mirror of
https://github.com/mruby/mruby
synced 2026-06-08 16:11:16 +00:00
Yukihiro "Matz" Matsumoto
755 lines
16 KiB
C
755 lines
16 KiB
C
/*
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** math.c - Math module
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**
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** See Copyright Notice in mruby.h
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*/
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#include <mruby.h>
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#ifdef MRB_NO_FLOAT
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# error Math conflicts with 'MRB_NO_FLOAT' configuration
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#endif
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#include <mruby/array.h>
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#include <mruby/presym.h>
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static void
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domain_error(mrb_state *mrb, const char *func)
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{
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struct RClass *math = mrb_module_get_id(mrb, MRB_SYM(Math));
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struct RClass *domainerror = mrb_class_get_under_id(mrb, math, MRB_SYM(DomainError));
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mrb_raisef(mrb, domainerror, "Numerical argument is out of domain - %s", func);
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}
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/* math functions not provided by Microsoft Visual C++ 2012 or older */
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#if defined _MSC_VER && _MSC_VER <= 1700
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double
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asinh(double x)
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{
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double xa, ya, y;
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/* Basic formula loses precision for x < 0, but asinh is an odd function */
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xa = fabs(x);
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if (xa > 3.16227E+18) {
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/* Prevent x*x from overflowing; basic formula reduces to log(2*x) */
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ya = log(xa) + 0.69314718055994530942;
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}
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else {
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/* Basic formula for asinh */
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ya = log(xa + sqrt(xa*xa + 1.0));
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}
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y = _copysign(ya, x);
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return y;
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}
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double
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acosh(double x)
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{
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double y;
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if (x > 3.16227E+18) {
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/* Prevent x*x from overflowing; basic formula reduces to log(2*x) */
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y = log(x) + 0.69314718055994530942;
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}
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else {
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/* Basic formula for acosh */
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y = log(x + sqrt(x*x - 1.0));
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}
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return y;
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}
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double
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atanh(double x)
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{
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double y;
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if (fabs(x) < 1E-2) {
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/* The sums 1+x and 1-x lose precision for small x. Use the polynomial
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instead. */
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double x2 = x * x;
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y = x*(1.0 + x2*(1.0/3.0 + x2*(1.0/5.0 + x2*(1.0/7.0))));
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}
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else {
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/* Basic formula for atanh */
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y = 0.5 * (log1p(x) - log1p(-x));
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}
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return y;
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}
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double
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cbrt(double x)
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{
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double xa, ya, y;
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/* pow(x, y) is undefined for x < 0 and y not an integer, but cbrt is an
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odd function */
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xa = fabs(x);
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ya = pow(xa, 1.0/3.0);
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y = _copysign(ya, x);
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return y;
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}
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/* Declaration of complementary Error function */
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double erfc(double x);
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/*
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** Implementations of error functions
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** credits to http://www.digitalmars.com/archives/cplusplus/3634.html
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*/
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/* Implementation of Error function */
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double
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erf(double x)
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{
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static const double two_sqrtpi = 1.128379167095512574;
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double sum = x;
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double term = x;
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double xsqr = x*x;
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int j= 1;
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if (fabs(x) > 2.2) {
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return 1.0 - erfc(x);
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}
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do {
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term *= xsqr/j;
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sum -= term/(2*j+1);
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j++;
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term *= xsqr/j;
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sum += term/(2*j+1);
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j++;
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if (sum == 0) break;
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} while (fabs(term/sum) > DBL_EPSILON);
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return two_sqrtpi*sum;
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}
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/* Implementation of complementary Error function */
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double
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erfc(double x)
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{
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static const double one_sqrtpi = 0.564189583547756287;
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double a = 1;
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double b = x;
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double c = x;
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double d = x*x+0.5;
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double q1;
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double q2 = b/d;
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double n = 1.0;
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if (fabs(x) < 2.2) {
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return erfc(x);
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}
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if (x < 0.0) { /*signbit(x)*/
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return 2.0 - erfc(-x);
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}
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do {
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double t = a*n+b*x;
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a = b;
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b = t;
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t = c*n+d*x;
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c = d;
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d = t;
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n += 0.5;
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q1 = q2;
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q2 = b/d;
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} while (fabs(q1-q2)/q2 > DBL_EPSILON);
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return one_sqrtpi*exp(-x*x)*q2;
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}
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#endif
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#if defined __FreeBSD__ && !defined __FreeBSD_version
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#include <osreldate.h> /* for __FreeBSD_version */
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#endif
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#if (defined _MSC_VER && _MSC_VER < 1800) || defined __ANDROID__ || (defined __FreeBSD__ && __FreeBSD_version < 803000)
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double
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log2(double x)
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{
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return log10(x)/log10(2.0);
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}
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#endif
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#define get_float_arg(mrb) mrb_as_float((mrb), mrb_get_arg1(mrb))
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/*
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TRIGONOMETRIC FUNCTIONS
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*/
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/*
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* call-seq:
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* Math.sin(x) -> float
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*
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* Computes the sine of *x* (expressed in radians). Returns
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* -1..1.
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*/
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static mrb_value
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math_sin(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = sin(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.cos(x) -> float
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*
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* Computes the cosine of *x* (expressed in radians). Returns
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* -1..1.
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*/
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static mrb_value
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math_cos(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = cos(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.tan(x) -> float
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*
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* Returns the tangent of *x* (expressed in radians).
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*/
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static mrb_value
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math_tan(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = tan(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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INVERSE TRIGONOMETRIC FUNCTIONS
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*/
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/*
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* call-seq:
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* Math.asin(x) -> float
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*
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* Computes the arc sine of *x*.
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* @return computed value between `-(PI/2)` and `(PI/2)`.
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*/
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static mrb_value
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math_asin(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < -1.0 || x > 1.0) {
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domain_error(mrb, "asin");
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}
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x = asin(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.acos(x) -> float
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*
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* Computes the arc cosine of *x*. Returns 0..PI.
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*/
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static mrb_value
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math_acos(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < -1.0 || x > 1.0) {
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domain_error(mrb, "acos");
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}
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x = acos(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.atan(x) -> float
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*
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* Computes the arc tangent of *x*. Returns `-(PI/2) .. (PI/2)`.
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*/
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static mrb_value
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math_atan(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = atan(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.atan2(y, x) -> float
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*
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* Computes the arc tangent given *y* and *x*. Returns
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* -PI..PI.
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*
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* Math.atan2(-0.0, -1.0) #=> -3.141592653589793
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* Math.atan2(-1.0, -1.0) #=> -2.356194490192345
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* Math.atan2(-1.0, 0.0) #=> -1.5707963267948966
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* Math.atan2(-1.0, 1.0) #=> -0.7853981633974483
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* Math.atan2(-0.0, 1.0) #=> -0.0
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* Math.atan2(0.0, 1.0) #=> 0.0
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* Math.atan2(1.0, 1.0) #=> 0.7853981633974483
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* Math.atan2(1.0, 0.0) #=> 1.5707963267948966
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* Math.atan2(1.0, -1.0) #=> 2.356194490192345
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* Math.atan2(0.0, -1.0) #=> 3.141592653589793
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*
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*/
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static mrb_value
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math_atan2(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x, y;
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mrb_get_args(mrb, "ff", &x, &y);
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x = atan2(x, y);
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return mrb_float_value(mrb, x);
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}
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/*
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HYPERBOLIC TRIG FUNCTIONS
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*/
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/*
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* call-seq:
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* Math.sinh(x) -> float
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*
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* Computes the hyperbolic sine of *x* (expressed in
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* radians).
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*/
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static mrb_value
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math_sinh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = sinh(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.cosh(x) -> float
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*
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* Computes the hyperbolic cosine of *x* (expressed in radians).
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*/
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static mrb_value
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math_cosh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = cosh(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.tanh() -> float
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*
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* Computes the hyperbolic tangent of *x* (expressed in
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* radians).
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*/
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static mrb_value
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math_tanh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = tanh(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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INVERSE HYPERBOLIC TRIG FUNCTIONS
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*/
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/*
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* call-seq:
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* Math.asinh(x) -> float
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*
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* Computes the inverse hyperbolic sine of *x*.
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*/
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static mrb_value
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math_asinh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = asinh(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.acosh(x) -> float
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*
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* Computes the inverse hyperbolic cosine of *x*.
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*/
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static mrb_value
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math_acosh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < 1.0) {
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domain_error(mrb, "acosh");
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}
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x = acosh(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.atanh(x) -> float
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*
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* Computes the inverse hyperbolic tangent of *x*.
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*/
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static mrb_value
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math_atanh(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < -1.0 || x > 1.0) {
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domain_error(mrb, "atanh");
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}
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x = atanh(x);
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return mrb_float_value(mrb, x);
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}
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/*
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EXPONENTIALS AND LOGARITHMS
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*/
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/*
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* call-seq:
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* Math.exp(x) -> float
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*
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* Returns e**x.
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*
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* Math.exp(0) #=> 1.0
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* Math.exp(1) #=> 2.718281828459045
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* Math.exp(1.5) #=> 4.4816890703380645
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*
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*/
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static mrb_value
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math_exp(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = exp(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.expm1(x) -> float
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*
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* Returns exp(x) - 1.
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*/
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static mrb_value
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math_expm1(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = expm1(get_float_arg(mrb));
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.log1p(x) -> float
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*
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* Returns log(1 + x).
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*/
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static mrb_value
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math_log1p(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < -1.0) {
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domain_error(mrb, "log1p");
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}
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x = log1p(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.log(numeric) -> float
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* Math.log(num,base) -> float
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*
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* Returns the natural logarithm of *numeric*.
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* If additional second argument is given, it will be the base
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* of logarithm.
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*
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* Math.log(1) #=> 0.0
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* Math.log(Math::E) #=> 1.0
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* Math.log(Math::E**3) #=> 3.0
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* Math.log(12,3) #=> 2.2618595071429146
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*
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*/
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static mrb_value
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math_log(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x, base;
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mrb_int argc;
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argc = mrb_get_args(mrb, "f|f", &x, &base);
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if (x < 0.0) {
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domain_error(mrb, "log");
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}
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x = log(x);
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if (argc == 2) {
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if (base < 0.0) {
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domain_error(mrb, "log");
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}
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x /= log(base);
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}
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.log2(numeric) -> float
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*
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* Returns the base 2 logarithm of *numeric*.
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*
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* Math.log2(1) #=> 0.0
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* Math.log2(2) #=> 1.0
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* Math.log2(32768) #=> 15.0
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* Math.log2(65536) #=> 16.0
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*
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*/
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static mrb_value
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math_log2(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < 0.0) {
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domain_error(mrb, "log2");
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}
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x = log2(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.log10(numeric) -> float
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*
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* Returns the base 10 logarithm of *numeric*.
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*
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* Math.log10(1) #=> 0.0
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* Math.log10(10) #=> 1.0
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* Math.log10(10**100) #=> 100.0
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*
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*/
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static mrb_value
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math_log10(mrb_state *mrb, mrb_value obj)
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{
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mrb_float x = get_float_arg(mrb);
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if (x < 0.0) {
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domain_error(mrb, "log10");
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}
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x = log10(x);
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return mrb_float_value(mrb, x);
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}
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/*
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* call-seq:
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* Math.sqrt(numeric) -> float
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*
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* Returns the square root of *numeric*.
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*
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*/
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static mrb_value
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math_sqrt(mrb_state *mrb, mrb_value obj)
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{
|
|
mrb_float x = get_float_arg(mrb);
|
|
|
|
if (x < 0.0) {
|
|
domain_error(mrb, "sqrt");
|
|
}
|
|
x = sqrt(x);
|
|
|
|
return mrb_float_value(mrb, x);
|
|
}
|
|
|
|
|
|
/*
|
|
* call-seq:
|
|
* Math.cbrt(numeric) -> float
|
|
*
|
|
* Returns the cube root of *numeric*.
|
|
*
|
|
* -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 = cbrt(get_float_arg(mrb));
|
|
return mrb_float_value(mrb, x);
|
|
}
|
|
|
|
|
|
/*
|
|
* call-seq:
|
|
* Math.frexp(numeric) -> [ fraction, exponent ]
|
|
*
|
|
* Returns a two-element array containing the normalized fraction (a
|
|
* `Float`) and exponent (a `Integer`) of
|
|
* *numeric*.
|
|
*
|
|
* 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 = get_float_arg(mrb);
|
|
int exp;
|
|
|
|
x = frexp(x, &exp);
|
|
|
|
return mrb_assoc_new(mrb, mrb_float_value(mrb, x), mrb_fixnum_value(exp));
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* Math.ldexp(flt, int) -> float
|
|
*
|
|
* Returns the value of *flt**(2***int*).
|
|
*
|
|
* 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, (int)i);
|
|
|
|
return mrb_float_value(mrb, x);
|
|
}
|
|
|
|
/*
|
|
* 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 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(mrb, 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 = erf(get_float_arg(mrb));
|
|
return mrb_float_value(mrb, 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 = erfc(get_float_arg(mrb));
|
|
return mrb_float_value(mrb, x);
|
|
}
|
|
|
|
/* ------------------------------------------------------------------------*/
|
|
void
|
|
mrb_mruby_math_gem_init(mrb_state* mrb)
|
|
{
|
|
struct RClass *math = mrb_define_module_id(mrb, MRB_SYM(Math));
|
|
|
|
mrb_define_class_under_id(mrb, math, MRB_SYM(DomainError), E_STANDARD_ERROR);
|
|
|
|
#ifdef M_PI
|
|
mrb_define_const_id(mrb, math, MRB_SYM(PI), mrb_float_value(mrb, M_PI));
|
|
#else
|
|
mrb_define_const_id(mrb, math, MRB_SYM(PI), mrb_float_value(mrb, atan(1.0)*4.0));
|
|
#endif
|
|
|
|
#ifdef M_E
|
|
mrb_define_const_id(mrb, math, MRB_SYM(E), mrb_float_value(mrb, M_E));
|
|
#else
|
|
mrb_define_const_id(mrb, math, MRB_SYM(E), mrb_float_value(mrb, exp(1.0)));
|
|
#endif
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(sin), math_sin, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(cos), math_cos, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(tan), math_tan, MRB_ARGS_REQ(1));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(asin), math_asin, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(acos), math_acos, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(atan), math_atan, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(atan2), math_atan2, MRB_ARGS_REQ(2));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(sinh), math_sinh, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(cosh), math_cosh, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(tanh), math_tanh, MRB_ARGS_REQ(1));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(asinh), math_asinh, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(acosh), math_acosh, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(atanh), math_atanh, MRB_ARGS_REQ(1));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(exp), math_exp, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(expm1), math_expm1, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(log1p), math_log1p, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(log), math_log, MRB_ARGS_REQ(1)|MRB_ARGS_OPT(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(log2), math_log2, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(log10), math_log10, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(sqrt), math_sqrt, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(cbrt), math_cbrt, MRB_ARGS_REQ(1));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(frexp), math_frexp, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(ldexp), math_ldexp, MRB_ARGS_REQ(2));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(hypot), math_hypot, MRB_ARGS_REQ(2));
|
|
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(erf), math_erf, MRB_ARGS_REQ(1));
|
|
mrb_define_module_function_id(mrb, math, MRB_SYM(erfc), math_erfc, MRB_ARGS_REQ(1));
|
|
}
|
|
|
|
void
|
|
mrb_mruby_math_gem_final(mrb_state* mrb)
|
|
{
|
|
}
|