-
Notifications
You must be signed in to change notification settings - Fork 550
/
MathImpl.cs
1733 lines (1564 loc) · 60.8 KB
/
MathImpl.cs
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
using System;
using Cosmos.Debug.Kernel;
using IL2CPU.API;
using IL2CPU.API.Attribs;
namespace Cosmos.System_Plugs.System
{
[Plug(Target = typeof(Math))]
public static class MathImpl
{
/* @(#)fdlibm.h 1.5 04/04/22 */
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
//Following functions which have been implemented in this file are functions taken from http://www.netlib.org/fdlibm/ and have then be changed to work in C#
//Acos, Asin, Cos, _cos, __ieee754_rem_pio2, __kernel_rem_pio2, Scalbn, Log base e, Sin, _sin, exp, atan
internal static Debugger mDebugger = new Debugger("System", "Math Plugs");
#region Internal Constants
private const double sq2p1 = 2.414213562373095048802e0F;
private const double sq2m1 = .414213562373095048802e0F;
private const double pio2 = 1.570796326794896619231e0F;
private const double pio4 = .785398163397448309615e0F;
private const double log2e = 1.4426950408889634073599247F;
private const double sqrt2 = 1.4142135623730950488016887F;
private const double ln2 = 6.93147180559945286227e-01F;
private const double atan_p4 = .161536412982230228262e2F;
private const double atan_p3 = .26842548195503973794141e3F;
private const double atan_p2 = .11530293515404850115428136e4F;
private const double atan_p1 = .178040631643319697105464587e4F;
private const double atan_p0 = .89678597403663861959987488e3F;
private const double atan_q4 = .5895697050844462222791e2F;
private const double atan_q3 = .536265374031215315104235e3F;
private const double atan_q2 = .16667838148816337184521798e4F;
private const double atan_q1 = .207933497444540981287275926e4F;
private const double atan_q0 = .89678597403663861962481162e3F;
#endregion Internal Constants
public const double PI = 3.1415926535897932384626433832795;
public const double E = 2.71828182845904523536;
#region Abs
public static double Abs(double value)
{
if (value < 0)
{
return -value;
}
else
{
return value;
}
}
public static float Abs(float value)
{
if (value < 0)
{
return -value;
}
else
{
return value;
}
}
#endregion Abs
#region Acos
public static double Acos(double x)
{
double pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
double z, p, q, r, w, s, c, df;
int hx, ix;
hx = HighWord(x);
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000)
{ /* |x| >= 1 */
if (((ix - 0x3ff00000) | LowWord(x)) == 0)
{ /* |x|==1 */
if (hx > 0)
return 0.0; /* acos(1) = 0 */
else
return Math.PI + 2.0 * pio2_lo; /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
}
if (ix < 0x3fe00000)
{ /* |x| < 0.5 */
if (ix <= 0x3c600000)
return pio2_hi + pio2_lo;/*if|x|<2**-57*/
z = x * x;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = 1 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
return pio2_hi - (x - (pio2_lo - x * r));
}
else if (hx < 0)
{ /* x < -0.5 */
z = (1 + x) * 0.5;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = 1 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
s = Sqrt(z);
r = p / q;
w = r * s - pio2_lo;
return Math.PI - 2.0 * (s + w);
}
else
{ /* x > 0.5 */
z = (1 - x) * 0.5;
s = Sqrt(z);
df = s;
//__LO(df) = 0;
Byte[] bdf = BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(df));
for (int i = 0; i < 4; i++)
{
bdf[i + (BitConverter.IsLittleEndian ? 4 : 0)] = 0;
}
df = BitConverter.ToDouble(bdf, 0);
c = (z - df * df) / (s + df);
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = 1 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
w = r * s + c;
return 2.0 * (df + w);
}
}
#endregion Acos
#region Asin
public static double Asin(double x)
{
double huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
/* coefficient for R(x^2) */
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
double t = 0, w, p, q, c, r, s;
int hx, ix;
hx = HighWord(x);
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000)
{ /* |x|>= 1 */
if (((ix - 0x3ff00000) | LowWord(x)) == 0)
/* asin(1)=+-pi/2 with inexact */
return x * pio2_hi + x * pio2_lo;
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
}
else if (ix < 0x3fe00000)
{ /* |x|<0.5 */
if (ix < 0x3e400000)
{ /* if |x| < 2**-27 */
if (huge + x > 1) return x;/* return x with inexact if x!=0*/
}
else
t = x * x;
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
q = 1 + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
w = p / q;
return x + x * w;
}
/* 1> |x|>= 0.5 */
w = 1 - Abs(x);
t = w * 0.5;
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
q = 1 + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
s = Sqrt(t);
if (ix >= 0x3FEF3333)
{ /* if |x| > 0.975 */
w = p / q;
t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
}
else
{
w = s;
//__LO(w) = 0;
Byte[] bw = BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(w));
for (int i = 0; i < 4; i++)
{
bw[i + (BitConverter.IsLittleEndian ? 4 : 0)] = 0;
}
w = BitConverter.ToDouble(bw, 0);
c = (t - w * w) / (s + w);
r = p / q;
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
q = pio4_hi - 2.0 * w;
t = pio4_hi - (p - q);
}
if (hx > 0) return t; else return -t;
}
#endregion Asin
#region Atan
public static double Atan(double x)
{
if (double.IsNaN(x)) return double.NaN;
if (double.IsPositiveInfinity(x)) return Math.PI / 2;
if (double.IsNegativeInfinity(x)) return -Math.PI / 2;
double w, s1, s2, z;
int ix, hx, id;
double[] atanhi = {
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};
double[] atanlo = {
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};
double[] aT = {
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
hx = HighWord(x);
ix = hx & 0x7fffffff;
if (ix >= 0x44100000)
{ /* if |x| >= 2^66 */
if (ix > 0x7ff00000 ||
(ix == 0x7ff00000 && (LowWord(x) != 0)))
return x + x; /* NaN */
if (hx > 0) return atanhi[3] + atanlo[3];
else return -atanhi[3] - atanlo[3];
}
if (ix < 0x3fdc0000)
{ /* |x| < 0.4375 */
if (ix < 0x3e200000)
{ /* |x| < 2^-29 */
if (1.0e+300 + x > 1) return x; /* raise inexact */
}
id = -1;
}
else
{
x = Math.Abs(x);
if (ix < 0x3ff30000)
{ /* |x| < 1.1875 */
if (ix < 0x3fe60000)
{ /* 7/16 <=|x|<11/16 */
id = 0; x = (2.0 * x - 1) / (2.0 + x);
}
else
{ /* 11/16<=|x|< 19/16 */
id = 1; x = (x - 1) / (x + 1);
}
}
else
{
if (ix < 0x40038000)
{ /* |x| < 2.4375 */
id = 2; x = (x - 1.5) / (1 + 1.5 * x);
}
else
{ /* 2.4375 <= |x| < 2^66 */
id = 3; x = -1.0 / x;
}
}
}
/* end of argument reduction */
z = x * x;
w = z * z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
if (id < 0) return x - x * (s1 + s2);
else
{
z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
return (hx < 0) ? -z : z;
}
}
#endregion Atan
#region Atan2
public static double Atan2(double x, double y)
{
if ((x + y) == x)
{
if ((x == 0F) & (y == 0F))
return 0F;
if (x >= 0.0F)
return pio2;
return (-pio2);
}
if (y < 0.0F)
{
if (x >= 0.0F)
return ((pio2 * 2) - atans((-x) / y));
return (((-pio2) * 2) + atans(x / y));
}
if (x > 0.0F)
{
return (atans(x / y));
}
return (-atans((-x) / y));
//return (((x + y) == x) ? (((x == 0F) & (y == 0F)) ? 0F : ((x >= 0F) ? pio2 : (-pio2))) : ((y < 0F) ? ((x >= 0F) ? ((pio2 * 2) - atans((-x) / y)) : (((-pio2) * 2) + atans(x / y))) : ((x > 0F) ? atans(x / y) : -atans((-x) / y))));
}
#endregion Atan2
#region Ceiling
public static double Ceiling(double x)
{
if (double.IsNaN(x) || double.IsInfinity(x)) return x;
double huge = 1.0e+300;
int i0, i1, j0;
uint i, j;
i0 = HighWord(x);
i1 = LowWord(x);
j0 = ((i0 >> 20) & 0x7ff) - 0x3ff;
if (j0 < 20)
{
if (j0 < 0)
{ /* raise inexact if x != 0 */
if (huge + x > 0.0)
{/* return 0*sign(x) if |x|<1 */
if (i0 < 0)
{
i0 = (int)(0x80000000 - 1); //Cant set 0x80000000 to int
i1 = 0;
}
else if ((i0 | i1) != 0)
{
i0 = 0x3ff00000;
i1 = 0;
}
}
}
else
{
i = (uint)(0x000fffff) >> j0;
if (((i0 & i) | i1) == 0) return x; /* x is integral */
if (huge + x > 0.0)
{ /* raise inexact flag */
if (i0 > 0)
i0 += (0x00100000) >> j0;
i0 &= (int)~i;
i1 = 0;
}
}
}
else if (j0 > 51)
{
if (j0 == 0x400) return x + x; /* inf or NaN */
else return x; /* x is integral */
}
else
{
i = 0xffffffff >> (j0 - 20);
if ((i1 & i) == 0) return x; /* x is integral */
if (huge + x > 0.0)
{ /* raise inexact flag */
if (i0 > 0)
{
if (j0 == 20) i0 += 1;
else
{
j = (uint)(i1 + (1 << (52 - j0)));
if (j < i1) i0 += 1; /* got a carry */
i1 = (int)j;
}
}
i1 &= (int)~i;
}
}
Byte[] returnBytes = BitConverter.GetBytes(0d);
Byte[] highWord = BitConverter.GetBytes(i0);
Byte[] lowWord = BitConverter.GetBytes(i1);
for (int c = 0; c < 4; c++)
{
returnBytes[c + (BitConverter.IsLittleEndian ? 4 : 0)] = highWord[c];
}
for (int c = 0; c < 4; c++)
{
returnBytes[c + (BitConverter.IsLittleEndian ? 0 : 4)] = lowWord[c];
}
return BitConverter.ToDouble(returnBytes, 0);
}
#endregion Ceiling
#region Cos
public static double Cos(double x)
{
double[] y = new double[2];
double z = 0.0;
int n, ix;
/* High word of x. */
ix = HighWord(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) return _cos(x, z);
/* cos(Inf or NaN) is NaN */
else if (ix >= 0x7ff00000) return x - x;
/* argument reduction needed */
else
{
n = __ieee754_rem_pio2(x, y);
switch (n & 3)
{
case 0:
return _cos(y[0], y[1]);
case 1:
return -_sin(y[0], y[1], 1);
case 2:
return -_cos(y[0], y[1]);
default:
return _sin(y[0], y[1], 1);
}
}
}
private static double _cos(double x, double y)
{
const double one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
double a, hz, z, r, qx = 0;
int ix;
ix = HighWord(x) & 0x7fffffff; /* ix = |x|'s high word*/
if (ix < 0x3e400000)
{ /* if x < 2**27 */
if (((int)x) == 0)
return one; /* generate inexact */
}
z = x * x;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
if (ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5 * z - (z * r - x * y));
else
{
if (ix > 0x3fe90000)
{ /* x > 0.78125 */
qx = 0.28125;
}
else
{
//__HI(qx) = ix - 0x00200000; /* x/4 */
Byte[] bqx = BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(qx));
Byte[] bvh = BitConverter.GetBytes(ix - 0x00200000);
for (int i = 0; i < 4; i++)
{
bqx[i + (BitConverter.IsLittleEndian ? 4 : 0)] = bvh[i];
}
//__LO(qx) = 0;
for (int i = 0; i < 4; i++)
{
bqx[i + (BitConverter.IsLittleEndian ? 4 : 0)] = 0;
}
}
hz = 0.5 * z - qx;
a = one - qx;
return a - (hz - (z * r - x * y));
}
}
#endregion Cos
#region Cosh
public static double Cosh(double x)
{
if (x < 0.0F)
x = -x;
return ((x == 0F) ? 1F : ((x <= (ln2 / 2)) ? (1 + (_power((Exp(x) - 1), 2) / (2 * Exp(x)))) : ((x <= 22F) ? ((Exp(x) + (1 / Exp(x))) / 2) : (0.5F * (Exp(x) + Exp(-x))))));
}
#endregion Cosh
#region Exp
public static double Exp(double x)
{
double y, hi = 0, lo = 0, c, t;
int k = 0, xsb;
const double o_threshold = 7.09782712893383973096e+02;
const double u_threshold = -7.45133219101941108420e+02;
const double invln2 = 1.44269504088896338700e+00;
const double twom1000 = 9.33263618503218878990e-302;
const double P1 = 1.66666666666666019037e-01;
const double P2 = -2.77777777770155933842e-03;
const double P3 = 6.61375632143793436117e-05;
const double P4 = -1.65339022054652515390e-06;
const double P5 = 4.13813679705723846039e-08;
const double huge = 1.0e+300;
int hx = HighWord(x); //Highword of x
xsb = ((int)hx >> 31) & 1; //Get sign of x
hx &= 0x7fffffff; //Get the abs(x) of the highword
//Check if non-finite argument
if (hx >= 0x40862E42)
{ /* if |x|>=709.78... */
if (hx >= 0x7ff00000)
{
if (((hx & 0xfffff) | LowWord(x)) != 0) //Assume that __Lo(x) is lower word of x
return x; /* NaN */
else
return (xsb == 0) ? x : 0.0; /* exp(+-inf)={inf,0} */
}
if (x > o_threshold)
return double.PositiveInfinity; /* overflow */
if (x < u_threshold)
return 0; /* underflow */
}
/* argument reduction */
if (hx > 0x3fd62e42)
{ /* if |x| > 0.5 ln2 */
if (hx < 0x3FF0A2B2)
{ /* and |x| < 1.5 ln2 */
if (xsb == 0)
{
hi = x - 6.93147180369123816490e-01;
lo = 1.90821492927058770002e-10;
}
else
{
hi = x - -6.93147180369123816490e-01;
lo = -1.90821492927058770002e-10;
}
k = 1 - xsb - xsb;
}
else
{
if (xsb == 0)
k = (int)(invln2 * x + 0.5);
else
k = (int)(invln2 * x + -0.5);
t = k;
hi = x - t * 6.93147180369123816490e-01;
lo = t * 1.90821492927058770002e-10;
}
x = hi - lo;
}
else if (hx < 0x3e300000)
{ /* when |x|<2**-28 */
if (huge + x > 1)
return 1 + x;/* trigger inexact */
}
else
k = 0;
/* x is now in primary range */
t = x * x;
c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
if (k == 0)
return 1 - ((x * c) / (c - 2.0) - x);
else
y = 1 - ((lo - (x * c) / (2.0 - c)) - hi);
if (k >= -1021)
{
//The idea is to add hy to the exponent of y
long _y = BitConverter.DoubleToInt64Bits(y);
/* add k to y's exponent */
if (BitConverter.IsLittleEndian)
_y += ((long)k << 52);
else
_y += ((long)k << 20);
y = BitConverter.Int64BitsToDouble(_y);
return y;
}
else
{
//The idea is to add hy to the exponent of y
long _y = BitConverter.DoubleToInt64Bits(y);
if (BitConverter.IsLittleEndian)
_y += ((long)k + 1000 << 52);
else
_y += ((long)k + 1000 << 20);
y = BitConverter.Int64BitsToDouble(_y);
return y * twom1000;
}
}
#endregion Exp
#region Floor
public static double Floor(double x)
{
if (double.IsInfinity(x) || double.IsNaN(x)) return x;
int i0, i1, j0;
uint i, j;
i0 = HighWord(x);
i1 = LowWord(x);
j0 = ((i0 >> 20) & 0x7ff) - 0x3ff;
if (j0 < 20)
{
if (j0 < 0)
{ /* raise inexact if x != 0 */
if (1.0e+300 + x > 0.0)
{/* return 0*sign(x) if |x|<1 */
if (i0 >= 0)
{
i0 = i1 = 0;
}
else if (((i0 & 0x7fffffff) | i1) != 0)
{
i0 = Int32.MaxValue;
i1 = 0;
}
}
}
else
{
i = (uint)0x000fffff >> j0;
if ((((uint)i0 & i) | (uint)i1) == 0)
return x; /* x is integral */
if (1.0e+300 + x > 0.0)
{ /* raise inexact flag */
if (i0 < 0)
i0 += (0x00100000) >> j0;
i0 &= (int)~i;
i1 = 0;
}
}
}
else if (j0 > 51)
{
if (j0 == 0x400) return x + x; /* inf or NaN */
else return x; /* x is integral */
}
else
{
i = ((uint)(0xffffffff)) >> (j0 - 20);
if ((i1 & i) == 0) return x; /* x is integral */
if (1.0e+300 + x > 0.0)
{ /* raise inexact flag */
if (i0 < 0)
{
if (j0 == 20) i0 += 1;
else
{
j = (uint)i1 + (uint)(1 << (52 - j0));
if (j < i1) i0 += 1; /* got a carry */
i1 = (int)j;
}
}
i1 &= (int)~i;
}
}
Byte[] returnBytes = BitConverter.GetBytes(0d);
Byte[] highWord = BitConverter.GetBytes(i0);
Byte[] lowWord = BitConverter.GetBytes(i1);
for (int c = 0; c < 4; c++)
{
returnBytes[c + (BitConverter.IsLittleEndian ? 4 : 0)] = highWord[c];
}
for (int c = 0; c < 4; c++)
{
returnBytes[c + (BitConverter.IsLittleEndian ? 0 : 4)] = lowWord[c];
}
return BitConverter.ToDouble(returnBytes, 0);
}
#endregion Floor
#region Log (base e)
public static double Log(double x)
{
double ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
double hfsq, f, s, z, R, w, t1, t2, dk;
int k, hx, i, j;
uint lx;
hx = HighWord(x); /* high word of x */
lx = (uint)LowWord(x); /* low word of x */
k = 0;
if (hx < 0x00100000)
{ /* x < 2**-1022 */
if (x < 0 || double.IsNaN(x))
return double.NaN; /* log(-#) = NaN */
if (((hx & (uint)0x7fff) | lx) == 0)
return double.NegativeInfinity; /* log(+-0)=-inf */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = HighWord(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x + x;
k += (hx >> 20) - 1023;
hx &= 0x000fffff;
i = (hx + 0x95f64) & 0x100000;
//__HI(x) = hx | (i ^ 0x3ff00000); /* normalize x or x/2 */
Byte[] bx = BitConverter.GetBytes(BitConverter.DoubleToInt64Bits(x));
Byte[] bv = BitConverter.GetBytes(hx | (i ^ 0x3ff00000));
for (int _i = 0; _i < 4; _i++)
{
bx[_i + (BitConverter.IsLittleEndian ? 4 : 0)] = bv[_i];
}
x = BitConverter.ToDouble(bx, 0);
k += (i >> 20);
f = x - 1.0;
if ((0x000fffff & (2 + hx)) < 3)
{ /* |f| < 2**-20 */
if (f == 0)
if (k == 0)
return 0;
else
{
dk = k;
return dk * ln2_hi + dk * ln2_lo;
}
R = f * f * (0.5 - 0.33333333333333333 * f);
if (k == 0)
return f - R;
else
{
dk = k;
return dk * ln2_hi - ((R - dk * ln2_lo) - f);
}
}
s = f / (2.0 + f);
dk = k;
z = s * s;
i = hx - 0x6147a;
w = z * z;
j = 0x6b851 - hx;
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
i |= j;
R = t2 + t1;
if (i > 0)
{
hfsq = 0.5 * f * f;
if (k == 0)
return f - (hfsq - s * (hfsq + R));
else
return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f);
}
else
{
if (k == 0)
return f - s * (f - R);
else
return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
}
}
#endregion Log (base e)
#region Log (base specified)
public static double Log(double Exponent, double Base)
{
if (double.IsNaN(Exponent) || Exponent < 0)
return double.NaN;
if (Exponent == 0)
return double.NegativeInfinity;
return Log(Exponent) / Log(Base);
}
#endregion Log (base specified)
#region Log10
public static double Log10(double x)
{
//Use change of base formula
return Log(x, 10F);
}
#endregion Log10
#region Pow
public static double Pow(double b, double e)
{
if (e == 0) return 1;
if (e == 1) return b;
if (double.IsNaN(b) || double.IsNaN(e)) return double.NaN;
if (double.IsNegativeInfinity(b))
{
if (e < 0)
return 0;
if ((long)e % 2 == 0)
return double.PositiveInfinity;
else
return double.NegativeInfinity;
}
if (double.IsPositiveInfinity(b))
{
if (e < 0)
return 0;
else
return double.PositiveInfinity;
}
if (double.IsInfinity(e))
{
bool t = -1 < b;
bool t1 = 1 > b;
if (t && t1)
if (double.IsPositiveInfinity(e))
return 0;
else
return double.PositiveInfinity;
else
{
bool v = b < -1;
bool v1 = 1 < b;
if (v || v1)
{
if (double.IsPositiveInfinity(e))
return double.PositiveInfinity;
else
return 0;
}
else
return double.NaN;
}
}
if (b < 0)
{
if (Abs(e) - Abs((int)e) > (Double.Epsilon * 100)) return double.NaN;
double logedBase = Log(Abs(b));
double pow = Exp(logedBase * e);
if ((long)e % 2 == 0) return pow;
else return -1 * pow;
}
else
{
if (e < 0)
{
e = Abs(e);
double logedBase = Log(b);
return 1 / Exp(logedBase * e);
}
else
{
double logedBase = Log(b);
return Exp(logedBase * e);
}
}
}
#endregion Pow
#region Round
public static double Round(double d)
{
return ((Floor(d) % 2 == 0) ? Floor(d) : Ceiling(d));
}
#endregion Round
#region Sin
public static double Sin(double x)
{
double[] y = new double[2];
double z = 0.0;
int n, ix;
/* High word of x. */
ix = HighWord(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb)
return _sin(x, z, 0);
/* sin(Inf or NaN) is NaN */
else if (ix >= 0x7ff00000)
return x - x;
/* argument reduction needed */
else
{
n = __ieee754_rem_pio2(x, y);
switch (n & 3)
{
case 0:
return _sin(y[0], y[1], 1);
case 1:
return _cos(y[0], y[1]);
case 2:
return -_sin(y[0], y[1], 1);
default:
return -_cos(y[0], y[1]);
}
}
}
private static double _sin(double x, double y, int iy)
{
const double half = 5.00000000000000000000e-01; /* 0x3FE00000; 0x00000000 */
const double S1 = -1.66666666666666324348e-01; /* 0xBFC55555; 0x55555549 */
const double S2 = 8.33333333332248946124e-03; /* 0x3F811111; 0x1110F8A6 */
const double S3 = -1.98412698298579493134e-04; /* 0xBF2A01A0; 0x19C161D5 */
const double S4 = 2.75573137070700676789e-06; /* 0x3EC71DE3; 0x57B1FE7D */
const double S5 = -2.50507602534068634195e-08; /* 0xBE5AE5E6; 0x8A2B9CEB */
const double S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A; 0x5ACFD57C */
double z, r, v;
int ix;
ix = HighWord(x) & 0x7fffffff; /* high word of x */
if (ix < 0x3e400000) /* |x| < 2**-27 */
{ if ((int)x == 0) return x; } /* generate inexact */
z = x * x;
v = z * x;
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
if (iy == 0)
return x + v * (S1 + z * r);
else
return x - ((z * (half * y - v * r) - y) - v * S1);
}