diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 462 |
1 files changed, 223 insertions, 239 deletions
@@ -9,36 +9,43 @@ **********************************************************************/ -#include "internal.h" -#include <float.h> -#include <math.h> -#include <errno.h> +#include "ruby/internal/config.h" -#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ - !defined(signbit) - extern int signbit(double); +#ifdef _MSC_VER +# define _USE_MATH_DEFINES 1 #endif -#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM) +#include <errno.h> +#include <float.h> +#include <math.h> + +#include "internal.h" +#include "internal/bignum.h" +#include "internal/complex.h" +#include "internal/math.h" +#include "internal/object.h" +#include "internal/vm.h" VALUE rb_mMath; VALUE rb_eMathDomainError; -#define Need_Float(x) do {if (!RB_TYPE_P(x, T_FLOAT)) {(x) = rb_to_float(x);}} while(0) -#define Need_Float2(x,y) do {\ - Need_Float(x);\ - Need_Float(y);\ -} while (0) +#define Get_Double(x) rb_num_to_dbl(x) #define domain_error(msg) \ - rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #msg) + rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " msg) +#define domain_check_min(val, min, msg) \ + ((val) < (min) ? domain_error(msg) : (void)0) +#define domain_check_range(val, min, max, msg) \ + ((val) < (min) || (max) < (val) ? domain_error(msg) : (void)0) /* * call-seq: * Math.atan2(y, x) -> Float * * Computes the arc tangent given +y+ and +x+. - * Returns a Float in the range -PI..PI. + * 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) * @@ -62,15 +69,11 @@ VALUE rb_eMathDomainError; */ static VALUE -math_atan2(VALUE obj, VALUE y, VALUE x) +math_atan2(VALUE unused_obj, VALUE y, VALUE x) { -#ifndef M_PI -# define M_PI 3.14159265358979323846 -#endif double dx, dy; - Need_Float2(y, x); - dx = RFLOAT_VALUE(x); - dy = RFLOAT_VALUE(y); + dx = Get_Double(x); + dy = Get_Double(y); if (dx == 0.0 && dy == 0.0) { if (!signbit(dx)) return DBL2NUM(dy); @@ -111,10 +114,9 @@ math_atan2(VALUE obj, VALUE y, VALUE x) */ static VALUE -math_cos(VALUE obj, VALUE x) +math_cos(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(cos(RFLOAT_VALUE(x))); + return DBL2NUM(cos(Get_Double(x))); } /* @@ -133,10 +135,9 @@ math_cos(VALUE obj, VALUE x) */ static VALUE -math_sin(VALUE obj, VALUE x) +math_sin(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(sin(RFLOAT_VALUE(x))); + return DBL2NUM(sin(Get_Double(x))); } @@ -155,10 +156,9 @@ math_sin(VALUE obj, VALUE x) */ static VALUE -math_tan(VALUE obj, VALUE x) +math_tan(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(tan(RFLOAT_VALUE(x))); + return DBL2NUM(tan(Get_Double(x))); } /* @@ -176,16 +176,13 @@ math_tan(VALUE obj, VALUE x) */ static VALUE -math_acos(VALUE obj, VALUE x) +math_acos(VALUE unused_obj, VALUE x) { - double d0, d; + double 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); + d = Get_Double(x); + domain_check_range(d, -1.0, 1.0, "acos"); + return DBL2NUM(acos(d)); } /* @@ -202,16 +199,13 @@ math_acos(VALUE obj, VALUE x) */ static VALUE -math_asin(VALUE obj, VALUE x) +math_asin(VALUE unused_obj, VALUE x) { - double d0, d; + double 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); + d = Get_Double(x); + domain_check_range(d, -1.0, 1.0, "asin"); + return DBL2NUM(asin(d)); } /* @@ -228,10 +222,9 @@ math_asin(VALUE obj, VALUE x) */ static VALUE -math_atan(VALUE obj, VALUE x) +math_atan(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(atan(RFLOAT_VALUE(x))); + return DBL2NUM(atan(Get_Double(x))); } #ifndef HAVE_COSH @@ -257,10 +250,9 @@ cosh(double x) */ static VALUE -math_cosh(VALUE obj, VALUE x) +math_cosh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(cosh(RFLOAT_VALUE(x))); + return DBL2NUM(cosh(Get_Double(x))); } #ifndef HAVE_SINH @@ -286,17 +278,23 @@ sinh(double x) */ static VALUE -math_sinh(VALUE obj, VALUE x) +math_sinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(sinh(RFLOAT_VALUE(x))); + return DBL2NUM(sinh(Get_Double(x))); } #ifndef HAVE_TANH double tanh(double x) { - return sinh(x) / cosh(x); +# if defined(HAVE_SINH) && defined(HAVE_COSH) + const double c = cosh(x); + if (!isinf(c)) return sinh(x) / c; +# else + const double e = exp(x+x); + if (!isinf(e)) return (e - 1) / (e + 1); +# endif + return x > 0 ? 1.0 : -1.0; } #endif @@ -315,10 +313,9 @@ tanh(double x) */ static VALUE -math_tanh(VALUE obj, VALUE x) +math_tanh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(tanh(RFLOAT_VALUE(x))); + return DBL2NUM(tanh(Get_Double(x))); } /* @@ -336,16 +333,13 @@ math_tanh(VALUE obj, VALUE x) */ static VALUE -math_acosh(VALUE obj, VALUE x) +math_acosh(VALUE unused_obj, VALUE x) { - double d0, d; + double 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); + d = Get_Double(x); + domain_check_min(d, 1.0, "acosh"); + return DBL2NUM(acosh(d)); } /* @@ -363,10 +357,9 @@ math_acosh(VALUE obj, VALUE x) */ static VALUE -math_asinh(VALUE obj, VALUE x) +math_asinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(asinh(RFLOAT_VALUE(x))); + return DBL2NUM(asinh(Get_Double(x))); } /* @@ -384,19 +377,16 @@ math_asinh(VALUE obj, VALUE x) */ static VALUE -math_atanh(VALUE obj, VALUE x) +math_atanh(VALUE unused_obj, VALUE x) { - double d0, d; + double d; - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < -1.0 || +1.0 < d0) domain_error("atanh"); + d = Get_Double(x); + domain_check_range(d, -1.0, +1.0, "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); + if (d == -1.0) return DBL2NUM(-HUGE_VAL); + if (d == +1.0) return DBL2NUM(+HUGE_VAL); + return DBL2NUM(atanh(d)); } /* @@ -416,10 +406,9 @@ math_atanh(VALUE obj, VALUE x) */ static VALUE -math_exp(VALUE obj, VALUE x) +math_exp(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(exp(RFLOAT_VALUE(x))); + return DBL2NUM(exp(Get_Double(x))); } #if defined __CYGWIN__ @@ -431,7 +420,15 @@ math_exp(VALUE obj, VALUE x) # define log10(x) ((x) < 0.0 ? nan("") : log10(x)) #endif +#ifndef M_LN2 +# define M_LN2 0.693147180559945309417232121458176568 +#endif +#ifndef M_LN10 +# define M_LN10 2.30258509299404568401799145468436421 +#endif + static double math_log1(VALUE x); +FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE)); /* * call-seq: @@ -455,7 +452,13 @@ static double math_log1(VALUE x); */ static VALUE -math_log(int argc, const VALUE *argv, VALUE obj) +math_log(int argc, const VALUE *argv, VALUE unused_obj) +{ + return rb_math_log(argc, argv); +} + +VALUE +rb_math_log(int argc, const VALUE *argv) { VALUE x, base; double d; @@ -469,9 +472,8 @@ math_log(int argc, const VALUE *argv, VALUE obj) } static double -math_log1(VALUE x) +get_double_rshift(VALUE x, size_t *pnumbits) { - double d0, d; size_t numbits; if (RB_BIGNUM_TYPE_P(x) && BIGNUM_POSITIVE_P(x) && @@ -482,17 +484,21 @@ math_log1(VALUE x) else { numbits = 0; } + *pnumbits = numbits; + return Get_Double(x); +} - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log"); +static double +math_log1(VALUE x) +{ + size_t numbits; + double d = get_double_rshift(x, &numbits); + + domain_check_min(d, 0.0, "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; + if (d == 0.0) return -HUGE_VAL; + + return log(d) + numbits * M_LN2; /* log(d * 2 ** numbits) */ } #ifndef log2 @@ -525,29 +531,16 @@ extern double log2(double); */ static VALUE -math_log2(VALUE obj, VALUE x) +math_log2(VALUE unused_obj, VALUE x) { - double d0, d; size_t numbits; + double d = get_double_rshift(x, &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; - } - - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log2"); + domain_check_min(d, 0.0, "log2"); /* check for pole error */ - if (d0 == 0.0) return DBL2NUM(-INFINITY); - d = log2(d0); - d += numbits; - return DBL2NUM(d); + if (d == 0.0) return DBL2NUM(-HUGE_VAL); + + return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */ } /* @@ -567,32 +560,20 @@ math_log2(VALUE obj, VALUE x) */ static VALUE -math_log10(VALUE obj, VALUE x) +math_log10(VALUE unused_obj, VALUE x) { - double d0, d; size_t numbits; + double d = get_double_rshift(x, &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; - } - - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log10"); + domain_check_min(d, 0.0, "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); + if (d == 0.0) return DBL2NUM(-HUGE_VAL); + + return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */ } +static VALUE rb_math_sqrt(VALUE x); + /* * call-seq: * Math.sqrt(x) -> Float @@ -617,20 +598,56 @@ math_log10(VALUE obj, VALUE x) * # [8, 2.82842712474619, 8.0] * # [9, 3.0, 9.0] * # [10, 3.16227766016838, 10.0] + * + * Note that the limited precision of floating point arithmetic + * might lead to surprising results: + * + * Math.sqrt(10**46).to_i #=> 99999999999999991611392 (!) + * + * See also BigDecimal#sqrt and Integer.sqrt. */ static VALUE -math_sqrt(VALUE obj, VALUE x) +math_sqrt(VALUE unused_obj, VALUE x) { - double d0, d; + return rb_math_sqrt(x); +} - 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); +inline static VALUE +f_negative_p(VALUE x) +{ + if (FIXNUM_P(x)) + return RBOOL(FIX2LONG(x) < 0); + return rb_funcall(x, '<', 1, INT2FIX(0)); +} +inline static VALUE +f_signbit(VALUE x) +{ + if (RB_FLOAT_TYPE_P(x)) { + double f = RFLOAT_VALUE(x); + return RBOOL(!isnan(f) && signbit(f)); + } + return f_negative_p(x); +} + +static VALUE +rb_math_sqrt(VALUE x) +{ + double d; + + if (RB_TYPE_P(x, T_COMPLEX)) { + VALUE neg = f_signbit(RCOMPLEX(x)->imag); + double re = Get_Double(RCOMPLEX(x)->real), im; + d = Get_Double(rb_complex_abs(x)); + im = sqrt((d - re) / 2.0); + re = sqrt((d + re) / 2.0); + if (neg) im = -im; + return rb_complex_new(DBL2NUM(re), DBL2NUM(im)); + } + d = Get_Double(x); + domain_check_min(d, 0.0, "sqrt"); + if (d == 0.0) return DBL2NUM(0.0); + return DBL2NUM(sqrt(d)); } /* @@ -639,9 +656,9 @@ math_sqrt(VALUE obj, VALUE x) * * Returns the cube root of +x+. * - * Domain: [0, INFINITY) + * Domain: (-INFINITY, INFINITY) * - * Codomain:[0, INFINITY) + * Codomain: (-INFINITY, INFINITY) * * -9.upto(9) {|x| * p [x, Math.cbrt(x), Math.cbrt(x)**3] @@ -669,10 +686,16 @@ math_sqrt(VALUE obj, VALUE x) */ static VALUE -math_cbrt(VALUE obj, VALUE x) +math_cbrt(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(cbrt(RFLOAT_VALUE(x))); + double f = Get_Double(x); + double r = cbrt(f); +#if defined __GLIBC__ + if (isfinite(r) && !(f == 0.0 && r == 0.0)) { + r = (2.0 * r + (f / r / r)) / 3.0; + } +#endif + return DBL2NUM(r); } /* @@ -680,21 +703,19 @@ math_cbrt(VALUE obj, VALUE x) * Math.frexp(x) -> [fraction, exponent] * * Returns a two-element array containing the normalized fraction (a Float) - * and exponent (a Fixnum) of +x+. + * and exponent (an Integer) of +x+. * * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] * fraction * 2**exponent #=> 1234.0 */ static VALUE -math_frexp(VALUE obj, VALUE x) +math_frexp(VALUE unused_obj, VALUE x) { double d; int exp; - Need_Float(x); - - d = frexp(RFLOAT_VALUE(x), &exp); + d = frexp(Get_Double(x), &exp); return rb_assoc_new(DBL2NUM(d), INT2NUM(exp)); } @@ -709,10 +730,9 @@ math_frexp(VALUE obj, VALUE x) */ static VALUE -math_ldexp(VALUE obj, VALUE x, VALUE n) +math_ldexp(VALUE unused_obj, VALUE x, VALUE n) { - Need_Float(x); - return DBL2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n))); + return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n))); } /* @@ -726,10 +746,9 @@ math_ldexp(VALUE obj, VALUE x, VALUE n) */ static VALUE -math_hypot(VALUE obj, VALUE x, VALUE y) +math_hypot(VALUE unused_obj, VALUE x, VALUE y) { - Need_Float2(x, y); - return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y))); + return DBL2NUM(hypot(Get_Double(x), Get_Double(y))); } /* @@ -747,10 +766,9 @@ math_hypot(VALUE obj, VALUE x, VALUE y) */ static VALUE -math_erf(VALUE obj, VALUE x) +math_erf(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(erf(RFLOAT_VALUE(x))); + return DBL2NUM(erf(Get_Double(x))); } /* @@ -768,43 +786,10 @@ math_erf(VALUE obj, VALUE x) */ static VALUE -math_erfc(VALUE obj, VALUE x) -{ - Need_Float(x); - return DBL2NUM(erfc(RFLOAT_VALUE(x))); -} - -#if defined __MINGW32__ -static inline double -ruby_tgamma(const double d) +math_erfc(VALUE unused_obj, VALUE x) { - const double g = tgamma(d); - if (isinf(g)) { - if (d == 0.0 && signbit(d)) return -INFINITY; - } - if (isnan(g)) { - if (!signbit(d)) return INFINITY; - } - return g; + return DBL2NUM(erfc(Get_Double(x))); } -#define tgamma(d) ruby_tgamma(d) -#endif - -#if defined LGAMMA_R_M0_FIX -static inline double -ruby_lgamma_r(const double d, int *sign) -{ - const double g = lgamma_r(d, sign); - if (isinf(g)) { - if (d == 0.0 && signbit(d)) { - *sign = -1; - return INFINITY; - } - } - return g; -} -#define lgamma_r(d, sign) ruby_lgamma_r(d, sign) -#endif /* * call-seq: @@ -812,7 +797,7 @@ ruby_lgamma_r(const double d, int *sign) * * Calculates the gamma function of x. * - * Note that gamma(n) is same as fact(n-1) for integer n > 0. + * Note that gamma(n) is the 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 @@ -847,7 +832,7 @@ ruby_lgamma_r(const double d, int *sign) */ static VALUE -math_gamma(VALUE obj, VALUE x) +math_gamma(VALUE unused_obj, VALUE x) { static const double fact_table[] = { /* fact(0) */ 1.0, @@ -877,22 +862,24 @@ math_gamma(VALUE obj, VALUE x) * 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); + enum {NFACT_TABLE = numberof(fact_table)}; + double d; + d = 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]); + if (isinf(d)) { + if (signbit(d)) domain_error("gamma"); + return DBL2NUM(HUGE_VAL); + } + if (d == 0.0) { + return signbit(d) ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL); + } + if (d == floor(d)) { + domain_check_min(d, 0.0, "gamma"); + if (1.0 <= d && d <= (double)NFACT_TABLE) { + return DBL2NUM(fact_table[(int)d - 1]); } } - d = tgamma(d0); - return DBL2NUM(d); + return DBL2NUM(tgamma(d)); } /* @@ -901,29 +888,31 @@ math_gamma(VALUE obj, VALUE x) * * Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+. * - * Math.lgamma(x) is same as + * Math.lgamma(x) is the same as * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1] - * but avoid overflow by Math.gamma(x) for large x. + * but avoids overflow by Math.gamma(x) for large x. * * Math.lgamma(0) #=> [Infinity, 1] * */ static VALUE -math_lgamma(VALUE obj, VALUE x) +math_lgamma(VALUE unused_obj, VALUE x) { - double d0, d; + double d; int sign=1; VALUE v; - Need_Float(x); - d0 = RFLOAT_VALUE(x); + d = Get_Double(x); /* check for domain error */ - if (isinf(d0)) { - if (signbit(d0)) domain_error("lgamma"); - return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1)); + if (isinf(d)) { + if (signbit(d)) domain_error("lgamma"); + return rb_assoc_new(DBL2NUM(HUGE_VAL), INT2FIX(1)); } - d = lgamma_r(d0, &sign); - v = DBL2NUM(d); + if (d == 0.0) { + VALUE vsign = signbit(d) ? INT2FIX(-1) : INT2FIX(+1); + return rb_assoc_new(DBL2NUM(HUGE_VAL), vsign); + } + v = DBL2NUM(lgamma_r(d, &sign)); return rb_assoc_new(v, INT2FIX(sign)); } @@ -932,14 +921,14 @@ math_lgamma(VALUE obj, VALUE x) VALUE \ rb_math_##n(VALUE x)\ {\ - return math_##n(rb_mMath, x);\ + return math_##n(0, x);\ } #define exp2(n) \ VALUE \ rb_math_##n(VALUE x, VALUE y)\ {\ - return math_##n(rb_mMath, x, y);\ + return math_##n(0, x, y);\ } exp2(atan2) @@ -947,13 +936,6 @@ 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 @@ -990,20 +972,16 @@ exp1(sqrt) void -Init_Math(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. */ + /* Definition of the mathematical constant E for Euler's number (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))); @@ -1044,3 +1022,9 @@ Init_Math(void) rb_define_module_function(rb_mMath, "gamma", math_gamma, 1); rb_define_module_function(rb_mMath, "lgamma", math_lgamma, 1); } + +void +Init_Math(void) +{ + InitVM(Math); +} |