Ruby 2.7.0p0(2019-12-25revision647ee6f091eafcce70ffb75ddf7e121e192ab217)

math.c
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1 /**********************************************************************
2
3 math.c -
4
5 $Author$
6 created at: Tue Jan 25 14:12:56 JST 1994
7
8 Copyright (C) 1993-2007 Yukihiro Matsumoto
9
10 **********************************************************************/
11
12 #ifdef _MSC_VER
13 # define _USE_MATH_DEFINES 1
14 #endif
15 #include "internal.h"
16 #include <float.h>
17 #include <math.h>
18 #include <errno.h>
19
20 #if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
21 !defined(signbit)
22 extern int signbit(double);
23 #endif
24
25 #define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM)
26
27 VALUE rb_mMath;
28 VALUE rb_eMathDomainError;
29
30 #define Get_Double(x) rb_num_to_dbl(x)
31
32 #define domain_error(msg) \
33 rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)
34
35 /*
36 * call-seq:
37 * Math.atan2(y, x) -> Float
38 *
39 * Computes the arc tangent given +y+ and +x+.
40 * Returns a Float in the range -PI..PI. Return value is a angle
41 * in radians between the positive x-axis of cartesian plane
42 * and the point given by the coordinates (+x+, +y+) on it.
43 *
44 * Domain: (-INFINITY, INFINITY)
45 *
46 * Codomain: [-PI, PI]
47 *
48 * Math.atan2(-0.0, -1.0) #=> -3.141592653589793
49 * Math.atan2(-1.0, -1.0) #=> -2.356194490192345
50 * Math.atan2(-1.0, 0.0) #=> -1.5707963267948966
51 * Math.atan2(-1.0, 1.0) #=> -0.7853981633974483
52 * Math.atan2(-0.0, 1.0) #=> -0.0
53 * Math.atan2(0.0, 1.0) #=> 0.0
54 * Math.atan2(1.0, 1.0) #=> 0.7853981633974483
55 * Math.atan2(1.0, 0.0) #=> 1.5707963267948966
56 * Math.atan2(1.0, -1.0) #=> 2.356194490192345
57 * Math.atan2(0.0, -1.0) #=> 3.141592653589793
58 * Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483
59 * Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345
60 * Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483
61 * Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345
62 *
63 */
64
65 static VALUE
66 math_atan2(VALUE unused_obj, VALUE y, VALUE x)
67 {
68 double dx, dy;
69 dx = Get_Double(x);
70 dy = Get_Double(y);
71 if (dx == 0.0 && dy == 0.0) {
72 if (!signbit(dx))
73 return DBL2NUM(dy);
74 if (!signbit(dy))
75 return DBL2NUM(M_PI);
76 return DBL2NUM(-M_PI);
77 }
78 #ifndef ATAN2_INF_C99
79 if (isinf(dx) && isinf(dy)) {
80 /* optimization for FLONUM */
81 if (dx < 0.0) {
82 const double dz = (3.0 * M_PI / 4.0);
83 return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
84 }
85 else {
86 const double dz = (M_PI / 4.0);
87 return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
88 }
89 }
90 #endif
91 return DBL2NUM(atan2(dy, dx));
92 }
93
94
95 /*
96 * call-seq:
97 * Math.cos(x) -> Float
98 *
99 * Computes the cosine of +x+ (expressed in radians).
100 * Returns a Float in the range -1.0..1.0.
101 *
102 * Domain: (-INFINITY, INFINITY)
103 *
104 * Codomain: [-1, 1]
105 *
106 * Math.cos(Math::PI) #=> -1.0
107 *
108 */
109
110 static VALUE
111 math_cos(VALUE unused_obj, VALUE x)
112 {
113 return DBL2NUM(cos(Get_Double(x)));
114 }
115
116 /*
117 * call-seq:
118 * Math.sin(x) -> Float
119 *
120 * Computes the sine of +x+ (expressed in radians).
121 * Returns a Float in the range -1.0..1.0.
122 *
123 * Domain: (-INFINITY, INFINITY)
124 *
125 * Codomain: [-1, 1]
126 *
127 * Math.sin(Math::PI/2) #=> 1.0
128 *
129 */
130
131 static VALUE
132 math_sin(VALUE unused_obj, VALUE x)
133 {
134 return DBL2NUM(sin(Get_Double(x)));
135 }
136
137
138 /*
139 * call-seq:
140 * Math.tan(x) -> Float
141 *
142 * Computes the tangent of +x+ (expressed in radians).
143 *
144 * Domain: (-INFINITY, INFINITY)
145 *
146 * Codomain: (-INFINITY, INFINITY)
147 *
148 * Math.tan(0) #=> 0.0
149 *
150 */
151
152 static VALUE
153 math_tan(VALUE unused_obj, VALUE x)
154 {
155 return DBL2NUM(tan(Get_Double(x)));
156 }
157
158 /*
159 * call-seq:
160 * Math.acos(x) -> Float
161 *
162 * Computes the arc cosine of +x+. Returns 0..PI.
163 *
164 * Domain: [-1, 1]
165 *
166 * Codomain: [0, PI]
167 *
168 * Math.acos(0) == Math::PI/2 #=> true
169 *
170 */
171
172 static VALUE
173 math_acos(VALUE unused_obj, VALUE x)
174 {
175 double d;
176
177 d = Get_Double(x);
178 /* check for domain error */
179 if (d < -1.0 || 1.0 < d) domain_error("acos");
180 return DBL2NUM(acos(d));
181 }
182
183 /*
184 * call-seq:
185 * Math.asin(x) -> Float
186 *
187 * Computes the arc sine of +x+. Returns -PI/2..PI/2.
188 *
189 * Domain: [-1, -1]
190 *
191 * Codomain: [-PI/2, PI/2]
192 *
193 * Math.asin(1) == Math::PI/2 #=> true
194 */
195
196 static VALUE
197 math_asin(VALUE unused_obj, VALUE x)
198 {
199 double d;
200
201 d = Get_Double(x);
202 /* check for domain error */
203 if (d < -1.0 || 1.0 < d) domain_error("asin");
204 return DBL2NUM(asin(d));
205 }
206
207 /*
208 * call-seq:
209 * Math.atan(x) -> Float
210 *
211 * Computes the arc tangent of +x+. Returns -PI/2..PI/2.
212 *
213 * Domain: (-INFINITY, INFINITY)
214 *
215 * Codomain: (-PI/2, PI/2)
216 *
217 * Math.atan(0) #=> 0.0
218 */
219
220 static VALUE
221 math_atan(VALUE unused_obj, VALUE x)
222 {
223 return DBL2NUM(atan(Get_Double(x)));
224 }
225
226 #ifndef HAVE_COSH
227 double
228 cosh(double x)
229 {
230 return (exp(x) + exp(-x)) / 2;
231 }
232 #endif
233
234 /*
235 * call-seq:
236 * Math.cosh(x) -> Float
237 *
238 * Computes the hyperbolic cosine of +x+ (expressed in radians).
239 *
240 * Domain: (-INFINITY, INFINITY)
241 *
242 * Codomain: [1, INFINITY)
243 *
244 * Math.cosh(0) #=> 1.0
245 *
246 */
247
248 static VALUE
249 math_cosh(VALUE unused_obj, VALUE x)
250 {
251 return DBL2NUM(cosh(Get_Double(x)));
252 }
253
254 #ifndef HAVE_SINH
255 double
256 sinh(double x)
257 {
258 return (exp(x) - exp(-x)) / 2;
259 }
260 #endif
261
262 /*
263 * call-seq:
264 * Math.sinh(x) -> Float
265 *
266 * Computes the hyperbolic sine of +x+ (expressed in radians).
267 *
268 * Domain: (-INFINITY, INFINITY)
269 *
270 * Codomain: (-INFINITY, INFINITY)
271 *
272 * Math.sinh(0) #=> 0.0
273 *
274 */
275
276 static VALUE
277 math_sinh(VALUE unused_obj, VALUE x)
278 {
279 return DBL2NUM(sinh(Get_Double(x)));
280 }
281
282 #ifndef HAVE_TANH
283 double
284 tanh(double x)
285 {
286 # if defined(HAVE_SINH) && defined(HAVE_COSH)
287 const double c = cosh(x);
288 if (!isinf(c)) return sinh(x) / c;
289 # else
290 const double e = exp(x+x);
291 if (!isinf(e)) return (e - 1) / (e + 1);
292 # endif
293 return x > 0 ? 1.0 : -1.0;
294 }
295 #endif
296
297 /*
298 * call-seq:
299 * Math.tanh(x) -> Float
300 *
301 * Computes the hyperbolic tangent of +x+ (expressed in radians).
302 *
303 * Domain: (-INFINITY, INFINITY)
304 *
305 * Codomain: (-1, 1)
306 *
307 * Math.tanh(0) #=> 0.0
308 *
309 */
310
311 static VALUE
312 math_tanh(VALUE unused_obj, VALUE x)
313 {
314 return DBL2NUM(tanh(Get_Double(x)));
315 }
316
317 /*
318 * call-seq:
319 * Math.acosh(x) -> Float
320 *
321 * Computes the inverse hyperbolic cosine of +x+.
322 *
323 * Domain: [1, INFINITY)
324 *
325 * Codomain: [0, INFINITY)
326 *
327 * Math.acosh(1) #=> 0.0
328 *
329 */
330
331 static VALUE
332 math_acosh(VALUE unused_obj, VALUE x)
333 {
334 double d;
335
336 d = Get_Double(x);
337 /* check for domain error */
338 if (d < 1.0) domain_error("acosh");
339 return DBL2NUM(acosh(d));
340 }
341
342 /*
343 * call-seq:
344 * Math.asinh(x) -> Float
345 *
346 * Computes the inverse hyperbolic sine of +x+.
347 *
348 * Domain: (-INFINITY, INFINITY)
349 *
350 * Codomain: (-INFINITY, INFINITY)
351 *
352 * Math.asinh(1) #=> 0.881373587019543
353 *
354 */
355
356 static VALUE
357 math_asinh(VALUE unused_obj, VALUE x)
358 {
359 return DBL2NUM(asinh(Get_Double(x)));
360 }
361
362 /*
363 * call-seq:
364 * Math.atanh(x) -> Float
365 *
366 * Computes the inverse hyperbolic tangent of +x+.
367 *
368 * Domain: (-1, 1)
369 *
370 * Codomain: (-INFINITY, INFINITY)
371 *
372 * Math.atanh(1) #=> Infinity
373 *
374 */
375
376 static VALUE
377 math_atanh(VALUE unused_obj, VALUE x)
378 {
379 double d;
380
381 d = Get_Double(x);
382 /* check for domain error */
383 if (d < -1.0 || +1.0 < d) domain_error("atanh");
384 /* check for pole error */
385 if (d == -1.0) return DBL2NUM(-HUGE_VAL);
386 if (d == +1.0) return DBL2NUM(+HUGE_VAL);
387 return DBL2NUM(atanh(d));
388 }
389
390 /*
391 * call-seq:
392 * Math.exp(x) -> Float
393 *
394 * Returns e**x.
395 *
396 * Domain: (-INFINITY, INFINITY)
397 *
398 * Codomain: (0, INFINITY)
399 *
400 * Math.exp(0) #=> 1.0
401 * Math.exp(1) #=> 2.718281828459045
402 * Math.exp(1.5) #=> 4.4816890703380645
403 *
404 */
405
406 static VALUE
407 math_exp(VALUE unused_obj, VALUE x)
408 {
409 return DBL2NUM(exp(Get_Double(x)));
410 }
411
412 #if defined __CYGWIN__
413 # include <cygwin/version.h>
414 # if CYGWIN_VERSION_DLL_MAJOR < 1005
415 # define nan(x) nan()
416 # endif
417 # define log(x) ((x) < 0.0 ? nan("") : log(x))
418 # define log10(x) ((x) < 0.0 ? nan("") : log10(x))
419 #endif
420
421 #ifndef M_LN2
422 # define M_LN2 0.693147180559945309417232121458176568
423 #endif
424 #ifndef M_LN10
425 # define M_LN10 2.30258509299404568401799145468436421
426 #endif
427
428 static double math_log1(VALUE x);
429 FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE));
430
431 /*
432 * call-seq:
433 * Math.log(x) -> Float
434 * Math.log(x, base) -> Float
435 *
436 * Returns the logarithm of +x+.
437 * If additional second argument is given, it will be the base
438 * of logarithm. Otherwise it is +e+ (for the natural logarithm).
439 *
440 * Domain: (0, INFINITY)
441 *
442 * Codomain: (-INFINITY, INFINITY)
443 *
444 * Math.log(0) #=> -Infinity
445 * Math.log(1) #=> 0.0
446 * Math.log(Math::E) #=> 1.0
447 * Math.log(Math::E**3) #=> 3.0
448 * Math.log(12, 3) #=> 2.2618595071429146
449 *
450 */
451
452 static VALUE
453 math_log(int argc, const VALUE *argv, VALUE unused_obj)
454 {
455 return rb_math_log(argc, argv);
456 }
457
458 VALUE
459 rb_math_log(int argc, const VALUE *argv)
460 {
461 VALUE x, base;
462 double d;
463
464 rb_scan_args(argc, argv, "11", &x, &base);
465 d = math_log1(x);
466 if (argc == 2) {
467 d /= math_log1(base);
468 }
469 return DBL2NUM(d);
470 }
471
472 static double
473 get_double_rshift(VALUE x, size_t *pnumbits)
474 {
475 size_t numbits;
476
477 if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) &&
478 DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) {
479 numbits -= DBL_MANT_DIG;
480 x = rb_big_rshift(x, SIZET2NUM(numbits));
481 }
482 else {
483 numbits = 0;
484 }
485 *pnumbits = numbits;
486 return Get_Double(x);
487 }
488
489 static double
490 math_log1(VALUE x)
491 {
492 size_t numbits;
493 double d = get_double_rshift(x, &numbits);
494
495 /* check for domain error */
496 if (d < 0.0) domain_error("log");
497 /* check for pole error */
498 if (d == 0.0) return -HUGE_VAL;
499
500 return log(d) + numbits * M_LN2; /* log(d * 2 ** numbits) */
501 }
502
503 #ifndef log2
504 #ifndef HAVE_LOG2
505 double
506 log2(double x)
507 {
508 return log10(x)/log10(2.0);
509 }
510 #else
511 extern double log2(double);
512 #endif
513 #endif
514
515 /*
516 * call-seq:
517 * Math.log2(x) -> Float
518 *
519 * Returns the base 2 logarithm of +x+.
520 *
521 * Domain: (0, INFINITY)
522 *
523 * Codomain: (-INFINITY, INFINITY)
524 *
525 * Math.log2(1) #=> 0.0
526 * Math.log2(2) #=> 1.0
527 * Math.log2(32768) #=> 15.0
528 * Math.log2(65536) #=> 16.0
529 *
530 */
531
532 static VALUE
533 math_log2(VALUE unused_obj, VALUE x)
534 {
535 size_t numbits;
536 double d = get_double_rshift(x, &numbits);
537
538 /* check for domain error */
539 if (d < 0.0) domain_error("log2");
540 /* check for pole error */
541 if (d == 0.0) return DBL2NUM(-HUGE_VAL);
542
543 return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */
544 }
545
546 /*
547 * call-seq:
548 * Math.log10(x) -> Float
549 *
550 * Returns the base 10 logarithm of +x+.
551 *
552 * Domain: (0, INFINITY)
553 *
554 * Codomain: (-INFINITY, INFINITY)
555 *
556 * Math.log10(1) #=> 0.0
557 * Math.log10(10) #=> 1.0
558 * Math.log10(10**100) #=> 100.0
559 *
560 */
561
562 static VALUE
563 math_log10(VALUE unused_obj, VALUE x)
564 {
565 size_t numbits;
566 double d = get_double_rshift(x, &numbits);
567
568 /* check for domain error */
569 if (d < 0.0) domain_error("log10");
570 /* check for pole error */
571 if (d == 0.0) return DBL2NUM(-HUGE_VAL);
572
573 return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */
574 }
575
576 static VALUE rb_math_sqrt(VALUE x);
577
578 /*
579 * call-seq:
580 * Math.sqrt(x) -> Float
581 *
582 * Returns the non-negative square root of +x+.
583 *
584 * Domain: [0, INFINITY)
585 *
586 * Codomain:[0, INFINITY)
587 *
588 * 0.upto(10) {|x|
589 * p [x, Math.sqrt(x), Math.sqrt(x)**2]
590 * }
591 * #=> [0, 0.0, 0.0]
592 * # [1, 1.0, 1.0]
593 * # [2, 1.4142135623731, 2.0]
594 * # [3, 1.73205080756888, 3.0]
595 * # [4, 2.0, 4.0]
596 * # [5, 2.23606797749979, 5.0]
597 * # [6, 2.44948974278318, 6.0]
598 * # [7, 2.64575131106459, 7.0]
599 * # [8, 2.82842712474619, 8.0]
600 * # [9, 3.0, 9.0]
601 * # [10, 3.16227766016838, 10.0]
602 *
603 * Note that the limited precision of floating point arithmetic
604 * might lead to surprising results:
605 *
606 * Math.sqrt(10**46).to_i #=> 99999999999999991611392 (!)
607 *
608 * See also BigDecimal#sqrt and Integer.sqrt.
609 */
610
611 static VALUE
612 math_sqrt(VALUE unused_obj, VALUE x)
613 {
614 return rb_math_sqrt(x);
615 }
616
617 #define f_boolcast(x) ((x) ? Qtrue : Qfalse)
618 inline static VALUE
619 f_negative_p(VALUE x)
620 {
621 if (FIXNUM_P(x))
622 return f_boolcast(FIX2LONG(x) < 0);
623 return rb_funcall(x, '<', 1, INT2FIX(0));
624 }
625 inline static VALUE
626 f_signbit(VALUE x)
627 {
628 if (RB_TYPE_P(x, T_FLOAT)) {
629 double f = RFLOAT_VALUE(x);
630 return f_boolcast(!isnan(f) && signbit(f));
631 }
632 return f_negative_p(x);
633 }
634
635 static VALUE
636 rb_math_sqrt(VALUE x)
637 {
638 double d;
639
640 if (RB_TYPE_P(x, T_COMPLEX)) {
641 VALUE neg = f_signbit(RCOMPLEX(x)->imag);
642 double re = Get_Double(RCOMPLEX(x)->real), im;
643 d = Get_Double(rb_complex_abs(x));
644 im = sqrt((d - re) / 2.0);
645 re = sqrt((d + re) / 2.0);
646 if (neg) im = -im;
647 return rb_complex_new(DBL2NUM(re), DBL2NUM(im));
648 }
649 d = Get_Double(x);
650 /* check for domain error */
651 if (d < 0.0) domain_error("sqrt");
652 if (d == 0.0) return DBL2NUM(0.0);
653 return DBL2NUM(sqrt(d));
654 }
655
656 /*
657 * call-seq:
658 * Math.cbrt(x) -> Float
659 *
660 * Returns the cube root of +x+.
661 *
662 * Domain: (-INFINITY, INFINITY)
663 *
664 * Codomain: (-INFINITY, INFINITY)
665 *
666 * -9.upto(9) {|x|
667 * p [x, Math.cbrt(x), Math.cbrt(x)**3]
668 * }
669 * #=> [-9, -2.0800838230519, -9.0]
670 * # [-8, -2.0, -8.0]
671 * # [-7, -1.91293118277239, -7.0]
672 * # [-6, -1.81712059283214, -6.0]
673 * # [-5, -1.7099759466767, -5.0]
674 * # [-4, -1.5874010519682, -4.0]
675 * # [-3, -1.44224957030741, -3.0]
676 * # [-2, -1.25992104989487, -2.0]
677 * # [-1, -1.0, -1.0]
678 * # [0, 0.0, 0.0]
679 * # [1, 1.0, 1.0]
680 * # [2, 1.25992104989487, 2.0]
681 * # [3, 1.44224957030741, 3.0]
682 * # [4, 1.5874010519682, 4.0]
683 * # [5, 1.7099759466767, 5.0]
684 * # [6, 1.81712059283214, 6.0]
685 * # [7, 1.91293118277239, 7.0]
686 * # [8, 2.0, 8.0]
687 * # [9, 2.0800838230519, 9.0]
688 *
689 */
690
691 static VALUE
692 math_cbrt(VALUE unused_obj, VALUE x)
693 {
694 double f = Get_Double(x);
695 double r = cbrt(f);
696 #if defined __GLIBC__
697 if (isfinite(r)) {
698 r = (2.0 * r + (f / r / r)) / 3.0;
699 }
700 #endif
701 return DBL2NUM(r);
702 }
703
704 /*
705 * call-seq:
706 * Math.frexp(x) -> [fraction, exponent]
707 *
708 * Returns a two-element array containing the normalized fraction (a Float)
709 * and exponent (an Integer) of +x+.
710 *
711 * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
712 * fraction * 2**exponent #=> 1234.0
713 */
714
715 static VALUE
716 math_frexp(VALUE unused_obj, VALUE x)
717 {
718 double d;
719 int exp;
720
721 d = frexp(Get_Double(x), &exp);
722 return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
723 }
724
725 /*
726 * call-seq:
727 * Math.ldexp(fraction, exponent) -> float
728 *
729 * Returns the value of +fraction+*(2**+exponent+).
730 *
731 * fraction, exponent = Math.frexp(1234)
732 * Math.ldexp(fraction, exponent) #=> 1234.0
733 */
734
735 static VALUE
736 math_ldexp(VALUE unused_obj, VALUE x, VALUE n)
737 {
738 return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n)));
739 }
740
741 /*
742 * call-seq:
743 * Math.hypot(x, y) -> Float
744 *
745 * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with
746 * sides +x+ and +y+.
747 *
748 * Math.hypot(3, 4) #=> 5.0
749 */
750
751 static VALUE
752 math_hypot(VALUE unused_obj, VALUE x, VALUE y)
753 {
754 return DBL2NUM(hypot(Get_Double(x), Get_Double(y)));
755 }
756
757 /*
758 * call-seq:
759 * Math.erf(x) -> Float
760 *
761 * Calculates the error function of +x+.
762 *
763 * Domain: (-INFINITY, INFINITY)
764 *
765 * Codomain: (-1, 1)
766 *
767 * Math.erf(0) #=> 0.0
768 *
769 */
770
771 static VALUE
772 math_erf(VALUE unused_obj, VALUE x)
773 {
774 return DBL2NUM(erf(Get_Double(x)));
775 }
776
777 /*
778 * call-seq:
779 * Math.erfc(x) -> Float
780 *
781 * Calculates the complementary error function of x.
782 *
783 * Domain: (-INFINITY, INFINITY)
784 *
785 * Codomain: (0, 2)
786 *
787 * Math.erfc(0) #=> 1.0
788 *
789 */
790
791 static VALUE
792 math_erfc(VALUE unused_obj, VALUE x)
793 {
794 return DBL2NUM(erfc(Get_Double(x)));
795 }
796
797 /*
798 * call-seq:
799 * Math.gamma(x) -> Float
800 *
801 * Calculates the gamma function of x.
802 *
803 * Note that gamma(n) is same as fact(n-1) for integer n > 0.
804 * However gamma(n) returns float and can be an approximation.
805 *
806 * def fact(n) (1..n).inject(1) {|r,i| r*i } end
807 * 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }
808 * #=> [1, 1.0, 1]
809 * # [2, 1.0, 1]
810 * # [3, 2.0, 2]
811 * # [4, 6.0, 6]
812 * # [5, 24.0, 24]
813 * # [6, 120.0, 120]
814 * # [7, 720.0, 720]
815 * # [8, 5040.0, 5040]
816 * # [9, 40320.0, 40320]
817 * # [10, 362880.0, 362880]
818 * # [11, 3628800.0, 3628800]
819 * # [12, 39916800.0, 39916800]
820 * # [13, 479001600.0, 479001600]
821 * # [14, 6227020800.0, 6227020800]
822 * # [15, 87178291200.0, 87178291200]
823 * # [16, 1307674368000.0, 1307674368000]
824 * # [17, 20922789888000.0, 20922789888000]
825 * # [18, 355687428096000.0, 355687428096000]
826 * # [19, 6.402373705728e+15, 6402373705728000]
827 * # [20, 1.21645100408832e+17, 121645100408832000]
828 * # [21, 2.43290200817664e+18, 2432902008176640000]
829 * # [22, 5.109094217170944e+19, 51090942171709440000]
830 * # [23, 1.1240007277776077e+21, 1124000727777607680000]
831 * # [24, 2.5852016738885062e+22, 25852016738884976640000]
832 * # [25, 6.204484017332391e+23, 620448401733239439360000]
833 * # [26, 1.5511210043330954e+25, 15511210043330985984000000]
834 *
835 */
836
837 static VALUE
838 math_gamma(VALUE unused_obj, VALUE x)
839 {
840 static const double fact_table[] = {
841 /* fact(0) */ 1.0,
842 /* fact(1) */ 1.0,
843 /* fact(2) */ 2.0,
844 /* fact(3) */ 6.0,
845 /* fact(4) */ 24.0,
846 /* fact(5) */ 120.0,
847 /* fact(6) */ 720.0,
848 /* fact(7) */ 5040.0,
849 /* fact(8) */ 40320.0,
850 /* fact(9) */ 362880.0,
851 /* fact(10) */ 3628800.0,
852 /* fact(11) */ 39916800.0,
853 /* fact(12) */ 479001600.0,
854 /* fact(13) */ 6227020800.0,
855 /* fact(14) */ 87178291200.0,
856 /* fact(15) */ 1307674368000.0,
857 /* fact(16) */ 20922789888000.0,
858 /* fact(17) */ 355687428096000.0,
859 /* fact(18) */ 6402373705728000.0,
860 /* fact(19) */ 121645100408832000.0,
861 /* fact(20) */ 2432902008176640000.0,
862 /* fact(21) */ 51090942171709440000.0,
863 /* fact(22) */ 1124000727777607680000.0,
864 /* fact(23)=25852016738884976640000 needs 56bit mantissa which is
865 * impossible to represent exactly in IEEE 754 double which have
866 * 53bit mantissa. */
867 };
868 enum {NFACT_TABLE = numberof(fact_table)};
869 double d;
870 d = Get_Double(x);
871 /* check for domain error */
872 if (isinf(d)) {
873 if (signbit(d)) domain_error("gamma");
874 return DBL2NUM(HUGE_VAL);
875 }
876 if (d == 0.0) {
877 return signbit(d) ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
878 }
879 if (d == floor(d)) {
880 if (d < 0.0) domain_error("gamma");
881 if (1.0 <= d && d <= (double)NFACT_TABLE) {
882 return DBL2NUM(fact_table[(int)d - 1]);
883 }
884 }
885 return DBL2NUM(tgamma(d));
886 }
887
888 /*
889 * call-seq:
890 * Math.lgamma(x) -> [float, -1 or 1]
891 *
892 * Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+.
893 *
894 * Math.lgamma(x) is same as
895 * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
896 * but avoid overflow by Math.gamma(x) for large x.
897 *
898 * Math.lgamma(0) #=> [Infinity, 1]
899 *
900 */
901
902 static VALUE
903 math_lgamma(VALUE unused_obj, VALUE x)
904 {
905 double d;
906 int sign=1;
907 VALUE v;
908 d = Get_Double(x);
909 /* check for domain error */
910 if (isinf(d)) {
911 if (signbit(d)) domain_error("lgamma");
912 return rb_assoc_new(DBL2NUM(HUGE_VAL), INT2FIX(1));
913 }
914 if (d == 0.0) {
915 VALUE vsign = signbit(d) ? INT2FIX(-1) : INT2FIX(+1);
916 return rb_assoc_new(DBL2NUM(HUGE_VAL), vsign);
917 }
918 v = DBL2NUM(lgamma_r(d, &sign));
919 return rb_assoc_new(v, INT2FIX(sign));
920 }
921
922
923 #define exp1(n) \
924 VALUE \
925 rb_math_##n(VALUE x)\
926 {\
927 return math_##n(0, x);\
928 }
929
930 #define exp2(n) \
931 VALUE \
932 rb_math_##n(VALUE x, VALUE y)\
933 {\
934 return math_##n(0, x, y);\
935 }
936
937 exp2(atan2)
938 exp1(cos)
939 exp1(cosh)
940 exp1(exp)
941 exp2(hypot)
942 exp1(sin)
943 exp1(sinh)
944 #if 0
945 exp1(sqrt)
946 #endif
947
948
949 /*
950 * Document-class: Math::DomainError
951 *
952 * Raised when a mathematical function is evaluated outside of its
953 * domain of definition.
954 *
955 * For example, since +cos+ returns values in the range -1..1,
956 * its inverse function +acos+ is only defined on that interval:
957 *
958 * Math.acos(42)
959 *
960 * <em>produces:</em>
961 *
962 * Math::DomainError: Numerical argument is out of domain - "acos"
963 */
964
965 /*
966 * Document-class: Math
967 *
968 * The Math module contains module functions for basic
969 * trigonometric and transcendental functions. See class
970 * Float for a list of constants that
971 * define Ruby's floating point accuracy.
972 *
973 * Domains and codomains are given only for real (not complex) numbers.
974 */
975
976
977 void
978 InitVM_Math(void)
979 {
980 rb_mMath = rb_define_module("Math");
981 rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError);
982
983 /* Definition of the mathematical constant PI as a Float number. */
984 rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI));
985
986 #ifdef M_E
987 /* Definition of the mathematical constant E for Euler's number (e) as a Float number. */
988 rb_define_const(rb_mMath, "E", DBL2NUM(M_E));
989 #else
990 rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0)));
991 #endif
992
993 rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);
994 rb_define_module_function(rb_mMath, "cos", math_cos, 1);
995 rb_define_module_function(rb_mMath, "sin", math_sin, 1);
996 rb_define_module_function(rb_mMath, "tan", math_tan, 1);
997
998 rb_define_module_function(rb_mMath, "acos", math_acos, 1);
999 rb_define_module_function(rb_mMath, "asin", math_asin, 1);
1000 rb_define_module_function(rb_mMath, "atan", math_atan, 1);
1001
1002 rb_define_module_function(rb_mMath, "cosh", math_cosh, 1);
1003 rb_define_module_function(rb_mMath, "sinh", math_sinh, 1);
1004 rb_define_module_function(rb_mMath, "tanh", math_tanh, 1);
1005
1006 rb_define_module_function(rb_mMath, "acosh", math_acosh, 1);
1007 rb_define_module_function(rb_mMath, "asinh", math_asinh, 1);
1008 rb_define_module_function(rb_mMath, "atanh", math_atanh, 1);
1009
1010 rb_define_module_function(rb_mMath, "exp", math_exp, 1);
1011 rb_define_module_function(rb_mMath, "log", math_log, -1);
1012 rb_define_module_function(rb_mMath, "log2", math_log2, 1);
1013 rb_define_module_function(rb_mMath, "log10", math_log10, 1);
1014 rb_define_module_function(rb_mMath, "sqrt", math_sqrt, 1);
1015 rb_define_module_function(rb_mMath, "cbrt", math_cbrt, 1);
1016
1017 rb_define_module_function(rb_mMath, "frexp", math_frexp, 1);
1018 rb_define_module_function(rb_mMath, "ldexp", math_ldexp, 2);
1019
1020 rb_define_module_function(rb_mMath, "hypot", math_hypot, 2);
1021
1022 rb_define_module_function(rb_mMath, "erf", math_erf, 1);
1023 rb_define_module_function(rb_mMath, "erfc", math_erfc, 1);
1024
1025 rb_define_module_function(rb_mMath, "gamma", math_gamma, 1);
1026 rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1);
1027 }
1028
1029 void
1030 Init_Math(void)
1031 {
1032 InitVM(Math);
1033 }
tan
double tan(double)
T_FLOAT
#define T_FLOAT
Definition: ruby.h:527
atan
double atan(double)
rb_assoc_new
VALUE rb_assoc_new(VALUE car, VALUE cdr)
Definition: array.c:896
atan2
double atan2(double, double)
rb_scan_args
#define rb_scan_args(argc, argvp, fmt,...)
Definition: rb_mjit_min_header-2.7.0.h:6372
INT2FIX
#define INT2FIX(i)
Definition: ruby.h:263
VALUE
unsigned long VALUE
Definition: ruby.h:102
RB_TYPE_P
#define RB_TYPE_P(obj, type)
Definition: ruby.h:560
M_PI
#define M_PI
Definition: missing.h:41
rb_define_module
VALUE rb_define_module(const char *name)
Definition: class.c:772
sin
double sin(double)
exp2
#define exp2(n)
Definition: math.c:930
INT2NUM
#define INT2NUM(x)
Definition: ruby.h:1609
rb_math_log
VALUE rb_math_log(int argc, const VALUE *argv)
Definition: math.c:459
FUNC_MINIMIZED
FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE))
DBL2NUM
#define DBL2NUM(dbl)
Definition: ruby.h:967
M_LN2
#define M_LN2
Definition: math.c:422
NULL
#define NULL
Definition: _sdbm.c:101
T_COMPLEX
#define T_COMPLEX
Definition: ruby.h:542
FIX2LONG
#define FIX2LONG(x)
Definition: ruby.h:394
InitVM
#define InitVM(ext)
Definition: ruby.h:2329
v
int VALUE v
Definition: rb_mjit_min_header-2.7.0.h:12332
sqrt
double sqrt(double)
erfc
RUBY_EXTERN double erfc(double)
Definition: erf.c:81
BIGNUM_POSITIVE_P
#define BIGNUM_POSITIVE_P(b)
Definition: internal.h:765
HUGE_VAL
#define HUGE_VAL
Definition: missing.h:161
asin
double asin(double)
log2
double log2(double x)
Definition: math.c:506
rb_complex_new
VALUE rb_complex_new(VALUE x, VALUE y)
Definition: complex.c:1527
isnan
#define isnan(x)
Definition: win32.h:369
cosh
double cosh(double x)
Definition: math.c:228
lgamma_r
RUBY_EXTERN double lgamma_r(double, int *)
Definition: lgamma_r.c:63
isinf
#define isinf(__x)
Definition: rb_mjit_min_header-2.7.0.h:3673
FIXNUM_P
#define FIXNUM_P(f)
Definition: ruby.h:396
floor
double floor(double)
Init_Math
void Init_Math(void)
Definition: math.c:1030
frexp
double frexp(double, int *)
rb_eMathDomainError
VALUE rb_eMathDomainError
Definition: math.c:28
erf
RUBY_EXTERN double erf(double)
Definition: erf.c:71
signbit
#define signbit(__x)
Definition: rb_mjit_min_header-2.7.0.h:3676
RCOMPLEX
#define RCOMPLEX(obj)
Definition: internal.h:811
rb_big_rshift
VALUE rb_big_rshift(VALUE x, VALUE y)
Definition: bignum.c:6651
cos
double cos(double)
rb_define_module_function
void rb_define_module_function(VALUE module, const char *name, VALUE(*func)(ANYARGS), int argc)
Defines a module function for module.
Definition: class.c:1771
neg
#define neg(x)
Definition: time.c:141
isfinite
#define isfinite(x)
Definition: missing.h:192
n
const char size_t n
Definition: rb_mjit_min_header-2.7.0.h:5456
rb_funcall
#define rb_funcall(recv, mid, argc,...)
Definition: rb_mjit_min_header-2.7.0.h:6585
log
double log(double)
hypot
RUBY_EXTERN double hypot(double, double)
Definition: hypot.c:6
internal.h
argv
char ** argv
Definition: ruby.c:223
f
#define f
acos
double acos(double)
DBL_MANT_DIG
#define DBL_MANT_DIG
Definition: acosh.c:19
tanh
double tanh(double x)
Definition: math.c:284
rb_absint_numwords
size_t rb_absint_numwords(VALUE val, size_t word_numbits, size_t *nlz_bits_ret)
Definition: bignum.c:3382
M_E
#define M_E
Definition: rb_mjit_min_header-2.7.0.h:3869
DBL_MAX_EXP
#define DBL_MAX_EXP
Definition: numeric.c:46
exp
double exp(double)
log10
double log10(double)
rb_mMath
VALUE rb_mMath
Definition: math.c:27
exp1
#define exp1(n)
Definition: math.c:923
sinh
double sinh(double x)
Definition: math.c:256
argc
int argc
Definition: ruby.c:222
rb_define_const
void rb_define_const(VALUE, const char *, VALUE)
Definition: variable.c:2880
RFLOAT_VALUE
#define RFLOAT_VALUE(v)
Definition: ruby.h:966
acosh
RUBY_SYMBOL_EXPORT_BEGIN RUBY_EXTERN double acosh(double)
Definition: acosh.c:36
rb_complex_abs
VALUE rb_complex_abs(VALUE self)
Definition: complex.c:1161
domain_error
#define domain_error(msg)
Definition: math.c:32
rb_define_class_under
VALUE rb_define_class_under(VALUE outer, const char *name, VALUE super)
Defines a class under the namespace of outer.
Definition: class.c:698
SIZET2NUM
#define SIZET2NUM(v)
Definition: ruby.h:295
f_boolcast
#define f_boolcast(x)
Definition: math.c:617
asinh
RUBY_EXTERN double asinh(double)
Definition: acosh.c:52
NUM2INT
#define NUM2INT(x)
Definition: ruby.h:715
cbrt
RUBY_EXTERN double cbrt(double)
Definition: cbrt.c:4
RB_BIGNUM_TYPE_P
#define RB_BIGNUM_TYPE_P(x)
Definition: math.c:25
Get_Double
#define Get_Double(x)
Definition: math.c:30
rb_eStandardError
VALUE rb_eStandardError
Definition: error.c:919
atanh
RUBY_EXTERN double atanh(double)
Definition: acosh.c:75
numberof
#define numberof(array)
Definition: etc.c:618
tgamma
RUBY_EXTERN double tgamma(double)
Definition: tgamma.c:66
ldexp
double ldexp(double, int)