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/*
** math.c - Math module
**
** See Copyright Notice in mruby.h
*/
#include "mruby.h"
#include "mruby/array.h"
#ifdef ENABLE_MATH
#include <math.h>
#define domain_error(msg) \
mrb_raise(mrb, E_RANGE_ERROR, "Numerical argument is out of domain - " #msg);
/* math functions not provided under Microsoft Visual C++ */
#ifdef _MSC_VER
#define MATH_TOLERANCE 1E-12
#define asinh(x) log(x + sqrt(pow(x,2.0) + 1))
#define acosh(x) log(x + sqrt(pow(x,2.0) - 1))
#define atanh(x) (log(1+x) - log(1-x))/2.0
#define cbrt(x) pow(x,1.0/3.0)
/* Declaration of complementary Error function */
double
erfc(double x);
/*
** Implementations of error functions
** credits to http://www.digitalmars.com/archives/cplusplus/3634.html
*/
/* Implementation of Error function */
double
erf(double x)
{
static const double two_sqrtpi = 1.128379167095512574;
double sum = x;
double term = x;
double xsqr = x*x;
int j= 1;
if (fabs(x) > 2.2) {
return 1.0 - erfc(x);
}
do {
term *= xsqr/j;
sum -= term/(2*j+1);
++j;
term *= xsqr/j;
sum += term/(2*j+1);
++j;
} while (fabs(term)/sum > MATH_TOLERANCE);
return two_sqrtpi*sum;
}
/* Implementation of complementary Error function */
double
erfc(double x)
{
static const double one_sqrtpi= 0.564189583547756287;
double a = 1;
double b = x;
double c = x;
double d = x*x+0.5;
double q1, q2;
double n = 1.0;
double t;
if (fabs(x) < 2.2) {
return 1.0 - erf(x);
}
if (x < 0.0) { /*signbit(x)*/
return 2.0 - erfc(-x);
}
do {
t = a*n+b*x;
a = b;
b = t;
t = c*n+d*x;
c = d;
d = t;
n += 0.5;
q1 = q2;
q2 = b/d;
} while (fabs(q1-q2)/q2 > MATH_TOLERANCE);
return one_sqrtpi*exp(-x*x)*q2;
}
#endif
/*
TRIGONOMETRIC FUNCTIONS
*/
/*
* call-seq:
* Math.sin(x) -> float
*
* Computes the sine of <i>x</i> (expressed in radians). Returns
* -1..1.
*/
static mrb_value
math_sin(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = sin(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.cos(x) -> float
*
* Computes the cosine of <i>x</i> (expressed in radians). Returns
* -1..1.
*/
static mrb_value
math_cos(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = cos(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.tan(x) -> float
*
* Returns the tangent of <i>x</i> (expressed in radians).
*/
static mrb_value
math_tan(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = tan(x);
return mrb_float_value(x);
}
/*
INVERSE TRIGONOMETRIC FUNCTIONS
*/
/*
* call-seq:
* Math.asin(x) -> float
*
* Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}.
*/
static mrb_value
math_asin(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = asin(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.acos(x) -> float
*
* Computes the arc cosine of <i>x</i>. Returns 0..PI.
*/
static mrb_value
math_acos(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = acos(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.atan(x) -> float
*
* Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
*/
static mrb_value
math_atan(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = atan(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.atan2(y, x) -> float
*
* Computes the arc tangent given <i>y</i> and <i>x</i>. Returns
* -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
*
*/
static mrb_value
math_atan2(mrb_state *mrb, mrb_value obj)
{
mrb_float x, y;
mrb_get_args(mrb, "ff", &x, &y);
x = atan2(x, y);
return mrb_float_value(x);
}
/*
HYPERBOLIC TRIG FUNCTIONS
*/
/*
* call-seq:
* Math.sinh(x) -> float
*
* Computes the hyperbolic sine of <i>x</i> (expressed in
* radians).
*/
static mrb_value
math_sinh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = sinh(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.cosh(x) -> float
*
* Computes the hyperbolic cosine of <i>x</i> (expressed in radians).
*/
static mrb_value
math_cosh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = cosh(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.tanh() -> float
*
* Computes the hyperbolic tangent of <i>x</i> (expressed in
* radians).
*/
static mrb_value
math_tanh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = tanh(x);
return mrb_float_value(x);
}
/*
INVERSE HYPERBOLIC TRIG FUNCTIONS
*/
/*
* call-seq:
* Math.asinh(x) -> float
*
* Computes the inverse hyperbolic sine of <i>x</i>.
*/
static mrb_value
math_asinh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = asinh(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.acosh(x) -> float
*
* Computes the inverse hyperbolic cosine of <i>x</i>.
*/
static mrb_value
math_acosh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = acosh(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.atanh(x) -> float
*
* Computes the inverse hyperbolic tangent of <i>x</i>.
*/
static mrb_value
math_atanh(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = atanh(x);
return mrb_float_value(x);
}
/*
EXPONENTIALS AND LOGARITHMS
*/
#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
#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.exp(x) -> float
*
* Returns e**x.
*
* Math.exp(0) #=> 1.0
* Math.exp(1) #=> 2.718281828459045
* Math.exp(1.5) #=> 4.4816890703380645
*
*/
static mrb_value
math_exp(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = exp(x);
return mrb_float_value(x);
}
/*
* 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.
*
* 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 mrb_value
math_log(mrb_state *mrb, mrb_value obj)
{
mrb_float x, base;
int argc;
argc = mrb_get_args(mrb, "f|f", &x, &base);
x = log(x);
if (argc == 2) {
x /= log(base);
}
return mrb_float_value(x);
}
/*
* call-seq:
* Math.log2(numeric) -> float
*
* Returns the base 2 logarithm of <i>numeric</i>.
*
* Math.log2(1) #=> 0.0
* Math.log2(2) #=> 1.0
* Math.log2(32768) #=> 15.0
* Math.log2(65536) #=> 16.0
*
*/
static mrb_value
math_log2(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = log2(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.log10(numeric) -> float
*
* Returns the base 10 logarithm of <i>numeric</i>.
*
* Math.log10(1) #=> 0.0
* Math.log10(10) #=> 1.0
* Math.log10(10**100) #=> 100.0
*
*/
static mrb_value
math_log10(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = log10(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.sqrt(numeric) -> float
*
* Returns the square root of <i>numeric</i>.
*
*/
static mrb_value
math_sqrt(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = sqrt(x);
return mrb_float_value(x);
}
/*
* 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 mrb_value
math_cbrt(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = cbrt(x);
return mrb_float_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 mrb_value
math_frexp(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
int exp;
mrb_get_args(mrb, "f", &x);
x = frexp(x, &exp);
return mrb_assoc_new(mrb, mrb_float_value(x), mrb_fixnum_value(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 mrb_value
math_ldexp(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_int i;
mrb_get_args(mrb, "fi", &x, &i);
x = ldexp(x, i);
return mrb_float_value(x);
}
/*
* 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 mrb_value
math_hypot(mrb_state *mrb, mrb_value obj)
{
mrb_float x, y;
mrb_get_args(mrb, "ff", &x, &y);
x = hypot(x, y);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.erf(x) -> float
*
* Calculates the error function of x.
*/
static mrb_value
math_erf(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = erf(x);
return mrb_float_value(x);
}
/*
* call-seq:
* Math.erfc(x) -> float
*
* Calculates the complementary error function of x.
*/
static mrb_value
math_erfc(mrb_state *mrb, mrb_value obj)
{
mrb_float x;
mrb_get_args(mrb, "f", &x);
x = erfc(x);
return mrb_float_value(x);
}
/* ------------------------------------------------------------------------*/
void
mrb_init_math(mrb_state *mrb)
{
struct RClass *mrb_math;
mrb_math = mrb_define_module(mrb, "Math");
#ifdef M_PI
mrb_define_const(mrb, mrb_math, "PI", mrb_float_value(M_PI));
#else
mrb_define_const(mrb, mrb_math, "PI", mrb_float_value(atan(1.0)*4.0));
#endif
#ifdef M_E
mrb_define_const(mrb, mrb_math, "E", mrb_float_value(M_E));
#else
mrb_define_const(mrb, mrb_math, "E", mrb_float_value(exp(1.0)));
#endif
#ifdef MRB_USE_FLOAT
mrb_define_const(mrb, mrb_math, "TOLERANCE", mrb_float_value(1e-5));
#else
mrb_define_const(mrb, mrb_math, "TOLERANCE", mrb_float_value(1e-12));
#endif
mrb_define_module_function(mrb, mrb_math, "sin", math_sin, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "cos", math_cos, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "tan", math_tan, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "asin", math_asin, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "acos", math_acos, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "atan", math_atan, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "atan2", math_atan2, ARGS_REQ(2));
mrb_define_module_function(mrb, mrb_math, "sinh", math_sinh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "cosh", math_cosh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "tanh", math_tanh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "asinh", math_asinh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "acosh", math_acosh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "atanh", math_atanh, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "exp", math_exp, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "log", math_log, ARGS_REQ(1)|ARGS_OPT(1));
mrb_define_module_function(mrb, mrb_math, "log2", math_log2, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "log10", math_log10, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "sqrt", math_sqrt, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "cbrt", math_cbrt, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "frexp", math_frexp, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "ldexp", math_ldexp, ARGS_REQ(2));
mrb_define_module_function(mrb, mrb_math, "hypot", math_hypot, ARGS_REQ(2));
mrb_define_module_function(mrb, mrb_math, "erf", math_erf, ARGS_REQ(1));
mrb_define_module_function(mrb, mrb_math, "erfc", math_erfc, ARGS_REQ(1));
}
#endif /* ENABLE_MATH */
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