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DEFINITIONS
This source file includes following definitions.
- domain_check
- infinity_check
- math_atan2
- math_cos
- math_sin
- math_tan
- math_acos
- math_asin
- math_atan
- cosh
- math_cosh
- sinh
- math_sinh
- tanh
- math_tanh
- math_acosh
- math_asinh
- math_atanh
- math_exp
- math_log
- log2
- math_log2
- math_log10
- math_sqrt
- math_cbrt
- math_frexp
- math_ldexp
- math_hypot
- math_erf
- math_erfc
- math_gamma
- math_lgamma
- exp2
- exp1
/**********************************************************************
math.c -
$Author: yugui $
created at: Tue Jan 25 14:12:56 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#include "ruby/ruby.h"
#include <math.h>
#include <errno.h>
VALUE rb_mMath;
extern VALUE rb_to_float(VALUE val);
#define Need_Float(x) (x) = rb_to_float(x)
#define Need_Float2(x,y) do {\
Need_Float(x);\
Need_Float(y);\
} while (0)
static void
domain_check(double x, double y, const char *msg)
{
while(1) {
if (errno) {
rb_sys_fail(msg);
}
if (isnan(y)) {
if (isnan(x)) break;
#if defined(EDOM)
errno = EDOM;
#elif defined(ERANGE)
errno = ERANGE;
#endif
continue;
}
break;
}
}
static void
infinity_check(VALUE arg, double res, const char *msg)
{
while(1) {
if (errno) {
rb_sys_fail(msg);
}
if (isinf(res) && !isinf(RFLOAT_VALUE(arg))) {
#if defined(EDOM)
errno = EDOM;
#elif defined(ERANGE)
errno = ERANGE;
#endif
continue;
}
break;
}
}
/*
* call-seq:
* Math.atan2(y, x) => float
*
* Computes the arc tangent given <i>y</i> and <i>x</i>. Returns
* -PI..PI.
*
*/
static VALUE
math_atan2(VALUE obj, VALUE y, VALUE x)
{
Need_Float2(y, x);
return DBL2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.cos(x) => float
*
* Computes the cosine of <i>x</i> (expressed in radians). Returns
* -1..1.
*/
static VALUE
math_cos(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(cos(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.sin(x) => float
*
* Computes the sine of <i>x</i> (expressed in radians). Returns
* -1..1.
*/
static VALUE
math_sin(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(sin(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.tan(x) => float
*
* Returns the tangent of <i>x</i> (expressed in radians).
*/
static VALUE
math_tan(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(tan(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.acos(x) => float
*
* Computes the arc cosine of <i>x</i>. Returns 0..PI.
*/
static VALUE
math_acos(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = acos(d0);
domain_check(d0, d, "acos");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.asin(x) => float
*
* Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}.
*/
static VALUE
math_asin(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = asin(d0);
domain_check(d0, d, "asin");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.atan(x) => float
*
* Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
*/
static VALUE
math_atan(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(atan(RFLOAT_VALUE(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 <i>x</i> (expressed in radians).
*/
static VALUE
math_cosh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(cosh(RFLOAT_VALUE(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 <i>x</i> (expressed in
* radians).
*/
static VALUE
math_sinh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(sinh(RFLOAT_VALUE(x)));
}
#ifndef HAVE_TANH
double
tanh(double x)
{
return sinh(x) / cosh(x);
}
#endif
/*
* call-seq:
* Math.tanh() => float
*
* Computes the hyperbolic tangent of <i>x</i> (expressed in
* radians).
*/
static VALUE
math_tanh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(tanh(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.acosh(x) => float
*
* Computes the inverse hyperbolic cosine of <i>x</i>.
*/
static VALUE
math_acosh(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = acosh(d0);
domain_check(d0, d, "acosh");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.asinh(x) => float
*
* Computes the inverse hyperbolic sine of <i>x</i>.
*/
static VALUE
math_asinh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(asinh(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.atanh(x) => float
*
* Computes the inverse hyperbolic tangent of <i>x</i>.
*/
static VALUE
math_atanh(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = atanh(d0);
domain_check(d0, d, "atanh");
infinity_check(x, d, "atanh");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.exp(x) => float
*
* Returns e**x.
*/
static VALUE
math_exp(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(exp(RFLOAT_VALUE(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
/*
* call-seq:
* Math.log(numeric) => float
* Math.log(num,base) => float
*
* Returns the natural logarithm of <i>numeric</i>.
* If additional second argument is given, it will be the base
* of logarithm.
*/
static VALUE
math_log(int argc, VALUE *argv)
{
VALUE x, base;
double d0, d;
rb_scan_args(argc, argv, "11", &x, &base);
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = log(d0);
if (argc == 2) {
Need_Float(base);
d /= log(RFLOAT_VALUE(base));
}
domain_check(d0, d, "log");
infinity_check(x, d, "log");
return DBL2NUM(d);
}
#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(numeric) => float
*
* Returns the base 2 logarithm of <i>numeric</i>.
*/
static VALUE
math_log2(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = log2(d0);
domain_check(d0, d, "log2");
infinity_check(x, d, "log2");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.log10(numeric) => float
*
* Returns the base 10 logarithm of <i>numeric</i>.
*/
static VALUE
math_log10(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = log10(d0);
domain_check(d0, d, "log10");
infinity_check(x, d, "log10");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.sqrt(numeric) => float
*
* Returns the non-negative square root of <i>numeric</i>.
*
* 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 d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = sqrt(d0);
domain_check(d0, d, "sqrt");
return DBL2NUM(d);
}
/*
* call-seq:
* Math.cbrt(numeric) => float
*
* Returns the cube root of <i>numeric</i>.
*
* -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)
{
Need_Float(x);
return DBL2NUM(cbrt(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.frexp(numeric) => [ fraction, exponent ]
*
* Returns a two-element array containing the normalized fraction (a
* <code>Float</code>) and exponent (a <code>Fixnum</code>) of
* <i>numeric</i>.
*
* 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;
Need_Float(x);
d = frexp(RFLOAT_VALUE(x), &exp);
return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
}
/*
* call-seq:
* Math.ldexp(flt, int) -> float
*
* Returns the value of <i>flt</i>*(2**<i>int</i>).
*
* fraction, exponent = Math.frexp(1234)
* Math.ldexp(fraction, exponent) #=> 1234.0
*/
static VALUE
math_ldexp(VALUE obj, VALUE x, VALUE n)
{
Need_Float(x);
return DBL2NUM(ldexp(RFLOAT_VALUE(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 <i>x</i> and <i>y</i>.
*
* Math.hypot(3, 4) #=> 5.0
*/
static VALUE
math_hypot(VALUE obj, VALUE x, VALUE y)
{
Need_Float2(x, y);
return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
}
/*
* call-seq:
* Math.erf(x) => float
*
* Calculates the error function of x.
*/
static VALUE
math_erf(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(erf(RFLOAT_VALUE(x)));
}
/*
* call-seq:
* Math.erfc(x) => float
*
* Calculates the complementary error function of x.
*/
static VALUE
math_erfc(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(erfc(RFLOAT_VALUE(x)));
}
/*
* 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 possibly has error in calculation.
*
* def fact(n) (1..n).inject(1) {|r,i| r*i } end
* 0.upto(25) {|i| p [i, Math.gamma(i+1), fact(i)] }
* #=>
* [0, 1.0, 1]
* [1, 1.0, 1]
* [2, 2.0, 2]
* [3, 6.0, 6]
* [4, 24.0, 24]
* [5, 120.0, 120]
* [6, 720.0, 720]
* [7, 5040.0, 5040]
* [8, 40320.0, 40320]
* [9, 362880.0, 362880]
* [10, 3628800.0, 3628800]
* [11, 39916800.0, 39916800]
* [12, 479001599.999999, 479001600]
* [13, 6227020800.00001, 6227020800]
* [14, 87178291199.9998, 87178291200]
* [15, 1307674368000.0, 1307674368000]
* [16, 20922789888000.0, 20922789888000]
* [17, 3.55687428096001e+14, 355687428096000]
* [18, 6.40237370572799e+15, 6402373705728000]
* [19, 1.21645100408832e+17, 121645100408832000]
* [20, 2.43290200817664e+18, 2432902008176640000]
* [21, 5.10909421717094e+19, 51090942171709440000]
* [22, 1.12400072777761e+21, 1124000727777607680000]
* [23, 2.58520167388851e+22, 25852016738884976640000]
* [24, 6.20448401733239e+23, 620448401733239439360000]
* [25, 1.5511210043331e+25, 15511210043330985984000000]
*
*/
static VALUE
math_gamma(VALUE obj, VALUE x)
{
double d0, d;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = tgamma(d0);
domain_check(d0, d, "gamma");
return DBL2NUM(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.
*/
static VALUE
math_lgamma(VALUE obj, VALUE x)
{
double d0, d;
int sign;
VALUE v;
Need_Float(x);
errno = 0;
d0 = RFLOAT_VALUE(x);
d = lgamma_r(d0, &sign);
domain_check(d0, d, "lgamma");
v = DBL2NUM(d);
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, VALUE *argv)
{
return math_log(argc, argv);
}
exp1(sin)
exp1(sinh)
exp1(sqrt)
/*
* The <code>Math</code> module contains module functions for basic
* trigonometric and transcendental functions. See class
* <code>Float</code> for a list of constants that
* define Ruby's floating point accuracy.
*/
void
Init_Math(void)
{
rb_mMath = rb_define_module("Math");
#ifdef M_PI
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
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);
rb_define_module_function(rb_mMath, "acosh", math_acosh, 1);
rb_define_module_function(rb_mMath, "asinh", math_asinh, 1);
rb_define_module_function(rb_mMath, "atanh", math_atanh, 1);
rb_define_module_function(rb_mMath, "exp", math_exp, 1);
rb_define_module_function(rb_mMath, "log", math_log, -1);
rb_define_module_function(rb_mMath, "log2", math_log2, 1);
rb_define_module_function(rb_mMath, "log10", math_log10, 1);
rb_define_module_function(rb_mMath, "sqrt", math_sqrt, 1);
rb_define_module_function(rb_mMath, "cbrt", math_cbrt, 1);
rb_define_module_function(rb_mMath, "frexp", math_frexp, 1);
rb_define_module_function(rb_mMath, "ldexp", math_ldexp, 2);
rb_define_module_function(rb_mMath, "hypot", math_hypot, 2);
rb_define_module_function(rb_mMath, "erf", math_erf, 1);
rb_define_module_function(rb_mMath, "erfc", math_erfc, 1);
rb_define_module_function(rb_mMath, "gamma", math_gamma, 1);
rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1);
}
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