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
24VALUE rb_mMath;
25VALUE 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
56static VALUE
57math_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
86static VALUE
87math_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
101static VALUE
102math_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
117static VALUE
118math_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
132static VALUE
133math_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
152static VALUE
153math_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
172static VALUE
173math_atan(VALUE obj, VALUE x)
174{
175    Need_Float(x);
176    return DBL2NUM(atan(RFLOAT_VALUE(x)));
177}
178
179#ifndef HAVE_COSH
180double
181cosh(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
194static VALUE
195math_cosh(VALUE obj, VALUE x)
196{
197    Need_Float(x);
198
199    return DBL2NUM(cosh(RFLOAT_VALUE(x)));
200}
201
202#ifndef HAVE_SINH
203double
204sinh(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
218static VALUE
219math_sinh(VALUE obj, VALUE x)
220{
221    Need_Float(x);
222    return DBL2NUM(sinh(RFLOAT_VALUE(x)));
223}
224
225#ifndef HAVE_TANH
226double
227tanh(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
241static VALUE
242math_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
255static VALUE
256math_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
275static VALUE
276math_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
289static VALUE
290math_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
317static VALUE
318math_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
349static VALUE
350math_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
372double
373log2(double x)
374{
375    return log10(x)/log10(2.0);
376}
377#else
378extern 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
395static VALUE
396math_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
422static VALUE
423math_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
461static VALUE
462math_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
507static VALUE
508math_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
526static VALUE
527math_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
548static VALUE
549math_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
565static VALUE
566math_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
579static VALUE
580math_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
593static VALUE
594math_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
640static VALUE
641math_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
701static VALUE
702math_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) \
721VALUE \
722rb_math_##n(VALUE x)\
723{\
724    return math_##n(rb_mMath, x);\
725}
726
727#define exp2(n) \
728VALUE \
729rb_math_##n(VALUE x, VALUE y)\
730{\
731    return math_##n(rb_mMath, x, y);\
732}
733
734exp2(atan2)
735exp1(cos)
736exp1(cosh)
737exp1(exp)
738exp2(hypot)
739
740VALUE
741rb_math_log(int argc, VALUE *argv)
742{
743    return math_log(argc, argv);
744}
745
746exp1(sin)
747exp1(sinh)
748exp1(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
777void
778Init_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