/********************************************************************** math.c - \$Author\$ created at: Tue Jan 25 14:12:56 JST 1994 Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ #include "ruby/ruby.h" #include #include VALUE rb_mMath; #define Need_Float(x) (x) = rb_to_float(x) #define Need_Float2(x,y) do {\ Need_Float(x);\ Need_Float(y);\ } while (0) static void domain_check(double x, double y, const char *msg) { while(1) { if (errno) { rb_sys_fail(msg); } if (isnan(y)) { if (isnan(x)) break; #if defined(EDOM) errno = EDOM; #elif defined(ERANGE) errno = ERANGE; #endif continue; } break; } } static void infinity_check(VALUE arg, double res, const char *msg) { while(1) { if (errno) { rb_sys_fail(msg); } if (isinf(res) && !isinf(RFLOAT_VALUE(arg))) { #if defined(EDOM) errno = EDOM; #elif defined(ERANGE) errno = ERANGE; #endif continue; } break; } } /* * call-seq: * Math.atan2(y, x) => float * * Computes the arc tangent given y and x. Returns * -PI..PI. * */ static VALUE math_atan2(VALUE obj, VALUE y, VALUE x) { Need_Float2(y, x); return DBL2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(x))); } /* * call-seq: * Math.cos(x) => float * * Computes the cosine of x (expressed in radians). Returns * -1..1. */ static VALUE math_cos(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(cos(RFLOAT_VALUE(x))); } /* * call-seq: * Math.sin(x) => float * * Computes the sine of x (expressed in radians). Returns * -1..1. */ static VALUE math_sin(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(sin(RFLOAT_VALUE(x))); } /* * call-seq: * Math.tan(x) => float * * Returns the tangent of x (expressed in radians). */ static VALUE math_tan(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(tan(RFLOAT_VALUE(x))); } /* * call-seq: * Math.acos(x) => float * * Computes the arc cosine of x. Returns 0..PI. */ static VALUE math_acos(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = acos(d0); domain_check(d0, d, "acos"); return DBL2NUM(d); } /* * call-seq: * Math.asin(x) => float * * Computes the arc sine of x. Returns -{PI/2} .. {PI/2}. */ static VALUE math_asin(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = asin(d0); domain_check(d0, d, "asin"); return DBL2NUM(d); } /* * call-seq: * Math.atan(x) => float * * Computes the arc tangent of x. Returns -{PI/2} .. {PI/2}. */ static VALUE math_atan(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(atan(RFLOAT_VALUE(x))); } #ifndef HAVE_COSH double cosh(double x) { return (exp(x) + exp(-x)) / 2; } #endif /* * call-seq: * Math.cosh(x) => float * * Computes the hyperbolic cosine of x (expressed in radians). */ static VALUE math_cosh(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(cosh(RFLOAT_VALUE(x))); } #ifndef HAVE_SINH double sinh(double x) { return (exp(x) - exp(-x)) / 2; } #endif /* * call-seq: * Math.sinh(x) => float * * Computes the hyperbolic sine of x (expressed in * radians). */ static VALUE math_sinh(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(sinh(RFLOAT_VALUE(x))); } #ifndef HAVE_TANH double tanh(double x) { return sinh(x) / cosh(x); } #endif /* * call-seq: * Math.tanh() => float * * Computes the hyperbolic tangent of x (expressed in * radians). */ static VALUE math_tanh(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(tanh(RFLOAT_VALUE(x))); } /* * call-seq: * Math.acosh(x) => float * * Computes the inverse hyperbolic cosine of x. */ static VALUE math_acosh(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = acosh(d0); domain_check(d0, d, "acosh"); return DBL2NUM(d); } /* * call-seq: * Math.asinh(x) => float * * Computes the inverse hyperbolic sine of x. */ static VALUE math_asinh(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(asinh(RFLOAT_VALUE(x))); } /* * call-seq: * Math.atanh(x) => float * * Computes the inverse hyperbolic tangent of x. */ static VALUE math_atanh(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = atanh(d0); domain_check(d0, d, "atanh"); infinity_check(x, d, "atanh"); return DBL2NUM(d); } /* * call-seq: * Math.exp(x) => float * * Returns e**x. */ static VALUE math_exp(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(exp(RFLOAT_VALUE(x))); } #if defined __CYGWIN__ # include # if CYGWIN_VERSION_DLL_MAJOR < 1005 # define nan(x) nan() # endif # define log(x) ((x) < 0.0 ? nan("") : log(x)) # define log10(x) ((x) < 0.0 ? nan("") : log10(x)) #endif /* * call-seq: * Math.log(numeric) => float * Math.log(num,base) => float * * Returns the natural logarithm of numeric. * If additional second argument is given, it will be the base * of logarithm. */ static VALUE math_log(int argc, VALUE *argv) { VALUE x, base; double d0, d; rb_scan_args(argc, argv, "11", &x, &base); Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = log(d0); if (argc == 2) { Need_Float(base); d /= log(RFLOAT_VALUE(base)); } domain_check(d0, d, "log"); infinity_check(x, d, "log"); return DBL2NUM(d); } #ifndef log2 #ifndef HAVE_LOG2 double log2(double x) { return log10(x)/log10(2.0); } #else extern double log2(double); #endif #endif /* * call-seq: * Math.log2(numeric) => float * * Returns the base 2 logarithm of numeric. */ static VALUE math_log2(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = log2(d0); domain_check(d0, d, "log2"); infinity_check(x, d, "log2"); return DBL2NUM(d); } /* * call-seq: * Math.log10(numeric) => float * * Returns the base 10 logarithm of numeric. */ static VALUE math_log10(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = log10(d0); domain_check(d0, d, "log10"); infinity_check(x, d, "log10"); return DBL2NUM(d); } /* * call-seq: * Math.sqrt(numeric) => float * * Returns the non-negative square root of numeric. * * 0.upto(10) {|x| * p [x, Math.sqrt(x), Math.sqrt(x)**2] * } * #=> * [0, 0.0, 0.0] * [1, 1.0, 1.0] * [2, 1.4142135623731, 2.0] * [3, 1.73205080756888, 3.0] * [4, 2.0, 4.0] * [5, 2.23606797749979, 5.0] * [6, 2.44948974278318, 6.0] * [7, 2.64575131106459, 7.0] * [8, 2.82842712474619, 8.0] * [9, 3.0, 9.0] * [10, 3.16227766016838, 10.0] * */ static VALUE math_sqrt(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = sqrt(d0); domain_check(d0, d, "sqrt"); return DBL2NUM(d); } /* * call-seq: * Math.cbrt(numeric) => float * * Returns the cube root of 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 VALUE math_cbrt(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(cbrt(RFLOAT_VALUE(x))); } /* * call-seq: * Math.frexp(numeric) => [ fraction, exponent ] * * Returns a two-element array containing the normalized fraction (a * `Float`) and exponent (a `Fixnum`) of * numeric. * * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] * fraction * 2**exponent #=> 1234.0 */ static VALUE math_frexp(VALUE obj, VALUE x) { double d; int exp; Need_Float(x); d = frexp(RFLOAT_VALUE(x), &exp); return rb_assoc_new(DBL2NUM(d), INT2NUM(exp)); } /* * call-seq: * Math.ldexp(flt, int) -> float * * Returns the value of flt*(2**int). * * fraction, exponent = Math.frexp(1234) * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE math_ldexp(VALUE obj, VALUE x, VALUE n) { Need_Float(x); return DBL2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n))); } /* * call-seq: * Math.hypot(x, y) => float * * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle * with sides x and y. * * Math.hypot(3, 4) #=> 5.0 */ static VALUE math_hypot(VALUE obj, VALUE x, VALUE y) { Need_Float2(x, y); return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y))); } /* * call-seq: * Math.erf(x) => float * * Calculates the error function of x. */ static VALUE math_erf(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(erf(RFLOAT_VALUE(x))); } /* * call-seq: * Math.erfc(x) => float * * Calculates the complementary error function of x. */ static VALUE math_erfc(VALUE obj, VALUE x) { Need_Float(x); return DBL2NUM(erfc(RFLOAT_VALUE(x))); } /* * call-seq: * Math.gamma(x) => float * * Calculates the gamma function of x. * * Note that gamma(n) is same as fact(n-1) for integer n >= 0. * However gamma(n) returns float and possibly has error in calculation. * * def fact(n) (1..n).inject(1) {|r,i| r*i } end * 0.upto(25) {|i| p [i, Math.gamma(i+1), fact(i)] } * #=> * [0, 1.0, 1] * [1, 1.0, 1] * [2, 2.0, 2] * [3, 6.0, 6] * [4, 24.0, 24] * [5, 120.0, 120] * [6, 720.0, 720] * [7, 5040.0, 5040] * [8, 40320.0, 40320] * [9, 362880.0, 362880] * [10, 3628800.0, 3628800] * [11, 39916800.0, 39916800] * [12, 479001599.999999, 479001600] * [13, 6227020800.00001, 6227020800] * [14, 87178291199.9998, 87178291200] * [15, 1307674368000.0, 1307674368000] * [16, 20922789888000.0, 20922789888000] * [17, 3.55687428096001e+14, 355687428096000] * [18, 6.40237370572799e+15, 6402373705728000] * [19, 1.21645100408832e+17, 121645100408832000] * [20, 2.43290200817664e+18, 2432902008176640000] * [21, 5.10909421717094e+19, 51090942171709440000] * [22, 1.12400072777761e+21, 1124000727777607680000] * [23, 2.58520167388851e+22, 25852016738884976640000] * [24, 6.20448401733239e+23, 620448401733239439360000] * [25, 1.5511210043331e+25, 15511210043330985984000000] * */ static VALUE math_gamma(VALUE obj, VALUE x) { double d0, d; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = tgamma(d0); domain_check(d0, d, "gamma"); return DBL2NUM(d); } /* * call-seq: * Math.lgamma(x) => [float, -1 or 1] * * Calculates the logarithmic gamma of x and * the sign of gamma of x. * * Math.lgamma(x) is same as * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1] * but avoid overflow by Math.gamma(x) for large x. */ static VALUE math_lgamma(VALUE obj, VALUE x) { double d0, d; int sign; VALUE v; Need_Float(x); errno = 0; d0 = RFLOAT_VALUE(x); d = lgamma_r(d0, &sign); domain_check(d0, d, "lgamma"); v = DBL2NUM(d); return rb_assoc_new(v, INT2FIX(sign)); } #define exp1(n) \ VALUE \ rb_math_##n(VALUE x)\ {\ return math_##n(rb_mMath, x);\ } #define exp2(n) \ VALUE \ rb_math_##n(VALUE x, VALUE y)\ {\ return math_##n(rb_mMath, x, y);\ } exp2(atan2) exp1(cos) exp1(cosh) exp1(exp) exp2(hypot) VALUE rb_math_log(int argc, VALUE *argv) { return math_log(argc, argv); } exp1(sin) exp1(sinh) exp1(sqrt) /* * The `Math` module contains module functions for basic * trigonometric and transcendental functions. See class * `Float` for a list of constants that * define Ruby's floating point accuracy. */ 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); }