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math.c
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1 /**********************************************************************
2
3 math.c -
4
5 $Author: tadf $
6 created at: Tue Jan 25 14:12:56 JST 1994
7
8 Copyright (C) 1993-2007 Yukihiro Matsumoto
9
10 **********************************************************************/
11
12 #include "ruby/ruby.h"
13 #include "internal.h"
14 #include <math.h>
15 #include <errno.h>
16
17 #if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \
18 !defined(signbit)
19 extern int signbit(double);
20 #endif
21
22 #define numberof(array) (int)(sizeof(array) / sizeof((array)[0]))
23
24 VALUE rb_mMath;
25 VALUE rb_eMathDomainError;
26
27 #define Need_Float(x) do {if (!RB_TYPE_P(x, T_FLOAT)) {(x) = rb_to_float(x);}} while(0)
28 #define Need_Float2(x,y) do {\
29 Need_Float(x);\
30 Need_Float(y);\
31 } while (0)
32
33 #define domain_error(msg) \
34 rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)
35
36 /*
37 * call-seq:
38 * Math.atan2(y, x) -> float
39 *
40 * Computes the arc tangent given <i>y</i> and <i>x</i>. Returns
41 * -PI..PI.
42 *
43 * Math.atan2(-0.0, -1.0) #=> -3.141592653589793
44 * Math.atan2(-1.0, -1.0) #=> -2.356194490192345
45 * Math.atan2(-1.0, 0.0) #=> -1.5707963267948966
46 * Math.atan2(-1.0, 1.0) #=> -0.7853981633974483
47 * Math.atan2(-0.0, 1.0) #=> -0.0
48 * Math.atan2(0.0, 1.0) #=> 0.0
49 * Math.atan2(1.0, 1.0) #=> 0.7853981633974483
50 * Math.atan2(1.0, 0.0) #=> 1.5707963267948966
51 * Math.atan2(1.0, -1.0) #=> 2.356194490192345
52 * Math.atan2(0.0, -1.0) #=> 3.141592653589793
53 *
54 */
55
56 static VALUE
57 math_atan2(VALUE obj, VALUE y, VALUE x)
58 {
59 #ifndef M_PI
60 # define M_PI 3.14159265358979323846
61 #endif
62 double dx, dy;
63 Need_Float2(y, x);
64 dx = RFLOAT_VALUE(x);
65 dy = RFLOAT_VALUE(y);
66 if (dx == 0.0 && dy == 0.0) {
67 if (!signbit(dx))
68 return DBL2NUM(dy);
69 if (!signbit(dy))
70 return DBL2NUM(M_PI);
71 return DBL2NUM(-M_PI);
72 }
73 if (isinf(dx) && isinf(dy)) domain_error("atan2");
74 return DBL2NUM(atan2(dy, dx));
75 }
76
77
78 /*
79 * call-seq:
80 * Math.cos(x) -> float
81 *
82 * Computes the cosine of <i>x</i> (expressed in radians). Returns
83 * -1..1.
84 */
85
86 static VALUE
87 math_cos(VALUE obj, VALUE x)
88 {
89 Need_Float(x);
90 return DBL2NUM(cos(RFLOAT_VALUE(x)));
91 }
92
93 /*
94 * call-seq:
95 * Math.sin(x) -> float
96 *
97 * Computes the sine of <i>x</i> (expressed in radians). Returns
98 * -1..1.
99 */
100
101 static VALUE
102 math_sin(VALUE obj, VALUE x)
103 {
104 Need_Float(x);
105
106 return DBL2NUM(sin(RFLOAT_VALUE(x)));
107 }
108
109
110 /*
111 * call-seq:
112 * Math.tan(x) -> float
113 *
114 * Returns the tangent of <i>x</i> (expressed in radians).
115 */
116
117 static VALUE
118 math_tan(VALUE obj, VALUE x)
119 {
120 Need_Float(x);
121
122 return DBL2NUM(tan(RFLOAT_VALUE(x)));
123 }
124
125 /*
126 * call-seq:
127 * Math.acos(x) -> float
128 *
129 * Computes the arc cosine of <i>x</i>. Returns 0..PI.
130 */
131
132 static VALUE
133 math_acos(VALUE obj, VALUE x)
134 {
135 double d0, d;
136
137 Need_Float(x);
138 d0 = RFLOAT_VALUE(x);
139 /* check for domain error */
140 if (d0 < -1.0 || 1.0 < d0) domain_error("acos");
141 d = acos(d0);
142 return DBL2NUM(d);
143 }
144
145 /*
146 * call-seq:
147 * Math.asin(x) -> float
148 *
149 * Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}.
150 */
151
152 static VALUE
153 math_asin(VALUE obj, VALUE x)
154 {
155 double d0, d;
156
157 Need_Float(x);
158 d0 = RFLOAT_VALUE(x);
159 /* check for domain error */
160 if (d0 < -1.0 || 1.0 < d0) domain_error("asin");
161 d = asin(d0);
162 return DBL2NUM(d);
163 }
164
165 /*
166 * call-seq:
167 * Math.atan(x) -> float
168 *
169 * Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
170 */
171
172 static VALUE
173 math_atan(VALUE obj, VALUE x)
174 {
175 Need_Float(x);
176 return DBL2NUM(atan(RFLOAT_VALUE(x)));
177 }
178
179 #ifndef HAVE_COSH
180 double
181 cosh(double x)
182 {
183 return (exp(x) + exp(-x)) / 2;
184 }
185 #endif
186
187 /*
188 * call-seq:
189 * Math.cosh(x) -> float
190 *
191 * Computes the hyperbolic cosine of <i>x</i> (expressed in radians).
192 */
193
194 static VALUE
195 math_cosh(VALUE obj, VALUE x)
196 {
197 Need_Float(x);
198
199 return DBL2NUM(cosh(RFLOAT_VALUE(x)));
200 }
201
202 #ifndef HAVE_SINH
203 double
204 sinh(double x)
205 {
206 return (exp(x) - exp(-x)) / 2;
207 }
208 #endif
209
210 /*
211 * call-seq:
212 * Math.sinh(x) -> float
213 *
214 * Computes the hyperbolic sine of <i>x</i> (expressed in
215 * radians).
216 */
217
218 static VALUE
219 math_sinh(VALUE obj, VALUE x)
220 {
221 Need_Float(x);
222 return DBL2NUM(sinh(RFLOAT_VALUE(x)));
223 }
224
225 #ifndef HAVE_TANH
226 double
227 tanh(double x)
228 {
229 return sinh(x) / cosh(x);
230 }
231 #endif
232
233 /*
234 * call-seq:
235 * Math.tanh() -> float
236 *
237 * Computes the hyperbolic tangent of <i>x</i> (expressed in
238 * radians).
239 */
240
241 static VALUE
242 math_tanh(VALUE obj, VALUE x)
243 {
244 Need_Float(x);
245 return DBL2NUM(tanh(RFLOAT_VALUE(x)));
246 }
247
248 /*
249 * call-seq:
250 * Math.acosh(x) -> float
251 *
252 * Computes the inverse hyperbolic cosine of <i>x</i>.
253 */
254
255 static VALUE
256 math_acosh(VALUE obj, VALUE x)
257 {
258 double d0, d;
259
260 Need_Float(x);
261 d0 = RFLOAT_VALUE(x);
262 /* check for domain error */
263 if (d0 < 1.0) domain_error("acosh");
264 d = acosh(d0);
265 return DBL2NUM(d);
266 }
267
268 /*
269 * call-seq:
270 * Math.asinh(x) -> float
271 *
272 * Computes the inverse hyperbolic sine of <i>x</i>.
273 */
274
275 static VALUE
276 math_asinh(VALUE obj, VALUE x)
277 {
278 Need_Float(x);
279 return DBL2NUM(asinh(RFLOAT_VALUE(x)));
280 }
281
282 /*
283 * call-seq:
284 * Math.atanh(x) -> float
285 *
286 * Computes the inverse hyperbolic tangent of <i>x</i>.
287 */
288
289 static VALUE
290 math_atanh(VALUE obj, VALUE x)
291 {
292 double d0, d;
293
294 Need_Float(x);
295 d0 = RFLOAT_VALUE(x);
296 /* check for domain error */
297 if (d0 < -1.0 || +1.0 < d0) domain_error("atanh");
298 /* check for pole error */
299 if (d0 == -1.0) return DBL2NUM(-INFINITY);
300 if (d0 == +1.0) return DBL2NUM(+INFINITY);
301 d = atanh(d0);
302 return DBL2NUM(d);
303 }
304
305 /*
306 * call-seq:
307 * Math.exp(x) -> float
308 *
309 * Returns e**x.
310 *
311 * Math.exp(0) #=> 1.0
312 * Math.exp(1) #=> 2.718281828459045
313 * Math.exp(1.5) #=> 4.4816890703380645
314 *
315 */
316
317 static VALUE
318 math_exp(VALUE obj, VALUE x)
319 {
320 Need_Float(x);
321 return DBL2NUM(exp(RFLOAT_VALUE(x)));
322 }
323
324 #if defined __CYGWIN__
325 # include <cygwin/version.h>
326 # if CYGWIN_VERSION_DLL_MAJOR < 1005
327 # define nan(x) nan()
328 # endif
329 # define log(x) ((x) < 0.0 ? nan("") : log(x))
330 # define log10(x) ((x) < 0.0 ? nan("") : log10(x))
331 #endif
332
333 /*
334 * call-seq:
335 * Math.log(numeric) -> float
336 * Math.log(num,base) -> float
337 *
338 * Returns the natural logarithm of <i>numeric</i>.
339 * If additional second argument is given, it will be the base
340 * of logarithm.
341 *
342 * Math.log(1) #=> 0.0
343 * Math.log(Math::E) #=> 1.0
344 * Math.log(Math::E**3) #=> 3.0
345 * Math.log(12,3) #=> 2.2618595071429146
346 *
347 */
348
349 static VALUE
350 math_log(int argc, VALUE *argv)
351 {
352 VALUE x, base;
353 double d0, d;
354
355 rb_scan_args(argc, argv, "11", &x, &base);
356 Need_Float(x);
357 d0 = RFLOAT_VALUE(x);
358 /* check for domain error */
359 if (d0 < 0.0) domain_error("log");
360 /* check for pole error */
361 if (d0 == 0.0) return DBL2NUM(-INFINITY);
362 d = log(d0);
363 if (argc == 2) {
364 Need_Float(base);
365 d /= log(RFLOAT_VALUE(base));
366 }
367 return DBL2NUM(d);
368 }
369
370 #ifndef log2
371 #ifndef HAVE_LOG2
372 double
373 log2(double x)
374 {
375 return log10(x)/log10(2.0);
376 }
377 #else
378 extern double log2(double);
379 #endif
380 #endif
381
382 /*
383 * call-seq:
384 * Math.log2(numeric) -> float
385 *
386 * Returns the base 2 logarithm of <i>numeric</i>.
387 *
388 * Math.log2(1) #=> 0.0
389 * Math.log2(2) #=> 1.0
390 * Math.log2(32768) #=> 15.0
391 * Math.log2(65536) #=> 16.0
392 *
393 */
394
395 static VALUE
396 math_log2(VALUE obj, VALUE x)
397 {
398 double d0, d;
399
400 Need_Float(x);
401 d0 = RFLOAT_VALUE(x);
402 /* check for domain error */
403 if (d0 < 0.0) domain_error("log2");
404 /* check for pole error */
405 if (d0 == 0.0) return DBL2NUM(-INFINITY);
406 d = log2(d0);
407 return DBL2NUM(d);
408 }
409
410 /*
411 * call-seq:
412 * Math.log10(numeric) -> float
413 *
414 * Returns the base 10 logarithm of <i>numeric</i>.
415 *
416 * Math.log10(1) #=> 0.0
417 * Math.log10(10) #=> 1.0
418 * Math.log10(10**100) #=> 100.0
419 *
420 */
421
422 static VALUE
423 math_log10(VALUE obj, VALUE x)
424 {
425 double d0, d;
426
427 Need_Float(x);
428 d0 = RFLOAT_VALUE(x);
429 /* check for domain error */
430 if (d0 < 0.0) domain_error("log10");
431 /* check for pole error */
432 if (d0 == 0.0) return DBL2NUM(-INFINITY);
433 d = log10(d0);
434 return DBL2NUM(d);
435 }
436
437 /*
438 * call-seq:
439 * Math.sqrt(numeric) -> float
440 *
441 * Returns the non-negative square root of <i>numeric</i>.
442 *
443 * 0.upto(10) {|x|
444 * p [x, Math.sqrt(x), Math.sqrt(x)**2]
445 * }
446 * #=>
447 * [0, 0.0, 0.0]
448 * [1, 1.0, 1.0]
449 * [2, 1.4142135623731, 2.0]
450 * [3, 1.73205080756888, 3.0]
451 * [4, 2.0, 4.0]
452 * [5, 2.23606797749979, 5.0]
453 * [6, 2.44948974278318, 6.0]
454 * [7, 2.64575131106459, 7.0]
455 * [8, 2.82842712474619, 8.0]
456 * [9, 3.0, 9.0]
457 * [10, 3.16227766016838, 10.0]
458 *
459 */
460
461 static VALUE
462 math_sqrt(VALUE obj, VALUE x)
463 {
464 double d0, d;
465
466 Need_Float(x);
467 d0 = RFLOAT_VALUE(x);
468 /* check for domain error */
469 if (d0 < 0.0) domain_error("sqrt");
470 if (d0 == 0.0) return DBL2NUM(0.0);
471 d = sqrt(d0);
472 return DBL2NUM(d);
473 }
474
475 /*
476 * call-seq:
477 * Math.cbrt(numeric) -> float
478 *
479 * Returns the cube root of <i>numeric</i>.
480 *
481 * -9.upto(9) {|x|
482 * p [x, Math.cbrt(x), Math.cbrt(x)**3]
483 * }
484 * #=>
485 * [-9, -2.0800838230519, -9.0]
486 * [-8, -2.0, -8.0]
487 * [-7, -1.91293118277239, -7.0]
488 * [-6, -1.81712059283214, -6.0]
489 * [-5, -1.7099759466767, -5.0]
490 * [-4, -1.5874010519682, -4.0]
491 * [-3, -1.44224957030741, -3.0]
492 * [-2, -1.25992104989487, -2.0]
493 * [-1, -1.0, -1.0]
494 * [0, 0.0, 0.0]
495 * [1, 1.0, 1.0]
496 * [2, 1.25992104989487, 2.0]
497 * [3, 1.44224957030741, 3.0]
498 * [4, 1.5874010519682, 4.0]
499 * [5, 1.7099759466767, 5.0]
500 * [6, 1.81712059283214, 6.0]
501 * [7, 1.91293118277239, 7.0]
502 * [8, 2.0, 8.0]
503 * [9, 2.0800838230519, 9.0]
504 *
505 */
506
507 static VALUE
508 math_cbrt(VALUE obj, VALUE x)
509 {
510 Need_Float(x);
511 return DBL2NUM(cbrt(RFLOAT_VALUE(x)));
512 }
513
514 /*
515 * call-seq:
516 * Math.frexp(numeric) -> [ fraction, exponent ]
517 *
518 * Returns a two-element array containing the normalized fraction (a
519 * <code>Float</code>) and exponent (a <code>Fixnum</code>) of
520 * <i>numeric</i>.
521 *
522 * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
523 * fraction * 2**exponent #=> 1234.0
524 */
525
526 static VALUE
527 math_frexp(VALUE obj, VALUE x)
528 {
529 double d;
530 int exp;
531
532 Need_Float(x);
533
534 d = frexp(RFLOAT_VALUE(x), &exp);
535 return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
536 }
537
538 /*
539 * call-seq:
540 * Math.ldexp(flt, int) -> float
541 *
542 * Returns the value of <i>flt</i>*(2**<i>int</i>).
543 *
544 * fraction, exponent = Math.frexp(1234)
545 * Math.ldexp(fraction, exponent) #=> 1234.0
546 */
547
548 static VALUE
549 math_ldexp(VALUE obj, VALUE x, VALUE n)
550 {
551 Need_Float(x);
552 return DBL2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n)));
553 }
554
555 /*
556 * call-seq:
557 * Math.hypot(x, y) -> float
558 *
559 * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle
560 * with sides <i>x</i> and <i>y</i>.
561 *
562 * Math.hypot(3, 4) #=> 5.0
563 */
564
565 static VALUE
566 math_hypot(VALUE obj, VALUE x, VALUE y)
567 {
568 Need_Float2(x, y);
569 return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
570 }
571
572 /*
573 * call-seq:
574 * Math.erf(x) -> float
575 *
576 * Calculates the error function of x.
577 */
578
579 static VALUE
580 math_erf(VALUE obj, VALUE x)
581 {
582 Need_Float(x);
583 return DBL2NUM(erf(RFLOAT_VALUE(x)));
584 }
585
586 /*
587 * call-seq:
588 * Math.erfc(x) -> float
589 *
590 * Calculates the complementary error function of x.
591 */
592
593 static VALUE
594 math_erfc(VALUE obj, VALUE x)
595 {
596 Need_Float(x);
597 return DBL2NUM(erfc(RFLOAT_VALUE(x)));
598 }
599
600 /*
601 * call-seq:
602 * Math.gamma(x) -> float
603 *
604 * Calculates the gamma function of x.
605 *
606 * Note that gamma(n) is same as fact(n-1) for integer n > 0.
607 * However gamma(n) returns float and can be an approximation.
608 *
609 * def fact(n) (1..n).inject(1) {|r,i| r*i } end
610 * 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }
611 * #=> [1, 1.0, 1]
612 * # [2, 1.0, 1]
613 * # [3, 2.0, 2]
614 * # [4, 6.0, 6]
615 * # [5, 24.0, 24]
616 * # [6, 120.0, 120]
617 * # [7, 720.0, 720]
618 * # [8, 5040.0, 5040]
619 * # [9, 40320.0, 40320]
620 * # [10, 362880.0, 362880]
621 * # [11, 3628800.0, 3628800]
622 * # [12, 39916800.0, 39916800]
623 * # [13, 479001600.0, 479001600]
624 * # [14, 6227020800.0, 6227020800]
625 * # [15, 87178291200.0, 87178291200]
626 * # [16, 1307674368000.0, 1307674368000]
627 * # [17, 20922789888000.0, 20922789888000]
628 * # [18, 355687428096000.0, 355687428096000]
629 * # [19, 6.402373705728e+15, 6402373705728000]
630 * # [20, 1.21645100408832e+17, 121645100408832000]
631 * # [21, 2.43290200817664e+18, 2432902008176640000]
632 * # [22, 5.109094217170944e+19, 51090942171709440000]
633 * # [23, 1.1240007277776077e+21, 1124000727777607680000]
634 * # [24, 2.5852016738885062e+22, 25852016738884976640000]
635 * # [25, 6.204484017332391e+23, 620448401733239439360000]
636 * # [26, 1.5511210043330954e+25, 15511210043330985984000000]
637 *
638 */
639
640 static VALUE
641 math_gamma(VALUE obj, VALUE x)
642 {
643 static const double fact_table[] = {
644 /* fact(0) */ 1.0,
645 /* fact(1) */ 1.0,
646 /* fact(2) */ 2.0,
647 /* fact(3) */ 6.0,
648 /* fact(4) */ 24.0,
649 /* fact(5) */ 120.0,
650 /* fact(6) */ 720.0,
651 /* fact(7) */ 5040.0,
652 /* fact(8) */ 40320.0,
653 /* fact(9) */ 362880.0,
654 /* fact(10) */ 3628800.0,
655 /* fact(11) */ 39916800.0,
656 /* fact(12) */ 479001600.0,
657 /* fact(13) */ 6227020800.0,
658 /* fact(14) */ 87178291200.0,
659 /* fact(15) */ 1307674368000.0,
660 /* fact(16) */ 20922789888000.0,
661 /* fact(17) */ 355687428096000.0,
662 /* fact(18) */ 6402373705728000.0,
663 /* fact(19) */ 121645100408832000.0,
664 /* fact(20) */ 2432902008176640000.0,
665 /* fact(21) */ 51090942171709440000.0,
666 /* fact(22) */ 1124000727777607680000.0,
667 /* fact(23)=25852016738884976640000 needs 56bit mantissa which is
668 * impossible to represent exactly in IEEE 754 double which have
669 * 53bit mantissa. */
670 };
671 double d0, d;
672 double intpart, fracpart;
673 Need_Float(x);
674 d0 = RFLOAT_VALUE(x);
675 /* check for domain error */
676 if (isinf(d0) && signbit(d0)) domain_error("gamma");
677 fracpart = modf(d0, &intpart);
678 if (fracpart == 0.0) {
679 if (intpart < 0) domain_error("gamma");
680 if (0 < intpart &&
681 intpart - 1 < (double)numberof(fact_table)) {
682 return DBL2NUM(fact_table[(int)intpart - 1]);
683 }
684 }
685 d = tgamma(d0);
686 return DBL2NUM(d);
687 }
688
689 /*
690 * call-seq:
691 * Math.lgamma(x) -> [float, -1 or 1]
692 *
693 * Calculates the logarithmic gamma of x and
694 * the sign of gamma of x.
695 *
696 * Math.lgamma(x) is same as
697 * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
698 * but avoid overflow by Math.gamma(x) for large x.
699 */
700
701 static VALUE
702 math_lgamma(VALUE obj, VALUE x)
703 {
704 double d0, d;
705 int sign=1;
706 VALUE v;
707 Need_Float(x);
708 d0 = RFLOAT_VALUE(x);
709 /* check for domain error */
710 if (isinf(d0)) {
711 if (signbit(d0)) domain_error("lgamma");
712 return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1));
713 }
714 d = lgamma_r(d0, &sign);
715 v = DBL2NUM(d);
716 return rb_assoc_new(v, INT2FIX(sign));
717 }
718
719
720 #define exp1(n) \
721 VALUE \
722 rb_math_##n(VALUE x)\
723 {\
724 return math_##n(rb_mMath, x);\
725 }
726
727 #define exp2(n) \
728 VALUE \
729 rb_math_##n(VALUE x, VALUE y)\
730 {\
731 return math_##n(rb_mMath, x, y);\
732 }
733
734 exp2(atan2)
735 exp1(cos)
736 exp1(cosh)
737 exp1(exp)
738 exp2(hypot)
739
740 VALUE
741 rb_math_log(int argc, VALUE *argv)
742 {
743 return math_log(argc, argv);
744 }
745
746 exp1(sin)
747 exp1(sinh)
748 exp1(sqrt)
749
750
751 /*
752 * Document-class: Math::DomainError
753 *
754 * Raised when a mathematical function is evaluated outside of its
755 * domain of definition.
756 *
757 * For example, since +cos+ returns values in the range -1..1,
758 * its inverse function +acos+ is only defined on that interval:
759 *
760 * Math.acos(42)
761 *
762 * <em>produces:</em>
763 *
764 * Math::DomainError: Numerical argument is out of domain - "acos"
765 */
766
767 /*
768 * Document-class: Math
769 *
770 * The <code>Math</code> module contains module functions for basic
771 * trigonometric and transcendental functions. See class
772 * <code>Float</code> for a list of constants that
773 * define Ruby's floating point accuracy.
774 */
775
776
777 void
778 Init_Math(void)
779 {
780 rb_mMath = rb_define_module("Math");
781 rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError);
782
783 #ifdef M_PI
784 rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI));
785 #else
786 rb_define_const(rb_mMath, "PI", DBL2NUM(atan(1.0)*4.0));
787 #endif
788
789 #ifdef M_E
790 rb_define_const(rb_mMath, "E", DBL2NUM(M_E));
791 #else
792 rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0)));
793 #endif
794
795 rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);
796 rb_define_module_function(rb_mMath, "cos", math_cos, 1);
797 rb_define_module_function(rb_mMath, "sin", math_sin, 1);
798 rb_define_module_function(rb_mMath, "tan", math_tan, 1);
799
800 rb_define_module_function(rb_mMath, "acos", math_acos, 1);
801 rb_define_module_function(rb_mMath, "asin", math_asin, 1);
802 rb_define_module_function(rb_mMath, "atan", math_atan, 1);
803
804 rb_define_module_function(rb_mMath, "cosh", math_cosh, 1);
805 rb_define_module_function(rb_mMath, "sinh", math_sinh, 1);
806 rb_define_module_function(rb_mMath, "tanh", math_tanh, 1);
807
808 rb_define_module_function(rb_mMath, "acosh", math_acosh, 1);
809 rb_define_module_function(rb_mMath, "asinh", math_asinh, 1);
810 rb_define_module_function(rb_mMath, "atanh", math_atanh, 1);
811
812 rb_define_module_function(rb_mMath, "exp", math_exp, 1);
813 rb_define_module_function(rb_mMath, "log", math_log, -1);
814 rb_define_module_function(rb_mMath, "log2", math_log2, 1);
815 rb_define_module_function(rb_mMath, "log10", math_log10, 1);
816 rb_define_module_function(rb_mMath, "sqrt", math_sqrt, 1);
817 rb_define_module_function(rb_mMath, "cbrt", math_cbrt, 1);
818
819 rb_define_module_function(rb_mMath, "frexp", math_frexp, 1);
820 rb_define_module_function(rb_mMath, "ldexp", math_ldexp, 2);
821
822 rb_define_module_function(rb_mMath, "hypot", math_hypot, 2);
823
824 rb_define_module_function(rb_mMath, "erf", math_erf, 1);
825 rb_define_module_function(rb_mMath, "erfc", math_erfc, 1);
826
827 rb_define_module_function(rb_mMath, "gamma", math_gamma, 1);
828 rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1);
829 }
830