FazBrowse GitHub Viewer
|
Trending
|
URL:
|
Home
Tools:
[Download Repo ZIP]
[Original HTTPS Page]
cpython/Lib/numbers.py at main · python/cpython · GitHub
python
cpython
Repository navigation
Code
Issues
5k+
(5k+)
Pull requests
2.6k
(2.6k)
Actions
Projects
Security and quality
Insights
Expand file tree
Breadcrumbs
cpython
/
Lib
/
numbers.py
Copy path
More file actions
More file actions
Latest commit
History
History
History
427 lines (329 loc) · 11.5 KB
Breadcrumbs
cpython
/
Lib
/
numbers.py
Copy path
File metadata and controls
427 lines (329 loc) · 11.5 KB
Raw
Copy raw file
Download raw file
Open symbols panel
Edit and raw actions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
# Copyright 2007 Google, Inc. All Rights Reserved.
# Licensed to PSF under a Contributor Agreement.
"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators."""
############ Maintenance notes #########################################
#
# ABCs are different from other standard library modules in that they
# specify compliance tests. In general, once an ABC has been published,
# new methods (either abstract or concrete) cannot be added.
#
# Though classes that inherit from an ABC would automatically receive a
# new mixin method, registered classes would become non-compliant and
# violate the contract promised by ``isinstance(someobj, SomeABC)``.
#
# Though irritating, the correct procedure for adding new abstract or
# mixin methods is to create a new ABC as a subclass of the previous
# ABC.
#
# Because they are so hard to change, new ABCs should have their APIs
# carefully thought through prior to publication.
#
# Since ABCMeta only checks for the presence of methods, it is possible
# to alter the signature of a method by adding optional arguments
# or changing parameter names. This is still a bit dubious but at
# least it won't cause isinstance() to return an incorrect result.
#
#
#######################################################################
from
abc
import
ABCMeta
,
abstractmethod
__all__
=
[
"Number"
,
"Complex"
,
"Real"
,
"Rational"
,
"Integral"
]
class
Number
(
metaclass
=
ABCMeta
):
"""All numbers inherit from this class.
If you just want to check if an argument x is a number, without
caring what kind, use isinstance(x, Number).
"""
__slots__
=
()
# Concrete numeric types must provide their own hash implementation
__hash__
=
None
## Notes on Decimal
## ----------------
## Decimal has all of the methods specified by the Real abc, but it should
## not be registered as a Real because decimals do not interoperate with
## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,
## abstract reals are expected to interoperate (i.e. R1 + R2 should be
## expected to work if R1 and R2 are both Reals).
class
Complex
(
Number
):
"""Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, **, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
"""
__slots__
=
()
@
abstractmethod
def
__complex__
(
self
):
"""Return a builtin complex instance. Called for complex(self)."""
def
__bool__
(
self
):
"""True if self != 0. Called for bool(self)."""
return
self
!=
0
@
property
@
abstractmethod
def
real
(
self
):
"""Retrieve the real component of this number.
This should subclass Real.
"""
raise
NotImplementedError
@
property
@
abstractmethod
def
imag
(
self
):
"""Retrieve the imaginary component of this number.
This should subclass Real.
"""
raise
NotImplementedError
@
abstractmethod
def
__add__
(
self
,
other
):
"""self + other"""
raise
NotImplementedError
@
abstractmethod
def
__radd__
(
self
,
other
):
"""other + self"""
raise
NotImplementedError
@
abstractmethod
def
__neg__
(
self
):
"""-self"""
raise
NotImplementedError
@
abstractmethod
def
__pos__
(
self
):
"""+self"""
raise
NotImplementedError
def
__sub__
(
self
,
other
):
"""self - other"""
return
self
+
-
other
def
__rsub__
(
self
,
other
):
"""other - self"""
return
-
self
+
other
@
abstractmethod
def
__mul__
(
self
,
other
):
"""self * other"""
raise
NotImplementedError
@
abstractmethod
def
__rmul__
(
self
,
other
):
"""other * self"""
raise
NotImplementedError
@
abstractmethod
def
__truediv__
(
self
,
other
):
"""self / other: Should promote to float when necessary."""
raise
NotImplementedError
@
abstractmethod
def
__rtruediv__
(
self
,
other
):
"""other / self"""
raise
NotImplementedError
@
abstractmethod
def
__pow__
(
self
,
exponent
):
"""self ** exponent; should promote to float or complex when necessary."""
raise
NotImplementedError
@
abstractmethod
def
__rpow__
(
self
,
base
):
"""base ** self"""
raise
NotImplementedError
@
abstractmethod
def
__abs__
(
self
):
"""Returns the Real distance from 0. Called for abs(self)."""
raise
NotImplementedError
@
abstractmethod
def
conjugate
(
self
):
"""(x+y*i).conjugate() returns (x-y*i)."""
raise
NotImplementedError
@
abstractmethod
def
__eq__
(
self
,
other
):
"""self == other"""
raise
NotImplementedError
Complex
.
register
(
complex
)
class
Real
(
Complex
):
"""To Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
"""
__slots__
=
()
@
abstractmethod
def
__float__
(
self
):
"""Any Real can be converted to a native float object.
Called for float(self)."""
raise
NotImplementedError
@
abstractmethod
def
__trunc__
(
self
):
"""trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i > 0 iff self > 0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
"""
raise
NotImplementedError
@
abstractmethod
def
__floor__
(
self
):
"""Finds the greatest Integral <= self."""
raise
NotImplementedError
@
abstractmethod
def
__ceil__
(
self
):
"""Finds the least Integral >= self."""
raise
NotImplementedError
@
abstractmethod
def
__round__
(
self
,
ndigits
=
None
):
"""Rounds self to ndigits decimal places, defaulting to 0.
If ndigits is omitted or None, returns an Integral, otherwise
returns a Real. Rounds half toward even.
"""
raise
NotImplementedError
def
__divmod__
(
self
,
other
):
"""divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
"""
return
(
self
//
other
,
self
%
other
)
def
__rdivmod__
(
self
,
other
):
"""divmod(other, self): The pair (other // self, other % self).
Sometimes this can be computed faster than the pair of
operations.
"""
return
(
other
//
self
,
other
%
self
)
@
abstractmethod
def
__floordiv__
(
self
,
other
):
"""self // other: The floor() of self/other."""
raise
NotImplementedError
@
abstractmethod
def
__rfloordiv__
(
self
,
other
):
"""other // self: The floor() of other/self."""
raise
NotImplementedError
@
abstractmethod
def
__mod__
(
self
,
other
):
"""self % other"""
raise
NotImplementedError
@
abstractmethod
def
__rmod__
(
self
,
other
):
"""other % self"""
raise
NotImplementedError
@
abstractmethod
def
__lt__
(
self
,
other
):
"""self < other
< on Reals defines a total ordering, except perhaps for NaN."""
raise
NotImplementedError
@
abstractmethod
def
__le__
(
self
,
other
):
"""self <= other"""
raise
NotImplementedError
# Concrete implementations of Complex abstract methods.
def
__complex__
(
self
):
"""complex(self) == complex(float(self), 0)"""
return
complex
(
float
(
self
))
@
property
def
real
(
self
):
"""Real numbers are their real component."""
return
+
self
@
property
def
imag
(
self
):
"""Real numbers have no imaginary component."""
return
0
def
conjugate
(
self
):
"""Conjugate is a no-op for Reals."""
return
+
self
Real
.
register
(
float
)
class
Rational
(
Real
):
"""To Real, Rational adds numerator and denominator properties.
The numerator and denominator values should be in lowest terms,
with a positive denominator.
"""
__slots__
=
()
@
property
@
abstractmethod
def
numerator
(
self
):
"""The numerator of a rational number in lowest terms."""
raise
NotImplementedError
@
property
@
abstractmethod
def
denominator
(
self
):
"""The denominator of a rational number in lowest terms.
This denominator should be positive.
"""
raise
NotImplementedError
# Concrete implementation of Real's conversion to float.
def
__float__
(
self
):
"""float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
"""
return
int
(
self
.
numerator
)
/
int
(
self
.
denominator
)
class
Integral
(
Rational
):
"""Integral adds methods that work on integral numbers.
In short, these are conversion to int, pow with modulus, and the
bit-string operations.
"""
__slots__
=
()
@
abstractmethod
def
__int__
(
self
):
"""int(self)"""
raise
NotImplementedError
def
__index__
(
self
):
"""Called whenever an index is needed, such as in slicing"""
return
int
(
self
)
@
abstractmethod
def
__pow__
(
self
,
exponent
,
modulus
=
None
):
"""self ** exponent % modulus, but maybe faster.
Accept the modulus argument if you want to support the
3-argument version of pow(). Raise a TypeError if exponent < 0
or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
"""
raise
NotImplementedError
@
abstractmethod
def
__lshift__
(
self
,
other
):
"""self << other"""
raise
NotImplementedError
@
abstractmethod
def
__rlshift__
(
self
,
other
):
"""other << self"""
raise
NotImplementedError
@
abstractmethod
def
__rshift__
(
self
,
other
):
"""self >> other"""
raise
NotImplementedError
@
abstractmethod
def
__rrshift__
(
self
,
other
):
"""other >> self"""
raise
NotImplementedError
@
abstractmethod
def
__and__
(
self
,
other
):
"""self & other"""
raise
NotImplementedError
@
abstractmethod
def
__rand__
(
self
,
other
):
"""other & self"""
raise
NotImplementedError
@
abstractmethod
def
__xor__
(
self
,
other
):
"""self ^ other"""
raise
NotImplementedError
@
abstractmethod
def
__rxor__
(
self
,
other
):
"""other ^ self"""
raise
NotImplementedError
@
abstractmethod
def
__or__
(
self
,
other
):
"""self | other"""
raise
NotImplementedError
@
abstractmethod
def
__ror__
(
self
,
other
):
"""other | self"""
raise
NotImplementedError
@
abstractmethod
def
__invert__
(
self
):
"""~self"""
raise
NotImplementedError
# Concrete implementations of Rational and Real abstract methods.
def
__float__
(
self
):
"""float(self) == float(int(self))"""
return
float
(
int
(
self
))
@
property
def
numerator
(
self
):
"""Integers are their own numerators."""
return
+
self
@
property
def
denominator
(
self
):
"""Integers have a denominator of 1."""
return
1
Integral
.
register
(
int
)
Back
|
FazBrowse Home
|
New Git URL