/
MathH.kt
1001 lines (878 loc) · 25 KB
/
MathH.kt
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
/*
* Copyright 2010-2018 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license
* that can be found in the license/LICENSE.txt file.
*/
@file:kotlin.jvm.JvmMultifileClass
@file:kotlin.jvm.JvmName("MathKt")
package kotlin.math
// constants, can't use them from nativeMath as they are not constants there
/** Ratio of the circumference of a circle to its diameter, approximately 3.14159. */
@SinceKotlin("1.2")
public const val PI: Double = 3.141592653589793
/** Base of the natural logarithms, approximately 2.71828. */
@SinceKotlin("1.2")
public const val E: Double = 2.718281828459045
// ================ Double Math ========================================
/** Computes the sine of the angle [x] given in radians.
*
* Special cases:
* - `sin(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sin(x: Double): Double
/** Computes the cosine of the angle [x] given in radians.
*
* Special cases:
* - `cos(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun cos(x: Double): Double
/** Computes the tangent of the angle [x] given in radians.
*
* Special cases:
* - `tan(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun tan(x: Double): Double
/**
* Computes the arc sine of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `asin(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
public expect fun asin(x: Double): Double
/**
* Computes the arc cosine of the value [x];
* the returned value is an angle in the range from `0.0` to `PI` radians.
*
* Special cases:
* - `acos(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
public expect fun acos(x: Double): Double
/**
* Computes the arc tangent of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `atan(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun atan(x: Double): Double
/**
* Returns the angle `theta` of the polar coordinates `(r, theta)` that correspond
* to the rectangular coordinates `(x, y)` by computing the arc tangent of the value [y] / [x];
* the returned value is an angle in the range from `-PI` to `PI` radians.
*
* Special cases:
* - `atan2(0.0, 0.0)` is `0.0`
* - `atan2(0.0, x)` is `0.0` for `x > 0` and `PI` for `x < 0`
* - `atan2(-0.0, x)` is `-0.0` for 'x > 0` and `-PI` for `x < 0`
* - `atan2(y, +Inf)` is `0.0` for `0 < y < +Inf` and `-0.0` for '-Inf < y < 0`
* - `atan2(y, -Inf)` is `PI` for `0 < y < +Inf` and `-PI` for `-Inf < y < 0`
* - `atan2(y, 0.0)` is `PI/2` for `y > 0` and `-PI/2` for `y < 0`
* - `atan2(+Inf, x)` is `PI/2` for finite `x`y
* - `atan2(-Inf, x)` is `-PI/2` for finite `x`
* - `atan2(NaN, x)` and `atan2(y, NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun atan2(y: Double, x: Double): Double
/**
* Computes the hyperbolic sine of the value [x].
*
* Special cases:
* - `sinh(NaN)` is `NaN`
* - `sinh(+Inf)` is `+Inf`
* - `sinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun sinh(x: Double): Double
/**
* Computes the hyperbolic cosine of the value [x].
*
* Special cases:
* - `cosh(NaN)` is `NaN`
* - `cosh(+Inf|-Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
public expect fun cosh(x: Double): Double
/**
* Computes the hyperbolic tangent of the value [x].
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(+Inf)` is `1.0`
* - `tanh(-Inf)` is `-1.0`
*/
@SinceKotlin("1.2")
public expect fun tanh(x: Double): Double
/**
* Computes the inverse hyperbolic sine of the value [x].
*
* The returned value is `y` such that `sinh(y) == x`.
*
* Special cases:
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun asinh(x: Double): Double
/**
* Computes the inverse hyperbolic cosine of the value [x].
*
* The returned value is positive `y` such that `cosh(y) == x`.
*
* Special cases:
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
public expect fun acosh(x: Double): Double
/**
* Computes the inverse hyperbolic tangent of the value [x].
*
* The returned value is `y` such that `tanh(y) == x`.
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun atanh(x: Double): Double
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
* Special cases:
* - returns `+Inf` if any of arguments is infinite
* - returns `NaN` if any of arguments is `NaN` and the other is not infinite
*/
@SinceKotlin("1.2")
public expect fun hypot(x: Double, y: Double): Double
/**
* Computes the positive square root of the value [x].
*
* Special cases:
* - `sqrt(x)` is `NaN` when `x < 0` or `x` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sqrt(x: Double): Double
/**
* Computes Euler's number `e` raised to the power of the value [x].
*
* Special cases:
* - `exp(NaN)` is `NaN`
* - `exp(+Inf)` is `+Inf`
* - `exp(-Inf)` is `0.0`
*/
@SinceKotlin("1.2")
public expect fun exp(x: Double): Double
/**
* Computes `exp(x) - 1`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `expm1(NaN)` is `NaN`
* - `expm1(+Inf)` is `+Inf`
* - `expm1(-Inf)` is `-1.0`
*
* @see [exp] function.
*/
@SinceKotlin("1.2")
public expect fun expm1(x: Double): Double
/**
* Computes the logarithm of the value [x] to the given [base].
*
* Special cases:
* - `log(x, b)` is `NaN` if either `x` or `b` are `NaN`
* - `log(x, b)` is `NaN` when `x < 0` or `b <= 0` or `b == 1.0`
* - `log(+Inf, +Inf)` is `NaN`
* - `log(+Inf, b)` is `+Inf` for `b > 1` and `-Inf` for `b < 1`
* - `log(0.0, b)` is `-Inf` for `b > 1` and `+Inf` for `b > 1`
*
* See also logarithm functions for common fixed bases: [ln], [log10] and [log2].
*/
@SinceKotlin("1.2")
public expect fun log(x: Double, base: Double): Double
/**
* Computes the natural logarithm (base `E`) of the value [x].
*
* Special cases:
* - `ln(NaN)` is `NaN`
* - `ln(x)` is `NaN` when `x < 0.0`
* - `ln(+Inf)` is `+Inf`
* - `ln(0.0)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun ln(x: Double): Double
/**
* Computes the common logarithm (base 10) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public expect fun log10(x: Double): Double
/**
* Computes the binary logarithm (base 2) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public expect fun log2(x: Double): Double
/**
* Computes `ln(x + 1)`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `ln1p(NaN)` is `NaN`
* - `ln1p(x)` is `NaN` where `x < -1.0`
* - `ln1p(-1.0)` is `-Inf`
* - `ln1p(+Inf)` is `+Inf`
*
* @see [ln] function
* @see [expm1] function
*/
@SinceKotlin("1.2")
public expect fun ln1p(x: Double): Double
/**
* Rounds the given value [x] to an integer towards positive infinity.
* @return the smallest double value that is greater than the given value [x] and is a mathematical integer.
*
* Special cases:
* - `ceil(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun ceil(x: Double): Double
/**
* Rounds the given value [x] to an integer towards negative infinity.
* @return the largest double value that is smaller than the given value [x] and is a mathematical integer.
*
* Special cases:
* - `floor(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun floor(x: Double): Double
/**
* Rounds the given value [x] to an integer towards zero.
*
* @return the value [x] having its fractional part truncated.
*
* Special cases:
* - `truncate(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun truncate(x: Double): Double
/**
* Rounds the given value [x] towards the closest integer with ties rounded towards even integer.
*
* Special cases:
* - `round(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun round(x: Double): Double
/**
* Returns the absolute value of the given value [x].
*
* Special cases:
* - `abs(NaN)` is `NaN`
*
* @see absoluteValue extension property for [Double]
*/
@SinceKotlin("1.2")
public expect fun abs(x: Double): Double
/**
* Returns the sign of the given value [x]:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `sign(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sign(x: Double): Double
/**
* Returns the smaller of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
public expect fun min(a: Double, b: Double): Double
/**
* Returns the greater of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
public expect fun max(a: Double, b: Double): Double
// extensions
/**
* Raises this value to the power [x].
*
* Special cases:
* - `b.pow(0.0)` is `1.0`
* - `b.pow(1.0) == b`
* - `b.pow(NaN)` is `NaN`
* - `NaN.pow(x)` is `NaN` for `x != 0.0`
* - `b.pow(Inf)` is `NaN` for `abs(b) == 1.0`
* - `b.pow(x)` is `NaN` for `b < 0` and `x` is finite and not an integer
*/
@SinceKotlin("1.2")
public expect fun Double.pow(x: Double): Double
/**
* Raises this value to the integer power [n].
*
* See the other overload of [pow] for details.
*/
@SinceKotlin("1.2")
public expect fun Double.pow(n: Int): Double
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `NaN.absoluteValue` is `NaN`
*
* @see abs function
*/
@SinceKotlin("1.2")
public expect val Double.absoluteValue: Double
/**
* Returns the sign of this value:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `NaN.sign` is `NaN`
*/
@SinceKotlin("1.2")
public expect val Double.sign: Double
/**
* Returns this value with the sign bit same as of the [sign] value.
*
* If [sign] is `NaN` the sign of the result is undefined.
*/
@SinceKotlin("1.2")
public expect fun Double.withSign(sign: Double): Double
/**
* Returns this value with the sign bit same as of the [sign] value.
*/
@SinceKotlin("1.2")
public expect fun Double.withSign(sign: Int): Double
/**
* Returns the ulp (unit in the last place) of this value.
*
* An ulp is a positive distance between this value and the next nearest [Double] value larger in magnitude.
*
* Special Cases:
* - `NaN.ulp` is `NaN`
* - `x.ulp` is `+Inf` when `x` is `+Inf` or `-Inf`
* - `0.0.ulp` is `Double.MIN_VALUE`
*/
@SinceKotlin("1.2")
public expect val Double.ulp: Double
/**
* Returns the [Double] value nearest to this value in direction of positive infinity.
*/
@SinceKotlin("1.2")
public expect fun Double.nextUp(): Double
/**
* Returns the [Double] value nearest to this value in direction of negative infinity.
*/
@SinceKotlin("1.2")
public expect fun Double.nextDown(): Double
/**
* Returns the [Double] value nearest to this value in direction from this value towards the value [to].
*
* Special cases:
* - `x.nextTowards(y)` is `NaN` if either `x` or `y` are `NaN`
* - `x.nextTowards(x) == x`
*
*/
@SinceKotlin("1.2")
public expect fun Double.nextTowards(to: Double): Double
/**
* Rounds this [Double] value to the nearest integer and converts the result to [Int].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToInt() == Int.MAX_VALUE` when `x > Int.MAX_VALUE`
* - `x.roundToInt() == Int.MIN_VALUE` when `x < Int.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public expect fun Double.roundToInt(): Int
/**
* Rounds this [Double] value to the nearest integer and converts the result to [Long].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToLong() == Long.MAX_VALUE` when `x > Long.MAX_VALUE`
* - `x.roundToLong() == Long.MIN_VALUE` when `x < Long.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public expect fun Double.roundToLong(): Long
// ================ Float Math ========================================
/** Computes the sine of the angle [x] given in radians.
*
* Special cases:
* - `sin(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sin(x: Float): Float
/** Computes the cosine of the angle [x] given in radians.
*
* Special cases:
* - `cos(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun cos(x: Float): Float
/** Computes the tangent of the angle [x] given in radians.
*
* Special cases:
* - `tan(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun tan(x: Float): Float
/**
* Computes the arc sine of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `asin(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
public expect fun asin(x: Float): Float
/**
* Computes the arc cosine of the value [x];
* the returned value is an angle in the range from `0.0` to `PI` radians.
*
* Special cases:
* - `acos(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
public expect fun acos(x: Float): Float
/**
* Computes the arc tangent of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `atan(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun atan(x: Float): Float
/**
* Returns the angle `theta` of the polar coordinates `(r, theta)` that correspond
* to the rectangular coordinates `(x, y)` by computing the arc tangent of the value [y] / [x];
* the returned value is an angle in the range from `-PI` to `PI` radians.
*
* Special cases:
* - `atan2(0.0, 0.0)` is `0.0`
* - `atan2(0.0, x)` is `0.0` for `x > 0` and `PI` for `x < 0`
* - `atan2(-0.0, x)` is `-0.0` for 'x > 0` and `-PI` for `x < 0`
* - `atan2(y, +Inf)` is `0.0` for `0 < y < +Inf` and `-0.0` for '-Inf < y < 0`
* - `atan2(y, -Inf)` is `PI` for `0 < y < +Inf` and `-PI` for `-Inf < y < 0`
* - `atan2(y, 0.0)` is `PI/2` for `y > 0` and `-PI/2` for `y < 0`
* - `atan2(+Inf, x)` is `PI/2` for finite `x`y
* - `atan2(-Inf, x)` is `-PI/2` for finite `x`
* - `atan2(NaN, x)` and `atan2(y, NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun atan2(y: Float, x: Float): Float
/**
* Computes the hyperbolic sine of the value [x].
*
* Special cases:
* - `sinh(NaN)` is `NaN`
* - `sinh(+Inf)` is `+Inf`
* - `sinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun sinh(x: Float): Float
/**
* Computes the hyperbolic cosine of the value [x].
*
* Special cases:
* - `cosh(NaN)` is `NaN`
* - `cosh(+Inf|-Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
public expect fun cosh(x: Float): Float
/**
* Computes the hyperbolic tangent of the value [x].
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(+Inf)` is `1.0`
* - `tanh(-Inf)` is `-1.0`
*/
@SinceKotlin("1.2")
public expect fun tanh(x: Float): Float
/**
* Computes the inverse hyperbolic sine of the value [x].
*
* The returned value is `y` such that `sinh(y) == x`.
*
* Special cases:
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun asinh(x: Float): Float
/**
* Computes the inverse hyperbolic cosine of the value [x].
*
* The returned value is positive `y` such that `cosh(y) == x`.
*
* Special cases:
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
public expect fun acosh(x: Float): Float
/**
* Computes the inverse hyperbolic tangent of the value [x].
*
* The returned value is `y` such that `tanh(y) == x`.
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun atanh(x: Float): Float
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
* Special cases:
* - returns `+Inf` if any of arguments is infinite
* - returns `NaN` if any of arguments is `NaN` and the other is not infinite
*/
@SinceKotlin("1.2")
public expect fun hypot(x: Float, y: Float): Float
/**
* Computes the positive square root of the value [x].
*
* Special cases:
* - `sqrt(x)` is `NaN` when `x < 0` or `x` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sqrt(x: Float): Float
/**
* Computes Euler's number `e` raised to the power of the value [x].
*
* Special cases:
* - `exp(NaN)` is `NaN`
* - `exp(+Inf)` is `+Inf`
* - `exp(-Inf)` is `0.0`
*/
@SinceKotlin("1.2")
public expect fun exp(x: Float): Float
/**
* Computes `exp(x) - 1`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `expm1(NaN)` is `NaN`
* - `expm1(+Inf)` is `+Inf`
* - `expm1(-Inf)` is `-1.0`
*
* @see [exp] function.
*/
@SinceKotlin("1.2")
public expect fun expm1(x: Float): Float
/**
* Computes the logarithm of the value [x] to the given [base].
*
* Special cases:
* - `log(x, b)` is `NaN` if either `x` or `b` are `NaN`
* - `log(x, b)` is `NaN` when `x < 0` or `b <= 0` or `b == 1.0`
* - `log(+Inf, +Inf)` is `NaN`
* - `log(+Inf, b)` is `+Inf` for `b > 1` and `-Inf` for `b < 1`
* - `log(0.0, b)` is `-Inf` for `b > 1` and `+Inf` for `b > 1`
*
* See also logarithm functions for common fixed bases: [ln], [log10] and [log2].
*/
@SinceKotlin("1.2")
public expect fun log(x: Float, base: Float): Float
/**
* Computes the natural logarithm (base `E`) of the value [x].
*
* Special cases:
* - `ln(NaN)` is `NaN`
* - `ln(x)` is `NaN` when `x < 0.0`
* - `ln(+Inf)` is `+Inf`
* - `ln(0.0)` is `-Inf`
*/
@SinceKotlin("1.2")
public expect fun ln(x: Float): Float
/**
* Computes the common logarithm (base 10) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public expect fun log10(x: Float): Float
/**
* Computes the binary logarithm (base 2) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public expect fun log2(x: Float): Float
/**
* Computes `ln(a + 1)`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `ln1p(NaN)` is `NaN`
* - `ln1p(x)` is `NaN` where `x < -1.0`
* - `ln1p(-1.0)` is `-Inf`
* - `ln1p(+Inf)` is `+Inf`
*
* @see [ln] function
* @see [expm1] function
*/
@SinceKotlin("1.2")
public expect fun ln1p(x: Float): Float
/**
* Rounds the given value [x] to an integer towards positive infinity.
* @return the smallest Float value that is greater than the given value [x] and is a mathematical integer.
*
* Special cases:
* - `ceil(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun ceil(x: Float): Float
/**
* Rounds the given value [x] to an integer towards negative infinity.
* @return the largest Float value that is smaller than the given value [x] and is a mathematical integer.
*
* Special cases:
* - `floor(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun floor(x: Float): Float
/**
* Rounds the given value [x] to an integer towards zero.
*
* @return the value [x] having its fractional part truncated.
*
* Special cases:
* - `truncate(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun truncate(x: Float): Float
/**
* Rounds the given value [x] towards the closest integer with ties rounded towards even integer.
*
* Special cases:
* - `round(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public expect fun round(x: Float): Float
/**
* Returns the absolute value of the given value [x].
*
* Special cases:
* - `abs(NaN)` is `NaN`
*
* @see absoluteValue extension property for [Float]
*/
@SinceKotlin("1.2")
public expect fun abs(x: Float): Float
/**
* Returns the sign of the given value [x]:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `sign(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
public expect fun sign(x: Float): Float
/**
* Returns the smaller of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
public expect fun min(a: Float, b: Float): Float
/**
* Returns the greater of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
public expect fun max(a: Float, b: Float): Float
// extensions
/**
* Raises this value to the power [x].
*
* Special cases:
* - `b.pow(0.0)` is `1.0`
* - `b.pow(1.0) == b`
* - `b.pow(NaN)` is `NaN`
* - `NaN.pow(x)` is `NaN` for `x != 0.0`
* - `b.pow(Inf)` is `NaN` for `abs(b) == 1.0`
* - `b.pow(x)` is `NaN` for `b < 0` and `x` is finite and not an integer
*/
@SinceKotlin("1.2")
public expect fun Float.pow(x: Float): Float
/**
* Raises this value to the integer power [n].
*
* See the other overload of [pow] for details.
*/
@SinceKotlin("1.2")
public expect fun Float.pow(n: Int): Float
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `NaN.absoluteValue` is `NaN`
*
* @see abs function
*/
@SinceKotlin("1.2")
public expect val Float.absoluteValue: Float
/**
* Returns the sign of this value:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `NaN.sign` is `NaN`
*/
@SinceKotlin("1.2")
public expect val Float.sign: Float
/**
* Returns this value with the sign bit same as of the [sign] value.
*
* If [sign] is `NaN` the sign of the result is undefined.
*/
@SinceKotlin("1.2")
public expect fun Float.withSign(sign: Float): Float
/**
* Returns this value with the sign bit same as of the [sign] value.
*/
@SinceKotlin("1.2")
public expect fun Float.withSign(sign: Int): Float
/**
* Rounds this [Float] value to the nearest integer and converts the result to [Int].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToInt() == Int.MAX_VALUE` when `x > Int.MAX_VALUE`
* - `x.roundToInt() == Int.MIN_VALUE` when `x < Int.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public expect fun Float.roundToInt(): Int
/**
* Rounds this [Float] value to the nearest integer and converts the result to [Long].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToLong() == Long.MAX_VALUE` when `x > Long.MAX_VALUE`
* - `x.roundToLong() == Long.MIN_VALUE` when `x < Long.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public expect fun Float.roundToLong(): Long
/**
* Returns the absolute value of the given value [n].
*
* Special cases:
* - `abs(Int.MIN_VALUE)` is `Int.MIN_VALUE` due to an overflow
*
* @see absoluteValue extension property for [Int]
*/
@SinceKotlin("1.2")
public expect fun abs(n: Int): Int
/**
* Returns the smaller of two values.
*/
@SinceKotlin("1.2")
public expect fun min(a: Int, b: Int): Int
/**
* Returns the greater of two values.
*/
@SinceKotlin("1.2")
public expect fun max(a: Int, b: Int): Int
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `Int.MIN_VALUE.absoluteValue` is `Int.MIN_VALUE` due to an overflow
*
* @see abs function
*/
@SinceKotlin("1.2")
public expect val Int.absoluteValue: Int
/**
* Returns the sign of this value:
* - `-1` if the value is negative,
* - `0` if the value is zero,
* - `1` if the value is positive
*/
@SinceKotlin("1.2")
public expect val Int.sign: Int
/**
* Returns the absolute value of the given value [n].
*
* Special cases:
* - `abs(Long.MIN_VALUE)` is `Long.MIN_VALUE` due to an overflow
*
* @see absoluteValue extension property for [Long]
*/
@SinceKotlin("1.2")
public expect fun abs(n: Long): Long
/**
* Returns the smaller of two values.
*/
@SinceKotlin("1.2")
public expect fun min(a: Long, b: Long): Long
/**
* Returns the greater of two values.
*/
@SinceKotlin("1.2")
public expect fun max(a: Long, b: Long): Long
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `Long.MIN_VALUE.absoluteValue` is `Long.MIN_VALUE` due to an overflow
*
* @see abs function
*/
@SinceKotlin("1.2")
public expect val Long.absoluteValue: Long
/**
* Returns the sign of this value:
* - `-1` if the value is negative,
* - `0` if the value is zero,
* - `1` if the value is positive
*/
@SinceKotlin("1.2")
public expect val Long.sign: Int