-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathBuilt in types
3557 lines (2376 loc) · 154 KB
/
Built in types
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
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
Built-in Types
The following sections describe the standard types that are built into the interpreter.
The principal built-in types are numerics, sequences, mappings, classes, instances and exceptions.
Some collection classes are mutable. The methods that add, subtract, or rearrange their members in place, and don’t return a specific item, never return the collection instance itself but None.
Some operations are supported by several object types; in particular, practically all objects can be compared for equality, tested for truth value, and converted to a string (with the repr() function or the slightly different str() function). The latter function is implicitly used when an object is written by the print() function.
Truth Value Testing
Any object can be tested for truth value, for use in an if or while condition or as operand of the Boolean operations below.
By default, an object is considered true unless its class defines either a __bool__() method that returns False or a __len__() method that returns zero, when called with the object. 1 Here are most of the built-in objects considered false:
constants defined to be false: None and False.
zero of any numeric type: 0, 0.0, 0j, Decimal(0), Fraction(0, 1)
empty sequences and collections: '', (), [], {}, set(), range(0)
Operations and built-in functions that have a Boolean result always return 0 or False for false and 1 or True for true, unless otherwise stated. (Important exception: the Boolean operations or and and always return one of their operands.)
Boolean Operations — and, or, not
These are the Boolean operations, ordered by ascending priority:
Operation
Result
Notes
x or y
if x is true, then x, else y
(1)
x and y
if x is false, then x, else y
(2)
not x
if x is false, then True, else False
(3)
Notes:
This is a short-circuit operator, so it only evaluates the second argument if the first one is false.
This is a short-circuit operator, so it only evaluates the second argument if the first one is true.
not has a lower priority than non-Boolean operators, so not a == b is interpreted as not (a == b), and a == not b is a syntax error.
Comparisons
There are eight comparison operations in Python. They all have the same priority (which is higher than that of the Boolean operations). Comparisons can be chained arbitrarily; for example, x < y <= z is equivalent to x < y and y <= z, except that y is evaluated only once (but in both cases z is not evaluated at all when x < y is found to be false).
This table summarizes the comparison operations:
Operation
Meaning
<
strictly less than
<=
less than or equal
>
strictly greater than
>=
greater than or equal
==
equal
!=
not equal
is
object identity
is not
negated object identity
Objects of different types, except different numeric types, never compare equal. The == operator is always defined but for some object types (for example, class objects) is equivalent to is. The <, <=, > and >= operators are only defined where they make sense; for example, they raise a TypeError exception when one of the arguments is a complex number.
Non-identical instances of a class normally compare as non-equal unless the class defines the __eq__() method.
Instances of a class cannot be ordered with respect to other instances of the same class, or other types of object, unless the class defines enough of the methods __lt__(), __le__(), __gt__(), and __ge__() (in general, __lt__() and __eq__() are sufficient, if you want the conventional meanings of the comparison operators).
The behavior of the is and is not operators cannot be customized; also they can be applied to any two objects and never raise an exception.
Two more operations with the same syntactic priority, in and not in, are supported by types that are iterable or implement the __contains__() method.
Numeric Types — int, float, complex
There are three distinct numeric types: integers, floating point numbers, and complex numbers. In addition, Booleans are a subtype of integers. Integers have unlimited precision. Floating point numbers are usually implemented using double in C; information about the precision and internal representation of floating point numbers for the machine on which your program is running is available in sys.float_info. Complex numbers have a real and imaginary part, which are each a floating point number. To extract these parts from a complex number z, use z.real and z.imag. (The standard library includes the additional numeric types fractions.Fraction, for rationals, and decimal.Decimal, for floating-point numbers with user-definable precision.)
Numbers are created by numeric literals or as the result of built-in functions and operators. Unadorned integer literals (including hex, octal and binary numbers) yield integers. Numeric literals containing a decimal point or an exponent sign yield floating point numbers. Appending 'j' or 'J' to a numeric literal yields an imaginary number (a complex number with a zero real part) which you can add to an integer or float to get a complex number with real and imaginary parts.
Python fully supports mixed arithmetic: when a binary arithmetic operator has operands of different numeric types, the operand with the “narrower” type is widened to that of the other, where integer is narrower than floating point, which is narrower than complex. A comparison between numbers of different types behaves as though the exact values of those numbers were being compared. 2
The constructors int(), float(), and complex() can be used to produce numbers of a specific type.
All numeric types (except complex) support the following operations (for priorities of the operations, see Operator precedence):
Operation
Result
Notes
Full documentation
x + y
sum of x and y
x - y
difference of x and y
x * y
product of x and y
x / y
quotient of x and y
x // y
floored quotient of x and y
(1)
x % y
remainder of x / y
(2)
-x
x negated
+x
x unchanged
abs(x)
absolute value or magnitude of x
abs()
int(x)
x converted to integer
(3)(6)
int()
float(x)
x converted to floating point
(4)(6)
float()
complex(re, im)
a complex number with real part re, imaginary part im. im defaults to zero.
(6)
complex()
c.conjugate()
conjugate of the complex number c
divmod(x, y)
the pair (x // y, x % y)
(2)
divmod()
pow(x, y)
x to the power y
(5)
pow()
x ** y
x to the power y
(5)
Notes:
Also referred to as integer division. The resultant value is a whole integer, though the result’s type is not necessarily int. The result is always rounded towards minus infinity: 1//2 is 0, (-1)//2 is -1, 1//(-2) is -1, and (-1)//(-2) is 0.
Not for complex numbers. Instead convert to floats using abs() if appropriate.
Conversion from float to int truncates, discarding the fractional part. See functions math.floor() and math.ceil() for alternative conversions.
float also accepts the strings “nan” and “inf” with an optional prefix “+” or “-” for Not a Number (NaN) and positive or negative infinity.
Python defines pow(0, 0) and 0 ** 0 to be 1, as is common for programming languages.
The numeric literals accepted include the digits 0 to 9 or any Unicode equivalent (code points with the Nd property).
See https://www.unicode.org/Public/13.0.0/ucd/extracted/DerivedNumericType.txt for a complete list of code points with the Nd property.
All numbers.Real types (int and float) also include the following operations:
Operation
Result
math.trunc(x)
x truncated to Integral
round(x[, n])
x rounded to n digits, rounding half to even. If n is omitted, it defaults to 0.
math.floor(x)
the greatest Integral <= x
math.ceil(x)
the least Integral >= x
For additional numeric operations see the math and cmath modules.
Bitwise Operations on Integer Types
Bitwise operations only make sense for integers. The result of bitwise operations is calculated as though carried out in two’s complement with an infinite number of sign bits.
The priorities of the binary bitwise operations are all lower than the numeric operations and higher than the comparisons; the unary operation ~ has the same priority as the other unary numeric operations (+ and -).
This table lists the bitwise operations sorted in ascending priority:
Operation
Result
Notes
x | y
bitwise or of x and y
(4)
x ^ y
bitwise exclusive or of x and y
(4)
x & y
bitwise and of x and y
(4)
x << n
x shifted left by n bits
(1)(2)
x >> n
x shifted right by n bits
(1)(3)
~x
the bits of x inverted
Notes:
Negative shift counts are illegal and cause a ValueError to be raised.
A left shift by n bits is equivalent to multiplication by pow(2, n).
A right shift by n bits is equivalent to floor division by pow(2, n).
Performing these calculations with at least one extra sign extension bit in a finite two’s complement representation (a working bit-width of 1 + max(x.bit_length(), y.bit_length()) or more) is sufficient to get the same result as if there were an infinite number of sign bits.
Additional Methods on Integer Types
The int type implements the numbers.Integral abstract base class. In addition, it provides a few more methods:
int.bit_length()
Return the number of bits necessary to represent an integer in binary, excluding the sign and leading zeros:
>>>
>>> n = -37
>>> bin(n)
'-0b100101'
>>> n.bit_length()
6
More precisely, if x is nonzero, then x.bit_length() is the unique positive integer k such that 2**(k-1) <= abs(x) < 2**k. Equivalently, when abs(x) is small enough to have a correctly rounded logarithm, then k = 1 + int(log(abs(x), 2)). If x is zero, then x.bit_length() returns 0.
Equivalent to:
def bit_length(self):
s = bin(self) # binary representation: bin(-37) --> '-0b100101'
s = s.lstrip('-0b') # remove leading zeros and minus sign
return len(s) # len('100101') --> 6
New in version 3.1.
int.bit_count()
Return the number of ones in the binary representation of the absolute value of the integer. This is also known as the population count. Example:
>>>
>>> n = 19
>>> bin(n)
'0b10011'
>>> n.bit_count()
3
>>> (-n).bit_count()
3
Equivalent to:
def bit_count(self):
return bin(self).count("1")
New in version 3.10.
int.to_bytes(length, byteorder, *, signed=False)
Return an array of bytes representing an integer.
>>>
(1024).to_bytes(2, byteorder='big')
b'\x04\x00'
(1024).to_bytes(10, byteorder='big')
b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'
(-1024).to_bytes(10, byteorder='big', signed=True)
b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'
x = 1000
x.to_bytes((x.bit_length() + 7) // 8, byteorder='little')
b'\xe8\x03'
The integer is represented using length bytes. An OverflowError is raised if the integer is not representable with the given number of bytes.
The byteorder argument determines the byte order used to represent the integer. If byteorder is "big", the most significant byte is at the beginning of the byte array. If byteorder is "little", the most significant byte is at the end of the byte array. To request the native byte order of the host system, use sys.byteorder as the byte order value.
The signed argument determines whether two’s complement is used to represent the integer. If signed is False and a negative integer is given, an OverflowError is raised. The default value for signed is False.
New in version 3.2.
classmethod int.from_bytes(bytes, byteorder, *, signed=False)
Return the integer represented by the given array of bytes.
>>>
int.from_bytes(b'\x00\x10', byteorder='big')
16
int.from_bytes(b'\x00\x10', byteorder='little')
4096
int.from_bytes(b'\xfc\x00', byteorder='big', signed=True)
-1024
int.from_bytes(b'\xfc\x00', byteorder='big', signed=False)
64512
int.from_bytes([255, 0, 0], byteorder='big')
16711680
The argument bytes must either be a bytes-like object or an iterable producing bytes.
The byteorder argument determines the byte order used to represent the integer. If byteorder is "big", the most significant byte is at the beginning of the byte array. If byteorder is "little", the most significant byte is at the end of the byte array. To request the native byte order of the host system, use sys.byteorder as the byte order value.
The signed argument indicates whether two’s complement is used to represent the integer.
New in version 3.2.
int.as_integer_ratio()
Return a pair of integers whose ratio is exactly equal to the original integer and with a positive denominator. The integer ratio of integers (whole numbers) is always the integer as the numerator and 1 as the denominator.
New in version 3.8.
Additional Methods on Float
The float type implements the numbers.Real abstract base class. float also has the following additional methods.
float.as_integer_ratio()
Return a pair of integers whose ratio is exactly equal to the original float and with a positive denominator. Raises OverflowError on infinities and a ValueError on NaNs.
float.is_integer()
Return True if the float instance is finite with integral value, and False otherwise:
>>>
>>> (-2.0).is_integer()
True
>>> (3.2).is_integer()
False
Two methods support conversion to and from hexadecimal strings. Since Python’s floats are stored internally as binary numbers, converting a float to or from a decimal string usually involves a small rounding error. In contrast, hexadecimal strings allow exact representation and specification of floating-point numbers. This can be useful when debugging, and in numerical work.
float.hex()
Return a representation of a floating-point number as a hexadecimal string. For finite floating-point numbers, this representation will always include a leading 0x and a trailing p and exponent.
classmethod float.fromhex(s)
Class method to return the float represented by a hexadecimal string s. The string s may have leading and trailing whitespace.
Note that float.hex() is an instance method, while float.fromhex() is a class method.
A hexadecimal string takes the form:
[sign] ['0x'] integer ['.' fraction] ['p' exponent]
where the optional sign may by either + or -, integer and fraction are strings of hexadecimal digits, and exponent is a decimal integer with an optional leading sign. Case is not significant, and there must be at least one hexadecimal digit in either the integer or the fraction. This syntax is similar to the syntax specified in section 6.4.4.2 of the C99 standard, and also to the syntax used in Java 1.5 onwards. In particular, the output of float.hex() is usable as a hexadecimal floating-point literal in C or Java code, and hexadecimal strings produced by C’s %a format character or Java’s Double.toHexString are accepted by float.fromhex().
Note that the exponent is written in decimal rather than hexadecimal, and that it gives the power of 2 by which to multiply the coefficient. For example, the hexadecimal string 0x3.a7p10 represents the floating-point number (3 + 10./16 + 7./16**2) * 2.0**10, or 3740.0:
>>>
>>> float.fromhex('0x3.a7p10')
3740.0
Applying the reverse conversion to 3740.0 gives a different hexadecimal string representing the same number:
>>>
>>> float.hex(3740.0)
'0x1.d380000000000p+11'
Hashing of numeric types
For numbers x and y, possibly of different types, it’s a requirement that hash(x) == hash(y) whenever x == y (see the __hash__() method documentation for more details). For ease of implementation and efficiency across a variety of numeric types (including int, float, decimal.Decimal and fractions.Fraction) Python’s hash for numeric types is based on a single mathematical function that’s defined for any rational number, and hence applies to all instances of int and fractions.Fraction, and all finite instances of float and decimal.Decimal. Essentially, this function is given by reduction modulo P for a fixed prime P. The value of P is made available to Python as the modulus attribute of sys.hash_info.
CPython implementation detail: Currently, the prime used is P = 2**31 - 1 on machines with 32-bit C longs and P = 2**61 - 1 on machines with 64-bit C longs.
Here are the rules in detail:
If x = m / n is a nonnegative rational number and n is not divisible by P, define hash(x) as m * invmod(n, P) % P, where invmod(n, P) gives the inverse of n modulo P.
If x = m / n is a nonnegative rational number and n is divisible by P (but m is not) then n has no inverse modulo P and the rule above doesn’t apply; in this case define hash(x) to be the constant value sys.hash_info.inf.
If x = m / n is a negative rational number define hash(x) as -hash(-x). If the resulting hash is -1, replace it with -2.
The particular values sys.hash_info.inf and -sys.hash_info.inf are used as hash values for positive infinity or negative infinity (respectively).
For a complex number z, the hash values of the real and imaginary parts are combined by computing hash(z.real) + sys.hash_info.imag * hash(z.imag), reduced modulo 2**sys.hash_info.width so that it lies in range(-2**(sys.hash_info.width - 1), 2**(sys.hash_info.width - 1)). Again, if the result is -1, it’s replaced with -2.
To clarify the above rules, here’s some example Python code, equivalent to the built-in hash, for computing the hash of a rational number, float, or complex:
import sys, math
def hash_fraction(m, n):
"""Compute the hash of a rational number m / n.
Assumes m and n are integers, with n positive.
Equivalent to hash(fractions.Fraction(m, n)).
"""
P = sys.hash_info.modulus
# Remove common factors of P. (Unnecessary if m and n already coprime.)
while m % P == n % P == 0:
m, n = m // P, n // P
if n % P == 0:
hash_value = sys.hash_info.inf
else:
# Fermat's Little Theorem: pow(n, P-1, P) is 1, so
# pow(n, P-2, P) gives the inverse of n modulo P.
hash_value = (abs(m) % P) * pow(n, P - 2, P) % P
if m < 0:
hash_value = -hash_value
if hash_value == -1:
hash_value = -2
return hash_value
def hash_float(x):
"""Compute the hash of a float x."""
if math.isnan(x):
return object.__hash__(x)
elif math.isinf(x):
return sys.hash_info.inf if x > 0 else -sys.hash_info.inf
else:
return hash_fraction(*x.as_integer_ratio())
def hash_complex(z):
"""Compute the hash of a complex number z."""
hash_value = hash_float(z.real) + sys.hash_info.imag * hash_float(z.imag)
# do a signed reduction modulo 2**sys.hash_info.width
M = 2**(sys.hash_info.width - 1)
hash_value = (hash_value & (M - 1)) - (hash_value & M)
if hash_value == -1:
hash_value = -2
return hash_value
Iterator Types
Python supports a concept of iteration over containers. This is implemented using two distinct methods; these are used to allow user-defined classes to support iteration. Sequences, described below in more detail, always support the iteration methods.
One method needs to be defined for container objects to provide iterable support:
container.__iter__()
Return an iterator object. The object is required to support the iterator protocol described below. If a container supports different types of iteration, additional methods can be provided to specifically request iterators for those iteration types. (An example of an object supporting multiple forms of iteration would be a tree structure which supports both breadth-first and depth-first traversal.) This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API.
The iterator objects themselves are required to support the following two methods, which together form the iterator protocol:
iterator.__iter__()
Return the iterator object itself. This is required to allow both containers and iterators to be used with the for and in statements. This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API.
iterator.__next__()
Return the next item from the iterator. If there are no further items, raise the StopIteration exception. This method corresponds to the tp_iternext slot of the type structure for Python objects in the Python/C API.
Python defines several iterator objects to support iteration over general and specific sequence types, dictionaries, and other more specialized forms. The specific types are not important beyond their implementation of the iterator protocol.
Once an iterator’s __next__() method raises StopIteration, it must continue to do so on subsequent calls. Implementations that do not obey this property are deemed broken.
Generator Types
Python’s generators provide a convenient way to implement the iterator protocol. If a container object’s __iter__() method is implemented as a generator, it will automatically return an iterator object (technically, a generator object) supplying the __iter__() and __next__() methods. More information about generators can be found in the documentation for the yield expression.
Sequence Types — list, tuple, range
There are three basic sequence types: lists, tuples, and range objects. Additional sequence types tailored for processing of binary data and text strings are described in dedicated sections.
Common Sequence Operations
The operations in the following table are supported by most sequence types, both mutable and immutable. The collections.abc.Sequence ABC is provided to make it easier to correctly implement these operations on custom sequence types.
This table lists the sequence operations sorted in ascending priority. In the table, s and t are sequences of the same type, n, i, j and k are integers and x is an arbitrary object that meets any type and value restrictions imposed by s.
The in and not in operations have the same priorities as the comparison operations. The + (concatenation) and * (repetition) operations have the same priority as the corresponding numeric operations. 3
Operation
Result
Notes
x in s
True if an item of s is equal to x, else False
(1)
x not in s
False if an item of s is equal to x, else True
(1)
s + t
the concatenation of s and t
(6)(7)
s * n or n * s
equivalent to adding s to itself n times
(2)(7)
s[i]
ith item of s, origin 0
(3)
s[i:j]
slice of s from i to j
(3)(4)
s[i:j:k]
slice of s from i to j with step k
(3)(5)
len(s)
length of s
min(s)
smallest item of s
max(s)
largest item of s
s.index(x[, i[, j]])
index of the first occurrence of x in s (at or after index i and before index j)
(8)
s.count(x)
total number of occurrences of x in s
Sequences of the same type also support comparisons. In particular, tuples and lists are compared lexicographically by comparing corresponding elements. This means that to compare equal, every element must compare equal and the two sequences must be of the same type and have the same length. (For full details see Comparisons in the language reference.)
Forward and reversed iterators over mutable sequences access values using an index. That index will continue to march forward (or backward) even if the underlying sequence is mutated. The iterator terminates only when an IndexError or a StopIteration is encountered (or when the index drops below zero).
Notes:
While the in and not in operations are used only for simple containment testing in the general case, some specialised sequences (such as str, bytes and bytearray) also use them for subsequence testing:
>>>
>>> "gg" in "eggs"
True
Values of n less than 0 are treated as 0 (which yields an empty sequence of the same type as s). Note that items in the sequence s are not copied; they are referenced multiple times. This often haunts new Python programmers; consider:
>>>
>>> lists = [[]] * 3
>>> lists
[[], [], []]
>>> lists[0].append(3)
>>> lists
[[3], [3], [3]]
What has happened is that [[]] is a one-element list containing an empty list, so all three elements of [[]] * 3 are references to this single empty list. Modifying any of the elements of lists modifies this single list. You can create a list of different lists this way:
>>>
>>> lists = [[] for i in range(3)]
>>> lists[0].append(3)
>>> lists[1].append(5)
>>> lists[2].append(7)
>>> lists
[[3], [5], [7]]
Further explanation is available in the FAQ entry How do I create a multidimensional list?.
If i or j is negative, the index is relative to the end of sequence s: len(s) + i or len(s) + j is substituted. But note that -0 is still 0.
The slice of s from i to j is defined as the sequence of items with index k such that i <= k < j. If i or j is greater than len(s), use len(s). If i is omitted or None, use 0. If j is omitted or None, use len(s). If i is greater than or equal to j, the slice is empty.
The slice of s from i to j with step k is defined as the sequence of items with index x = i + n*k such that 0 <= n < (j-i)/k. In other words, the indices are i, i+k, i+2*k, i+3*k and so on, stopping when j is reached (but never including j). When k is positive, i and j are reduced to len(s) if they are greater. When k is negative, i and j are reduced to len(s) - 1 if they are greater. If i or j are omitted or None, they become “end” values (which end depends on the sign of k). Note, k cannot be zero. If k is None, it is treated like 1.
Concatenating immutable sequences always results in a new object. This means that building up a sequence by repeated concatenation will have a quadratic runtime cost in the total sequence length. To get a linear runtime cost, you must switch to one of the alternatives below:
if concatenating str objects, you can build a list and use str.join() at the end or else write to an io.StringIO instance and retrieve its value when complete
if concatenating bytes objects, you can similarly use bytes.join() or io.BytesIO, or you can do in-place concatenation with a bytearray object. bytearray objects are mutable and have an efficient overallocation mechanism
if concatenating tuple objects, extend a list instead
for other types, investigate the relevant class documentation
Some sequence types (such as range) only support item sequences that follow specific patterns, and hence don’t support sequence concatenation or repetition.
index raises ValueError when x is not found in s. Not all implementations support passing the additional arguments i and j. These arguments allow efficient searching of subsections of the sequence. Passing the extra arguments is roughly equivalent to using s[i:j].index(x), only without copying any data and with the returned index being relative to the start of the sequence rather than the start of the slice.
Immutable Sequence Types
The only operation that immutable sequence types generally implement that is not also implemented by mutable sequence types is support for the hash() built-in.
This support allows immutable sequences, such as tuple instances, to be used as dict keys and stored in set and frozenset instances.
Attempting to hash an immutable sequence that contains unhashable values will result in TypeError.
Mutable Sequence Types
The operations in the following table are defined on mutable sequence types. The collections.abc.MutableSequence ABC is provided to make it easier to correctly implement these operations on custom sequence types.
In the table s is an instance of a mutable sequence type, t is any iterable object and x is an arbitrary object that meets any type and value restrictions imposed by s (for example, bytearray only accepts integers that meet the value restriction 0 <= x <= 255).
Operation
Result
Notes
s[i] = x
item i of s is replaced by x
s[i:j] = t
slice of s from i to j is replaced by the contents of the iterable t
del s[i:j]
same as s[i:j] = []
s[i:j:k] = t
the elements of s[i:j:k] are replaced by those of t
(1)
del s[i:j:k]
removes the elements of s[i:j:k] from the list
s.append(x)
appends x to the end of the sequence (same as s[len(s):len(s)] = [x])
s.clear()
removes all items from s (same as del s[:])
(5)
s.copy()
creates a shallow copy of s (same as s[:])
(5)
s.extend(t) or s += t
extends s with the contents of t (for the most part the same as s[len(s):len(s)] = t)
s *= n
updates s with its contents repeated n times
(6)
s.insert(i, x)
inserts x into s at the index given by i (same as s[i:i] = [x])
s.pop() or s.pop(i)
retrieves the item at i and also removes it from s
(2)
s.remove(x)
remove the first item from s where s[i] is equal to x
(3)
s.reverse()
reverses the items of s in place
(4)
Notes:
t must have the same length as the slice it is replacing.
The optional argument i defaults to -1, so that by default the last item is removed and returned.
remove() raises ValueError when x is not found in s.
The reverse() method modifies the sequence in place for economy of space when reversing a large sequence. To remind users that it operates by side effect, it does not return the reversed sequence.
clear() and copy() are included for consistency with the interfaces of mutable containers that don’t support slicing operations (such as dict and set). copy() is not part of the collections.abc.MutableSequence ABC, but most concrete mutable sequence classes provide it.
New in version 3.3: clear() and copy() methods.
The value n is an integer, or an object implementing __index__(). Zero and negative values of n clear the sequence. Items in the sequence are not copied; they are referenced multiple times, as explained for s * n under Common Sequence Operations.
Lists
Lists are mutable sequences, typically used to store collections of homogeneous items (where the precise degree of similarity will vary by application).
class list([iterable])
Lists may be constructed in several ways:
Using a pair of square brackets to denote the empty list: []
Using square brackets, separating items with commas: [a], [a, b, c]
Using a list comprehension: [x for x in iterable]
Using the type constructor: list() or list(iterable)
The constructor builds a list whose items are the same and in the same order as iterable’s items. iterable may be either a sequence, a container that supports iteration, or an iterator object. If iterable is already a list, a copy is made and returned, similar to iterable[:]. For example, list('abc') returns ['a', 'b', 'c'] and list( (1, 2, 3) ) returns [1, 2, 3]. If no argument is given, the constructor creates a new empty list, [].
Many other operations also produce lists, including the sorted() built-in.
Lists implement all of the common and mutable sequence operations. Lists also provide the following additional method:
sort(*, key=None, reverse=False)
This method sorts the list in place, using only < comparisons between items. Exceptions are not suppressed - if any comparison operations fail, the entire sort operation will fail (and the list will likely be left in a partially modified state).
sort() accepts two arguments that can only be passed by keyword (keyword-only arguments):
key specifies a function of one argument that is used to extract a comparison key from each list element (for example, key=str.lower). The key corresponding to each item in the list is calculated once and then used for the entire sorting process. The default value of None means that list items are sorted directly without calculating a separate key value.
The functools.cmp_to_key() utility is available to convert a 2.x style cmp function to a key function.
reverse is a boolean value. If set to True, then the list elements are sorted as if each comparison were reversed.
This method modifies the sequence in place for economy of space when sorting a large sequence. To remind users that it operates by side effect, it does not return the sorted sequence (use sorted() to explicitly request a new sorted list instance).
The sort() method is guaranteed to be stable. A sort is stable if it guarantees not to change the relative order of elements that compare equal — this is helpful for sorting in multiple passes (for example, sort by department, then by salary grade).
For sorting examples and a brief sorting tutorial, see Sorting HOW TO.
CPython implementation detail: While a list is being sorted, the effect of attempting to mutate, or even inspect, the list is undefined. The C implementation of Python makes the list appear empty for the duration, and raises ValueError if it can detect that the list has been mutated during a sort.
Tuples
Tuples are immutable sequences, typically used to store collections of heterogeneous data (such as the 2-tuples produced by the enumerate() built-in). Tuples are also used for cases where an immutable sequence of homogeneous data is needed (such as allowing storage in a set or dict instance).
class tuple([iterable])
Tuples may be constructed in a number of ways:
Using a pair of parentheses to denote the empty tuple: ()
Using a trailing comma for a singleton tuple: a, or (a,)
Separating items with commas: a, b, c or (a, b, c)
Using the tuple() built-in: tuple() or tuple(iterable)
The constructor builds a tuple whose items are the same and in the same order as iterable’s items. iterable may be either a sequence, a container that supports iteration, or an iterator object. If iterable is already a tuple, it is returned unchanged. For example, tuple('abc') returns ('a', 'b', 'c') and tuple( [1, 2, 3] ) returns (1, 2, 3). If no argument is given, the constructor creates a new empty tuple, ().
Note that it is actually the comma which makes a tuple, not the parentheses. The parentheses are optional, except in the empty tuple case, or when they are needed to avoid syntactic ambiguity. For example, f(a, b, c) is a function call with three arguments, while f((a, b, c)) is a function call with a 3-tuple as the sole argument.
Tuples implement all of the common sequence operations.
For heterogeneous collections of data where access by name is clearer than access by index, collections.namedtuple() may be a more appropriate choice than a simple tuple object.
Ranges
The range type represents an immutable sequence of numbers and is commonly used for looping a specific number of times in for loops.
class range(stop)
class range(start, stop[, step])
The arguments to the range constructor must be integers (either built-in int or any object that implements the __index__() special method). If the step argument is omitted, it defaults to 1. If the start argument is omitted, it defaults to 0. If step is zero, ValueError is raised.
For a positive step, the contents of a range r are determined by the formula r[i] = start + step*i where i >= 0 and r[i] < stop.
For a negative step, the contents of the range are still determined by the formula r[i] = start + step*i, but the constraints are i >= 0 and r[i] > stop.
A range object will be empty if r[0] does not meet the value constraint. Ranges do support negative indices, but these are interpreted as indexing from the end of the sequence determined by the positive indices.
Ranges containing absolute values larger than sys.maxsize are permitted but some features (such as len()) may raise OverflowError.
Range examples:
>>>
>>> list(range(10))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> list(range(1, 11))
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>> list(range(0, 30, 5))
[0, 5, 10, 15, 20, 25]
>>> list(range(0, 10, 3))
[0, 3, 6, 9]
>>> list(range(0, -10, -1))
[0, -1, -2, -3, -4, -5, -6, -7, -8, -9]
>>> list(range(0))
[]
>>> list(range(1, 0))
[]
Ranges implement all of the common sequence operations except concatenation and repetition (due to the fact that range objects can only represent sequences that follow a strict pattern and repetition and concatenation will usually violate that pattern).
start
The value of the start parameter (or 0 if the parameter was not supplied)
stop
The value of the stop parameter
step
The value of the step parameter (or 1 if the parameter was not supplied)
The advantage of the range type over a regular list or tuple is that a range object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the start, stop and step values, calculating individual items and subranges as needed).
Range objects implement the collections.abc.Sequence ABC, and provide features such as containment tests, element index lookup, slicing and support for negative indices (see Sequence Types — list, tuple, range):
>>>
r = range(0, 20, 2)
r
range(0, 20, 2)
11 in r
False
10 in r
True
r.index(10)
5
r[5]
10
r[:5]
range(0, 10, 2)
r[-1]
18
Testing range objects for equality with == and != compares them as sequences. That is, two range objects are considered equal if they represent the same sequence of values. (Note that two range objects that compare equal might have different start, stop and step attributes, for example range(0) == range(2, 1, 3) or range(0, 3, 2) == range(0, 4, 2).)
Changed in version 3.2: Implement the Sequence ABC. Support slicing and negative indices. Test int objects for membership in constant time instead of iterating through all items.
Changed in version 3.3: Define ‘==’ and ‘!=’ to compare range objects based on the sequence of values they define (instead of comparing based on object identity).
New in version 3.3: The start, stop and step attributes.
See also
The linspace recipe shows how to implement a lazy version of range suitable for floating point applications.
Text Sequence Type — str
Textual data in Python is handled with str objects, or strings. Strings are immutable sequences of Unicode code points. String literals are written in a variety of ways:
Single quotes: 'allows embedded "double" quotes'
Double quotes: "allows embedded 'single' quotes"
Triple quoted: '''Three single quotes''', """Three double quotes"""
Triple quoted strings may span multiple lines - all associated whitespace will be included in the string literal.
String literals that are part of a single expression and have only whitespace between them will be implicitly converted to a single string literal. That is, ("spam " "eggs") == "spam eggs".
See String and Bytes literals for more about the various forms of string literal, including supported escape sequences, and the r (“raw”) prefix that disables most escape sequence processing.
Strings may also be created from other objects using the str constructor.
Since there is no separate “character” type, indexing a string produces strings of length 1. That is, for a non-empty string s, s[0] == s[0:1].
There is also no mutable string type, but str.join() or io.StringIO can be used to efficiently construct strings from multiple fragments.
Changed in version 3.3: For backwards compatibility with the Python 2 series, the u prefix is once again permitted on string literals. It has no effect on the meaning of string literals and cannot be combined with the r prefix.
class str(object='')
class str(object=b'', encoding='utf-8', errors='strict')
Return a string version of object. If object is not provided, returns the empty string. Otherwise, the behavior of str() depends on whether encoding or errors is given, as follows.
If neither encoding nor errors is given, str(object) returns type(object).__str__(object), which is the “informal” or nicely printable string representation of object. For string objects, this is the string itself. If object does not have a __str__() method, then str() falls back to returning repr(object).
If at least one of encoding or errors is given, object should be a bytes-like object (e.g. bytes or bytearray). In this case, if object is a bytes (or bytearray) object, then str(bytes, encoding, errors) is equivalent to bytes.decode(encoding, errors). Otherwise, the bytes object underlying the buffer object is obtained before calling bytes.decode(). See Binary Sequence Types — bytes, bytearray, memoryview and Buffer Protocol for information on buffer objects.
Passing a bytes object to str() without the encoding or errors arguments falls under the first case of returning the informal string representation (see also the -b command-line option to Python). For example:
>>>
>>> str(b'Zoot!')
"b'Zoot!'"
For more information on the str class and its methods, see Text Sequence Type — str and the String Methods section below. To output formatted strings, see the Formatted string literals and Format String Syntax sections. In addition, see the Text Processing Services section.
String Methods
Strings implement all of the common sequence operations, along with the additional methods described below.
Strings also support two styles of string formatting, one providing a large degree of flexibility and customization (see str.format(), Format String Syntax and Custom String Formatting) and the other based on C printf style formatting that handles a narrower range of types and is slightly harder to use correctly, but is often faster for the cases it can handle (printf-style String Formatting).
The Text Processing Services section of the standard library covers a number of other modules that provide various text related utilities (including regular expression support in the re module).
str.capitalize()
Return a copy of the string with its first character capitalized and the rest lowercased.
Changed in version 3.8: The first character is now put into titlecase rather than uppercase. This means that characters like digraphs will only have their first letter capitalized, instead of the full character.
str.casefold()
Return a casefolded copy of the string. Casefolded strings may be used for caseless matching.
Casefolding is similar to lowercasing but more aggressive because it is intended to remove all case distinctions in a string. For example, the German lowercase letter 'ß' is equivalent to "ss". Since it is already lowercase, lower() would do nothing to 'ß'; casefold() converts it to "ss".
The casefolding algorithm is described in section 3.13 of the Unicode Standard.
New in version 3.3.
str.center(width[, fillchar])
Return centered in a string of length width. Padding is done using the specified fillchar (default is an ASCII space). The original string is returned if width is less than or equal to len(s).
str.count(sub[, start[, end]])
Return the number of non-overlapping occurrences of substring sub in the range [start, end]. Optional arguments start and end are interpreted as in slice notation.
If sub is empty, returns the number of empty strings between characters which is the length of the string plus one.
str.encode(encoding='utf-8', errors='strict')
Return the string encoded to bytes.
encoding defaults to 'utf-8'; see Standard Encodings for possible values.
errors controls how encoding errors are handled. If 'strict' (the default), a UnicodeError exception is raised. Other possible values are 'ignore', 'replace', 'xmlcharrefreplace', 'backslashreplace' and any other name registered via codecs.register_error(). See Error Handlers for details.
For performance reasons, the value of errors is not checked for validity unless an encoding error actually occurs, Python Development Mode is enabled or a debug build is used.
Changed in version 3.1: Added support for keyword arguments.
Changed in version 3.9: The value of the errors argument is now checked in Python Development Mode and in debug mode.
str.endswith(suffix[, start[, end]])
Return True if the string ends with the specified suffix, otherwise return False. suffix can also be a tuple of suffixes to look for. With optional start, test beginning at that position. With optional end, stop comparing at that position.
str.expandtabs(tabsize=8)
Return a copy of the string where all tab characters are replaced by one or more spaces, depending on the current column and the given tab size. Tab positions occur every tabsize characters (default is 8, giving tab positions at columns 0, 8, 16 and so on). To expand the string, the current column is set to zero and the string is examined character by character. If the character is a tab (\t), one or more space characters are inserted in the result until the current column is equal to the next tab position. (The tab character itself is not copied.) If the character is a newline (\n) or return (\r), it is copied and the current column is reset to zero. Any other character is copied unchanged and the current column is incremented by one regardless of how the character is represented when printed.
>>>
'01\t012\t0123\t01234'.expandtabs()
'01 012 0123 01234'
'01\t012\t0123\t01234'.expandtabs(4)
'01 012 0123 01234'
str.find(sub[, start[, end]])
Return the lowest index in the string where substring sub is found within the slice s[start:end]. Optional arguments start and end are interpreted as in slice notation. Return -1 if sub is not found.
Note The find() method should be used only if you need to know the position of sub. To check if sub is a substring or not, use the in operator:
>>>
>>> 'Py' in 'Python'
True
str.format(*args, **kwargs)