/********************************************************************** math.c - \$Author\$ created at: Tue Jan 25 14:12:56 JST 1994 Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ #include "internal.h" #include #include #include #if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ !defined(signbit) extern int signbit(double); #endif #define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM) static ID id_to_f; VALUE rb_mMath; VALUE rb_eMathDomainError; static inline int basic_to_f_p(VALUE klass) { return rb_method_basic_definition_p(klass, id_to_f); } static inline double num2dbl_with_to_f(VALUE num) { if (SPECIAL_CONST_P(num)) { if (FIXNUM_P(num)) { if (basic_to_f_p(rb_cFixnum)) return (double)FIX2LONG(num); } else if (FLONUM_P(num)) { return RFLOAT_VALUE(num); } } else { switch (BUILTIN_TYPE(num)) { case T_FLOAT: return RFLOAT_VALUE(num); case T_BIGNUM: if (basic_to_f_p(rb_cBignum)) return rb_big2dbl(num); break; } } return RFLOAT_VALUE(rb_to_float(num)); } #define Get_Double(x) num2dbl_with_to_f(x) #define domain_error(msg) \ rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg) /* * call-seq: * Math.atan2(y, x) -> Float * * Computes the arc tangent given +y+ and +x+. * Returns a Float in the range -PI..PI. Return value is a angle * in radians between the positive x-axis of cartesian plane * and the point given by the coordinates (+x+, +y+) on it. * * Domain: (-INFINITY, INFINITY) * * Codomain: [-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 * Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483 * Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345 * Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483 * Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345 * */ static VALUE math_atan2(VALUE obj, VALUE y, VALUE x) { #ifndef M_PI # define M_PI 3.14159265358979323846 #endif double dx, dy; dx = Get_Double(x); dy = Get_Double(y); if (dx == 0.0 && dy == 0.0) { if (!signbit(dx)) return DBL2NUM(dy); if (!signbit(dy)) return DBL2NUM(M_PI); return DBL2NUM(-M_PI); } #ifndef ATAN2_INF_C99 if (isinf(dx) && isinf(dy)) { /* optimization for FLONUM */ if (dx < 0.0) { const double dz = (3.0 * M_PI / 4.0); return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz); } else { const double dz = (M_PI / 4.0); return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz); } } #endif return DBL2NUM(atan2(dy, dx)); } /* * call-seq: * Math.cos(x) -> Float * * Computes the cosine of +x+ (expressed in radians). * Returns a Float in the range -1.0..1.0. * * Domain: (-INFINITY, INFINITY) * * Codomain: [-1, 1] * * Math.cos(Math::PI) #=> -1.0 * */ static VALUE math_cos(VALUE obj, VALUE x) { return DBL2NUM(cos(Get_Double(x))); } /* * call-seq: * Math.sin(x) -> Float * * Computes the sine of +x+ (expressed in radians). * Returns a Float in the range -1.0..1.0. * * Domain: (-INFINITY, INFINITY) * * Codomain: [-1, 1] * * Math.sin(Math::PI/2) #=> 1.0 * */ static VALUE math_sin(VALUE obj, VALUE x) { return DBL2NUM(sin(Get_Double(x))); } /* * call-seq: * Math.tan(x) -> Float * * Computes the tangent of +x+ (expressed in radians). * * Domain: (-INFINITY, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.tan(0) #=> 0.0 * */ static VALUE math_tan(VALUE obj, VALUE x) { return DBL2NUM(tan(Get_Double(x))); } /* * call-seq: * Math.acos(x) -> Float * * Computes the arc cosine of +x+. Returns 0..PI. * * Domain: [-1, 1] * * Codomain: [0, PI] * * Math.acos(0) == Math::PI/2 #=> true * */ static VALUE math_acos(VALUE obj, VALUE x) { double d0, d; d0 = Get_Double(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. * * Domain: [-1, -1] * * Codomain: [-PI/2, PI/2] * * Math.asin(1) == Math::PI/2 #=> true */ static VALUE math_asin(VALUE obj, VALUE x) { double d0, d; d0 = Get_Double(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. * * Domain: (-INFINITY, INFINITY) * * Codomain: (-PI/2, PI/2) * * Math.atan(0) #=> 0.0 */ static VALUE math_atan(VALUE obj, VALUE x) { return DBL2NUM(atan(Get_Double(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). * * Domain: (-INFINITY, INFINITY) * * Codomain: [1, INFINITY) * * Math.cosh(0) #=> 1.0 * */ static VALUE math_cosh(VALUE obj, VALUE x) { return DBL2NUM(cosh(Get_Double(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). * * Domain: (-INFINITY, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.sinh(0) #=> 0.0 * */ static VALUE math_sinh(VALUE obj, VALUE x) { return DBL2NUM(sinh(Get_Double(x))); } #ifndef HAVE_TANH double tanh(double x) { return sinh(x) / cosh(x); } #endif /* * call-seq: * Math.tanh(x) -> Float * * Computes the hyperbolic tangent of +x+ (expressed in radians). * * Domain: (-INFINITY, INFINITY) * * Codomain: (-1, 1) * * Math.tanh(0) #=> 0.0 * */ static VALUE math_tanh(VALUE obj, VALUE x) { return DBL2NUM(tanh(Get_Double(x))); } /* * call-seq: * Math.acosh(x) -> Float * * Computes the inverse hyperbolic cosine of +x+. * * Domain: [1, INFINITY) * * Codomain: [0, INFINITY) * * Math.acosh(1) #=> 0.0 * */ static VALUE math_acosh(VALUE obj, VALUE x) { double d0, d; d0 = Get_Double(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+. * * Domain: (-INFINITY, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.asinh(1) #=> 0.881373587019543 * */ static VALUE math_asinh(VALUE obj, VALUE x) { return DBL2NUM(asinh(Get_Double(x))); } /* * call-seq: * Math.atanh(x) -> Float * * Computes the inverse hyperbolic tangent of +x+. * * Domain: (-1, 1) * * Codomain: (-INFINITY, INFINITY) * * Math.atanh(1) #=> Infinity * */ static VALUE math_atanh(VALUE obj, VALUE x) { double d0, d; d0 = Get_Double(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. * * Domain: (-INFINITY, INFINITY) * * Codomain: (0, INFINITY) * * Math.exp(0) #=> 1.0 * Math.exp(1) #=> 2.718281828459045 * Math.exp(1.5) #=> 4.4816890703380645 * */ static VALUE math_exp(VALUE obj, VALUE x) { return DBL2NUM(exp(Get_Double(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 static double math_log1(VALUE x); /* * call-seq: * Math.log(x) -> Float * Math.log(x, base) -> Float * * Returns the logarithm of +x+. * If additional second argument is given, it will be the base * of logarithm. Otherwise it is +e+ (for the natural logarithm). * * Domain: (0, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.log(0) #=> -Infinity * 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 VALUE math_log(int argc, const VALUE *argv, VALUE obj) { VALUE x, base; double d; rb_scan_args(argc, argv, "11", &x, &base); d = math_log1(x); if (argc == 2) { d /= math_log1(base); } return DBL2NUM(d); } static double math_log1(VALUE x) { double d0, d; size_t numbits; if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) && DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) { numbits -= DBL_MANT_DIG; x = rb_big_rshift(x, SIZET2NUM(numbits)); } else { numbits = 0; } d0 = Get_Double(x); /* check for domain error */ if (d0 < 0.0) domain_error("log"); /* check for pole error */ if (d0 == 0.0) return -INFINITY; d = log(d0); if (numbits) d += numbits * log(2); /* log(2**numbits) */ return 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(x) -> Float * * Returns the base 2 logarithm of +x+. * * Domain: (0, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.log2(1) #=> 0.0 * Math.log2(2) #=> 1.0 * Math.log2(32768) #=> 15.0 * Math.log2(65536) #=> 16.0 * */ static VALUE math_log2(VALUE obj, VALUE x) { double d0, d; size_t numbits; if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) && DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) { numbits -= DBL_MANT_DIG; x = rb_big_rshift(x, SIZET2NUM(numbits)); } else { numbits = 0; } d0 = Get_Double(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); d += numbits; return DBL2NUM(d); } /* * call-seq: * Math.log10(x) -> Float * * Returns the base 10 logarithm of +x+. * * Domain: (0, INFINITY) * * Codomain: (-INFINITY, INFINITY) * * Math.log10(1) #=> 0.0 * Math.log10(10) #=> 1.0 * Math.log10(10**100) #=> 100.0 * */ static VALUE math_log10(VALUE obj, VALUE x) { double d0, d; size_t numbits; if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) && DBL_MAX_EXP <= (numbits = rb_absint_numwords(x, 1, NULL))) { numbits -= DBL_MANT_DIG; x = rb_big_rshift(x, SIZET2NUM(numbits)); } else { numbits = 0; } d0 = Get_Double(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); if (numbits) d += numbits * log10(2); /* log10(2**numbits) */ return DBL2NUM(d); } /* * call-seq: * Math.sqrt(x) -> Float * * Returns the non-negative square root of +x+. * * Domain: [0, INFINITY) * * Codomain:[0, INFINITY) * * 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; d0 = Get_Double(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(x) -> Float * * Returns the cube root of +x+. * * Domain: [0, INFINITY) * * Codomain:[0, INFINITY) * * -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) { return DBL2NUM(cbrt(Get_Double(x))); } /* * call-seq: * Math.frexp(x) -> [fraction, exponent] * * Returns a two-element array containing the normalized fraction (a Float) * and exponent (a Fixnum) of +x+. * * 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; d = frexp(Get_Double(x), &exp); return rb_assoc_new(DBL2NUM(d), INT2NUM(exp)); } /* * call-seq: * Math.ldexp(fraction, exponent) -> float * * Returns the value of +fraction+*(2**+exponent+). * * fraction, exponent = Math.frexp(1234) * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE math_ldexp(VALUE obj, VALUE x, VALUE n) { return DBL2NUM(ldexp(Get_Double(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) { return DBL2NUM(hypot(Get_Double(x), Get_Double(y))); } /* * call-seq: * Math.erf(x) -> Float * * Calculates the error function of +x+. * * Domain: (-INFINITY, INFINITY) * * Codomain: (-1, 1) * * Math.erf(0) #=> 0.0 * */ static VALUE math_erf(VALUE obj, VALUE x) { return DBL2NUM(erf(Get_Double(x))); } /* * call-seq: * Math.erfc(x) -> Float * * Calculates the complementary error function of x. * * Domain: (-INFINITY, INFINITY) * * Codomain: (0, 2) * * Math.erfc(0) #=> 1.0 * */ static VALUE math_erfc(VALUE obj, VALUE x) { return DBL2NUM(erfc(Get_Double(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; d0 = Get_Double(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. * * Math.lgamma(0) #=> [Infinity, 1] * */ static VALUE math_lgamma(VALUE obj, VALUE x) { double d0, d; int sign=1; VALUE v; d0 = Get_Double(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)); } #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, const VALUE *argv) { return math_log(argc, argv, rb_mMath); } exp1(sin) exp1(sinh) #if 0 exp1(sqrt) #endif /* * Document-class: Math::DomainError * * Raised when a mathematical function is evaluated outside of its * domain of definition. * * For example, since +cos+ returns values in the range -1..1, * its inverse function +acos+ is only defined on that interval: * * Math.acos(42) * * produces: * * Math::DomainError: Numerical argument is out of domain - "acos" */ /* * Document-class: Math * * 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. * * Domains and codomains are given only for real (not complex) numbers. */ void InitVM_Math(void) { rb_mMath = rb_define_module("Math"); rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError); #ifdef M_PI /* Definition of the mathematical constant PI as a Float number. */ 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 /* Definition of the mathematical constant E (e) as a Float number. */ 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); } void Init_Math(void) { id_to_f = rb_intern_const("to_f"); InitVM(Math); }