# mruby/mruby

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 /* ** math.c - Math module ** ** See Copyright Notice in mruby.h */ #include "mruby.h" #include "mruby/array.h" #ifdef ENABLE_MATH #include #define domain_error(msg) \ mrb_raise(mrb, E_RANGE_ERROR, "Numerical argument is out of domain - " #msg); /* math functions not provided under Microsoft Visual C++ */ #ifdef _MSC_VER #define MATH_TOLERANCE 1E-12 #define asinh(x) log(x + sqrt(pow(x,2.0) + 1)) #define acosh(x) log(x + sqrt(pow(x,2.0) - 1)) #define atanh(x) (log(1+x) - log(1-x))/2.0 #define cbrt(x) pow(x,1.0/3.0) /* Declaration of complementary Error function */ double erfc(double x); /* ** Implementations of error functions ** credits to http://www.digitalmars.com/archives/cplusplus/3634.html */ /* Implementation of Error function */ double erf(double x) { static const double two_sqrtpi = 1.128379167095512574; double sum = x; double term = x; double xsqr = x*x; int j= 1; if (fabs(x) > 2.2) { return 1.0 - erfc(x); } do { term *= xsqr/j; sum -= term/(2*j+1); ++j; term *= xsqr/j; sum += term/(2*j+1); ++j; } while (fabs(term)/sum > MATH_TOLERANCE); return two_sqrtpi*sum; } /* Implementation of complementary Error function */ double erfc(double x) { static const double one_sqrtpi= 0.564189583547756287; double a = 1; double b = x; double c = x; double d = x*x+0.5; double q1, q2; double n = 1.0; double t; if (fabs(x) < 2.2) { return 1.0 - erf(x); } if (x < 0.0) { /*signbit(x)*/ return 2.0 - erfc(-x); } do { t = a*n+b*x; a = b; b = t; t = c*n+d*x; c = d; d = t; n += 0.5; q1 = q2; q2 = b/d; } while (fabs(q1-q2)/q2 > MATH_TOLERANCE); return one_sqrtpi*exp(-x*x)*q2; } #endif /* TRIGONOMETRIC FUNCTIONS */ /* * call-seq: * Math.sin(x) -> float * * Computes the sine of x (expressed in radians). Returns * -1..1. */ static mrb_value math_sin(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = sin(x); return mrb_float_value(x); } /* * call-seq: * Math.cos(x) -> float * * Computes the cosine of x (expressed in radians). Returns * -1..1. */ static mrb_value math_cos(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = cos(x); return mrb_float_value(x); } /* * call-seq: * Math.tan(x) -> float * * Returns the tangent of x (expressed in radians). */ static mrb_value math_tan(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = tan(x); return mrb_float_value(x); } /* INVERSE TRIGONOMETRIC FUNCTIONS */ /* * call-seq: * Math.asin(x) -> float * * Computes the arc sine of x. Returns -{PI/2} .. {PI/2}. */ static mrb_value math_asin(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = asin(x); return mrb_float_value(x); } /* * call-seq: * Math.acos(x) -> float * * Computes the arc cosine of x. Returns 0..PI. */ static mrb_value math_acos(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = acos(x); return mrb_float_value(x); } /* * call-seq: * Math.atan(x) -> float * * Computes the arc tangent of x. Returns -{PI/2} .. {PI/2}. */ static mrb_value math_atan(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = atan(x); return mrb_float_value(x); } /* * call-seq: * Math.atan2(y, x) -> float * * Computes the arc tangent given y and x. Returns * -PI..PI. * * Math.atan2(-0.0, -1.0) #=> -3.141592653589793 * Math.atan2(-1.0, -1.0) #=> -2.356194490192345 * Math.atan2(-1.0, 0.0) #=> -1.5707963267948966 * Math.atan2(-1.0, 1.0) #=> -0.7853981633974483 * Math.atan2(-0.0, 1.0) #=> -0.0 * Math.atan2(0.0, 1.0) #=> 0.0 * Math.atan2(1.0, 1.0) #=> 0.7853981633974483 * Math.atan2(1.0, 0.0) #=> 1.5707963267948966 * Math.atan2(1.0, -1.0) #=> 2.356194490192345 * Math.atan2(0.0, -1.0) #=> 3.141592653589793 * */ static mrb_value math_atan2(mrb_state *mrb, mrb_value obj) { mrb_float x, y; mrb_get_args(mrb, "ff", &x, &y); x = atan2(x, y); return mrb_float_value(x); } /* HYPERBOLIC TRIG FUNCTIONS */ /* * call-seq: * Math.sinh(x) -> float * * Computes the hyperbolic sine of x (expressed in * radians). */ static mrb_value math_sinh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = sinh(x); return mrb_float_value(x); } /* * call-seq: * Math.cosh(x) -> float * * Computes the hyperbolic cosine of x (expressed in radians). */ static mrb_value math_cosh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = cosh(x); return mrb_float_value(x); } /* * call-seq: * Math.tanh() -> float * * Computes the hyperbolic tangent of x (expressed in * radians). */ static mrb_value math_tanh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = tanh(x); return mrb_float_value(x); } /* INVERSE HYPERBOLIC TRIG FUNCTIONS */ /* * call-seq: * Math.asinh(x) -> float * * Computes the inverse hyperbolic sine of x. */ static mrb_value math_asinh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = asinh(x); return mrb_float_value(x); } /* * call-seq: * Math.acosh(x) -> float * * Computes the inverse hyperbolic cosine of x. */ static mrb_value math_acosh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = acosh(x); return mrb_float_value(x); } /* * call-seq: * Math.atanh(x) -> float * * Computes the inverse hyperbolic tangent of x. */ static mrb_value math_atanh(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = atanh(x); return mrb_float_value(x); } /* EXPONENTIALS AND LOGARITHMS */ #if defined __CYGWIN__ # include # if CYGWIN_VERSION_DLL_MAJOR < 1005 # define nan(x) nan() # endif # define log(x) ((x) < 0.0 ? nan("") : log(x)) # define log10(x) ((x) < 0.0 ? nan("") : log10(x)) #endif #ifndef log2 #ifndef HAVE_LOG2 double log2(double x) { return log10(x)/log10(2.0); } #else extern double log2(double); #endif #endif /* * call-seq: * Math.exp(x) -> float * * Returns e**x. * * Math.exp(0) #=> 1.0 * Math.exp(1) #=> 2.718281828459045 * Math.exp(1.5) #=> 4.4816890703380645 * */ static mrb_value math_exp(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = exp(x); return mrb_float_value(x); } /* * call-seq: * Math.log(numeric) -> float * Math.log(num,base) -> float * * Returns the natural logarithm of numeric. * If additional second argument is given, it will be the base * of logarithm. * * Math.log(1) #=> 0.0 * Math.log(Math::E) #=> 1.0 * Math.log(Math::E**3) #=> 3.0 * Math.log(12,3) #=> 2.2618595071429146 * */ static mrb_value math_log(mrb_state *mrb, mrb_value obj) { mrb_float x, base; int argc; argc = mrb_get_args(mrb, "f|f", &x, &base); x = log(x); if (argc == 2) { x /= log(base); } return mrb_float_value(x); } /* * call-seq: * Math.log2(numeric) -> float * * Returns the base 2 logarithm of numeric. * * Math.log2(1) #=> 0.0 * Math.log2(2) #=> 1.0 * Math.log2(32768) #=> 15.0 * Math.log2(65536) #=> 16.0 * */ static mrb_value math_log2(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = log2(x); return mrb_float_value(x); } /* * call-seq: * Math.log10(numeric) -> float * * Returns the base 10 logarithm of numeric. * * Math.log10(1) #=> 0.0 * Math.log10(10) #=> 1.0 * Math.log10(10**100) #=> 100.0 * */ static mrb_value math_log10(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = log10(x); return mrb_float_value(x); } /* * call-seq: * Math.sqrt(numeric) -> float * * Returns the square root of numeric. * */ static mrb_value math_sqrt(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = sqrt(x); return mrb_float_value(x); } /* * call-seq: * Math.cbrt(numeric) -> float * * Returns the cube root of 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; mrb_get_args(mrb, "f", &x); x = cbrt(x); return mrb_float_value(x); } /* * call-seq: * Math.frexp(numeric) -> [ fraction, exponent ] * * Returns a two-element array containing the normalized fraction (a * Float) and exponent (a Fixnum) 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; int exp; mrb_get_args(mrb, "f", &x); x = frexp(x, &exp); return mrb_assoc_new(mrb, mrb_float_value(x), mrb_fixnum_value(exp)); } /* * call-seq: * Math.ldexp(flt, int) -> float * * Returns the value of 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, i); return mrb_float_value(x); } /* * call-seq: * Math.hypot(x, y) -> float * * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle * with sides 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(x); } /* * call-seq: * Math.erf(x) -> float * * Calculates the error function of x. */ static mrb_value math_erf(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = erf(x); return mrb_float_value(x); } /* * call-seq: * Math.erfc(x) -> float * * Calculates the complementary error function of x. */ static mrb_value math_erfc(mrb_state *mrb, mrb_value obj) { mrb_float x; mrb_get_args(mrb, "f", &x); x = erfc(x); return mrb_float_value(x); } /* ------------------------------------------------------------------------*/ void mrb_init_math(mrb_state *mrb) { struct RClass *mrb_math; mrb_math = mrb_define_module(mrb, "Math"); #ifdef M_PI mrb_define_const(mrb, mrb_math, "PI", mrb_float_value(M_PI)); #else mrb_define_const(mrb, mrb_math, "PI", mrb_float_value(atan(1.0)*4.0)); #endif #ifdef M_E mrb_define_const(mrb, mrb_math, "E", mrb_float_value(M_E)); #else mrb_define_const(mrb, mrb_math, "E", mrb_float_value(exp(1.0))); #endif #ifdef MRB_USE_FLOAT mrb_define_const(mrb, mrb_math, "TOLERANCE", mrb_float_value(1e-5)); #else mrb_define_const(mrb, mrb_math, "TOLERANCE", mrb_float_value(1e-12)); #endif mrb_define_module_function(mrb, mrb_math, "sin", math_sin, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "cos", math_cos, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "tan", math_tan, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "asin", math_asin, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "acos", math_acos, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "atan", math_atan, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "atan2", math_atan2, ARGS_REQ(2)); mrb_define_module_function(mrb, mrb_math, "sinh", math_sinh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "cosh", math_cosh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "tanh", math_tanh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "asinh", math_asinh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "acosh", math_acosh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "atanh", math_atanh, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "exp", math_exp, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "log", math_log, ARGS_REQ(1)|ARGS_OPT(1)); mrb_define_module_function(mrb, mrb_math, "log2", math_log2, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "log10", math_log10, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "sqrt", math_sqrt, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "cbrt", math_cbrt, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "frexp", math_frexp, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "ldexp", math_ldexp, ARGS_REQ(2)); mrb_define_module_function(mrb, mrb_math, "hypot", math_hypot, ARGS_REQ(2)); mrb_define_module_function(mrb, mrb_math, "erf", math_erf, ARGS_REQ(1)); mrb_define_module_function(mrb, mrb_math, "erfc", math_erfc, ARGS_REQ(1)); } #endif /* ENABLE_MATH */
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