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fcd2fb4e87
lgamma(NaN) doesn't set the sign in OpenSolaris. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@26608 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
815 lines
17 KiB
C
815 lines
17 KiB
C
/**********************************************************************
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math.c -
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$Author$
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created at: Tue Jan 25 14:12:56 JST 1994
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Copyright (C) 1993-2007 Yukihiro Matsumoto
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**********************************************************************/
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#include "ruby/ruby.h"
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#include <math.h>
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#include <errno.h>
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#define numberof(array) (int)(sizeof(array) / sizeof((array)[0]))
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VALUE rb_mMath;
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extern VALUE rb_to_float(VALUE val);
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#define Need_Float(x) do {if (TYPE(x) != T_FLOAT) {(x) = rb_to_float(x);}} while(0)
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#define Need_Float2(x,y) do {\
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Need_Float(x);\
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Need_Float(y);\
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} while (0)
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static void
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domain_check(double x, double y, const char *msg)
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{
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if (errno) {
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if (isinf(y)) return;
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}
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else {
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if (!isnan(y)) return;
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else if (isnan(x)) return;
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else {
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#if defined(EDOM)
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errno = EDOM;
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#else
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errno = ERANGE;
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#endif
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}
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}
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rb_sys_fail(msg);
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}
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static void
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infinity_check(VALUE arg, double res, const char *msg)
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{
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while(1) {
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if (errno) {
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rb_sys_fail(msg);
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}
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if (isinf(res) && !isinf(RFLOAT_VALUE(arg))) {
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#if defined(EDOM)
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errno = EDOM;
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#elif defined(ERANGE)
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errno = ERANGE;
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#endif
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continue;
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}
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break;
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}
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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 <i>y</i> and <i>x</i>. 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 VALUE
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math_atan2(VALUE obj, VALUE y, VALUE x)
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{
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Need_Float2(y, x);
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return DBL2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(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 <i>x</i> (expressed in radians). Returns
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* -1..1.
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*/
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static VALUE
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math_cos(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(cos(RFLOAT_VALUE(x)));
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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 <i>x</i> (expressed in radians). Returns
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* -1..1.
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*/
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static VALUE
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math_sin(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(sin(RFLOAT_VALUE(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 <i>x</i> (expressed in radians).
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*/
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static VALUE
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math_tan(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(tan(RFLOAT_VALUE(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 <i>x</i>. Returns 0..PI.
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*/
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static VALUE
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math_acos(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = acos(d0);
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domain_check(d0, d, "acos");
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return DBL2NUM(d);
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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 <i>x</i>. Returns -{PI/2} .. {PI/2}.
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*/
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static VALUE
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math_asin(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = asin(d0);
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domain_check(d0, d, "asin");
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return DBL2NUM(d);
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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 <i>x</i>. Returns -{PI/2} .. {PI/2}.
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*/
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static VALUE
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math_atan(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(atan(RFLOAT_VALUE(x)));
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}
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#ifndef HAVE_COSH
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double
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cosh(double x)
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{
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return (exp(x) + exp(-x)) / 2;
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}
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#endif
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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 <i>x</i> (expressed in radians).
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*/
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static VALUE
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math_cosh(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(cosh(RFLOAT_VALUE(x)));
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}
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#ifndef HAVE_SINH
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double
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sinh(double x)
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{
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return (exp(x) - exp(-x)) / 2;
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}
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#endif
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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 <i>x</i> (expressed in
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* radians).
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*/
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static VALUE
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math_sinh(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(sinh(RFLOAT_VALUE(x)));
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}
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#ifndef HAVE_TANH
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double
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tanh(double x)
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{
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return sinh(x) / cosh(x);
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}
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#endif
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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 <i>x</i> (expressed in
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* radians).
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*/
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static VALUE
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math_tanh(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(tanh(RFLOAT_VALUE(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 <i>x</i>.
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*/
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static VALUE
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math_acosh(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = acosh(d0);
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domain_check(d0, d, "acosh");
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return DBL2NUM(d);
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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 <i>x</i>.
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*/
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static VALUE
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math_asinh(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(asinh(RFLOAT_VALUE(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 <i>x</i>.
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*/
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static VALUE
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math_atanh(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = atanh(d0);
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domain_check(d0, d, "atanh");
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infinity_check(x, d, "atanh");
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return DBL2NUM(d);
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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 VALUE
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math_exp(VALUE obj, VALUE x)
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{
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Need_Float(x);
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return DBL2NUM(exp(RFLOAT_VALUE(x)));
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}
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#if defined __CYGWIN__
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# include <cygwin/version.h>
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# if CYGWIN_VERSION_DLL_MAJOR < 1005
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# define nan(x) nan()
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# endif
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# define log(x) ((x) < 0.0 ? nan("") : log(x))
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# define log10(x) ((x) < 0.0 ? nan("") : log10(x))
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#endif
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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 <i>numeric</i>.
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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 VALUE
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math_log(int argc, VALUE *argv)
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{
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VALUE x, base;
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double d0, d;
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rb_scan_args(argc, argv, "11", &x, &base);
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = log(d0);
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if (argc == 2) {
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Need_Float(base);
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d /= log(RFLOAT_VALUE(base));
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}
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domain_check(d0, d, "log");
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infinity_check(x, d, "log");
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return DBL2NUM(d);
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}
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#ifndef log2
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#ifndef HAVE_LOG2
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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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#else
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extern double log2(double);
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#endif
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#endif
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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 <i>numeric</i>.
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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 VALUE
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math_log2(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = log2(d0);
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domain_check(d0, d, "log2");
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infinity_check(x, d, "log2");
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return DBL2NUM(d);
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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 <i>numeric</i>.
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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 VALUE
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math_log10(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = log10(d0);
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domain_check(d0, d, "log10");
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infinity_check(x, d, "log10");
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return DBL2NUM(d);
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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 non-negative square root of <i>numeric</i>.
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*
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* 0.upto(10) {|x|
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* p [x, Math.sqrt(x), Math.sqrt(x)**2]
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* }
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* #=>
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* [0, 0.0, 0.0]
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* [1, 1.0, 1.0]
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* [2, 1.4142135623731, 2.0]
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* [3, 1.73205080756888, 3.0]
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* [4, 2.0, 4.0]
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* [5, 2.23606797749979, 5.0]
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* [6, 2.44948974278318, 6.0]
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* [7, 2.64575131106459, 7.0]
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* [8, 2.82842712474619, 8.0]
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* [9, 3.0, 9.0]
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* [10, 3.16227766016838, 10.0]
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*
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*/
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static VALUE
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math_sqrt(VALUE obj, VALUE x)
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{
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double d0, d;
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Need_Float(x);
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errno = 0;
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d0 = RFLOAT_VALUE(x);
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d = sqrt(d0);
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domain_check(d0, d, "sqrt");
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return DBL2NUM(d);
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}
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|
|
/*
|
|
* call-seq:
|
|
* Math.cbrt(numeric) => float
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|
*
|
|
* Returns the cube root of <i>numeric</i>.
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*
|
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* -9.upto(9) {|x|
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* p [x, Math.cbrt(x), Math.cbrt(x)**3]
|
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* }
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* #=>
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* [-9, -2.0800838230519, -9.0]
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* [-8, -2.0, -8.0]
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* [-7, -1.91293118277239, -7.0]
|
|
* [-6, -1.81712059283214, -6.0]
|
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* [-5, -1.7099759466767, -5.0]
|
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* [-4, -1.5874010519682, -4.0]
|
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* [-3, -1.44224957030741, -3.0]
|
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* [-2, -1.25992104989487, -2.0]
|
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* [-1, -1.0, -1.0]
|
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* [0, 0.0, 0.0]
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* [1, 1.0, 1.0]
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* [2, 1.25992104989487, 2.0]
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* [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]
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* [8, 2.0, 8.0]
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* [9, 2.0800838230519, 9.0]
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*
|
|
*/
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|
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static VALUE
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|
math_cbrt(VALUE obj, VALUE x)
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{
|
|
Need_Float(x);
|
|
return DBL2NUM(cbrt(RFLOAT_VALUE(x)));
|
|
}
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|
|
|
/*
|
|
* 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
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* <i>numeric</i>.
|
|
*
|
|
* fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
|
|
* fraction * 2**exponent #=> 1234.0
|
|
*/
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|
|
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static VALUE
|
|
math_frexp(VALUE obj, VALUE x)
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|
{
|
|
double d;
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|
int exp;
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|
|
Need_Float(x);
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|
|
|
d = frexp(RFLOAT_VALUE(x), &exp);
|
|
return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
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|
}
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|
|
|
/*
|
|
* 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
|
|
*/
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|
|
|
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 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. */
|
|
};
|
|
double d0, d;
|
|
double intpart, fracpart;
|
|
Need_Float(x);
|
|
d0 = RFLOAT_VALUE(x);
|
|
fracpart = modf(d0, &intpart);
|
|
if (fracpart == 0.0 &&
|
|
0 < intpart &&
|
|
intpart - 1 < (double)numberof(fact_table)) {
|
|
return DBL2NUM(fact_table[(int)intpart - 1]);
|
|
}
|
|
errno = 0;
|
|
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=1;
|
|
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);
|
|
}
|