/**********************************************************************

math.c -

$Author$

created at: Tue Jan 25 14:12:56 JST 1994

Copyright (C) 1993-2007 Yukihiro Matsumoto

**********************************************************************/

#include "internal.h"

#include <float.h>

#include <math.h>

#include <errno.h>

#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \

!defined(signbit)

extern int signbit(double);

#endif

#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM)

static ID id_to_f;

VALUE rb_mMath;

VALUE rb_eMathDomainError;

static inline int

basic_to_f_p(VALUE klass)

{

return rb_method_basic_definition_p(klass, id_to_f);

}

#define fix2dbl_without_to_f(x) (double)FIX2LONG(x)

#define big2dbl_without_to_f(x) rb_big2dbl(x)

#define int2dbl_without_to_f(x) (FIXNUM_P(x) ? fix2dbl_without_to_f(x) : big2dbl_without_to_f(x))

#define rat2dbl_without_to_f(x) \

(int2dbl_without_to_f(rb_rational_num(x)) / \

int2dbl_without_to_f(rb_rational_den(x)))

static inline double

num2dbl_with_to_f(VALUE num)

{

if (SPECIAL_CONST_P(num)) {

if (FIXNUM_P(num)) {

if (basic_to_f_p(rb_cFixnum))

return fix2dbl_without_to_f(num);

}

else if (FLONUM_P(num)) {

return RFLOAT_VALUE(num);

}

}

else {

switch (BUILTIN_TYPE(num)) {

case T_FLOAT:

return RFLOAT_VALUE(num);

case T_BIGNUM:

if (basic_to_f_p(rb_cBignum))

return big2dbl_without_to_f(num);

break;

case T_RATIONAL:

if (basic_to_f_p(rb_cRational))

return rat2dbl_without_to_f(num);

break;

}

}

return RFLOAT_VALUE(rb_to_float(num));

}

#define Get_Double(x) num2dbl_with_to_f(x)

#define domain_error(msg) \

rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg)

/*

* call-seq:

* Math.atan2(y, x) -> Float

*

* Computes the arc tangent given +y+ and +x+.

* Returns a Float in the range -PI..PI. Return value is a angle

* in radians between the positive x-axis of cartesian plane

* and the point given by the coordinates (+x+, +y+) on it.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: [-PI, PI]

*

* Math.atan2(-0.0, -1.0) #=> -3.141592653589793

* Math.atan2(-1.0, -1.0) #=> -2.356194490192345

* Math.atan2(-1.0, 0.0) #=> -1.5707963267948966

* Math.atan2(-1.0, 1.0) #=> -0.7853981633974483

* Math.atan2(-0.0, 1.0) #=> -0.0

* Math.atan2(0.0, 1.0) #=> 0.0

* Math.atan2(1.0, 1.0) #=> 0.7853981633974483

* Math.atan2(1.0, 0.0) #=> 1.5707963267948966

* Math.atan2(1.0, -1.0) #=> 2.356194490192345

* Math.atan2(0.0, -1.0) #=> 3.141592653589793

* Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483

* Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345

* Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483

* Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345

*

*/

static VALUE

math_atan2(VALUE obj, VALUE y, VALUE x)

{

double dx, dy;

dx = Get_Double(x);

dy = Get_Double(y);

if (dx == 0.0 && dy == 0.0) {

if (!signbit(dx))

return DBL2NUM(dy);

if (!signbit(dy))

return DBL2NUM(M_PI);

return DBL2NUM(-M_PI);

}

#ifndef ATAN2_INF_C99

if (isinf(dx) && isinf(dy)) {

/* optimization for FLONUM */

if (dx < 0.0) {

const double dz = (3.0 * M_PI / 4.0);

return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);

}

else {

const double dz = (M_PI / 4.0);

return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);

}

}

#endif

return DBL2NUM(atan2(dy, dx));

}

/*

* call-seq:

* Math.cos(x) -> Float

*

* Computes the cosine of +x+ (expressed in radians).

* Returns a Float in the range -1.0..1.0.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: [-1, 1]

*

* Math.cos(Math::PI) #=> -1.0

*

*/

static VALUE

math_cos(VALUE obj, VALUE x)

{

return DBL2NUM(cos(Get_Double(x)));

}

/*

* call-seq:

* Math.sin(x) -> Float

*

* Computes the sine of +x+ (expressed in radians).

* Returns a Float in the range -1.0..1.0.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: [-1, 1]

*

* Math.sin(Math::PI/2) #=> 1.0

*

*/

static VALUE

math_sin(VALUE obj, VALUE x)

{

return DBL2NUM(sin(Get_Double(x)));

}

/*

* call-seq:

* Math.tan(x) -> Float

*

* Computes the tangent of +x+ (expressed in radians).

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.tan(0) #=> 0.0

*

*/

static VALUE

math_tan(VALUE obj, VALUE x)

{

return DBL2NUM(tan(Get_Double(x)));

}

/*

* call-seq:

* Math.acos(x) -> Float

*

* Computes the arc cosine of +x+. Returns 0..PI.

*

* Domain: [-1, 1]

*

* Codomain: [0, PI]

*

* Math.acos(0) == Math::PI/2 #=> true

*

*/

static VALUE

math_acos(VALUE obj, VALUE x)

{

double d;

d = Get_Double(x);

/* check for domain error */

if (d < -1.0 || 1.0 < d) domain_error("acos");

return DBL2NUM(acos(d));

}

/*

* call-seq:

* Math.asin(x) -> Float

*

* Computes the arc sine of +x+. Returns -PI/2..PI/2.

*

* Domain: [-1, -1]

*

* Codomain: [-PI/2, PI/2]

*

* Math.asin(1) == Math::PI/2 #=> true

*/

static VALUE

math_asin(VALUE obj, VALUE x)

{

double d;

d = Get_Double(x);

/* check for domain error */

if (d < -1.0 || 1.0 < d) domain_error("asin");

return DBL2NUM(asin(d));

}

/*

* call-seq:

* Math.atan(x) -> Float

*

* Computes the arc tangent of +x+. Returns -PI/2..PI/2.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-PI/2, PI/2)

*

* Math.atan(0) #=> 0.0

*/

static VALUE

math_atan(VALUE obj, VALUE x)

{

return DBL2NUM(atan(Get_Double(x)));

}

#ifndef HAVE_COSH

double

cosh(double x)

{

return (exp(x) + exp(-x)) / 2;

}

#endif

/*

* call-seq:

* Math.cosh(x) -> Float

*

* Computes the hyperbolic cosine of +x+ (expressed in radians).

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: [1, INFINITY)

*

* Math.cosh(0) #=> 1.0

*

*/

static VALUE

math_cosh(VALUE obj, VALUE x)

{

return DBL2NUM(cosh(Get_Double(x)));

}

#ifndef HAVE_SINH

double

sinh(double x)

{

return (exp(x) - exp(-x)) / 2;

}

#endif

/*

* call-seq:

* Math.sinh(x) -> Float

*

* Computes the hyperbolic sine of +x+ (expressed in radians).

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.sinh(0) #=> 0.0

*

*/

static VALUE

math_sinh(VALUE obj, VALUE x)

{

return DBL2NUM(sinh(Get_Double(x)));

}

#ifndef HAVE_TANH

double

tanh(double x)

{

return sinh(x) / cosh(x);

}

#endif

/*

* call-seq:

* Math.tanh(x) -> Float

*

* Computes the hyperbolic tangent of +x+ (expressed in radians).

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-1, 1)

*

* Math.tanh(0) #=> 0.0

*

*/

static VALUE

math_tanh(VALUE obj, VALUE x)

{

return DBL2NUM(tanh(Get_Double(x)));

}

/*

* call-seq:

* Math.acosh(x) -> Float

*

* Computes the inverse hyperbolic cosine of +x+.

*

* Domain: [1, INFINITY)

*

* Codomain: [0, INFINITY)

*

* Math.acosh(1) #=> 0.0

*

*/

static VALUE

math_acosh(VALUE obj, VALUE x)

{

double d;

d = Get_Double(x);

/* check for domain error */

if (d < 1.0) domain_error("acosh");

return DBL2NUM(acosh(d));

}

/*

* call-seq:

* Math.asinh(x) -> Float

*

* Computes the inverse hyperbolic sine of +x+.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.asinh(1) #=> 0.881373587019543

*

*/

static VALUE

math_asinh(VALUE obj, VALUE x)

{

return DBL2NUM(asinh(Get_Double(x)));

}

/*

* call-seq:

* Math.atanh(x) -> Float

*

* Computes the inverse hyperbolic tangent of +x+.

*

* Domain: (-1, 1)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.atanh(1) #=> Infinity

*

*/

static VALUE

math_atanh(VALUE obj, VALUE x)

{

double d;

d = Get_Double(x);

/* check for domain error */

if (d < -1.0 || +1.0 < d) domain_error("atanh");

/* check for pole error */

if (d == -1.0) return DBL2NUM(-INFINITY);

if (d == +1.0) return DBL2NUM(+INFINITY);

return DBL2NUM(atanh(d));

}

/*

* call-seq:

* Math.exp(x) -> Float

*

* Returns e**x.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (0, INFINITY)

*

* Math.exp(0) #=> 1.0

* Math.exp(1) #=> 2.718281828459045

* Math.exp(1.5) #=> 4.4816890703380645

*

*/

static VALUE

math_exp(VALUE obj, VALUE x)

{

return DBL2NUM(exp(Get_Double(x)));

}

#if defined __CYGWIN__

# include <cygwin/version.h>

# if CYGWIN_VERSION_DLL_MAJOR < 1005

# define nan(x) nan()

# endif

# define log(x) ((x) < 0.0 ? nan("") : log(x))

# define log10(x) ((x) < 0.0 ? nan("") : log10(x))

#endif

static double math_log1(VALUE x);

/*

* call-seq:

* Math.log(x) -> Float

* Math.log(x, base) -> Float

*

* Returns the logarithm of +x+.

* If additional second argument is given, it will be the base

* of logarithm. Otherwise it is +e+ (for the natural logarithm).

*

* Domain: (0, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.log(0) #=> -Infinity

* Math.log(1) #=> 0.0

* Math.log(Math::E) #=> 1.0

* Math.log(Math::E**3) #=> 3.0

* Math.log(12, 3) #=> 2.2618595071429146

*

*/

static VALUE

math_log(int argc, const VALUE *argv, VALUE obj)

{

VALUE x, base;

double d;

rb_scan_args(argc, argv, "11", &x, &base);

d = math_log1(x);

if (argc == 2) {

d /= math_log1(base);

}

return DBL2NUM(d);

}

static double

math_log1(VALUE x)

{

double d;

size_t numbits;

if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) &&

DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) {

numbits -= DBL_MANT_DIG;

x = rb_big_rshift(x, SIZET2NUM(numbits));

}

else {

numbits = 0;

}

d = Get_Double(x);

/* check for domain error */

if (d < 0.0) domain_error("log");

/* check for pole error */

if (d == 0.0) return -INFINITY;

return log(d) + numbits * log(2); /* log(d * 2 ** numbits) */

}

#ifndef log2

#ifndef HAVE_LOG2

double

log2(double x)

{

return log10(x)/log10(2.0);

}

#else

extern double log2(double);

#endif

#endif

/*

* call-seq:

* Math.log2(x) -> Float

*

* Returns the base 2 logarithm of +x+.

*

* Domain: (0, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.log2(1) #=> 0.0

* Math.log2(2) #=> 1.0

* Math.log2(32768) #=> 15.0

* Math.log2(65536) #=> 16.0

*

*/

static VALUE

math_log2(VALUE obj, VALUE x)

{

double d;

size_t numbits;

if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) &&

DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) {

numbits -= DBL_MANT_DIG;

x = rb_big_rshift(x, SIZET2NUM(numbits));

}

else {

numbits = 0;

}

d = Get_Double(x);

/* check for domain error */

if (d < 0.0) domain_error("log2");

/* check for pole error */

if (d == 0.0) return DBL2NUM(-INFINITY);

return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */

}

/*

* call-seq:

* Math.log10(x) -> Float

*

* Returns the base 10 logarithm of +x+.

*

* Domain: (0, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* Math.log10(1) #=> 0.0

* Math.log10(10) #=> 1.0

* Math.log10(10**100) #=> 100.0

*

*/

static VALUE

math_log10(VALUE obj, VALUE x)

{

double d;

size_t numbits;

if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) &&

DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) {

numbits -= DBL_MANT_DIG;

x = rb_big_rshift(x, SIZET2NUM(numbits));

}

else {

numbits = 0;

}

d = Get_Double(x);

/* check for domain error */

if (d < 0.0) domain_error("log10");

/* check for pole error */

if (d == 0.0) return DBL2NUM(-INFINITY);

return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */

}

/*

* call-seq:

* Math.sqrt(x) -> Float

*

* Returns the non-negative square root of +x+.

*

* Domain: [0, INFINITY)

*

* Codomain:[0, INFINITY)

*

* 0.upto(10) {|x|

* p [x, Math.sqrt(x), Math.sqrt(x)**2]

* }

* #=> [0, 0.0, 0.0]

* # [1, 1.0, 1.0]

* # [2, 1.4142135623731, 2.0]

* # [3, 1.73205080756888, 3.0]

* # [4, 2.0, 4.0]

* # [5, 2.23606797749979, 5.0]

* # [6, 2.44948974278318, 6.0]

* # [7, 2.64575131106459, 7.0]

* # [8, 2.82842712474619, 8.0]

* # [9, 3.0, 9.0]

* # [10, 3.16227766016838, 10.0]

*/

static VALUE

math_sqrt(VALUE obj, VALUE x)

{

double d;

d = Get_Double(x);

/* check for domain error */

if (d < 0.0) domain_error("sqrt");

if (d == 0.0) return DBL2NUM(0.0);

return DBL2NUM(sqrt(d));

}

/*

* call-seq:

* Math.cbrt(x) -> Float

*

* Returns the cube root of +x+.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-INFINITY, INFINITY)

*

* -9.upto(9) {|x|

* p [x, Math.cbrt(x), Math.cbrt(x)**3]

* }

* #=> [-9, -2.0800838230519, -9.0]

* # [-8, -2.0, -8.0]

* # [-7, -1.91293118277239, -7.0]

* # [-6, -1.81712059283214, -6.0]

* # [-5, -1.7099759466767, -5.0]

* # [-4, -1.5874010519682, -4.0]

* # [-3, -1.44224957030741, -3.0]

* # [-2, -1.25992104989487, -2.0]

* # [-1, -1.0, -1.0]

* # [0, 0.0, 0.0]

* # [1, 1.0, 1.0]

* # [2, 1.25992104989487, 2.0]

* # [3, 1.44224957030741, 3.0]

* # [4, 1.5874010519682, 4.0]

* # [5, 1.7099759466767, 5.0]

* # [6, 1.81712059283214, 6.0]

* # [7, 1.91293118277239, 7.0]

* # [8, 2.0, 8.0]

* # [9, 2.0800838230519, 9.0]

*

*/

static VALUE

math_cbrt(VALUE obj, VALUE x)

{

return DBL2NUM(cbrt(Get_Double(x)));

}

/*

* call-seq:

* Math.frexp(x) -> [fraction, exponent]

*

* Returns a two-element array containing the normalized fraction (a Float)

* and exponent (a Fixnum) of +x+.

*

* fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]

* fraction * 2**exponent #=> 1234.0

*/

static VALUE

math_frexp(VALUE obj, VALUE x)

{

double d;

int exp;

d = frexp(Get_Double(x), &exp);

return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));

}

/*

* call-seq:

* Math.ldexp(fraction, exponent) -> float

*

* Returns the value of +fraction+*(2**+exponent+).

*

* fraction, exponent = Math.frexp(1234)

* Math.ldexp(fraction, exponent) #=> 1234.0

*/

static VALUE

math_ldexp(VALUE obj, VALUE x, VALUE n)

{

return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n)));

}

/*

* call-seq:

* Math.hypot(x, y) -> Float

*

* Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with

* sides +x+ and +y+.

*

* Math.hypot(3, 4) #=> 5.0

*/

static VALUE

math_hypot(VALUE obj, VALUE x, VALUE y)

{

return DBL2NUM(hypot(Get_Double(x), Get_Double(y)));

}

/*

* call-seq:

* Math.erf(x) -> Float

*

* Calculates the error function of +x+.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (-1, 1)

*

* Math.erf(0) #=> 0.0

*

*/

static VALUE

math_erf(VALUE obj, VALUE x)

{

return DBL2NUM(erf(Get_Double(x)));

}

/*

* call-seq:

* Math.erfc(x) -> Float

*

* Calculates the complementary error function of x.

*

* Domain: (-INFINITY, INFINITY)

*

* Codomain: (0, 2)

*

* Math.erfc(0) #=> 1.0

*

*/

static VALUE

math_erfc(VALUE obj, VALUE x)

{

return DBL2NUM(erfc(Get_Double(x)));

}

#ifdef __MINGW32__

static inline double

mingw_tgamma(const double d)

{

const double g = tgamma(d);

return (isnan(g) && !signbit(d)) ? INFINITY : g;

}

#define tgamma(d) mingw_tgamma(d)

#endif

/*

* call-seq:

* Math.gamma(x) -> Float

*

* Calculates the gamma function of x.

*

* Note that gamma(n) is same as fact(n-1) for integer n > 0.

* However gamma(n) returns float and can be an approximation.

*

* def fact(n) (1..n).inject(1) {|r,i| r*i } end

* 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }

* #=> [1, 1.0, 1]

* # [2, 1.0, 1]

* # [3, 2.0, 2]

* # [4, 6.0, 6]

* # [5, 24.0, 24]

* # [6, 120.0, 120]

* # [7, 720.0, 720]

* # [8, 5040.0, 5040]

* # [9, 40320.0, 40320]

* # [10, 362880.0, 362880]

* # [11, 3628800.0, 3628800]

* # [12, 39916800.0, 39916800]

* # [13, 479001600.0, 479001600]

* # [14, 6227020800.0, 6227020800]

* # [15, 87178291200.0, 87178291200]

* # [16, 1307674368000.0, 1307674368000]

* # [17, 20922789888000.0, 20922789888000]

* # [18, 355687428096000.0, 355687428096000]

* # [19, 6.402373705728e+15, 6402373705728000]

* # [20, 1.21645100408832e+17, 121645100408832000]

* # [21, 2.43290200817664e+18, 2432902008176640000]

* # [22, 5.109094217170944e+19, 51090942171709440000]

* # [23, 1.1240007277776077e+21, 1124000727777607680000]

* # [24, 2.5852016738885062e+22, 25852016738884976640000]

* # [25, 6.204484017332391e+23, 620448401733239439360000]

* # [26, 1.5511210043330954e+25, 15511210043330985984000000]

*

*/

static VALUE

math_gamma(VALUE obj, VALUE x)

{

static const double fact_table[] = {

/* fact(0) */ 1.0,

/* fact(1) */ 1.0,

/* fact(2) */ 2.0,

/* fact(3) */ 6.0,

/* fact(4) */ 24.0,

/* fact(5) */ 120.0,

/* fact(6) */ 720.0,

/* fact(7) */ 5040.0,

/* fact(8) */ 40320.0,

/* fact(9) */ 362880.0,

/* fact(10) */ 3628800.0,

/* fact(11) */ 39916800.0,

/* fact(12) */ 479001600.0,

/* fact(13) */ 6227020800.0,

/* fact(14) */ 87178291200.0,

/* fact(15) */ 1307674368000.0,

/* fact(16) */ 20922789888000.0,

/* fact(17) */ 355687428096000.0,

/* fact(18) */ 6402373705728000.0,

/* fact(19) */ 121645100408832000.0,

/* fact(20) */ 2432902008176640000.0,

/* fact(21) */ 51090942171709440000.0,

/* fact(22) */ 1124000727777607680000.0,

/* fact(23)=25852016738884976640000 needs 56bit mantissa which is

* impossible to represent exactly in IEEE 754 double which have

* 53bit mantissa. */

};

enum {NFACT_TABLE = numberof(fact_table)};

double d;

d = Get_Double(x);

/* check for domain error */

if (isinf(d) && signbit(d)) domain_error("gamma");

if (d == floor(d)) {

if (d < 0.0) domain_error("gamma");

if (1.0 <= d && d <= (double)NFACT_TABLE) {

return DBL2NUM(fact_table[(int)d - 1]);

}

}

return DBL2NUM(tgamma(d));

}

/*

* call-seq:

* Math.lgamma(x) -> [float, -1 or 1]

*

* Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+.

*

* Math.lgamma(x) is same as

* [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]

* but avoid overflow by Math.gamma(x) for large x.

*

* Math.lgamma(0) #=> [Infinity, 1]

*

*/

static VALUE

math_lgamma(VALUE obj, VALUE x)

{

double d;

int sign=1;

VALUE v;

d = Get_Double(x);

/* check for domain error */

if (isinf(d)) {

if (signbit(d)) domain_error("lgamma");

return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1));

}

v = DBL2NUM(lgamma_r(d, &sign));

return rb_assoc_new(v, INT2FIX(sign));

}

#define exp1(n) \

VALUE \

rb_math_##n(VALUE x)\

{\

return math_##n(rb_mMath, x);\

}

#define exp2(n) \

VALUE \

rb_math_##n(VALUE x, VALUE y)\

{\

return math_##n(rb_mMath, x, y);\

}

exp2(atan2)

exp1(cos)

exp1(cosh)

exp1(exp)

exp2(hypot)

VALUE

rb_math_log(int argc, const VALUE *argv)

{

return math_log(argc, argv, rb_mMath);

}

exp1(sin)

exp1(sinh)

#if 0

exp1(sqrt)

#endif

/*

* Document-class: Math::DomainError

*

* Raised when a mathematical function is evaluated outside of its

* domain of definition.

*

* For example, since +cos+ returns values in the range -1..1,

* its inverse function +acos+ is only defined on that interval:

*

* Math.acos(42)

*

* <em>produces:</em>

*

* Math::DomainError: Numerical argument is out of domain - "acos"

*/

/*

* Document-class: Math

*

* The Math module contains module functions for basic

* trigonometric and transcendental functions. See class

* Float for a list of constants that

* define Ruby's floating point accuracy.

*

* Domains and codomains are given only for real (not complex) numbers.

*/

void

InitVM_Math(void)

{

rb_mMath = rb_define_module("Math");

rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError);

#ifdef M_PI

/* Definition of the mathematical constant PI as a Float number. */

rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI));

#else

rb_define_const(rb_mMath, "PI", DBL2NUM(atan(1.0)*4.0));

#endif

#ifdef M_E

/* Definition of the mathematical constant E (e) as a Float number. */

rb_define_const(rb_mMath, "E", DBL2NUM(M_E));

#else

rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0)));

#endif

rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);

rb_define_module_function(rb_mMath, "cos", math_cos, 1);

rb_define_module_function(rb_mMath, "sin", math_sin, 1);

rb_define_module_function(rb_mMath, "tan", math_tan, 1);

rb_define_module_function(rb_mMath, "acos", math_acos, 1);

rb_define_module_function(rb_mMath, "asin", math_asin, 1);

rb_define_module_function(rb_mMath, "atan", math_atan, 1);

rb_define_module_function(rb_mMath, "cosh", math_cosh, 1);

rb_define_module_function(rb_mMath, "sinh", math_sinh, 1);

rb_define_module_function(rb_mMath, "tanh", math_tanh, 1);