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# MacRuby/MacRuby

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 /********************************************************************** math.c - \$Author: nobu \$ created at: Tue Jan 25 14:12:56 JST 1994 Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ #include "ruby/macruby.h" #include #include VALUE rb_mMath; VALUE rb_eMathDomainError; #define numberof(array) (int)(sizeof(array) / sizeof((array)[0])) #define domain_error(msg) \ rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg); static VALUE to_flo(VALUE x) { if (CLASS_OF(x) == rb_cFloat) { return x; } if (!rb_obj_is_kind_of(x, rb_cNumeric)) { rb_raise(rb_eTypeError, "can't convert %s into Float", NIL_P(x) ? "nil" : x == Qtrue ? "true" : x == Qfalse ? "false" : rb_obj_classname(x)); } return rb_convert_type(x, T_FLOAT, "Float", "to_f"); } #define Need_Float(x) do {if (TYPE(x) != T_FLOAT) {(x) = to_flo(x);}} while(0) #define Need_Float2(x,y) do {\ Need_Float(x);\ Need_Float(y);\ } while (0) /* * call-seq: * Math.atan2(y, x) => float * * Computes the arc tangent given y and x. Returns * -PI..PI. * */ VALUE math_atan2(VALUE obj, SEL sel, VALUE y, VALUE x) { double dx, dy; Need_Float2(y, x); dx = RFLOAT_VALUE(x); dy = RFLOAT_VALUE(y); if (dx == 0.0 && dy == 0.0) { domain_error("atan2"); } if (isinf(dx) && isinf(dy)) { domain_error("atan2"); } return DBL2NUM(atan2(dy, dx)); } /* * call-seq: * Math.cos(x) => float * * Computes the cosine of x (expressed in radians). Returns * -1..1. */ VALUE math_cos(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(cos(RFLOAT_VALUE(x))); } /* * call-seq: * Math.sin(x) => float * * Computes the sine of x (expressed in radians). Returns * -1..1. */ VALUE math_sin(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(sin(RFLOAT_VALUE(x))); } /* * call-seq: * Math.tan(x) => float * * Returns the tangent of x (expressed in radians). */ static VALUE math_tan(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < -1.0 || 1.0 < d0) { domain_error("acos"); } d = acos(d0); 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, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < -1.0 || 1.0 < d0) { domain_error("asin"); } d = asin(d0); 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, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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). */ VALUE math_cosh(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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). */ VALUE math_sinh(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(tanh(RFLOAT_VALUE(x))); } /* * call-seq: * Math.acosh(x) => float * * Computes the inverse hyperbolic cosine of x. */ static VALUE math_acosh(VALUE obj, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < 1.0) { domain_error("acosh"); } d = acosh(d0); return DBL2NUM(d); } /* * call-seq: * Math.asinh(x) => float * * Computes the inverse hyperbolic sine of x. */ static VALUE math_asinh(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(asinh(RFLOAT_VALUE(x))); } /* * call-seq: * Math.atanh(x) => float * * Computes the inverse hyperbolic tangent of x. */ static VALUE math_atanh(VALUE obj, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < -1.0 || +1.0 < d0) { domain_error("atanh"); } /* check for pole error */ if (d0 == -1.0) return DBL2NUM(-INFINITY); if (d0 == +1.0) return DBL2NUM(+INFINITY); d = atanh(d0); return DBL2NUM(d); } /* * call-seq: * Math.exp(x) => float * * Returns e**x. */ VALUE math_exp(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(exp(RFLOAT_VALUE(x))); } /* * 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. */ VALUE math_log(VALUE rcv, SEL sel, int argc, VALUE *argv) { VALUE x, base; double d0, d; rb_scan_args(argc, argv, "11", &x, &base); Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < 0.0) { domain_error("log"); } /* check for pole error */ if (d0 == 0.0) { return DBL2NUM(-INFINITY); } d = log(d0); if (argc == 2) { Need_Float(base); d /= log(RFLOAT_VALUE(base)); } 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, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < 0.0) { domain_error("log2"); } /* check for pole error */ if (d0 == 0.0) { return DBL2NUM(-INFINITY); } d = log2(d0); return DBL2NUM(d); } /* * call-seq: * Math.log10(numeric) => float * * Returns the base 10 logarithm of numeric. */ static VALUE math_log10(VALUE obj, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < 0.0) { domain_error("log10"); } /* check for pole error */ if (d0 == 0.0) { return DBL2NUM(-INFINITY); } d = log10(d0); return DBL2NUM(d); } /* * call-seq: * Math.sqrt(numeric) => float * * Returns the non-negative square root of numeric. */ VALUE math_sqrt(VALUE obj, SEL sel, VALUE x) { double d0, d; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (d0 < 0.0) { domain_error("sqrt"); } if (d0 == 0.0) { return DBL2NUM(0.0); } d = sqrt(d0); return DBL2NUM(d); } /* * call-seq: * Math.cbrt(numeric) => float * * Returns the cube root of numeric. */ static VALUE math_cbrt(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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, SEL sel, VALUE x) { double d; int exp; Need_Float(x); d = frexp(RFLOAT_VALUE(x), &exp); return rb_assoc_new(DOUBLE2NUM(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, SEL sel, VALUE x, VALUE n) { Need_Float(x); return DOUBLE2NUM(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 */ VALUE math_hypot(VALUE obj, SEL sel, VALUE x, VALUE y) { Need_Float2(x, y); return DOUBLE2NUM(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, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(erf(RFLOAT_VALUE(x))); } /* * call-seq: * Math.erfc(x) => float * * Calculates the complementary error function of x. */ static VALUE math_erfc(VALUE obj, SEL sel, VALUE x) { Need_Float(x); return DOUBLE2NUM(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, SEL sel, 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); /* check for domain error */ if (isinf(d0) && signbit(d0)) { domain_error("gamma"); } fracpart = modf(d0, &intpart); if (fracpart == 0.0) { if (intpart < 0) { domain_error("gamma"); } if (0 < intpart && intpart - 1 < (double)numberof(fact_table)) { return DBL2NUM(fact_table[(int)intpart - 1]); } } d = tgamma(d0); 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. */ #include "lgamma_r.c" static VALUE math_lgamma(VALUE obj, SEL sel, VALUE x) { double d0, d; int sign = 1; VALUE v; Need_Float(x); d0 = RFLOAT_VALUE(x); /* check for domain error */ if (isinf(d0)) { if (signbit(d0)) { domain_error("lgamma"); } return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1)); } d = lgamma_r(d0, &sign); v = DBL2NUM(d); return rb_assoc_new(v, INT2FIX(sign)); } /* * 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"); rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError); #ifdef M_PI rb_define_const(rb_mMath, "PI", DOUBLE2NUM(M_PI)); #else rb_define_const(rb_mMath, "PI", DOUBLE2NUM(atan(1.0)*4.0)); #endif #ifdef M_E rb_define_const(rb_mMath, "E", DOUBLE2NUM(M_E)); #else rb_define_const(rb_mMath, "E", DOUBLE2NUM(exp(1.0))); #endif rb_objc_define_module_function(rb_mMath, "atan2", math_atan2, 2); rb_objc_define_module_function(rb_mMath, "cos", math_cos, 1); rb_objc_define_module_function(rb_mMath, "sin", math_sin, 1); rb_objc_define_module_function(rb_mMath, "tan", math_tan, 1); rb_objc_define_module_function(rb_mMath, "acos", math_acos, 1); rb_objc_define_module_function(rb_mMath, "asin", math_asin, 1); rb_objc_define_module_function(rb_mMath, "atan", math_atan, 1); rb_objc_define_module_function(rb_mMath, "cosh", math_cosh, 1); rb_objc_define_module_function(rb_mMath, "sinh", math_sinh, 1); rb_objc_define_module_function(rb_mMath, "tanh", math_tanh, 1); rb_objc_define_module_function(rb_mMath, "acosh", math_acosh, 1); rb_objc_define_module_function(rb_mMath, "asinh", math_asinh, 1); rb_objc_define_module_function(rb_mMath, "atanh", math_atanh, 1); rb_objc_define_module_function(rb_mMath, "exp", math_exp, 1); rb_objc_define_module_function(rb_mMath, "log", math_log, -1); rb_objc_define_module_function(rb_mMath, "log2", math_log2, 1); rb_objc_define_module_function(rb_mMath, "log10", math_log10, 1); rb_objc_define_module_function(rb_mMath, "sqrt", math_sqrt, 1); rb_objc_define_module_function(rb_mMath, "cbrt", math_cbrt, 1); rb_objc_define_module_function(rb_mMath, "frexp", math_frexp, 1); rb_objc_define_module_function(rb_mMath, "ldexp", math_ldexp, 2); rb_objc_define_module_function(rb_mMath, "hypot", math_hypot, 2); rb_objc_define_module_function(rb_mMath, "erf", math_erf, 1); rb_objc_define_module_function(rb_mMath, "erfc", math_erfc, 1); rb_objc_define_module_function(rb_mMath, "gamma", math_gamma, 1); rb_objc_define_module_function(rb_mMath, "lgamma", math_lgamma, 1); }
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