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4710c53d | 1 | # Copyright (c) 2004 Python Software Foundation.\r |
2 | # All rights reserved.\r | |
3 | \r | |
4 | # Written by Eric Price <eprice at tjhsst.edu>\r | |
5 | # and Facundo Batista <facundo at taniquetil.com.ar>\r | |
6 | # and Raymond Hettinger <python at rcn.com>\r | |
7 | # and Aahz <aahz at pobox.com>\r | |
8 | # and Tim Peters\r | |
9 | \r | |
10 | # This module is currently Py2.3 compatible and should be kept that way\r | |
11 | # unless a major compelling advantage arises. IOW, 2.3 compatibility is\r | |
12 | # strongly preferred, but not guaranteed.\r | |
13 | \r | |
14 | # Also, this module should be kept in sync with the latest updates of\r | |
15 | # the IBM specification as it evolves. Those updates will be treated\r | |
16 | # as bug fixes (deviation from the spec is a compatibility, usability\r | |
17 | # bug) and will be backported. At this point the spec is stabilizing\r | |
18 | # and the updates are becoming fewer, smaller, and less significant.\r | |
19 | \r | |
20 | """\r | |
21 | This is a Py2.3 implementation of decimal floating point arithmetic based on\r | |
22 | the General Decimal Arithmetic Specification:\r | |
23 | \r | |
24 | www2.hursley.ibm.com/decimal/decarith.html\r | |
25 | \r | |
26 | and IEEE standard 854-1987:\r | |
27 | \r | |
28 | www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html\r | |
29 | \r | |
30 | Decimal floating point has finite precision with arbitrarily large bounds.\r | |
31 | \r | |
32 | The purpose of this module is to support arithmetic using familiar\r | |
33 | "schoolhouse" rules and to avoid some of the tricky representation\r | |
34 | issues associated with binary floating point. The package is especially\r | |
35 | useful for financial applications or for contexts where users have\r | |
36 | expectations that are at odds with binary floating point (for instance,\r | |
37 | in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead\r | |
38 | of the expected Decimal('0.00') returned by decimal floating point).\r | |
39 | \r | |
40 | Here are some examples of using the decimal module:\r | |
41 | \r | |
42 | >>> from decimal import *\r | |
43 | >>> setcontext(ExtendedContext)\r | |
44 | >>> Decimal(0)\r | |
45 | Decimal('0')\r | |
46 | >>> Decimal('1')\r | |
47 | Decimal('1')\r | |
48 | >>> Decimal('-.0123')\r | |
49 | Decimal('-0.0123')\r | |
50 | >>> Decimal(123456)\r | |
51 | Decimal('123456')\r | |
52 | >>> Decimal('123.45e12345678901234567890')\r | |
53 | Decimal('1.2345E+12345678901234567892')\r | |
54 | >>> Decimal('1.33') + Decimal('1.27')\r | |
55 | Decimal('2.60')\r | |
56 | >>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')\r | |
57 | Decimal('-2.20')\r | |
58 | >>> dig = Decimal(1)\r | |
59 | >>> print dig / Decimal(3)\r | |
60 | 0.333333333\r | |
61 | >>> getcontext().prec = 18\r | |
62 | >>> print dig / Decimal(3)\r | |
63 | 0.333333333333333333\r | |
64 | >>> print dig.sqrt()\r | |
65 | 1\r | |
66 | >>> print Decimal(3).sqrt()\r | |
67 | 1.73205080756887729\r | |
68 | >>> print Decimal(3) ** 123\r | |
69 | 4.85192780976896427E+58\r | |
70 | >>> inf = Decimal(1) / Decimal(0)\r | |
71 | >>> print inf\r | |
72 | Infinity\r | |
73 | >>> neginf = Decimal(-1) / Decimal(0)\r | |
74 | >>> print neginf\r | |
75 | -Infinity\r | |
76 | >>> print neginf + inf\r | |
77 | NaN\r | |
78 | >>> print neginf * inf\r | |
79 | -Infinity\r | |
80 | >>> print dig / 0\r | |
81 | Infinity\r | |
82 | >>> getcontext().traps[DivisionByZero] = 1\r | |
83 | >>> print dig / 0\r | |
84 | Traceback (most recent call last):\r | |
85 | ...\r | |
86 | ...\r | |
87 | ...\r | |
88 | DivisionByZero: x / 0\r | |
89 | >>> c = Context()\r | |
90 | >>> c.traps[InvalidOperation] = 0\r | |
91 | >>> print c.flags[InvalidOperation]\r | |
92 | 0\r | |
93 | >>> c.divide(Decimal(0), Decimal(0))\r | |
94 | Decimal('NaN')\r | |
95 | >>> c.traps[InvalidOperation] = 1\r | |
96 | >>> print c.flags[InvalidOperation]\r | |
97 | 1\r | |
98 | >>> c.flags[InvalidOperation] = 0\r | |
99 | >>> print c.flags[InvalidOperation]\r | |
100 | 0\r | |
101 | >>> print c.divide(Decimal(0), Decimal(0))\r | |
102 | Traceback (most recent call last):\r | |
103 | ...\r | |
104 | ...\r | |
105 | ...\r | |
106 | InvalidOperation: 0 / 0\r | |
107 | >>> print c.flags[InvalidOperation]\r | |
108 | 1\r | |
109 | >>> c.flags[InvalidOperation] = 0\r | |
110 | >>> c.traps[InvalidOperation] = 0\r | |
111 | >>> print c.divide(Decimal(0), Decimal(0))\r | |
112 | NaN\r | |
113 | >>> print c.flags[InvalidOperation]\r | |
114 | 1\r | |
115 | >>>\r | |
116 | """\r | |
117 | \r | |
118 | __all__ = [\r | |
119 | # Two major classes\r | |
120 | 'Decimal', 'Context',\r | |
121 | \r | |
122 | # Contexts\r | |
123 | 'DefaultContext', 'BasicContext', 'ExtendedContext',\r | |
124 | \r | |
125 | # Exceptions\r | |
126 | 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',\r | |
127 | 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',\r | |
128 | \r | |
129 | # Constants for use in setting up contexts\r | |
130 | 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',\r | |
131 | 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP',\r | |
132 | \r | |
133 | # Functions for manipulating contexts\r | |
134 | 'setcontext', 'getcontext', 'localcontext'\r | |
135 | ]\r | |
136 | \r | |
137 | __version__ = '1.70' # Highest version of the spec this complies with\r | |
138 | \r | |
139 | import copy as _copy\r | |
140 | import math as _math\r | |
141 | import numbers as _numbers\r | |
142 | \r | |
143 | try:\r | |
144 | from collections import namedtuple as _namedtuple\r | |
145 | DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent')\r | |
146 | except ImportError:\r | |
147 | DecimalTuple = lambda *args: args\r | |
148 | \r | |
149 | # Rounding\r | |
150 | ROUND_DOWN = 'ROUND_DOWN'\r | |
151 | ROUND_HALF_UP = 'ROUND_HALF_UP'\r | |
152 | ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'\r | |
153 | ROUND_CEILING = 'ROUND_CEILING'\r | |
154 | ROUND_FLOOR = 'ROUND_FLOOR'\r | |
155 | ROUND_UP = 'ROUND_UP'\r | |
156 | ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'\r | |
157 | ROUND_05UP = 'ROUND_05UP'\r | |
158 | \r | |
159 | # Errors\r | |
160 | \r | |
161 | class DecimalException(ArithmeticError):\r | |
162 | """Base exception class.\r | |
163 | \r | |
164 | Used exceptions derive from this.\r | |
165 | If an exception derives from another exception besides this (such as\r | |
166 | Underflow (Inexact, Rounded, Subnormal) that indicates that it is only\r | |
167 | called if the others are present. This isn't actually used for\r | |
168 | anything, though.\r | |
169 | \r | |
170 | handle -- Called when context._raise_error is called and the\r | |
171 | trap_enabler is not set. First argument is self, second is the\r | |
172 | context. More arguments can be given, those being after\r | |
173 | the explanation in _raise_error (For example,\r | |
174 | context._raise_error(NewError, '(-x)!', self._sign) would\r | |
175 | call NewError().handle(context, self._sign).)\r | |
176 | \r | |
177 | To define a new exception, it should be sufficient to have it derive\r | |
178 | from DecimalException.\r | |
179 | """\r | |
180 | def handle(self, context, *args):\r | |
181 | pass\r | |
182 | \r | |
183 | \r | |
184 | class Clamped(DecimalException):\r | |
185 | """Exponent of a 0 changed to fit bounds.\r | |
186 | \r | |
187 | This occurs and signals clamped if the exponent of a result has been\r | |
188 | altered in order to fit the constraints of a specific concrete\r | |
189 | representation. This may occur when the exponent of a zero result would\r | |
190 | be outside the bounds of a representation, or when a large normal\r | |
191 | number would have an encoded exponent that cannot be represented. In\r | |
192 | this latter case, the exponent is reduced to fit and the corresponding\r | |
193 | number of zero digits are appended to the coefficient ("fold-down").\r | |
194 | """\r | |
195 | \r | |
196 | class InvalidOperation(DecimalException):\r | |
197 | """An invalid operation was performed.\r | |
198 | \r | |
199 | Various bad things cause this:\r | |
200 | \r | |
201 | Something creates a signaling NaN\r | |
202 | -INF + INF\r | |
203 | 0 * (+-)INF\r | |
204 | (+-)INF / (+-)INF\r | |
205 | x % 0\r | |
206 | (+-)INF % x\r | |
207 | x._rescale( non-integer )\r | |
208 | sqrt(-x) , x > 0\r | |
209 | 0 ** 0\r | |
210 | x ** (non-integer)\r | |
211 | x ** (+-)INF\r | |
212 | An operand is invalid\r | |
213 | \r | |
214 | The result of the operation after these is a quiet positive NaN,\r | |
215 | except when the cause is a signaling NaN, in which case the result is\r | |
216 | also a quiet NaN, but with the original sign, and an optional\r | |
217 | diagnostic information.\r | |
218 | """\r | |
219 | def handle(self, context, *args):\r | |
220 | if args:\r | |
221 | ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True)\r | |
222 | return ans._fix_nan(context)\r | |
223 | return _NaN\r | |
224 | \r | |
225 | class ConversionSyntax(InvalidOperation):\r | |
226 | """Trying to convert badly formed string.\r | |
227 | \r | |
228 | This occurs and signals invalid-operation if an string is being\r | |
229 | converted to a number and it does not conform to the numeric string\r | |
230 | syntax. The result is [0,qNaN].\r | |
231 | """\r | |
232 | def handle(self, context, *args):\r | |
233 | return _NaN\r | |
234 | \r | |
235 | class DivisionByZero(DecimalException, ZeroDivisionError):\r | |
236 | """Division by 0.\r | |
237 | \r | |
238 | This occurs and signals division-by-zero if division of a finite number\r | |
239 | by zero was attempted (during a divide-integer or divide operation, or a\r | |
240 | power operation with negative right-hand operand), and the dividend was\r | |
241 | not zero.\r | |
242 | \r | |
243 | The result of the operation is [sign,inf], where sign is the exclusive\r | |
244 | or of the signs of the operands for divide, or is 1 for an odd power of\r | |
245 | -0, for power.\r | |
246 | """\r | |
247 | \r | |
248 | def handle(self, context, sign, *args):\r | |
249 | return _SignedInfinity[sign]\r | |
250 | \r | |
251 | class DivisionImpossible(InvalidOperation):\r | |
252 | """Cannot perform the division adequately.\r | |
253 | \r | |
254 | This occurs and signals invalid-operation if the integer result of a\r | |
255 | divide-integer or remainder operation had too many digits (would be\r | |
256 | longer than precision). The result is [0,qNaN].\r | |
257 | """\r | |
258 | \r | |
259 | def handle(self, context, *args):\r | |
260 | return _NaN\r | |
261 | \r | |
262 | class DivisionUndefined(InvalidOperation, ZeroDivisionError):\r | |
263 | """Undefined result of division.\r | |
264 | \r | |
265 | This occurs and signals invalid-operation if division by zero was\r | |
266 | attempted (during a divide-integer, divide, or remainder operation), and\r | |
267 | the dividend is also zero. The result is [0,qNaN].\r | |
268 | """\r | |
269 | \r | |
270 | def handle(self, context, *args):\r | |
271 | return _NaN\r | |
272 | \r | |
273 | class Inexact(DecimalException):\r | |
274 | """Had to round, losing information.\r | |
275 | \r | |
276 | This occurs and signals inexact whenever the result of an operation is\r | |
277 | not exact (that is, it needed to be rounded and any discarded digits\r | |
278 | were non-zero), or if an overflow or underflow condition occurs. The\r | |
279 | result in all cases is unchanged.\r | |
280 | \r | |
281 | The inexact signal may be tested (or trapped) to determine if a given\r | |
282 | operation (or sequence of operations) was inexact.\r | |
283 | """\r | |
284 | \r | |
285 | class InvalidContext(InvalidOperation):\r | |
286 | """Invalid context. Unknown rounding, for example.\r | |
287 | \r | |
288 | This occurs and signals invalid-operation if an invalid context was\r | |
289 | detected during an operation. This can occur if contexts are not checked\r | |
290 | on creation and either the precision exceeds the capability of the\r | |
291 | underlying concrete representation or an unknown or unsupported rounding\r | |
292 | was specified. These aspects of the context need only be checked when\r | |
293 | the values are required to be used. The result is [0,qNaN].\r | |
294 | """\r | |
295 | \r | |
296 | def handle(self, context, *args):\r | |
297 | return _NaN\r | |
298 | \r | |
299 | class Rounded(DecimalException):\r | |
300 | """Number got rounded (not necessarily changed during rounding).\r | |
301 | \r | |
302 | This occurs and signals rounded whenever the result of an operation is\r | |
303 | rounded (that is, some zero or non-zero digits were discarded from the\r | |
304 | coefficient), or if an overflow or underflow condition occurs. The\r | |
305 | result in all cases is unchanged.\r | |
306 | \r | |
307 | The rounded signal may be tested (or trapped) to determine if a given\r | |
308 | operation (or sequence of operations) caused a loss of precision.\r | |
309 | """\r | |
310 | \r | |
311 | class Subnormal(DecimalException):\r | |
312 | """Exponent < Emin before rounding.\r | |
313 | \r | |
314 | This occurs and signals subnormal whenever the result of a conversion or\r | |
315 | operation is subnormal (that is, its adjusted exponent is less than\r | |
316 | Emin, before any rounding). The result in all cases is unchanged.\r | |
317 | \r | |
318 | The subnormal signal may be tested (or trapped) to determine if a given\r | |
319 | or operation (or sequence of operations) yielded a subnormal result.\r | |
320 | """\r | |
321 | \r | |
322 | class Overflow(Inexact, Rounded):\r | |
323 | """Numerical overflow.\r | |
324 | \r | |
325 | This occurs and signals overflow if the adjusted exponent of a result\r | |
326 | (from a conversion or from an operation that is not an attempt to divide\r | |
327 | by zero), after rounding, would be greater than the largest value that\r | |
328 | can be handled by the implementation (the value Emax).\r | |
329 | \r | |
330 | The result depends on the rounding mode:\r | |
331 | \r | |
332 | For round-half-up and round-half-even (and for round-half-down and\r | |
333 | round-up, if implemented), the result of the operation is [sign,inf],\r | |
334 | where sign is the sign of the intermediate result. For round-down, the\r | |
335 | result is the largest finite number that can be represented in the\r | |
336 | current precision, with the sign of the intermediate result. For\r | |
337 | round-ceiling, the result is the same as for round-down if the sign of\r | |
338 | the intermediate result is 1, or is [0,inf] otherwise. For round-floor,\r | |
339 | the result is the same as for round-down if the sign of the intermediate\r | |
340 | result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded\r | |
341 | will also be raised.\r | |
342 | """\r | |
343 | \r | |
344 | def handle(self, context, sign, *args):\r | |
345 | if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN,\r | |
346 | ROUND_HALF_DOWN, ROUND_UP):\r | |
347 | return _SignedInfinity[sign]\r | |
348 | if sign == 0:\r | |
349 | if context.rounding == ROUND_CEILING:\r | |
350 | return _SignedInfinity[sign]\r | |
351 | return _dec_from_triple(sign, '9'*context.prec,\r | |
352 | context.Emax-context.prec+1)\r | |
353 | if sign == 1:\r | |
354 | if context.rounding == ROUND_FLOOR:\r | |
355 | return _SignedInfinity[sign]\r | |
356 | return _dec_from_triple(sign, '9'*context.prec,\r | |
357 | context.Emax-context.prec+1)\r | |
358 | \r | |
359 | \r | |
360 | class Underflow(Inexact, Rounded, Subnormal):\r | |
361 | """Numerical underflow with result rounded to 0.\r | |
362 | \r | |
363 | This occurs and signals underflow if a result is inexact and the\r | |
364 | adjusted exponent of the result would be smaller (more negative) than\r | |
365 | the smallest value that can be handled by the implementation (the value\r | |
366 | Emin). That is, the result is both inexact and subnormal.\r | |
367 | \r | |
368 | The result after an underflow will be a subnormal number rounded, if\r | |
369 | necessary, so that its exponent is not less than Etiny. This may result\r | |
370 | in 0 with the sign of the intermediate result and an exponent of Etiny.\r | |
371 | \r | |
372 | In all cases, Inexact, Rounded, and Subnormal will also be raised.\r | |
373 | """\r | |
374 | \r | |
375 | # List of public traps and flags\r | |
376 | _signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,\r | |
377 | Underflow, InvalidOperation, Subnormal]\r | |
378 | \r | |
379 | # Map conditions (per the spec) to signals\r | |
380 | _condition_map = {ConversionSyntax:InvalidOperation,\r | |
381 | DivisionImpossible:InvalidOperation,\r | |
382 | DivisionUndefined:InvalidOperation,\r | |
383 | InvalidContext:InvalidOperation}\r | |
384 | \r | |
385 | ##### Context Functions ##################################################\r | |
386 | \r | |
387 | # The getcontext() and setcontext() function manage access to a thread-local\r | |
388 | # current context. Py2.4 offers direct support for thread locals. If that\r | |
389 | # is not available, use threading.currentThread() which is slower but will\r | |
390 | # work for older Pythons. If threads are not part of the build, create a\r | |
391 | # mock threading object with threading.local() returning the module namespace.\r | |
392 | \r | |
393 | try:\r | |
394 | import threading\r | |
395 | except ImportError:\r | |
396 | # Python was compiled without threads; create a mock object instead\r | |
397 | import sys\r | |
398 | class MockThreading(object):\r | |
399 | def local(self, sys=sys):\r | |
400 | return sys.modules[__name__]\r | |
401 | threading = MockThreading()\r | |
402 | del sys, MockThreading\r | |
403 | \r | |
404 | try:\r | |
405 | threading.local\r | |
406 | \r | |
407 | except AttributeError:\r | |
408 | \r | |
409 | # To fix reloading, force it to create a new context\r | |
410 | # Old contexts have different exceptions in their dicts, making problems.\r | |
411 | if hasattr(threading.currentThread(), '__decimal_context__'):\r | |
412 | del threading.currentThread().__decimal_context__\r | |
413 | \r | |
414 | def setcontext(context):\r | |
415 | """Set this thread's context to context."""\r | |
416 | if context in (DefaultContext, BasicContext, ExtendedContext):\r | |
417 | context = context.copy()\r | |
418 | context.clear_flags()\r | |
419 | threading.currentThread().__decimal_context__ = context\r | |
420 | \r | |
421 | def getcontext():\r | |
422 | """Returns this thread's context.\r | |
423 | \r | |
424 | If this thread does not yet have a context, returns\r | |
425 | a new context and sets this thread's context.\r | |
426 | New contexts are copies of DefaultContext.\r | |
427 | """\r | |
428 | try:\r | |
429 | return threading.currentThread().__decimal_context__\r | |
430 | except AttributeError:\r | |
431 | context = Context()\r | |
432 | threading.currentThread().__decimal_context__ = context\r | |
433 | return context\r | |
434 | \r | |
435 | else:\r | |
436 | \r | |
437 | local = threading.local()\r | |
438 | if hasattr(local, '__decimal_context__'):\r | |
439 | del local.__decimal_context__\r | |
440 | \r | |
441 | def getcontext(_local=local):\r | |
442 | """Returns this thread's context.\r | |
443 | \r | |
444 | If this thread does not yet have a context, returns\r | |
445 | a new context and sets this thread's context.\r | |
446 | New contexts are copies of DefaultContext.\r | |
447 | """\r | |
448 | try:\r | |
449 | return _local.__decimal_context__\r | |
450 | except AttributeError:\r | |
451 | context = Context()\r | |
452 | _local.__decimal_context__ = context\r | |
453 | return context\r | |
454 | \r | |
455 | def setcontext(context, _local=local):\r | |
456 | """Set this thread's context to context."""\r | |
457 | if context in (DefaultContext, BasicContext, ExtendedContext):\r | |
458 | context = context.copy()\r | |
459 | context.clear_flags()\r | |
460 | _local.__decimal_context__ = context\r | |
461 | \r | |
462 | del threading, local # Don't contaminate the namespace\r | |
463 | \r | |
464 | def localcontext(ctx=None):\r | |
465 | """Return a context manager for a copy of the supplied context\r | |
466 | \r | |
467 | Uses a copy of the current context if no context is specified\r | |
468 | The returned context manager creates a local decimal context\r | |
469 | in a with statement:\r | |
470 | def sin(x):\r | |
471 | with localcontext() as ctx:\r | |
472 | ctx.prec += 2\r | |
473 | # Rest of sin calculation algorithm\r | |
474 | # uses a precision 2 greater than normal\r | |
475 | return +s # Convert result to normal precision\r | |
476 | \r | |
477 | def sin(x):\r | |
478 | with localcontext(ExtendedContext):\r | |
479 | # Rest of sin calculation algorithm\r | |
480 | # uses the Extended Context from the\r | |
481 | # General Decimal Arithmetic Specification\r | |
482 | return +s # Convert result to normal context\r | |
483 | \r | |
484 | >>> setcontext(DefaultContext)\r | |
485 | >>> print getcontext().prec\r | |
486 | 28\r | |
487 | >>> with localcontext():\r | |
488 | ... ctx = getcontext()\r | |
489 | ... ctx.prec += 2\r | |
490 | ... print ctx.prec\r | |
491 | ...\r | |
492 | 30\r | |
493 | >>> with localcontext(ExtendedContext):\r | |
494 | ... print getcontext().prec\r | |
495 | ...\r | |
496 | 9\r | |
497 | >>> print getcontext().prec\r | |
498 | 28\r | |
499 | """\r | |
500 | if ctx is None: ctx = getcontext()\r | |
501 | return _ContextManager(ctx)\r | |
502 | \r | |
503 | \r | |
504 | ##### Decimal class #######################################################\r | |
505 | \r | |
506 | class Decimal(object):\r | |
507 | """Floating point class for decimal arithmetic."""\r | |
508 | \r | |
509 | __slots__ = ('_exp','_int','_sign', '_is_special')\r | |
510 | # Generally, the value of the Decimal instance is given by\r | |
511 | # (-1)**_sign * _int * 10**_exp\r | |
512 | # Special values are signified by _is_special == True\r | |
513 | \r | |
514 | # We're immutable, so use __new__ not __init__\r | |
515 | def __new__(cls, value="0", context=None):\r | |
516 | """Create a decimal point instance.\r | |
517 | \r | |
518 | >>> Decimal('3.14') # string input\r | |
519 | Decimal('3.14')\r | |
520 | >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent)\r | |
521 | Decimal('3.14')\r | |
522 | >>> Decimal(314) # int or long\r | |
523 | Decimal('314')\r | |
524 | >>> Decimal(Decimal(314)) # another decimal instance\r | |
525 | Decimal('314')\r | |
526 | >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay\r | |
527 | Decimal('3.14')\r | |
528 | """\r | |
529 | \r | |
530 | # Note that the coefficient, self._int, is actually stored as\r | |
531 | # a string rather than as a tuple of digits. This speeds up\r | |
532 | # the "digits to integer" and "integer to digits" conversions\r | |
533 | # that are used in almost every arithmetic operation on\r | |
534 | # Decimals. This is an internal detail: the as_tuple function\r | |
535 | # and the Decimal constructor still deal with tuples of\r | |
536 | # digits.\r | |
537 | \r | |
538 | self = object.__new__(cls)\r | |
539 | \r | |
540 | # From a string\r | |
541 | # REs insist on real strings, so we can too.\r | |
542 | if isinstance(value, basestring):\r | |
543 | m = _parser(value.strip())\r | |
544 | if m is None:\r | |
545 | if context is None:\r | |
546 | context = getcontext()\r | |
547 | return context._raise_error(ConversionSyntax,\r | |
548 | "Invalid literal for Decimal: %r" % value)\r | |
549 | \r | |
550 | if m.group('sign') == "-":\r | |
551 | self._sign = 1\r | |
552 | else:\r | |
553 | self._sign = 0\r | |
554 | intpart = m.group('int')\r | |
555 | if intpart is not None:\r | |
556 | # finite number\r | |
557 | fracpart = m.group('frac') or ''\r | |
558 | exp = int(m.group('exp') or '0')\r | |
559 | self._int = str(int(intpart+fracpart))\r | |
560 | self._exp = exp - len(fracpart)\r | |
561 | self._is_special = False\r | |
562 | else:\r | |
563 | diag = m.group('diag')\r | |
564 | if diag is not None:\r | |
565 | # NaN\r | |
566 | self._int = str(int(diag or '0')).lstrip('0')\r | |
567 | if m.group('signal'):\r | |
568 | self._exp = 'N'\r | |
569 | else:\r | |
570 | self._exp = 'n'\r | |
571 | else:\r | |
572 | # infinity\r | |
573 | self._int = '0'\r | |
574 | self._exp = 'F'\r | |
575 | self._is_special = True\r | |
576 | return self\r | |
577 | \r | |
578 | # From an integer\r | |
579 | if isinstance(value, (int,long)):\r | |
580 | if value >= 0:\r | |
581 | self._sign = 0\r | |
582 | else:\r | |
583 | self._sign = 1\r | |
584 | self._exp = 0\r | |
585 | self._int = str(abs(value))\r | |
586 | self._is_special = False\r | |
587 | return self\r | |
588 | \r | |
589 | # From another decimal\r | |
590 | if isinstance(value, Decimal):\r | |
591 | self._exp = value._exp\r | |
592 | self._sign = value._sign\r | |
593 | self._int = value._int\r | |
594 | self._is_special = value._is_special\r | |
595 | return self\r | |
596 | \r | |
597 | # From an internal working value\r | |
598 | if isinstance(value, _WorkRep):\r | |
599 | self._sign = value.sign\r | |
600 | self._int = str(value.int)\r | |
601 | self._exp = int(value.exp)\r | |
602 | self._is_special = False\r | |
603 | return self\r | |
604 | \r | |
605 | # tuple/list conversion (possibly from as_tuple())\r | |
606 | if isinstance(value, (list,tuple)):\r | |
607 | if len(value) != 3:\r | |
608 | raise ValueError('Invalid tuple size in creation of Decimal '\r | |
609 | 'from list or tuple. The list or tuple '\r | |
610 | 'should have exactly three elements.')\r | |
611 | # process sign. The isinstance test rejects floats\r | |
612 | if not (isinstance(value[0], (int, long)) and value[0] in (0,1)):\r | |
613 | raise ValueError("Invalid sign. The first value in the tuple "\r | |
614 | "should be an integer; either 0 for a "\r | |
615 | "positive number or 1 for a negative number.")\r | |
616 | self._sign = value[0]\r | |
617 | if value[2] == 'F':\r | |
618 | # infinity: value[1] is ignored\r | |
619 | self._int = '0'\r | |
620 | self._exp = value[2]\r | |
621 | self._is_special = True\r | |
622 | else:\r | |
623 | # process and validate the digits in value[1]\r | |
624 | digits = []\r | |
625 | for digit in value[1]:\r | |
626 | if isinstance(digit, (int, long)) and 0 <= digit <= 9:\r | |
627 | # skip leading zeros\r | |
628 | if digits or digit != 0:\r | |
629 | digits.append(digit)\r | |
630 | else:\r | |
631 | raise ValueError("The second value in the tuple must "\r | |
632 | "be composed of integers in the range "\r | |
633 | "0 through 9.")\r | |
634 | if value[2] in ('n', 'N'):\r | |
635 | # NaN: digits form the diagnostic\r | |
636 | self._int = ''.join(map(str, digits))\r | |
637 | self._exp = value[2]\r | |
638 | self._is_special = True\r | |
639 | elif isinstance(value[2], (int, long)):\r | |
640 | # finite number: digits give the coefficient\r | |
641 | self._int = ''.join(map(str, digits or [0]))\r | |
642 | self._exp = value[2]\r | |
643 | self._is_special = False\r | |
644 | else:\r | |
645 | raise ValueError("The third value in the tuple must "\r | |
646 | "be an integer, or one of the "\r | |
647 | "strings 'F', 'n', 'N'.")\r | |
648 | return self\r | |
649 | \r | |
650 | if isinstance(value, float):\r | |
651 | value = Decimal.from_float(value)\r | |
652 | self._exp = value._exp\r | |
653 | self._sign = value._sign\r | |
654 | self._int = value._int\r | |
655 | self._is_special = value._is_special\r | |
656 | return self\r | |
657 | \r | |
658 | raise TypeError("Cannot convert %r to Decimal" % value)\r | |
659 | \r | |
660 | # @classmethod, but @decorator is not valid Python 2.3 syntax, so\r | |
661 | # don't use it (see notes on Py2.3 compatibility at top of file)\r | |
662 | def from_float(cls, f):\r | |
663 | """Converts a float to a decimal number, exactly.\r | |
664 | \r | |
665 | Note that Decimal.from_float(0.1) is not the same as Decimal('0.1').\r | |
666 | Since 0.1 is not exactly representable in binary floating point, the\r | |
667 | value is stored as the nearest representable value which is\r | |
668 | 0x1.999999999999ap-4. The exact equivalent of the value in decimal\r | |
669 | is 0.1000000000000000055511151231257827021181583404541015625.\r | |
670 | \r | |
671 | >>> Decimal.from_float(0.1)\r | |
672 | Decimal('0.1000000000000000055511151231257827021181583404541015625')\r | |
673 | >>> Decimal.from_float(float('nan'))\r | |
674 | Decimal('NaN')\r | |
675 | >>> Decimal.from_float(float('inf'))\r | |
676 | Decimal('Infinity')\r | |
677 | >>> Decimal.from_float(-float('inf'))\r | |
678 | Decimal('-Infinity')\r | |
679 | >>> Decimal.from_float(-0.0)\r | |
680 | Decimal('-0')\r | |
681 | \r | |
682 | """\r | |
683 | if isinstance(f, (int, long)): # handle integer inputs\r | |
684 | return cls(f)\r | |
685 | if _math.isinf(f) or _math.isnan(f): # raises TypeError if not a float\r | |
686 | return cls(repr(f))\r | |
687 | if _math.copysign(1.0, f) == 1.0:\r | |
688 | sign = 0\r | |
689 | else:\r | |
690 | sign = 1\r | |
691 | n, d = abs(f).as_integer_ratio()\r | |
692 | k = d.bit_length() - 1\r | |
693 | result = _dec_from_triple(sign, str(n*5**k), -k)\r | |
694 | if cls is Decimal:\r | |
695 | return result\r | |
696 | else:\r | |
697 | return cls(result)\r | |
698 | from_float = classmethod(from_float)\r | |
699 | \r | |
700 | def _isnan(self):\r | |
701 | """Returns whether the number is not actually one.\r | |
702 | \r | |
703 | 0 if a number\r | |
704 | 1 if NaN\r | |
705 | 2 if sNaN\r | |
706 | """\r | |
707 | if self._is_special:\r | |
708 | exp = self._exp\r | |
709 | if exp == 'n':\r | |
710 | return 1\r | |
711 | elif exp == 'N':\r | |
712 | return 2\r | |
713 | return 0\r | |
714 | \r | |
715 | def _isinfinity(self):\r | |
716 | """Returns whether the number is infinite\r | |
717 | \r | |
718 | 0 if finite or not a number\r | |
719 | 1 if +INF\r | |
720 | -1 if -INF\r | |
721 | """\r | |
722 | if self._exp == 'F':\r | |
723 | if self._sign:\r | |
724 | return -1\r | |
725 | return 1\r | |
726 | return 0\r | |
727 | \r | |
728 | def _check_nans(self, other=None, context=None):\r | |
729 | """Returns whether the number is not actually one.\r | |
730 | \r | |
731 | if self, other are sNaN, signal\r | |
732 | if self, other are NaN return nan\r | |
733 | return 0\r | |
734 | \r | |
735 | Done before operations.\r | |
736 | """\r | |
737 | \r | |
738 | self_is_nan = self._isnan()\r | |
739 | if other is None:\r | |
740 | other_is_nan = False\r | |
741 | else:\r | |
742 | other_is_nan = other._isnan()\r | |
743 | \r | |
744 | if self_is_nan or other_is_nan:\r | |
745 | if context is None:\r | |
746 | context = getcontext()\r | |
747 | \r | |
748 | if self_is_nan == 2:\r | |
749 | return context._raise_error(InvalidOperation, 'sNaN',\r | |
750 | self)\r | |
751 | if other_is_nan == 2:\r | |
752 | return context._raise_error(InvalidOperation, 'sNaN',\r | |
753 | other)\r | |
754 | if self_is_nan:\r | |
755 | return self._fix_nan(context)\r | |
756 | \r | |
757 | return other._fix_nan(context)\r | |
758 | return 0\r | |
759 | \r | |
760 | def _compare_check_nans(self, other, context):\r | |
761 | """Version of _check_nans used for the signaling comparisons\r | |
762 | compare_signal, __le__, __lt__, __ge__, __gt__.\r | |
763 | \r | |
764 | Signal InvalidOperation if either self or other is a (quiet\r | |
765 | or signaling) NaN. Signaling NaNs take precedence over quiet\r | |
766 | NaNs.\r | |
767 | \r | |
768 | Return 0 if neither operand is a NaN.\r | |
769 | \r | |
770 | """\r | |
771 | if context is None:\r | |
772 | context = getcontext()\r | |
773 | \r | |
774 | if self._is_special or other._is_special:\r | |
775 | if self.is_snan():\r | |
776 | return context._raise_error(InvalidOperation,\r | |
777 | 'comparison involving sNaN',\r | |
778 | self)\r | |
779 | elif other.is_snan():\r | |
780 | return context._raise_error(InvalidOperation,\r | |
781 | 'comparison involving sNaN',\r | |
782 | other)\r | |
783 | elif self.is_qnan():\r | |
784 | return context._raise_error(InvalidOperation,\r | |
785 | 'comparison involving NaN',\r | |
786 | self)\r | |
787 | elif other.is_qnan():\r | |
788 | return context._raise_error(InvalidOperation,\r | |
789 | 'comparison involving NaN',\r | |
790 | other)\r | |
791 | return 0\r | |
792 | \r | |
793 | def __nonzero__(self):\r | |
794 | """Return True if self is nonzero; otherwise return False.\r | |
795 | \r | |
796 | NaNs and infinities are considered nonzero.\r | |
797 | """\r | |
798 | return self._is_special or self._int != '0'\r | |
799 | \r | |
800 | def _cmp(self, other):\r | |
801 | """Compare the two non-NaN decimal instances self and other.\r | |
802 | \r | |
803 | Returns -1 if self < other, 0 if self == other and 1\r | |
804 | if self > other. This routine is for internal use only."""\r | |
805 | \r | |
806 | if self._is_special or other._is_special:\r | |
807 | self_inf = self._isinfinity()\r | |
808 | other_inf = other._isinfinity()\r | |
809 | if self_inf == other_inf:\r | |
810 | return 0\r | |
811 | elif self_inf < other_inf:\r | |
812 | return -1\r | |
813 | else:\r | |
814 | return 1\r | |
815 | \r | |
816 | # check for zeros; Decimal('0') == Decimal('-0')\r | |
817 | if not self:\r | |
818 | if not other:\r | |
819 | return 0\r | |
820 | else:\r | |
821 | return -((-1)**other._sign)\r | |
822 | if not other:\r | |
823 | return (-1)**self._sign\r | |
824 | \r | |
825 | # If different signs, neg one is less\r | |
826 | if other._sign < self._sign:\r | |
827 | return -1\r | |
828 | if self._sign < other._sign:\r | |
829 | return 1\r | |
830 | \r | |
831 | self_adjusted = self.adjusted()\r | |
832 | other_adjusted = other.adjusted()\r | |
833 | if self_adjusted == other_adjusted:\r | |
834 | self_padded = self._int + '0'*(self._exp - other._exp)\r | |
835 | other_padded = other._int + '0'*(other._exp - self._exp)\r | |
836 | if self_padded == other_padded:\r | |
837 | return 0\r | |
838 | elif self_padded < other_padded:\r | |
839 | return -(-1)**self._sign\r | |
840 | else:\r | |
841 | return (-1)**self._sign\r | |
842 | elif self_adjusted > other_adjusted:\r | |
843 | return (-1)**self._sign\r | |
844 | else: # self_adjusted < other_adjusted\r | |
845 | return -((-1)**self._sign)\r | |
846 | \r | |
847 | # Note: The Decimal standard doesn't cover rich comparisons for\r | |
848 | # Decimals. In particular, the specification is silent on the\r | |
849 | # subject of what should happen for a comparison involving a NaN.\r | |
850 | # We take the following approach:\r | |
851 | #\r | |
852 | # == comparisons involving a quiet NaN always return False\r | |
853 | # != comparisons involving a quiet NaN always return True\r | |
854 | # == or != comparisons involving a signaling NaN signal\r | |
855 | # InvalidOperation, and return False or True as above if the\r | |
856 | # InvalidOperation is not trapped.\r | |
857 | # <, >, <= and >= comparisons involving a (quiet or signaling)\r | |
858 | # NaN signal InvalidOperation, and return False if the\r | |
859 | # InvalidOperation is not trapped.\r | |
860 | #\r | |
861 | # This behavior is designed to conform as closely as possible to\r | |
862 | # that specified by IEEE 754.\r | |
863 | \r | |
864 | def __eq__(self, other, context=None):\r | |
865 | other = _convert_other(other, allow_float=True)\r | |
866 | if other is NotImplemented:\r | |
867 | return other\r | |
868 | if self._check_nans(other, context):\r | |
869 | return False\r | |
870 | return self._cmp(other) == 0\r | |
871 | \r | |
872 | def __ne__(self, other, context=None):\r | |
873 | other = _convert_other(other, allow_float=True)\r | |
874 | if other is NotImplemented:\r | |
875 | return other\r | |
876 | if self._check_nans(other, context):\r | |
877 | return True\r | |
878 | return self._cmp(other) != 0\r | |
879 | \r | |
880 | def __lt__(self, other, context=None):\r | |
881 | other = _convert_other(other, allow_float=True)\r | |
882 | if other is NotImplemented:\r | |
883 | return other\r | |
884 | ans = self._compare_check_nans(other, context)\r | |
885 | if ans:\r | |
886 | return False\r | |
887 | return self._cmp(other) < 0\r | |
888 | \r | |
889 | def __le__(self, other, context=None):\r | |
890 | other = _convert_other(other, allow_float=True)\r | |
891 | if other is NotImplemented:\r | |
892 | return other\r | |
893 | ans = self._compare_check_nans(other, context)\r | |
894 | if ans:\r | |
895 | return False\r | |
896 | return self._cmp(other) <= 0\r | |
897 | \r | |
898 | def __gt__(self, other, context=None):\r | |
899 | other = _convert_other(other, allow_float=True)\r | |
900 | if other is NotImplemented:\r | |
901 | return other\r | |
902 | ans = self._compare_check_nans(other, context)\r | |
903 | if ans:\r | |
904 | return False\r | |
905 | return self._cmp(other) > 0\r | |
906 | \r | |
907 | def __ge__(self, other, context=None):\r | |
908 | other = _convert_other(other, allow_float=True)\r | |
909 | if other is NotImplemented:\r | |
910 | return other\r | |
911 | ans = self._compare_check_nans(other, context)\r | |
912 | if ans:\r | |
913 | return False\r | |
914 | return self._cmp(other) >= 0\r | |
915 | \r | |
916 | def compare(self, other, context=None):\r | |
917 | """Compares one to another.\r | |
918 | \r | |
919 | -1 => a < b\r | |
920 | 0 => a = b\r | |
921 | 1 => a > b\r | |
922 | NaN => one is NaN\r | |
923 | Like __cmp__, but returns Decimal instances.\r | |
924 | """\r | |
925 | other = _convert_other(other, raiseit=True)\r | |
926 | \r | |
927 | # Compare(NaN, NaN) = NaN\r | |
928 | if (self._is_special or other and other._is_special):\r | |
929 | ans = self._check_nans(other, context)\r | |
930 | if ans:\r | |
931 | return ans\r | |
932 | \r | |
933 | return Decimal(self._cmp(other))\r | |
934 | \r | |
935 | def __hash__(self):\r | |
936 | """x.__hash__() <==> hash(x)"""\r | |
937 | # Decimal integers must hash the same as the ints\r | |
938 | #\r | |
939 | # The hash of a nonspecial noninteger Decimal must depend only\r | |
940 | # on the value of that Decimal, and not on its representation.\r | |
941 | # For example: hash(Decimal('100E-1')) == hash(Decimal('10')).\r | |
942 | \r | |
943 | # Equality comparisons involving signaling nans can raise an\r | |
944 | # exception; since equality checks are implicitly and\r | |
945 | # unpredictably used when checking set and dict membership, we\r | |
946 | # prevent signaling nans from being used as set elements or\r | |
947 | # dict keys by making __hash__ raise an exception.\r | |
948 | if self._is_special:\r | |
949 | if self.is_snan():\r | |
950 | raise TypeError('Cannot hash a signaling NaN value.')\r | |
951 | elif self.is_nan():\r | |
952 | # 0 to match hash(float('nan'))\r | |
953 | return 0\r | |
954 | else:\r | |
955 | # values chosen to match hash(float('inf')) and\r | |
956 | # hash(float('-inf')).\r | |
957 | if self._sign:\r | |
958 | return -271828\r | |
959 | else:\r | |
960 | return 314159\r | |
961 | \r | |
962 | # In Python 2.7, we're allowing comparisons (but not\r | |
963 | # arithmetic operations) between floats and Decimals; so if\r | |
964 | # a Decimal instance is exactly representable as a float then\r | |
965 | # its hash should match that of the float.\r | |
966 | self_as_float = float(self)\r | |
967 | if Decimal.from_float(self_as_float) == self:\r | |
968 | return hash(self_as_float)\r | |
969 | \r | |
970 | if self._isinteger():\r | |
971 | op = _WorkRep(self.to_integral_value())\r | |
972 | # to make computation feasible for Decimals with large\r | |
973 | # exponent, we use the fact that hash(n) == hash(m) for\r | |
974 | # any two nonzero integers n and m such that (i) n and m\r | |
975 | # have the same sign, and (ii) n is congruent to m modulo\r | |
976 | # 2**64-1. So we can replace hash((-1)**s*c*10**e) with\r | |
977 | # hash((-1)**s*c*pow(10, e, 2**64-1).\r | |
978 | return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1))\r | |
979 | # The value of a nonzero nonspecial Decimal instance is\r | |
980 | # faithfully represented by the triple consisting of its sign,\r | |
981 | # its adjusted exponent, and its coefficient with trailing\r | |
982 | # zeros removed.\r | |
983 | return hash((self._sign,\r | |
984 | self._exp+len(self._int),\r | |
985 | self._int.rstrip('0')))\r | |
986 | \r | |
987 | def as_tuple(self):\r | |
988 | """Represents the number as a triple tuple.\r | |
989 | \r | |
990 | To show the internals exactly as they are.\r | |
991 | """\r | |
992 | return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp)\r | |
993 | \r | |
994 | def __repr__(self):\r | |
995 | """Represents the number as an instance of Decimal."""\r | |
996 | # Invariant: eval(repr(d)) == d\r | |
997 | return "Decimal('%s')" % str(self)\r | |
998 | \r | |
999 | def __str__(self, eng=False, context=None):\r | |
1000 | """Return string representation of the number in scientific notation.\r | |
1001 | \r | |
1002 | Captures all of the information in the underlying representation.\r | |
1003 | """\r | |
1004 | \r | |
1005 | sign = ['', '-'][self._sign]\r | |
1006 | if self._is_special:\r | |
1007 | if self._exp == 'F':\r | |
1008 | return sign + 'Infinity'\r | |
1009 | elif self._exp == 'n':\r | |
1010 | return sign + 'NaN' + self._int\r | |
1011 | else: # self._exp == 'N'\r | |
1012 | return sign + 'sNaN' + self._int\r | |
1013 | \r | |
1014 | # number of digits of self._int to left of decimal point\r | |
1015 | leftdigits = self._exp + len(self._int)\r | |
1016 | \r | |
1017 | # dotplace is number of digits of self._int to the left of the\r | |
1018 | # decimal point in the mantissa of the output string (that is,\r | |
1019 | # after adjusting the exponent)\r | |
1020 | if self._exp <= 0 and leftdigits > -6:\r | |
1021 | # no exponent required\r | |
1022 | dotplace = leftdigits\r | |
1023 | elif not eng:\r | |
1024 | # usual scientific notation: 1 digit on left of the point\r | |
1025 | dotplace = 1\r | |
1026 | elif self._int == '0':\r | |
1027 | # engineering notation, zero\r | |
1028 | dotplace = (leftdigits + 1) % 3 - 1\r | |
1029 | else:\r | |
1030 | # engineering notation, nonzero\r | |
1031 | dotplace = (leftdigits - 1) % 3 + 1\r | |
1032 | \r | |
1033 | if dotplace <= 0:\r | |
1034 | intpart = '0'\r | |
1035 | fracpart = '.' + '0'*(-dotplace) + self._int\r | |
1036 | elif dotplace >= len(self._int):\r | |
1037 | intpart = self._int+'0'*(dotplace-len(self._int))\r | |
1038 | fracpart = ''\r | |
1039 | else:\r | |
1040 | intpart = self._int[:dotplace]\r | |
1041 | fracpart = '.' + self._int[dotplace:]\r | |
1042 | if leftdigits == dotplace:\r | |
1043 | exp = ''\r | |
1044 | else:\r | |
1045 | if context is None:\r | |
1046 | context = getcontext()\r | |
1047 | exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace)\r | |
1048 | \r | |
1049 | return sign + intpart + fracpart + exp\r | |
1050 | \r | |
1051 | def to_eng_string(self, context=None):\r | |
1052 | """Convert to engineering-type string.\r | |
1053 | \r | |
1054 | Engineering notation has an exponent which is a multiple of 3, so there\r | |
1055 | are up to 3 digits left of the decimal place.\r | |
1056 | \r | |
1057 | Same rules for when in exponential and when as a value as in __str__.\r | |
1058 | """\r | |
1059 | return self.__str__(eng=True, context=context)\r | |
1060 | \r | |
1061 | def __neg__(self, context=None):\r | |
1062 | """Returns a copy with the sign switched.\r | |
1063 | \r | |
1064 | Rounds, if it has reason.\r | |
1065 | """\r | |
1066 | if self._is_special:\r | |
1067 | ans = self._check_nans(context=context)\r | |
1068 | if ans:\r | |
1069 | return ans\r | |
1070 | \r | |
1071 | if context is None:\r | |
1072 | context = getcontext()\r | |
1073 | \r | |
1074 | if not self and context.rounding != ROUND_FLOOR:\r | |
1075 | # -Decimal('0') is Decimal('0'), not Decimal('-0'), except\r | |
1076 | # in ROUND_FLOOR rounding mode.\r | |
1077 | ans = self.copy_abs()\r | |
1078 | else:\r | |
1079 | ans = self.copy_negate()\r | |
1080 | \r | |
1081 | return ans._fix(context)\r | |
1082 | \r | |
1083 | def __pos__(self, context=None):\r | |
1084 | """Returns a copy, unless it is a sNaN.\r | |
1085 | \r | |
1086 | Rounds the number (if more then precision digits)\r | |
1087 | """\r | |
1088 | if self._is_special:\r | |
1089 | ans = self._check_nans(context=context)\r | |
1090 | if ans:\r | |
1091 | return ans\r | |
1092 | \r | |
1093 | if context is None:\r | |
1094 | context = getcontext()\r | |
1095 | \r | |
1096 | if not self and context.rounding != ROUND_FLOOR:\r | |
1097 | # + (-0) = 0, except in ROUND_FLOOR rounding mode.\r | |
1098 | ans = self.copy_abs()\r | |
1099 | else:\r | |
1100 | ans = Decimal(self)\r | |
1101 | \r | |
1102 | return ans._fix(context)\r | |
1103 | \r | |
1104 | def __abs__(self, round=True, context=None):\r | |
1105 | """Returns the absolute value of self.\r | |
1106 | \r | |
1107 | If the keyword argument 'round' is false, do not round. The\r | |
1108 | expression self.__abs__(round=False) is equivalent to\r | |
1109 | self.copy_abs().\r | |
1110 | """\r | |
1111 | if not round:\r | |
1112 | return self.copy_abs()\r | |
1113 | \r | |
1114 | if self._is_special:\r | |
1115 | ans = self._check_nans(context=context)\r | |
1116 | if ans:\r | |
1117 | return ans\r | |
1118 | \r | |
1119 | if self._sign:\r | |
1120 | ans = self.__neg__(context=context)\r | |
1121 | else:\r | |
1122 | ans = self.__pos__(context=context)\r | |
1123 | \r | |
1124 | return ans\r | |
1125 | \r | |
1126 | def __add__(self, other, context=None):\r | |
1127 | """Returns self + other.\r | |
1128 | \r | |
1129 | -INF + INF (or the reverse) cause InvalidOperation errors.\r | |
1130 | """\r | |
1131 | other = _convert_other(other)\r | |
1132 | if other is NotImplemented:\r | |
1133 | return other\r | |
1134 | \r | |
1135 | if context is None:\r | |
1136 | context = getcontext()\r | |
1137 | \r | |
1138 | if self._is_special or other._is_special:\r | |
1139 | ans = self._check_nans(other, context)\r | |
1140 | if ans:\r | |
1141 | return ans\r | |
1142 | \r | |
1143 | if self._isinfinity():\r | |
1144 | # If both INF, same sign => same as both, opposite => error.\r | |
1145 | if self._sign != other._sign and other._isinfinity():\r | |
1146 | return context._raise_error(InvalidOperation, '-INF + INF')\r | |
1147 | return Decimal(self)\r | |
1148 | if other._isinfinity():\r | |
1149 | return Decimal(other) # Can't both be infinity here\r | |
1150 | \r | |
1151 | exp = min(self._exp, other._exp)\r | |
1152 | negativezero = 0\r | |
1153 | if context.rounding == ROUND_FLOOR and self._sign != other._sign:\r | |
1154 | # If the answer is 0, the sign should be negative, in this case.\r | |
1155 | negativezero = 1\r | |
1156 | \r | |
1157 | if not self and not other:\r | |
1158 | sign = min(self._sign, other._sign)\r | |
1159 | if negativezero:\r | |
1160 | sign = 1\r | |
1161 | ans = _dec_from_triple(sign, '0', exp)\r | |
1162 | ans = ans._fix(context)\r | |
1163 | return ans\r | |
1164 | if not self:\r | |
1165 | exp = max(exp, other._exp - context.prec-1)\r | |
1166 | ans = other._rescale(exp, context.rounding)\r | |
1167 | ans = ans._fix(context)\r | |
1168 | return ans\r | |
1169 | if not other:\r | |
1170 | exp = max(exp, self._exp - context.prec-1)\r | |
1171 | ans = self._rescale(exp, context.rounding)\r | |
1172 | ans = ans._fix(context)\r | |
1173 | return ans\r | |
1174 | \r | |
1175 | op1 = _WorkRep(self)\r | |
1176 | op2 = _WorkRep(other)\r | |
1177 | op1, op2 = _normalize(op1, op2, context.prec)\r | |
1178 | \r | |
1179 | result = _WorkRep()\r | |
1180 | if op1.sign != op2.sign:\r | |
1181 | # Equal and opposite\r | |
1182 | if op1.int == op2.int:\r | |
1183 | ans = _dec_from_triple(negativezero, '0', exp)\r | |
1184 | ans = ans._fix(context)\r | |
1185 | return ans\r | |
1186 | if op1.int < op2.int:\r | |
1187 | op1, op2 = op2, op1\r | |
1188 | # OK, now abs(op1) > abs(op2)\r | |
1189 | if op1.sign == 1:\r | |
1190 | result.sign = 1\r | |
1191 | op1.sign, op2.sign = op2.sign, op1.sign\r | |
1192 | else:\r | |
1193 | result.sign = 0\r | |
1194 | # So we know the sign, and op1 > 0.\r | |
1195 | elif op1.sign == 1:\r | |
1196 | result.sign = 1\r | |
1197 | op1.sign, op2.sign = (0, 0)\r | |
1198 | else:\r | |
1199 | result.sign = 0\r | |
1200 | # Now, op1 > abs(op2) > 0\r | |
1201 | \r | |
1202 | if op2.sign == 0:\r | |
1203 | result.int = op1.int + op2.int\r | |
1204 | else:\r | |
1205 | result.int = op1.int - op2.int\r | |
1206 | \r | |
1207 | result.exp = op1.exp\r | |
1208 | ans = Decimal(result)\r | |
1209 | ans = ans._fix(context)\r | |
1210 | return ans\r | |
1211 | \r | |
1212 | __radd__ = __add__\r | |
1213 | \r | |
1214 | def __sub__(self, other, context=None):\r | |
1215 | """Return self - other"""\r | |
1216 | other = _convert_other(other)\r | |
1217 | if other is NotImplemented:\r | |
1218 | return other\r | |
1219 | \r | |
1220 | if self._is_special or other._is_special:\r | |
1221 | ans = self._check_nans(other, context=context)\r | |
1222 | if ans:\r | |
1223 | return ans\r | |
1224 | \r | |
1225 | # self - other is computed as self + other.copy_negate()\r | |
1226 | return self.__add__(other.copy_negate(), context=context)\r | |
1227 | \r | |
1228 | def __rsub__(self, other, context=None):\r | |
1229 | """Return other - self"""\r | |
1230 | other = _convert_other(other)\r | |
1231 | if other is NotImplemented:\r | |
1232 | return other\r | |
1233 | \r | |
1234 | return other.__sub__(self, context=context)\r | |
1235 | \r | |
1236 | def __mul__(self, other, context=None):\r | |
1237 | """Return self * other.\r | |
1238 | \r | |
1239 | (+-) INF * 0 (or its reverse) raise InvalidOperation.\r | |
1240 | """\r | |
1241 | other = _convert_other(other)\r | |
1242 | if other is NotImplemented:\r | |
1243 | return other\r | |
1244 | \r | |
1245 | if context is None:\r | |
1246 | context = getcontext()\r | |
1247 | \r | |
1248 | resultsign = self._sign ^ other._sign\r | |
1249 | \r | |
1250 | if self._is_special or other._is_special:\r | |
1251 | ans = self._check_nans(other, context)\r | |
1252 | if ans:\r | |
1253 | return ans\r | |
1254 | \r | |
1255 | if self._isinfinity():\r | |
1256 | if not other:\r | |
1257 | return context._raise_error(InvalidOperation, '(+-)INF * 0')\r | |
1258 | return _SignedInfinity[resultsign]\r | |
1259 | \r | |
1260 | if other._isinfinity():\r | |
1261 | if not self:\r | |
1262 | return context._raise_error(InvalidOperation, '0 * (+-)INF')\r | |
1263 | return _SignedInfinity[resultsign]\r | |
1264 | \r | |
1265 | resultexp = self._exp + other._exp\r | |
1266 | \r | |
1267 | # Special case for multiplying by zero\r | |
1268 | if not self or not other:\r | |
1269 | ans = _dec_from_triple(resultsign, '0', resultexp)\r | |
1270 | # Fixing in case the exponent is out of bounds\r | |
1271 | ans = ans._fix(context)\r | |
1272 | return ans\r | |
1273 | \r | |
1274 | # Special case for multiplying by power of 10\r | |
1275 | if self._int == '1':\r | |
1276 | ans = _dec_from_triple(resultsign, other._int, resultexp)\r | |
1277 | ans = ans._fix(context)\r | |
1278 | return ans\r | |
1279 | if other._int == '1':\r | |
1280 | ans = _dec_from_triple(resultsign, self._int, resultexp)\r | |
1281 | ans = ans._fix(context)\r | |
1282 | return ans\r | |
1283 | \r | |
1284 | op1 = _WorkRep(self)\r | |
1285 | op2 = _WorkRep(other)\r | |
1286 | \r | |
1287 | ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp)\r | |
1288 | ans = ans._fix(context)\r | |
1289 | \r | |
1290 | return ans\r | |
1291 | __rmul__ = __mul__\r | |
1292 | \r | |
1293 | def __truediv__(self, other, context=None):\r | |
1294 | """Return self / other."""\r | |
1295 | other = _convert_other(other)\r | |
1296 | if other is NotImplemented:\r | |
1297 | return NotImplemented\r | |
1298 | \r | |
1299 | if context is None:\r | |
1300 | context = getcontext()\r | |
1301 | \r | |
1302 | sign = self._sign ^ other._sign\r | |
1303 | \r | |
1304 | if self._is_special or other._is_special:\r | |
1305 | ans = self._check_nans(other, context)\r | |
1306 | if ans:\r | |
1307 | return ans\r | |
1308 | \r | |
1309 | if self._isinfinity() and other._isinfinity():\r | |
1310 | return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')\r | |
1311 | \r | |
1312 | if self._isinfinity():\r | |
1313 | return _SignedInfinity[sign]\r | |
1314 | \r | |
1315 | if other._isinfinity():\r | |
1316 | context._raise_error(Clamped, 'Division by infinity')\r | |
1317 | return _dec_from_triple(sign, '0', context.Etiny())\r | |
1318 | \r | |
1319 | # Special cases for zeroes\r | |
1320 | if not other:\r | |
1321 | if not self:\r | |
1322 | return context._raise_error(DivisionUndefined, '0 / 0')\r | |
1323 | return context._raise_error(DivisionByZero, 'x / 0', sign)\r | |
1324 | \r | |
1325 | if not self:\r | |
1326 | exp = self._exp - other._exp\r | |
1327 | coeff = 0\r | |
1328 | else:\r | |
1329 | # OK, so neither = 0, INF or NaN\r | |
1330 | shift = len(other._int) - len(self._int) + context.prec + 1\r | |
1331 | exp = self._exp - other._exp - shift\r | |
1332 | op1 = _WorkRep(self)\r | |
1333 | op2 = _WorkRep(other)\r | |
1334 | if shift >= 0:\r | |
1335 | coeff, remainder = divmod(op1.int * 10**shift, op2.int)\r | |
1336 | else:\r | |
1337 | coeff, remainder = divmod(op1.int, op2.int * 10**-shift)\r | |
1338 | if remainder:\r | |
1339 | # result is not exact; adjust to ensure correct rounding\r | |
1340 | if coeff % 5 == 0:\r | |
1341 | coeff += 1\r | |
1342 | else:\r | |
1343 | # result is exact; get as close to ideal exponent as possible\r | |
1344 | ideal_exp = self._exp - other._exp\r | |
1345 | while exp < ideal_exp and coeff % 10 == 0:\r | |
1346 | coeff //= 10\r | |
1347 | exp += 1\r | |
1348 | \r | |
1349 | ans = _dec_from_triple(sign, str(coeff), exp)\r | |
1350 | return ans._fix(context)\r | |
1351 | \r | |
1352 | def _divide(self, other, context):\r | |
1353 | """Return (self // other, self % other), to context.prec precision.\r | |
1354 | \r | |
1355 | Assumes that neither self nor other is a NaN, that self is not\r | |
1356 | infinite and that other is nonzero.\r | |
1357 | """\r | |
1358 | sign = self._sign ^ other._sign\r | |
1359 | if other._isinfinity():\r | |
1360 | ideal_exp = self._exp\r | |
1361 | else:\r | |
1362 | ideal_exp = min(self._exp, other._exp)\r | |
1363 | \r | |
1364 | expdiff = self.adjusted() - other.adjusted()\r | |
1365 | if not self or other._isinfinity() or expdiff <= -2:\r | |
1366 | return (_dec_from_triple(sign, '0', 0),\r | |
1367 | self._rescale(ideal_exp, context.rounding))\r | |
1368 | if expdiff <= context.prec:\r | |
1369 | op1 = _WorkRep(self)\r | |
1370 | op2 = _WorkRep(other)\r | |
1371 | if op1.exp >= op2.exp:\r | |
1372 | op1.int *= 10**(op1.exp - op2.exp)\r | |
1373 | else:\r | |
1374 | op2.int *= 10**(op2.exp - op1.exp)\r | |
1375 | q, r = divmod(op1.int, op2.int)\r | |
1376 | if q < 10**context.prec:\r | |
1377 | return (_dec_from_triple(sign, str(q), 0),\r | |
1378 | _dec_from_triple(self._sign, str(r), ideal_exp))\r | |
1379 | \r | |
1380 | # Here the quotient is too large to be representable\r | |
1381 | ans = context._raise_error(DivisionImpossible,\r | |
1382 | 'quotient too large in //, % or divmod')\r | |
1383 | return ans, ans\r | |
1384 | \r | |
1385 | def __rtruediv__(self, other, context=None):\r | |
1386 | """Swaps self/other and returns __truediv__."""\r | |
1387 | other = _convert_other(other)\r | |
1388 | if other is NotImplemented:\r | |
1389 | return other\r | |
1390 | return other.__truediv__(self, context=context)\r | |
1391 | \r | |
1392 | __div__ = __truediv__\r | |
1393 | __rdiv__ = __rtruediv__\r | |
1394 | \r | |
1395 | def __divmod__(self, other, context=None):\r | |
1396 | """\r | |
1397 | Return (self // other, self % other)\r | |
1398 | """\r | |
1399 | other = _convert_other(other)\r | |
1400 | if other is NotImplemented:\r | |
1401 | return other\r | |
1402 | \r | |
1403 | if context is None:\r | |
1404 | context = getcontext()\r | |
1405 | \r | |
1406 | ans = self._check_nans(other, context)\r | |
1407 | if ans:\r | |
1408 | return (ans, ans)\r | |
1409 | \r | |
1410 | sign = self._sign ^ other._sign\r | |
1411 | if self._isinfinity():\r | |
1412 | if other._isinfinity():\r | |
1413 | ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')\r | |
1414 | return ans, ans\r | |
1415 | else:\r | |
1416 | return (_SignedInfinity[sign],\r | |
1417 | context._raise_error(InvalidOperation, 'INF % x'))\r | |
1418 | \r | |
1419 | if not other:\r | |
1420 | if not self:\r | |
1421 | ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')\r | |
1422 | return ans, ans\r | |
1423 | else:\r | |
1424 | return (context._raise_error(DivisionByZero, 'x // 0', sign),\r | |
1425 | context._raise_error(InvalidOperation, 'x % 0'))\r | |
1426 | \r | |
1427 | quotient, remainder = self._divide(other, context)\r | |
1428 | remainder = remainder._fix(context)\r | |
1429 | return quotient, remainder\r | |
1430 | \r | |
1431 | def __rdivmod__(self, other, context=None):\r | |
1432 | """Swaps self/other and returns __divmod__."""\r | |
1433 | other = _convert_other(other)\r | |
1434 | if other is NotImplemented:\r | |
1435 | return other\r | |
1436 | return other.__divmod__(self, context=context)\r | |
1437 | \r | |
1438 | def __mod__(self, other, context=None):\r | |
1439 | """\r | |
1440 | self % other\r | |
1441 | """\r | |
1442 | other = _convert_other(other)\r | |
1443 | if other is NotImplemented:\r | |
1444 | return other\r | |
1445 | \r | |
1446 | if context is None:\r | |
1447 | context = getcontext()\r | |
1448 | \r | |
1449 | ans = self._check_nans(other, context)\r | |
1450 | if ans:\r | |
1451 | return ans\r | |
1452 | \r | |
1453 | if self._isinfinity():\r | |
1454 | return context._raise_error(InvalidOperation, 'INF % x')\r | |
1455 | elif not other:\r | |
1456 | if self:\r | |
1457 | return context._raise_error(InvalidOperation, 'x % 0')\r | |
1458 | else:\r | |
1459 | return context._raise_error(DivisionUndefined, '0 % 0')\r | |
1460 | \r | |
1461 | remainder = self._divide(other, context)[1]\r | |
1462 | remainder = remainder._fix(context)\r | |
1463 | return remainder\r | |
1464 | \r | |
1465 | def __rmod__(self, other, context=None):\r | |
1466 | """Swaps self/other and returns __mod__."""\r | |
1467 | other = _convert_other(other)\r | |
1468 | if other is NotImplemented:\r | |
1469 | return other\r | |
1470 | return other.__mod__(self, context=context)\r | |
1471 | \r | |
1472 | def remainder_near(self, other, context=None):\r | |
1473 | """\r | |
1474 | Remainder nearest to 0- abs(remainder-near) <= other/2\r | |
1475 | """\r | |
1476 | if context is None:\r | |
1477 | context = getcontext()\r | |
1478 | \r | |
1479 | other = _convert_other(other, raiseit=True)\r | |
1480 | \r | |
1481 | ans = self._check_nans(other, context)\r | |
1482 | if ans:\r | |
1483 | return ans\r | |
1484 | \r | |
1485 | # self == +/-infinity -> InvalidOperation\r | |
1486 | if self._isinfinity():\r | |
1487 | return context._raise_error(InvalidOperation,\r | |
1488 | 'remainder_near(infinity, x)')\r | |
1489 | \r | |
1490 | # other == 0 -> either InvalidOperation or DivisionUndefined\r | |
1491 | if not other:\r | |
1492 | if self:\r | |
1493 | return context._raise_error(InvalidOperation,\r | |
1494 | 'remainder_near(x, 0)')\r | |
1495 | else:\r | |
1496 | return context._raise_error(DivisionUndefined,\r | |
1497 | 'remainder_near(0, 0)')\r | |
1498 | \r | |
1499 | # other = +/-infinity -> remainder = self\r | |
1500 | if other._isinfinity():\r | |
1501 | ans = Decimal(self)\r | |
1502 | return ans._fix(context)\r | |
1503 | \r | |
1504 | # self = 0 -> remainder = self, with ideal exponent\r | |
1505 | ideal_exponent = min(self._exp, other._exp)\r | |
1506 | if not self:\r | |
1507 | ans = _dec_from_triple(self._sign, '0', ideal_exponent)\r | |
1508 | return ans._fix(context)\r | |
1509 | \r | |
1510 | # catch most cases of large or small quotient\r | |
1511 | expdiff = self.adjusted() - other.adjusted()\r | |
1512 | if expdiff >= context.prec + 1:\r | |
1513 | # expdiff >= prec+1 => abs(self/other) > 10**prec\r | |
1514 | return context._raise_error(DivisionImpossible)\r | |
1515 | if expdiff <= -2:\r | |
1516 | # expdiff <= -2 => abs(self/other) < 0.1\r | |
1517 | ans = self._rescale(ideal_exponent, context.rounding)\r | |
1518 | return ans._fix(context)\r | |
1519 | \r | |
1520 | # adjust both arguments to have the same exponent, then divide\r | |
1521 | op1 = _WorkRep(self)\r | |
1522 | op2 = _WorkRep(other)\r | |
1523 | if op1.exp >= op2.exp:\r | |
1524 | op1.int *= 10**(op1.exp - op2.exp)\r | |
1525 | else:\r | |
1526 | op2.int *= 10**(op2.exp - op1.exp)\r | |
1527 | q, r = divmod(op1.int, op2.int)\r | |
1528 | # remainder is r*10**ideal_exponent; other is +/-op2.int *\r | |
1529 | # 10**ideal_exponent. Apply correction to ensure that\r | |
1530 | # abs(remainder) <= abs(other)/2\r | |
1531 | if 2*r + (q&1) > op2.int:\r | |
1532 | r -= op2.int\r | |
1533 | q += 1\r | |
1534 | \r | |
1535 | if q >= 10**context.prec:\r | |
1536 | return context._raise_error(DivisionImpossible)\r | |
1537 | \r | |
1538 | # result has same sign as self unless r is negative\r | |
1539 | sign = self._sign\r | |
1540 | if r < 0:\r | |
1541 | sign = 1-sign\r | |
1542 | r = -r\r | |
1543 | \r | |
1544 | ans = _dec_from_triple(sign, str(r), ideal_exponent)\r | |
1545 | return ans._fix(context)\r | |
1546 | \r | |
1547 | def __floordiv__(self, other, context=None):\r | |
1548 | """self // other"""\r | |
1549 | other = _convert_other(other)\r | |
1550 | if other is NotImplemented:\r | |
1551 | return other\r | |
1552 | \r | |
1553 | if context is None:\r | |
1554 | context = getcontext()\r | |
1555 | \r | |
1556 | ans = self._check_nans(other, context)\r | |
1557 | if ans:\r | |
1558 | return ans\r | |
1559 | \r | |
1560 | if self._isinfinity():\r | |
1561 | if other._isinfinity():\r | |
1562 | return context._raise_error(InvalidOperation, 'INF // INF')\r | |
1563 | else:\r | |
1564 | return _SignedInfinity[self._sign ^ other._sign]\r | |
1565 | \r | |
1566 | if not other:\r | |
1567 | if self:\r | |
1568 | return context._raise_error(DivisionByZero, 'x // 0',\r | |
1569 | self._sign ^ other._sign)\r | |
1570 | else:\r | |
1571 | return context._raise_error(DivisionUndefined, '0 // 0')\r | |
1572 | \r | |
1573 | return self._divide(other, context)[0]\r | |
1574 | \r | |
1575 | def __rfloordiv__(self, other, context=None):\r | |
1576 | """Swaps self/other and returns __floordiv__."""\r | |
1577 | other = _convert_other(other)\r | |
1578 | if other is NotImplemented:\r | |
1579 | return other\r | |
1580 | return other.__floordiv__(self, context=context)\r | |
1581 | \r | |
1582 | def __float__(self):\r | |
1583 | """Float representation."""\r | |
1584 | return float(str(self))\r | |
1585 | \r | |
1586 | def __int__(self):\r | |
1587 | """Converts self to an int, truncating if necessary."""\r | |
1588 | if self._is_special:\r | |
1589 | if self._isnan():\r | |
1590 | raise ValueError("Cannot convert NaN to integer")\r | |
1591 | elif self._isinfinity():\r | |
1592 | raise OverflowError("Cannot convert infinity to integer")\r | |
1593 | s = (-1)**self._sign\r | |
1594 | if self._exp >= 0:\r | |
1595 | return s*int(self._int)*10**self._exp\r | |
1596 | else:\r | |
1597 | return s*int(self._int[:self._exp] or '0')\r | |
1598 | \r | |
1599 | __trunc__ = __int__\r | |
1600 | \r | |
1601 | def real(self):\r | |
1602 | return self\r | |
1603 | real = property(real)\r | |
1604 | \r | |
1605 | def imag(self):\r | |
1606 | return Decimal(0)\r | |
1607 | imag = property(imag)\r | |
1608 | \r | |
1609 | def conjugate(self):\r | |
1610 | return self\r | |
1611 | \r | |
1612 | def __complex__(self):\r | |
1613 | return complex(float(self))\r | |
1614 | \r | |
1615 | def __long__(self):\r | |
1616 | """Converts to a long.\r | |
1617 | \r | |
1618 | Equivalent to long(int(self))\r | |
1619 | """\r | |
1620 | return long(self.__int__())\r | |
1621 | \r | |
1622 | def _fix_nan(self, context):\r | |
1623 | """Decapitate the payload of a NaN to fit the context"""\r | |
1624 | payload = self._int\r | |
1625 | \r | |
1626 | # maximum length of payload is precision if _clamp=0,\r | |
1627 | # precision-1 if _clamp=1.\r | |
1628 | max_payload_len = context.prec - context._clamp\r | |
1629 | if len(payload) > max_payload_len:\r | |
1630 | payload = payload[len(payload)-max_payload_len:].lstrip('0')\r | |
1631 | return _dec_from_triple(self._sign, payload, self._exp, True)\r | |
1632 | return Decimal(self)\r | |
1633 | \r | |
1634 | def _fix(self, context):\r | |
1635 | """Round if it is necessary to keep self within prec precision.\r | |
1636 | \r | |
1637 | Rounds and fixes the exponent. Does not raise on a sNaN.\r | |
1638 | \r | |
1639 | Arguments:\r | |
1640 | self - Decimal instance\r | |
1641 | context - context used.\r | |
1642 | """\r | |
1643 | \r | |
1644 | if self._is_special:\r | |
1645 | if self._isnan():\r | |
1646 | # decapitate payload if necessary\r | |
1647 | return self._fix_nan(context)\r | |
1648 | else:\r | |
1649 | # self is +/-Infinity; return unaltered\r | |
1650 | return Decimal(self)\r | |
1651 | \r | |
1652 | # if self is zero then exponent should be between Etiny and\r | |
1653 | # Emax if _clamp==0, and between Etiny and Etop if _clamp==1.\r | |
1654 | Etiny = context.Etiny()\r | |
1655 | Etop = context.Etop()\r | |
1656 | if not self:\r | |
1657 | exp_max = [context.Emax, Etop][context._clamp]\r | |
1658 | new_exp = min(max(self._exp, Etiny), exp_max)\r | |
1659 | if new_exp != self._exp:\r | |
1660 | context._raise_error(Clamped)\r | |
1661 | return _dec_from_triple(self._sign, '0', new_exp)\r | |
1662 | else:\r | |
1663 | return Decimal(self)\r | |
1664 | \r | |
1665 | # exp_min is the smallest allowable exponent of the result,\r | |
1666 | # equal to max(self.adjusted()-context.prec+1, Etiny)\r | |
1667 | exp_min = len(self._int) + self._exp - context.prec\r | |
1668 | if exp_min > Etop:\r | |
1669 | # overflow: exp_min > Etop iff self.adjusted() > Emax\r | |
1670 | ans = context._raise_error(Overflow, 'above Emax', self._sign)\r | |
1671 | context._raise_error(Inexact)\r | |
1672 | context._raise_error(Rounded)\r | |
1673 | return ans\r | |
1674 | \r | |
1675 | self_is_subnormal = exp_min < Etiny\r | |
1676 | if self_is_subnormal:\r | |
1677 | exp_min = Etiny\r | |
1678 | \r | |
1679 | # round if self has too many digits\r | |
1680 | if self._exp < exp_min:\r | |
1681 | digits = len(self._int) + self._exp - exp_min\r | |
1682 | if digits < 0:\r | |
1683 | self = _dec_from_triple(self._sign, '1', exp_min-1)\r | |
1684 | digits = 0\r | |
1685 | rounding_method = self._pick_rounding_function[context.rounding]\r | |
1686 | changed = rounding_method(self, digits)\r | |
1687 | coeff = self._int[:digits] or '0'\r | |
1688 | if changed > 0:\r | |
1689 | coeff = str(int(coeff)+1)\r | |
1690 | if len(coeff) > context.prec:\r | |
1691 | coeff = coeff[:-1]\r | |
1692 | exp_min += 1\r | |
1693 | \r | |
1694 | # check whether the rounding pushed the exponent out of range\r | |
1695 | if exp_min > Etop:\r | |
1696 | ans = context._raise_error(Overflow, 'above Emax', self._sign)\r | |
1697 | else:\r | |
1698 | ans = _dec_from_triple(self._sign, coeff, exp_min)\r | |
1699 | \r | |
1700 | # raise the appropriate signals, taking care to respect\r | |
1701 | # the precedence described in the specification\r | |
1702 | if changed and self_is_subnormal:\r | |
1703 | context._raise_error(Underflow)\r | |
1704 | if self_is_subnormal:\r | |
1705 | context._raise_error(Subnormal)\r | |
1706 | if changed:\r | |
1707 | context._raise_error(Inexact)\r | |
1708 | context._raise_error(Rounded)\r | |
1709 | if not ans:\r | |
1710 | # raise Clamped on underflow to 0\r | |
1711 | context._raise_error(Clamped)\r | |
1712 | return ans\r | |
1713 | \r | |
1714 | if self_is_subnormal:\r | |
1715 | context._raise_error(Subnormal)\r | |
1716 | \r | |
1717 | # fold down if _clamp == 1 and self has too few digits\r | |
1718 | if context._clamp == 1 and self._exp > Etop:\r | |
1719 | context._raise_error(Clamped)\r | |
1720 | self_padded = self._int + '0'*(self._exp - Etop)\r | |
1721 | return _dec_from_triple(self._sign, self_padded, Etop)\r | |
1722 | \r | |
1723 | # here self was representable to begin with; return unchanged\r | |
1724 | return Decimal(self)\r | |
1725 | \r | |
1726 | # for each of the rounding functions below:\r | |
1727 | # self is a finite, nonzero Decimal\r | |
1728 | # prec is an integer satisfying 0 <= prec < len(self._int)\r | |
1729 | #\r | |
1730 | # each function returns either -1, 0, or 1, as follows:\r | |
1731 | # 1 indicates that self should be rounded up (away from zero)\r | |
1732 | # 0 indicates that self should be truncated, and that all the\r | |
1733 | # digits to be truncated are zeros (so the value is unchanged)\r | |
1734 | # -1 indicates that there are nonzero digits to be truncated\r | |
1735 | \r | |
1736 | def _round_down(self, prec):\r | |
1737 | """Also known as round-towards-0, truncate."""\r | |
1738 | if _all_zeros(self._int, prec):\r | |
1739 | return 0\r | |
1740 | else:\r | |
1741 | return -1\r | |
1742 | \r | |
1743 | def _round_up(self, prec):\r | |
1744 | """Rounds away from 0."""\r | |
1745 | return -self._round_down(prec)\r | |
1746 | \r | |
1747 | def _round_half_up(self, prec):\r | |
1748 | """Rounds 5 up (away from 0)"""\r | |
1749 | if self._int[prec] in '56789':\r | |
1750 | return 1\r | |
1751 | elif _all_zeros(self._int, prec):\r | |
1752 | return 0\r | |
1753 | else:\r | |
1754 | return -1\r | |
1755 | \r | |
1756 | def _round_half_down(self, prec):\r | |
1757 | """Round 5 down"""\r | |
1758 | if _exact_half(self._int, prec):\r | |
1759 | return -1\r | |
1760 | else:\r | |
1761 | return self._round_half_up(prec)\r | |
1762 | \r | |
1763 | def _round_half_even(self, prec):\r | |
1764 | """Round 5 to even, rest to nearest."""\r | |
1765 | if _exact_half(self._int, prec) and \\r | |
1766 | (prec == 0 or self._int[prec-1] in '02468'):\r | |
1767 | return -1\r | |
1768 | else:\r | |
1769 | return self._round_half_up(prec)\r | |
1770 | \r | |
1771 | def _round_ceiling(self, prec):\r | |
1772 | """Rounds up (not away from 0 if negative.)"""\r | |
1773 | if self._sign:\r | |
1774 | return self._round_down(prec)\r | |
1775 | else:\r | |
1776 | return -self._round_down(prec)\r | |
1777 | \r | |
1778 | def _round_floor(self, prec):\r | |
1779 | """Rounds down (not towards 0 if negative)"""\r | |
1780 | if not self._sign:\r | |
1781 | return self._round_down(prec)\r | |
1782 | else:\r | |
1783 | return -self._round_down(prec)\r | |
1784 | \r | |
1785 | def _round_05up(self, prec):\r | |
1786 | """Round down unless digit prec-1 is 0 or 5."""\r | |
1787 | if prec and self._int[prec-1] not in '05':\r | |
1788 | return self._round_down(prec)\r | |
1789 | else:\r | |
1790 | return -self._round_down(prec)\r | |
1791 | \r | |
1792 | _pick_rounding_function = dict(\r | |
1793 | ROUND_DOWN = _round_down,\r | |
1794 | ROUND_UP = _round_up,\r | |
1795 | ROUND_HALF_UP = _round_half_up,\r | |
1796 | ROUND_HALF_DOWN = _round_half_down,\r | |
1797 | ROUND_HALF_EVEN = _round_half_even,\r | |
1798 | ROUND_CEILING = _round_ceiling,\r | |
1799 | ROUND_FLOOR = _round_floor,\r | |
1800 | ROUND_05UP = _round_05up,\r | |
1801 | )\r | |
1802 | \r | |
1803 | def fma(self, other, third, context=None):\r | |
1804 | """Fused multiply-add.\r | |
1805 | \r | |
1806 | Returns self*other+third with no rounding of the intermediate\r | |
1807 | product self*other.\r | |
1808 | \r | |
1809 | self and other are multiplied together, with no rounding of\r | |
1810 | the result. The third operand is then added to the result,\r | |
1811 | and a single final rounding is performed.\r | |
1812 | """\r | |
1813 | \r | |
1814 | other = _convert_other(other, raiseit=True)\r | |
1815 | \r | |
1816 | # compute product; raise InvalidOperation if either operand is\r | |
1817 | # a signaling NaN or if the product is zero times infinity.\r | |
1818 | if self._is_special or other._is_special:\r | |
1819 | if context is None:\r | |
1820 | context = getcontext()\r | |
1821 | if self._exp == 'N':\r | |
1822 | return context._raise_error(InvalidOperation, 'sNaN', self)\r | |
1823 | if other._exp == 'N':\r | |
1824 | return context._raise_error(InvalidOperation, 'sNaN', other)\r | |
1825 | if self._exp == 'n':\r | |
1826 | product = self\r | |
1827 | elif other._exp == 'n':\r | |
1828 | product = other\r | |
1829 | elif self._exp == 'F':\r | |
1830 | if not other:\r | |
1831 | return context._raise_error(InvalidOperation,\r | |
1832 | 'INF * 0 in fma')\r | |
1833 | product = _SignedInfinity[self._sign ^ other._sign]\r | |
1834 | elif other._exp == 'F':\r | |
1835 | if not self:\r | |
1836 | return context._raise_error(InvalidOperation,\r | |
1837 | '0 * INF in fma')\r | |
1838 | product = _SignedInfinity[self._sign ^ other._sign]\r | |
1839 | else:\r | |
1840 | product = _dec_from_triple(self._sign ^ other._sign,\r | |
1841 | str(int(self._int) * int(other._int)),\r | |
1842 | self._exp + other._exp)\r | |
1843 | \r | |
1844 | third = _convert_other(third, raiseit=True)\r | |
1845 | return product.__add__(third, context)\r | |
1846 | \r | |
1847 | def _power_modulo(self, other, modulo, context=None):\r | |
1848 | """Three argument version of __pow__"""\r | |
1849 | \r | |
1850 | # if can't convert other and modulo to Decimal, raise\r | |
1851 | # TypeError; there's no point returning NotImplemented (no\r | |
1852 | # equivalent of __rpow__ for three argument pow)\r | |
1853 | other = _convert_other(other, raiseit=True)\r | |
1854 | modulo = _convert_other(modulo, raiseit=True)\r | |
1855 | \r | |
1856 | if context is None:\r | |
1857 | context = getcontext()\r | |
1858 | \r | |
1859 | # deal with NaNs: if there are any sNaNs then first one wins,\r | |
1860 | # (i.e. behaviour for NaNs is identical to that of fma)\r | |
1861 | self_is_nan = self._isnan()\r | |
1862 | other_is_nan = other._isnan()\r | |
1863 | modulo_is_nan = modulo._isnan()\r | |
1864 | if self_is_nan or other_is_nan or modulo_is_nan:\r | |
1865 | if self_is_nan == 2:\r | |
1866 | return context._raise_error(InvalidOperation, 'sNaN',\r | |
1867 | self)\r | |
1868 | if other_is_nan == 2:\r | |
1869 | return context._raise_error(InvalidOperation, 'sNaN',\r | |
1870 | other)\r | |
1871 | if modulo_is_nan == 2:\r | |
1872 | return context._raise_error(InvalidOperation, 'sNaN',\r | |
1873 | modulo)\r | |
1874 | if self_is_nan:\r | |
1875 | return self._fix_nan(context)\r | |
1876 | if other_is_nan:\r | |
1877 | return other._fix_nan(context)\r | |
1878 | return modulo._fix_nan(context)\r | |
1879 | \r | |
1880 | # check inputs: we apply same restrictions as Python's pow()\r | |
1881 | if not (self._isinteger() and\r | |
1882 | other._isinteger() and\r | |
1883 | modulo._isinteger()):\r | |
1884 | return context._raise_error(InvalidOperation,\r | |
1885 | 'pow() 3rd argument not allowed '\r | |
1886 | 'unless all arguments are integers')\r | |
1887 | if other < 0:\r | |
1888 | return context._raise_error(InvalidOperation,\r | |
1889 | 'pow() 2nd argument cannot be '\r | |
1890 | 'negative when 3rd argument specified')\r | |
1891 | if not modulo:\r | |
1892 | return context._raise_error(InvalidOperation,\r | |
1893 | 'pow() 3rd argument cannot be 0')\r | |
1894 | \r | |
1895 | # additional restriction for decimal: the modulus must be less\r | |
1896 | # than 10**prec in absolute value\r | |
1897 | if modulo.adjusted() >= context.prec:\r | |
1898 | return context._raise_error(InvalidOperation,\r | |
1899 | 'insufficient precision: pow() 3rd '\r | |
1900 | 'argument must not have more than '\r | |
1901 | 'precision digits')\r | |
1902 | \r | |
1903 | # define 0**0 == NaN, for consistency with two-argument pow\r | |
1904 | # (even though it hurts!)\r | |
1905 | if not other and not self:\r | |
1906 | return context._raise_error(InvalidOperation,\r | |
1907 | 'at least one of pow() 1st argument '\r | |
1908 | 'and 2nd argument must be nonzero ;'\r | |
1909 | '0**0 is not defined')\r | |
1910 | \r | |
1911 | # compute sign of result\r | |
1912 | if other._iseven():\r | |
1913 | sign = 0\r | |
1914 | else:\r | |
1915 | sign = self._sign\r | |
1916 | \r | |
1917 | # convert modulo to a Python integer, and self and other to\r | |
1918 | # Decimal integers (i.e. force their exponents to be >= 0)\r | |
1919 | modulo = abs(int(modulo))\r | |
1920 | base = _WorkRep(self.to_integral_value())\r | |
1921 | exponent = _WorkRep(other.to_integral_value())\r | |
1922 | \r | |
1923 | # compute result using integer pow()\r | |
1924 | base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo\r | |
1925 | for i in xrange(exponent.exp):\r | |
1926 | base = pow(base, 10, modulo)\r | |
1927 | base = pow(base, exponent.int, modulo)\r | |
1928 | \r | |
1929 | return _dec_from_triple(sign, str(base), 0)\r | |
1930 | \r | |
1931 | def _power_exact(self, other, p):\r | |
1932 | """Attempt to compute self**other exactly.\r | |
1933 | \r | |
1934 | Given Decimals self and other and an integer p, attempt to\r | |
1935 | compute an exact result for the power self**other, with p\r | |
1936 | digits of precision. Return None if self**other is not\r | |
1937 | exactly representable in p digits.\r | |
1938 | \r | |
1939 | Assumes that elimination of special cases has already been\r | |
1940 | performed: self and other must both be nonspecial; self must\r | |
1941 | be positive and not numerically equal to 1; other must be\r | |
1942 | nonzero. For efficiency, other._exp should not be too large,\r | |
1943 | so that 10**abs(other._exp) is a feasible calculation."""\r | |
1944 | \r | |
1945 | # In the comments below, we write x for the value of self and\r | |
1946 | # y for the value of other. Write x = xc*10**xe and y =\r | |
1947 | # yc*10**ye.\r | |
1948 | \r | |
1949 | # The main purpose of this method is to identify the *failure*\r | |
1950 | # of x**y to be exactly representable with as little effort as\r | |
1951 | # possible. So we look for cheap and easy tests that\r | |
1952 | # eliminate the possibility of x**y being exact. Only if all\r | |
1953 | # these tests are passed do we go on to actually compute x**y.\r | |
1954 | \r | |
1955 | # Here's the main idea. First normalize both x and y. We\r | |
1956 | # express y as a rational m/n, with m and n relatively prime\r | |
1957 | # and n>0. Then for x**y to be exactly representable (at\r | |
1958 | # *any* precision), xc must be the nth power of a positive\r | |
1959 | # integer and xe must be divisible by n. If m is negative\r | |
1960 | # then additionally xc must be a power of either 2 or 5, hence\r | |
1961 | # a power of 2**n or 5**n.\r | |
1962 | #\r | |
1963 | # There's a limit to how small |y| can be: if y=m/n as above\r | |
1964 | # then:\r | |
1965 | #\r | |
1966 | # (1) if xc != 1 then for the result to be representable we\r | |
1967 | # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So\r | |
1968 | # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <=\r | |
1969 | # 2**(1/|y|), hence xc**|y| < 2 and the result is not\r | |
1970 | # representable.\r | |
1971 | #\r | |
1972 | # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if\r | |
1973 | # |y| < 1/|xe| then the result is not representable.\r | |
1974 | #\r | |
1975 | # Note that since x is not equal to 1, at least one of (1) and\r | |
1976 | # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) <\r | |
1977 | # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye.\r | |
1978 | #\r | |
1979 | # There's also a limit to how large y can be, at least if it's\r | |
1980 | # positive: the normalized result will have coefficient xc**y,\r | |
1981 | # so if it's representable then xc**y < 10**p, and y <\r | |
1982 | # p/log10(xc). Hence if y*log10(xc) >= p then the result is\r | |
1983 | # not exactly representable.\r | |
1984 | \r | |
1985 | # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye,\r | |
1986 | # so |y| < 1/xe and the result is not representable.\r | |
1987 | # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y|\r | |
1988 | # < 1/nbits(xc).\r | |
1989 | \r | |
1990 | x = _WorkRep(self)\r | |
1991 | xc, xe = x.int, x.exp\r | |
1992 | while xc % 10 == 0:\r | |
1993 | xc //= 10\r | |
1994 | xe += 1\r | |
1995 | \r | |
1996 | y = _WorkRep(other)\r | |
1997 | yc, ye = y.int, y.exp\r | |
1998 | while yc % 10 == 0:\r | |
1999 | yc //= 10\r | |
2000 | ye += 1\r | |
2001 | \r | |
2002 | # case where xc == 1: result is 10**(xe*y), with xe*y\r | |
2003 | # required to be an integer\r | |
2004 | if xc == 1:\r | |
2005 | xe *= yc\r | |
2006 | # result is now 10**(xe * 10**ye); xe * 10**ye must be integral\r | |
2007 | while xe % 10 == 0:\r | |
2008 | xe //= 10\r | |
2009 | ye += 1\r | |
2010 | if ye < 0:\r | |
2011 | return None\r | |
2012 | exponent = xe * 10**ye\r | |
2013 | if y.sign == 1:\r | |
2014 | exponent = -exponent\r | |
2015 | # if other is a nonnegative integer, use ideal exponent\r | |
2016 | if other._isinteger() and other._sign == 0:\r | |
2017 | ideal_exponent = self._exp*int(other)\r | |
2018 | zeros = min(exponent-ideal_exponent, p-1)\r | |
2019 | else:\r | |
2020 | zeros = 0\r | |
2021 | return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros)\r | |
2022 | \r | |
2023 | # case where y is negative: xc must be either a power\r | |
2024 | # of 2 or a power of 5.\r | |
2025 | if y.sign == 1:\r | |
2026 | last_digit = xc % 10\r | |
2027 | if last_digit in (2,4,6,8):\r | |
2028 | # quick test for power of 2\r | |
2029 | if xc & -xc != xc:\r | |
2030 | return None\r | |
2031 | # now xc is a power of 2; e is its exponent\r | |
2032 | e = _nbits(xc)-1\r | |
2033 | # find e*y and xe*y; both must be integers\r | |
2034 | if ye >= 0:\r | |
2035 | y_as_int = yc*10**ye\r | |
2036 | e = e*y_as_int\r | |
2037 | xe = xe*y_as_int\r | |
2038 | else:\r | |
2039 | ten_pow = 10**-ye\r | |
2040 | e, remainder = divmod(e*yc, ten_pow)\r | |
2041 | if remainder:\r | |
2042 | return None\r | |
2043 | xe, remainder = divmod(xe*yc, ten_pow)\r | |
2044 | if remainder:\r | |
2045 | return None\r | |
2046 | \r | |
2047 | if e*65 >= p*93: # 93/65 > log(10)/log(5)\r | |
2048 | return None\r | |
2049 | xc = 5**e\r | |
2050 | \r | |
2051 | elif last_digit == 5:\r | |
2052 | # e >= log_5(xc) if xc is a power of 5; we have\r | |
2053 | # equality all the way up to xc=5**2658\r | |
2054 | e = _nbits(xc)*28//65\r | |
2055 | xc, remainder = divmod(5**e, xc)\r | |
2056 | if remainder:\r | |
2057 | return None\r | |
2058 | while xc % 5 == 0:\r | |
2059 | xc //= 5\r | |
2060 | e -= 1\r | |
2061 | if ye >= 0:\r | |
2062 | y_as_integer = yc*10**ye\r | |
2063 | e = e*y_as_integer\r | |
2064 | xe = xe*y_as_integer\r | |
2065 | else:\r | |
2066 | ten_pow = 10**-ye\r | |
2067 | e, remainder = divmod(e*yc, ten_pow)\r | |
2068 | if remainder:\r | |
2069 | return None\r | |
2070 | xe, remainder = divmod(xe*yc, ten_pow)\r | |
2071 | if remainder:\r | |
2072 | return None\r | |
2073 | if e*3 >= p*10: # 10/3 > log(10)/log(2)\r | |
2074 | return None\r | |
2075 | xc = 2**e\r | |
2076 | else:\r | |
2077 | return None\r | |
2078 | \r | |
2079 | if xc >= 10**p:\r | |
2080 | return None\r | |
2081 | xe = -e-xe\r | |
2082 | return _dec_from_triple(0, str(xc), xe)\r | |
2083 | \r | |
2084 | # now y is positive; find m and n such that y = m/n\r | |
2085 | if ye >= 0:\r | |
2086 | m, n = yc*10**ye, 1\r | |
2087 | else:\r | |
2088 | if xe != 0 and len(str(abs(yc*xe))) <= -ye:\r | |
2089 | return None\r | |
2090 | xc_bits = _nbits(xc)\r | |
2091 | if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye:\r | |
2092 | return None\r | |
2093 | m, n = yc, 10**(-ye)\r | |
2094 | while m % 2 == n % 2 == 0:\r | |
2095 | m //= 2\r | |
2096 | n //= 2\r | |
2097 | while m % 5 == n % 5 == 0:\r | |
2098 | m //= 5\r | |
2099 | n //= 5\r | |
2100 | \r | |
2101 | # compute nth root of xc*10**xe\r | |
2102 | if n > 1:\r | |
2103 | # if 1 < xc < 2**n then xc isn't an nth power\r | |
2104 | if xc != 1 and xc_bits <= n:\r | |
2105 | return None\r | |
2106 | \r | |
2107 | xe, rem = divmod(xe, n)\r | |
2108 | if rem != 0:\r | |
2109 | return None\r | |
2110 | \r | |
2111 | # compute nth root of xc using Newton's method\r | |
2112 | a = 1L << -(-_nbits(xc)//n) # initial estimate\r | |
2113 | while True:\r | |
2114 | q, r = divmod(xc, a**(n-1))\r | |
2115 | if a <= q:\r | |
2116 | break\r | |
2117 | else:\r | |
2118 | a = (a*(n-1) + q)//n\r | |
2119 | if not (a == q and r == 0):\r | |
2120 | return None\r | |
2121 | xc = a\r | |
2122 | \r | |
2123 | # now xc*10**xe is the nth root of the original xc*10**xe\r | |
2124 | # compute mth power of xc*10**xe\r | |
2125 | \r | |
2126 | # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m >\r | |
2127 | # 10**p and the result is not representable.\r | |
2128 | if xc > 1 and m > p*100//_log10_lb(xc):\r | |
2129 | return None\r | |
2130 | xc = xc**m\r | |
2131 | xe *= m\r | |
2132 | if xc > 10**p:\r | |
2133 | return None\r | |
2134 | \r | |
2135 | # by this point the result *is* exactly representable\r | |
2136 | # adjust the exponent to get as close as possible to the ideal\r | |
2137 | # exponent, if necessary\r | |
2138 | str_xc = str(xc)\r | |
2139 | if other._isinteger() and other._sign == 0:\r | |
2140 | ideal_exponent = self._exp*int(other)\r | |
2141 | zeros = min(xe-ideal_exponent, p-len(str_xc))\r | |
2142 | else:\r | |
2143 | zeros = 0\r | |
2144 | return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros)\r | |
2145 | \r | |
2146 | def __pow__(self, other, modulo=None, context=None):\r | |
2147 | """Return self ** other [ % modulo].\r | |
2148 | \r | |
2149 | With two arguments, compute self**other.\r | |
2150 | \r | |
2151 | With three arguments, compute (self**other) % modulo. For the\r | |
2152 | three argument form, the following restrictions on the\r | |
2153 | arguments hold:\r | |
2154 | \r | |
2155 | - all three arguments must be integral\r | |
2156 | - other must be nonnegative\r | |
2157 | - either self or other (or both) must be nonzero\r | |
2158 | - modulo must be nonzero and must have at most p digits,\r | |
2159 | where p is the context precision.\r | |
2160 | \r | |
2161 | If any of these restrictions is violated the InvalidOperation\r | |
2162 | flag is raised.\r | |
2163 | \r | |
2164 | The result of pow(self, other, modulo) is identical to the\r | |
2165 | result that would be obtained by computing (self**other) %\r | |
2166 | modulo with unbounded precision, but is computed more\r | |
2167 | efficiently. It is always exact.\r | |
2168 | """\r | |
2169 | \r | |
2170 | if modulo is not None:\r | |
2171 | return self._power_modulo(other, modulo, context)\r | |
2172 | \r | |
2173 | other = _convert_other(other)\r | |
2174 | if other is NotImplemented:\r | |
2175 | return other\r | |
2176 | \r | |
2177 | if context is None:\r | |
2178 | context = getcontext()\r | |
2179 | \r | |
2180 | # either argument is a NaN => result is NaN\r | |
2181 | ans = self._check_nans(other, context)\r | |
2182 | if ans:\r | |
2183 | return ans\r | |
2184 | \r | |
2185 | # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity)\r | |
2186 | if not other:\r | |
2187 | if not self:\r | |
2188 | return context._raise_error(InvalidOperation, '0 ** 0')\r | |
2189 | else:\r | |
2190 | return _One\r | |
2191 | \r | |
2192 | # result has sign 1 iff self._sign is 1 and other is an odd integer\r | |
2193 | result_sign = 0\r | |
2194 | if self._sign == 1:\r | |
2195 | if other._isinteger():\r | |
2196 | if not other._iseven():\r | |
2197 | result_sign = 1\r | |
2198 | else:\r | |
2199 | # -ve**noninteger = NaN\r | |
2200 | # (-0)**noninteger = 0**noninteger\r | |
2201 | if self:\r | |
2202 | return context._raise_error(InvalidOperation,\r | |
2203 | 'x ** y with x negative and y not an integer')\r | |
2204 | # negate self, without doing any unwanted rounding\r | |
2205 | self = self.copy_negate()\r | |
2206 | \r | |
2207 | # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity\r | |
2208 | if not self:\r | |
2209 | if other._sign == 0:\r | |
2210 | return _dec_from_triple(result_sign, '0', 0)\r | |
2211 | else:\r | |
2212 | return _SignedInfinity[result_sign]\r | |
2213 | \r | |
2214 | # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0\r | |
2215 | if self._isinfinity():\r | |
2216 | if other._sign == 0:\r | |
2217 | return _SignedInfinity[result_sign]\r | |
2218 | else:\r | |
2219 | return _dec_from_triple(result_sign, '0', 0)\r | |
2220 | \r | |
2221 | # 1**other = 1, but the choice of exponent and the flags\r | |
2222 | # depend on the exponent of self, and on whether other is a\r | |
2223 | # positive integer, a negative integer, or neither\r | |
2224 | if self == _One:\r | |
2225 | if other._isinteger():\r | |
2226 | # exp = max(self._exp*max(int(other), 0),\r | |
2227 | # 1-context.prec) but evaluating int(other) directly\r | |
2228 | # is dangerous until we know other is small (other\r | |
2229 | # could be 1e999999999)\r | |
2230 | if other._sign == 1:\r | |
2231 | multiplier = 0\r | |
2232 | elif other > context.prec:\r | |
2233 | multiplier = context.prec\r | |
2234 | else:\r | |
2235 | multiplier = int(other)\r | |
2236 | \r | |
2237 | exp = self._exp * multiplier\r | |
2238 | if exp < 1-context.prec:\r | |
2239 | exp = 1-context.prec\r | |
2240 | context._raise_error(Rounded)\r | |
2241 | else:\r | |
2242 | context._raise_error(Inexact)\r | |
2243 | context._raise_error(Rounded)\r | |
2244 | exp = 1-context.prec\r | |
2245 | \r | |
2246 | return _dec_from_triple(result_sign, '1'+'0'*-exp, exp)\r | |
2247 | \r | |
2248 | # compute adjusted exponent of self\r | |
2249 | self_adj = self.adjusted()\r | |
2250 | \r | |
2251 | # self ** infinity is infinity if self > 1, 0 if self < 1\r | |
2252 | # self ** -infinity is infinity if self < 1, 0 if self > 1\r | |
2253 | if other._isinfinity():\r | |
2254 | if (other._sign == 0) == (self_adj < 0):\r | |
2255 | return _dec_from_triple(result_sign, '0', 0)\r | |
2256 | else:\r | |
2257 | return _SignedInfinity[result_sign]\r | |
2258 | \r | |
2259 | # from here on, the result always goes through the call\r | |
2260 | # to _fix at the end of this function.\r | |
2261 | ans = None\r | |
2262 | exact = False\r | |
2263 | \r | |
2264 | # crude test to catch cases of extreme overflow/underflow. If\r | |
2265 | # log10(self)*other >= 10**bound and bound >= len(str(Emax))\r | |
2266 | # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence\r | |
2267 | # self**other >= 10**(Emax+1), so overflow occurs. The test\r | |
2268 | # for underflow is similar.\r | |
2269 | bound = self._log10_exp_bound() + other.adjusted()\r | |
2270 | if (self_adj >= 0) == (other._sign == 0):\r | |
2271 | # self > 1 and other +ve, or self < 1 and other -ve\r | |
2272 | # possibility of overflow\r | |
2273 | if bound >= len(str(context.Emax)):\r | |
2274 | ans = _dec_from_triple(result_sign, '1', context.Emax+1)\r | |
2275 | else:\r | |
2276 | # self > 1 and other -ve, or self < 1 and other +ve\r | |
2277 | # possibility of underflow to 0\r | |
2278 | Etiny = context.Etiny()\r | |
2279 | if bound >= len(str(-Etiny)):\r | |
2280 | ans = _dec_from_triple(result_sign, '1', Etiny-1)\r | |
2281 | \r | |
2282 | # try for an exact result with precision +1\r | |
2283 | if ans is None:\r | |
2284 | ans = self._power_exact(other, context.prec + 1)\r | |
2285 | if ans is not None:\r | |
2286 | if result_sign == 1:\r | |
2287 | ans = _dec_from_triple(1, ans._int, ans._exp)\r | |
2288 | exact = True\r | |
2289 | \r | |
2290 | # usual case: inexact result, x**y computed directly as exp(y*log(x))\r | |
2291 | if ans is None:\r | |
2292 | p = context.prec\r | |
2293 | x = _WorkRep(self)\r | |
2294 | xc, xe = x.int, x.exp\r | |
2295 | y = _WorkRep(other)\r | |
2296 | yc, ye = y.int, y.exp\r | |
2297 | if y.sign == 1:\r | |
2298 | yc = -yc\r | |
2299 | \r | |
2300 | # compute correctly rounded result: start with precision +3,\r | |
2301 | # then increase precision until result is unambiguously roundable\r | |
2302 | extra = 3\r | |
2303 | while True:\r | |
2304 | coeff, exp = _dpower(xc, xe, yc, ye, p+extra)\r | |
2305 | if coeff % (5*10**(len(str(coeff))-p-1)):\r | |
2306 | break\r | |
2307 | extra += 3\r | |
2308 | \r | |
2309 | ans = _dec_from_triple(result_sign, str(coeff), exp)\r | |
2310 | \r | |
2311 | # unlike exp, ln and log10, the power function respects the\r | |
2312 | # rounding mode; no need to switch to ROUND_HALF_EVEN here\r | |
2313 | \r | |
2314 | # There's a difficulty here when 'other' is not an integer and\r | |
2315 | # the result is exact. In this case, the specification\r | |
2316 | # requires that the Inexact flag be raised (in spite of\r | |
2317 | # exactness), but since the result is exact _fix won't do this\r | |
2318 | # for us. (Correspondingly, the Underflow signal should also\r | |
2319 | # be raised for subnormal results.) We can't directly raise\r | |
2320 | # these signals either before or after calling _fix, since\r | |
2321 | # that would violate the precedence for signals. So we wrap\r | |
2322 | # the ._fix call in a temporary context, and reraise\r | |
2323 | # afterwards.\r | |
2324 | if exact and not other._isinteger():\r | |
2325 | # pad with zeros up to length context.prec+1 if necessary; this\r | |
2326 | # ensures that the Rounded signal will be raised.\r | |
2327 | if len(ans._int) <= context.prec:\r | |
2328 | expdiff = context.prec + 1 - len(ans._int)\r | |
2329 | ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff,\r | |
2330 | ans._exp-expdiff)\r | |
2331 | \r | |
2332 | # create a copy of the current context, with cleared flags/traps\r | |
2333 | newcontext = context.copy()\r | |
2334 | newcontext.clear_flags()\r | |
2335 | for exception in _signals:\r | |
2336 | newcontext.traps[exception] = 0\r | |
2337 | \r | |
2338 | # round in the new context\r | |
2339 | ans = ans._fix(newcontext)\r | |
2340 | \r | |
2341 | # raise Inexact, and if necessary, Underflow\r | |
2342 | newcontext._raise_error(Inexact)\r | |
2343 | if newcontext.flags[Subnormal]:\r | |
2344 | newcontext._raise_error(Underflow)\r | |
2345 | \r | |
2346 | # propagate signals to the original context; _fix could\r | |
2347 | # have raised any of Overflow, Underflow, Subnormal,\r | |
2348 | # Inexact, Rounded, Clamped. Overflow needs the correct\r | |
2349 | # arguments. Note that the order of the exceptions is\r | |
2350 | # important here.\r | |
2351 | if newcontext.flags[Overflow]:\r | |
2352 | context._raise_error(Overflow, 'above Emax', ans._sign)\r | |
2353 | for exception in Underflow, Subnormal, Inexact, Rounded, Clamped:\r | |
2354 | if newcontext.flags[exception]:\r | |
2355 | context._raise_error(exception)\r | |
2356 | \r | |
2357 | else:\r | |
2358 | ans = ans._fix(context)\r | |
2359 | \r | |
2360 | return ans\r | |
2361 | \r | |
2362 | def __rpow__(self, other, context=None):\r | |
2363 | """Swaps self/other and returns __pow__."""\r | |
2364 | other = _convert_other(other)\r | |
2365 | if other is NotImplemented:\r | |
2366 | return other\r | |
2367 | return other.__pow__(self, context=context)\r | |
2368 | \r | |
2369 | def normalize(self, context=None):\r | |
2370 | """Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""\r | |
2371 | \r | |
2372 | if context is None:\r | |
2373 | context = getcontext()\r | |
2374 | \r | |
2375 | if self._is_special:\r | |
2376 | ans = self._check_nans(context=context)\r | |
2377 | if ans:\r | |
2378 | return ans\r | |
2379 | \r | |
2380 | dup = self._fix(context)\r | |
2381 | if dup._isinfinity():\r | |
2382 | return dup\r | |
2383 | \r | |
2384 | if not dup:\r | |
2385 | return _dec_from_triple(dup._sign, '0', 0)\r | |
2386 | exp_max = [context.Emax, context.Etop()][context._clamp]\r | |
2387 | end = len(dup._int)\r | |
2388 | exp = dup._exp\r | |
2389 | while dup._int[end-1] == '0' and exp < exp_max:\r | |
2390 | exp += 1\r | |
2391 | end -= 1\r | |
2392 | return _dec_from_triple(dup._sign, dup._int[:end], exp)\r | |
2393 | \r | |
2394 | def quantize(self, exp, rounding=None, context=None, watchexp=True):\r | |
2395 | """Quantize self so its exponent is the same as that of exp.\r | |
2396 | \r | |
2397 | Similar to self._rescale(exp._exp) but with error checking.\r | |
2398 | """\r | |
2399 | exp = _convert_other(exp, raiseit=True)\r | |
2400 | \r | |
2401 | if context is None:\r | |
2402 | context = getcontext()\r | |
2403 | if rounding is None:\r | |
2404 | rounding = context.rounding\r | |
2405 | \r | |
2406 | if self._is_special or exp._is_special:\r | |
2407 | ans = self._check_nans(exp, context)\r | |
2408 | if ans:\r | |
2409 | return ans\r | |
2410 | \r | |
2411 | if exp._isinfinity() or self._isinfinity():\r | |
2412 | if exp._isinfinity() and self._isinfinity():\r | |
2413 | return Decimal(self) # if both are inf, it is OK\r | |
2414 | return context._raise_error(InvalidOperation,\r | |
2415 | 'quantize with one INF')\r | |
2416 | \r | |
2417 | # if we're not watching exponents, do a simple rescale\r | |
2418 | if not watchexp:\r | |
2419 | ans = self._rescale(exp._exp, rounding)\r | |
2420 | # raise Inexact and Rounded where appropriate\r | |
2421 | if ans._exp > self._exp:\r | |
2422 | context._raise_error(Rounded)\r | |
2423 | if ans != self:\r | |
2424 | context._raise_error(Inexact)\r | |
2425 | return ans\r | |
2426 | \r | |
2427 | # exp._exp should be between Etiny and Emax\r | |
2428 | if not (context.Etiny() <= exp._exp <= context.Emax):\r | |
2429 | return context._raise_error(InvalidOperation,\r | |
2430 | 'target exponent out of bounds in quantize')\r | |
2431 | \r | |
2432 | if not self:\r | |
2433 | ans = _dec_from_triple(self._sign, '0', exp._exp)\r | |
2434 | return ans._fix(context)\r | |
2435 | \r | |
2436 | self_adjusted = self.adjusted()\r | |
2437 | if self_adjusted > context.Emax:\r | |
2438 | return context._raise_error(InvalidOperation,\r | |
2439 | 'exponent of quantize result too large for current context')\r | |
2440 | if self_adjusted - exp._exp + 1 > context.prec:\r | |
2441 | return context._raise_error(InvalidOperation,\r | |
2442 | 'quantize result has too many digits for current context')\r | |
2443 | \r | |
2444 | ans = self._rescale(exp._exp, rounding)\r | |
2445 | if ans.adjusted() > context.Emax:\r | |
2446 | return context._raise_error(InvalidOperation,\r | |
2447 | 'exponent of quantize result too large for current context')\r | |
2448 | if len(ans._int) > context.prec:\r | |
2449 | return context._raise_error(InvalidOperation,\r | |
2450 | 'quantize result has too many digits for current context')\r | |
2451 | \r | |
2452 | # raise appropriate flags\r | |
2453 | if ans and ans.adjusted() < context.Emin:\r | |
2454 | context._raise_error(Subnormal)\r | |
2455 | if ans._exp > self._exp:\r | |
2456 | if ans != self:\r | |
2457 | context._raise_error(Inexact)\r | |
2458 | context._raise_error(Rounded)\r | |
2459 | \r | |
2460 | # call to fix takes care of any necessary folddown, and\r | |
2461 | # signals Clamped if necessary\r | |
2462 | ans = ans._fix(context)\r | |
2463 | return ans\r | |
2464 | \r | |
2465 | def same_quantum(self, other):\r | |
2466 | """Return True if self and other have the same exponent; otherwise\r | |
2467 | return False.\r | |
2468 | \r | |
2469 | If either operand is a special value, the following rules are used:\r | |
2470 | * return True if both operands are infinities\r | |
2471 | * return True if both operands are NaNs\r | |
2472 | * otherwise, return False.\r | |
2473 | """\r | |
2474 | other = _convert_other(other, raiseit=True)\r | |
2475 | if self._is_special or other._is_special:\r | |
2476 | return (self.is_nan() and other.is_nan() or\r | |
2477 | self.is_infinite() and other.is_infinite())\r | |
2478 | return self._exp == other._exp\r | |
2479 | \r | |
2480 | def _rescale(self, exp, rounding):\r | |
2481 | """Rescale self so that the exponent is exp, either by padding with zeros\r | |
2482 | or by truncating digits, using the given rounding mode.\r | |
2483 | \r | |
2484 | Specials are returned without change. This operation is\r | |
2485 | quiet: it raises no flags, and uses no information from the\r | |
2486 | context.\r | |
2487 | \r | |
2488 | exp = exp to scale to (an integer)\r | |
2489 | rounding = rounding mode\r | |
2490 | """\r | |
2491 | if self._is_special:\r | |
2492 | return Decimal(self)\r | |
2493 | if not self:\r | |
2494 | return _dec_from_triple(self._sign, '0', exp)\r | |
2495 | \r | |
2496 | if self._exp >= exp:\r | |
2497 | # pad answer with zeros if necessary\r | |
2498 | return _dec_from_triple(self._sign,\r | |
2499 | self._int + '0'*(self._exp - exp), exp)\r | |
2500 | \r | |
2501 | # too many digits; round and lose data. If self.adjusted() <\r | |
2502 | # exp-1, replace self by 10**(exp-1) before rounding\r | |
2503 | digits = len(self._int) + self._exp - exp\r | |
2504 | if digits < 0:\r | |
2505 | self = _dec_from_triple(self._sign, '1', exp-1)\r | |
2506 | digits = 0\r | |
2507 | this_function = self._pick_rounding_function[rounding]\r | |
2508 | changed = this_function(self, digits)\r | |
2509 | coeff = self._int[:digits] or '0'\r | |
2510 | if changed == 1:\r | |
2511 | coeff = str(int(coeff)+1)\r | |
2512 | return _dec_from_triple(self._sign, coeff, exp)\r | |
2513 | \r | |
2514 | def _round(self, places, rounding):\r | |
2515 | """Round a nonzero, nonspecial Decimal to a fixed number of\r | |
2516 | significant figures, using the given rounding mode.\r | |
2517 | \r | |
2518 | Infinities, NaNs and zeros are returned unaltered.\r | |
2519 | \r | |
2520 | This operation is quiet: it raises no flags, and uses no\r | |
2521 | information from the context.\r | |
2522 | \r | |
2523 | """\r | |
2524 | if places <= 0:\r | |
2525 | raise ValueError("argument should be at least 1 in _round")\r | |
2526 | if self._is_special or not self:\r | |
2527 | return Decimal(self)\r | |
2528 | ans = self._rescale(self.adjusted()+1-places, rounding)\r | |
2529 | # it can happen that the rescale alters the adjusted exponent;\r | |
2530 | # for example when rounding 99.97 to 3 significant figures.\r | |
2531 | # When this happens we end up with an extra 0 at the end of\r | |
2532 | # the number; a second rescale fixes this.\r | |
2533 | if ans.adjusted() != self.adjusted():\r | |
2534 | ans = ans._rescale(ans.adjusted()+1-places, rounding)\r | |
2535 | return ans\r | |
2536 | \r | |
2537 | def to_integral_exact(self, rounding=None, context=None):\r | |
2538 | """Rounds to a nearby integer.\r | |
2539 | \r | |
2540 | If no rounding mode is specified, take the rounding mode from\r | |
2541 | the context. This method raises the Rounded and Inexact flags\r | |
2542 | when appropriate.\r | |
2543 | \r | |
2544 | See also: to_integral_value, which does exactly the same as\r | |
2545 | this method except that it doesn't raise Inexact or Rounded.\r | |
2546 | """\r | |
2547 | if self._is_special:\r | |
2548 | ans = self._check_nans(context=context)\r | |
2549 | if ans:\r | |
2550 | return ans\r | |
2551 | return Decimal(self)\r | |
2552 | if self._exp >= 0:\r | |
2553 | return Decimal(self)\r | |
2554 | if not self:\r | |
2555 | return _dec_from_triple(self._sign, '0', 0)\r | |
2556 | if context is None:\r | |
2557 | context = getcontext()\r | |
2558 | if rounding is None:\r | |
2559 | rounding = context.rounding\r | |
2560 | ans = self._rescale(0, rounding)\r | |
2561 | if ans != self:\r | |
2562 | context._raise_error(Inexact)\r | |
2563 | context._raise_error(Rounded)\r | |
2564 | return ans\r | |
2565 | \r | |
2566 | def to_integral_value(self, rounding=None, context=None):\r | |
2567 | """Rounds to the nearest integer, without raising inexact, rounded."""\r | |
2568 | if context is None:\r | |
2569 | context = getcontext()\r | |
2570 | if rounding is None:\r | |
2571 | rounding = context.rounding\r | |
2572 | if self._is_special:\r | |
2573 | ans = self._check_nans(context=context)\r | |
2574 | if ans:\r | |
2575 | return ans\r | |
2576 | return Decimal(self)\r | |
2577 | if self._exp >= 0:\r | |
2578 | return Decimal(self)\r | |
2579 | else:\r | |
2580 | return self._rescale(0, rounding)\r | |
2581 | \r | |
2582 | # the method name changed, but we provide also the old one, for compatibility\r | |
2583 | to_integral = to_integral_value\r | |
2584 | \r | |
2585 | def sqrt(self, context=None):\r | |
2586 | """Return the square root of self."""\r | |
2587 | if context is None:\r | |
2588 | context = getcontext()\r | |
2589 | \r | |
2590 | if self._is_special:\r | |
2591 | ans = self._check_nans(context=context)\r | |
2592 | if ans:\r | |
2593 | return ans\r | |
2594 | \r | |
2595 | if self._isinfinity() and self._sign == 0:\r | |
2596 | return Decimal(self)\r | |
2597 | \r | |
2598 | if not self:\r | |
2599 | # exponent = self._exp // 2. sqrt(-0) = -0\r | |
2600 | ans = _dec_from_triple(self._sign, '0', self._exp // 2)\r | |
2601 | return ans._fix(context)\r | |
2602 | \r | |
2603 | if self._sign == 1:\r | |
2604 | return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')\r | |
2605 | \r | |
2606 | # At this point self represents a positive number. Let p be\r | |
2607 | # the desired precision and express self in the form c*100**e\r | |
2608 | # with c a positive real number and e an integer, c and e\r | |
2609 | # being chosen so that 100**(p-1) <= c < 100**p. Then the\r | |
2610 | # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1)\r | |
2611 | # <= sqrt(c) < 10**p, so the closest representable Decimal at\r | |
2612 | # precision p is n*10**e where n = round_half_even(sqrt(c)),\r | |
2613 | # the closest integer to sqrt(c) with the even integer chosen\r | |
2614 | # in the case of a tie.\r | |
2615 | #\r | |
2616 | # To ensure correct rounding in all cases, we use the\r | |
2617 | # following trick: we compute the square root to an extra\r | |
2618 | # place (precision p+1 instead of precision p), rounding down.\r | |
2619 | # Then, if the result is inexact and its last digit is 0 or 5,\r | |
2620 | # we increase the last digit to 1 or 6 respectively; if it's\r | |
2621 | # exact we leave the last digit alone. Now the final round to\r | |
2622 | # p places (or fewer in the case of underflow) will round\r | |
2623 | # correctly and raise the appropriate flags.\r | |
2624 | \r | |
2625 | # use an extra digit of precision\r | |
2626 | prec = context.prec+1\r | |
2627 | \r | |
2628 | # write argument in the form c*100**e where e = self._exp//2\r | |
2629 | # is the 'ideal' exponent, to be used if the square root is\r | |
2630 | # exactly representable. l is the number of 'digits' of c in\r | |
2631 | # base 100, so that 100**(l-1) <= c < 100**l.\r | |
2632 | op = _WorkRep(self)\r | |
2633 | e = op.exp >> 1\r | |
2634 | if op.exp & 1:\r | |
2635 | c = op.int * 10\r | |
2636 | l = (len(self._int) >> 1) + 1\r | |
2637 | else:\r | |
2638 | c = op.int\r | |
2639 | l = len(self._int)+1 >> 1\r | |
2640 | \r | |
2641 | # rescale so that c has exactly prec base 100 'digits'\r | |
2642 | shift = prec-l\r | |
2643 | if shift >= 0:\r | |
2644 | c *= 100**shift\r | |
2645 | exact = True\r | |
2646 | else:\r | |
2647 | c, remainder = divmod(c, 100**-shift)\r | |
2648 | exact = not remainder\r | |
2649 | e -= shift\r | |
2650 | \r | |
2651 | # find n = floor(sqrt(c)) using Newton's method\r | |
2652 | n = 10**prec\r | |
2653 | while True:\r | |
2654 | q = c//n\r | |
2655 | if n <= q:\r | |
2656 | break\r | |
2657 | else:\r | |
2658 | n = n + q >> 1\r | |
2659 | exact = exact and n*n == c\r | |
2660 | \r | |
2661 | if exact:\r | |
2662 | # result is exact; rescale to use ideal exponent e\r | |
2663 | if shift >= 0:\r | |
2664 | # assert n % 10**shift == 0\r | |
2665 | n //= 10**shift\r | |
2666 | else:\r | |
2667 | n *= 10**-shift\r | |
2668 | e += shift\r | |
2669 | else:\r | |
2670 | # result is not exact; fix last digit as described above\r | |
2671 | if n % 5 == 0:\r | |
2672 | n += 1\r | |
2673 | \r | |
2674 | ans = _dec_from_triple(0, str(n), e)\r | |
2675 | \r | |
2676 | # round, and fit to current context\r | |
2677 | context = context._shallow_copy()\r | |
2678 | rounding = context._set_rounding(ROUND_HALF_EVEN)\r | |
2679 | ans = ans._fix(context)\r | |
2680 | context.rounding = rounding\r | |
2681 | \r | |
2682 | return ans\r | |
2683 | \r | |
2684 | def max(self, other, context=None):\r | |
2685 | """Returns the larger value.\r | |
2686 | \r | |
2687 | Like max(self, other) except if one is not a number, returns\r | |
2688 | NaN (and signals if one is sNaN). Also rounds.\r | |
2689 | """\r | |
2690 | other = _convert_other(other, raiseit=True)\r | |
2691 | \r | |
2692 | if context is None:\r | |
2693 | context = getcontext()\r | |
2694 | \r | |
2695 | if self._is_special or other._is_special:\r | |
2696 | # If one operand is a quiet NaN and the other is number, then the\r | |
2697 | # number is always returned\r | |
2698 | sn = self._isnan()\r | |
2699 | on = other._isnan()\r | |
2700 | if sn or on:\r | |
2701 | if on == 1 and sn == 0:\r | |
2702 | return self._fix(context)\r | |
2703 | if sn == 1 and on == 0:\r | |
2704 | return other._fix(context)\r | |
2705 | return self._check_nans(other, context)\r | |
2706 | \r | |
2707 | c = self._cmp(other)\r | |
2708 | if c == 0:\r | |
2709 | # If both operands are finite and equal in numerical value\r | |
2710 | # then an ordering is applied:\r | |
2711 | #\r | |
2712 | # If the signs differ then max returns the operand with the\r | |
2713 | # positive sign and min returns the operand with the negative sign\r | |
2714 | #\r | |
2715 | # If the signs are the same then the exponent is used to select\r | |
2716 | # the result. This is exactly the ordering used in compare_total.\r | |
2717 | c = self.compare_total(other)\r | |
2718 | \r | |
2719 | if c == -1:\r | |
2720 | ans = other\r | |
2721 | else:\r | |
2722 | ans = self\r | |
2723 | \r | |
2724 | return ans._fix(context)\r | |
2725 | \r | |
2726 | def min(self, other, context=None):\r | |
2727 | """Returns the smaller value.\r | |
2728 | \r | |
2729 | Like min(self, other) except if one is not a number, returns\r | |
2730 | NaN (and signals if one is sNaN). Also rounds.\r | |
2731 | """\r | |
2732 | other = _convert_other(other, raiseit=True)\r | |
2733 | \r | |
2734 | if context is None:\r | |
2735 | context = getcontext()\r | |
2736 | \r | |
2737 | if self._is_special or other._is_special:\r | |
2738 | # If one operand is a quiet NaN and the other is number, then the\r | |
2739 | # number is always returned\r | |
2740 | sn = self._isnan()\r | |
2741 | on = other._isnan()\r | |
2742 | if sn or on:\r | |
2743 | if on == 1 and sn == 0:\r | |
2744 | return self._fix(context)\r | |
2745 | if sn == 1 and on == 0:\r | |
2746 | return other._fix(context)\r | |
2747 | return self._check_nans(other, context)\r | |
2748 | \r | |
2749 | c = self._cmp(other)\r | |
2750 | if c == 0:\r | |
2751 | c = self.compare_total(other)\r | |
2752 | \r | |
2753 | if c == -1:\r | |
2754 | ans = self\r | |
2755 | else:\r | |
2756 | ans = other\r | |
2757 | \r | |
2758 | return ans._fix(context)\r | |
2759 | \r | |
2760 | def _isinteger(self):\r | |
2761 | """Returns whether self is an integer"""\r | |
2762 | if self._is_special:\r | |
2763 | return False\r | |
2764 | if self._exp >= 0:\r | |
2765 | return True\r | |
2766 | rest = self._int[self._exp:]\r | |
2767 | return rest == '0'*len(rest)\r | |
2768 | \r | |
2769 | def _iseven(self):\r | |
2770 | """Returns True if self is even. Assumes self is an integer."""\r | |
2771 | if not self or self._exp > 0:\r | |
2772 | return True\r | |
2773 | return self._int[-1+self._exp] in '02468'\r | |
2774 | \r | |
2775 | def adjusted(self):\r | |
2776 | """Return the adjusted exponent of self"""\r | |
2777 | try:\r | |
2778 | return self._exp + len(self._int) - 1\r | |
2779 | # If NaN or Infinity, self._exp is string\r | |
2780 | except TypeError:\r | |
2781 | return 0\r | |
2782 | \r | |
2783 | def canonical(self, context=None):\r | |
2784 | """Returns the same Decimal object.\r | |
2785 | \r | |
2786 | As we do not have different encodings for the same number, the\r | |
2787 | received object already is in its canonical form.\r | |
2788 | """\r | |
2789 | return self\r | |
2790 | \r | |
2791 | def compare_signal(self, other, context=None):\r | |
2792 | """Compares self to the other operand numerically.\r | |
2793 | \r | |
2794 | It's pretty much like compare(), but all NaNs signal, with signaling\r | |
2795 | NaNs taking precedence over quiet NaNs.\r | |
2796 | """\r | |
2797 | other = _convert_other(other, raiseit = True)\r | |
2798 | ans = self._compare_check_nans(other, context)\r | |
2799 | if ans:\r | |
2800 | return ans\r | |
2801 | return self.compare(other, context=context)\r | |
2802 | \r | |
2803 | def compare_total(self, other):\r | |
2804 | """Compares self to other using the abstract representations.\r | |
2805 | \r | |
2806 | This is not like the standard compare, which use their numerical\r | |
2807 | value. Note that a total ordering is defined for all possible abstract\r | |
2808 | representations.\r | |
2809 | """\r | |
2810 | other = _convert_other(other, raiseit=True)\r | |
2811 | \r | |
2812 | # if one is negative and the other is positive, it's easy\r | |
2813 | if self._sign and not other._sign:\r | |
2814 | return _NegativeOne\r | |
2815 | if not self._sign and other._sign:\r | |
2816 | return _One\r | |
2817 | sign = self._sign\r | |
2818 | \r | |
2819 | # let's handle both NaN types\r | |
2820 | self_nan = self._isnan()\r | |
2821 | other_nan = other._isnan()\r | |
2822 | if self_nan or other_nan:\r | |
2823 | if self_nan == other_nan:\r | |
2824 | # compare payloads as though they're integers\r | |
2825 | self_key = len(self._int), self._int\r | |
2826 | other_key = len(other._int), other._int\r | |
2827 | if self_key < other_key:\r | |
2828 | if sign:\r | |
2829 | return _One\r | |
2830 | else:\r | |
2831 | return _NegativeOne\r | |
2832 | if self_key > other_key:\r | |
2833 | if sign:\r | |
2834 | return _NegativeOne\r | |
2835 | else:\r | |
2836 | return _One\r | |
2837 | return _Zero\r | |
2838 | \r | |
2839 | if sign:\r | |
2840 | if self_nan == 1:\r | |
2841 | return _NegativeOne\r | |
2842 | if other_nan == 1:\r | |
2843 | return _One\r | |
2844 | if self_nan == 2:\r | |
2845 | return _NegativeOne\r | |
2846 | if other_nan == 2:\r | |
2847 | return _One\r | |
2848 | else:\r | |
2849 | if self_nan == 1:\r | |
2850 | return _One\r | |
2851 | if other_nan == 1:\r | |
2852 | return _NegativeOne\r | |
2853 | if self_nan == 2:\r | |
2854 | return _One\r | |
2855 | if other_nan == 2:\r | |
2856 | return _NegativeOne\r | |
2857 | \r | |
2858 | if self < other:\r | |
2859 | return _NegativeOne\r | |
2860 | if self > other:\r | |
2861 | return _One\r | |
2862 | \r | |
2863 | if self._exp < other._exp:\r | |
2864 | if sign:\r | |
2865 | return _One\r | |
2866 | else:\r | |
2867 | return _NegativeOne\r | |
2868 | if self._exp > other._exp:\r | |
2869 | if sign:\r | |
2870 | return _NegativeOne\r | |
2871 | else:\r | |
2872 | return _One\r | |
2873 | return _Zero\r | |
2874 | \r | |
2875 | \r | |
2876 | def compare_total_mag(self, other):\r | |
2877 | """Compares self to other using abstract repr., ignoring sign.\r | |
2878 | \r | |
2879 | Like compare_total, but with operand's sign ignored and assumed to be 0.\r | |
2880 | """\r | |
2881 | other = _convert_other(other, raiseit=True)\r | |
2882 | \r | |
2883 | s = self.copy_abs()\r | |
2884 | o = other.copy_abs()\r | |
2885 | return s.compare_total(o)\r | |
2886 | \r | |
2887 | def copy_abs(self):\r | |
2888 | """Returns a copy with the sign set to 0. """\r | |
2889 | return _dec_from_triple(0, self._int, self._exp, self._is_special)\r | |
2890 | \r | |
2891 | def copy_negate(self):\r | |
2892 | """Returns a copy with the sign inverted."""\r | |
2893 | if self._sign:\r | |
2894 | return _dec_from_triple(0, self._int, self._exp, self._is_special)\r | |
2895 | else:\r | |
2896 | return _dec_from_triple(1, self._int, self._exp, self._is_special)\r | |
2897 | \r | |
2898 | def copy_sign(self, other):\r | |
2899 | """Returns self with the sign of other."""\r | |
2900 | other = _convert_other(other, raiseit=True)\r | |
2901 | return _dec_from_triple(other._sign, self._int,\r | |
2902 | self._exp, self._is_special)\r | |
2903 | \r | |
2904 | def exp(self, context=None):\r | |
2905 | """Returns e ** self."""\r | |
2906 | \r | |
2907 | if context is None:\r | |
2908 | context = getcontext()\r | |
2909 | \r | |
2910 | # exp(NaN) = NaN\r | |
2911 | ans = self._check_nans(context=context)\r | |
2912 | if ans:\r | |
2913 | return ans\r | |
2914 | \r | |
2915 | # exp(-Infinity) = 0\r | |
2916 | if self._isinfinity() == -1:\r | |
2917 | return _Zero\r | |
2918 | \r | |
2919 | # exp(0) = 1\r | |
2920 | if not self:\r | |
2921 | return _One\r | |
2922 | \r | |
2923 | # exp(Infinity) = Infinity\r | |
2924 | if self._isinfinity() == 1:\r | |
2925 | return Decimal(self)\r | |
2926 | \r | |
2927 | # the result is now guaranteed to be inexact (the true\r | |
2928 | # mathematical result is transcendental). There's no need to\r | |
2929 | # raise Rounded and Inexact here---they'll always be raised as\r | |
2930 | # a result of the call to _fix.\r | |
2931 | p = context.prec\r | |
2932 | adj = self.adjusted()\r | |
2933 | \r | |
2934 | # we only need to do any computation for quite a small range\r | |
2935 | # of adjusted exponents---for example, -29 <= adj <= 10 for\r | |
2936 | # the default context. For smaller exponent the result is\r | |
2937 | # indistinguishable from 1 at the given precision, while for\r | |
2938 | # larger exponent the result either overflows or underflows.\r | |
2939 | if self._sign == 0 and adj > len(str((context.Emax+1)*3)):\r | |
2940 | # overflow\r | |
2941 | ans = _dec_from_triple(0, '1', context.Emax+1)\r | |
2942 | elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)):\r | |
2943 | # underflow to 0\r | |
2944 | ans = _dec_from_triple(0, '1', context.Etiny()-1)\r | |
2945 | elif self._sign == 0 and adj < -p:\r | |
2946 | # p+1 digits; final round will raise correct flags\r | |
2947 | ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p)\r | |
2948 | elif self._sign == 1 and adj < -p-1:\r | |
2949 | # p+1 digits; final round will raise correct flags\r | |
2950 | ans = _dec_from_triple(0, '9'*(p+1), -p-1)\r | |
2951 | # general case\r | |
2952 | else:\r | |
2953 | op = _WorkRep(self)\r | |
2954 | c, e = op.int, op.exp\r | |
2955 | if op.sign == 1:\r | |
2956 | c = -c\r | |
2957 | \r | |
2958 | # compute correctly rounded result: increase precision by\r | |
2959 | # 3 digits at a time until we get an unambiguously\r | |
2960 | # roundable result\r | |
2961 | extra = 3\r | |
2962 | while True:\r | |
2963 | coeff, exp = _dexp(c, e, p+extra)\r | |
2964 | if coeff % (5*10**(len(str(coeff))-p-1)):\r | |
2965 | break\r | |
2966 | extra += 3\r | |
2967 | \r | |
2968 | ans = _dec_from_triple(0, str(coeff), exp)\r | |
2969 | \r | |
2970 | # at this stage, ans should round correctly with *any*\r | |
2971 | # rounding mode, not just with ROUND_HALF_EVEN\r | |
2972 | context = context._shallow_copy()\r | |
2973 | rounding = context._set_rounding(ROUND_HALF_EVEN)\r | |
2974 | ans = ans._fix(context)\r | |
2975 | context.rounding = rounding\r | |
2976 | \r | |
2977 | return ans\r | |
2978 | \r | |
2979 | def is_canonical(self):\r | |
2980 | """Return True if self is canonical; otherwise return False.\r | |
2981 | \r | |
2982 | Currently, the encoding of a Decimal instance is always\r | |
2983 | canonical, so this method returns True for any Decimal.\r | |
2984 | """\r | |
2985 | return True\r | |
2986 | \r | |
2987 | def is_finite(self):\r | |
2988 | """Return True if self is finite; otherwise return False.\r | |
2989 | \r | |
2990 | A Decimal instance is considered finite if it is neither\r | |
2991 | infinite nor a NaN.\r | |
2992 | """\r | |
2993 | return not self._is_special\r | |
2994 | \r | |
2995 | def is_infinite(self):\r | |
2996 | """Return True if self is infinite; otherwise return False."""\r | |
2997 | return self._exp == 'F'\r | |
2998 | \r | |
2999 | def is_nan(self):\r | |
3000 | """Return True if self is a qNaN or sNaN; otherwise return False."""\r | |
3001 | return self._exp in ('n', 'N')\r | |
3002 | \r | |
3003 | def is_normal(self, context=None):\r | |
3004 | """Return True if self is a normal number; otherwise return False."""\r | |
3005 | if self._is_special or not self:\r | |
3006 | return False\r | |
3007 | if context is None:\r | |
3008 | context = getcontext()\r | |
3009 | return context.Emin <= self.adjusted()\r | |
3010 | \r | |
3011 | def is_qnan(self):\r | |
3012 | """Return True if self is a quiet NaN; otherwise return False."""\r | |
3013 | return self._exp == 'n'\r | |
3014 | \r | |
3015 | def is_signed(self):\r | |
3016 | """Return True if self is negative; otherwise return False."""\r | |
3017 | return self._sign == 1\r | |
3018 | \r | |
3019 | def is_snan(self):\r | |
3020 | """Return True if self is a signaling NaN; otherwise return False."""\r | |
3021 | return self._exp == 'N'\r | |
3022 | \r | |
3023 | def is_subnormal(self, context=None):\r | |
3024 | """Return True if self is subnormal; otherwise return False."""\r | |
3025 | if self._is_special or not self:\r | |
3026 | return False\r | |
3027 | if context is None:\r | |
3028 | context = getcontext()\r | |
3029 | return self.adjusted() < context.Emin\r | |
3030 | \r | |
3031 | def is_zero(self):\r | |
3032 | """Return True if self is a zero; otherwise return False."""\r | |
3033 | return not self._is_special and self._int == '0'\r | |
3034 | \r | |
3035 | def _ln_exp_bound(self):\r | |
3036 | """Compute a lower bound for the adjusted exponent of self.ln().\r | |
3037 | In other words, compute r such that self.ln() >= 10**r. Assumes\r | |
3038 | that self is finite and positive and that self != 1.\r | |
3039 | """\r | |
3040 | \r | |
3041 | # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1\r | |
3042 | adj = self._exp + len(self._int) - 1\r | |
3043 | if adj >= 1:\r | |
3044 | # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10)\r | |
3045 | return len(str(adj*23//10)) - 1\r | |
3046 | if adj <= -2:\r | |
3047 | # argument <= 0.1\r | |
3048 | return len(str((-1-adj)*23//10)) - 1\r | |
3049 | op = _WorkRep(self)\r | |
3050 | c, e = op.int, op.exp\r | |
3051 | if adj == 0:\r | |
3052 | # 1 < self < 10\r | |
3053 | num = str(c-10**-e)\r | |
3054 | den = str(c)\r | |
3055 | return len(num) - len(den) - (num < den)\r | |
3056 | # adj == -1, 0.1 <= self < 1\r | |
3057 | return e + len(str(10**-e - c)) - 1\r | |
3058 | \r | |
3059 | \r | |
3060 | def ln(self, context=None):\r | |
3061 | """Returns the natural (base e) logarithm of self."""\r | |
3062 | \r | |
3063 | if context is None:\r | |
3064 | context = getcontext()\r | |
3065 | \r | |
3066 | # ln(NaN) = NaN\r | |
3067 | ans = self._check_nans(context=context)\r | |
3068 | if ans:\r | |
3069 | return ans\r | |
3070 | \r | |
3071 | # ln(0.0) == -Infinity\r | |
3072 | if not self:\r | |
3073 | return _NegativeInfinity\r | |
3074 | \r | |
3075 | # ln(Infinity) = Infinity\r | |
3076 | if self._isinfinity() == 1:\r | |
3077 | return _Infinity\r | |
3078 | \r | |
3079 | # ln(1.0) == 0.0\r | |
3080 | if self == _One:\r | |
3081 | return _Zero\r | |
3082 | \r | |
3083 | # ln(negative) raises InvalidOperation\r | |
3084 | if self._sign == 1:\r | |
3085 | return context._raise_error(InvalidOperation,\r | |
3086 | 'ln of a negative value')\r | |
3087 | \r | |
3088 | # result is irrational, so necessarily inexact\r | |
3089 | op = _WorkRep(self)\r | |
3090 | c, e = op.int, op.exp\r | |
3091 | p = context.prec\r | |
3092 | \r | |
3093 | # correctly rounded result: repeatedly increase precision by 3\r | |
3094 | # until we get an unambiguously roundable result\r | |
3095 | places = p - self._ln_exp_bound() + 2 # at least p+3 places\r | |
3096 | while True:\r | |
3097 | coeff = _dlog(c, e, places)\r | |
3098 | # assert len(str(abs(coeff)))-p >= 1\r | |
3099 | if coeff % (5*10**(len(str(abs(coeff)))-p-1)):\r | |
3100 | break\r | |
3101 | places += 3\r | |
3102 | ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)\r | |
3103 | \r | |
3104 | context = context._shallow_copy()\r | |
3105 | rounding = context._set_rounding(ROUND_HALF_EVEN)\r | |
3106 | ans = ans._fix(context)\r | |
3107 | context.rounding = rounding\r | |
3108 | return ans\r | |
3109 | \r | |
3110 | def _log10_exp_bound(self):\r | |
3111 | """Compute a lower bound for the adjusted exponent of self.log10().\r | |
3112 | In other words, find r such that self.log10() >= 10**r.\r | |
3113 | Assumes that self is finite and positive and that self != 1.\r | |
3114 | """\r | |
3115 | \r | |
3116 | # For x >= 10 or x < 0.1 we only need a bound on the integer\r | |
3117 | # part of log10(self), and this comes directly from the\r | |
3118 | # exponent of x. For 0.1 <= x <= 10 we use the inequalities\r | |
3119 | # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| >\r | |
3120 | # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0\r | |
3121 | \r | |
3122 | adj = self._exp + len(self._int) - 1\r | |
3123 | if adj >= 1:\r | |
3124 | # self >= 10\r | |
3125 | return len(str(adj))-1\r | |
3126 | if adj <= -2:\r | |
3127 | # self < 0.1\r | |
3128 | return len(str(-1-adj))-1\r | |
3129 | op = _WorkRep(self)\r | |
3130 | c, e = op.int, op.exp\r | |
3131 | if adj == 0:\r | |
3132 | # 1 < self < 10\r | |
3133 | num = str(c-10**-e)\r | |
3134 | den = str(231*c)\r | |
3135 | return len(num) - len(den) - (num < den) + 2\r | |
3136 | # adj == -1, 0.1 <= self < 1\r | |
3137 | num = str(10**-e-c)\r | |
3138 | return len(num) + e - (num < "231") - 1\r | |
3139 | \r | |
3140 | def log10(self, context=None):\r | |
3141 | """Returns the base 10 logarithm of self."""\r | |
3142 | \r | |
3143 | if context is None:\r | |
3144 | context = getcontext()\r | |
3145 | \r | |
3146 | # log10(NaN) = NaN\r | |
3147 | ans = self._check_nans(context=context)\r | |
3148 | if ans:\r | |
3149 | return ans\r | |
3150 | \r | |
3151 | # log10(0.0) == -Infinity\r | |
3152 | if not self:\r | |
3153 | return _NegativeInfinity\r | |
3154 | \r | |
3155 | # log10(Infinity) = Infinity\r | |
3156 | if self._isinfinity() == 1:\r | |
3157 | return _Infinity\r | |
3158 | \r | |
3159 | # log10(negative or -Infinity) raises InvalidOperation\r | |
3160 | if self._sign == 1:\r | |
3161 | return context._raise_error(InvalidOperation,\r | |
3162 | 'log10 of a negative value')\r | |
3163 | \r | |
3164 | # log10(10**n) = n\r | |
3165 | if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1):\r | |
3166 | # answer may need rounding\r | |
3167 | ans = Decimal(self._exp + len(self._int) - 1)\r | |
3168 | else:\r | |
3169 | # result is irrational, so necessarily inexact\r | |
3170 | op = _WorkRep(self)\r | |
3171 | c, e = op.int, op.exp\r | |
3172 | p = context.prec\r | |
3173 | \r | |
3174 | # correctly rounded result: repeatedly increase precision\r | |
3175 | # until result is unambiguously roundable\r | |
3176 | places = p-self._log10_exp_bound()+2\r | |
3177 | while True:\r | |
3178 | coeff = _dlog10(c, e, places)\r | |
3179 | # assert len(str(abs(coeff)))-p >= 1\r | |
3180 | if coeff % (5*10**(len(str(abs(coeff)))-p-1)):\r | |
3181 | break\r | |
3182 | places += 3\r | |
3183 | ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)\r | |
3184 | \r | |
3185 | context = context._shallow_copy()\r | |
3186 | rounding = context._set_rounding(ROUND_HALF_EVEN)\r | |
3187 | ans = ans._fix(context)\r | |
3188 | context.rounding = rounding\r | |
3189 | return ans\r | |
3190 | \r | |
3191 | def logb(self, context=None):\r | |
3192 | """ Returns the exponent of the magnitude of self's MSD.\r | |
3193 | \r | |
3194 | The result is the integer which is the exponent of the magnitude\r | |
3195 | of the most significant digit of self (as though it were truncated\r | |
3196 | to a single digit while maintaining the value of that digit and\r | |
3197 | without limiting the resulting exponent).\r | |
3198 | """\r | |
3199 | # logb(NaN) = NaN\r | |
3200 | ans = self._check_nans(context=context)\r | |
3201 | if ans:\r | |
3202 | return ans\r | |
3203 | \r | |
3204 | if context is None:\r | |
3205 | context = getcontext()\r | |
3206 | \r | |
3207 | # logb(+/-Inf) = +Inf\r | |
3208 | if self._isinfinity():\r | |
3209 | return _Infinity\r | |
3210 | \r | |
3211 | # logb(0) = -Inf, DivisionByZero\r | |
3212 | if not self:\r | |
3213 | return context._raise_error(DivisionByZero, 'logb(0)', 1)\r | |
3214 | \r | |
3215 | # otherwise, simply return the adjusted exponent of self, as a\r | |
3216 | # Decimal. Note that no attempt is made to fit the result\r | |
3217 | # into the current context.\r | |
3218 | ans = Decimal(self.adjusted())\r | |
3219 | return ans._fix(context)\r | |
3220 | \r | |
3221 | def _islogical(self):\r | |
3222 | """Return True if self is a logical operand.\r | |
3223 | \r | |
3224 | For being logical, it must be a finite number with a sign of 0,\r | |
3225 | an exponent of 0, and a coefficient whose digits must all be\r | |
3226 | either 0 or 1.\r | |
3227 | """\r | |
3228 | if self._sign != 0 or self._exp != 0:\r | |
3229 | return False\r | |
3230 | for dig in self._int:\r | |
3231 | if dig not in '01':\r | |
3232 | return False\r | |
3233 | return True\r | |
3234 | \r | |
3235 | def _fill_logical(self, context, opa, opb):\r | |
3236 | dif = context.prec - len(opa)\r | |
3237 | if dif > 0:\r | |
3238 | opa = '0'*dif + opa\r | |
3239 | elif dif < 0:\r | |
3240 | opa = opa[-context.prec:]\r | |
3241 | dif = context.prec - len(opb)\r | |
3242 | if dif > 0:\r | |
3243 | opb = '0'*dif + opb\r | |
3244 | elif dif < 0:\r | |
3245 | opb = opb[-context.prec:]\r | |
3246 | return opa, opb\r | |
3247 | \r | |
3248 | def logical_and(self, other, context=None):\r | |
3249 | """Applies an 'and' operation between self and other's digits."""\r | |
3250 | if context is None:\r | |
3251 | context = getcontext()\r | |
3252 | \r | |
3253 | other = _convert_other(other, raiseit=True)\r | |
3254 | \r | |
3255 | if not self._islogical() or not other._islogical():\r | |
3256 | return context._raise_error(InvalidOperation)\r | |
3257 | \r | |
3258 | # fill to context.prec\r | |
3259 | (opa, opb) = self._fill_logical(context, self._int, other._int)\r | |
3260 | \r | |
3261 | # make the operation, and clean starting zeroes\r | |
3262 | result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)])\r | |
3263 | return _dec_from_triple(0, result.lstrip('0') or '0', 0)\r | |
3264 | \r | |
3265 | def logical_invert(self, context=None):\r | |
3266 | """Invert all its digits."""\r | |
3267 | if context is None:\r | |
3268 | context = getcontext()\r | |
3269 | return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0),\r | |
3270 | context)\r | |
3271 | \r | |
3272 | def logical_or(self, other, context=None):\r | |
3273 | """Applies an 'or' operation between self and other's digits."""\r | |
3274 | if context is None:\r | |
3275 | context = getcontext()\r | |
3276 | \r | |
3277 | other = _convert_other(other, raiseit=True)\r | |
3278 | \r | |
3279 | if not self._islogical() or not other._islogical():\r | |
3280 | return context._raise_error(InvalidOperation)\r | |
3281 | \r | |
3282 | # fill to context.prec\r | |
3283 | (opa, opb) = self._fill_logical(context, self._int, other._int)\r | |
3284 | \r | |
3285 | # make the operation, and clean starting zeroes\r | |
3286 | result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)])\r | |
3287 | return _dec_from_triple(0, result.lstrip('0') or '0', 0)\r | |
3288 | \r | |
3289 | def logical_xor(self, other, context=None):\r | |
3290 | """Applies an 'xor' operation between self and other's digits."""\r | |
3291 | if context is None:\r | |
3292 | context = getcontext()\r | |
3293 | \r | |
3294 | other = _convert_other(other, raiseit=True)\r | |
3295 | \r | |
3296 | if not self._islogical() or not other._islogical():\r | |
3297 | return context._raise_error(InvalidOperation)\r | |
3298 | \r | |
3299 | # fill to context.prec\r | |
3300 | (opa, opb) = self._fill_logical(context, self._int, other._int)\r | |
3301 | \r | |
3302 | # make the operation, and clean starting zeroes\r | |
3303 | result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)])\r | |
3304 | return _dec_from_triple(0, result.lstrip('0') or '0', 0)\r | |
3305 | \r | |
3306 | def max_mag(self, other, context=None):\r | |
3307 | """Compares the values numerically with their sign ignored."""\r | |
3308 | other = _convert_other(other, raiseit=True)\r | |
3309 | \r | |
3310 | if context is None:\r | |
3311 | context = getcontext()\r | |
3312 | \r | |
3313 | if self._is_special or other._is_special:\r | |
3314 | # If one operand is a quiet NaN and the other is number, then the\r | |
3315 | # number is always returned\r | |
3316 | sn = self._isnan()\r | |
3317 | on = other._isnan()\r | |
3318 | if sn or on:\r | |
3319 | if on == 1 and sn == 0:\r | |
3320 | return self._fix(context)\r | |
3321 | if sn == 1 and on == 0:\r | |
3322 | return other._fix(context)\r | |
3323 | return self._check_nans(other, context)\r | |
3324 | \r | |
3325 | c = self.copy_abs()._cmp(other.copy_abs())\r | |
3326 | if c == 0:\r | |
3327 | c = self.compare_total(other)\r | |
3328 | \r | |
3329 | if c == -1:\r | |
3330 | ans = other\r | |
3331 | else:\r | |
3332 | ans = self\r | |
3333 | \r | |
3334 | return ans._fix(context)\r | |
3335 | \r | |
3336 | def min_mag(self, other, context=None):\r | |
3337 | """Compares the values numerically with their sign ignored."""\r | |
3338 | other = _convert_other(other, raiseit=True)\r | |
3339 | \r | |
3340 | if context is None:\r | |
3341 | context = getcontext()\r | |
3342 | \r | |
3343 | if self._is_special or other._is_special:\r | |
3344 | # If one operand is a quiet NaN and the other is number, then the\r | |
3345 | # number is always returned\r | |
3346 | sn = self._isnan()\r | |
3347 | on = other._isnan()\r | |
3348 | if sn or on:\r | |
3349 | if on == 1 and sn == 0:\r | |
3350 | return self._fix(context)\r | |
3351 | if sn == 1 and on == 0:\r | |
3352 | return other._fix(context)\r | |
3353 | return self._check_nans(other, context)\r | |
3354 | \r | |
3355 | c = self.copy_abs()._cmp(other.copy_abs())\r | |
3356 | if c == 0:\r | |
3357 | c = self.compare_total(other)\r | |
3358 | \r | |
3359 | if c == -1:\r | |
3360 | ans = self\r | |
3361 | else:\r | |
3362 | ans = other\r | |
3363 | \r | |
3364 | return ans._fix(context)\r | |
3365 | \r | |
3366 | def next_minus(self, context=None):\r | |
3367 | """Returns the largest representable number smaller than itself."""\r | |
3368 | if context is None:\r | |
3369 | context = getcontext()\r | |
3370 | \r | |
3371 | ans = self._check_nans(context=context)\r | |
3372 | if ans:\r | |
3373 | return ans\r | |
3374 | \r | |
3375 | if self._isinfinity() == -1:\r | |
3376 | return _NegativeInfinity\r | |
3377 | if self._isinfinity() == 1:\r | |
3378 | return _dec_from_triple(0, '9'*context.prec, context.Etop())\r | |
3379 | \r | |
3380 | context = context.copy()\r | |
3381 | context._set_rounding(ROUND_FLOOR)\r | |
3382 | context._ignore_all_flags()\r | |
3383 | new_self = self._fix(context)\r | |
3384 | if new_self != self:\r | |
3385 | return new_self\r | |
3386 | return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1),\r | |
3387 | context)\r | |
3388 | \r | |
3389 | def next_plus(self, context=None):\r | |
3390 | """Returns the smallest representable number larger than itself."""\r | |
3391 | if context is None:\r | |
3392 | context = getcontext()\r | |
3393 | \r | |
3394 | ans = self._check_nans(context=context)\r | |
3395 | if ans:\r | |
3396 | return ans\r | |
3397 | \r | |
3398 | if self._isinfinity() == 1:\r | |
3399 | return _Infinity\r | |
3400 | if self._isinfinity() == -1:\r | |
3401 | return _dec_from_triple(1, '9'*context.prec, context.Etop())\r | |
3402 | \r | |
3403 | context = context.copy()\r | |
3404 | context._set_rounding(ROUND_CEILING)\r | |
3405 | context._ignore_all_flags()\r | |
3406 | new_self = self._fix(context)\r | |
3407 | if new_self != self:\r | |
3408 | return new_self\r | |
3409 | return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1),\r | |
3410 | context)\r | |
3411 | \r | |
3412 | def next_toward(self, other, context=None):\r | |
3413 | """Returns the number closest to self, in the direction towards other.\r | |
3414 | \r | |
3415 | The result is the closest representable number to self\r | |
3416 | (excluding self) that is in the direction towards other,\r | |
3417 | unless both have the same value. If the two operands are\r | |
3418 | numerically equal, then the result is a copy of self with the\r | |
3419 | sign set to be the same as the sign of other.\r | |
3420 | """\r | |
3421 | other = _convert_other(other, raiseit=True)\r | |
3422 | \r | |
3423 | if context is None:\r | |
3424 | context = getcontext()\r | |
3425 | \r | |
3426 | ans = self._check_nans(other, context)\r | |
3427 | if ans:\r | |
3428 | return ans\r | |
3429 | \r | |
3430 | comparison = self._cmp(other)\r | |
3431 | if comparison == 0:\r | |
3432 | return self.copy_sign(other)\r | |
3433 | \r | |
3434 | if comparison == -1:\r | |
3435 | ans = self.next_plus(context)\r | |
3436 | else: # comparison == 1\r | |
3437 | ans = self.next_minus(context)\r | |
3438 | \r | |
3439 | # decide which flags to raise using value of ans\r | |
3440 | if ans._isinfinity():\r | |
3441 | context._raise_error(Overflow,\r | |
3442 | 'Infinite result from next_toward',\r | |
3443 | ans._sign)\r | |
3444 | context._raise_error(Inexact)\r | |
3445 | context._raise_error(Rounded)\r | |
3446 | elif ans.adjusted() < context.Emin:\r | |
3447 | context._raise_error(Underflow)\r | |
3448 | context._raise_error(Subnormal)\r | |
3449 | context._raise_error(Inexact)\r | |
3450 | context._raise_error(Rounded)\r | |
3451 | # if precision == 1 then we don't raise Clamped for a\r | |
3452 | # result 0E-Etiny.\r | |
3453 | if not ans:\r | |
3454 | context._raise_error(Clamped)\r | |
3455 | \r | |
3456 | return ans\r | |
3457 | \r | |
3458 | def number_class(self, context=None):\r | |
3459 | """Returns an indication of the class of self.\r | |
3460 | \r | |
3461 | The class is one of the following strings:\r | |
3462 | sNaN\r | |
3463 | NaN\r | |
3464 | -Infinity\r | |
3465 | -Normal\r | |
3466 | -Subnormal\r | |
3467 | -Zero\r | |
3468 | +Zero\r | |
3469 | +Subnormal\r | |
3470 | +Normal\r | |
3471 | +Infinity\r | |
3472 | """\r | |
3473 | if self.is_snan():\r | |
3474 | return "sNaN"\r | |
3475 | if self.is_qnan():\r | |
3476 | return "NaN"\r | |
3477 | inf = self._isinfinity()\r | |
3478 | if inf == 1:\r | |
3479 | return "+Infinity"\r | |
3480 | if inf == -1:\r | |
3481 | return "-Infinity"\r | |
3482 | if self.is_zero():\r | |
3483 | if self._sign:\r | |
3484 | return "-Zero"\r | |
3485 | else:\r | |
3486 | return "+Zero"\r | |
3487 | if context is None:\r | |
3488 | context = getcontext()\r | |
3489 | if self.is_subnormal(context=context):\r | |
3490 | if self._sign:\r | |
3491 | return "-Subnormal"\r | |
3492 | else:\r | |
3493 | return "+Subnormal"\r | |
3494 | # just a normal, regular, boring number, :)\r | |
3495 | if self._sign:\r | |
3496 | return "-Normal"\r | |
3497 | else:\r | |
3498 | return "+Normal"\r | |
3499 | \r | |
3500 | def radix(self):\r | |
3501 | """Just returns 10, as this is Decimal, :)"""\r | |
3502 | return Decimal(10)\r | |
3503 | \r | |
3504 | def rotate(self, other, context=None):\r | |
3505 | """Returns a rotated copy of self, value-of-other times."""\r | |
3506 | if context is None:\r | |
3507 | context = getcontext()\r | |
3508 | \r | |
3509 | other = _convert_other(other, raiseit=True)\r | |
3510 | \r | |
3511 | ans = self._check_nans(other, context)\r | |
3512 | if ans:\r | |
3513 | return ans\r | |
3514 | \r | |
3515 | if other._exp != 0:\r | |
3516 | return context._raise_error(InvalidOperation)\r | |
3517 | if not (-context.prec <= int(other) <= context.prec):\r | |
3518 | return context._raise_error(InvalidOperation)\r | |
3519 | \r | |
3520 | if self._isinfinity():\r | |
3521 | return Decimal(self)\r | |
3522 | \r | |
3523 | # get values, pad if necessary\r | |
3524 | torot = int(other)\r | |
3525 | rotdig = self._int\r | |
3526 | topad = context.prec - len(rotdig)\r | |
3527 | if topad > 0:\r | |
3528 | rotdig = '0'*topad + rotdig\r | |
3529 | elif topad < 0:\r | |
3530 | rotdig = rotdig[-topad:]\r | |
3531 | \r | |
3532 | # let's rotate!\r | |
3533 | rotated = rotdig[torot:] + rotdig[:torot]\r | |
3534 | return _dec_from_triple(self._sign,\r | |
3535 | rotated.lstrip('0') or '0', self._exp)\r | |
3536 | \r | |
3537 | def scaleb(self, other, context=None):\r | |
3538 | """Returns self operand after adding the second value to its exp."""\r | |
3539 | if context is None:\r | |
3540 | context = getcontext()\r | |
3541 | \r | |
3542 | other = _convert_other(other, raiseit=True)\r | |
3543 | \r | |
3544 | ans = self._check_nans(other, context)\r | |
3545 | if ans:\r | |
3546 | return ans\r | |
3547 | \r | |
3548 | if other._exp != 0:\r | |
3549 | return context._raise_error(InvalidOperation)\r | |
3550 | liminf = -2 * (context.Emax + context.prec)\r | |
3551 | limsup = 2 * (context.Emax + context.prec)\r | |
3552 | if not (liminf <= int(other) <= limsup):\r | |
3553 | return context._raise_error(InvalidOperation)\r | |
3554 | \r | |
3555 | if self._isinfinity():\r | |
3556 | return Decimal(self)\r | |
3557 | \r | |
3558 | d = _dec_from_triple(self._sign, self._int, self._exp + int(other))\r | |
3559 | d = d._fix(context)\r | |
3560 | return d\r | |
3561 | \r | |
3562 | def shift(self, other, context=None):\r | |
3563 | """Returns a shifted copy of self, value-of-other times."""\r | |
3564 | if context is None:\r | |
3565 | context = getcontext()\r | |
3566 | \r | |
3567 | other = _convert_other(other, raiseit=True)\r | |
3568 | \r | |
3569 | ans = self._check_nans(other, context)\r | |
3570 | if ans:\r | |
3571 | return ans\r | |
3572 | \r | |
3573 | if other._exp != 0:\r | |
3574 | return context._raise_error(InvalidOperation)\r | |
3575 | if not (-context.prec <= int(other) <= context.prec):\r | |
3576 | return context._raise_error(InvalidOperation)\r | |
3577 | \r | |
3578 | if self._isinfinity():\r | |
3579 | return Decimal(self)\r | |
3580 | \r | |
3581 | # get values, pad if necessary\r | |
3582 | torot = int(other)\r | |
3583 | rotdig = self._int\r | |
3584 | topad = context.prec - len(rotdig)\r | |
3585 | if topad > 0:\r | |
3586 | rotdig = '0'*topad + rotdig\r | |
3587 | elif topad < 0:\r | |
3588 | rotdig = rotdig[-topad:]\r | |
3589 | \r | |
3590 | # let's shift!\r | |
3591 | if torot < 0:\r | |
3592 | shifted = rotdig[:torot]\r | |
3593 | else:\r | |
3594 | shifted = rotdig + '0'*torot\r | |
3595 | shifted = shifted[-context.prec:]\r | |
3596 | \r | |
3597 | return _dec_from_triple(self._sign,\r | |
3598 | shifted.lstrip('0') or '0', self._exp)\r | |
3599 | \r | |
3600 | # Support for pickling, copy, and deepcopy\r | |
3601 | def __reduce__(self):\r | |
3602 | return (self.__class__, (str(self),))\r | |
3603 | \r | |
3604 | def __copy__(self):\r | |
3605 | if type(self) is Decimal:\r | |
3606 | return self # I'm immutable; therefore I am my own clone\r | |
3607 | return self.__class__(str(self))\r | |
3608 | \r | |
3609 | def __deepcopy__(self, memo):\r | |
3610 | if type(self) is Decimal:\r | |
3611 | return self # My components are also immutable\r | |
3612 | return self.__class__(str(self))\r | |
3613 | \r | |
3614 | # PEP 3101 support. the _localeconv keyword argument should be\r | |
3615 | # considered private: it's provided for ease of testing only.\r | |
3616 | def __format__(self, specifier, context=None, _localeconv=None):\r | |
3617 | """Format a Decimal instance according to the given specifier.\r | |
3618 | \r | |
3619 | The specifier should be a standard format specifier, with the\r | |
3620 | form described in PEP 3101. Formatting types 'e', 'E', 'f',\r | |
3621 | 'F', 'g', 'G', 'n' and '%' are supported. If the formatting\r | |
3622 | type is omitted it defaults to 'g' or 'G', depending on the\r | |
3623 | value of context.capitals.\r | |
3624 | """\r | |
3625 | \r | |
3626 | # Note: PEP 3101 says that if the type is not present then\r | |
3627 | # there should be at least one digit after the decimal point.\r | |
3628 | # We take the liberty of ignoring this requirement for\r | |
3629 | # Decimal---it's presumably there to make sure that\r | |
3630 | # format(float, '') behaves similarly to str(float).\r | |
3631 | if context is None:\r | |
3632 | context = getcontext()\r | |
3633 | \r | |
3634 | spec = _parse_format_specifier(specifier, _localeconv=_localeconv)\r | |
3635 | \r | |
3636 | # special values don't care about the type or precision\r | |
3637 | if self._is_special:\r | |
3638 | sign = _format_sign(self._sign, spec)\r | |
3639 | body = str(self.copy_abs())\r | |
3640 | return _format_align(sign, body, spec)\r | |
3641 | \r | |
3642 | # a type of None defaults to 'g' or 'G', depending on context\r | |
3643 | if spec['type'] is None:\r | |
3644 | spec['type'] = ['g', 'G'][context.capitals]\r | |
3645 | \r | |
3646 | # if type is '%', adjust exponent of self accordingly\r | |
3647 | if spec['type'] == '%':\r | |
3648 | self = _dec_from_triple(self._sign, self._int, self._exp+2)\r | |
3649 | \r | |
3650 | # round if necessary, taking rounding mode from the context\r | |
3651 | rounding = context.rounding\r | |
3652 | precision = spec['precision']\r | |
3653 | if precision is not None:\r | |
3654 | if spec['type'] in 'eE':\r | |
3655 | self = self._round(precision+1, rounding)\r | |
3656 | elif spec['type'] in 'fF%':\r | |
3657 | self = self._rescale(-precision, rounding)\r | |
3658 | elif spec['type'] in 'gG' and len(self._int) > precision:\r | |
3659 | self = self._round(precision, rounding)\r | |
3660 | # special case: zeros with a positive exponent can't be\r | |
3661 | # represented in fixed point; rescale them to 0e0.\r | |
3662 | if not self and self._exp > 0 and spec['type'] in 'fF%':\r | |
3663 | self = self._rescale(0, rounding)\r | |
3664 | \r | |
3665 | # figure out placement of the decimal point\r | |
3666 | leftdigits = self._exp + len(self._int)\r | |
3667 | if spec['type'] in 'eE':\r | |
3668 | if not self and precision is not None:\r | |
3669 | dotplace = 1 - precision\r | |
3670 | else:\r | |
3671 | dotplace = 1\r | |
3672 | elif spec['type'] in 'fF%':\r | |
3673 | dotplace = leftdigits\r | |
3674 | elif spec['type'] in 'gG':\r | |
3675 | if self._exp <= 0 and leftdigits > -6:\r | |
3676 | dotplace = leftdigits\r | |
3677 | else:\r | |
3678 | dotplace = 1\r | |
3679 | \r | |
3680 | # find digits before and after decimal point, and get exponent\r | |
3681 | if dotplace < 0:\r | |
3682 | intpart = '0'\r | |
3683 | fracpart = '0'*(-dotplace) + self._int\r | |
3684 | elif dotplace > len(self._int):\r | |
3685 | intpart = self._int + '0'*(dotplace-len(self._int))\r | |
3686 | fracpart = ''\r | |
3687 | else:\r | |
3688 | intpart = self._int[:dotplace] or '0'\r | |
3689 | fracpart = self._int[dotplace:]\r | |
3690 | exp = leftdigits-dotplace\r | |
3691 | \r | |
3692 | # done with the decimal-specific stuff; hand over the rest\r | |
3693 | # of the formatting to the _format_number function\r | |
3694 | return _format_number(self._sign, intpart, fracpart, exp, spec)\r | |
3695 | \r | |
3696 | def _dec_from_triple(sign, coefficient, exponent, special=False):\r | |
3697 | """Create a decimal instance directly, without any validation,\r | |
3698 | normalization (e.g. removal of leading zeros) or argument\r | |
3699 | conversion.\r | |
3700 | \r | |
3701 | This function is for *internal use only*.\r | |
3702 | """\r | |
3703 | \r | |
3704 | self = object.__new__(Decimal)\r | |
3705 | self._sign = sign\r | |
3706 | self._int = coefficient\r | |
3707 | self._exp = exponent\r | |
3708 | self._is_special = special\r | |
3709 | \r | |
3710 | return self\r | |
3711 | \r | |
3712 | # Register Decimal as a kind of Number (an abstract base class).\r | |
3713 | # However, do not register it as Real (because Decimals are not\r | |
3714 | # interoperable with floats).\r | |
3715 | _numbers.Number.register(Decimal)\r | |
3716 | \r | |
3717 | \r | |
3718 | ##### Context class #######################################################\r | |
3719 | \r | |
3720 | class _ContextManager(object):\r | |
3721 | """Context manager class to support localcontext().\r | |
3722 | \r | |
3723 | Sets a copy of the supplied context in __enter__() and restores\r | |
3724 | the previous decimal context in __exit__()\r | |
3725 | """\r | |
3726 | def __init__(self, new_context):\r | |
3727 | self.new_context = new_context.copy()\r | |
3728 | def __enter__(self):\r | |
3729 | self.saved_context = getcontext()\r | |
3730 | setcontext(self.new_context)\r | |
3731 | return self.new_context\r | |
3732 | def __exit__(self, t, v, tb):\r | |
3733 | setcontext(self.saved_context)\r | |
3734 | \r | |
3735 | class Context(object):\r | |
3736 | """Contains the context for a Decimal instance.\r | |
3737 | \r | |
3738 | Contains:\r | |
3739 | prec - precision (for use in rounding, division, square roots..)\r | |
3740 | rounding - rounding type (how you round)\r | |
3741 | traps - If traps[exception] = 1, then the exception is\r | |
3742 | raised when it is caused. Otherwise, a value is\r | |
3743 | substituted in.\r | |
3744 | flags - When an exception is caused, flags[exception] is set.\r | |
3745 | (Whether or not the trap_enabler is set)\r | |
3746 | Should be reset by user of Decimal instance.\r | |
3747 | Emin - Minimum exponent\r | |
3748 | Emax - Maximum exponent\r | |
3749 | capitals - If 1, 1*10^1 is printed as 1E+1.\r | |
3750 | If 0, printed as 1e1\r | |
3751 | _clamp - If 1, change exponents if too high (Default 0)\r | |
3752 | """\r | |
3753 | \r | |
3754 | def __init__(self, prec=None, rounding=None,\r | |
3755 | traps=None, flags=None,\r | |
3756 | Emin=None, Emax=None,\r | |
3757 | capitals=None, _clamp=0,\r | |
3758 | _ignored_flags=None):\r | |
3759 | # Set defaults; for everything except flags and _ignored_flags,\r | |
3760 | # inherit from DefaultContext.\r | |
3761 | try:\r | |
3762 | dc = DefaultContext\r | |
3763 | except NameError:\r | |
3764 | pass\r | |
3765 | \r | |
3766 | self.prec = prec if prec is not None else dc.prec\r | |
3767 | self.rounding = rounding if rounding is not None else dc.rounding\r | |
3768 | self.Emin = Emin if Emin is not None else dc.Emin\r | |
3769 | self.Emax = Emax if Emax is not None else dc.Emax\r | |
3770 | self.capitals = capitals if capitals is not None else dc.capitals\r | |
3771 | self._clamp = _clamp if _clamp is not None else dc._clamp\r | |
3772 | \r | |
3773 | if _ignored_flags is None:\r | |
3774 | self._ignored_flags = []\r | |
3775 | else:\r | |
3776 | self._ignored_flags = _ignored_flags\r | |
3777 | \r | |
3778 | if traps is None:\r | |
3779 | self.traps = dc.traps.copy()\r | |
3780 | elif not isinstance(traps, dict):\r | |
3781 | self.traps = dict((s, int(s in traps)) for s in _signals)\r | |
3782 | else:\r | |
3783 | self.traps = traps\r | |
3784 | \r | |
3785 | if flags is None:\r | |
3786 | self.flags = dict.fromkeys(_signals, 0)\r | |
3787 | elif not isinstance(flags, dict):\r | |
3788 | self.flags = dict((s, int(s in flags)) for s in _signals)\r | |
3789 | else:\r | |
3790 | self.flags = flags\r | |
3791 | \r | |
3792 | def __repr__(self):\r | |
3793 | """Show the current context."""\r | |
3794 | s = []\r | |
3795 | s.append('Context(prec=%(prec)d, rounding=%(rounding)s, '\r | |
3796 | 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d'\r | |
3797 | % vars(self))\r | |
3798 | names = [f.__name__ for f, v in self.flags.items() if v]\r | |
3799 | s.append('flags=[' + ', '.join(names) + ']')\r | |
3800 | names = [t.__name__ for t, v in self.traps.items() if v]\r | |
3801 | s.append('traps=[' + ', '.join(names) + ']')\r | |
3802 | return ', '.join(s) + ')'\r | |
3803 | \r | |
3804 | def clear_flags(self):\r | |
3805 | """Reset all flags to zero"""\r | |
3806 | for flag in self.flags:\r | |
3807 | self.flags[flag] = 0\r | |
3808 | \r | |
3809 | def _shallow_copy(self):\r | |
3810 | """Returns a shallow copy from self."""\r | |
3811 | nc = Context(self.prec, self.rounding, self.traps,\r | |
3812 | self.flags, self.Emin, self.Emax,\r | |
3813 | self.capitals, self._clamp, self._ignored_flags)\r | |
3814 | return nc\r | |
3815 | \r | |
3816 | def copy(self):\r | |
3817 | """Returns a deep copy from self."""\r | |
3818 | nc = Context(self.prec, self.rounding, self.traps.copy(),\r | |
3819 | self.flags.copy(), self.Emin, self.Emax,\r | |
3820 | self.capitals, self._clamp, self._ignored_flags)\r | |
3821 | return nc\r | |
3822 | __copy__ = copy\r | |
3823 | \r | |
3824 | def _raise_error(self, condition, explanation = None, *args):\r | |
3825 | """Handles an error\r | |
3826 | \r | |
3827 | If the flag is in _ignored_flags, returns the default response.\r | |
3828 | Otherwise, it sets the flag, then, if the corresponding\r | |
3829 | trap_enabler is set, it reraises the exception. Otherwise, it returns\r | |
3830 | the default value after setting the flag.\r | |
3831 | """\r | |
3832 | error = _condition_map.get(condition, condition)\r | |
3833 | if error in self._ignored_flags:\r | |
3834 | # Don't touch the flag\r | |
3835 | return error().handle(self, *args)\r | |
3836 | \r | |
3837 | self.flags[error] = 1\r | |
3838 | if not self.traps[error]:\r | |
3839 | # The errors define how to handle themselves.\r | |
3840 | return condition().handle(self, *args)\r | |
3841 | \r | |
3842 | # Errors should only be risked on copies of the context\r | |
3843 | # self._ignored_flags = []\r | |
3844 | raise error(explanation)\r | |
3845 | \r | |
3846 | def _ignore_all_flags(self):\r | |
3847 | """Ignore all flags, if they are raised"""\r | |
3848 | return self._ignore_flags(*_signals)\r | |
3849 | \r | |
3850 | def _ignore_flags(self, *flags):\r | |
3851 | """Ignore the flags, if they are raised"""\r | |
3852 | # Do not mutate-- This way, copies of a context leave the original\r | |
3853 | # alone.\r | |
3854 | self._ignored_flags = (self._ignored_flags + list(flags))\r | |
3855 | return list(flags)\r | |
3856 | \r | |
3857 | def _regard_flags(self, *flags):\r | |
3858 | """Stop ignoring the flags, if they are raised"""\r | |
3859 | if flags and isinstance(flags[0], (tuple,list)):\r | |
3860 | flags = flags[0]\r | |
3861 | for flag in flags:\r | |
3862 | self._ignored_flags.remove(flag)\r | |
3863 | \r | |
3864 | # We inherit object.__hash__, so we must deny this explicitly\r | |
3865 | __hash__ = None\r | |
3866 | \r | |
3867 | def Etiny(self):\r | |
3868 | """Returns Etiny (= Emin - prec + 1)"""\r | |
3869 | return int(self.Emin - self.prec + 1)\r | |
3870 | \r | |
3871 | def Etop(self):\r | |
3872 | """Returns maximum exponent (= Emax - prec + 1)"""\r | |
3873 | return int(self.Emax - self.prec + 1)\r | |
3874 | \r | |
3875 | def _set_rounding(self, type):\r | |
3876 | """Sets the rounding type.\r | |
3877 | \r | |
3878 | Sets the rounding type, and returns the current (previous)\r | |
3879 | rounding type. Often used like:\r | |
3880 | \r | |
3881 | context = context.copy()\r | |
3882 | # so you don't change the calling context\r | |
3883 | # if an error occurs in the middle.\r | |
3884 | rounding = context._set_rounding(ROUND_UP)\r | |
3885 | val = self.__sub__(other, context=context)\r | |
3886 | context._set_rounding(rounding)\r | |
3887 | \r | |
3888 | This will make it round up for that operation.\r | |
3889 | """\r | |
3890 | rounding = self.rounding\r | |
3891 | self.rounding= type\r | |
3892 | return rounding\r | |
3893 | \r | |
3894 | def create_decimal(self, num='0'):\r | |
3895 | """Creates a new Decimal instance but using self as context.\r | |
3896 | \r | |
3897 | This method implements the to-number operation of the\r | |
3898 | IBM Decimal specification."""\r | |
3899 | \r | |
3900 | if isinstance(num, basestring) and num != num.strip():\r | |
3901 | return self._raise_error(ConversionSyntax,\r | |
3902 | "no trailing or leading whitespace is "\r | |
3903 | "permitted.")\r | |
3904 | \r | |
3905 | d = Decimal(num, context=self)\r | |
3906 | if d._isnan() and len(d._int) > self.prec - self._clamp:\r | |
3907 | return self._raise_error(ConversionSyntax,\r | |
3908 | "diagnostic info too long in NaN")\r | |
3909 | return d._fix(self)\r | |
3910 | \r | |
3911 | def create_decimal_from_float(self, f):\r | |
3912 | """Creates a new Decimal instance from a float but rounding using self\r | |
3913 | as the context.\r | |
3914 | \r | |
3915 | >>> context = Context(prec=5, rounding=ROUND_DOWN)\r | |
3916 | >>> context.create_decimal_from_float(3.1415926535897932)\r | |
3917 | Decimal('3.1415')\r | |
3918 | >>> context = Context(prec=5, traps=[Inexact])\r | |
3919 | >>> context.create_decimal_from_float(3.1415926535897932)\r | |
3920 | Traceback (most recent call last):\r | |
3921 | ...\r | |
3922 | Inexact: None\r | |
3923 | \r | |
3924 | """\r | |
3925 | d = Decimal.from_float(f) # An exact conversion\r | |
3926 | return d._fix(self) # Apply the context rounding\r | |
3927 | \r | |
3928 | # Methods\r | |
3929 | def abs(self, a):\r | |
3930 | """Returns the absolute value of the operand.\r | |
3931 | \r | |
3932 | If the operand is negative, the result is the same as using the minus\r | |
3933 | operation on the operand. Otherwise, the result is the same as using\r | |
3934 | the plus operation on the operand.\r | |
3935 | \r | |
3936 | >>> ExtendedContext.abs(Decimal('2.1'))\r | |
3937 | Decimal('2.1')\r | |
3938 | >>> ExtendedContext.abs(Decimal('-100'))\r | |
3939 | Decimal('100')\r | |
3940 | >>> ExtendedContext.abs(Decimal('101.5'))\r | |
3941 | Decimal('101.5')\r | |
3942 | >>> ExtendedContext.abs(Decimal('-101.5'))\r | |
3943 | Decimal('101.5')\r | |
3944 | >>> ExtendedContext.abs(-1)\r | |
3945 | Decimal('1')\r | |
3946 | """\r | |
3947 | a = _convert_other(a, raiseit=True)\r | |
3948 | return a.__abs__(context=self)\r | |
3949 | \r | |
3950 | def add(self, a, b):\r | |
3951 | """Return the sum of the two operands.\r | |
3952 | \r | |
3953 | >>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))\r | |
3954 | Decimal('19.00')\r | |
3955 | >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))\r | |
3956 | Decimal('1.02E+4')\r | |
3957 | >>> ExtendedContext.add(1, Decimal(2))\r | |
3958 | Decimal('3')\r | |
3959 | >>> ExtendedContext.add(Decimal(8), 5)\r | |
3960 | Decimal('13')\r | |
3961 | >>> ExtendedContext.add(5, 5)\r | |
3962 | Decimal('10')\r | |
3963 | """\r | |
3964 | a = _convert_other(a, raiseit=True)\r | |
3965 | r = a.__add__(b, context=self)\r | |
3966 | if r is NotImplemented:\r | |
3967 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
3968 | else:\r | |
3969 | return r\r | |
3970 | \r | |
3971 | def _apply(self, a):\r | |
3972 | return str(a._fix(self))\r | |
3973 | \r | |
3974 | def canonical(self, a):\r | |
3975 | """Returns the same Decimal object.\r | |
3976 | \r | |
3977 | As we do not have different encodings for the same number, the\r | |
3978 | received object already is in its canonical form.\r | |
3979 | \r | |
3980 | >>> ExtendedContext.canonical(Decimal('2.50'))\r | |
3981 | Decimal('2.50')\r | |
3982 | """\r | |
3983 | return a.canonical(context=self)\r | |
3984 | \r | |
3985 | def compare(self, a, b):\r | |
3986 | """Compares values numerically.\r | |
3987 | \r | |
3988 | If the signs of the operands differ, a value representing each operand\r | |
3989 | ('-1' if the operand is less than zero, '0' if the operand is zero or\r | |
3990 | negative zero, or '1' if the operand is greater than zero) is used in\r | |
3991 | place of that operand for the comparison instead of the actual\r | |
3992 | operand.\r | |
3993 | \r | |
3994 | The comparison is then effected by subtracting the second operand from\r | |
3995 | the first and then returning a value according to the result of the\r | |
3996 | subtraction: '-1' if the result is less than zero, '0' if the result is\r | |
3997 | zero or negative zero, or '1' if the result is greater than zero.\r | |
3998 | \r | |
3999 | >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))\r | |
4000 | Decimal('-1')\r | |
4001 | >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))\r | |
4002 | Decimal('0')\r | |
4003 | >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))\r | |
4004 | Decimal('0')\r | |
4005 | >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))\r | |
4006 | Decimal('1')\r | |
4007 | >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))\r | |
4008 | Decimal('1')\r | |
4009 | >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))\r | |
4010 | Decimal('-1')\r | |
4011 | >>> ExtendedContext.compare(1, 2)\r | |
4012 | Decimal('-1')\r | |
4013 | >>> ExtendedContext.compare(Decimal(1), 2)\r | |
4014 | Decimal('-1')\r | |
4015 | >>> ExtendedContext.compare(1, Decimal(2))\r | |
4016 | Decimal('-1')\r | |
4017 | """\r | |
4018 | a = _convert_other(a, raiseit=True)\r | |
4019 | return a.compare(b, context=self)\r | |
4020 | \r | |
4021 | def compare_signal(self, a, b):\r | |
4022 | """Compares the values of the two operands numerically.\r | |
4023 | \r | |
4024 | It's pretty much like compare(), but all NaNs signal, with signaling\r | |
4025 | NaNs taking precedence over quiet NaNs.\r | |
4026 | \r | |
4027 | >>> c = ExtendedContext\r | |
4028 | >>> c.compare_signal(Decimal('2.1'), Decimal('3'))\r | |
4029 | Decimal('-1')\r | |
4030 | >>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))\r | |
4031 | Decimal('0')\r | |
4032 | >>> c.flags[InvalidOperation] = 0\r | |
4033 | >>> print c.flags[InvalidOperation]\r | |
4034 | 0\r | |
4035 | >>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))\r | |
4036 | Decimal('NaN')\r | |
4037 | >>> print c.flags[InvalidOperation]\r | |
4038 | 1\r | |
4039 | >>> c.flags[InvalidOperation] = 0\r | |
4040 | >>> print c.flags[InvalidOperation]\r | |
4041 | 0\r | |
4042 | >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1'))\r | |
4043 | Decimal('NaN')\r | |
4044 | >>> print c.flags[InvalidOperation]\r | |
4045 | 1\r | |
4046 | >>> c.compare_signal(-1, 2)\r | |
4047 | Decimal('-1')\r | |
4048 | >>> c.compare_signal(Decimal(-1), 2)\r | |
4049 | Decimal('-1')\r | |
4050 | >>> c.compare_signal(-1, Decimal(2))\r | |
4051 | Decimal('-1')\r | |
4052 | """\r | |
4053 | a = _convert_other(a, raiseit=True)\r | |
4054 | return a.compare_signal(b, context=self)\r | |
4055 | \r | |
4056 | def compare_total(self, a, b):\r | |
4057 | """Compares two operands using their abstract representation.\r | |
4058 | \r | |
4059 | This is not like the standard compare, which use their numerical\r | |
4060 | value. Note that a total ordering is defined for all possible abstract\r | |
4061 | representations.\r | |
4062 | \r | |
4063 | >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))\r | |
4064 | Decimal('-1')\r | |
4065 | >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12'))\r | |
4066 | Decimal('-1')\r | |
4067 | >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))\r | |
4068 | Decimal('-1')\r | |
4069 | >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))\r | |
4070 | Decimal('0')\r | |
4071 | >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300'))\r | |
4072 | Decimal('1')\r | |
4073 | >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN'))\r | |
4074 | Decimal('-1')\r | |
4075 | >>> ExtendedContext.compare_total(1, 2)\r | |
4076 | Decimal('-1')\r | |
4077 | >>> ExtendedContext.compare_total(Decimal(1), 2)\r | |
4078 | Decimal('-1')\r | |
4079 | >>> ExtendedContext.compare_total(1, Decimal(2))\r | |
4080 | Decimal('-1')\r | |
4081 | """\r | |
4082 | a = _convert_other(a, raiseit=True)\r | |
4083 | return a.compare_total(b)\r | |
4084 | \r | |
4085 | def compare_total_mag(self, a, b):\r | |
4086 | """Compares two operands using their abstract representation ignoring sign.\r | |
4087 | \r | |
4088 | Like compare_total, but with operand's sign ignored and assumed to be 0.\r | |
4089 | """\r | |
4090 | a = _convert_other(a, raiseit=True)\r | |
4091 | return a.compare_total_mag(b)\r | |
4092 | \r | |
4093 | def copy_abs(self, a):\r | |
4094 | """Returns a copy of the operand with the sign set to 0.\r | |
4095 | \r | |
4096 | >>> ExtendedContext.copy_abs(Decimal('2.1'))\r | |
4097 | Decimal('2.1')\r | |
4098 | >>> ExtendedContext.copy_abs(Decimal('-100'))\r | |
4099 | Decimal('100')\r | |
4100 | >>> ExtendedContext.copy_abs(-1)\r | |
4101 | Decimal('1')\r | |
4102 | """\r | |
4103 | a = _convert_other(a, raiseit=True)\r | |
4104 | return a.copy_abs()\r | |
4105 | \r | |
4106 | def copy_decimal(self, a):\r | |
4107 | """Returns a copy of the decimal object.\r | |
4108 | \r | |
4109 | >>> ExtendedContext.copy_decimal(Decimal('2.1'))\r | |
4110 | Decimal('2.1')\r | |
4111 | >>> ExtendedContext.copy_decimal(Decimal('-1.00'))\r | |
4112 | Decimal('-1.00')\r | |
4113 | >>> ExtendedContext.copy_decimal(1)\r | |
4114 | Decimal('1')\r | |
4115 | """\r | |
4116 | a = _convert_other(a, raiseit=True)\r | |
4117 | return Decimal(a)\r | |
4118 | \r | |
4119 | def copy_negate(self, a):\r | |
4120 | """Returns a copy of the operand with the sign inverted.\r | |
4121 | \r | |
4122 | >>> ExtendedContext.copy_negate(Decimal('101.5'))\r | |
4123 | Decimal('-101.5')\r | |
4124 | >>> ExtendedContext.copy_negate(Decimal('-101.5'))\r | |
4125 | Decimal('101.5')\r | |
4126 | >>> ExtendedContext.copy_negate(1)\r | |
4127 | Decimal('-1')\r | |
4128 | """\r | |
4129 | a = _convert_other(a, raiseit=True)\r | |
4130 | return a.copy_negate()\r | |
4131 | \r | |
4132 | def copy_sign(self, a, b):\r | |
4133 | """Copies the second operand's sign to the first one.\r | |
4134 | \r | |
4135 | In detail, it returns a copy of the first operand with the sign\r | |
4136 | equal to the sign of the second operand.\r | |
4137 | \r | |
4138 | >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))\r | |
4139 | Decimal('1.50')\r | |
4140 | >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))\r | |
4141 | Decimal('1.50')\r | |
4142 | >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))\r | |
4143 | Decimal('-1.50')\r | |
4144 | >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))\r | |
4145 | Decimal('-1.50')\r | |
4146 | >>> ExtendedContext.copy_sign(1, -2)\r | |
4147 | Decimal('-1')\r | |
4148 | >>> ExtendedContext.copy_sign(Decimal(1), -2)\r | |
4149 | Decimal('-1')\r | |
4150 | >>> ExtendedContext.copy_sign(1, Decimal(-2))\r | |
4151 | Decimal('-1')\r | |
4152 | """\r | |
4153 | a = _convert_other(a, raiseit=True)\r | |
4154 | return a.copy_sign(b)\r | |
4155 | \r | |
4156 | def divide(self, a, b):\r | |
4157 | """Decimal division in a specified context.\r | |
4158 | \r | |
4159 | >>> ExtendedContext.divide(Decimal('1'), Decimal('3'))\r | |
4160 | Decimal('0.333333333')\r | |
4161 | >>> ExtendedContext.divide(Decimal('2'), Decimal('3'))\r | |
4162 | Decimal('0.666666667')\r | |
4163 | >>> ExtendedContext.divide(Decimal('5'), Decimal('2'))\r | |
4164 | Decimal('2.5')\r | |
4165 | >>> ExtendedContext.divide(Decimal('1'), Decimal('10'))\r | |
4166 | Decimal('0.1')\r | |
4167 | >>> ExtendedContext.divide(Decimal('12'), Decimal('12'))\r | |
4168 | Decimal('1')\r | |
4169 | >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))\r | |
4170 | Decimal('4.00')\r | |
4171 | >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))\r | |
4172 | Decimal('1.20')\r | |
4173 | >>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))\r | |
4174 | Decimal('10')\r | |
4175 | >>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))\r | |
4176 | Decimal('1000')\r | |
4177 | >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))\r | |
4178 | Decimal('1.20E+6')\r | |
4179 | >>> ExtendedContext.divide(5, 5)\r | |
4180 | Decimal('1')\r | |
4181 | >>> ExtendedContext.divide(Decimal(5), 5)\r | |
4182 | Decimal('1')\r | |
4183 | >>> ExtendedContext.divide(5, Decimal(5))\r | |
4184 | Decimal('1')\r | |
4185 | """\r | |
4186 | a = _convert_other(a, raiseit=True)\r | |
4187 | r = a.__div__(b, context=self)\r | |
4188 | if r is NotImplemented:\r | |
4189 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
4190 | else:\r | |
4191 | return r\r | |
4192 | \r | |
4193 | def divide_int(self, a, b):\r | |
4194 | """Divides two numbers and returns the integer part of the result.\r | |
4195 | \r | |
4196 | >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))\r | |
4197 | Decimal('0')\r | |
4198 | >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))\r | |
4199 | Decimal('3')\r | |
4200 | >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))\r | |
4201 | Decimal('3')\r | |
4202 | >>> ExtendedContext.divide_int(10, 3)\r | |
4203 | Decimal('3')\r | |
4204 | >>> ExtendedContext.divide_int(Decimal(10), 3)\r | |
4205 | Decimal('3')\r | |
4206 | >>> ExtendedContext.divide_int(10, Decimal(3))\r | |
4207 | Decimal('3')\r | |
4208 | """\r | |
4209 | a = _convert_other(a, raiseit=True)\r | |
4210 | r = a.__floordiv__(b, context=self)\r | |
4211 | if r is NotImplemented:\r | |
4212 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
4213 | else:\r | |
4214 | return r\r | |
4215 | \r | |
4216 | def divmod(self, a, b):\r | |
4217 | """Return (a // b, a % b).\r | |
4218 | \r | |
4219 | >>> ExtendedContext.divmod(Decimal(8), Decimal(3))\r | |
4220 | (Decimal('2'), Decimal('2'))\r | |
4221 | >>> ExtendedContext.divmod(Decimal(8), Decimal(4))\r | |
4222 | (Decimal('2'), Decimal('0'))\r | |
4223 | >>> ExtendedContext.divmod(8, 4)\r | |
4224 | (Decimal('2'), Decimal('0'))\r | |
4225 | >>> ExtendedContext.divmod(Decimal(8), 4)\r | |
4226 | (Decimal('2'), Decimal('0'))\r | |
4227 | >>> ExtendedContext.divmod(8, Decimal(4))\r | |
4228 | (Decimal('2'), Decimal('0'))\r | |
4229 | """\r | |
4230 | a = _convert_other(a, raiseit=True)\r | |
4231 | r = a.__divmod__(b, context=self)\r | |
4232 | if r is NotImplemented:\r | |
4233 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
4234 | else:\r | |
4235 | return r\r | |
4236 | \r | |
4237 | def exp(self, a):\r | |
4238 | """Returns e ** a.\r | |
4239 | \r | |
4240 | >>> c = ExtendedContext.copy()\r | |
4241 | >>> c.Emin = -999\r | |
4242 | >>> c.Emax = 999\r | |
4243 | >>> c.exp(Decimal('-Infinity'))\r | |
4244 | Decimal('0')\r | |
4245 | >>> c.exp(Decimal('-1'))\r | |
4246 | Decimal('0.367879441')\r | |
4247 | >>> c.exp(Decimal('0'))\r | |
4248 | Decimal('1')\r | |
4249 | >>> c.exp(Decimal('1'))\r | |
4250 | Decimal('2.71828183')\r | |
4251 | >>> c.exp(Decimal('0.693147181'))\r | |
4252 | Decimal('2.00000000')\r | |
4253 | >>> c.exp(Decimal('+Infinity'))\r | |
4254 | Decimal('Infinity')\r | |
4255 | >>> c.exp(10)\r | |
4256 | Decimal('22026.4658')\r | |
4257 | """\r | |
4258 | a =_convert_other(a, raiseit=True)\r | |
4259 | return a.exp(context=self)\r | |
4260 | \r | |
4261 | def fma(self, a, b, c):\r | |
4262 | """Returns a multiplied by b, plus c.\r | |
4263 | \r | |
4264 | The first two operands are multiplied together, using multiply,\r | |
4265 | the third operand is then added to the result of that\r | |
4266 | multiplication, using add, all with only one final rounding.\r | |
4267 | \r | |
4268 | >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))\r | |
4269 | Decimal('22')\r | |
4270 | >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))\r | |
4271 | Decimal('-8')\r | |
4272 | >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))\r | |
4273 | Decimal('1.38435736E+12')\r | |
4274 | >>> ExtendedContext.fma(1, 3, 4)\r | |
4275 | Decimal('7')\r | |
4276 | >>> ExtendedContext.fma(1, Decimal(3), 4)\r | |
4277 | Decimal('7')\r | |
4278 | >>> ExtendedContext.fma(1, 3, Decimal(4))\r | |
4279 | Decimal('7')\r | |
4280 | """\r | |
4281 | a = _convert_other(a, raiseit=True)\r | |
4282 | return a.fma(b, c, context=self)\r | |
4283 | \r | |
4284 | def is_canonical(self, a):\r | |
4285 | """Return True if the operand is canonical; otherwise return False.\r | |
4286 | \r | |
4287 | Currently, the encoding of a Decimal instance is always\r | |
4288 | canonical, so this method returns True for any Decimal.\r | |
4289 | \r | |
4290 | >>> ExtendedContext.is_canonical(Decimal('2.50'))\r | |
4291 | True\r | |
4292 | """\r | |
4293 | return a.is_canonical()\r | |
4294 | \r | |
4295 | def is_finite(self, a):\r | |
4296 | """Return True if the operand is finite; otherwise return False.\r | |
4297 | \r | |
4298 | A Decimal instance is considered finite if it is neither\r | |
4299 | infinite nor a NaN.\r | |
4300 | \r | |
4301 | >>> ExtendedContext.is_finite(Decimal('2.50'))\r | |
4302 | True\r | |
4303 | >>> ExtendedContext.is_finite(Decimal('-0.3'))\r | |
4304 | True\r | |
4305 | >>> ExtendedContext.is_finite(Decimal('0'))\r | |
4306 | True\r | |
4307 | >>> ExtendedContext.is_finite(Decimal('Inf'))\r | |
4308 | False\r | |
4309 | >>> ExtendedContext.is_finite(Decimal('NaN'))\r | |
4310 | False\r | |
4311 | >>> ExtendedContext.is_finite(1)\r | |
4312 | True\r | |
4313 | """\r | |
4314 | a = _convert_other(a, raiseit=True)\r | |
4315 | return a.is_finite()\r | |
4316 | \r | |
4317 | def is_infinite(self, a):\r | |
4318 | """Return True if the operand is infinite; otherwise return False.\r | |
4319 | \r | |
4320 | >>> ExtendedContext.is_infinite(Decimal('2.50'))\r | |
4321 | False\r | |
4322 | >>> ExtendedContext.is_infinite(Decimal('-Inf'))\r | |
4323 | True\r | |
4324 | >>> ExtendedContext.is_infinite(Decimal('NaN'))\r | |
4325 | False\r | |
4326 | >>> ExtendedContext.is_infinite(1)\r | |
4327 | False\r | |
4328 | """\r | |
4329 | a = _convert_other(a, raiseit=True)\r | |
4330 | return a.is_infinite()\r | |
4331 | \r | |
4332 | def is_nan(self, a):\r | |
4333 | """Return True if the operand is a qNaN or sNaN;\r | |
4334 | otherwise return False.\r | |
4335 | \r | |
4336 | >>> ExtendedContext.is_nan(Decimal('2.50'))\r | |
4337 | False\r | |
4338 | >>> ExtendedContext.is_nan(Decimal('NaN'))\r | |
4339 | True\r | |
4340 | >>> ExtendedContext.is_nan(Decimal('-sNaN'))\r | |
4341 | True\r | |
4342 | >>> ExtendedContext.is_nan(1)\r | |
4343 | False\r | |
4344 | """\r | |
4345 | a = _convert_other(a, raiseit=True)\r | |
4346 | return a.is_nan()\r | |
4347 | \r | |
4348 | def is_normal(self, a):\r | |
4349 | """Return True if the operand is a normal number;\r | |
4350 | otherwise return False.\r | |
4351 | \r | |
4352 | >>> c = ExtendedContext.copy()\r | |
4353 | >>> c.Emin = -999\r | |
4354 | >>> c.Emax = 999\r | |
4355 | >>> c.is_normal(Decimal('2.50'))\r | |
4356 | True\r | |
4357 | >>> c.is_normal(Decimal('0.1E-999'))\r | |
4358 | False\r | |
4359 | >>> c.is_normal(Decimal('0.00'))\r | |
4360 | False\r | |
4361 | >>> c.is_normal(Decimal('-Inf'))\r | |
4362 | False\r | |
4363 | >>> c.is_normal(Decimal('NaN'))\r | |
4364 | False\r | |
4365 | >>> c.is_normal(1)\r | |
4366 | True\r | |
4367 | """\r | |
4368 | a = _convert_other(a, raiseit=True)\r | |
4369 | return a.is_normal(context=self)\r | |
4370 | \r | |
4371 | def is_qnan(self, a):\r | |
4372 | """Return True if the operand is a quiet NaN; otherwise return False.\r | |
4373 | \r | |
4374 | >>> ExtendedContext.is_qnan(Decimal('2.50'))\r | |
4375 | False\r | |
4376 | >>> ExtendedContext.is_qnan(Decimal('NaN'))\r | |
4377 | True\r | |
4378 | >>> ExtendedContext.is_qnan(Decimal('sNaN'))\r | |
4379 | False\r | |
4380 | >>> ExtendedContext.is_qnan(1)\r | |
4381 | False\r | |
4382 | """\r | |
4383 | a = _convert_other(a, raiseit=True)\r | |
4384 | return a.is_qnan()\r | |
4385 | \r | |
4386 | def is_signed(self, a):\r | |
4387 | """Return True if the operand is negative; otherwise return False.\r | |
4388 | \r | |
4389 | >>> ExtendedContext.is_signed(Decimal('2.50'))\r | |
4390 | False\r | |
4391 | >>> ExtendedContext.is_signed(Decimal('-12'))\r | |
4392 | True\r | |
4393 | >>> ExtendedContext.is_signed(Decimal('-0'))\r | |
4394 | True\r | |
4395 | >>> ExtendedContext.is_signed(8)\r | |
4396 | False\r | |
4397 | >>> ExtendedContext.is_signed(-8)\r | |
4398 | True\r | |
4399 | """\r | |
4400 | a = _convert_other(a, raiseit=True)\r | |
4401 | return a.is_signed()\r | |
4402 | \r | |
4403 | def is_snan(self, a):\r | |
4404 | """Return True if the operand is a signaling NaN;\r | |
4405 | otherwise return False.\r | |
4406 | \r | |
4407 | >>> ExtendedContext.is_snan(Decimal('2.50'))\r | |
4408 | False\r | |
4409 | >>> ExtendedContext.is_snan(Decimal('NaN'))\r | |
4410 | False\r | |
4411 | >>> ExtendedContext.is_snan(Decimal('sNaN'))\r | |
4412 | True\r | |
4413 | >>> ExtendedContext.is_snan(1)\r | |
4414 | False\r | |
4415 | """\r | |
4416 | a = _convert_other(a, raiseit=True)\r | |
4417 | return a.is_snan()\r | |
4418 | \r | |
4419 | def is_subnormal(self, a):\r | |
4420 | """Return True if the operand is subnormal; otherwise return False.\r | |
4421 | \r | |
4422 | >>> c = ExtendedContext.copy()\r | |
4423 | >>> c.Emin = -999\r | |
4424 | >>> c.Emax = 999\r | |
4425 | >>> c.is_subnormal(Decimal('2.50'))\r | |
4426 | False\r | |
4427 | >>> c.is_subnormal(Decimal('0.1E-999'))\r | |
4428 | True\r | |
4429 | >>> c.is_subnormal(Decimal('0.00'))\r | |
4430 | False\r | |
4431 | >>> c.is_subnormal(Decimal('-Inf'))\r | |
4432 | False\r | |
4433 | >>> c.is_subnormal(Decimal('NaN'))\r | |
4434 | False\r | |
4435 | >>> c.is_subnormal(1)\r | |
4436 | False\r | |
4437 | """\r | |
4438 | a = _convert_other(a, raiseit=True)\r | |
4439 | return a.is_subnormal(context=self)\r | |
4440 | \r | |
4441 | def is_zero(self, a):\r | |
4442 | """Return True if the operand is a zero; otherwise return False.\r | |
4443 | \r | |
4444 | >>> ExtendedContext.is_zero(Decimal('0'))\r | |
4445 | True\r | |
4446 | >>> ExtendedContext.is_zero(Decimal('2.50'))\r | |
4447 | False\r | |
4448 | >>> ExtendedContext.is_zero(Decimal('-0E+2'))\r | |
4449 | True\r | |
4450 | >>> ExtendedContext.is_zero(1)\r | |
4451 | False\r | |
4452 | >>> ExtendedContext.is_zero(0)\r | |
4453 | True\r | |
4454 | """\r | |
4455 | a = _convert_other(a, raiseit=True)\r | |
4456 | return a.is_zero()\r | |
4457 | \r | |
4458 | def ln(self, a):\r | |
4459 | """Returns the natural (base e) logarithm of the operand.\r | |
4460 | \r | |
4461 | >>> c = ExtendedContext.copy()\r | |
4462 | >>> c.Emin = -999\r | |
4463 | >>> c.Emax = 999\r | |
4464 | >>> c.ln(Decimal('0'))\r | |
4465 | Decimal('-Infinity')\r | |
4466 | >>> c.ln(Decimal('1.000'))\r | |
4467 | Decimal('0')\r | |
4468 | >>> c.ln(Decimal('2.71828183'))\r | |
4469 | Decimal('1.00000000')\r | |
4470 | >>> c.ln(Decimal('10'))\r | |
4471 | Decimal('2.30258509')\r | |
4472 | >>> c.ln(Decimal('+Infinity'))\r | |
4473 | Decimal('Infinity')\r | |
4474 | >>> c.ln(1)\r | |
4475 | Decimal('0')\r | |
4476 | """\r | |
4477 | a = _convert_other(a, raiseit=True)\r | |
4478 | return a.ln(context=self)\r | |
4479 | \r | |
4480 | def log10(self, a):\r | |
4481 | """Returns the base 10 logarithm of the operand.\r | |
4482 | \r | |
4483 | >>> c = ExtendedContext.copy()\r | |
4484 | >>> c.Emin = -999\r | |
4485 | >>> c.Emax = 999\r | |
4486 | >>> c.log10(Decimal('0'))\r | |
4487 | Decimal('-Infinity')\r | |
4488 | >>> c.log10(Decimal('0.001'))\r | |
4489 | Decimal('-3')\r | |
4490 | >>> c.log10(Decimal('1.000'))\r | |
4491 | Decimal('0')\r | |
4492 | >>> c.log10(Decimal('2'))\r | |
4493 | Decimal('0.301029996')\r | |
4494 | >>> c.log10(Decimal('10'))\r | |
4495 | Decimal('1')\r | |
4496 | >>> c.log10(Decimal('70'))\r | |
4497 | Decimal('1.84509804')\r | |
4498 | >>> c.log10(Decimal('+Infinity'))\r | |
4499 | Decimal('Infinity')\r | |
4500 | >>> c.log10(0)\r | |
4501 | Decimal('-Infinity')\r | |
4502 | >>> c.log10(1)\r | |
4503 | Decimal('0')\r | |
4504 | """\r | |
4505 | a = _convert_other(a, raiseit=True)\r | |
4506 | return a.log10(context=self)\r | |
4507 | \r | |
4508 | def logb(self, a):\r | |
4509 | """ Returns the exponent of the magnitude of the operand's MSD.\r | |
4510 | \r | |
4511 | The result is the integer which is the exponent of the magnitude\r | |
4512 | of the most significant digit of the operand (as though the\r | |
4513 | operand were truncated to a single digit while maintaining the\r | |
4514 | value of that digit and without limiting the resulting exponent).\r | |
4515 | \r | |
4516 | >>> ExtendedContext.logb(Decimal('250'))\r | |
4517 | Decimal('2')\r | |
4518 | >>> ExtendedContext.logb(Decimal('2.50'))\r | |
4519 | Decimal('0')\r | |
4520 | >>> ExtendedContext.logb(Decimal('0.03'))\r | |
4521 | Decimal('-2')\r | |
4522 | >>> ExtendedContext.logb(Decimal('0'))\r | |
4523 | Decimal('-Infinity')\r | |
4524 | >>> ExtendedContext.logb(1)\r | |
4525 | Decimal('0')\r | |
4526 | >>> ExtendedContext.logb(10)\r | |
4527 | Decimal('1')\r | |
4528 | >>> ExtendedContext.logb(100)\r | |
4529 | Decimal('2')\r | |
4530 | """\r | |
4531 | a = _convert_other(a, raiseit=True)\r | |
4532 | return a.logb(context=self)\r | |
4533 | \r | |
4534 | def logical_and(self, a, b):\r | |
4535 | """Applies the logical operation 'and' between each operand's digits.\r | |
4536 | \r | |
4537 | The operands must be both logical numbers.\r | |
4538 | \r | |
4539 | >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))\r | |
4540 | Decimal('0')\r | |
4541 | >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))\r | |
4542 | Decimal('0')\r | |
4543 | >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))\r | |
4544 | Decimal('0')\r | |
4545 | >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))\r | |
4546 | Decimal('1')\r | |
4547 | >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))\r | |
4548 | Decimal('1000')\r | |
4549 | >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))\r | |
4550 | Decimal('10')\r | |
4551 | >>> ExtendedContext.logical_and(110, 1101)\r | |
4552 | Decimal('100')\r | |
4553 | >>> ExtendedContext.logical_and(Decimal(110), 1101)\r | |
4554 | Decimal('100')\r | |
4555 | >>> ExtendedContext.logical_and(110, Decimal(1101))\r | |
4556 | Decimal('100')\r | |
4557 | """\r | |
4558 | a = _convert_other(a, raiseit=True)\r | |
4559 | return a.logical_and(b, context=self)\r | |
4560 | \r | |
4561 | def logical_invert(self, a):\r | |
4562 | """Invert all the digits in the operand.\r | |
4563 | \r | |
4564 | The operand must be a logical number.\r | |
4565 | \r | |
4566 | >>> ExtendedContext.logical_invert(Decimal('0'))\r | |
4567 | Decimal('111111111')\r | |
4568 | >>> ExtendedContext.logical_invert(Decimal('1'))\r | |
4569 | Decimal('111111110')\r | |
4570 | >>> ExtendedContext.logical_invert(Decimal('111111111'))\r | |
4571 | Decimal('0')\r | |
4572 | >>> ExtendedContext.logical_invert(Decimal('101010101'))\r | |
4573 | Decimal('10101010')\r | |
4574 | >>> ExtendedContext.logical_invert(1101)\r | |
4575 | Decimal('111110010')\r | |
4576 | """\r | |
4577 | a = _convert_other(a, raiseit=True)\r | |
4578 | return a.logical_invert(context=self)\r | |
4579 | \r | |
4580 | def logical_or(self, a, b):\r | |
4581 | """Applies the logical operation 'or' between each operand's digits.\r | |
4582 | \r | |
4583 | The operands must be both logical numbers.\r | |
4584 | \r | |
4585 | >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))\r | |
4586 | Decimal('0')\r | |
4587 | >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))\r | |
4588 | Decimal('1')\r | |
4589 | >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))\r | |
4590 | Decimal('1')\r | |
4591 | >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))\r | |
4592 | Decimal('1')\r | |
4593 | >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))\r | |
4594 | Decimal('1110')\r | |
4595 | >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))\r | |
4596 | Decimal('1110')\r | |
4597 | >>> ExtendedContext.logical_or(110, 1101)\r | |
4598 | Decimal('1111')\r | |
4599 | >>> ExtendedContext.logical_or(Decimal(110), 1101)\r | |
4600 | Decimal('1111')\r | |
4601 | >>> ExtendedContext.logical_or(110, Decimal(1101))\r | |
4602 | Decimal('1111')\r | |
4603 | """\r | |
4604 | a = _convert_other(a, raiseit=True)\r | |
4605 | return a.logical_or(b, context=self)\r | |
4606 | \r | |
4607 | def logical_xor(self, a, b):\r | |
4608 | """Applies the logical operation 'xor' between each operand's digits.\r | |
4609 | \r | |
4610 | The operands must be both logical numbers.\r | |
4611 | \r | |
4612 | >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))\r | |
4613 | Decimal('0')\r | |
4614 | >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))\r | |
4615 | Decimal('1')\r | |
4616 | >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))\r | |
4617 | Decimal('1')\r | |
4618 | >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))\r | |
4619 | Decimal('0')\r | |
4620 | >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))\r | |
4621 | Decimal('110')\r | |
4622 | >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))\r | |
4623 | Decimal('1101')\r | |
4624 | >>> ExtendedContext.logical_xor(110, 1101)\r | |
4625 | Decimal('1011')\r | |
4626 | >>> ExtendedContext.logical_xor(Decimal(110), 1101)\r | |
4627 | Decimal('1011')\r | |
4628 | >>> ExtendedContext.logical_xor(110, Decimal(1101))\r | |
4629 | Decimal('1011')\r | |
4630 | """\r | |
4631 | a = _convert_other(a, raiseit=True)\r | |
4632 | return a.logical_xor(b, context=self)\r | |
4633 | \r | |
4634 | def max(self, a, b):\r | |
4635 | """max compares two values numerically and returns the maximum.\r | |
4636 | \r | |
4637 | If either operand is a NaN then the general rules apply.\r | |
4638 | Otherwise, the operands are compared as though by the compare\r | |
4639 | operation. If they are numerically equal then the left-hand operand\r | |
4640 | is chosen as the result. Otherwise the maximum (closer to positive\r | |
4641 | infinity) of the two operands is chosen as the result.\r | |
4642 | \r | |
4643 | >>> ExtendedContext.max(Decimal('3'), Decimal('2'))\r | |
4644 | Decimal('3')\r | |
4645 | >>> ExtendedContext.max(Decimal('-10'), Decimal('3'))\r | |
4646 | Decimal('3')\r | |
4647 | >>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))\r | |
4648 | Decimal('1')\r | |
4649 | >>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))\r | |
4650 | Decimal('7')\r | |
4651 | >>> ExtendedContext.max(1, 2)\r | |
4652 | Decimal('2')\r | |
4653 | >>> ExtendedContext.max(Decimal(1), 2)\r | |
4654 | Decimal('2')\r | |
4655 | >>> ExtendedContext.max(1, Decimal(2))\r | |
4656 | Decimal('2')\r | |
4657 | """\r | |
4658 | a = _convert_other(a, raiseit=True)\r | |
4659 | return a.max(b, context=self)\r | |
4660 | \r | |
4661 | def max_mag(self, a, b):\r | |
4662 | """Compares the values numerically with their sign ignored.\r | |
4663 | \r | |
4664 | >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))\r | |
4665 | Decimal('7')\r | |
4666 | >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))\r | |
4667 | Decimal('-10')\r | |
4668 | >>> ExtendedContext.max_mag(1, -2)\r | |
4669 | Decimal('-2')\r | |
4670 | >>> ExtendedContext.max_mag(Decimal(1), -2)\r | |
4671 | Decimal('-2')\r | |
4672 | >>> ExtendedContext.max_mag(1, Decimal(-2))\r | |
4673 | Decimal('-2')\r | |
4674 | """\r | |
4675 | a = _convert_other(a, raiseit=True)\r | |
4676 | return a.max_mag(b, context=self)\r | |
4677 | \r | |
4678 | def min(self, a, b):\r | |
4679 | """min compares two values numerically and returns the minimum.\r | |
4680 | \r | |
4681 | If either operand is a NaN then the general rules apply.\r | |
4682 | Otherwise, the operands are compared as though by the compare\r | |
4683 | operation. If they are numerically equal then the left-hand operand\r | |
4684 | is chosen as the result. Otherwise the minimum (closer to negative\r | |
4685 | infinity) of the two operands is chosen as the result.\r | |
4686 | \r | |
4687 | >>> ExtendedContext.min(Decimal('3'), Decimal('2'))\r | |
4688 | Decimal('2')\r | |
4689 | >>> ExtendedContext.min(Decimal('-10'), Decimal('3'))\r | |
4690 | Decimal('-10')\r | |
4691 | >>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))\r | |
4692 | Decimal('1.0')\r | |
4693 | >>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))\r | |
4694 | Decimal('7')\r | |
4695 | >>> ExtendedContext.min(1, 2)\r | |
4696 | Decimal('1')\r | |
4697 | >>> ExtendedContext.min(Decimal(1), 2)\r | |
4698 | Decimal('1')\r | |
4699 | >>> ExtendedContext.min(1, Decimal(29))\r | |
4700 | Decimal('1')\r | |
4701 | """\r | |
4702 | a = _convert_other(a, raiseit=True)\r | |
4703 | return a.min(b, context=self)\r | |
4704 | \r | |
4705 | def min_mag(self, a, b):\r | |
4706 | """Compares the values numerically with their sign ignored.\r | |
4707 | \r | |
4708 | >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))\r | |
4709 | Decimal('-2')\r | |
4710 | >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))\r | |
4711 | Decimal('-3')\r | |
4712 | >>> ExtendedContext.min_mag(1, -2)\r | |
4713 | Decimal('1')\r | |
4714 | >>> ExtendedContext.min_mag(Decimal(1), -2)\r | |
4715 | Decimal('1')\r | |
4716 | >>> ExtendedContext.min_mag(1, Decimal(-2))\r | |
4717 | Decimal('1')\r | |
4718 | """\r | |
4719 | a = _convert_other(a, raiseit=True)\r | |
4720 | return a.min_mag(b, context=self)\r | |
4721 | \r | |
4722 | def minus(self, a):\r | |
4723 | """Minus corresponds to unary prefix minus in Python.\r | |
4724 | \r | |
4725 | The operation is evaluated using the same rules as subtract; the\r | |
4726 | operation minus(a) is calculated as subtract('0', a) where the '0'\r | |
4727 | has the same exponent as the operand.\r | |
4728 | \r | |
4729 | >>> ExtendedContext.minus(Decimal('1.3'))\r | |
4730 | Decimal('-1.3')\r | |
4731 | >>> ExtendedContext.minus(Decimal('-1.3'))\r | |
4732 | Decimal('1.3')\r | |
4733 | >>> ExtendedContext.minus(1)\r | |
4734 | Decimal('-1')\r | |
4735 | """\r | |
4736 | a = _convert_other(a, raiseit=True)\r | |
4737 | return a.__neg__(context=self)\r | |
4738 | \r | |
4739 | def multiply(self, a, b):\r | |
4740 | """multiply multiplies two operands.\r | |
4741 | \r | |
4742 | If either operand is a special value then the general rules apply.\r | |
4743 | Otherwise, the operands are multiplied together\r | |
4744 | ('long multiplication'), resulting in a number which may be as long as\r | |
4745 | the sum of the lengths of the two operands.\r | |
4746 | \r | |
4747 | >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))\r | |
4748 | Decimal('3.60')\r | |
4749 | >>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))\r | |
4750 | Decimal('21')\r | |
4751 | >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))\r | |
4752 | Decimal('0.72')\r | |
4753 | >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))\r | |
4754 | Decimal('-0.0')\r | |
4755 | >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))\r | |
4756 | Decimal('4.28135971E+11')\r | |
4757 | >>> ExtendedContext.multiply(7, 7)\r | |
4758 | Decimal('49')\r | |
4759 | >>> ExtendedContext.multiply(Decimal(7), 7)\r | |
4760 | Decimal('49')\r | |
4761 | >>> ExtendedContext.multiply(7, Decimal(7))\r | |
4762 | Decimal('49')\r | |
4763 | """\r | |
4764 | a = _convert_other(a, raiseit=True)\r | |
4765 | r = a.__mul__(b, context=self)\r | |
4766 | if r is NotImplemented:\r | |
4767 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
4768 | else:\r | |
4769 | return r\r | |
4770 | \r | |
4771 | def next_minus(self, a):\r | |
4772 | """Returns the largest representable number smaller than a.\r | |
4773 | \r | |
4774 | >>> c = ExtendedContext.copy()\r | |
4775 | >>> c.Emin = -999\r | |
4776 | >>> c.Emax = 999\r | |
4777 | >>> ExtendedContext.next_minus(Decimal('1'))\r | |
4778 | Decimal('0.999999999')\r | |
4779 | >>> c.next_minus(Decimal('1E-1007'))\r | |
4780 | Decimal('0E-1007')\r | |
4781 | >>> ExtendedContext.next_minus(Decimal('-1.00000003'))\r | |
4782 | Decimal('-1.00000004')\r | |
4783 | >>> c.next_minus(Decimal('Infinity'))\r | |
4784 | Decimal('9.99999999E+999')\r | |
4785 | >>> c.next_minus(1)\r | |
4786 | Decimal('0.999999999')\r | |
4787 | """\r | |
4788 | a = _convert_other(a, raiseit=True)\r | |
4789 | return a.next_minus(context=self)\r | |
4790 | \r | |
4791 | def next_plus(self, a):\r | |
4792 | """Returns the smallest representable number larger than a.\r | |
4793 | \r | |
4794 | >>> c = ExtendedContext.copy()\r | |
4795 | >>> c.Emin = -999\r | |
4796 | >>> c.Emax = 999\r | |
4797 | >>> ExtendedContext.next_plus(Decimal('1'))\r | |
4798 | Decimal('1.00000001')\r | |
4799 | >>> c.next_plus(Decimal('-1E-1007'))\r | |
4800 | Decimal('-0E-1007')\r | |
4801 | >>> ExtendedContext.next_plus(Decimal('-1.00000003'))\r | |
4802 | Decimal('-1.00000002')\r | |
4803 | >>> c.next_plus(Decimal('-Infinity'))\r | |
4804 | Decimal('-9.99999999E+999')\r | |
4805 | >>> c.next_plus(1)\r | |
4806 | Decimal('1.00000001')\r | |
4807 | """\r | |
4808 | a = _convert_other(a, raiseit=True)\r | |
4809 | return a.next_plus(context=self)\r | |
4810 | \r | |
4811 | def next_toward(self, a, b):\r | |
4812 | """Returns the number closest to a, in direction towards b.\r | |
4813 | \r | |
4814 | The result is the closest representable number from the first\r | |
4815 | operand (but not the first operand) that is in the direction\r | |
4816 | towards the second operand, unless the operands have the same\r | |
4817 | value.\r | |
4818 | \r | |
4819 | >>> c = ExtendedContext.copy()\r | |
4820 | >>> c.Emin = -999\r | |
4821 | >>> c.Emax = 999\r | |
4822 | >>> c.next_toward(Decimal('1'), Decimal('2'))\r | |
4823 | Decimal('1.00000001')\r | |
4824 | >>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))\r | |
4825 | Decimal('-0E-1007')\r | |
4826 | >>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))\r | |
4827 | Decimal('-1.00000002')\r | |
4828 | >>> c.next_toward(Decimal('1'), Decimal('0'))\r | |
4829 | Decimal('0.999999999')\r | |
4830 | >>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))\r | |
4831 | Decimal('0E-1007')\r | |
4832 | >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))\r | |
4833 | Decimal('-1.00000004')\r | |
4834 | >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))\r | |
4835 | Decimal('-0.00')\r | |
4836 | >>> c.next_toward(0, 1)\r | |
4837 | Decimal('1E-1007')\r | |
4838 | >>> c.next_toward(Decimal(0), 1)\r | |
4839 | Decimal('1E-1007')\r | |
4840 | >>> c.next_toward(0, Decimal(1))\r | |
4841 | Decimal('1E-1007')\r | |
4842 | """\r | |
4843 | a = _convert_other(a, raiseit=True)\r | |
4844 | return a.next_toward(b, context=self)\r | |
4845 | \r | |
4846 | def normalize(self, a):\r | |
4847 | """normalize reduces an operand to its simplest form.\r | |
4848 | \r | |
4849 | Essentially a plus operation with all trailing zeros removed from the\r | |
4850 | result.\r | |
4851 | \r | |
4852 | >>> ExtendedContext.normalize(Decimal('2.1'))\r | |
4853 | Decimal('2.1')\r | |
4854 | >>> ExtendedContext.normalize(Decimal('-2.0'))\r | |
4855 | Decimal('-2')\r | |
4856 | >>> ExtendedContext.normalize(Decimal('1.200'))\r | |
4857 | Decimal('1.2')\r | |
4858 | >>> ExtendedContext.normalize(Decimal('-120'))\r | |
4859 | Decimal('-1.2E+2')\r | |
4860 | >>> ExtendedContext.normalize(Decimal('120.00'))\r | |
4861 | Decimal('1.2E+2')\r | |
4862 | >>> ExtendedContext.normalize(Decimal('0.00'))\r | |
4863 | Decimal('0')\r | |
4864 | >>> ExtendedContext.normalize(6)\r | |
4865 | Decimal('6')\r | |
4866 | """\r | |
4867 | a = _convert_other(a, raiseit=True)\r | |
4868 | return a.normalize(context=self)\r | |
4869 | \r | |
4870 | def number_class(self, a):\r | |
4871 | """Returns an indication of the class of the operand.\r | |
4872 | \r | |
4873 | The class is one of the following strings:\r | |
4874 | -sNaN\r | |
4875 | -NaN\r | |
4876 | -Infinity\r | |
4877 | -Normal\r | |
4878 | -Subnormal\r | |
4879 | -Zero\r | |
4880 | +Zero\r | |
4881 | +Subnormal\r | |
4882 | +Normal\r | |
4883 | +Infinity\r | |
4884 | \r | |
4885 | >>> c = Context(ExtendedContext)\r | |
4886 | >>> c.Emin = -999\r | |
4887 | >>> c.Emax = 999\r | |
4888 | >>> c.number_class(Decimal('Infinity'))\r | |
4889 | '+Infinity'\r | |
4890 | >>> c.number_class(Decimal('1E-10'))\r | |
4891 | '+Normal'\r | |
4892 | >>> c.number_class(Decimal('2.50'))\r | |
4893 | '+Normal'\r | |
4894 | >>> c.number_class(Decimal('0.1E-999'))\r | |
4895 | '+Subnormal'\r | |
4896 | >>> c.number_class(Decimal('0'))\r | |
4897 | '+Zero'\r | |
4898 | >>> c.number_class(Decimal('-0'))\r | |
4899 | '-Zero'\r | |
4900 | >>> c.number_class(Decimal('-0.1E-999'))\r | |
4901 | '-Subnormal'\r | |
4902 | >>> c.number_class(Decimal('-1E-10'))\r | |
4903 | '-Normal'\r | |
4904 | >>> c.number_class(Decimal('-2.50'))\r | |
4905 | '-Normal'\r | |
4906 | >>> c.number_class(Decimal('-Infinity'))\r | |
4907 | '-Infinity'\r | |
4908 | >>> c.number_class(Decimal('NaN'))\r | |
4909 | 'NaN'\r | |
4910 | >>> c.number_class(Decimal('-NaN'))\r | |
4911 | 'NaN'\r | |
4912 | >>> c.number_class(Decimal('sNaN'))\r | |
4913 | 'sNaN'\r | |
4914 | >>> c.number_class(123)\r | |
4915 | '+Normal'\r | |
4916 | """\r | |
4917 | a = _convert_other(a, raiseit=True)\r | |
4918 | return a.number_class(context=self)\r | |
4919 | \r | |
4920 | def plus(self, a):\r | |
4921 | """Plus corresponds to unary prefix plus in Python.\r | |
4922 | \r | |
4923 | The operation is evaluated using the same rules as add; the\r | |
4924 | operation plus(a) is calculated as add('0', a) where the '0'\r | |
4925 | has the same exponent as the operand.\r | |
4926 | \r | |
4927 | >>> ExtendedContext.plus(Decimal('1.3'))\r | |
4928 | Decimal('1.3')\r | |
4929 | >>> ExtendedContext.plus(Decimal('-1.3'))\r | |
4930 | Decimal('-1.3')\r | |
4931 | >>> ExtendedContext.plus(-1)\r | |
4932 | Decimal('-1')\r | |
4933 | """\r | |
4934 | a = _convert_other(a, raiseit=True)\r | |
4935 | return a.__pos__(context=self)\r | |
4936 | \r | |
4937 | def power(self, a, b, modulo=None):\r | |
4938 | """Raises a to the power of b, to modulo if given.\r | |
4939 | \r | |
4940 | With two arguments, compute a**b. If a is negative then b\r | |
4941 | must be integral. The result will be inexact unless b is\r | |
4942 | integral and the result is finite and can be expressed exactly\r | |
4943 | in 'precision' digits.\r | |
4944 | \r | |
4945 | With three arguments, compute (a**b) % modulo. For the\r | |
4946 | three argument form, the following restrictions on the\r | |
4947 | arguments hold:\r | |
4948 | \r | |
4949 | - all three arguments must be integral\r | |
4950 | - b must be nonnegative\r | |
4951 | - at least one of a or b must be nonzero\r | |
4952 | - modulo must be nonzero and have at most 'precision' digits\r | |
4953 | \r | |
4954 | The result of pow(a, b, modulo) is identical to the result\r | |
4955 | that would be obtained by computing (a**b) % modulo with\r | |
4956 | unbounded precision, but is computed more efficiently. It is\r | |
4957 | always exact.\r | |
4958 | \r | |
4959 | >>> c = ExtendedContext.copy()\r | |
4960 | >>> c.Emin = -999\r | |
4961 | >>> c.Emax = 999\r | |
4962 | >>> c.power(Decimal('2'), Decimal('3'))\r | |
4963 | Decimal('8')\r | |
4964 | >>> c.power(Decimal('-2'), Decimal('3'))\r | |
4965 | Decimal('-8')\r | |
4966 | >>> c.power(Decimal('2'), Decimal('-3'))\r | |
4967 | Decimal('0.125')\r | |
4968 | >>> c.power(Decimal('1.7'), Decimal('8'))\r | |
4969 | Decimal('69.7575744')\r | |
4970 | >>> c.power(Decimal('10'), Decimal('0.301029996'))\r | |
4971 | Decimal('2.00000000')\r | |
4972 | >>> c.power(Decimal('Infinity'), Decimal('-1'))\r | |
4973 | Decimal('0')\r | |
4974 | >>> c.power(Decimal('Infinity'), Decimal('0'))\r | |
4975 | Decimal('1')\r | |
4976 | >>> c.power(Decimal('Infinity'), Decimal('1'))\r | |
4977 | Decimal('Infinity')\r | |
4978 | >>> c.power(Decimal('-Infinity'), Decimal('-1'))\r | |
4979 | Decimal('-0')\r | |
4980 | >>> c.power(Decimal('-Infinity'), Decimal('0'))\r | |
4981 | Decimal('1')\r | |
4982 | >>> c.power(Decimal('-Infinity'), Decimal('1'))\r | |
4983 | Decimal('-Infinity')\r | |
4984 | >>> c.power(Decimal('-Infinity'), Decimal('2'))\r | |
4985 | Decimal('Infinity')\r | |
4986 | >>> c.power(Decimal('0'), Decimal('0'))\r | |
4987 | Decimal('NaN')\r | |
4988 | \r | |
4989 | >>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))\r | |
4990 | Decimal('11')\r | |
4991 | >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))\r | |
4992 | Decimal('-11')\r | |
4993 | >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))\r | |
4994 | Decimal('1')\r | |
4995 | >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))\r | |
4996 | Decimal('11')\r | |
4997 | >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))\r | |
4998 | Decimal('11729830')\r | |
4999 | >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))\r | |
5000 | Decimal('-0')\r | |
5001 | >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))\r | |
5002 | Decimal('1')\r | |
5003 | >>> ExtendedContext.power(7, 7)\r | |
5004 | Decimal('823543')\r | |
5005 | >>> ExtendedContext.power(Decimal(7), 7)\r | |
5006 | Decimal('823543')\r | |
5007 | >>> ExtendedContext.power(7, Decimal(7), 2)\r | |
5008 | Decimal('1')\r | |
5009 | """\r | |
5010 | a = _convert_other(a, raiseit=True)\r | |
5011 | r = a.__pow__(b, modulo, context=self)\r | |
5012 | if r is NotImplemented:\r | |
5013 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
5014 | else:\r | |
5015 | return r\r | |
5016 | \r | |
5017 | def quantize(self, a, b):\r | |
5018 | """Returns a value equal to 'a' (rounded), having the exponent of 'b'.\r | |
5019 | \r | |
5020 | The coefficient of the result is derived from that of the left-hand\r | |
5021 | operand. It may be rounded using the current rounding setting (if the\r | |
5022 | exponent is being increased), multiplied by a positive power of ten (if\r | |
5023 | the exponent is being decreased), or is unchanged (if the exponent is\r | |
5024 | already equal to that of the right-hand operand).\r | |
5025 | \r | |
5026 | Unlike other operations, if the length of the coefficient after the\r | |
5027 | quantize operation would be greater than precision then an Invalid\r | |
5028 | operation condition is raised. This guarantees that, unless there is\r | |
5029 | an error condition, the exponent of the result of a quantize is always\r | |
5030 | equal to that of the right-hand operand.\r | |
5031 | \r | |
5032 | Also unlike other operations, quantize will never raise Underflow, even\r | |
5033 | if the result is subnormal and inexact.\r | |
5034 | \r | |
5035 | >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))\r | |
5036 | Decimal('2.170')\r | |
5037 | >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))\r | |
5038 | Decimal('2.17')\r | |
5039 | >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))\r | |
5040 | Decimal('2.2')\r | |
5041 | >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))\r | |
5042 | Decimal('2')\r | |
5043 | >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))\r | |
5044 | Decimal('0E+1')\r | |
5045 | >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))\r | |
5046 | Decimal('-Infinity')\r | |
5047 | >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))\r | |
5048 | Decimal('NaN')\r | |
5049 | >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))\r | |
5050 | Decimal('-0')\r | |
5051 | >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))\r | |
5052 | Decimal('-0E+5')\r | |
5053 | >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))\r | |
5054 | Decimal('NaN')\r | |
5055 | >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))\r | |
5056 | Decimal('NaN')\r | |
5057 | >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))\r | |
5058 | Decimal('217.0')\r | |
5059 | >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))\r | |
5060 | Decimal('217')\r | |
5061 | >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))\r | |
5062 | Decimal('2.2E+2')\r | |
5063 | >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))\r | |
5064 | Decimal('2E+2')\r | |
5065 | >>> ExtendedContext.quantize(1, 2)\r | |
5066 | Decimal('1')\r | |
5067 | >>> ExtendedContext.quantize(Decimal(1), 2)\r | |
5068 | Decimal('1')\r | |
5069 | >>> ExtendedContext.quantize(1, Decimal(2))\r | |
5070 | Decimal('1')\r | |
5071 | """\r | |
5072 | a = _convert_other(a, raiseit=True)\r | |
5073 | return a.quantize(b, context=self)\r | |
5074 | \r | |
5075 | def radix(self):\r | |
5076 | """Just returns 10, as this is Decimal, :)\r | |
5077 | \r | |
5078 | >>> ExtendedContext.radix()\r | |
5079 | Decimal('10')\r | |
5080 | """\r | |
5081 | return Decimal(10)\r | |
5082 | \r | |
5083 | def remainder(self, a, b):\r | |
5084 | """Returns the remainder from integer division.\r | |
5085 | \r | |
5086 | The result is the residue of the dividend after the operation of\r | |
5087 | calculating integer division as described for divide-integer, rounded\r | |
5088 | to precision digits if necessary. The sign of the result, if\r | |
5089 | non-zero, is the same as that of the original dividend.\r | |
5090 | \r | |
5091 | This operation will fail under the same conditions as integer division\r | |
5092 | (that is, if integer division on the same two operands would fail, the\r | |
5093 | remainder cannot be calculated).\r | |
5094 | \r | |
5095 | >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))\r | |
5096 | Decimal('2.1')\r | |
5097 | >>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))\r | |
5098 | Decimal('1')\r | |
5099 | >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))\r | |
5100 | Decimal('-1')\r | |
5101 | >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))\r | |
5102 | Decimal('0.2')\r | |
5103 | >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))\r | |
5104 | Decimal('0.1')\r | |
5105 | >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))\r | |
5106 | Decimal('1.0')\r | |
5107 | >>> ExtendedContext.remainder(22, 6)\r | |
5108 | Decimal('4')\r | |
5109 | >>> ExtendedContext.remainder(Decimal(22), 6)\r | |
5110 | Decimal('4')\r | |
5111 | >>> ExtendedContext.remainder(22, Decimal(6))\r | |
5112 | Decimal('4')\r | |
5113 | """\r | |
5114 | a = _convert_other(a, raiseit=True)\r | |
5115 | r = a.__mod__(b, context=self)\r | |
5116 | if r is NotImplemented:\r | |
5117 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
5118 | else:\r | |
5119 | return r\r | |
5120 | \r | |
5121 | def remainder_near(self, a, b):\r | |
5122 | """Returns to be "a - b * n", where n is the integer nearest the exact\r | |
5123 | value of "x / b" (if two integers are equally near then the even one\r | |
5124 | is chosen). If the result is equal to 0 then its sign will be the\r | |
5125 | sign of a.\r | |
5126 | \r | |
5127 | This operation will fail under the same conditions as integer division\r | |
5128 | (that is, if integer division on the same two operands would fail, the\r | |
5129 | remainder cannot be calculated).\r | |
5130 | \r | |
5131 | >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))\r | |
5132 | Decimal('-0.9')\r | |
5133 | >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))\r | |
5134 | Decimal('-2')\r | |
5135 | >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))\r | |
5136 | Decimal('1')\r | |
5137 | >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))\r | |
5138 | Decimal('-1')\r | |
5139 | >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))\r | |
5140 | Decimal('0.2')\r | |
5141 | >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))\r | |
5142 | Decimal('0.1')\r | |
5143 | >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))\r | |
5144 | Decimal('-0.3')\r | |
5145 | >>> ExtendedContext.remainder_near(3, 11)\r | |
5146 | Decimal('3')\r | |
5147 | >>> ExtendedContext.remainder_near(Decimal(3), 11)\r | |
5148 | Decimal('3')\r | |
5149 | >>> ExtendedContext.remainder_near(3, Decimal(11))\r | |
5150 | Decimal('3')\r | |
5151 | """\r | |
5152 | a = _convert_other(a, raiseit=True)\r | |
5153 | return a.remainder_near(b, context=self)\r | |
5154 | \r | |
5155 | def rotate(self, a, b):\r | |
5156 | """Returns a rotated copy of a, b times.\r | |
5157 | \r | |
5158 | The coefficient of the result is a rotated copy of the digits in\r | |
5159 | the coefficient of the first operand. The number of places of\r | |
5160 | rotation is taken from the absolute value of the second operand,\r | |
5161 | with the rotation being to the left if the second operand is\r | |
5162 | positive or to the right otherwise.\r | |
5163 | \r | |
5164 | >>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))\r | |
5165 | Decimal('400000003')\r | |
5166 | >>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))\r | |
5167 | Decimal('12')\r | |
5168 | >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))\r | |
5169 | Decimal('891234567')\r | |
5170 | >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))\r | |
5171 | Decimal('123456789')\r | |
5172 | >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))\r | |
5173 | Decimal('345678912')\r | |
5174 | >>> ExtendedContext.rotate(1333333, 1)\r | |
5175 | Decimal('13333330')\r | |
5176 | >>> ExtendedContext.rotate(Decimal(1333333), 1)\r | |
5177 | Decimal('13333330')\r | |
5178 | >>> ExtendedContext.rotate(1333333, Decimal(1))\r | |
5179 | Decimal('13333330')\r | |
5180 | """\r | |
5181 | a = _convert_other(a, raiseit=True)\r | |
5182 | return a.rotate(b, context=self)\r | |
5183 | \r | |
5184 | def same_quantum(self, a, b):\r | |
5185 | """Returns True if the two operands have the same exponent.\r | |
5186 | \r | |
5187 | The result is never affected by either the sign or the coefficient of\r | |
5188 | either operand.\r | |
5189 | \r | |
5190 | >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))\r | |
5191 | False\r | |
5192 | >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))\r | |
5193 | True\r | |
5194 | >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))\r | |
5195 | False\r | |
5196 | >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))\r | |
5197 | True\r | |
5198 | >>> ExtendedContext.same_quantum(10000, -1)\r | |
5199 | True\r | |
5200 | >>> ExtendedContext.same_quantum(Decimal(10000), -1)\r | |
5201 | True\r | |
5202 | >>> ExtendedContext.same_quantum(10000, Decimal(-1))\r | |
5203 | True\r | |
5204 | """\r | |
5205 | a = _convert_other(a, raiseit=True)\r | |
5206 | return a.same_quantum(b)\r | |
5207 | \r | |
5208 | def scaleb (self, a, b):\r | |
5209 | """Returns the first operand after adding the second value its exp.\r | |
5210 | \r | |
5211 | >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))\r | |
5212 | Decimal('0.0750')\r | |
5213 | >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))\r | |
5214 | Decimal('7.50')\r | |
5215 | >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))\r | |
5216 | Decimal('7.50E+3')\r | |
5217 | >>> ExtendedContext.scaleb(1, 4)\r | |
5218 | Decimal('1E+4')\r | |
5219 | >>> ExtendedContext.scaleb(Decimal(1), 4)\r | |
5220 | Decimal('1E+4')\r | |
5221 | >>> ExtendedContext.scaleb(1, Decimal(4))\r | |
5222 | Decimal('1E+4')\r | |
5223 | """\r | |
5224 | a = _convert_other(a, raiseit=True)\r | |
5225 | return a.scaleb(b, context=self)\r | |
5226 | \r | |
5227 | def shift(self, a, b):\r | |
5228 | """Returns a shifted copy of a, b times.\r | |
5229 | \r | |
5230 | The coefficient of the result is a shifted copy of the digits\r | |
5231 | in the coefficient of the first operand. The number of places\r | |
5232 | to shift is taken from the absolute value of the second operand,\r | |
5233 | with the shift being to the left if the second operand is\r | |
5234 | positive or to the right otherwise. Digits shifted into the\r | |
5235 | coefficient are zeros.\r | |
5236 | \r | |
5237 | >>> ExtendedContext.shift(Decimal('34'), Decimal('8'))\r | |
5238 | Decimal('400000000')\r | |
5239 | >>> ExtendedContext.shift(Decimal('12'), Decimal('9'))\r | |
5240 | Decimal('0')\r | |
5241 | >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))\r | |
5242 | Decimal('1234567')\r | |
5243 | >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))\r | |
5244 | Decimal('123456789')\r | |
5245 | >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))\r | |
5246 | Decimal('345678900')\r | |
5247 | >>> ExtendedContext.shift(88888888, 2)\r | |
5248 | Decimal('888888800')\r | |
5249 | >>> ExtendedContext.shift(Decimal(88888888), 2)\r | |
5250 | Decimal('888888800')\r | |
5251 | >>> ExtendedContext.shift(88888888, Decimal(2))\r | |
5252 | Decimal('888888800')\r | |
5253 | """\r | |
5254 | a = _convert_other(a, raiseit=True)\r | |
5255 | return a.shift(b, context=self)\r | |
5256 | \r | |
5257 | def sqrt(self, a):\r | |
5258 | """Square root of a non-negative number to context precision.\r | |
5259 | \r | |
5260 | If the result must be inexact, it is rounded using the round-half-even\r | |
5261 | algorithm.\r | |
5262 | \r | |
5263 | >>> ExtendedContext.sqrt(Decimal('0'))\r | |
5264 | Decimal('0')\r | |
5265 | >>> ExtendedContext.sqrt(Decimal('-0'))\r | |
5266 | Decimal('-0')\r | |
5267 | >>> ExtendedContext.sqrt(Decimal('0.39'))\r | |
5268 | Decimal('0.624499800')\r | |
5269 | >>> ExtendedContext.sqrt(Decimal('100'))\r | |
5270 | Decimal('10')\r | |
5271 | >>> ExtendedContext.sqrt(Decimal('1'))\r | |
5272 | Decimal('1')\r | |
5273 | >>> ExtendedContext.sqrt(Decimal('1.0'))\r | |
5274 | Decimal('1.0')\r | |
5275 | >>> ExtendedContext.sqrt(Decimal('1.00'))\r | |
5276 | Decimal('1.0')\r | |
5277 | >>> ExtendedContext.sqrt(Decimal('7'))\r | |
5278 | Decimal('2.64575131')\r | |
5279 | >>> ExtendedContext.sqrt(Decimal('10'))\r | |
5280 | Decimal('3.16227766')\r | |
5281 | >>> ExtendedContext.sqrt(2)\r | |
5282 | Decimal('1.41421356')\r | |
5283 | >>> ExtendedContext.prec\r | |
5284 | 9\r | |
5285 | """\r | |
5286 | a = _convert_other(a, raiseit=True)\r | |
5287 | return a.sqrt(context=self)\r | |
5288 | \r | |
5289 | def subtract(self, a, b):\r | |
5290 | """Return the difference between the two operands.\r | |
5291 | \r | |
5292 | >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))\r | |
5293 | Decimal('0.23')\r | |
5294 | >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))\r | |
5295 | Decimal('0.00')\r | |
5296 | >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))\r | |
5297 | Decimal('-0.77')\r | |
5298 | >>> ExtendedContext.subtract(8, 5)\r | |
5299 | Decimal('3')\r | |
5300 | >>> ExtendedContext.subtract(Decimal(8), 5)\r | |
5301 | Decimal('3')\r | |
5302 | >>> ExtendedContext.subtract(8, Decimal(5))\r | |
5303 | Decimal('3')\r | |
5304 | """\r | |
5305 | a = _convert_other(a, raiseit=True)\r | |
5306 | r = a.__sub__(b, context=self)\r | |
5307 | if r is NotImplemented:\r | |
5308 | raise TypeError("Unable to convert %s to Decimal" % b)\r | |
5309 | else:\r | |
5310 | return r\r | |
5311 | \r | |
5312 | def to_eng_string(self, a):\r | |
5313 | """Converts a number to a string, using scientific notation.\r | |
5314 | \r | |
5315 | The operation is not affected by the context.\r | |
5316 | """\r | |
5317 | a = _convert_other(a, raiseit=True)\r | |
5318 | return a.to_eng_string(context=self)\r | |
5319 | \r | |
5320 | def to_sci_string(self, a):\r | |
5321 | """Converts a number to a string, using scientific notation.\r | |
5322 | \r | |
5323 | The operation is not affected by the context.\r | |
5324 | """\r | |
5325 | a = _convert_other(a, raiseit=True)\r | |
5326 | return a.__str__(context=self)\r | |
5327 | \r | |
5328 | def to_integral_exact(self, a):\r | |
5329 | """Rounds to an integer.\r | |
5330 | \r | |
5331 | When the operand has a negative exponent, the result is the same\r | |
5332 | as using the quantize() operation using the given operand as the\r | |
5333 | left-hand-operand, 1E+0 as the right-hand-operand, and the precision\r | |
5334 | of the operand as the precision setting; Inexact and Rounded flags\r | |
5335 | are allowed in this operation. The rounding mode is taken from the\r | |
5336 | context.\r | |
5337 | \r | |
5338 | >>> ExtendedContext.to_integral_exact(Decimal('2.1'))\r | |
5339 | Decimal('2')\r | |
5340 | >>> ExtendedContext.to_integral_exact(Decimal('100'))\r | |
5341 | Decimal('100')\r | |
5342 | >>> ExtendedContext.to_integral_exact(Decimal('100.0'))\r | |
5343 | Decimal('100')\r | |
5344 | >>> ExtendedContext.to_integral_exact(Decimal('101.5'))\r | |
5345 | Decimal('102')\r | |
5346 | >>> ExtendedContext.to_integral_exact(Decimal('-101.5'))\r | |
5347 | Decimal('-102')\r | |
5348 | >>> ExtendedContext.to_integral_exact(Decimal('10E+5'))\r | |
5349 | Decimal('1.0E+6')\r | |
5350 | >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))\r | |
5351 | Decimal('7.89E+77')\r | |
5352 | >>> ExtendedContext.to_integral_exact(Decimal('-Inf'))\r | |
5353 | Decimal('-Infinity')\r | |
5354 | """\r | |
5355 | a = _convert_other(a, raiseit=True)\r | |
5356 | return a.to_integral_exact(context=self)\r | |
5357 | \r | |
5358 | def to_integral_value(self, a):\r | |
5359 | """Rounds to an integer.\r | |
5360 | \r | |
5361 | When the operand has a negative exponent, the result is the same\r | |
5362 | as using the quantize() operation using the given operand as the\r | |
5363 | left-hand-operand, 1E+0 as the right-hand-operand, and the precision\r | |
5364 | of the operand as the precision setting, except that no flags will\r | |
5365 | be set. The rounding mode is taken from the context.\r | |
5366 | \r | |
5367 | >>> ExtendedContext.to_integral_value(Decimal('2.1'))\r | |
5368 | Decimal('2')\r | |
5369 | >>> ExtendedContext.to_integral_value(Decimal('100'))\r | |
5370 | Decimal('100')\r | |
5371 | >>> ExtendedContext.to_integral_value(Decimal('100.0'))\r | |
5372 | Decimal('100')\r | |
5373 | >>> ExtendedContext.to_integral_value(Decimal('101.5'))\r | |
5374 | Decimal('102')\r | |
5375 | >>> ExtendedContext.to_integral_value(Decimal('-101.5'))\r | |
5376 | Decimal('-102')\r | |
5377 | >>> ExtendedContext.to_integral_value(Decimal('10E+5'))\r | |
5378 | Decimal('1.0E+6')\r | |
5379 | >>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))\r | |
5380 | Decimal('7.89E+77')\r | |
5381 | >>> ExtendedContext.to_integral_value(Decimal('-Inf'))\r | |
5382 | Decimal('-Infinity')\r | |
5383 | """\r | |
5384 | a = _convert_other(a, raiseit=True)\r | |
5385 | return a.to_integral_value(context=self)\r | |
5386 | \r | |
5387 | # the method name changed, but we provide also the old one, for compatibility\r | |
5388 | to_integral = to_integral_value\r | |
5389 | \r | |
5390 | class _WorkRep(object):\r | |
5391 | __slots__ = ('sign','int','exp')\r | |
5392 | # sign: 0 or 1\r | |
5393 | # int: int or long\r | |
5394 | # exp: None, int, or string\r | |
5395 | \r | |
5396 | def __init__(self, value=None):\r | |
5397 | if value is None:\r | |
5398 | self.sign = None\r | |
5399 | self.int = 0\r | |
5400 | self.exp = None\r | |
5401 | elif isinstance(value, Decimal):\r | |
5402 | self.sign = value._sign\r | |
5403 | self.int = int(value._int)\r | |
5404 | self.exp = value._exp\r | |
5405 | else:\r | |
5406 | # assert isinstance(value, tuple)\r | |
5407 | self.sign = value[0]\r | |
5408 | self.int = value[1]\r | |
5409 | self.exp = value[2]\r | |
5410 | \r | |
5411 | def __repr__(self):\r | |
5412 | return "(%r, %r, %r)" % (self.sign, self.int, self.exp)\r | |
5413 | \r | |
5414 | __str__ = __repr__\r | |
5415 | \r | |
5416 | \r | |
5417 | \r | |
5418 | def _normalize(op1, op2, prec = 0):\r | |
5419 | """Normalizes op1, op2 to have the same exp and length of coefficient.\r | |
5420 | \r | |
5421 | Done during addition.\r | |
5422 | """\r | |
5423 | if op1.exp < op2.exp:\r | |
5424 | tmp = op2\r | |
5425 | other = op1\r | |
5426 | else:\r | |
5427 | tmp = op1\r | |
5428 | other = op2\r | |
5429 | \r | |
5430 | # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1).\r | |
5431 | # Then adding 10**exp to tmp has the same effect (after rounding)\r | |
5432 | # as adding any positive quantity smaller than 10**exp; similarly\r | |
5433 | # for subtraction. So if other is smaller than 10**exp we replace\r | |
5434 | # it with 10**exp. This avoids tmp.exp - other.exp getting too large.\r | |
5435 | tmp_len = len(str(tmp.int))\r | |
5436 | other_len = len(str(other.int))\r | |
5437 | exp = tmp.exp + min(-1, tmp_len - prec - 2)\r | |
5438 | if other_len + other.exp - 1 < exp:\r | |
5439 | other.int = 1\r | |
5440 | other.exp = exp\r | |
5441 | \r | |
5442 | tmp.int *= 10 ** (tmp.exp - other.exp)\r | |
5443 | tmp.exp = other.exp\r | |
5444 | return op1, op2\r | |
5445 | \r | |
5446 | ##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####\r | |
5447 | \r | |
5448 | # This function from Tim Peters was taken from here:\r | |
5449 | # http://mail.python.org/pipermail/python-list/1999-July/007758.html\r | |
5450 | # The correction being in the function definition is for speed, and\r | |
5451 | # the whole function is not resolved with math.log because of avoiding\r | |
5452 | # the use of floats.\r | |
5453 | def _nbits(n, correction = {\r | |
5454 | '0': 4, '1': 3, '2': 2, '3': 2,\r | |
5455 | '4': 1, '5': 1, '6': 1, '7': 1,\r | |
5456 | '8': 0, '9': 0, 'a': 0, 'b': 0,\r | |
5457 | 'c': 0, 'd': 0, 'e': 0, 'f': 0}):\r | |
5458 | """Number of bits in binary representation of the positive integer n,\r | |
5459 | or 0 if n == 0.\r | |
5460 | """\r | |
5461 | if n < 0:\r | |
5462 | raise ValueError("The argument to _nbits should be nonnegative.")\r | |
5463 | hex_n = "%x" % n\r | |
5464 | return 4*len(hex_n) - correction[hex_n[0]]\r | |
5465 | \r | |
5466 | def _sqrt_nearest(n, a):\r | |
5467 | """Closest integer to the square root of the positive integer n. a is\r | |
5468 | an initial approximation to the square root. Any positive integer\r | |
5469 | will do for a, but the closer a is to the square root of n the\r | |
5470 | faster convergence will be.\r | |
5471 | \r | |
5472 | """\r | |
5473 | if n <= 0 or a <= 0:\r | |
5474 | raise ValueError("Both arguments to _sqrt_nearest should be positive.")\r | |
5475 | \r | |
5476 | b=0\r | |
5477 | while a != b:\r | |
5478 | b, a = a, a--n//a>>1\r | |
5479 | return a\r | |
5480 | \r | |
5481 | def _rshift_nearest(x, shift):\r | |
5482 | """Given an integer x and a nonnegative integer shift, return closest\r | |
5483 | integer to x / 2**shift; use round-to-even in case of a tie.\r | |
5484 | \r | |
5485 | """\r | |
5486 | b, q = 1L << shift, x >> shift\r | |
5487 | return q + (2*(x & (b-1)) + (q&1) > b)\r | |
5488 | \r | |
5489 | def _div_nearest(a, b):\r | |
5490 | """Closest integer to a/b, a and b positive integers; rounds to even\r | |
5491 | in the case of a tie.\r | |
5492 | \r | |
5493 | """\r | |
5494 | q, r = divmod(a, b)\r | |
5495 | return q + (2*r + (q&1) > b)\r | |
5496 | \r | |
5497 | def _ilog(x, M, L = 8):\r | |
5498 | """Integer approximation to M*log(x/M), with absolute error boundable\r | |
5499 | in terms only of x/M.\r | |
5500 | \r | |
5501 | Given positive integers x and M, return an integer approximation to\r | |
5502 | M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference\r | |
5503 | between the approximation and the exact result is at most 22. For\r | |
5504 | L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In\r | |
5505 | both cases these are upper bounds on the error; it will usually be\r | |
5506 | much smaller."""\r | |
5507 | \r | |
5508 | # The basic algorithm is the following: let log1p be the function\r | |
5509 | # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use\r | |
5510 | # the reduction\r | |
5511 | #\r | |
5512 | # log1p(y) = 2*log1p(y/(1+sqrt(1+y)))\r | |
5513 | #\r | |
5514 | # repeatedly until the argument to log1p is small (< 2**-L in\r | |
5515 | # absolute value). For small y we can use the Taylor series\r | |
5516 | # expansion\r | |
5517 | #\r | |
5518 | # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T\r | |
5519 | #\r | |
5520 | # truncating at T such that y**T is small enough. The whole\r | |
5521 | # computation is carried out in a form of fixed-point arithmetic,\r | |
5522 | # with a real number z being represented by an integer\r | |
5523 | # approximation to z*M. To avoid loss of precision, the y below\r | |
5524 | # is actually an integer approximation to 2**R*y*M, where R is the\r | |
5525 | # number of reductions performed so far.\r | |
5526 | \r | |
5527 | y = x-M\r | |
5528 | # argument reduction; R = number of reductions performed\r | |
5529 | R = 0\r | |
5530 | while (R <= L and long(abs(y)) << L-R >= M or\r | |
5531 | R > L and abs(y) >> R-L >= M):\r | |
5532 | y = _div_nearest(long(M*y) << 1,\r | |
5533 | M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M))\r | |
5534 | R += 1\r | |
5535 | \r | |
5536 | # Taylor series with T terms\r | |
5537 | T = -int(-10*len(str(M))//(3*L))\r | |
5538 | yshift = _rshift_nearest(y, R)\r | |
5539 | w = _div_nearest(M, T)\r | |
5540 | for k in xrange(T-1, 0, -1):\r | |
5541 | w = _div_nearest(M, k) - _div_nearest(yshift*w, M)\r | |
5542 | \r | |
5543 | return _div_nearest(w*y, M)\r | |
5544 | \r | |
5545 | def _dlog10(c, e, p):\r | |
5546 | """Given integers c, e and p with c > 0, p >= 0, compute an integer\r | |
5547 | approximation to 10**p * log10(c*10**e), with an absolute error of\r | |
5548 | at most 1. Assumes that c*10**e is not exactly 1."""\r | |
5549 | \r | |
5550 | # increase precision by 2; compensate for this by dividing\r | |
5551 | # final result by 100\r | |
5552 | p += 2\r | |
5553 | \r | |
5554 | # write c*10**e as d*10**f with either:\r | |
5555 | # f >= 0 and 1 <= d <= 10, or\r | |
5556 | # f <= 0 and 0.1 <= d <= 1.\r | |
5557 | # Thus for c*10**e close to 1, f = 0\r | |
5558 | l = len(str(c))\r | |
5559 | f = e+l - (e+l >= 1)\r | |
5560 | \r | |
5561 | if p > 0:\r | |
5562 | M = 10**p\r | |
5563 | k = e+p-f\r | |
5564 | if k >= 0:\r | |
5565 | c *= 10**k\r | |
5566 | else:\r | |
5567 | c = _div_nearest(c, 10**-k)\r | |
5568 | \r | |
5569 | log_d = _ilog(c, M) # error < 5 + 22 = 27\r | |
5570 | log_10 = _log10_digits(p) # error < 1\r | |
5571 | log_d = _div_nearest(log_d*M, log_10)\r | |
5572 | log_tenpower = f*M # exact\r | |
5573 | else:\r | |
5574 | log_d = 0 # error < 2.31\r | |
5575 | log_tenpower = _div_nearest(f, 10**-p) # error < 0.5\r | |
5576 | \r | |
5577 | return _div_nearest(log_tenpower+log_d, 100)\r | |
5578 | \r | |
5579 | def _dlog(c, e, p):\r | |
5580 | """Given integers c, e and p with c > 0, compute an integer\r | |
5581 | approximation to 10**p * log(c*10**e), with an absolute error of\r | |
5582 | at most 1. Assumes that c*10**e is not exactly 1."""\r | |
5583 | \r | |
5584 | # Increase precision by 2. The precision increase is compensated\r | |
5585 | # for at the end with a division by 100.\r | |
5586 | p += 2\r | |
5587 | \r | |
5588 | # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10,\r | |
5589 | # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e)\r | |
5590 | # as 10**p * log(d) + 10**p*f * log(10).\r | |
5591 | l = len(str(c))\r | |
5592 | f = e+l - (e+l >= 1)\r | |
5593 | \r | |
5594 | # compute approximation to 10**p*log(d), with error < 27\r | |
5595 | if p > 0:\r | |
5596 | k = e+p-f\r | |
5597 | if k >= 0:\r | |
5598 | c *= 10**k\r | |
5599 | else:\r | |
5600 | c = _div_nearest(c, 10**-k) # error of <= 0.5 in c\r | |
5601 | \r | |
5602 | # _ilog magnifies existing error in c by a factor of at most 10\r | |
5603 | log_d = _ilog(c, 10**p) # error < 5 + 22 = 27\r | |
5604 | else:\r | |
5605 | # p <= 0: just approximate the whole thing by 0; error < 2.31\r | |
5606 | log_d = 0\r | |
5607 | \r | |
5608 | # compute approximation to f*10**p*log(10), with error < 11.\r | |
5609 | if f:\r | |
5610 | extra = len(str(abs(f)))-1\r | |
5611 | if p + extra >= 0:\r | |
5612 | # error in f * _log10_digits(p+extra) < |f| * 1 = |f|\r | |
5613 | # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11\r | |
5614 | f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra)\r | |
5615 | else:\r | |
5616 | f_log_ten = 0\r | |
5617 | else:\r | |
5618 | f_log_ten = 0\r | |
5619 | \r | |
5620 | # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1\r | |
5621 | return _div_nearest(f_log_ten + log_d, 100)\r | |
5622 | \r | |
5623 | class _Log10Memoize(object):\r | |
5624 | """Class to compute, store, and allow retrieval of, digits of the\r | |
5625 | constant log(10) = 2.302585.... This constant is needed by\r | |
5626 | Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__."""\r | |
5627 | def __init__(self):\r | |
5628 | self.digits = "23025850929940456840179914546843642076011014886"\r | |
5629 | \r | |
5630 | def getdigits(self, p):\r | |
5631 | """Given an integer p >= 0, return floor(10**p)*log(10).\r | |
5632 | \r | |
5633 | For example, self.getdigits(3) returns 2302.\r | |
5634 | """\r | |
5635 | # digits are stored as a string, for quick conversion to\r | |
5636 | # integer in the case that we've already computed enough\r | |
5637 | # digits; the stored digits should always be correct\r | |
5638 | # (truncated, not rounded to nearest).\r | |
5639 | if p < 0:\r | |
5640 | raise ValueError("p should be nonnegative")\r | |
5641 | \r | |
5642 | if p >= len(self.digits):\r | |
5643 | # compute p+3, p+6, p+9, ... digits; continue until at\r | |
5644 | # least one of the extra digits is nonzero\r | |
5645 | extra = 3\r | |
5646 | while True:\r | |
5647 | # compute p+extra digits, correct to within 1ulp\r | |
5648 | M = 10**(p+extra+2)\r | |
5649 | digits = str(_div_nearest(_ilog(10*M, M), 100))\r | |
5650 | if digits[-extra:] != '0'*extra:\r | |
5651 | break\r | |
5652 | extra += 3\r | |
5653 | # keep all reliable digits so far; remove trailing zeros\r | |
5654 | # and next nonzero digit\r | |
5655 | self.digits = digits.rstrip('0')[:-1]\r | |
5656 | return int(self.digits[:p+1])\r | |
5657 | \r | |
5658 | _log10_digits = _Log10Memoize().getdigits\r | |
5659 | \r | |
5660 | def _iexp(x, M, L=8):\r | |
5661 | """Given integers x and M, M > 0, such that x/M is small in absolute\r | |
5662 | value, compute an integer approximation to M*exp(x/M). For 0 <=\r | |
5663 | x/M <= 2.4, the absolute error in the result is bounded by 60 (and\r | |
5664 | is usually much smaller)."""\r | |
5665 | \r | |
5666 | # Algorithm: to compute exp(z) for a real number z, first divide z\r | |
5667 | # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then\r | |
5668 | # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor\r | |
5669 | # series\r | |
5670 | #\r | |
5671 | # expm1(x) = x + x**2/2! + x**3/3! + ...\r | |
5672 | #\r | |
5673 | # Now use the identity\r | |
5674 | #\r | |
5675 | # expm1(2x) = expm1(x)*(expm1(x)+2)\r | |
5676 | #\r | |
5677 | # R times to compute the sequence expm1(z/2**R),\r | |
5678 | # expm1(z/2**(R-1)), ... , exp(z/2), exp(z).\r | |
5679 | \r | |
5680 | # Find R such that x/2**R/M <= 2**-L\r | |
5681 | R = _nbits((long(x)<<L)//M)\r | |
5682 | \r | |
5683 | # Taylor series. (2**L)**T > M\r | |
5684 | T = -int(-10*len(str(M))//(3*L))\r | |
5685 | y = _div_nearest(x, T)\r | |
5686 | Mshift = long(M)<<R\r | |
5687 | for i in xrange(T-1, 0, -1):\r | |
5688 | y = _div_nearest(x*(Mshift + y), Mshift * i)\r | |
5689 | \r | |
5690 | # Expansion\r | |
5691 | for k in xrange(R-1, -1, -1):\r | |
5692 | Mshift = long(M)<<(k+2)\r | |
5693 | y = _div_nearest(y*(y+Mshift), Mshift)\r | |
5694 | \r | |
5695 | return M+y\r | |
5696 | \r | |
5697 | def _dexp(c, e, p):\r | |
5698 | """Compute an approximation to exp(c*10**e), with p decimal places of\r | |
5699 | precision.\r | |
5700 | \r | |
5701 | Returns integers d, f such that:\r | |
5702 | \r | |
5703 | 10**(p-1) <= d <= 10**p, and\r | |
5704 | (d-1)*10**f < exp(c*10**e) < (d+1)*10**f\r | |
5705 | \r | |
5706 | In other words, d*10**f is an approximation to exp(c*10**e) with p\r | |
5707 | digits of precision, and with an error in d of at most 1. This is\r | |
5708 | almost, but not quite, the same as the error being < 1ulp: when d\r | |
5709 | = 10**(p-1) the error could be up to 10 ulp."""\r | |
5710 | \r | |
5711 | # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision\r | |
5712 | p += 2\r | |
5713 | \r | |
5714 | # compute log(10) with extra precision = adjusted exponent of c*10**e\r | |
5715 | extra = max(0, e + len(str(c)) - 1)\r | |
5716 | q = p + extra\r | |
5717 | \r | |
5718 | # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q),\r | |
5719 | # rounding down\r | |
5720 | shift = e+q\r | |
5721 | if shift >= 0:\r | |
5722 | cshift = c*10**shift\r | |
5723 | else:\r | |
5724 | cshift = c//10**-shift\r | |
5725 | quot, rem = divmod(cshift, _log10_digits(q))\r | |
5726 | \r | |
5727 | # reduce remainder back to original precision\r | |
5728 | rem = _div_nearest(rem, 10**extra)\r | |
5729 | \r | |
5730 | # error in result of _iexp < 120; error after division < 0.62\r | |
5731 | return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3\r | |
5732 | \r | |
5733 | def _dpower(xc, xe, yc, ye, p):\r | |
5734 | """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and\r | |
5735 | y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that:\r | |
5736 | \r | |
5737 | 10**(p-1) <= c <= 10**p, and\r | |
5738 | (c-1)*10**e < x**y < (c+1)*10**e\r | |
5739 | \r | |
5740 | in other words, c*10**e is an approximation to x**y with p digits\r | |
5741 | of precision, and with an error in c of at most 1. (This is\r | |
5742 | almost, but not quite, the same as the error being < 1ulp: when c\r | |
5743 | == 10**(p-1) we can only guarantee error < 10ulp.)\r | |
5744 | \r | |
5745 | We assume that: x is positive and not equal to 1, and y is nonzero.\r | |
5746 | """\r | |
5747 | \r | |
5748 | # Find b such that 10**(b-1) <= |y| <= 10**b\r | |
5749 | b = len(str(abs(yc))) + ye\r | |
5750 | \r | |
5751 | # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point\r | |
5752 | lxc = _dlog(xc, xe, p+b+1)\r | |
5753 | \r | |
5754 | # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1)\r | |
5755 | shift = ye-b\r | |
5756 | if shift >= 0:\r | |
5757 | pc = lxc*yc*10**shift\r | |
5758 | else:\r | |
5759 | pc = _div_nearest(lxc*yc, 10**-shift)\r | |
5760 | \r | |
5761 | if pc == 0:\r | |
5762 | # we prefer a result that isn't exactly 1; this makes it\r | |
5763 | # easier to compute a correctly rounded result in __pow__\r | |
5764 | if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1:\r | |
5765 | coeff, exp = 10**(p-1)+1, 1-p\r | |
5766 | else:\r | |
5767 | coeff, exp = 10**p-1, -p\r | |
5768 | else:\r | |
5769 | coeff, exp = _dexp(pc, -(p+1), p+1)\r | |
5770 | coeff = _div_nearest(coeff, 10)\r | |
5771 | exp += 1\r | |
5772 | \r | |
5773 | return coeff, exp\r | |
5774 | \r | |
5775 | def _log10_lb(c, correction = {\r | |
5776 | '1': 100, '2': 70, '3': 53, '4': 40, '5': 31,\r | |
5777 | '6': 23, '7': 16, '8': 10, '9': 5}):\r | |
5778 | """Compute a lower bound for 100*log10(c) for a positive integer c."""\r | |
5779 | if c <= 0:\r | |
5780 | raise ValueError("The argument to _log10_lb should be nonnegative.")\r | |
5781 | str_c = str(c)\r | |
5782 | return 100*len(str_c) - correction[str_c[0]]\r | |
5783 | \r | |
5784 | ##### Helper Functions ####################################################\r | |
5785 | \r | |
5786 | def _convert_other(other, raiseit=False, allow_float=False):\r | |
5787 | """Convert other to Decimal.\r | |
5788 | \r | |
5789 | Verifies that it's ok to use in an implicit construction.\r | |
5790 | If allow_float is true, allow conversion from float; this\r | |
5791 | is used in the comparison methods (__eq__ and friends).\r | |
5792 | \r | |
5793 | """\r | |
5794 | if isinstance(other, Decimal):\r | |
5795 | return other\r | |
5796 | if isinstance(other, (int, long)):\r | |
5797 | return Decimal(other)\r | |
5798 | if allow_float and isinstance(other, float):\r | |
5799 | return Decimal.from_float(other)\r | |
5800 | \r | |
5801 | if raiseit:\r | |
5802 | raise TypeError("Unable to convert %s to Decimal" % other)\r | |
5803 | return NotImplemented\r | |
5804 | \r | |
5805 | ##### Setup Specific Contexts ############################################\r | |
5806 | \r | |
5807 | # The default context prototype used by Context()\r | |
5808 | # Is mutable, so that new contexts can have different default values\r | |
5809 | \r | |
5810 | DefaultContext = Context(\r | |
5811 | prec=28, rounding=ROUND_HALF_EVEN,\r | |
5812 | traps=[DivisionByZero, Overflow, InvalidOperation],\r | |
5813 | flags=[],\r | |
5814 | Emax=999999999,\r | |
5815 | Emin=-999999999,\r | |
5816 | capitals=1\r | |
5817 | )\r | |
5818 | \r | |
5819 | # Pre-made alternate contexts offered by the specification\r | |
5820 | # Don't change these; the user should be able to select these\r | |
5821 | # contexts and be able to reproduce results from other implementations\r | |
5822 | # of the spec.\r | |
5823 | \r | |
5824 | BasicContext = Context(\r | |
5825 | prec=9, rounding=ROUND_HALF_UP,\r | |
5826 | traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow],\r | |
5827 | flags=[],\r | |
5828 | )\r | |
5829 | \r | |
5830 | ExtendedContext = Context(\r | |
5831 | prec=9, rounding=ROUND_HALF_EVEN,\r | |
5832 | traps=[],\r | |
5833 | flags=[],\r | |
5834 | )\r | |
5835 | \r | |
5836 | \r | |
5837 | ##### crud for parsing strings #############################################\r | |
5838 | #\r | |
5839 | # Regular expression used for parsing numeric strings. Additional\r | |
5840 | # comments:\r | |
5841 | #\r | |
5842 | # 1. Uncomment the two '\s*' lines to allow leading and/or trailing\r | |
5843 | # whitespace. But note that the specification disallows whitespace in\r | |
5844 | # a numeric string.\r | |
5845 | #\r | |
5846 | # 2. For finite numbers (not infinities and NaNs) the body of the\r | |
5847 | # number between the optional sign and the optional exponent must have\r | |
5848 | # at least one decimal digit, possibly after the decimal point. The\r | |
5849 | # lookahead expression '(?=\d|\.\d)' checks this.\r | |
5850 | \r | |
5851 | import re\r | |
5852 | _parser = re.compile(r""" # A numeric string consists of:\r | |
5853 | # \s*\r | |
5854 | (?P<sign>[-+])? # an optional sign, followed by either...\r | |
5855 | (\r | |
5856 | (?=\d|\.\d) # ...a number (with at least one digit)\r | |
5857 | (?P<int>\d*) # having a (possibly empty) integer part\r | |
5858 | (\.(?P<frac>\d*))? # followed by an optional fractional part\r | |
5859 | (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or...\r | |
5860 | |\r | |
5861 | Inf(inity)? # ...an infinity, or...\r | |
5862 | |\r | |
5863 | (?P<signal>s)? # ...an (optionally signaling)\r | |
5864 | NaN # NaN\r | |
5865 | (?P<diag>\d*) # with (possibly empty) diagnostic info.\r | |
5866 | )\r | |
5867 | # \s*\r | |
5868 | \Z\r | |
5869 | """, re.VERBOSE | re.IGNORECASE | re.UNICODE).match\r | |
5870 | \r | |
5871 | _all_zeros = re.compile('0*$').match\r | |
5872 | _exact_half = re.compile('50*$').match\r | |
5873 | \r | |
5874 | ##### PEP3101 support functions ##############################################\r | |
5875 | # The functions in this section have little to do with the Decimal\r | |
5876 | # class, and could potentially be reused or adapted for other pure\r | |
5877 | # Python numeric classes that want to implement __format__\r | |
5878 | #\r | |
5879 | # A format specifier for Decimal looks like:\r | |
5880 | #\r | |
5881 | # [[fill]align][sign][0][minimumwidth][,][.precision][type]\r | |
5882 | \r | |
5883 | _parse_format_specifier_regex = re.compile(r"""\A\r | |
5884 | (?:\r | |
5885 | (?P<fill>.)?\r | |
5886 | (?P<align>[<>=^])\r | |
5887 | )?\r | |
5888 | (?P<sign>[-+ ])?\r | |
5889 | (?P<zeropad>0)?\r | |
5890 | (?P<minimumwidth>(?!0)\d+)?\r | |
5891 | (?P<thousands_sep>,)?\r | |
5892 | (?:\.(?P<precision>0|(?!0)\d+))?\r | |
5893 | (?P<type>[eEfFgGn%])?\r | |
5894 | \Z\r | |
5895 | """, re.VERBOSE)\r | |
5896 | \r | |
5897 | del re\r | |
5898 | \r | |
5899 | # The locale module is only needed for the 'n' format specifier. The\r | |
5900 | # rest of the PEP 3101 code functions quite happily without it, so we\r | |
5901 | # don't care too much if locale isn't present.\r | |
5902 | try:\r | |
5903 | import locale as _locale\r | |
5904 | except ImportError:\r | |
5905 | pass\r | |
5906 | \r | |
5907 | def _parse_format_specifier(format_spec, _localeconv=None):\r | |
5908 | """Parse and validate a format specifier.\r | |
5909 | \r | |
5910 | Turns a standard numeric format specifier into a dict, with the\r | |
5911 | following entries:\r | |
5912 | \r | |
5913 | fill: fill character to pad field to minimum width\r | |
5914 | align: alignment type, either '<', '>', '=' or '^'\r | |
5915 | sign: either '+', '-' or ' '\r | |
5916 | minimumwidth: nonnegative integer giving minimum width\r | |
5917 | zeropad: boolean, indicating whether to pad with zeros\r | |
5918 | thousands_sep: string to use as thousands separator, or ''\r | |
5919 | grouping: grouping for thousands separators, in format\r | |
5920 | used by localeconv\r | |
5921 | decimal_point: string to use for decimal point\r | |
5922 | precision: nonnegative integer giving precision, or None\r | |
5923 | type: one of the characters 'eEfFgG%', or None\r | |
5924 | unicode: boolean (always True for Python 3.x)\r | |
5925 | \r | |
5926 | """\r | |
5927 | m = _parse_format_specifier_regex.match(format_spec)\r | |
5928 | if m is None:\r | |
5929 | raise ValueError("Invalid format specifier: " + format_spec)\r | |
5930 | \r | |
5931 | # get the dictionary\r | |
5932 | format_dict = m.groupdict()\r | |
5933 | \r | |
5934 | # zeropad; defaults for fill and alignment. If zero padding\r | |
5935 | # is requested, the fill and align fields should be absent.\r | |
5936 | fill = format_dict['fill']\r | |
5937 | align = format_dict['align']\r | |
5938 | format_dict['zeropad'] = (format_dict['zeropad'] is not None)\r | |
5939 | if format_dict['zeropad']:\r | |
5940 | if fill is not None:\r | |
5941 | raise ValueError("Fill character conflicts with '0'"\r | |
5942 | " in format specifier: " + format_spec)\r | |
5943 | if align is not None:\r | |
5944 | raise ValueError("Alignment conflicts with '0' in "\r | |
5945 | "format specifier: " + format_spec)\r | |
5946 | format_dict['fill'] = fill or ' '\r | |
5947 | # PEP 3101 originally specified that the default alignment should\r | |
5948 | # be left; it was later agreed that right-aligned makes more sense\r | |
5949 | # for numeric types. See http://bugs.python.org/issue6857.\r | |
5950 | format_dict['align'] = align or '>'\r | |
5951 | \r | |
5952 | # default sign handling: '-' for negative, '' for positive\r | |
5953 | if format_dict['sign'] is None:\r | |
5954 | format_dict['sign'] = '-'\r | |
5955 | \r | |
5956 | # minimumwidth defaults to 0; precision remains None if not given\r | |
5957 | format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0')\r | |
5958 | if format_dict['precision'] is not None:\r | |
5959 | format_dict['precision'] = int(format_dict['precision'])\r | |
5960 | \r | |
5961 | # if format type is 'g' or 'G' then a precision of 0 makes little\r | |
5962 | # sense; convert it to 1. Same if format type is unspecified.\r | |
5963 | if format_dict['precision'] == 0:\r | |
5964 | if format_dict['type'] is None or format_dict['type'] in 'gG':\r | |
5965 | format_dict['precision'] = 1\r | |
5966 | \r | |
5967 | # determine thousands separator, grouping, and decimal separator, and\r | |
5968 | # add appropriate entries to format_dict\r | |
5969 | if format_dict['type'] == 'n':\r | |
5970 | # apart from separators, 'n' behaves just like 'g'\r | |
5971 | format_dict['type'] = 'g'\r | |
5972 | if _localeconv is None:\r | |
5973 | _localeconv = _locale.localeconv()\r | |
5974 | if format_dict['thousands_sep'] is not None:\r | |
5975 | raise ValueError("Explicit thousands separator conflicts with "\r | |
5976 | "'n' type in format specifier: " + format_spec)\r | |
5977 | format_dict['thousands_sep'] = _localeconv['thousands_sep']\r | |
5978 | format_dict['grouping'] = _localeconv['grouping']\r | |
5979 | format_dict['decimal_point'] = _localeconv['decimal_point']\r | |
5980 | else:\r | |
5981 | if format_dict['thousands_sep'] is None:\r | |
5982 | format_dict['thousands_sep'] = ''\r | |
5983 | format_dict['grouping'] = [3, 0]\r | |
5984 | format_dict['decimal_point'] = '.'\r | |
5985 | \r | |
5986 | # record whether return type should be str or unicode\r | |
5987 | format_dict['unicode'] = isinstance(format_spec, unicode)\r | |
5988 | \r | |
5989 | return format_dict\r | |
5990 | \r | |
5991 | def _format_align(sign, body, spec):\r | |
5992 | """Given an unpadded, non-aligned numeric string 'body' and sign\r | |
5993 | string 'sign', add padding and alignment conforming to the given\r | |
5994 | format specifier dictionary 'spec' (as produced by\r | |
5995 | parse_format_specifier).\r | |
5996 | \r | |
5997 | Also converts result to unicode if necessary.\r | |
5998 | \r | |
5999 | """\r | |
6000 | # how much extra space do we have to play with?\r | |
6001 | minimumwidth = spec['minimumwidth']\r | |
6002 | fill = spec['fill']\r | |
6003 | padding = fill*(minimumwidth - len(sign) - len(body))\r | |
6004 | \r | |
6005 | align = spec['align']\r | |
6006 | if align == '<':\r | |
6007 | result = sign + body + padding\r | |
6008 | elif align == '>':\r | |
6009 | result = padding + sign + body\r | |
6010 | elif align == '=':\r | |
6011 | result = sign + padding + body\r | |
6012 | elif align == '^':\r | |
6013 | half = len(padding)//2\r | |
6014 | result = padding[:half] + sign + body + padding[half:]\r | |
6015 | else:\r | |
6016 | raise ValueError('Unrecognised alignment field')\r | |
6017 | \r | |
6018 | # make sure that result is unicode if necessary\r | |
6019 | if spec['unicode']:\r | |
6020 | result = unicode(result)\r | |
6021 | \r | |
6022 | return result\r | |
6023 | \r | |
6024 | def _group_lengths(grouping):\r | |
6025 | """Convert a localeconv-style grouping into a (possibly infinite)\r | |
6026 | iterable of integers representing group lengths.\r | |
6027 | \r | |
6028 | """\r | |
6029 | # The result from localeconv()['grouping'], and the input to this\r | |
6030 | # function, should be a list of integers in one of the\r | |
6031 | # following three forms:\r | |
6032 | #\r | |
6033 | # (1) an empty list, or\r | |
6034 | # (2) nonempty list of positive integers + [0]\r | |
6035 | # (3) list of positive integers + [locale.CHAR_MAX], or\r | |
6036 | \r | |
6037 | from itertools import chain, repeat\r | |
6038 | if not grouping:\r | |
6039 | return []\r | |
6040 | elif grouping[-1] == 0 and len(grouping) >= 2:\r | |
6041 | return chain(grouping[:-1], repeat(grouping[-2]))\r | |
6042 | elif grouping[-1] == _locale.CHAR_MAX:\r | |
6043 | return grouping[:-1]\r | |
6044 | else:\r | |
6045 | raise ValueError('unrecognised format for grouping')\r | |
6046 | \r | |
6047 | def _insert_thousands_sep(digits, spec, min_width=1):\r | |
6048 | """Insert thousands separators into a digit string.\r | |
6049 | \r | |
6050 | spec is a dictionary whose keys should include 'thousands_sep' and\r | |
6051 | 'grouping'; typically it's the result of parsing the format\r | |
6052 | specifier using _parse_format_specifier.\r | |
6053 | \r | |
6054 | The min_width keyword argument gives the minimum length of the\r | |
6055 | result, which will be padded on the left with zeros if necessary.\r | |
6056 | \r | |
6057 | If necessary, the zero padding adds an extra '0' on the left to\r | |
6058 | avoid a leading thousands separator. For example, inserting\r | |
6059 | commas every three digits in '123456', with min_width=8, gives\r | |
6060 | '0,123,456', even though that has length 9.\r | |
6061 | \r | |
6062 | """\r | |
6063 | \r | |
6064 | sep = spec['thousands_sep']\r | |
6065 | grouping = spec['grouping']\r | |
6066 | \r | |
6067 | groups = []\r | |
6068 | for l in _group_lengths(grouping):\r | |
6069 | if l <= 0:\r | |
6070 | raise ValueError("group length should be positive")\r | |
6071 | # max(..., 1) forces at least 1 digit to the left of a separator\r | |
6072 | l = min(max(len(digits), min_width, 1), l)\r | |
6073 | groups.append('0'*(l - len(digits)) + digits[-l:])\r | |
6074 | digits = digits[:-l]\r | |
6075 | min_width -= l\r | |
6076 | if not digits and min_width <= 0:\r | |
6077 | break\r | |
6078 | min_width -= len(sep)\r | |
6079 | else:\r | |
6080 | l = max(len(digits), min_width, 1)\r | |
6081 | groups.append('0'*(l - len(digits)) + digits[-l:])\r | |
6082 | return sep.join(reversed(groups))\r | |
6083 | \r | |
6084 | def _format_sign(is_negative, spec):\r | |
6085 | """Determine sign character."""\r | |
6086 | \r | |
6087 | if is_negative:\r | |
6088 | return '-'\r | |
6089 | elif spec['sign'] in ' +':\r | |
6090 | return spec['sign']\r | |
6091 | else:\r | |
6092 | return ''\r | |
6093 | \r | |
6094 | def _format_number(is_negative, intpart, fracpart, exp, spec):\r | |
6095 | """Format a number, given the following data:\r | |
6096 | \r | |
6097 | is_negative: true if the number is negative, else false\r | |
6098 | intpart: string of digits that must appear before the decimal point\r | |
6099 | fracpart: string of digits that must come after the point\r | |
6100 | exp: exponent, as an integer\r | |
6101 | spec: dictionary resulting from parsing the format specifier\r | |
6102 | \r | |
6103 | This function uses the information in spec to:\r | |
6104 | insert separators (decimal separator and thousands separators)\r | |
6105 | format the sign\r | |
6106 | format the exponent\r | |
6107 | add trailing '%' for the '%' type\r | |
6108 | zero-pad if necessary\r | |
6109 | fill and align if necessary\r | |
6110 | """\r | |
6111 | \r | |
6112 | sign = _format_sign(is_negative, spec)\r | |
6113 | \r | |
6114 | if fracpart:\r | |
6115 | fracpart = spec['decimal_point'] + fracpart\r | |
6116 | \r | |
6117 | if exp != 0 or spec['type'] in 'eE':\r | |
6118 | echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']]\r | |
6119 | fracpart += "{0}{1:+}".format(echar, exp)\r | |
6120 | if spec['type'] == '%':\r | |
6121 | fracpart += '%'\r | |
6122 | \r | |
6123 | if spec['zeropad']:\r | |
6124 | min_width = spec['minimumwidth'] - len(fracpart) - len(sign)\r | |
6125 | else:\r | |
6126 | min_width = 0\r | |
6127 | intpart = _insert_thousands_sep(intpart, spec, min_width)\r | |
6128 | \r | |
6129 | return _format_align(sign, intpart+fracpart, spec)\r | |
6130 | \r | |
6131 | \r | |
6132 | ##### Useful Constants (internal use only) ################################\r | |
6133 | \r | |
6134 | # Reusable defaults\r | |
6135 | _Infinity = Decimal('Inf')\r | |
6136 | _NegativeInfinity = Decimal('-Inf')\r | |
6137 | _NaN = Decimal('NaN')\r | |
6138 | _Zero = Decimal(0)\r | |
6139 | _One = Decimal(1)\r | |
6140 | _NegativeOne = Decimal(-1)\r | |
6141 | \r | |
6142 | # _SignedInfinity[sign] is infinity w/ that sign\r | |
6143 | _SignedInfinity = (_Infinity, _NegativeInfinity)\r | |
6144 | \r | |
6145 | \r | |
6146 | \r | |
6147 | if __name__ == '__main__':\r | |
6148 | import doctest, sys\r | |
6149 | doctest.testmod(sys.modules[__name__])\r |