decimal.py revision 27dbcf2162c61d5ba248c57c89ff4fa3d85a21c7
17c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Copyright (c) 2004 Python Software Foundation. 27c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# All rights reserved. 37c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 47c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Written by Eric Price <eprice at tjhsst.edu> 57c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Facundo Batista <facundo at taniquetil.com.ar> 67c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Raymond Hettinger <python at rcn.com> 71f34eb17b501687c1251678bcffab9accd432591Fred Drake# and Aahz <aahz at pobox.com> 87c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# and Tim Peters 97c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1027dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# This module is currently Py2.3 compatible and should be kept that way 1127dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# unless a major compelling advantage arises. IOW, 2.3 compatibility is 1227dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# strongly preferred, but not guaranteed. 1327dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger 1427dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# Also, this module should be kept in sync with the latest updates of 1527dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# the IBM specification as it evolves. Those updates will be treated 1627dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# as bug fixes (deviation from the spec is a compatibility, usability 1727dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# bug) and will be backported. At this point the spec is stabilizing 1827dbcf2162c61d5ba248c57c89ff4fa3d85a21c7Raymond Hettinger# and the updates are becoming fewer, smaller, and less significant. 197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerThis is a Py2.3 implementation of decimal floating point arithmetic based on 227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerthe General Decimal Arithmetic Specification: 237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www2.hursley.ibm.com/decimal/decarith.html 257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 260ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerand IEEE standard 854-1987: 277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html 297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal floating point has finite precision with arbitrarily large bounds. 317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerThe purpose of the module is to support arithmetic using familiar 337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger"schoolhouse" rules and to avoid the some of tricky representation 347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerissues associated with binary floating point. The package is especially 357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingeruseful for financial applications or for contexts where users have 367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerexpectations that are at odds with binary floating point (for instance, 377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerin binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead 387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerof the expected Decimal("0.00") returned by decimal floating point). 397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerHere are some examples of using the decimal module: 417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> from decimal import * 43bd7f76dd04780304c397323ae994092ce759d5a2Raymond Hettinger>>> setcontext(ExtendedContext) 447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(0) 457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("0") 467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1") 477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1") 487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("-.0123") 497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("-0.0123") 507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal(123456) 517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("123456") 527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("123.45e12345678901234567890") 537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("1.2345E+12345678901234567892") 547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("1.33") + Decimal("1.27") 557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("2.60") 567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41") 577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("-2.20") 587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> dig = Decimal(1) 597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333 617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> getcontext().prec = 18 627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / Decimal(3) 637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0.333333333333333333 647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig.sqrt() 657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3).sqrt() 677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1.73205080756887729 687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print Decimal(3) ** 123 697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger4.85192780976896427E+58 707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> inf = Decimal(1) / Decimal(0) 717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print inf 727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> neginf = Decimal(-1) / Decimal(0) 747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf 757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf + inf 777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print neginf * inf 797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger-Infinity 807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfinity 82bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> getcontext().traps[DivisionByZero] = 1 837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print dig / 0 847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDivisionByZero: x / 0 897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c = Context() 90bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 915aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> c.divide(Decimal(0), Decimal(0)) 947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDecimal("NaN") 95bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 1 965aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 985aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 995aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger0 1017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 1027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerTraceback (most recent call last): 1037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ... 1065aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond HettingerInvalidOperation: 0 / 0 1075aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1095aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> c.flags[InvalidOperation] = 0 110bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger>>> c.traps[InvalidOperation] = 0 1117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> print c.divide(Decimal(0), Decimal(0)) 1127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN 1135aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger>>> print c.flags[InvalidOperation] 1147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger1 1157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger>>> 1167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""" 1177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger__all__ = [ 1197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Two major classes 1207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'Decimal', 'Context', 1217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Contexts 1239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 'DefaultContext', 'BasicContext', 'ExtendedContext', 1247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Exceptions 126d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', 127d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', 1287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Constants for use in setting up contexts 1307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', 1317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 1327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Functions for manipulating contexts 1340ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger 'setcontext', 'getcontext' 1357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger] 1367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport threading 1387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport copy 1397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport operator 1407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Rounding 1420ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1430ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1440ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1450ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1460ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1470ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1480ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 1497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger#Rounding decision (not part of the public API) 1510ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerNEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY 1520ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. 1537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Errors 1557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1575aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger handle -- Called when context._raise_error is called and the 1667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set. First argument is self, second is the 1677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context. More arguments can be given, those being after 1687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the explanation in _raise_error (For example, 1697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(NewError, '(-x)!', self._sign) would 1707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger call NewError().handle(context, self._sign).) 1717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger representation. This may occur when the exponent of a zero result would 1857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be outside the bounds of a representation, or when a large normal 1867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number would have an encoded exponent that cannot be represented. In 1877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 1997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 * (+-)INF 2007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF / (+-)INF 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 2097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 2127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args[0] == 1: #sNaN, must drop 's' but keep diagnostics 2137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (args[1]._sign, args[1]._int, 'n') ) 2147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger syntax. The result is [0,qNaN]. 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (0, (0,), 'n') #Passed to something which uses a tuple. 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, double = None, *args): 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if double is not None: 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign],)*2 2437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger longer than precision). The result is [0,qNaN]. 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) 2557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the dividend is also zero. The result is [0,qNaN]. 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, tup=None, *args): 2657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tup is not None: 2667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) #for 0 %0, 0 // 0 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger were non-zero), or if an overflow or underflow condition occurs. The 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 2867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger detected during an operation. This can occur if contexts are not checked 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 2897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger was specified. These aspects of the context need only be checked when 2907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the values are required to be used. The result is [0,qNaN]. 2917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 2987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 3007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 3017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger coefficient), or if an overflow or underflow condition occurs. The 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 3057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3075aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin, before any rounding). The result in all cases is unchanged. 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger where sign is the sign of the intermediate result. For round-down, the 3347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger current precision, with the sign of the intermediate result. For 3367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 3397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ROUND_HALF_DOWN, ROUND_UP): 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, (9,)*context.prec, 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (9,)*context.prec, 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 3657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin). That is, the result is both inexact and subnormal. 3667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger necessary, so that its exponent is not less than Etiny. This may result 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3745aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 375fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 3765aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger Underflow, InvalidOperation, Subnormal] 3777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3815aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3825aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Context Functions ####################################### 3857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 386ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 387ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 388ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 389ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# work for older Pythons. 390ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 391ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 392ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 393ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 394ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 395ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 396ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #To fix reloading, force it to create a new context 397ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #Old contexts have different exceptions in their dicts, making problems. 398ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 399ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 400ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4049fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 40561992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 407ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 414ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 415ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 416ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 417ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4259fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4269fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 435ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 436ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 437ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 441ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4459fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 44661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading, local # Don't contaminate the namespace 4507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Decimal class ########################################### 4537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 4557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 4567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('_exp','_int','_sign') 4587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value="0", context=None): 4607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 4617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 4637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent) 4657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 4677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 4697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 4727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 4737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 4757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value = str(value) 4767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # String? 4787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # REs insist on real strings, so we can too. 4797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, basestring): 4800ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isinfinity(value): 4817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'F' 4827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = (0,) 4830ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger sign = _isinfinity(value) 4847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 4857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 0 4867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 4877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 1 4887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 4890ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isnan(value): 4900ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger sig, sign, diag = _isnan(value) 4917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(diag) > context.prec: #Diagnostic info too long 4927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign, self._int, self._exp = \ 4937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(ConversionSyntax) 4947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 4957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sig == 1: 4967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'n' #qNaN 4977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: #sig == 2 4987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'N' #sNaN 4997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = sign 5007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(map(int, diag)) #Diagnostic info 5017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 502d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger try: 503d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = _string2exact(value) 504d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger except ValueError: 505d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = context._raise_error(ConversionSyntax) 5067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 5077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 5097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (list,tuple)): 5107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(value) != 3: 5117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, 'Invalid arguments' 5127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value[0] not in [0,1]: 5137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, 'Invalid sign' 5147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in value[1]: 5157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not isinstance(digit, (int,long)) or digit < 0: 5167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError, "The second value in the tuple must be composed of non negative integer elements." 5177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = value[0] 5197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(value[1]) 5207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value[2] in ('F','n','N'): 5217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = value[2] 5227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 5237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = int(value[2]) 5247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 5257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Turn an intermediate value back to Decimal() 5277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, _WorkRep): 5287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value.sign == 1: 5297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 0 5307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 5317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 1 5327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(value.int) 5337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = int(value.exp) 5347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 5357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, Decimal): 5374e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._exp = value._exp 5384e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._sign = value._sign 5394e0e1b6a540e664e89739456db4c706701bf062bTim Peters self._int = value._int 5404e0e1b6a540e664e89739456db4c706701bf062bTim Peters return 5417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 542bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if isinstance(value, float): 543bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 544bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger "First convert the float to a string") 545bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger 546bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger raise TypeError("Cannot convert %r" % value) 5477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _convert_other(self, other): 5497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert other to Decimal. 5507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Verifies that it's ok to use in an implicit construction. 5527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(other, Decimal): 5547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 5557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(other, (int, long)): 5567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = Decimal(other) 5577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 5587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise TypeError, "You can interact Decimal only with int, long or Decimal data types." 5607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 5627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 5637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 5657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if NaN 5667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 5677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'n': 5697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 5707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp == 'N': 5717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 2 5727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 5757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 5767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 5787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 5797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 5807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 5827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 5837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 5847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 5857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _check_nans(self, other = None, context=None): 5887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 5897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 5917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 5927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 5957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 5977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 5987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() == 2: 6007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 6017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1, self) 6027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other is not None and other._isnan() == 2: 6037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 6047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1, other) 6057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 6067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 6077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other is not None and other._isnan(): 6087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 6097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 6127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Is the number non-zero? 6137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if self == 0 6157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if self != 0 6167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(self._exp, str): 6187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._int != (0,)*len(self._int) 6207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __cmp__(self, other, context=None): 6227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 6237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 6247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 6257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 6277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 6287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 6317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #If both 0, sign comparison isn't certain. 6327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If different signs, neg one is less 6347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 6357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 6377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # INF = INF 6407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() and other._isinfinity(): 6417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 6437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 6447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 6457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**other._sign) 6467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.adjusted() == other.adjusted() and \ 6487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int + (0,)*(self._exp - other._exp) == \ 6497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other._int + (0,)*(other._exp - self._exp): 6507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #equal, except in precision. ([0]*(-x) = []) 6517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self.adjusted() > other.adjusted() and self._int[0] != 0: 6527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 6537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self.adjusted < other.adjusted() and other._int[0] != 0: 6547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 6557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6569fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 6577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) #round away from 0 6587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 6607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res = self.__sub__(other, context=context) 6617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 6637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 6657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not res: 6677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif res._sign: 6697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6720aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 6730aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 6740aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return False 6750aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) == 0 6760aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 6770aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 6780aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 6790aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return True 6800aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) != 0 6810aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 6827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 6837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 6847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 6867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 6877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 6887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 6927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 6937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #compare(NaN, NaN) = NaN 6967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 6977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 6987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 6997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self.__cmp__(other, context)) 7017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 7037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 7047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 7057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Non-integer decimals are normalized and hashed as strings 7067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Normalization assures that hast(100E-1) == hash(10) 7077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger i = int(self) 7087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(i): 7097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(i) 7107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger assert self.__nonzero__() # '-0' handled by integer case 7117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(str(self.normalize())) 7127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 7147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 7157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 7177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self._sign, self._int, self._exp) 7197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 7217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 7237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 'Decimal("%s")' % str(self) 7247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __str__(self, eng = 0, context=None): 7267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 7277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 7297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 7327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger minus = '-'*self._sign 7337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int == (0,): 7347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger info = '' 7357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger info = ''.join(map(str, self._int)) 7377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() == 2: 7387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'sNaN' + info 7397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'NaN' + info 7407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 7417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger minus = '-'*self._sign 7427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return minus + 'Infinity' 7437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 7457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 7467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(str, self._int) 7487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(self._int) 7497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger leftdigits = self._exp + numdigits 7507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY 7517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp < 0 and self._exp >= -6: #short, no need for e/E 7527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + '0.' + '0'*(abs(self._exp)) 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 7547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exp is closest mult. of 3 >= self._exp 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = ((self._exp - 1)// 3 + 1) * 3 7567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != self._exp: 7577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0.'+'0'*(exp - self._exp) 7587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0' 7607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != 0: 7617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.capitals: 7627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'E' 7637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'e' 7657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp > 0: 7667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += '+' #0.0e+3, not 0.0e3 7677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += str(exp) 7687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + s 7697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 7707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 7717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = (leftdigits-1)%3+1 7727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits -1 - (leftdigits-1)%3 7737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits-1 7757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 7767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 0: 7777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 7787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= 0: 7797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(leftdigits, '.') 7807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= -6: 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] * int(-leftdigits) 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '0.') 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits > dotplace: 7857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(dotplace, '.') 7867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif numdigits < dotplace: 7877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend(['0']*(dotplace-numdigits)) 7887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp: 7897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not context.capitals: 7907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('e') 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('E') 7937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp > 0: 7947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('+') 7957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append(str(adjexp)) 7967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp[0:1] == ['0']: 7987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:1] = [] 7997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e': 8007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] 8017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 8027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '-') 8037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ''.join(tmp) 8057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 8077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 8087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 8107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 8117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 8137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__str__(eng=1, context=context) 8177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 8197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 8317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._sign: 8337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 8367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 8377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, self._int, self._exp))._fix(context=context) 8387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, self._int, self._exp)) 8397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 8417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 8427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 8447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign 8527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 8547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 8577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._fix(context=context) 8587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 8607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._sign = sign 8617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self, round=1, context=None): 8647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 8657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the second argument is 0, do not round. 8677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 8717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not round: 8759fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 8767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(NEVER_ROUND) 8777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 8797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 8807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 8827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 8867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 8877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 8897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 8927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 8997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If both INF, same sign => same as both, opposite => error. 9007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 9017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 9027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 9037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 9047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(other) #Can't both be infinity here 9057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 9077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 9097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 9107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 9117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If the answer is 0, the sign should be negative, in this case. 9127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 9137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 9157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 9167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 9177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 9187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), exp)) 9197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 9207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < other._exp - context.prec-1: 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = other._exp - context.prec-1 9227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other._rescale(exp, watchexp=0, context=context) 9237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 9277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < self._exp - context.prec-1: 9287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp - context.prec-1 9297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(exp, watchexp=0, context=context) 9307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 9357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 9367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = _normalize(op1, op2, shouldround, context.prec) 9377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 9397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 9417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = cmp(abs(op1), abs(op2)) 9427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 9437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if diff == 0: 9447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < context.Etiny(): 9457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Etiny() 9467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 9477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((negativezero, (0,), exp)) 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if diff < 0: 9497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, now abs(op1) > abs(op2) 9517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign == -1: 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = -1 9537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #So we know the sign, and op1 > 0. 9577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif op1.sign == -1: 9587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = -1 9597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = (1, 1) 9607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 9627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, op1 > abs(op2) > 0 9637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.reverse() 9657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.reverse() 9667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op2.sign == 1: 9687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.int = resultint = map(operator.add, op1.int, op2.int) 9697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 9707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op1.int)): 9717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = resultint[i] + carry 9727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 9737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp > 9: 9747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 1 9757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp -= 10 9767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint[i] = tmp 9777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 9787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.append(1) 9797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.int = resultint = map(operator.sub, op1.int, op2.int) 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 0 9827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op1.int)): 9837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = resultint[i] - loan 9847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 0 9857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp < 0: 9867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger loan = 1 9877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp += 10 9887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint[i] = tmp 9897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger assert not loan 9907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while resultint[-1] == 0: 9927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.pop() 9937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultint.reverse() 9947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 9967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 9977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 9987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 9997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 10027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self + (-other)""" 10057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 10087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context=context) 10107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal(0) = Decimal(0), which we don't want since 10147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.) 10157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so we change the sign directly to a copy 10167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(other) 10177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1-tmp._sign 10187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__add__(tmp, context=context) 10207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 10227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return other + (-self)""" 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 10267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 10287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1 - tmp._sign 10297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__add__(tmp, context=context) 10307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _increment(self, round=1, context=None): 10327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Special case of add, adding 1eExponent 10337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Since it is common, (rounding, for example) this adds 10357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (sign)*one E self._exp to the number more efficiently than add. 10367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For example: 10387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal('5.624e10')._increment() == Decimal('5.625e10') 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 10407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 10437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L = list(self._int) 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[-1] += 1 10487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = len(L)-1 10497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while L[spot] == 10: 10507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot] = 0 10517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot == 0: 10527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[0:0] = [1] 10537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 10547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot-1] += 1 10557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot -= 1 10567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, L, self._exp)) 10577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if round and context._rounding_decision == ALWAYS_ROUND: 10597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 10637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 10647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 10667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 10677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 10707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 10737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1075d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 10767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 10787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[resultsign] 10807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 10827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 10837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 10847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[resultsign] 10857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 10877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 10887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 10907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 10917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, (0,), resultexp)) 10927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 10937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Fixing in case the exponent is out of bounds 10947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 10957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 10987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int == (1,): 10997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, other._int, resultexp)) 11007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 11017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 11027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._int == (1,): 11047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, self._int, resultexp)) 11057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 11067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 11077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = list(self._int) 11107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = list(other._int) 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.reverse() 11127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.reverse() 11137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Minimize Decimal additions 11147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op2) > len(op1): 11157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 11167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _divmod = divmod 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator = [0]*(len(self._int) + len(other._int)) 11197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(op2)): 11207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op2[i] == 0: 11217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger continue 11227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mult = op2[i] 11237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 11247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for j in xrange(len(op1)): 11257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry, accumulator[i+j] = _divmod( mult * op1[j] + carry 11267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger + accumulator[i+j], 10) 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 11297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator[i + j + 1] += carry 11307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while not accumulator[-1]: 11317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator.pop() 11327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger accumulator.reverse() 11337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (resultsign, accumulator, resultexp)) 11357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 11377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 11427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 11437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, context=context) 11447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __truediv__ = __div__ 11457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _divide(self, other, divmod = 0, context=None): 11477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return a / b, to context.prec precision. 11487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divmod: 11507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => true division 11517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => (a //b, a%b) 11527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 => a //b 11537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3 => a%b 11547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Actually, if divmod is 2 or 3 a tuple is returned, but errors for 11567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger computing the other value are not raised. 11577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 11587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 11617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 11637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 11647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 11657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (ans, ans) 11667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 11677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1169d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger sign = self._sign ^ other._sign 11707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 11717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 11727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0', 1) 11737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0') 11747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() and other._isinfinity(): 11757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not divmod: 11767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 11777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 11787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (context._raise_error(InvalidOperation, 11797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '(+-)INF // (+-)INF'), 11807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 11817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '(+-)INF % (+-)INF')) 11827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not divmod: 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 11857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 11867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, (0,), context.Etiny())) 11877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 11887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 11897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #These two have different precision. 11907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 11917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp - other._exp 11927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < context.Etiny(): 11937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Etiny() 11947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, '0e-x / y') 11957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp > context.Emax: 11967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Emax 11977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped, '0e+x / y') 11987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), exp) ) 11997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 12017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 12027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 12037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._isinfinity(): 12047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal((sign, (0,), 0)), Decimal(self)) 12057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 12067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1: 12077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 12087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 12097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 12107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], NaN) 12117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 3: 12127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 12137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 12147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 12157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(self) 12167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside._exp = min(self._exp, other._exp) 12177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal((sign, (0,), 0)), otherside) 12187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 12207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionByZero, 'divmod(x,0)', 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign, 1) 12227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, so neither = 0, INF 12247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 12267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If we're dividing into ints, and self < other, stop. 12287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self.__abs__(0) does not round. 12297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): 12307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1 or divmod == 3: 12327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2 = self._rescale(exp, context=context, watchexp=0) 12347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 12357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2 = ans2._fix(context=context) 12367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), 12377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2) 12387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 12407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't round the mod part, if we don't need it. 12417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), Decimal(self)) 12427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign: 12447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = -1 12457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 12467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 12477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = 0 12487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 12497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 12507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2, adjust = _adjust_coefficients(op1, op2) 12517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res = _WorkRep( (sign, [0], (op1.exp - op2.exp)) ) 12527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and res.exp > context.prec + 1: 12537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = None 12567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 12577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while( (len(op2.int) < len(op1.int) and op1.int[0]) or 12587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (len(op2.int) == len(op1.int) and op2.int <= op1.int)): 12597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Meaning, while op2.int < op1.int, when normalized. 12607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res._increment() 12617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.subtract(op2.int) 12627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if res.exp == 0 and divmod: 12637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(res.int) > context.prec and shouldround: 12647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 12667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 12677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._rescale(exp, context=context, 12707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger watchexp=0) 12717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 12727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._fix(context=context) 12747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 12757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.int == [0]*len(op1.int) and adjust >= 0 and not divmod: 12777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 12787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if (len(res.int) > context.prec) and shouldround: 12797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 12807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround=1 12827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Really, the answer is a bit higher, so adding a one to 12837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # the end will make sure the rounding is right. 12847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.int != [0]*len(op1.int): 12857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.int.append(1) 12867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 12897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust += 1 12917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.int.append(0) 12927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.append(0) 12937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 12947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if res.exp == 0 and divmod and (len(op2.int) > len(op1.int) or 12967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (len(op2.int) == len(op1.int) and 12977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int > op1.int)): 12987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Solves an error in precision. Same as a previous block. 12997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(res.int) > context.prec and shouldround: 13017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 13027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 13037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 13047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 13067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._rescale(exp, context=context) 13077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 13097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 13117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(res) 13137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 13147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 13157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 13187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 13197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 13217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 13227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 13247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (self // other, self % other) 13267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 1, context) 13287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 13307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 13317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 13337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 13357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 13377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 13397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 13407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 13437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 13447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 3, context)[1] 13507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 13527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 13537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 13557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 13617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 13627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 13637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(other, context) 13657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 13667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # If DivisionImpossible causes an error, do not leave Rounded/Inexact 13717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # ignored in the calling function. 13729fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 13747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #keep DivisionImpossible flags 13757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 13767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 13787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 13807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13819fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 13837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign: 13857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(-2), context=context) 13867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 13877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(2), context=context) 13887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 13907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 13937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r < comparison: 13967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 13977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Get flags now 13987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.__divmod__(other, context=context) 13997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r._fix(context=context) 14007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 14037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 14057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 14067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 14077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 14087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger decrease = not side._iseven() 14107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 14117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger side = side.__abs__(context=context) 14127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 14137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 14157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 14167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r > comparison or decrease and r == comparison: 14177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += 1 14197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(side.__add__(Decimal(1), context=context)._int) >= context.prec: 14207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible)[1] 14227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == other._sign: 14247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__sub__(other, context=context) 14257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__add__(other, context=context) 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r._fix(context=context) 14317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 14347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 2, context)[0] 14357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 14387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 14397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 14407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 14427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 14437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 14447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 14467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts self to a int, truncating if necessary.""" 14477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan(): 14487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidContext) 14507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._isinfinity(): 14517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise OverflowError, "Cannot convert infinity to long" 14527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 14537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 14547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = '-'*self._sign 14557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 14567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = sign + ''.join(map(str, self._int)) + '0'*self._exp 14577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(s) 14587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = sign + ''.join(map(str, self._int))[:self._exp] 14597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(s) 14607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = list(self._int) 14617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.reverse() 14627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = 0 14637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp: 14647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val *= 10 14657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val += tmp.pop() 14667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(((-1) ** self._sign) * val * 10.**int(self._exp)) 14677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 14697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 14707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 14727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 14747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _fix(self, prec=None, rounding=None, folddown=None, context=None): 14767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 14777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 14797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 14817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 14827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision to which to round. By default, the context decides. 14837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding - Rounding method. By default, the context decides. 14847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger folddown - Fold down high elements, by default context._clamp 14857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 14867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() or self._isnan(): 14887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 14897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 14917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 14927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 14937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 14947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fixexponents(prec, rounding, folddown=folddown, 14957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context) 14967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(ans._int) > prec: 14977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._round(prec, rounding, context=context) 14987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fixexponents(prec, rounding, folddown=folddown, 14997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context) 15007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _fixexponents(self, prec=None, rounding=None, folddown=None, 15037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=None): 15047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Fix the exponents and return a copy with the exponent in bounds.""" 15057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 15067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 15077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 15087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 15097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 15107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 15117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if folddown is None: 15127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger folddown = context._clamp 15137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin, Emax = context.Emin, context.Emax 15147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Etop = context.Etop() 15157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 15167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans.adjusted() < Emin: 15177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Etiny = context.Etiny() 15187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans._exp < Etiny: 15197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans: 15207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = Etiny 15217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(Etiny, context=context) 15247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #It isn't zero, and exp < Emin => subnormal 15257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 15267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.flags[Inexact]: 15277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Underflow) 15287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 15307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Only raise subnormal if non-zero. 15317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 15327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif folddown and ans._exp > Etop: 15337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(Etop, context=context) 15357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif ans.adjusted() > Emax: 15367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans: 15377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = Emax 15387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 15417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(Overflow, 'above Emax', ans._sign) 15437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round(self, prec=None, rounding=None, context=None): 15467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a rounded version of self. 15477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger You can specify the precision or rounding method. Otherwise, the 15497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context determines it. 15507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 15517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 15537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 15547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 15557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 15567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 15597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 15607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if rounding is None: 15627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context.rounding 15637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 15647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 15657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 15677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec <= 0: 15687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) 15697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) - prec + self._exp 15707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) * prec 15727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) + self._exp - prec 15737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, dig, exp)) 15747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == 0: 15787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp._int = (0,)+temp._int 15807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif prec < 0: 15827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp + len(self._int) - prec - 1 15837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal( (self._sign, (0, 1), exp)) 15847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(temp._int) 15897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == numdigits: 15907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return temp 15917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # See if we need to extend precision 15937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger expdiff = prec - numdigits 15947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if expdiff > 0: 15957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = list(temp._int) 15967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend([0] * expdiff) 15977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, tmp, temp._exp - expdiff)) 15987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, but maybe all the lost digits are 0. 16017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lostdigits = self._int[expdiff:] 16027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lostdigits == (0,) * len(lostdigits): 16037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff)) 16047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Rounded, but not Inexact 16057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Okay, let's round and lose data 16097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this_function = getattr(temp, self._pick_rounding_function[rounding]) 16117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now we've got the rounding function 16127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec != context.prec: 16149fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 16157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = prec 16167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = this_function(prec, expdiff, context) 16177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact, 'Changed in rounding') 16197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 16237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_down(self, prec, expdiff, context): 16257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Also known as round-towards-0, truncate.""" 16267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_up(self, prec, expdiff, context, tmp = None): 16297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds 5 up (away from 0)""" 16307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp is None: 16327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff)) 16337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int[prec] >= 5: 16347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=0, context=context) 16357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_even(self, prec, expdiff, context): 16407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 to even, rest to nearest.""" 16417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 165061992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if self._int[prec-1] & 1 == 0: 16517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_down(self, prec, expdiff, context): 16557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 16567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_up(self, prec, expdiff, context): 16697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds away from 0.""" 16707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec:]: 16727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=1, context=context) 16747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_ceiling(self, prec, expdiff, context): 16817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 16827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 16837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_down(prec, expdiff, context) 16847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_up(prec, expdiff, context) 16867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_floor(self, prec, expdiff, context): 16887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 16897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self._sign: 16907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_down(prec, expdiff, context) 16917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_up(prec, expdiff, context) 16937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pow__(self, n, modulo = None, context=None): 16957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self ** n (mod modulo) 16967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If modulo is None (default), don't take it mod modulo. 16987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 16997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 17007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 17017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = self._convert_other(n) 17027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Because the spot << doesn't work with really big exponents 17047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n._isinfinity() or n.adjusted() > 8: 17057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** INF') 17067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(n, context) 17087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 17097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 17107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not n._isinfinity() and not n._isinteger(): 17127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** (non-integer)') 17137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not n: 17157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '0 ** 0') 17167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not n: 17187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(1): 17217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign and not n._iseven() 17247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = int(n) 17257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 17277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo: 17287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'INF % x') 17297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n > 0: 17307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 17317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), 0) ) 17327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #with ludicrously large exponent, just raise an overflow and return inf. 17347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \ 17357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger and self: 17367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal('inf') 17387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = sign 17397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 17407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 17417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Overflow, 'Big power', sign) 17427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 17437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elength = len(str(abs(n))) 17457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 17467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 174799148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger if not modulo and firstprec + elength + 1 > DefaultContext.Emax: 17487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(Overflow, 'Too much precision.', sign) 17497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(self) 17517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Decimal(1) 17529fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 17537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + elength + 1 17547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context.rounding 17557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n < 0: 17567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #n is a long now, not Decimal instance 17577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = -n 17587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(1).__div__(mul, context=context) 17597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 17617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = 1 17637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot <= n: 17647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot <<= 1 17657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Spot is the highest power of 2 less than n 17687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot: 17697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(val, context=context) 17707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val._isinfinity(): 17717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Infsign[sign] 17727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 17737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot & n: 17747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(mul, context=context) 17757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo is not None: 17767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mod__(modulo, context=context) 17777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 17797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 17817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return val._fix(context=context) 17827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return val 17837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rpow__(self, other, context=None): 17857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __pow__.""" 17867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 17877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__pow__(self, context=context) 17887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, context=None): 17907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 17917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 17927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 17937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 17957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 17967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 17977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dup = self._fix(context=context) 17997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if dup._isinfinity(): 18007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return dup 18017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not dup: 18037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, (0,), 0) ) 18047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end = len(dup._int) 18057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 18067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while dup._int[end-1] == 0: 18077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 18087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 18097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, dup._int[:end], exp) ) 18107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, exp, rounding = None, context=None, watchexp = 1): 18137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 18147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 18167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(exp, context) 18217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 18227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 18257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 18267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self #if both are inf, it is OK 18277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 18287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'quantize with one INF') 18297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._rescale(exp._exp, rounding, context, watchexp) 18307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 18327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Test whether self and other have the same exponent. 18337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger same as self._exp == other._exp, except NaN == sNaN 18357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isnan() or other._isnan(): 18377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._isnan() and other._isnan() and True 18387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity() or other._isinfinity(): 18397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._isinfinity() and other._isinfinity() and True 18407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 18417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _rescale(self, exp, rounding = None, context=None, watchexp = 1): 18437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rescales so that the exponent is exp. 18447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 18467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = rounding version 18477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger watchexp: if set (default) an error is returned if exp is greater 18487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger than Emax or less than Etiny. 18497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 18547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale with an INF') 18557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 18577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 18587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger out = 0 18617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and (context.Emax < exp or context.Etiny() > exp): 18637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 18667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 18677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int = (0,) 18687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = exp 18697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = self._exp - exp 18727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits = len(self._int)+diff 18737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and digits > context.prec: 18757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'Rescale > prec') 18767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 18787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = (0,)+tmp._int 18797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits += 1 18807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prevexact = context.flags[Inexact] 18827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 18837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = -digits + tmp._exp 18847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = (0,1) 18857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits = 1 18867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._round(digits, rounding, context=context) 18877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp._int[0] == 0 and len(tmp._int) > 1: 18897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = tmp._int[1:] 18907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = exp 18917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp and tmp.adjusted() < context.Emin: 18937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 18947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif tmp and tmp.adjusted() > context.Emax: 18957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 18977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_integral(self, rounding = None, context=None): 18997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to the nearest integer, without raising inexact, rounded.""" 19007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 19017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 19027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 19037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 19047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 19067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 19077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 19087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(0, rounding, context=context) 19097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 19107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, context=None): 19137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the square root of self. 19147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn)) 19167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should quadratically approach the right answer. 19177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 19187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 19197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 19207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._check_nans(context=context) 19227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 19237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 19267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exponent = self._exp / 2, using round_down. 19277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 19287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp+1) // 2 19297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 19307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = (self._exp) // 2 19317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #sqrt(-0) = -0 19337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (1, (0,), exp)) 19347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (0, (0,), exp)) 19367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 19397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 19417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self) 19427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 19447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger expadd = tmp._exp / 2 194661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp._exp & 1: 19477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int += (0,) 19487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19529fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 19537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 19547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 19557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = 3 195661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp.adjusted() & 1 == 0: 19577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (8,1,9), tmp.adjusted() - 2) ) 19587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)), 19597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 + tmp.adjusted()/2 19617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) ) 19637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)), 19647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 + tmp.adjusted()/2 19667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #ans is now a linear approximation. 19687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emax, Emin = context.Emax, context.Emin 197099148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin 19717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = Decimal('0.5') 19737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger count = 1 19757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger maxp = firstprec + 2 19767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_HALF_EVEN) 19777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 19787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = min(2*context.prec - 2, maxp) 19797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context), 19807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.prec == maxp: 19827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 19837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #round to the answer's precision-- the only error can be 1 ulp. 19857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 19867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prevexp = ans.adjusted() 19877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._round(context=context) 19887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, check if the other last digits are better. 19907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + 1 19917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # In case we rounded up another digit and we should actually go lower. 19927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prevexp != ans.adjusted(): 19937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int += (0,) 19947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 19957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context) 19987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_UP) 19997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lower.__mul__(lower, context=context) > (tmp): 20007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context) 20017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 20037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context) 20047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_DOWN) 20057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if upper.__mul__(upper, context=context) < tmp: 20067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context) 20077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp += expadd 20097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 20127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._fix(context=context) 20137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 20157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans.__mul__(ans, context=context) == self: 20167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Only rounded/inexact if here. 20177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 20197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 20207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 20217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Exact answer, so let's set the exponent right. 20227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 20237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp +1)// 2 20247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 20257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp // 2 20267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += ans._exp - exp 20277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(exp, context=context) 20287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax, context.Emin = Emax, Emin 20317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans._fix(context=context) 20337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 20357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 20367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like max(self, other) except if one is not a number, returns 20387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 20407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 20417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 20427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 20437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2044d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2045d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # number is always returned 2046d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger sn = self._isnan() 2047d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger on = other._isnan() 2048d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn or on: 2049d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if on == 1 and sn != 2: 2050d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self 2051d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn == 1 and on != 2: 2052d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return other 2053d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self._check_nans(other, context) 20547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2056d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2057d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2058d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2059d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2060d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2061d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2062d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2063d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2064d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2065d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2066d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2067d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign: 2068d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2069d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and not self._sign: 2070d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2071d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and self._sign: 2072d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2073d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == -1: 20747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2075d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger context._rounding_decision == ALWAYS_ROUND 2076d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return ans._fix(context=context) 20777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 20797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 20807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like min(self, other) except if one is not a number, returns 20827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 20847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 20857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 20867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = self._convert_other(other) 20877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2088d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2089d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # number is always returned 2090d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger sn = self._isnan() 2091d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger on = other._isnan() 2092d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn or on: 2093d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if on == 1 and sn != 2: 2094d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self 2095d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if sn == 1 and on != 2: 2096d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return other 2097d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return self._check_nans(other, context) 20987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2100d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2101d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2102d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2103d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2104d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2105d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2106d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2107d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2108d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2109d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2110d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2111d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if other._sign: 2112d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2113d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and not self._sign: 2114d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2115d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and self._sign: 2116d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2117d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == 1: 21187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2119d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger context._rounding_decision == ALWAYS_ROUND 2120d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger return ans._fix(context=context) 21217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 21237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 21247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 21257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 21267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 21277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rest == (0,)*len(rest) 21287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 21307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns 1 if self is even. Assumes self is an integer.""" 21317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp > 0: 21327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 213361992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger return self._int[-1+self._exp] & 1 == 0 21347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 21367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 21377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 21387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 21397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If NaN or Infinity, self._exp is string 21407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 21417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 21427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # support for pickling, copy, and deepcopy 21447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 21457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 21467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 21487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # I'm immutable; therefore I am my own clone 21507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 21537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # My components are also immutable 21557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2157d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Context class ########################################### 2158d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 21597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# get rounding method function: 21617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerrounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')] 21627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 21637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 21647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 21657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 21667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 21677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 21697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 21717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 21727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 21747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 21757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding - rounding type. (how you round) 21767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round? 2177bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 21787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 21797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 21807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 21817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 21827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 21830ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 21840ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 21857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 21867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 2187e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 21887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 21899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 21907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 2191bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=None, flags=[], 21927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=None, 21930ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 2194e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 21957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _ignored_flags=[]): 2196bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 2197fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 2198b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 2199bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 2200fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 2201b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 22027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 22037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 22047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, copy.copy(getattr(DefaultContext, name))) 22057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 22067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 22077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 22087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2209b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 2210bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 2211b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 2212bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self)) 2213bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']') 2214bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']') 2215b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 2216b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 2217d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 2218d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 2219d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 2220b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 2221d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 22229fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 22239fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 2224bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger nc = Context(self.prec, self.rounding, self.traps, self.flags, 22257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 22289fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 22299fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 22309fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 22319fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger nc = Context(self.prec, self.rounding, self.traps.copy(), self.flags.copy(), 22329fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22339fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22349fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 22359ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 22367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22375aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 22387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 22397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 22417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 22427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 22437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 22447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22455aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 22467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 22477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't touch the flag 22487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 22497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 2251bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 22527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #The errors define how to handle themselves. 22535aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 22547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 22567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self._ignored_flags = [] 22577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 22587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 22607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 2261fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 22627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 22647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 22657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 22667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 22677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 22687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 22697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 22717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 22727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 22737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 22747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 22757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 22767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 22785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 22795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 22805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger raise TypeError, "Cannot hash a Context." 22815aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 22827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 22837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 22847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 22857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 2287e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 22887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 22897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding_decision(self, type): 22917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding decision. 22927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding decision, and returns the current (previous) 22947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding decision. Often used like: 22957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22969fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 22977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # That so you don't change the calling context 22987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle (say DivisionImpossible is raised). 22997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 23017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger instance = instance / Decimal(2) 23027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 23037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it not round for that operation. 23057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self._rounding_decision 23087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision = type 23097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 23127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 23137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 23157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 23167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 23187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 23197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 23207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 23217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 23227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 23237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 23257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 23277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 23287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2330fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 23317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Creates a new Decimal instance but using self as context.""" 23327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 23337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return d._fix(context=self) 23347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Methods 23367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 23377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 23387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 23407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation on the operand. Otherwise, the result is the same as using 23417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23439ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 23447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 23459ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 23467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 23479ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 23487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23499ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 23507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 23537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 23557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 23567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 23587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("19.00") 23599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 23607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.02E+4") 23617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 23637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 23657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return str(a._fix(context=self)) 23667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 23687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 23697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 23717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 23727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 23737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 23747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 23757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 23777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 23787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 23797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 23807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 23827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 23839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 23847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 23859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 23867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 23879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 23887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 23899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 23907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 23919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 23927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 23937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 23957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 23977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 23987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23999ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 24007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.333333333") 24019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 24027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.666666667") 24039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 24047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.5") 24059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 24067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 24079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 24087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 24099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 24107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.00") 24119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 24127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20") 24139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 24147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 24159ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 24167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1000") 24179ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 24187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20E+6") 24197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 24217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 24237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 24247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 24267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 24279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 24287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 24307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 24337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 24357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 24367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 24387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 24397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 24437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the maximum (closer to positive 24447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 24457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 24477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 24497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 2451d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("1") 2452d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 2453d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 24547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 24567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 24587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 24597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 24637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the minimum (closer to negative 24647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 24657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 24677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 24689ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 24697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-10") 24709ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 24717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 2472d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 2473d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 24747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 24767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 24787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 24797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 24817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 24827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 24837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 24857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 24869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 24877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 24887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 24907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 24927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 24937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a special value then the general rules apply. 24957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are multiplied together ('long multiplication'), 24967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resulting in a number which may be as long as the sum of the lengths 24977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the two operands. 24987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24999ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 25007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.60") 25019ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("21") 25039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 25047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.72") 25059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 25067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.0") 25079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 25087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.28135971E+11") 25097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 25117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 2513e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 25147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 25167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 25177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 25197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 25209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 25217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 25229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 25237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2") 25249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 25257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.2E+2") 25269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 25277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2E+2") 25289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 25297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 25327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 25347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 25377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 25387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 25397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 25417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 25429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 25437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 25447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 25467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 25487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 25497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The right-hand operand must be a whole number whose integer part (after 25517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger any exponent has been applied) has no more than 9 digits and whose 25527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fractional part (if any) is all zeros before any rounding. The operand 25537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger may be positive, negative, or zero; if negative, the absolute value of 25547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the power is used, and the left-hand operand is inverted (divided into 25557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1) before use. 25567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the increased precision needed for the intermediate calculations 25587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exceeds the capabilities of the implementation then an Invalid operation 25597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger condition is raised. 25607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If, when raising to a negative power, an underflow occurs during the 25627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger division into 1, the operation is not halted at that point but 25637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger continues. 25647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('3')) 25667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("8") 25679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('-3')) 25687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.125") 25699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('1.7'), Decimal('8')) 25707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("69.7575744") 25719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2')) 25727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1')) 25747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0')) 25767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 25779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1')) 25787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2')) 25807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25819ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2')) 25827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1')) 25847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 25859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0')) 25867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 25879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1')) 25887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 25899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2')) 25907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 25919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('0'), Decimal('0')) 25927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 25937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 25957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 25977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a value equal to 'a' (rounded) and having the exponent of 'b'. 25987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 26007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. It may be rounded using the current rounding setting (if the 26017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 26027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 26037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 26047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 26067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 26077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation condition is raised. This guarantees that, unless there is an 26087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger error condition, the exponent of the result of a quantize is always 26097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 26107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 26127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 26137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 26157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.170") 26169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 26177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.17") 26189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 26197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2") 26209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 26217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 26229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 26237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0E+1") 26249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 26257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 26269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 26277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 26297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 26309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 26317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0E+5") 26329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 26337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 26357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 26377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217.0") 26389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 26397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217") 26409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 26417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2E+2") 26429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 26437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2E+2") 26447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 26467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 26487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 26497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 26517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger calculating integer division as described for divide-integer, rounded to 26527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger precision digits if necessary. The sign of the result, if non-zero, is 26537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the same as that of the original dividend. 26547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 26567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 26577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 26587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 26607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 26619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 26627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 26647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 26659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 26667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 26679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 26687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 26699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 26707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 26717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 26737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 26757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 26767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 26777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen). If the result is equal to 0 then its sign will be the 26787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 26797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 26817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 26827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 26837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 26857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.9") 26869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 26877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 26889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 26897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 26917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 26929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 26937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 26949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 26957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 26969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 26977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.3") 26987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 27007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 27027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 27037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 27057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 27067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 27087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27099ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 27107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27119ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 27127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27139ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 27147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 27177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 27197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the square root of a non-negative number to context precision. 27207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 27227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 27237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 27257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 27269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 27277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 27289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 27297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.624499800") 27309ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 27317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 27329ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 27337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 27349ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 27357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 27377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 27397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.64575131") 27409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 27417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.16227766") 27429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 27436ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 27447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 27467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 27487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 27497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 27517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.23") 27529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 27537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.00") 27549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 27557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.77") 27567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 27587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 27607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 27617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 27637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 27657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 27677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 27687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 27707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 27727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_integral(self, a): 27747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 27757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 27777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 27787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 27797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 27807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be set. The rounding mode is taken from the context. 27817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('2.1')) 27837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 27849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100')) 27857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 27869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100.0')) 27877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 27889ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('101.5')) 27897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("102") 27909ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-101.5')) 27917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-102") 27929ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('10E+5')) 27937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0E+6") 27949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('7.89E+77')) 27957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("7.89E+77") 27969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-Inf')) 27977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 27987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_integral(context=self) 28007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 28027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 28037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # sign: -1 None 1 28047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # int: list 28057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 28067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 28087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 28097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 28107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = [] 28117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 28127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, Decimal): 28137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value._sign: 28147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = -1 28157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = 1 28177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = list(value._int) 28187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 28197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, tuple): 28207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 28217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 28227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 28237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 28257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 28267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 28287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self): 28307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == 1: 28317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _WorkRep( (-1, self.int, self.exp) ) 28327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _WorkRep( (1, self.int, self.exp) ) 28347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self): 28367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -self 28387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 28407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __cmp__(self, other): 28427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.exp != other.exp: 28437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError("Operands not normalized: %r, %r" % (self, other)) 28447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign != other.sign: 28457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 28477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 28497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self.sign == -1: 28507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger direction = -1 28517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger direction = 1 28537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger int1 = self.int 28547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger int2 = other.int 28557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(int1) > len(int2): 28567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * 1 28577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(int1) < len(int2): 28587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * -1 28597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for i in xrange(len(int1)): 28607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if int1[i] > int2[i]: 28617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * 1 28627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if int1[i] < int2[i]: 28637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return direction * -1 28647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 28657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _increment(self): 28677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger curspot = len(self.int) - 1 28687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot]+= 1 28697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while (self.int[curspot] >= 10): 28707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot] -= 10 28717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if curspot == 0: 28727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[0:0] = [1] 28737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 28747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int[curspot-1] += 1 28757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger curspot -= 1 28767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, alist): 28787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Subtract a list from the current int (in place). 28797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger It is assured that (len(list) = len(self.int) and list < self.int) or 28817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger len(list) = len(self.int)-1 28827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (i.e. that int(join(list)) < int(join(self.int))) 28837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint = self.int 28867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint.reverse() 28877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger alist.reverse() 28887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 0 28907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for x in xrange(len(alist)): 28917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x] -= alist[x] + carry 28927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if selfint[x] < 0: 28937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger carry = 1 28947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x] += 10 28957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28964e0e1b6a540e664e89739456db4c706701bf062bTim Peters carry = 0 28977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if carry: 28987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[x+1] -= 1 28997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger last = len(selfint)-1 29007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while len(selfint) > 1 and selfint[last] == 0: 29017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger last -= 1 29027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if last == 0: 29037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 29047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint[last+1:]=[] 29057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger selfint.reverse() 29067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger alist.reverse() 29077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 29087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _normalize(op1, op2, shouldround = 0, prec = 0): 29117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 29127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 29147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Yes, the exponent is a long, but the difference between exponents 29167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # must be an int-- otherwise you'd get a big memory problem. 29177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = int(op1.exp - op2.exp) 29187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits < 0: 29197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = -numdigits 29207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 29217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 29227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 29237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 29247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 29257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround and numdigits > len(other.int) + prec + 1 -len(tmp.int): 29277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # If the difference in adjusted exps is > prec+1, we know 29287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # other is insignificant, so might as well put a 1 after the precision. 29297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # (since this is only for addition.) Also stops MemoryErrors. 29307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger extend = prec + 2 -len(tmp.int) 29327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if extend <= 0: 29337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger extend = 1 29347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int.extend([0]*extend) 29357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.exp -= extend 29367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other.int[:] = [0]*(len(tmp.int)-1)+[1] 29377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other.exp = tmp.exp 29387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 29397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int.extend([0] * numdigits) 29417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.exp = tmp.exp - numdigits 29427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(op1.int) - len(op2.int) 29437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # numdigits != 0 => They have the same exponent, but not the same length 29447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # of the coefficient. 29457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits < 0: 29467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = -numdigits 29477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 29487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 29497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 29507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.int[0:0] = [0] * numdigits 29517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 29527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _adjust_coefficients(op1, op2): 29547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Adjust op1, op2 so that op2.int+[0] > op1.int >= op2.int. 29557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp. 29577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used on _WorkRep instances during division. 29597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = 0 29617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If op1 is smaller, get it to same size 29627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op2.int) > len(op1.int): 29637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = len(op2.int) - len(op1.int) 29647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.extend([0]*diff) 29657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= diff 29667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = diff 29677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Same length, wrong order 29697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) == len(op2.int) and op1.int < op2.int: 29707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.int.append(0) 29717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 29727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust+= 1 29737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2, adjust 29747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) > len(op2.int) + 1: 29767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = len(op1.int) - len(op2.int) - 1 29777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.extend([0]*diff) 29787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.exp -= diff 29797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust -= diff 29807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(op1.int) == len(op2.int)+1 and op1.int > op2.int: 29827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.int.append(0) 29847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.exp -= 1 29857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust -= 1 29867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2, adjust 29877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Helper Functions ######################################## 29897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_infinity_map = { 29917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'inf' : 1, 29927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'infinity' : 1, 29937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+inf' : 1, 29947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+infinity' : 1, 29957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-inf' : -1, 29967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-infinity' : -1 29977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger} 29987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29990ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isinfinity(num): 30007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is infinity. 30017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30020ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger +1 for negative infinity; 0 for finite ; +1 for positive infinity 30037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 30047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 30057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _infinity_map.get(num, 0) 30067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30070ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isnan(num): 30087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is NaN 30097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (1, sign, diagnostic info as string) => NaN 30117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (2, sign, diagnostic info as string) => sNaN 30127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => not a NaN 30137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 30147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 30157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not num: 30167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #get the sign, get rid of trailing [+-] 30197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 30207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num[0] == '+': 30217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 30227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif num[0] == '-': #elif avoids '+-nan' 30237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 30247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 30257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('nan'): 30277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 3 and not num[3:].isdigit(): #diagnostic info 30287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (1, sign, num[3:].lstrip('0')) 30307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('snan'): 30317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 4 and not num[4:].isdigit(): 30327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (2, sign, num[4:].lstrip('0')) 30347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 30357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Setup Specific Contexts ################################ 30387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 3040fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 30417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 30436ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 3044bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 3045bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=ALWAYS_ROUND, 304799148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 304899148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 3049e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 30507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 30537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 30547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 30557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 30567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 30587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 3059bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 3060bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 30646ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 3065bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 3066bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3070d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Useful Constants (internal use only) #################### 30717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Reusable defaults 30737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInf = Decimal('Inf') 30747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingernegInf = Decimal('-Inf') 30757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Infsign[sign] is infinity w/ that sign 30777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfsign = (Inf, negInf) 30787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN = Decimal('NaN') 30807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### crud for parsing strings ################################# 30837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport re 30847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# There's an optional sign at the start, and an optional exponent 30867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# at the end. The exponent has an optional sign and at least one 30877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# digit. In between, must have either at least one digit followed 30887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# by an optional fraction, or a decimal point followed by at least 30897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# one digit. Yuck. 30907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_parser = re.compile(r""" 30927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 30937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<sign>[-+])? 30947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 30957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<int>\d+) (\. (?P<frac>\d*))? 30967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 30977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger \. (?P<onlyfrac>\d+) 30987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 30997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ([eE](?P<exp>[-+]? \d+))? 31007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 31017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger $ 31027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces. 31037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 31057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly 31077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _string2exact(s): 31097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger m = _parser(s) 31107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m is None: 31117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError("invalid literal for Decimal: %r" % s) 31127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m.group('sign') == "-": 31147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 31157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 31177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = m.group('exp') 31197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp is None: 31207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = 0 31217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = int(exp) 31237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = m.group('int') 31257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if intpart is None: 31267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = "" 31277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('onlyfrac') 31287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 31297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('frac') 31307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if fracpart is None: 31317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = "" 31327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp -= len(fracpart) 31347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = intpart + fracpart 31367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(int, mantissa) 31377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger backup = tmp 31387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp and tmp[0] == 0: 31397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del tmp[0] 31407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # It's a zero 31427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not tmp: 31437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if backup: 31447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, tuple(backup), exp) 31457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, (0,), exp) 31467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = tuple(tmp) 31477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, mantissa, exp) 31497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 31527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 31537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 3154