decimal.py revision 1fb9f528bd69efa135bacda917ec7bb166068d5d
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 137eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettingerimport copy as _copy 1387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Rounding 1400ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_DOWN = 'ROUND_DOWN' 1410ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_UP = 'ROUND_HALF_UP' 1420ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_EVEN = 'ROUND_HALF_EVEN' 1430ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_CEILING = 'ROUND_CEILING' 1440ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_FLOOR = 'ROUND_FLOOR' 1450ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_UP = 'ROUND_UP' 1460ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerROUND_HALF_DOWN = 'ROUND_HALF_DOWN' 1477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger#Rounding decision (not part of the public API) 1490ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerNEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY 1500ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond HettingerALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end. 1517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Errors 1537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DecimalException(ArithmeticError): 1555aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """Base exception class. 1567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used exceptions derive from this. 1587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If an exception derives from another exception besides this (such as 1597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Underflow (Inexact, Rounded, Subnormal) that indicates that it is only 1607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger called if the others are present. This isn't actually used for 1617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger anything, though. 1627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger handle -- Called when context._raise_error is called and the 1647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set. First argument is self, second is the 1657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context. More arguments can be given, those being after 1667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the explanation in _raise_error (For example, 1677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(NewError, '(-x)!', self._sign) would 1687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger call NewError().handle(context, self._sign).) 1697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To define a new exception, it should be sufficient to have it derive 1717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger from DecimalException. 1727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 1747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 1757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Clamped(DecimalException): 1787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent of a 0 changed to fit bounds. 1797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals clamped if the exponent of a result has been 1817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger altered in order to fit the constraints of a specific concrete 1827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger representation. This may occur when the exponent of a zero result would 1837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be outside the bounds of a representation, or when a large normal 1847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number would have an encoded exponent that cannot be represented. In 1857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this latter case, the exponent is reduced to fit and the corresponding 1867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger number of zero digits are appended to the coefficient ("fold-down"). 1877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidOperation(DecimalException): 1917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """An invalid operation was performed. 1927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Various bad things cause this: 1947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Something creates a signaling NaN 1967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF 1977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 * (+-)INF 1987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF / (+-)INF 1997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x % 0 2007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-)INF % x 2017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x._rescale( non-integer ) 2027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sqrt(-x) , x > 0 2037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 ** 0 2047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (non-integer) 2057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger x ** (+-)INF 2067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger An operand is invalid 2077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args: 2107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if args[0] == 1: #sNaN, must drop 's' but keep diagnostics 2117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (args[1]._sign, args[1]._int, 'n') ) 2127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass ConversionSyntax(InvalidOperation): 2157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Trying to convert badly formed string. 2167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an string is being 2187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger converted to a number and it does not conform to the numeric string 2197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger syntax. The result is [0,qNaN]. 2207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (0, (0,), 'n') #Passed to something which uses a tuple. 2247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionByZero(DecimalException, ZeroDivisionError): 2267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Division by 0. 2277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals division-by-zero if division of a finite number 2297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero was attempted (during a divide-integer or divide operation, or a 2307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger power operation with negative right-hand operand), and the dividend was 2317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not zero. 2327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result of the operation is [sign,inf], where sign is the exclusive 2347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or of the signs of the operands for divide, or is 1 for an odd power of 2357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -0, for power. 2367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, double = None, *args): 2397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if double is not None: 2407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign],)*2 2417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 2427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionImpossible(InvalidOperation): 2447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Cannot perform the division adequately. 2457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if the integer result of a 2477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divide-integer or remainder operation had too many digits (would be 2487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger longer than precision). The result is [0,qNaN]. 2497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) 2537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass DivisionUndefined(InvalidOperation, ZeroDivisionError): 2557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Undefined result of division. 2567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if division by zero was 2587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger attempted (during a divide-integer, divide, or remainder operation), and 2597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the dividend is also zero. The result is [0,qNaN]. 2607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, tup=None, *args): 2637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tup is not None: 2647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (NaN, NaN) #for 0 %0, 0 // 0 2657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Inexact(DecimalException): 2687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Had to round, losing information. 2697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals inexact whenever the result of an operation is 2717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger not exact (that is, it needed to be rounded and any discarded digits 2727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger were non-zero), or if an overflow or underflow condition occurs. The 2737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 2747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The inexact signal may be tested (or trapped) to determine if a given 2767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) was inexact. 2777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 2797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass InvalidContext(InvalidOperation): 2817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Invalid context. Unknown rounding, for example. 2827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals invalid-operation if an invalid context was 2847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger detected during an operation. This can occur if contexts are not checked 2857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger on creation and either the precision exceeds the capability of the 2867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger underlying concrete representation or an unknown or unsupported rounding 2877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger was specified. These aspects of the context need only be checked when 2887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the values are required to be used. The result is [0,qNaN]. 2897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, *args): 2927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return NaN 2937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Rounded(DecimalException): 2957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Number got rounded (not necessarily changed during rounding). 2967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals rounded whenever the result of an operation is 2987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounded (that is, some zero or non-zero digits were discarded from the 2997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger coefficient), or if an overflow or underflow condition occurs. The 3007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result in all cases is unchanged. 3017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The rounded signal may be tested (or trapped) to determine if a given 3037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation (or sequence of operations) caused a loss of precision. 3047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3055aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger pass 3067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Subnormal(DecimalException): 3087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Exponent < Emin before rounding. 3097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals subnormal whenever the result of a conversion or 3117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation is subnormal (that is, its adjusted exponent is less than 3127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin, before any rounding). The result in all cases is unchanged. 3137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The subnormal signal may be tested (or trapped) to determine if a given 3157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger or operation (or sequence of operations) yielded a subnormal result. 3167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 3187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Overflow(Inexact, Rounded): 3207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical overflow. 3217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals overflow if the adjusted exponent of a result 3237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (from a conversion or from an operation that is not an attempt to divide 3247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger by zero), after rounding, would be greater than the largest value that 3257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger can be handled by the implementation (the value Emax). 3267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result depends on the rounding mode: 3287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For round-half-up and round-half-even (and for round-half-down and 3307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-up, if implemented), the result of the operation is [sign,inf], 3317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger where sign is the sign of the intermediate result. For round-down, the 3327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is the largest finite number that can be represented in the 3337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger current precision, with the sign of the intermediate result. For 3347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger round-ceiling, the result is the same as for round-down if the sign of 3357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the intermediate result is 1, or is [0,inf] otherwise. For round-floor, 3367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the result is the same as for round-down if the sign of the intermediate 3377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded 3387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger will also be raised. 3397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def handle(self, context, sign, *args): 3427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, 3437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ROUND_HALF_DOWN, ROUND_UP): 3447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 0: 3467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_CEILING: 3477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((sign, (9,)*context.prec, 3497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sign == 1: 3517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR: 3527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 3537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (9,)*context.prec, 3547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax-context.prec+1)) 3557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Underflow(Inexact, Rounded, Subnormal): 3587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Numerical underflow with result rounded to 0. 3597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This occurs and signals underflow if a result is inexact and the 3617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjusted exponent of the result would be smaller (more negative) than 3627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the smallest value that can be handled by the implementation (the value 3637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emin). That is, the result is both inexact and subnormal. 3647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result after an underflow will be a subnormal number rounded, if 3667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger necessary, so that its exponent is not less than Etiny. This may result 3677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger in 0 with the sign of the intermediate result and an exponent of Etiny. 3687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger In all cases, Inexact, Rounded, and Subnormal will also be raised. 3707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 3717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3725aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# List of public traps and flags 373fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, 3745aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger Underflow, InvalidOperation, Subnormal] 3757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3765aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger# Map conditions (per the spec) to signals 3775aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger_condition_map = {ConversionSyntax:InvalidOperation, 3785aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionImpossible:InvalidOperation, 3795aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger DivisionUndefined:InvalidOperation, 3805aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger InvalidContext:InvalidOperation} 3817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Context Functions ####################################### 3837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 384ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# The getcontext() and setcontext() function manage access to a thread-local 385ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# current context. Py2.4 offers direct support for thread locals. If that 386ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger# is not available, use threading.currentThread() which is slower but will 3877e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# work for older Pythons. If threads are not part of the build, create a 3887e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger# mock threading object with threading.local() returning the module namespace. 3897e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger 3907e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingertry: 3917e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import threading 3927e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettingerexcept ImportError: 3937e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger # Python was compiled without threads; create a mock object instead 3947e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger import sys 3957e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger class MockThreading: 3967e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger def local(self, sys=sys): 3977e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger return sys.modules[__name__] 3987e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger threading = MockThreading() 3997e71fa5cfa250968eafdb77356621e3a9bbb0648Raymond Hettinger del sys, MockThreading 400ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 401ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingertry: 402ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.local 403ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 404ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerexcept AttributeError: 405ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 406ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #To fix reloading, force it to create a new context 407ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger #Old contexts have different exceptions in their dicts, making problems. 408ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if hasattr(threading.currentThread(), '__decimal_context__'): 409ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading.currentThread().__decimal_context__ 410ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 411ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context): 412ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 413ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4149fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 41561992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 4167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger threading.currentThread().__decimal_context__ = context 417ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 418ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(): 419ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 420ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 421ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 422ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 423ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 424ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 425ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 426ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return threading.currentThread().__decimal_context__ 427ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 428ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 429ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger threading.currentThread().__decimal_context__ = context 430ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 431ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 432ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettingerelse: 433ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 434ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger local = threading.local() 4359fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger if hasattr(local, '__decimal_context__'): 4369fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger del local.__decimal_context__ 437ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 438ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def getcontext(_local=local): 439ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Returns this thread's context. 440ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 441ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger If this thread does not yet have a context, returns 442ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger a new context and sets this thread's context. 443ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger New contexts are copies of DefaultContext. 444ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """ 445ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger try: 446ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return _local.__decimal_context__ 447ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger except AttributeError: 448ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger context = Context() 449ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 450ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger return context 451ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 452ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger def setcontext(context, _local=local): 453ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger """Set this thread's context to context.""" 454ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger if context in (DefaultContext, BasicContext, ExtendedContext): 4559fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context.copy() 45661992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger context.clear_flags() 457ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger _local.__decimal_context__ = context 458ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger 459ef66debd7ef590304466d13dde4082632750fa7cRaymond Hettinger del threading, local # Don't contaminate the namespace 4607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Decimal class ########################################### 4637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Decimal(object): 4657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Floating point class for decimal arithmetic.""" 4667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 467636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger __slots__ = ('_exp','_int','_sign', '_is_special') 468636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Generally, the value of the Decimal instance is given by 469636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (-1)**_sign * _int * 10**_exp 470636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special values are signified by _is_special == True 4717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 472dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger # We're immutable, so use __new__ not __init__ 473636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger def __new__(cls, value="0", context=None): 4747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Create a decimal point instance. 4757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 4767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal('3.14') # string input 4777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal((0, (3, 1, 4), -2)) # tuple input (sign, digit_tuple, exponent) 4797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.14") 4807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(314) # int or long 4817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger >>> Decimal(Decimal(314)) # another decimal instance 4837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("314") 4847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 4857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 486636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self = object.__new__(cls) 487636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = False 488636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 489636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From an internal working value 490636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, _WorkRep): 49117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self._sign = value.sign 492636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._int = tuple(map(int, str(value.int))) 493636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = int(value.exp) 494636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 495636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 496636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From another decimal 497636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, Decimal): 498636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = value._exp 499636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = value._sign 500636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._int = value._int 501636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = value._is_special 502636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 503636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 504636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From an integer 5057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, (int,long)): 506636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if value >= 0: 507636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 0 508636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 509636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = 1 510636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = 0 511636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._int = tuple(map(int, str(abs(value)))) 512636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 513636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 514636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # tuple/list conversion (possibly from as_tuple()) 515636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, (list,tuple)): 516636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if len(value) != 3: 517636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise ValueError, 'Invalid arguments' 518dbecd93b7203cd187c1978de1207c29d3a9a686cRaymond Hettinger if value[0] not in (0,1): 519636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise ValueError, 'Invalid sign' 520636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger for digit in value[1]: 521636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not isinstance(digit, (int,long)) or digit < 0: 522636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise ValueError, "The second value in the tuple must be composed of non negative integer elements." 523636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 524636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._sign = value[0] 525636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._int = tuple(value[1]) 526636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if value[2] in ('F','n','N'): 527636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = value[2] 528636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 529636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 530636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._exp = int(value[2]) 531636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 532636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 533636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(value, float): 534636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert float to Decimal. " + 535636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger "First convert the float to a string") 5367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 537636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Other argument types may require the context during interpretation 538636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 539636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 540636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 541636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # From a string 5427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # REs insist on real strings, so we can too. 5437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if isinstance(value, basestring): 5440ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isinfinity(value): 5457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'F' 5467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = (0,) 547636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 548636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if _isinfinity(value) == 1: 5497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 0 5507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 5517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = 1 552636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 5530ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger if _isnan(value): 5540ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger sig, sign, diag = _isnan(value) 555636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 5567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(diag) > context.prec: #Diagnostic info too long 5577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign, self._int, self._exp = \ 5587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(ConversionSyntax) 559636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 5607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if sig == 1: 5617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'n' #qNaN 5627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: #sig == 2 5637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._exp = 'N' #sNaN 5647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._sign = sign 5657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int = tuple(map(int, diag)) #Diagnostic info 566636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 567d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger try: 568d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = _string2exact(value) 569d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger except ValueError: 570636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self._is_special = True 571d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger self._sign, self._int, self._exp = context._raise_error(ConversionSyntax) 572636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 5737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 574636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise TypeError("Cannot convert %r to Decimal" % value) 5757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isnan(self): 5777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 5787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if a number 5807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if NaN 5817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 if sNaN 5827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 583636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 584636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = self._exp 585636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp == 'n': 586636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 1 587636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif exp == 'N': 588636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 2 5897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 5907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinfinity(self): 5927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is infinite 5937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 5947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if finite or not a number 5957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if +INF 5967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 if -INF 5977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 5987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 'F': 5997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 6007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _check_nans(self, other = None, context=None): 6057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether the number is not actually one. 6067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are sNaN, signal 6087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self, other are NaN return nan 6097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done before operations. 6127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 6137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 614636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_is_nan = self._isnan() 615636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other is None: 616636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = False 617636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 618636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_is_nan = other._isnan() 619636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 620636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan or other_is_nan: 621636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 622636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 623636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 624636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan == 2: 625636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 626636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, self) 627636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other_is_nan == 2: 628636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'sNaN', 629636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1, other) 630636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_is_nan: 631636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 632636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 6337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other 6347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __nonzero__(self): 6377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Is the number non-zero? 6387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 if self == 0 6407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 if self != 0 6417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 642636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 6437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 644636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return sum(self._int) != 0 6457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __cmp__(self, other, context=None): 647636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 648267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 649267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 6507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 651636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 652636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 653636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 654636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return 1 # Comparison involving NaN's always reports self > other 655636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 656636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # INF = INF 657636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return cmp(self._isinfinity(), other._isinfinity()) 6587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 6607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #If both 0, sign comparison isn't certain. 6617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If different signs, neg one is less 6637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign < self._sign: 6647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign < other._sign: 6667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 668636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self_adjusted = self.adjusted() 669636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_adjusted = other.adjusted() 670636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self_adjusted == other_adjusted and \ 6717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._int + (0,)*(self._exp - other._exp) == \ 6727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other._int + (0,)*(other._exp - self._exp): 6737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 #equal, except in precision. ([0]*(-x) = []) 674636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self_adjusted > other_adjusted and self._int[0] != 0: 6757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (-1)**self._sign 676636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self_adjusted < other_adjusted and other._int[0] != 0: 6777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -((-1)**self._sign) 6787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 679636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Need to round, so make sure we have a valid context 680636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 681636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 682636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 6839fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 6847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) #round away from 0 6857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 6877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res = self.__sub__(other, context=context) 6887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 6907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 6927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not res: 6947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 6957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif res._sign: 6967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return -1 6977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 6987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 6990aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __eq__(self, other): 7000aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 701267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7020aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) == 0 7030aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7040aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger def __ne__(self, other): 7050aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger if not isinstance(other, (Decimal, int, long)): 706267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 7070aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger return self.__cmp__(other) != 0 7080aeac107cadd1472e5ea109f7f29e6a6527ae1ecRaymond Hettinger 7097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, other, context=None): 7107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares one to another. 7117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -1 => a < b 7137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => a = b 7147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => a > b 7157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN => one is NaN 7167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Like __cmp__, but returns Decimal instances. 7177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 718636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 719267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 720267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 7217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #compare(NaN, NaN) = NaN 723636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if (self._is_special or other and other._is_special): 724636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 725636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 726636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 7277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(self.__cmp__(other, context)) 7297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __hash__(self): 7317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """x.__hash__() <==> hash(x)""" 7327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Decimal integers must hash the same as the ints 7337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Non-integer decimals are normalized and hashed as strings 7341fb9f528bd69efa135bacda917ec7bb166068d5dGeorg Brandl # Normalization assures that hash(100E-1) == hash(10) 735bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._is_special: 736bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger if self._isnan(): 737bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger raise TypeError('Cannot hash a NaN value.') 738bea3f6f5c788eb4f0f7639913ff89654152864c0Raymond Hettinger return hash(str(self)) 7397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger i = int(self) 7407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(i): 7417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(i) 7427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger assert self.__nonzero__() # '-0' handled by integer case 7437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return hash(str(self.normalize())) 7447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def as_tuple(self): 7467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as a triple tuple. 7477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger To show the internals exactly as they are. 7497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self._sign, self._int, self._exp) 7517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 7537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Represents the number as an instance of Decimal.""" 7547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Invariant: eval(repr(d)) == d 7557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 'Decimal("%s")' % str(self) 7567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __str__(self, eng = 0, context=None): 7587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return string representation of the number in scientific notation. 7597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Captures all of the information in the underlying representation. 7617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 7627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 763e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._is_special: 764e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._isnan(): 765e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger minus = '-'*self._sign 766e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._int == (0,): 767e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger info = '' 768e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger else: 769e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger info = ''.join(map(str, self._int)) 770e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._isnan() == 2: 771e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger return minus + 'sNaN' + info 772e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger return minus + 'NaN' + info 773e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger if self._isinfinity(): 774e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger minus = '-'*self._sign 775e5a0a9609faea9afdc6f81f1f6dfa07b1437e3aeRaymond Hettinger return minus + 'Infinity' 7767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 7787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 7797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 7807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(str, self._int) 7817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(self._int) 7827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger leftdigits = self._exp + numdigits 7837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY 7847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp < 0 and self._exp >= -6: #short, no need for e/E 7857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + '0.' + '0'*(abs(self._exp)) 7867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 7877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exp is closest mult. of 3 >= self._exp 7887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = ((self._exp - 1)// 3 + 1) * 3 7897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != self._exp: 7907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0.'+'0'*(exp - self._exp) 7917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '0' 7937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp != 0: 7947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.capitals: 7957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'E' 7967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 7977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += 'e' 7987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp > 0: 7997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += '+' #0.0e+3, not 0.0e3 8007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s += str(exp) 8017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s = '-'*self._sign + s 8027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return s 8037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 8047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = (leftdigits-1)%3+1 8057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits -1 - (leftdigits-1)%3 8067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjexp = leftdigits-1 8087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dotplace = 1 8097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp == 0: 8107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger pass 8117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= 0: 8127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(leftdigits, '.') 8137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._exp < 0 and adjexp >= -6: 8147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] * int(-leftdigits) 8157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '0.') 8167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits > dotplace: 8187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(dotplace, '.') 8197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif numdigits < dotplace: 8207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend(['0']*(dotplace-numdigits)) 8217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp: 8227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not context.capitals: 8237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('e') 8247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('E') 8267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if adjexp > 0: 8277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append('+') 8287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.append(str(adjexp)) 8297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if eng: 8307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp[0:1] == ['0']: 8317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:1] = [] 8327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e': 8337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp[0:0] = ['0'] 8347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 8357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.insert(0, '-') 8367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ''.join(tmp) 8387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, context=None): 8407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Convert to engineering-type string. 8417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Engineering notation has an exponent which is a multiple of 3, so there 8437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger are up to 3 digits left of the decimal place. 8447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Same rules for when in exponential and when as a value as in __str__. 8467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 8477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__str__(eng=1, context=context) 8487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __neg__(self, context=None): 8507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy with the sign switched. 8517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds, if it has reason. 8537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 854636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 855636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 856636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 857636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 8587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal('0') is Decimal('0'), not Decimal('-0') 8617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif self._sign: 8637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 866636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 867636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 868636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 8697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 870dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return Decimal((sign, self._int, self._exp))._fix(context) 8717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, self._int, self._exp)) 8727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __pos__(self, context=None): 8747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a copy, unless it is a sNaN. 8757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds the number (if more then precision digits) 8777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 878636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 879636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 880636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 881636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 8827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign 8847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 8857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # + (-0) = 0 8867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 8877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 888636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 889636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 890636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 8917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 892dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = self._fix(context) 8937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 8947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 8957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._sign = sign 8967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 8977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 8987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __abs__(self, round=1, context=None): 8997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of self. 9007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the second argument is 0, do not round. 9027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 903636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 904636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 905636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 906636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not round: 909636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 910636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 9119fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 9127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(NEVER_ROUND) 9137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 9157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__neg__(context=context) 9167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 9177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self.__pos__(context=context) 9187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __add__(self, other, context=None): 9227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns self + other. 9237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger -INF + INF (or the reverse) cause InvalidOperation errors. 9257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 926636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 927267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 928267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 929636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 9307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 9317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 9327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 933636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 934636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 935636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 936636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 9377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 938636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 939636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger #If both INF, same sign => same as both, opposite => error. 940636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._sign != other._sign and other._isinfinity(): 941636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '-INF + INF') 942636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 943636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 944636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) #Can't both be infinity here 9457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 9477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 9497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 0 9507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.rounding == ROUND_FLOOR and self._sign != other._sign: 9517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If the answer is 0, the sign should be negative, in this case. 9527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negativezero = 1 9537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not other: 9557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = min(self._sign, other._sign) 9567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if negativezero: 9577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 9587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), exp)) 9597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 96099b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, other._exp - context.prec-1) 9617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other._rescale(exp, watchexp=0, context=context) 9627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 963dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 9647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not other: 96699b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista exp = max(exp, self._exp - context.prec-1) 9677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(exp, watchexp=0, context=context) 9687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 969dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 9707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 9717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 9737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 9747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = _normalize(op1, op2, shouldround, context.prec) 9757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 9767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result = _WorkRep() 9777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if op1.sign != op2.sign: 9787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Equal and opposite 97917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int == op2.int: 9807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp < context.Etiny(): 9817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = context.Etiny() 9827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 9837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal((negativezero, (0,), exp)) 98417931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.int < op2.int: 9857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2 = op2, op1 9867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, now abs(op1) > abs(op2) 98717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op1.sign == 1: 98817931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 1 9897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.sign, op2.sign = op2.sign, op1.sign 9907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 99117931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 9927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #So we know the sign, and op1 > 0. 99317931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif op1.sign == 1: 9947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.sign = 1 99517931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger op1.sign, op2.sign = (0, 0) 99617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 99717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger result.sign = 0 9987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, op1 > abs(op2) > 0 9997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 100017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger if op2.sign == 0: 1001636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int + op2.int 10027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 1003636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger result.int = op1.int - op2.int 10047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result.exp = op1.exp 10067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(result) 10077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1008dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 10097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __radd__ = __add__ 10127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __sub__(self, other, context=None): 10147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self + (-other)""" 1015636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1016267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1017267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1019636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1020636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context=context) 1021636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1022636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 10237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # -Decimal(0) = Decimal(0), which we don't want since 10257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.) 10267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so we change the sign directly to a copy 10277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(other) 10287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1-tmp._sign 10297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__add__(tmp, context=context) 10317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rsub__(self, other, context=None): 10337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return other + (-self)""" 1034636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1035267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1036267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 10377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 10397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = 1 - tmp._sign 10407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__add__(tmp, context=context) 10417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _increment(self, round=1, context=None): 10437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Special case of add, adding 1eExponent 10447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Since it is common, (rounding, for example) this adds 10467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (sign)*one E self._exp to the number more efficiently than add. 10477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger For example: 10497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal('5.624e10')._increment() == Decimal('5.625e10') 10507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1051636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1052636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1053636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1054636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1055636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1056636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) # Must be infinite, and incrementing makes no difference 10577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L = list(self._int) 10597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[-1] += 1 10607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = len(L)-1 10617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while L[spot] == 10: 10627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot] = 0 10637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot == 0: 10647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[0:0] = [1] 10657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 10667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger L[spot-1] += 1 10677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot -= 1 10687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, L, self._exp)) 10697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1070636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1071636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 10727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if round and context._rounding_decision == ALWAYS_ROUND: 1073dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 10747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 10757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mul__(self, other, context=None): 10777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self * other. 10787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 10797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (+-) INF * 0 (or its reverse) raise InvalidOperation. 10807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1081636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1082267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1083267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 1084636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 10857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 10867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 10877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1088d87ac8f24da5dce860b559b69e6af59edd2c3eecRaymond Hettinger resultsign = self._sign ^ other._sign 10897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1090636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1091636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1092636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1093636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1094636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1095636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1096636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1097636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF * 0') 1098636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 1099636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1100636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1101636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1102636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, '0 * (+-)INF') 1103636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[resultsign] 11047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resultexp = self._exp + other._exp 11067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 11077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by zero 11097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self or not other: 11107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, (0,), resultexp)) 11117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 11127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Fixing in case the exponent is out of bounds 1113dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Special case for multiplying by power of 10 11177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int == (1,): 11187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, other._int, resultexp)) 11197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1120dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._int == (1,): 11237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((resultsign, self._int, resultexp)) 11247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1125dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1128636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1 = _WorkRep(self) 1129636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2 = _WorkRep(other) 1130636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1131636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp)) 11327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1133dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 11347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rmul__ = __mul__ 11377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __div__(self, other, context=None): 11397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self / other.""" 11407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, context=context) 11417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __truediv__ = __div__ 11427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _divide(self, other, divmod = 0, context=None): 11447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return a / b, to context.prec precision. 11457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger divmod: 11477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => true division 11487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1 => (a //b, a%b) 11497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2 => a //b 11507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3 => a%b 11517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Actually, if divmod is 2 or 3 a tuple is returned, but errors for 11537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger computing the other value are not raised. 11547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1155636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1156267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1157267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if divmod in (0, 1): 1158267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 1159267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return (NotImplemented, NotImplemented) 1160636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 11617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 11627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 11637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1164636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sign = self._sign ^ other._sign 1165636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1166636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1167636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1168636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1169636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 1170636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return (ans, ans) 11717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 11727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1173636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and other._isinfinity(): 1174636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 1175636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return (context._raise_error(InvalidOperation, 1176636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger '(+-)INF // (+-)INF'), 1177636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(InvalidOperation, 1178636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger '(+-)INF % (+-)INF')) 11797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') 11807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 11817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 11827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1: 11837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 11847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 11857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 11867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], NaN) 11877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 3: 11887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Infsign[sign], 11897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(InvalidOperation, 'INF % x')) 1190636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Infsign[sign] 1191636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1192636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if other._isinfinity(): 1193636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 1194636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return (Decimal((sign, (0,), 0)), Decimal(self)) 1195636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, 'Division by infinity') 1196636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal((sign, (0,), context.Etiny())) 1197636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1198636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Special cases for zeroes 1199636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self and not other: 1200636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 1201636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0', 1) 1202636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionUndefined, '0 / 0') 1203636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1204636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not self: 1205636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 12067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(self) 12077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside._exp = min(self._exp, other._exp) 12087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal((sign, (0,), 0)), otherside) 1209636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = self._exp - other._exp 1210636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp < context.Etiny(): 1211636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = context.Etiny() 1212636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, '0e-x / y') 1213636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp > context.Emax: 1214636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger exp = context.Emax 1215636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped, '0e+x / y') 1216636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal( (sign, (0,), exp) ) 12177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1218636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not other: 1219636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if divmod: 12207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionByZero, 'divmod(x,0)', 12217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign, 1) 1222636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(DivisionByZero, 'x / 0', sign) 12237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1224636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger #OK, so neither = 0, INF or NaN 12257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround = context._rounding_decision == ALWAYS_ROUND 12277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If we're dividing into ints, and self < other, stop. 12297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self.__abs__(0) does not round. 12307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): 12317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod == 1 or divmod == 3: 12337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2 = self._rescale(exp, context=context, watchexp=0) 12357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1236dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans2 = ans2._fix(context) 12377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), 12387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans2) 12397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif divmod == 2: 12417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't round the mod part, if we don't need it. 12427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal( (sign, (0,), 0) ), Decimal(self)) 12437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1 = _WorkRep(self) 12457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2 = _WorkRep(other) 12467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1, op2, adjust = _adjust_coefficients(op1, op2) 1247636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) ) 12487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod and res.exp > context.prec + 1: 12497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1251636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger prec_limit = 10 ** context.prec 12527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 1253636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger while op2.int <= op1.int: 1254636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger res.int += 1 1255636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1.int -= op2.int 12567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if res.exp == 0 and divmod: 1257636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if res.int >= prec_limit and shouldround: 12587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 12607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 12617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 126317931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger otherside = otherside._rescale(exp, context=context, watchexp=0) 12647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 12657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1266dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger otherside = otherside._fix(context) 12677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 12687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1269636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if op1.int == 0 and adjust >= 0 and not divmod: 12707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 1271636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if res.int >= prec_limit and shouldround: 12727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if divmod: 12737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger shouldround=1 12757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Really, the answer is a bit higher, so adding a one to 12767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # the end will make sure the rounding is right. 1277636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if op1.int != 0: 1278636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger res.int *= 10 1279636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger res.int += 1 12807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 1283636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger res.int *= 10 12847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger res.exp -= 1 12857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust += 1 1286636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1.int *= 10 12877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 12887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1289636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if res.exp == 0 and divmod and op2.int > op1.int: 12907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Solves an error in precision. Same as a previous block. 12917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1292636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if res.int >= prec_limit and shouldround: 12937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible) 12947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = Decimal(op1) 12957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger frozen = context._ignore_all_flags() 12967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 12977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = min(self._exp, other._exp) 12987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger otherside = otherside._rescale(exp, context=context) 12997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*frozen) 13017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (Decimal(res), otherside) 13037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(res) 13057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if shouldround: 1306dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 13077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 13087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdiv__(self, other, context=None): 13107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __div__.""" 1311636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1312267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1313267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__div__(self, context=context) 13157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __rtruediv__ = __rdiv__ 13167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __divmod__(self, other, context=None): 13187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (self // other, self % other) 13207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 1, context) 13227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rdivmod__(self, other, context=None): 13247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __divmod__.""" 1325636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1326267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1327267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__divmod__(self, context=context) 13297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __mod__(self, other, context=None): 13317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self % other 13337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1334636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1335267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1336267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1338636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1339636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1340636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1341636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 13427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 3, context)[1] 13477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rmod__(self, other, context=None): 13497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __mod__.""" 1350636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1351267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1352267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__mod__(self, context=context) 13547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, other, context=None): 13567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 13577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Remainder nearest to 0- abs(remainder-near) <= other/2 13587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1359636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1360267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1361267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 13627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1363636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1364636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(other, context) 1365636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1366636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 13677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self and not other: 13687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x % 0') 13697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1370636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1371636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 13727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # If DivisionImpossible causes an error, do not leave Rounded/Inexact 13737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # ignored in the calling function. 13749fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 13767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #keep DivisionImpossible flags 13777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 13787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 13807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 13827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13839fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 13847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 13857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if other._sign: 13877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(-2), context=context) 13887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 13897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger comparison = other.__div__(Decimal(2), context=context) 13907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 13927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(*flags) 13937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 13957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 13967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 13977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r < comparison: 13987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 13997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Get flags now 14007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.__divmod__(other, context=context) 1401dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return r._fix(context) 14027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 14057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (side, r) = self.__divmod__(other, context=context) 14077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 14087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r._isnan(): 14097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return r 14107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger decrease = not side._iseven() 14127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 14137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger side = side.__abs__(context=context) 14147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 14157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger s1, s2 = r._sign, comparison._sign 14177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = 0, 0 14187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if r > comparison or decrease and r == comparison: 14197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += 1 14217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(side.__add__(Decimal(1), context=context)._int) >= context.prec: 14227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(DivisionImpossible)[1] 14247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec -= 1 14257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == other._sign: 14267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__sub__(other, context=context) 14277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r = r.__add__(other, context=context) 14297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 14307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger r._sign, comparison._sign = s1, s2 14317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1432dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return r._fix(context) 14337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __floordiv__(self, other, context=None): 14357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """self // other""" 14367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._divide(other, 2, context)[0] 14377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rfloordiv__(self, other, context=None): 14397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __floordiv__.""" 1440636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1441267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1442267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 14437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__floordiv__(self, context=context) 14447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __float__(self): 14467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Float representation.""" 14477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return float(str(self)) 14487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __int__(self): 145046b0802ccd9a9c47b27a285526fbb2a8bee5b8cbBrett Cannon """Converts self to an int, truncating if necessary.""" 1451636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1452636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan(): 1453636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1454636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidContext) 1455636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif self._isinfinity(): 1456636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger raise OverflowError, "Cannot convert infinity to long" 14577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 1458605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger s = ''.join(map(str, self._int)) + '0'*self._exp 1459605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger else: 1460605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger s = ''.join(map(str, self._int))[:self._exp] 1461605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger if s == '': 1462605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger s = '0' 1463605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger sign = '-'*self._sign 1464605ed0248375bbf87bbd1d80afc7c6918fd3ce2bRaymond Hettinger return int(sign + s) 14657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __long__(self): 14677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts to a long. 14687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Equivalent to long(int(self)) 14707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 14717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return long(self.__int__()) 14727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1473dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _fix(self, context): 14747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round if it is necessary to keep self within prec precision. 14757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Rounds and fixes the exponent. Does not raise on a sNaN. 14777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 14787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Arguments: 14797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self - Decimal instance 14807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context - context used. 14817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1482636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 14837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 14847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 14857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 1486dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger prec = context.prec 148799b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista ans = self._fixexponents(context) 14887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(ans._int) > prec: 1489dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._round(prec, context=context) 149099b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista ans = ans._fixexponents(context) 14917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 14927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 149399b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista def _fixexponents(self, context): 1494dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger """Fix the exponents and return a copy with the exponent in bounds. 1495dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger Only call if known to not be a special value. 1496dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger """ 1497dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger folddown = context._clamp 1498636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Emin = context.Emin 149999b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista ans = self 1500636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans_adjusted = ans.adjusted() 1501636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans_adjusted < Emin: 15027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Etiny = context.Etiny() 15037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans._exp < Etiny: 15047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans: 150599b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista ans = Decimal(self) 15067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = Etiny 15077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 15087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(Etiny, context=context) 15107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #It isn't zero, and exp < Emin => subnormal 15117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 15127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.flags[Inexact]: 15137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Underflow) 15147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if ans: 15167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Only raise subnormal if non-zero. 15177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 1518636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 1519636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Etop = context.Etop() 1520636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if folddown and ans._exp > Etop: 15217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Clamped) 1522636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = ans._rescale(Etop, context=context) 1523636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger else: 1524636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Emax = context.Emax 1525636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans_adjusted > Emax: 1526636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not ans: 152799b5548298ffc2ae5f03bd9ef873ce45a9844f0eFacundo Batista ans = Decimal(self) 1528636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans._exp = Emax 1529636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Clamped) 1530636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1531636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Inexact) 1532636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context._raise_error(Rounded) 1533636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(Overflow, 'above Emax', ans._sign) 15347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round(self, prec=None, rounding=None, context=None): 15377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a rounded version of self. 15387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger You can specify the precision or rounding method. Otherwise, the 15407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context determines it. 15417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 15427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1543636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1544636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1545636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1546636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 1547636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 1548636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1549636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 1550636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 15517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 15527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 15537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if rounding is None: 15557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context.rounding 15567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec is None: 15577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = context.prec 15587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 15607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec <= 0: 15617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) 15627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) - prec + self._exp 15637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger dig = (0,) * prec 15657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = len(self._int) + self._exp - prec 15667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal((self._sign, dig, exp)) 15677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == 0: 15717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp._int = (0,)+temp._int 15737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif prec < 0: 15757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp + len(self._int) - prec - 1 15767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal( (self._sign, (0, 1), exp)) 15777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec = 1 15787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 15797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger temp = Decimal(self) 15807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = len(temp._int) 15827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec == numdigits: 15837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return temp 15847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # See if we need to extend precision 15867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger expdiff = prec - numdigits 15877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if expdiff > 0: 15887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = list(temp._int) 15897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp.extend([0] * expdiff) 15907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, tmp, temp._exp - expdiff)) 15917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 15927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 15937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #OK, but maybe all the lost digits are 0. 15947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lostdigits = self._int[expdiff:] 15957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lostdigits == (0,) * len(lostdigits): 15967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff)) 15977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Rounded, but not Inexact 15987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 15997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Okay, let's round and lose data 16027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger this_function = getattr(temp, self._pick_rounding_function[rounding]) 16047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now we've got the rounding function 16057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prec != context.prec: 16079fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 16087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = prec 16097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = this_function(prec, expdiff, context) 16107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 16117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact, 'Changed in rounding') 16127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 16147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _pick_rounding_function = {} 16167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_down(self, prec, expdiff, context): 16187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Also known as round-towards-0, truncate.""" 16197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_up(self, prec, expdiff, context, tmp = None): 16227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds 5 up (away from 0)""" 16237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp is None: 16257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff)) 16267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._int[prec] >= 5: 16277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=0, context=context) 16287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_even(self, prec, expdiff, context): 16337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 to even, rest to nearest.""" 16347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 164361992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if self._int[prec-1] & 1 == 0: 16447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_half_down(self, prec, expdiff, context): 16487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Round 5 down""" 16497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff)) 16517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = (self._int[prec] == 5) 16527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec+1:]: 16547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = 0 16567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 16577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if half: 16587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_half_up(prec, expdiff, context, tmp) 16607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_up(self, prec, expdiff, context): 16627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds away from 0.""" 16637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) ) 16647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for digit in self._int[prec:]: 16657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digit != 0: 16667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._increment(round=1, context=context) 16677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(tmp._int) > prec: 16687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1)) 16697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 16727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_ceiling(self, prec, expdiff, context): 16747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds up (not away from 0 if negative.)""" 16757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign: 16767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_down(prec, expdiff, context) 16777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 16787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._round_up(prec, expdiff, context) 16797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _round_floor(self, prec, expdiff, context): 16817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds down (not towards 0 if negative)""" 16827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not 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 __pow__(self, n, modulo = None, context=None): 16887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return self ** n (mod modulo) 16897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 16907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If modulo is None (default), don't take it mod modulo. 16917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1692636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger n = _convert_other(n) 1693267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if n is NotImplemented: 1694267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return n 1695636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 16967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 16977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 16987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1699636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or n._is_special or n.adjusted() > 8: 1700636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger #Because the spot << doesn't work with really big exponents 1701636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if n._isinfinity() or n.adjusted() > 8: 1702636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** INF') 17037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1704636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(n, context) 1705636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1706636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 17077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1708636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if not n._isinteger(): 17097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'x ** (non-integer)') 17107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self and not n: 17127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, '0 ** 0') 17137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not n: 17157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self == Decimal(1): 17187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal(1) 17197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = self._sign and not n._iseven() 17217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = int(n) 17227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._isinfinity(): 17247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo: 17257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'INF % x') 17267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n > 0: 17277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Infsign[sign] 17287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (sign, (0,), 0) ) 17297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #with ludicrously large exponent, just raise an overflow and return inf. 17317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \ 17327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger and self: 17337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal('inf') 17357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._sign = sign 17367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 17377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 17387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Overflow, 'Big power', sign) 17397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 17407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elength = len(str(abs(n))) 17427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 17437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 174499148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger if not modulo and firstprec + elength + 1 > DefaultContext.Emax: 17457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(Overflow, 'Too much precision.', sign) 17467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(self) 17487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Decimal(1) 17499fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 17507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + elength + 1 17517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if n < 0: 17527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #n is a long now, not Decimal instance 17537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger n = -n 17547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mul = Decimal(1).__div__(mul, context=context) 17557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot = 1 17577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot <= n: 17587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot <<= 1 17597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Spot is the highest power of 2 less than n 17627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while spot: 17637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(val, context=context) 17647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val._isinfinity(): 17657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = Infsign[sign] 17667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 17677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if spot & n: 17687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mul__(mul, context=context) 17697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if modulo is not None: 17707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = val.__mod__(modulo, context=context) 17717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger spot >>= 1 17727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 17737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 177476e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 1775dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return val._fix(context) 17767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return val 17777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __rpow__(self, other, context=None): 17797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Swaps self/other and returns __pow__.""" 1780636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 1781267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 1782267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 17837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return other.__pow__(self, context=context) 17847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, context=None): 17867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" 17877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1788636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1789636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1790636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1791636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 17927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1793dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger dup = self._fix(context) 17947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if dup._isinfinity(): 17957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return dup 17967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 17977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not dup: 17987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, (0,), 0) ) 17997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end = len(dup._int) 18007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = dup._exp 18017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while dup._int[end-1] == 0: 18027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp += 1 18037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger end -= 1 18047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (dup._sign, dup._int[:end], exp) ) 18057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1807dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def quantize(self, exp, rounding=None, context=None, watchexp=1): 18087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Quantize self so its exponent is the same as that of exp. 18097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Similar to self._rescale(exp._exp) but with error checking. 18117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1812636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or exp._is_special: 1813636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(exp, context) 1814636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1815636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 18167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1817636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() or self._isinfinity(): 1818636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if exp._isinfinity() and self._isinfinity(): 1819636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self #if both are inf, it is OK 1820636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1821636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1822636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 1823636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 'quantize with one INF') 18247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._rescale(exp._exp, rounding, context, watchexp) 18257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, other): 18277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Test whether self and other have the same exponent. 18287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger same as self._exp == other._exp, except NaN == sNaN 18307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1831636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 1832636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isnan() or other._isnan(): 1833636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._isnan() and other._isnan() and True 1834636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() or other._isinfinity(): 1835636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._isinfinity() and other._isinfinity() and True 18367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp == other._exp 18377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1838dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def _rescale(self, exp, rounding=None, context=None, watchexp=1): 18397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rescales so that the exponent is exp. 18407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = exp to scale to (an integer) 18427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = rounding version 18437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger watchexp: if set (default) an error is returned if exp is greater 18447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger than Emax or less than Etiny. 18457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 18467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context is None: 18477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = getcontext() 18487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1849636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1850636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity(): 1851636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale with an INF') 18527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1853636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1854636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1855636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 18567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and (context.Emax < exp or context.Etiny() > exp): 18587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 18617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal(self) 18627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int = (0,) 18637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp = exp 18647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 18657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger diff = self._exp - exp 1867dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger digits = len(self._int) + diff 18687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if watchexp and digits > context.prec: 18707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'Rescale > prec') 18717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 1873dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger tmp._int = (0,) + tmp._int 18747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits += 1 18757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if digits < 0: 18777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = -digits + tmp._exp 18787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = (0,1) 18797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger digits = 1 18807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = tmp._round(digits, rounding, context=context) 18817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 18827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if tmp._int[0] == 0 and len(tmp._int) > 1: 18837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int = tmp._int[1:] 18847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = exp 18857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1886636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp_adjusted = tmp.adjusted() 1887636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if tmp and tmp_adjusted < context.Emin: 18887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Subnormal) 1889636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger elif tmp and tmp_adjusted > context.Emax: 18907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'rescale(a, INF)') 18917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return tmp 18927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1893dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger def to_integral(self, rounding=None, context=None): 18947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to the nearest integer, without raising inexact, rounded.""" 1895636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1896636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1897636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1898636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 18997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 19007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self 1901636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1902636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 19037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_flags(Rounded, Inexact) 19047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self._rescale(0, rounding, context=context) 19057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 19067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return ans 19077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, context=None): 19097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the square root of self. 19107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn)) 19127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should quadratically approach the right answer. 19137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 1914636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special: 1915636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger ans = self._check_nans(context=context) 1916636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if ans: 1917636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return ans 19187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1919636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._isinfinity() and self._sign == 0: 1920636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(self) 19217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not self: 19237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #exponent = self._exp / 2, using round_down. 19247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 19257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp+1) // 2 19267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 19277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = (self._exp) // 2 19287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #sqrt(-0) = -0 19307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (1, (0,), exp)) 19317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return Decimal( (0, (0,), exp)) 19337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1934636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 1935636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 1936636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 19377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._sign == 1: 19387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') 19397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = Decimal(self) 19417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19424837a223eea09681f0bf41d41882cad5ade0f6abRaymond Hettinger expadd = tmp._exp // 2 194361992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp._exp & 1: 19447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._int += (0,) 19457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp._exp = 0 19487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19499fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 19507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = context._ignore_all_flags() 19517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger firstprec = context.prec 19527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = 3 195361992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger if tmp.adjusted() & 1 == 0: 19547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (8,1,9), tmp.adjusted() - 2) ) 19557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)), 19567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19574837a223eea09681f0bf41d41882cad5ade0f6abRaymond Hettinger ans._exp -= 1 + tmp.adjusted() // 2 19587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) ) 19607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)), 19617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19624837a223eea09681f0bf41d41882cad5ade0f6abRaymond Hettinger ans._exp -= 1 + tmp.adjusted() // 2 19637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #ans is now a linear approximation. 19657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Emax, Emin = context.Emax, context.Emin 196799148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin 19687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger half = Decimal('0.5') 19707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger maxp = firstprec + 2 19727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_HALF_EVEN) 19737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while 1: 19747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = min(2*context.prec - 2, maxp) 19757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context), 19767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context=context), context=context) 19777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if context.prec == maxp: 19787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger break 19797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #round to the answer's precision-- the only error can be 1 ulp. 19817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 19827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prevexp = ans.adjusted() 19837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._round(context=context) 19847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Now, check if the other last digits are better. 19867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec + 1 19877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # In case we rounded up another digit and we should actually go lower. 19887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if prevexp != ans.adjusted(): 19897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._int += (0,) 19907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp -= 1 19917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context) 19947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_UP) 19957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if lower.__mul__(lower, context=context) > (tmp): 19967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context) 19977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 19987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 19997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context) 20007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(ROUND_DOWN) 20017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if upper.__mul__(upper, context=context) < tmp: 20027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context) 20037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans._exp += expadd 20057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.rounding = rounding 2008dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger ans = ans._fix(context) 20097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 20117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not ans.__mul__(ans, context=context) == self: 20127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Only rounded/inexact if here. 20137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Rounded) 20157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._raise_error(Inexact) 20167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 20177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Exact answer, so let's set the exponent right. 20187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #if self._exp < 0: 20197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp = (self._exp +1)// 2 20207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #else: 20217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = self._exp // 2 20227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec += ans._exp - exp 20237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = ans._rescale(exp, context=context) 20247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.prec = firstprec 20257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._regard_flags(flags) 20267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context.Emax, context.Emin = Emax, Emin 20277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2028dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return ans._fix(context) 20297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, other, context=None): 20317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the larger value. 20327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like max(self, other) except if one is not a number, returns 20347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2036636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 2037267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 2038267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 2039636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2040636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 2041636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2042636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2043636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2044636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2045636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2046636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 2047636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 2048636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 2049636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 2050636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 20517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2053d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2054d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2055d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2056d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2057d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2058d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2059d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2060d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2061d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2062d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2063d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2064d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign: 2065d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2066d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and not self._sign: 2067d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2068d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and self._sign: 2069d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2070d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == -1: 20717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2072636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2073636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2074636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 207576e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 207676e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans._fix(context) 207776e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans 20787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, other, context=None): 20807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the smaller value. 20817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 20827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger like min(self, other) except if one is not a number, returns 20837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger NaN (and signals if one is sNaN). Also rounds. 20847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 2085636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other = _convert_other(other) 2086267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger if other is NotImplemented: 2087267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return other 2088636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2089636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if self._is_special or other._is_special: 2090636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # if one operand is a quiet NaN and the other is number, then the 2091636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # number is always returned 2092636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger sn = self._isnan() 2093636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger on = other._isnan() 2094636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn or on: 2095636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if on == 1 and sn != 2: 2096636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self 2097636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if sn == 1 and on != 2: 2098636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 2099636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return self._check_nans(other, context) 21007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = self 2102d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger c = self.__cmp__(other) 2103d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if c == 0: 2104d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if both operands are finite and equal in numerical value 2105d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # then an ordering is applied: 2106d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2107d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs differ then max returns the operand with the 2108d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # positive sign and min returns the operand with the negative sign 2109d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # 2110d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # if the signs are the same then the exponent is used to select 2111d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger # the result. 2112d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if self._sign != other._sign: 2113d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger if other._sign: 2114d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2115d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp > other._exp and not self._sign: 2116d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2117d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif self._exp < other._exp and self._sign: 2118d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger ans = other 2119d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger elif c == 1: 21207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ans = other 2121636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2122636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if context is None: 2123636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger context = getcontext() 212476e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger if context._rounding_decision == ALWAYS_ROUND: 212576e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans._fix(context) 212676e60d687dde9d987f39e16f8fe7814daf1f1e26Raymond Hettinger return ans 21277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _isinteger(self): 21297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns whether self is an integer""" 21307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp >= 0: 21317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return True 21327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rest = self._int[self._exp:] 21337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rest == (0,)*len(rest) 21347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _iseven(self): 21367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns 1 if self is even. Assumes self is an integer.""" 21377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if self._exp > 0: 21387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 1 213961992efc4bb413ae7a19752215eca5af09be6b6dRaymond Hettinger return self._int[-1+self._exp] & 1 == 0 21407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def adjusted(self): 21427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the adjusted exponent of self""" 21437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger try: 21447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self._exp + len(self._int) - 1 21457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #If NaN or Infinity, self._exp is string 21467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger except TypeError: 21477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 21487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # support for pickling, copy, and deepcopy 21507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __reduce__(self): 21517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (self.__class__, (str(self),)) 21527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __copy__(self): 21547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # I'm immutable; therefore I am my own clone 21567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __deepcopy__(self, memo): 21597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if type(self) == Decimal: 21607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self # My components are also immutable 21617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return self.__class__(str(self)) 21627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2163d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Context class ########################################### 2164d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 21657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# get rounding method function: 21677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerrounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')] 21687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerfor name in rounding_functions: 21697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. 21707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger globalname = name[1:].upper() 21717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = globals()[globalname] 21727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal._pick_rounding_function[val] = name 21737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 21749ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettingerdel name, val, globalname, rounding_functions 21757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2176afd5e63e243b600e5344a34760d9e6565dafe1a9Nick Coghlanclass ContextManager(object): 21771a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum """Helper class to simplify Context management. 21781a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 21791a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum Sample usage: 21801a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 21811a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum with decimal.ExtendedContext: 21821a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum s = ... 21831a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return +s # Convert result to normal precision 21841a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 21851a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum with decimal.getcontext() as ctx: 21861a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum ctx.prec += 2 21871a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum s = ... 21881a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return +s 21891a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 21901a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum """ 21911a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __init__(self, new_context): 21921a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.new_context = new_context 21931a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __enter__(self): 21941a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum self.saved_context = getcontext() 21951a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.new_context) 21961a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum return self.new_context 21971a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum def __exit__(self, t, v, tb): 21981a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum setcontext(self.saved_context) 21991a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 22007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass Context(object): 22017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Contains the context for a Decimal instance. 22027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Contains: 22047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec - precision (for use in rounding, division, square roots..) 22057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding - rounding type. (how you round) 22067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round? 2207bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps - If traps[exception] = 1, then the exception is 22087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raised when it is caused. Otherwise, a value is 22097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger substituted in. 22107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags - When an exception is caused, flags[exception] is incremented. 22117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (Whether or not the trap_enabler is set) 22127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Should be reset by user of Decimal instance. 22130ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin - Minimum exponent 22140ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emax - Maximum exponent 22157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger capitals - If 1, 1*10^1 is printed as 1E+1. 22167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If 0, printed as 1e1 2217e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger _clamp - If 1, change exponents if too high (Default 0) 22187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger 22207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, prec=None, rounding=None, 2221abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger traps=None, flags=None, 22227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=None, 22230ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger Emin=None, Emax=None, 2224e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=None, _clamp=0, 2225abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags=None): 2226abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if flags is None: 2227abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger flags = [] 2228abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger if _ignored_flags is None: 2229abf8a56e68a38f5bcff1fa1aa3742ff35854dd45Raymond Hettinger _ignored_flags = [] 2230bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not isinstance(flags, dict): 2231fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger flags = dict([(s,s in flags) for s in _signals]) 2232b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 2233bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if traps is not None and not isinstance(traps, dict): 2234fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger traps = dict([(s,s in traps) for s in _signals]) 2235b91af521fddac47b14c57cd9ba736775334e6379Raymond Hettinger del s 22367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for name, val in locals().items(): 22377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if val is None: 2238eb2608415ee4eb8aaea746f6a313937e264d0cdaRaymond Hettinger setattr(self, name, _copy.copy(getattr(DefaultContext, name))) 22397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 22407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger setattr(self, name, val) 22417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del self.self 22427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2243b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger def __repr__(self): 2244bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger """Show the current context.""" 2245b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger s = [] 2246bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self)) 2247bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']') 2248bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']') 2249b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger return ', '.join(s) + ')' 2250b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger 2251afd5e63e243b600e5344a34760d9e6565dafe1a9Nick Coghlan def get_manager(self): 2252afd5e63e243b600e5344a34760d9e6565dafe1a9Nick Coghlan return ContextManager(self.copy()) 22531a5e21e0334a6d4e1c756575023c7157fc9ee306Guido van Rossum 2254d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger def clear_flags(self): 2255d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger """Reset all flags to zero""" 2256d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger for flag in self.flags: 2257b1b605ef546c45eac3c53db369ea6e881f05dc8bRaymond Hettinger self.flags[flag] = 0 2258d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger 22599fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def _shallow_copy(self): 22609fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a shallow copy from self.""" 2261bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger nc = Context(self.prec, self.rounding, self.traps, self.flags, 22627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return nc 22659fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger 22669fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger def copy(self): 22679fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger """Returns a deep copy from self.""" 22689fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger nc = Context(self.prec, self.rounding, self.traps.copy(), self.flags.copy(), 22699fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self._rounding_decision, self.Emin, self.Emax, 22709fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger self.capitals, self._clamp, self._ignored_flags) 22719fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger return nc 22729ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger __copy__ = copy 22737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22745aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def _raise_error(self, condition, explanation = None, *args): 22757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Handles an error 22767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the flag is in _ignored_flags, returns the default response. 22787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, it increments the flag, then, if the corresponding 22797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger trap_enabler is set, it reaises the exception. Otherwise, it returns 22807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the default value after incrementing the flag. 22817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 22825aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger error = _condition_map.get(condition, condition) 22837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if error in self._ignored_flags: 22847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Don't touch the flag 22857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return error().handle(self, *args) 22867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.flags[error] += 1 2288bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger if not self.traps[error]: 22897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #The errors define how to handle themselves. 22905aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger return condition().handle(self, *args) 22917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Errors should only be risked on copies of the context 22937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #self._ignored_flags = [] 22947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise error, explanation 22957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 22967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_all_flags(self): 22977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore all flags, if they are raised""" 2298fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger return self._ignore_flags(*_signals) 22997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _ignore_flags(self, *flags): 23017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Ignore the flags, if they are raised""" 23027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Do not mutate-- This way, copies of a context leave the original 23037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # alone. 23047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags = (self._ignored_flags + list(flags)) 23057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return list(flags) 23067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _regard_flags(self, *flags): 23087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Stop ignoring the flags, if they are raised""" 23097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if flags and isinstance(flags[0], (tuple,list)): 23107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger flags = flags[0] 23117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger for flag in flags: 23127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._ignored_flags.remove(flag) 23137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23145aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger def __hash__(self): 23155aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger """A Context cannot be hashed.""" 23165aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger # We inherit object.__hash__, so we must deny this explicitly 23175aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger raise TypeError, "Cannot hash a Context." 23185aa478badfabb005e6f17c98fcf007a0bc54eeccRaymond Hettinger 23197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etiny(self): 23207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns Etiny (= Emin - prec + 1)""" 23217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emin - self.prec + 1) 23227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def Etop(self): 2324e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """Returns maximum exponent (= Emax - prec + 1)""" 23257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return int(self.Emax - self.prec + 1) 23267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding_decision(self, type): 23287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding decision. 23297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding decision, and returns the current (previous) 23317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding decision. Often used like: 23327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23339fce44bc8cfb57d247e81ed18ac521db0fa015f5Raymond Hettinger context = context._shallow_copy() 23347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # That so you don't change the calling context 23357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle (say DivisionImpossible is raised). 23367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding_decision(NEVER_ROUND) 23387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger instance = instance / Decimal(2) 23397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding_decision(rounding) 23407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it not round for that operation. 23427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self._rounding_decision 23457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self._rounding_decision = type 23467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _set_rounding(self, type): 23497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Sets the rounding type. 23507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Sets the rounding type, and returns the current (previous) 23527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding type. Often used like: 23537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context = context.copy() 23557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # so you don't change the calling context 23567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # if an error occurs in the middle. 23577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = context._set_rounding(ROUND_UP) 23587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger val = self.__sub__(other, context=context) 23597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger context._set_rounding(rounding) 23607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This will make it round up for that operation. 23627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger rounding = self.rounding 23647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.rounding= type 23657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return rounding 23667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2367fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger def create_decimal(self, num='0'): 23687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Creates a new Decimal instance but using self as context.""" 23697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger d = Decimal(num, context=self) 2370dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return d._fix(self) 23717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #Methods 23737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def abs(self, a): 23747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the absolute value of the operand. 23757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the operand is negative, the result is the same as using the minus 23777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation on the operand. Otherwise, the result is the same as using 23787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the plus operation on the operand. 23797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23809ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('2.1')) 23817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 23829ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-100')) 23837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 23849ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('101.5')) 23857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23869ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.abs(Decimal('-101.5')) 23877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("101.5") 23887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__abs__(context=self) 23907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def add(self, a, b): 23927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Return the sum of the two operands. 23937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 23949ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) 23957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("19.00") 23969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) 23977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.02E+4") 23987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 23997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__add__(b, context=self) 24007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def _apply(self, a): 2402dab988dd23e6328dadfe8408cd96abf4b017380dRaymond Hettinger return str(a._fix(self)) 24037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def compare(self, a, b): 24057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Compares values numerically. 24067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the signs of the operands differ, a value representing each operand 24087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ('-1' if the operand is less than zero, '0' if the operand is zero or 24097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger negative zero, or '1' if the operand is greater than zero) is used in 24107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger place of that operand for the comparison instead of the actual 24117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. 24127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The comparison is then effected by subtracting the second operand from 24147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the first and then returning a value according to the result of the 24157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger subtraction: '-1' if the result is less than zero, '0' if the result is 24167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger zero or negative zero, or '1' if the result is greater than zero. 24177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) 24197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 24209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) 24217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 24229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) 24237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 24249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) 24257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 24269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) 24277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 24289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) 24297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 24307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.compare(b, context=self) 24327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide(self, a, b): 24347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Decimal division in a specified context. 24357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) 24377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.333333333") 24389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) 24397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.666666667") 24409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) 24417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.5") 24429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) 24437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 24449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) 24457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 24469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) 24477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.00") 24489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) 24497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20") 24509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) 24517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 24529ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) 24537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1000") 24549ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) 24557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.20E+6") 24567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__div__(b, context=self) 24587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divide_int(self, a, b): 24607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Divides two numbers and returns the integer part of the result. 24617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24629ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) 24637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 24649ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) 24657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24669ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) 24677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__floordiv__(b, context=self) 24707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def divmod(self, a, b): 24727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__divmod__(b, context=self) 24737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def max(self, a,b): 24757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """max compares two values numerically and returns the maximum. 24767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 24807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the maximum (closer to positive 24817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 24827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24839ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('3'), Decimal('2')) 24847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24859ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) 24867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3") 24879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) 2488d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("1") 2489d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) 2490d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 24917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 24927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.max(b, context=self) 24937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def min(self, a,b): 24957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """min compares two values numerically and returns the minimum. 24967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 24977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a NaN then the general rules apply. 24987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are compared as as though by the compare 24997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation. If they are numerically equal then the left-hand operand 25007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen as the result. Otherwise the minimum (closer to negative 25017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger infinity) of the two operands is chosen as the result. 25027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25039ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('3'), Decimal('2')) 25047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 25059ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) 25067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-10") 25079ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) 25087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 2509d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) 2510d6c700a320eacd6f04cbcc60996b84e765766890Raymond Hettinger Decimal("7") 25117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.min(b, context=self) 25137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def minus(self, a): 25157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Minus corresponds to unary prefix minus in Python. 25167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as subtract; the 25187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation minus(a) is calculated as subtract('0', a) where the '0' 25197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 25207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('1.3')) 25227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 25239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.minus(Decimal('-1.3')) 25247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 25257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__neg__(context=self) 25277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def multiply(self, a, b): 25297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """multiply multiplies two operands. 25307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If either operand is a special value then the general rules apply. 25327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Otherwise, the operands are multiplied together ('long multiplication'), 25337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger resulting in a number which may be as long as the sum of the lengths 25347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the two operands. 25357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25369ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) 25377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.60") 25389ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) 25397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("21") 25409ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) 25417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.72") 25429ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) 25437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.0") 25449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) 25457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("4.28135971E+11") 25467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mul__(b, context=self) 25487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def normalize(self, a): 2550e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger """normalize reduces an operand to its simplest form. 25517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Essentially a plus operation with all trailing zeros removed from the 25537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger result. 25547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25559ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('2.1')) 25567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 25579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-2.0')) 25587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 25599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('1.200')) 25607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2") 25619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('-120')) 25627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.2E+2") 25639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('120.00')) 25647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.2E+2") 25659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.normalize(Decimal('0.00')) 25667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 25677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.normalize(context=self) 25697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def plus(self, a): 25717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Plus corresponds to unary prefix plus in Python. 25727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is evaluated using the same rules as add; the 25747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation plus(a) is calculated as add('0', a) where the '0' 25757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger has the same exponent as the operand. 25767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('1.3')) 25787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.3") 25799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.plus(Decimal('-1.3')) 25807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1.3") 25817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 25827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pos__(context=self) 25837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def power(self, a, b, modulo=None): 25857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Raises a to the power of b, to modulo if given. 25867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The right-hand operand must be a whole number whose integer part (after 25887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger any exponent has been applied) has no more than 9 digits and whose 25897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fractional part (if any) is all zeros before any rounding. The operand 25907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger may be positive, negative, or zero; if negative, the absolute value of 25917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the power is used, and the left-hand operand is inverted (divided into 25927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 1) before use. 25937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the increased precision needed for the intermediate calculations 25957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exceeds the capabilities of the implementation then an Invalid operation 25967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger condition is raised. 25977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 25987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If, when raising to a negative power, an underflow occurs during the 25997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger division into 1, the operation is not halted at that point but 26007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger continues. 26017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('3')) 26037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("8") 26049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('2'), Decimal('-3')) 26057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.125") 26069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('1.7'), Decimal('8')) 26077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("69.7575744") 26089ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2')) 26097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 26109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1')) 26117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 26129ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0')) 26137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26149ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1')) 26157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 26169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2')) 26177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 26189ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2')) 26197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 26209ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1')) 26217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 26229ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0')) 26237c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 26249ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1')) 26257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 26269ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2')) 26277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("Infinity") 26289ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.power(Decimal('0'), Decimal('0')) 26297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__pow__(b, modulo, context=self) 26327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def quantize(self, a, b): 26347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns a value equal to 'a' (rounded) and having the exponent of 'b'. 26357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The coefficient of the result is derived from that of the left-hand 26377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operand. It may be rounded using the current rounding setting (if the 26387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exponent is being increased), multiplied by a positive power of ten (if 26397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the exponent is being decreased), or is unchanged (if the exponent is 26407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger already equal to that of the right-hand operand). 26417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Unlike other operations, if the length of the coefficient after the 26437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger quantize operation would be greater than precision then an Invalid 26447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger operation condition is raised. This guarantees that, unless there is an 26457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger error condition, the exponent of the result of a quantize is always 26467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger equal to that of the right-hand operand. 26477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Also unlike other operations, quantize will never raise Underflow, even 26497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if the result is subnormal and inexact. 26507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26519ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) 26527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.170") 26539ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) 26547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.17") 26559ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) 26567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2") 26579ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) 26587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 26599ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) 26607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0E+1") 26619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) 26627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 26639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) 26647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) 26667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 26679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) 26687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0E+5") 26699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) 26707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) 26727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("NaN") 26739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) 26747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217.0") 26759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) 26767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("217") 26779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) 26787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.2E+2") 26799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) 26807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2E+2") 26817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 26827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.quantize(b, context=self) 26837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder(self, a, b): 26857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the remainder from integer division. 26867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is the residue of the dividend after the operation of 26887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger calculating integer division as described for divide-integer, rounded to 26897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger precision digits if necessary. The sign of the result, if non-zero, is 26907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger the same as that of the original dividend. 26917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 26937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 26947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 26957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 26969ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) 26977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.1") 26989ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) 26997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 27009ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) 27017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 27029ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) 27037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 27049ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) 27057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 27069ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) 27077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__mod__(b, context=self) 27107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def remainder_near(self, a, b): 27127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns to be "a - b * n", where n is the integer nearest the exact 27137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger value of "x / b" (if two integers are equally near then the even one 27147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger is chosen). If the result is equal to 0 then its sign will be the 27157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign of a. 27167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger This operation will fail under the same conditions as integer division 27187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (that is, if integer division on the same two operands would fail, the 27197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger remainder cannot be calculated). 27207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) 27227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.9") 27239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) 27247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-2") 27259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) 27267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 27279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) 27287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-1") 27299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) 27307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.2") 27319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) 27327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.1") 27339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) 27347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.3") 27357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.remainder_near(b, context=self) 27377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def same_quantum(self, a, b): 27397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns True if the two operands have the same exponent. 27407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The result is never affected by either the sign or the coefficient of 27427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger either operand. 27437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27449ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) 27457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27469ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) 27477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27489ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) 27497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger False 27509ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) 27517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger True 27527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.same_quantum(b) 27547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def sqrt(self, a): 27567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Returns the square root of a non-negative number to context precision. 27577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger If the result must be inexact, it is rounded using the round-half-even 27597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger algorithm. 27607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27619ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0')) 27627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0") 27639ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('-0')) 27647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0") 27659ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('0.39')) 27667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.624499800") 27679ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('100')) 27687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("10") 27699ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1')) 27707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1") 27719ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.0')) 27727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27739ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('1.00')) 27747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0") 27759ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('7')) 27767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2.64575131") 27779ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.sqrt(Decimal('10')) 27787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("3.16227766") 27799ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.prec 27806ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger 9 27817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.sqrt(context=self) 27837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def subtract(self, a, b): 2785f33d01d304c349a7f555779c7c99930f1203adb7Georg Brandl """Return the difference between the two operands. 27867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27879ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) 27887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.23") 27899ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) 27907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("0.00") 27919ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) 27927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-0.77") 27937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 27947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__sub__(b, context=self) 27957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_eng_string(self, a): 27977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 27987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 27997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 28007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_eng_string(context=self) 28027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_sci_string(self, a): 28047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Converts a number to a string, using scientific notation. 28057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger The operation is not affected by the context. 28077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.__str__(context=self) 28097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def to_integral(self, a): 28117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Rounds to an integer. 28127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger When the operand has a negative exponent, the result is the same 28147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger as using the quantize() operation using the given operand as the 28157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger left-hand-operand, 1E+0 as the right-hand-operand, and the precision 28167c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger of the operand as the precision setting, except that no flags will 28177c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger be set. The rounding mode is taken from the context. 28187c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28199ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('2.1')) 28207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("2") 28219ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100')) 28227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 28239ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('100.0')) 28247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("100") 28259ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('101.5')) 28267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("102") 28279ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-101.5')) 28287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-102") 28299ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('10E+5')) 28307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("1.0E+6") 28319ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('7.89E+77')) 28327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("7.89E+77") 28339ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond Hettinger >>> ExtendedContext.to_integral(Decimal('-Inf')) 28347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Decimal("-Infinity") 28357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return a.to_integral(context=self) 28377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerclass _WorkRep(object): 28397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __slots__ = ('sign','int','exp') 284017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # sign: 0 or 1 2841636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # int: int or long 28427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # exp: None, int, or string 28437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __init__(self, value=None): 28457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if value is None: 28467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = None 2847636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = 0 28487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = None 284917931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger elif isinstance(value, Decimal): 285017931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger self.sign = value._sign 2851636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger cum = 0 285217931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger for digit in value._int: 2853636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger cum = cum * 10 + digit 2854636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger self.int = cum 28557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value._exp 285617931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger else: 285717931de110ac84e6b0eb88d77a95798f8670765aRaymond Hettinger # assert isinstance(value, tuple) 28587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.sign = value[0] 28597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.int = value[1] 28607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger self.exp = value[2] 28617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger def __repr__(self): 28637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return "(%r, %r, %r)" % (self.sign, self.int, self.exp) 28647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger __str__ = __repr__ 28667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _normalize(op1, op2, shouldround = 0, prec = 0): 28707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Normalizes op1, op2 to have the same exp and length of coefficient. 28717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 28727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Done during addition. 28737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 28747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # Yes, the exponent is a long, but the difference between exponents 28757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # must be an int-- otherwise you'd get a big memory problem. 28767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = int(op1.exp - op2.exp) 28777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if numdigits < 0: 28787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger numdigits = -numdigits 28797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op2 28807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op1 28817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 28827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = op1 28837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger other = op2 28847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2885636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2886636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if shouldround and numdigits > prec + 1: 2887636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # Big difference in exponents - check the adjusted exponents 2888636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp_len = len(str(tmp.int)) 2889636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other_len = len(str(other.int)) 2890636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if numdigits > (other_len + prec + 1 - tmp_len): 2891636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # If the difference in adjusted exps is > prec+1, we know 2892636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # other is insignificant, so might as well put a 1 after the precision. 2893636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger # (since this is only for addition.) Also stops use of massive longs. 2894636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2895636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger extend = prec + 2 - tmp_len 2896636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if extend <= 0: 2897636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger extend = 1 2898636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp.int *= 10 ** extend 2899636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp.exp -= extend 2900636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other.int = 1 2901636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger other.exp = tmp.exp 2902636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return op1, op2 2903636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2904636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp.int *= 10 ** numdigits 2905636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger tmp.exp -= numdigits 29067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2 29077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _adjust_coefficients(op1, op2): 2909636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int. 29107c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp. 29127c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29137c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger Used on _WorkRep instances during division. 29147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust = 0 2916636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger #If op1 is smaller, make it larger 2917636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger while op2.int > op1.int: 2918636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op1.int *= 10 29197c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op1.exp -= 1 2920636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger adjust += 1 29217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2922636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger #If op2 is too small, make it larger 2923636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger while op1.int >= (10 * op2.int): 2924636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger op2.int *= 10 29257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger op2.exp -= 1 29267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger adjust -= 1 2927636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 29287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return op1, op2, adjust 29297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Helper Functions ######################################## 29317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 2932636a6b100fe6083388bc5315758326078abe65b4Raymond Hettingerdef _convert_other(other): 2933636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """Convert other to Decimal. 2934636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 2935636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger Verifies that it's ok to use in an implicit construction. 2936636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger """ 2937636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, Decimal): 2938636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return other 2939636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger if isinstance(other, (int, long)): 2940636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger return Decimal(other) 2941267b868f23a85c6a63a06452c85487355cf9ab8aRaymond Hettinger return NotImplemented 2942636a6b100fe6083388bc5315758326078abe65b4Raymond Hettinger 29437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_infinity_map = { 29447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'inf' : 1, 29457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 'infinity' : 1, 29467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+inf' : 1, 29477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '+infinity' : 1, 29487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-inf' : -1, 29497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger '-infinity' : -1 29507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger} 29517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29520ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isinfinity(num): 29537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is infinity. 29547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29550ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettinger +1 for negative infinity; 0 for finite ; +1 for positive infinity 29567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 29587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return _infinity_map.get(num, 0) 29597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29600ea241e9e2d2accb625c4b1d3af6dd1f8df23a75Raymond Hettingerdef _isnan(num): 29617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """Determines whether a string or float is NaN 29627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (1, sign, diagnostic info as string) => NaN 29647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (2, sign, diagnostic info as string) => sNaN 29657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 0 => not a NaN 29667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger """ 29677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = str(num).lower() 29687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not num: 29697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 29707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger #get the sign, get rid of trailing [+-] 29727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 29737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num[0] == '+': 29747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 29757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger elif num[0] == '-': #elif avoids '+-nan' 29767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger num = num[1:] 29777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 29787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('nan'): 29807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 3 and not num[3:].isdigit(): #diagnostic info 29817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 29827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (1, sign, num[3:].lstrip('0')) 29837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if num.startswith('snan'): 29847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if len(num) > 4 and not num[4:].isdigit(): 29857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 29867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (2, sign, num[4:].lstrip('0')) 29877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return 0 29887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### Setup Specific Contexts ################################ 29917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# The default context prototype used by Context() 2993fed52963fcf97154e0b7d1d82514767d95eb27e5Raymond Hettinger# Is mutable, so that new contexts can have different default values 29947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 29957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerDefaultContext = Context( 29966ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=28, rounding=ROUND_HALF_EVEN, 2997bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation], 2998bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 29997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger _rounding_decision=ALWAYS_ROUND, 300099148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emax=999999999, 300199148e7eaad7741fbfb0822009b7c9b216ecc227Raymond Hettinger Emin=-999999999, 3002e0f1581babe682552d7eadc4e54636b1c2775f0bRaymond Hettinger capitals=1 30037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Pre-made alternate contexts offered by the specification 30067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# Don't change these; the user should be able to select these 30077c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# contexts and be able to reproduce results from other implementations 30087c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# of the spec. 30097c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30109ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerBasicContext = Context( 30117c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger prec=9, rounding=ROUND_HALF_UP, 3012bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], 3013bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30147c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30157c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30169ec3e3b6eb4b36870bd28682e6c7a6c36911e5e0Raymond HettingerExtendedContext = Context( 30176ea484582238a65d44a76e3a831e3ba7c77a1a25Raymond Hettinger prec=9, rounding=ROUND_HALF_EVEN, 3018bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger traps=[], 3019bf4406971ce34434ed914d17fab70370948d2aabRaymond Hettinger flags=[], 30207c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger) 30217c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30227c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 3023d9c0a7ae94ef81e69d927d834131bad760d4d99dRaymond Hettinger##### Useful Constants (internal use only) #################### 30247c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30257c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Reusable defaults 30267c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInf = Decimal('Inf') 30277c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingernegInf = Decimal('-Inf') 30287c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30297c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger#Infsign[sign] is infinity w/ that sign 30307c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerInfsign = (Inf, negInf) 30317c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30327c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond HettingerNaN = Decimal('NaN') 30337c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30347c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30357c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger##### crud for parsing strings ################################# 30367c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerimport re 30377c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30387c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# There's an optional sign at the start, and an optional exponent 30397c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# at the end. The exponent has an optional sign and at least one 30407c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# digit. In between, must have either at least one digit followed 30417c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# by an optional fraction, or a decimal point followed by at least 30427c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# one digit. Yuck. 30437c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30447c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger_parser = re.compile(r""" 30457c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 30467c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<sign>[-+])? 30477c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ( 30487c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger (?P<int>\d+) (\. (?P<frac>\d*))? 30497c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger | 30507c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger \. (?P<onlyfrac>\d+) 30517c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ) 30527c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger ([eE](?P<exp>[-+]? \d+))? 30537c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# \s* 30547c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger $ 30557c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces. 30567c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30577c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdel re 30587c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30597c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly 30607c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30617c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerdef _string2exact(s): 30627c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger m = _parser(s) 30637c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m is None: 30647c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger raise ValueError("invalid literal for Decimal: %r" % s) 30657c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30667c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if m.group('sign') == "-": 30677c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 1 30687c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 30697c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger sign = 0 30707c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30717c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = m.group('exp') 30727c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if exp is None: 30737c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = 0 30747c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 30757c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp = int(exp) 30767c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30777c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = m.group('int') 30787c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if intpart is None: 30797c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger intpart = "" 30807c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('onlyfrac') 30817c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger else: 30827c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = m.group('frac') 30837c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if fracpart is None: 30847c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger fracpart = "" 30857c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30867c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger exp -= len(fracpart) 30877c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30887c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = intpart + fracpart 30897c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger tmp = map(int, mantissa) 30907c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger backup = tmp 30917c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger while tmp and tmp[0] == 0: 30927c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger del tmp[0] 30937c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 30947c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger # It's a zero 30957c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if not tmp: 30967c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger if backup: 30977c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, tuple(backup), exp) 30987c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, (0,), exp) 30997c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger mantissa = tuple(tmp) 31007c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31017c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger return (sign, mantissa, exp) 31027c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31037c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger 31047c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettingerif __name__ == '__main__': 31057c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger import doctest, sys 31067c85fa4a5203912aca564ce719a0fdd0fd5411e5Raymond Hettinger doctest.testmod(sys.modules[__name__]) 3107