divmod: 11677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 11687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 11697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (context._raise_error(InvalidOperation, 11707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '(+-)INF // (+-)INF'), 11717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 11727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '(+-)INF % (+-)INF')) 11737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not divmod: 11757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 11767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 11777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, (0,), context.Etiny())) 11787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 11797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 11807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #These two have different precision. 11817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 11827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp - other._exp 11837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < context.Etiny(): 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Etiny() 11857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, '0e-x / y') 11867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp > context.Emax: 11877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Emax 11887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, '0e+x / y') 11897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), exp) ) 11907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 11927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 11937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 11947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 11957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal((sign, (0,), 0)), Decimal(self)) 11967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 11977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1: 11987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 11997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 12007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 12017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], NaN) 12027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 3: 12037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 12047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 12057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 12067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(self) 12077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside._exp = min(self._exp, other._exp) 12087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal((sign, (0,), 0)), otherside) 12097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 12117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionByZero, 'divmod(x,0)', 12127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign, 1) 12137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, so neither = 0, INF 12157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 12177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If we're dividing into ints, and self < other, stop. 12197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self.__abs__(0) does not round. 12207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1 or divmod == 3: 12237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2 = self._rescale(exp, context=context, watchexp=0) 12257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 12267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2 = ans2._fix(context=context) 12277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), 12287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2) 12297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 12317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't round the mod part, if we don't need it. 12327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), Decimal(self)) 12337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign: 12357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = -1 12367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 12377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 12387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = 0 12397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 12407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 12417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2, adjust = _adjust_coefficients(op1, op2) 12427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res = _WorkRep( (sign, [0], (op1.exp - op2.exp)) ) 12437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and res.exp > context.prec + 1: 12447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = None 12477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 12487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while( (len(op2.int) < len(op1.int) and op1.int[0]) or 12497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (len(op2.int) == len(op1.int) and op2.int <= op1.int)): 12507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Meaning, while op2.int < op1.int, when normalized. 12517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res._increment() 12527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.subtract(op2.int) 12537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if res.exp == 0 and divmod: 12547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(res.int) > context.prec and shouldround: 12557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 12577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 12587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._rescale(exp, context=context, 12617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger watchexp=0) 12627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 12637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 12647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._fix(context=context) 12657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 12667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.int == [0]*len(op1.int) and adjust >= 0 and not divmod: 12687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 12697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if (len(res.int) > context.prec) and shouldround: 12707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 12717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround=1 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Really, the answer is a bit higher, so adding a one to 12747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # the end will make sure the rounding is right. 12757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.int != [0]*len(op1.int): 12767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.int.append(1) 12777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 12807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust += 1 12827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.int.append(0) 12837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.append(0) 12847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 12857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if res.exp == 0 and divmod and (len(op2.int) > len(op1.int) or 12877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (len(op2.int) == len(op1.int) and 12887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int > op1.int)): 12897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Solves an error in precision. Same as a previous block. 12907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(res.int) > context.prec and shouldround: 12927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 12947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 12957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._rescale(exp, context=context) 12987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 13007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 13027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(res) 13047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 13057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 13067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 13097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 13107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 13127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 13137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 13157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (self // other, self % other) 13177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 1, context) 13197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 13217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 13227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 13247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 13267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 13287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 13307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 13317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 13347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 13357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 3, context)[1] 13417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 13437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 13447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 13467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 13527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 13537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 13567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 13577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # If DivisionImpossible causes an error, do not leave Rounded/Inexact 13627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # ignored in the calling function. 13639fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 13657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #keep DivisionImpossible flags 13667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 13677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 13697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 13717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13729fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 13747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign: 13767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(-2), context=context) 13777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 13787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(2), context=context) 13797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 13817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 13847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 13857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r < comparison: 13877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 13887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Get flags now 13897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.__divmod__(other, context=context) 13907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r._fix(context=context) 13917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 13927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 13967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 13977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 13987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 13997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger decrease = not side._iseven() 14017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 14027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger side = side.__abs__(context=context) 14037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 14047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 14067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 14077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r > comparison or decrease and r == comparison: 14087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += 1 14107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(side.__add__(Decimal(1), context=context)._int) >= context.prec: 14117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible)[1] 14137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == other._sign: 14157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__sub__(other, context=context) 14167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__add__(other, context=context) 14187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r._fix(context=context) 14227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 14247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 14257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 2, context)[0] 14267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 14307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 14317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 14347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 14357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 14377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts self to a int, truncating if necessary.""" 14387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 14397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidContext) 14417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._isinfinity(): 14427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise OverflowError, "Cannot convert infinity to long" 14437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 14447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 14457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = '-'*self._sign 14467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 14477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = sign + ''.join(map(str, self._int)) + '0'*self._exp 14487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(s) 14497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = sign + ''.join(map(str, self._int))[:self._exp] 14507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(s) 14517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = list(self._int) 14527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.reverse() 14537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = 0 14547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp: 14557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val *= 10 14567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val += tmp.pop() 14577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(((-1) ** self._sign) * val * 10.**int(self._exp)) 14587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 14607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 14617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 14637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 14657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _fix(self, prec=None, rounding=None, folddown=None, context=None): 14677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 14687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 14707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 14727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 14737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision to which to round. By default, the context decides. 14747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding - Rounding method. By default, the context decides. 14757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger folddown - Fold down high elements, by default context._clamp 14767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 14777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() or self._isnan(): 14797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 14807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 14837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 14847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 14857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fixexponents(prec, rounding, folddown=folddown, 14867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context) 14877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(ans._int) > prec: 14887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._round(prec, rounding, context=context) 14897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fixexponents(prec, rounding, folddown=folddown, 14907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context) 14917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 14927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _fixexponents(self, prec=None, rounding=None, folddown=None, 14947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=None): 14957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Fix the exponents and return a copy with the exponent in bounds.""" 14967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 14977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 14987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 15007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 15017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 15027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if folddown is None: 15037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger folddown = context._clamp 15047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin, Emax = context.Emin, context.Emax 15057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Etop = context.Etop() 15067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 15077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans.adjusted() < Emin: 15087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Etiny = context.Etiny() 15097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans._exp < Etiny: 15107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans: 15117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = Etiny 15127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(Etiny, context=context) 15157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #It isn't zero, and exp < Emin => subnormal 15167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 15177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.flags[Inexact]: 15187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Underflow) 15197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 15217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Only raise subnormal if non-zero. 15227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 15237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif folddown and ans._exp > Etop: 15247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(Etop, context=context) 15267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif ans.adjusted() > Emax: 15277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans: 15287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = Emax 15297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 15327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(Overflow, 'above Emax', ans._sign) 15347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round(self, prec=None, rounding=None, context=None): 15377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a rounded version of self. 15387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger You can specify the precision or rounding method. Otherwise, the 15407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context determines it. 15417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 15427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 15447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 15457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 15467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 15477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 15507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 15517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if rounding is None: 15537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context.rounding 15547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 15557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 15567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec <= 0: 15597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) 15607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) - prec + self._exp 15617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) * prec 15637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) + self._exp - prec 15647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, dig, exp)) 15657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == 0: 15697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp._int = (0,)+temp._int 15717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif prec < 0: 15737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp + len(self._int) - prec - 1 15747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal( (self._sign, (0, 1), exp)) 15757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(temp._int) 15807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == numdigits: 15817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return temp 15827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # See if we need to extend precision 15847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger expdiff = prec - numdigits 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if expdiff > 0: 15867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = list(temp._int) 15877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend([0] * expdiff) 15887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, tmp, temp._exp - expdiff)) 15897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, but maybe all the lost digits are 0. 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lostdigits = self._int[expdiff:] 15937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lostdigits == (0,) * len(lostdigits): 15947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff)) 15957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Rounded, but not Inexact 15967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Okay, let's round and lose data 16007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this_function = getattr(temp, self._pick_rounding_function[rounding]) 16027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now we've got the rounding function 16037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec != context.prec: 16059fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 16067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = prec 16077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = this_function(prec, expdiff, context) 16087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact, 'Changed in rounding') 16107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 16147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_down(self, prec, expdiff, context): 16167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Also known as round-towards-0, truncate.""" 16177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_up(self, prec, expdiff, context, tmp = None): 16207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds 5 up (away from 0)""" 16217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp is None: 16237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff)) 16247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int[prec] >= 5: 16257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=0, context=context) 16267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_even(self, prec, expdiff, context): 16317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 to even, rest to nearest.""" 16327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 164161992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if self._int[prec-1] & 1 == 0: 16427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_down(self, prec, expdiff, context): 16467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 16477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_up(self, prec, expdiff, context): 16607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds away from 0.""" 16617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec:]: 16637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=1, context=context) 16657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_ceiling(self, prec, expdiff, context): 16727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 16737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 16747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_down(prec, expdiff, context) 16757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_up(prec, expdiff, context) 16777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_floor(self, prec, expdiff, context): 16797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 16807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 16817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_down(prec, expdiff, context) 16827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_up(prec, expdiff, context) 16847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pow__(self, n, modulo = None, context=None): 16867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self ** n (mod modulo) 16877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If modulo is None (default), don't take it mod modulo. 16897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 16907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 16917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 16927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = self._convert_other(n) 16937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Because the spot << doesn't work with really big exponents 16957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n._isinfinity() or n.adjusted() > 8: 16967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** INF') 16977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(n, context) 16997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 17007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 17017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not n._isinfinity() and not n._isinteger(): 17037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** (non-integer)') 17047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not n: 17067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '0 ** 0') 17077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not n: 17097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(1): 17127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign and not n._iseven() 17157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = int(n) 17167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 17187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo: 17197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'INF % x') 17207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n > 0: 17217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 17227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), 0) ) 17237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #with ludicrously large exponent, just raise an overflow and return inf. 17257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \ 17267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger and self: 17277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal('inf') 17297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = sign 17307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 17317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 17327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Overflow, 'Big power', sign) 17337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 17347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elength = len(str(abs(n))) 17367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 17377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 173899148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger if not modulo and firstprec + elength + 1 > DefaultContext.Emax: 17397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(Overflow, 'Too much precision.', sign) 17407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(self) 17427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Decimal(1) 17439fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 17447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + elength + 1 17457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context.rounding 17467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n < 0: 17477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #n is a long now, not Decimal instance 17487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = -n 17497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(1).__div__(mul, context=context) 17507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 17527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = 1 17547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot <= n: 17557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot <<= 1 17567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Spot is the highest power of 2 less than n 17597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot: 17607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(val, context=context) 17617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val._isinfinity(): 17627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Infsign[sign] 17637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 17647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot & n: 17657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(mul, context=context) 17667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo is not None: 17677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mod__(modulo, context=context) 17687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 17707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 17727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return val._fix(context=context) 17737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return val 17747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rpow__(self, other, context=None): 17767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __pow__.""" 17777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 17787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__pow__(self, context=context) 17797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, context=None): 17817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 17827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 17837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 17847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 17867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 17877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 17887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dup = self._fix(context=context) 17907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if dup._isinfinity(): 17917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return dup 17927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not dup: 17947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, (0,), 0) ) 17957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end = len(dup._int) 17967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 17977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while dup._int[end-1] == 0: 17987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 17997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 18007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, dup._int[:end], exp) ) 18017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, exp, rounding = None, context=None, watchexp = 1): 18047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 18057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 18077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(exp, context) 18127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 18137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 18167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 18177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self #if both are inf, it is OK 18187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 18197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'quantize with one INF') 18207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._rescale(exp._exp, rounding, context, watchexp) 18217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 18237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Test whether self and other have the same exponent. 18247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger same as self._exp == other._exp, except NaN == sNaN 18267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() or other._isnan(): 18287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._isnan() and other._isnan() and True 18297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() or other._isinfinity(): 18307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._isinfinity() and other._isinfinity() and True 18317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 18327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _rescale(self, exp, rounding = None, context=None, watchexp = 1): 18347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rescales so that the exponent is exp. 18357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 18377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = rounding version 18387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger watchexp: if set (default) an error is returned if exp is greater 18397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger than Emax or less than Etiny. 18407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 18457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale with an INF') 18467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 18487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 18497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger out = 0 18527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and (context.Emax < exp or context.Etiny() > exp): 18547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 18577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 18587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int = (0,) 18597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = exp 18607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = self._exp - exp 18637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits = len(self._int)+diff 18647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and digits > context.prec: 18667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'Rescale > prec') 18677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 18697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = (0,)+tmp._int 18707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits += 1 18717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prevexact = context.flags[Inexact] 18737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 18747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = -digits + tmp._exp 18757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = (0,1) 18767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits = 1 18777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._round(digits, rounding, context=context) 18787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp._int[0] == 0 and len(tmp._int) > 1: 18807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = tmp._int[1:] 18817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = exp 18827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp and tmp.adjusted() < context.Emin: 18847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 18857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif tmp and tmp.adjusted() > context.Emax: 18867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 18887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_integral(self, rounding = None, context=None): 18907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to the nearest integer, without raising inexact, rounded.""" 18917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 18947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 18957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 18977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 18987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 18997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(0, rounding, context=context) 19007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 19017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, context=None): 19047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the square root of self. 19057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn)) 19077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should quadratically approach the right answer. 19087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 19097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 19107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 19117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 19137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 19147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 19177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exponent = self._exp / 2, using round_down. 19187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 19197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp+1) // 2 19207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 19217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = (self._exp) // 2 19227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #sqrt(-0) = -0 19247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (1, (0,), exp)) 19257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (0, (0,), exp)) 19277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 19307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 19327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 19337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 19357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger expadd = tmp._exp / 2 193761992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp._exp & 1: 19387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int += (0,) 19397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19439fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 19447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 19457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 19467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = 3 194761992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp.adjusted() & 1 == 0: 19487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (8,1,9), tmp.adjusted() - 2) ) 19497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)), 19507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 + tmp.adjusted()/2 19527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) ) 19547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)), 19557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 + tmp.adjusted()/2 19577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #ans is now a linear approximation. 19597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emax, Emin = context.Emax, context.Emin 196199148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin 19627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = Decimal('0.5') 19647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger count = 1 19667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger maxp = firstprec + 2 19677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_HALF_EVEN) 19687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 19697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = min(2*context.prec - 2, maxp) 19707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context), 19717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.prec == maxp: 19737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 19747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #round to the answer's precision-- the only error can be 1 ulp. 19767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 19777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prevexp = ans.adjusted() 19787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._round(context=context) 19797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, check if the other last digits are better. 19817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + 1 19827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # In case we rounded up another digit and we should actually go lower. 19837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prevexp != ans.adjusted(): 19847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int += (0,) 19857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 19867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context) 19897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_UP) 19907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lower.__mul__(lower, context=context) > (tmp): 19917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context) 19927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context) 19957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_DOWN) 19967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if upper.__mul__(upper, context=context) < tmp: 19977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context) 19987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp += expadd 20007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 20037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 20047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 20067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans.__mul__(ans, context=context) == self: 20077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Only rounded/inexact if here. 20087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 20107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 20117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 20127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Exact answer, so let's set the exponent right. 20137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 20147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp +1)// 2 20157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 20167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp // 2 20177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += ans._exp - exp 20187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(exp, context=context) 20197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax, context.Emin = Emax, Emin 20227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans._fix(context=context) 20247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 20267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 20277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like max(self, other) except if one is not a number, returns 20297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 20317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 20327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 20337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 20347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2035d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2036d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # number is always returned 2037d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger sn = self._isnan() 2038d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger on = other._isnan() 2039d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn or on: 2040d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if on == 1 and sn != 2: 2041d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self 2042d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn == 1 and on != 2: 2043d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return other 2044d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self._check_nans(other, context) 20457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2047d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2048d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2049d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2050d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2051d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2052d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2053d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2054d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2055d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2056d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2057d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2058d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign: 2059d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2060d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and not self._sign: 2061d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2062d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and self._sign: 2063d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2064d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == -1: 20657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2066d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger context._rounding_decision == ALWAYS_ROUND 2067d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return ans._fix(context=context) 20687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 20707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 20717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like min(self, other) except if one is not a number, returns 20737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 20757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 20767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 20777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 20787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2079d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2080d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # number is always returned 2081d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger sn = self._isnan() 2082d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger on = other._isnan() 2083d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn or on: 2084d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if on == 1 and sn != 2: 2085d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self 2086d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn == 1 and on != 2: 2087d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return other 2088d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self._check_nans(other, context) 20897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2091d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2092d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2093d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2094d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2095d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2096d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2097d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2098d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2099d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2100d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2101d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2102d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if other._sign: 2103d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2104d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and not self._sign: 2105d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2106d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and self._sign: 2107d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2108d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == 1: 21097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2110d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger context._rounding_decision == ALWAYS_ROUND 2111d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return ans._fix(context=context) 21127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 21147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 21157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 21167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 21177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 21187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rest == (0,)*len(rest) 21197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 21217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns 1 if self is even. Assumes self is an integer.""" 21227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp > 0: 21237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 212461992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger return self._int[-1+self._exp] & 1 == 0 21257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 21277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 21287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 21297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 21307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If NaN or Infinity, self._exp is string 21317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 21327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 21337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # support for pickling, copy, and deepcopy 21357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 21367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 21377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 21397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # I'm immutable; therefore I am my own clone 21417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 21447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # My components are also immutable 21467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2148d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Context class ########################################### 2149d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 21507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# get rounding method function: 21527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerrounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')] 21537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 21547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 21557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 21567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 21577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 21587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 21607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 21627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 21637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 21657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 21667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding - rounding type. (how you round) 21677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round? 2168bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 21697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 21707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 21717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 21727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 21737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 21740ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 21750ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 21767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 21777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 2178e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 21797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 21809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 21817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 2182bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=None, flags=[], 21837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=None, 21840ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 2185e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 21867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _ignored_flags=[]): 2187bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 2188fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 2189b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 2190bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 2191fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 2192b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 21937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 21947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 21957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, copy.copy(getattr(DefaultContext, name))) 21967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 21977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 21987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 21997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2200b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 2201bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 2202b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 2203bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self)) 2204bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']') 2205bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']') 2206b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 2207b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 2208d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 2209d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 2210d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 2211b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 2212d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 22139fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 22149fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 2215bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger nc = Context(self.prec, self.rounding, self.traps, self.flags, 22167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 22199fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 22209fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 22219fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 22229fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger nc = Context(self.prec, self.rounding, self.traps.copy(), self.flags.copy(), 22239fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22249fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22259fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 22269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 22277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22285aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 22297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 22307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 22327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 22337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 22347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 22357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22365aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 22377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 22387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't touch the flag 22397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 22407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 2242bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 22437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #The errors define how to handle themselves. 22445aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 22457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 22477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self._ignored_flags = [] 22487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 22497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 22517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 2252fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 22537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 22557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 22567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 22577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 22587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 22597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 22607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 22627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 22637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 22647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 22657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 22667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 22677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22685aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 22695aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 22705aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 22715aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger raise TypeError, "Cannot hash a Context." 22725aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 22737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 22747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 22757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 22767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 2278e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 22797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 22807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding_decision(self, type): 22827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding decision. 22837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding decision, and returns the current (previous) 22857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding decision. Often used like: 22867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22879fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 22887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # That so you don't change the calling context 22897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle (say DivisionImpossible is raised). 22907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 22927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger instance = instance / Decimal(2) 22937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 22947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it not round for that operation. 22967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self._rounding_decision 22997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision = type 23007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 23037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 23047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 23067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 23077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 23097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 23107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 23117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 23127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 23137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 23147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 23167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 23187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 23197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2321fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 23227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Creates a new Decimal instance but using self as context.""" 23237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 23247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return d._fix(context=self) 23257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Methods 23277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 23287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 23297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 23317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation on the operand. Otherwise, the result is the same as using 23327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 23337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 23357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 23369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 23377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 23389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 23397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 23417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 23447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 23467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 23477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 23497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("19.00") 23509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 23517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.02E+4") 23527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 23547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 23567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return str(a._fix(context=self)) 23577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 23597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 23607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 23627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 23637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 23647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 23657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 23667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 23687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 23697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 23707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 23717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 23737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 23749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 23757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 23769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 23777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 23789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 23797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 23809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 23817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 23829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 23837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 23847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 23867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 23887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 23897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 23917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.333333333") 23929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 23937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.666666667") 23949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 23957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.5") 23969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 23977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 23989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 23997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 24009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 24017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.00") 24029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 24037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20") 24049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 24057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 24069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 24077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1000") 24089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 24097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20E+6") 24107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 24127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 24147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 24157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 24177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 24189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 24197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 24217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 24247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 24267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 24277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 24297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 24307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 24347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the maximum (closer to positive 24357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 24367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24379ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 24387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24399ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 24407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24419ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 2442d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("1") 2443d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 2444d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 24457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 24477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 24497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 24507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 24547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the minimum (closer to negative 24557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 24567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 24587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 24599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 24607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-10") 24619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 24627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 2463d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 2464d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 24657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 24677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 24697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 24707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 24727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 24737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 24747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 24767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 24779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 24787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 24797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 24817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 24837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 24847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a special value then the general rules apply. 24867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are multiplied together ('long multiplication'), 24877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resulting in a number which may be as long as the sum of the lengths 24887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the two operands. 24897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 24917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.60") 24929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 24937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("21") 24949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 24957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.72") 24969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 24977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.0") 24989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 24997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.28135971E+11") 25007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 2504e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 25057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 25077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 25087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 25107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 25119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 25127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 25139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 25147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2") 25159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 25167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.2E+2") 25179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 25187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2E+2") 25199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 25207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 25237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 25257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 25267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 25287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 25297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 25307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 25327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 25339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 25347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 25377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 25397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 25407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The right-hand operand must be a whole number whose integer part (after 25427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger any exponent has been applied) has no more than 9 digits and whose 25437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fractional part (if any) is all zeros before any rounding. The operand 25447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger may be positive, negative, or zero; if negative, the absolute value of 25457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the power is used, and the left-hand operand is inverted (divided into 25467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1) before use. 25477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the increased precision needed for the intermediate calculations 25497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exceeds the capabilities of the implementation then an Invalid operation 25507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger condition is raised. 25517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If, when raising to a negative power, an underflow occurs during the 25537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger division into 1, the operation is not halted at that point but 25547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger continues. 25557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('3')) 25577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("8") 25589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('-3')) 25597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.125") 25609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('1.7'), Decimal('8')) 25617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("69.7575744") 25629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2')) 25637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1')) 25657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0')) 25677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 25689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1')) 25697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2')) 25717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2')) 25737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1')) 25757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 25769ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0')) 25777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 25789ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1')) 25797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 25809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2')) 25817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('0'), Decimal('0')) 25837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 25847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 25867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 25887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a value equal to 'a' (rounded) and having the exponent of 'b'. 25897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 25917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. It may be rounded using the current rounding setting (if the 25927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 25937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 25947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 25957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 25977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 25987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation condition is raised. This guarantees that, unless there is an 25997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger error condition, the exponent of the result of a quantize is always 26007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 26017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 26037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 26047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 26067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.170") 26079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 26087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.17") 26099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 26107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2") 26119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 26127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 26139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 26147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0E+1") 26159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 26167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 26179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 26187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 26207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 26219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 26227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0E+5") 26239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 26247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 26267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 26287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217.0") 26299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 26307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217") 26319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 26327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2E+2") 26339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 26347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2E+2") 26357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 26377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 26397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 26407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 26427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger calculating integer division as described for divide-integer, rounded to 26437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger precision digits if necessary. The sign of the result, if non-zero, is 26447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the same as that of the original dividend. 26457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 26477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 26487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 26497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 26517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 26529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 26537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 26557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 26569ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 26577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 26589ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 26597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 26609ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 26617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 26627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 26647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 26667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 26677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 26687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen). If the result is equal to 0 then its sign will be the 26697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 26707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 26727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 26737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 26747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 26767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.9") 26779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 26787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 26799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 26807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 26827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 26839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 26847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 26859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 26867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 26879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 26887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.3") 26897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 26917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 26937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 26947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 26967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 26977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 26997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 27017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 27037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 27057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 27087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 27107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the square root of a non-negative number to context precision. 27117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 27137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 27147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 27167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 27179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 27187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 27199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 27207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.624499800") 27219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 27227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 27239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 27247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 27259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 27267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 27287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 27307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.64575131") 27319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 27327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.16227766") 27339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 27346ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 27357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 27377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 27397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 27407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27419ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 27427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.23") 27439ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 27447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.00") 27459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 27467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.77") 27477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 27497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 27517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 27527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 27547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 27567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 27587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 27597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 27617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 27637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_integral(self, a): 27657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 27667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 27687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 27697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 27707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 27717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be set. The rounding mode is taken from the context. 27727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('2.1')) 27747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 27759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100')) 27767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 27779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100.0')) 27787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 27799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('101.5')) 27807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("102") 27819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-101.5')) 27827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-102") 27839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('10E+5')) 27847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0E+6") 27859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('7.89E+77')) 27867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("7.89E+77") 27879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-Inf')) 27887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 27897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_integral(context=self) 27917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 27937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 27947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # sign: -1 None 1 27957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # int: list 27967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 27977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 27997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 28007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 28017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = [] 28027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 28037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, Decimal): 28047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value._sign: 28057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = -1 28067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = 1 28087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = list(value._int) 28097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 28107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, tuple): 28117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 28127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 28137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 28147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 28167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 28177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 28197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self): 28217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == 1: 28227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _WorkRep( (-1, self.int, self.exp) ) 28237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _WorkRep( (1, self.int, self.exp) ) 28257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self): 28277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -self 28297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 28317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __cmp__(self, other): 28337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.exp != other.exp: 28347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError("Operands not normalized: %r, %r" % (self, other)) 28357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign != other.sign: 28367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 28387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 28407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger direction = -1 28427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger direction = 1 28447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger int1 = self.int 28457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger int2 = other.int 28467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(int1) > len(int2): 28477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * 1 28487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(int1) < len(int2): 28497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * -1 28507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(int1)): 28517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if int1[i] > int2[i]: 28527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * 1 28537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if int1[i] < int2[i]: 28547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * -1 28557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 28567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _increment(self): 28587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger curspot = len(self.int) - 1 28597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot]+= 1 28607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while (self.int[curspot] >= 10): 28617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot] -= 10 28627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if curspot == 0: 28637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[0:0] = [1] 28647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 28657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot-1] += 1 28667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger curspot -= 1 28677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, alist): 28697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Subtract a list from the current int (in place). 28707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger It is assured that (len(list) = len(self.int) and list < self.int) or 28727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger len(list) = len(self.int)-1 28737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (i.e. that int(join(list)) < int(join(self.int))) 28747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint = self.int 28777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint.reverse() 28787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger alist.reverse() 28797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 28817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for x in xrange(len(alist)): 28827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x] -= alist[x] + carry 28837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if selfint[x] < 0: 28847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 1 28857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x] += 10 28867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28874e0e1b6a540e664e89739456db4c706701bf062bTim Peters carry = 0 28887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 28897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x+1] -= 1 28907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger last = len(selfint)-1 28917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while len(selfint) > 1 and selfint[last] == 0: 28927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger last -= 1 28937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if last == 0: 28947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 28957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[last+1:]=[] 28967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint.reverse() 28977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger alist.reverse() 28987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 28997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _normalize(op1, op2, shouldround = 0, prec = 0): 29027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 29037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 29057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Yes, the exponent is a long, but the difference between exponents 29077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # must be an int-- otherwise you'd get a big memory problem. 29087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = int(op1.exp - op2.exp) 29097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits < 0: 29107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = -numdigits 29117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 29127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 29137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 29147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 29157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 29167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround and numdigits > len(other.int) + prec + 1 -len(tmp.int): 29187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # If the difference in adjusted exps is > prec+1, we know 29197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # other is insignificant, so might as well put a 1 after the precision. 29207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # (since this is only for addition.) Also stops MemoryErrors. 29217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger extend = prec + 2 -len(tmp.int) 29237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if extend <= 0: 29247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger extend = 1 29257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int.extend([0]*extend) 29267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.exp -= extend 29277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other.int[:] = [0]*(len(tmp.int)-1)+[1] 29287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other.exp = tmp.exp 29297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 29307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int.extend([0] * numdigits) 29327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.exp = tmp.exp - numdigits 29337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(op1.int) - len(op2.int) 29347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # numdigits != 0 => They have the same exponent, but not the same length 29357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # of the coefficient. 29367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits < 0: 29377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = -numdigits 29387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 29397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 29407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 29417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int[0:0] = [0] * numdigits 29427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 29437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _adjust_coefficients(op1, op2): 29457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Adjust op1, op2 so that op2.int+[0] > op1.int >= op2.int. 29467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp. 29487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used on _WorkRep instances during division. 29507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = 0 29527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If op1 is smaller, get it to same size 29537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op2.int) > len(op1.int): 29547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = len(op2.int) - len(op1.int) 29557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.extend([0]*diff) 29567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= diff 29577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = diff 29587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Same length, wrong order 29607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) == len(op2.int) and op1.int < op2.int: 29617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.append(0) 29627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 29637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust+= 1 29647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2, adjust 29657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) > len(op2.int) + 1: 29677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = len(op1.int) - len(op2.int) - 1 29687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.extend([0]*diff) 29697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.exp -= diff 29707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust -= diff 29717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) == len(op2.int)+1 and op1.int > op2.int: 29737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.append(0) 29757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.exp -= 1 29767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust -= 1 29777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2, adjust 29787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Helper Functions ######################################## 29807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_infinity_map = { 29827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'inf' : 1, 29837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'infinity' : 1, 29847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+inf' : 1, 29857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+infinity' : 1, 29867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-inf' : -1, 29877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-infinity' : -1 29887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger} 29897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29900ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isinfinity(num): 29917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is infinity. 29927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29930ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger +1 for negative infinity; 0 for finite ; +1 for positive infinity 29947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 29967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _infinity_map.get(num, 0) 29977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29980ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isnan(num): 29997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is NaN 30007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (1, sign, diagnostic info as string) => NaN 30027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (2, sign, diagnostic info as string) => sNaN 30037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => not a NaN 30047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 30057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 30067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not num: 30077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #get the sign, get rid of trailing [+-] 30107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 30117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num[0] == '+': 30127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 30137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif num[0] == '-': #elif avoids '+-nan' 30147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 30157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 30167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('nan'): 30187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 3 and not num[3:].isdigit(): #diagnostic info 30197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (1, sign, num[3:].lstrip('0')) 30217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('snan'): 30227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 4 and not num[4:].isdigit(): 30237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (2, sign, num[4:].lstrip('0')) 30257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Setup Specific Contexts ################################ 30297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 3031fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 30327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 30346ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 3035bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 3036bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=ALWAYS_ROUND, 303899148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 303999148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 3040e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 30417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 30447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 30457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 30467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 30477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 30497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 3050bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 3051bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 30556ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 3056bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 3057bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3061d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Useful Constants (internal use only) #################### 30627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Reusable defaults 30647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInf = Decimal('Inf') 30657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingernegInf = Decimal('-Inf') 30667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Infsign[sign] is infinity w/ that sign 30687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfsign = (Inf, negInf) 30697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN = Decimal('NaN') 30717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### crud for parsing strings ################################# 30747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport re 30757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# There's an optional sign at the start, and an optional exponent 30777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# at the end. The exponent has an optional sign and at least one 30787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# digit. In between, must have either at least one digit followed 30797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# by an optional fraction, or a decimal point followed by at least 30807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# one digit. Yuck. 30817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_parser = re.compile(r""" 30837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 30847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<sign>[-+])? 30857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 30867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<int>\d+) (\. (?P<frac>\d*))? 30877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 30887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger \. (?P<onlyfrac>\d+) 30897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 30907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ([eE](?P<exp>[-+]? \d+))? 30917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 30927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger $ 30937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces. 30947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 30967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly 30987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _string2exact(s): 31007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger m = _parser(s) 31017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m is None: 31027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError("invalid literal for Decimal: %r" % s) 31037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m.group('sign') == "-": 31057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 31067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 31087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = m.group('exp') 31107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp is None: 31117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = 0 31127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = int(exp) 31147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = m.group('int') 31167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if intpart is None: 31177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = "" 31187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('onlyfrac') 31197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('frac') 31217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if fracpart is None: 31227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = "" 31237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp -= len(fracpart) 31257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = intpart + fracpart 31277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(int, mantissa) 31287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger backup = tmp 31297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp and tmp[0] == 0: 31307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del tmp[0] 31317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # It's a zero 31337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not tmp: 31347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if backup: 31357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, tuple(backup), exp) 31367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, (0,), exp) 31377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = tuple(tmp) 31387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, mantissa, exp) 31407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 31437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 31447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 3145