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1 files changed, 1013 insertions, 0 deletions

diff --git a/jni/ruby/math.c b/jni/ruby/math.c
new file mode 100644
index 0000000..6bac192
--- /dev/null
+++ b/jni/ruby/math.c
@@ -0,0 +1,1013 @@
+/**********************************************************************
+
+  math.c -
+
+  $Author: akr $
+  created at: Tue Jan 25 14:12:56 JST 1994
+
+  Copyright (C) 1993-2007 Yukihiro Matsumoto
+
+**********************************************************************/
+
+#include "internal.h"
+#include <float.h>
+#include <math.h>
+#include <errno.h>
+
+#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)
+
+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 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.
+ *
+ *  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;
+    Need_Float2(y, x);
+    dx = RFLOAT_VALUE(x);
+    dy = RFLOAT_VALUE(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)
+{
+    Need_Float(x);
+    return DBL2NUM(cos(RFLOAT_VALUE(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)
+{
+    Need_Float(x);
+    return DBL2NUM(sin(RFLOAT_VALUE(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)
+{
+    Need_Float(x);
+    return DBL2NUM(tan(RFLOAT_VALUE(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;
+
+    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.
+ *
+ *  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;
+
+    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.
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: (-PI/2, PI/2)
+ *
+ *    Math.atan(0) #=> 0.0
+ */
+
+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).
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: [1, INFINITY)
+ *
+ *    Math.cosh(0) #=> 1.0
+ *
+ */
+
+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).
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: (-INFINITY, INFINITY)
+ *
+ *    Math.sinh(0) #=> 0.0
+ *
+ */
+
+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(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)
+{
+    Need_Float(x);
+    return DBL2NUM(tanh(RFLOAT_VALUE(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;
+
+    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+.
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: (-INFINITY, INFINITY)
+ *
+ *    Math.asinh(1) #=> 0.881373587019543
+ *
+ */
+
+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+.
+ *
+ *  Domain: (-1, 1)
+ *
+ *  Codomain: (-INFINITY, INFINITY)
+ *
+ *   Math.atanh(1) #=> Infinity
+ *
+ */
+
+static VALUE
+math_atanh(VALUE obj, 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.
+ *
+ *  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)
+{
+    Need_Float(x);
+    return DBL2NUM(exp(RFLOAT_VALUE(x)));
+}
+
+#if defined __CYGWIN__
+# include <cygwin/version.h>
+# 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;
+    }
+
+    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 -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;
+    }
+
+    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);
+    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;
+    }
+
+    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);
+    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;
+
+    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(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)
+{
+    Need_Float(x);
+    return DBL2NUM(cbrt(RFLOAT_VALUE(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;
+
+    Need_Float(x);
+
+    d = frexp(RFLOAT_VALUE(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)
+{
+    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+.
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: (-1, 1)
+ *
+ *    Math.erf(0) #=> 0.0
+ *
+ */
+
+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.
+ *
+ *  Domain: (-INFINITY, INFINITY)
+ *
+ *  Codomain: (0, 2)
+ *
+ *    Math.erfc(0) #=> 1.0
+ *
+ */
+
+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 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;
+    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.
+ *
+ *    Math.lgamma(0) #=> [Infinity, 1]
+ *
+ */
+
+static VALUE
+math_lgamma(VALUE obj, 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));
+}
+
+
+#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)
+ *
+ *  <em>produces:</em>
+ *
+ *     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
+Init_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);
+}