/math.c
C | 1030 lines | 451 code | 109 blank | 470 comment | 55 complexity | 59ae56c1863ed75523424f8e927b2ea1 MD5 | raw file
Possible License(s): LGPL-2.1, AGPL-3.0, 0BSD, Unlicense, GPL-2.0, BSD-3-Clause
- /**********************************************************************
- math.c -
- $Author$
- created at: Tue Jan 25 14:12:56 JST 1994
- Copyright (C) 1993-2007 Yukihiro Matsumoto
- **********************************************************************/
- #include "ruby/internal/config.h"
- #ifdef _MSC_VER
- # define _USE_MATH_DEFINES 1
- #endif
- #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 Get_Double(x) rb_num_to_dbl(x)
- #define domain_error(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. 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 unused_obj, VALUE y, VALUE x)
- {
- 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 unused_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 unused_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 unused_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 unused_obj, VALUE x)
- {
- double d;
- d = Get_Double(x);
- domain_check_range(d, -1.0, 1.0, "acos");
- return DBL2NUM(acos(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 unused_obj, VALUE x)
- {
- double d;
- d = Get_Double(x);
- domain_check_range(d, -1.0, 1.0, "asin");
- return DBL2NUM(asin(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 unused_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 unused_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 unused_obj, VALUE x)
- {
- return DBL2NUM(sinh(Get_Double(x)));
- }
- #ifndef HAVE_TANH
- double
- tanh(double 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
- /*
- * 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 unused_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 unused_obj, VALUE x)
- {
- double d;
- d = Get_Double(x);
- domain_check_min(d, 1.0, "acosh");
- return DBL2NUM(acosh(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 unused_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 unused_obj, VALUE x)
- {
- double d;
- d = Get_Double(x);
- domain_check_range(d, -1.0, +1.0, "atanh");
- /* check for pole error */
- if (d == -1.0) return DBL2NUM(-HUGE_VAL);
- if (d == +1.0) return DBL2NUM(+HUGE_VAL);
- return DBL2NUM(atanh(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 unused_obj, VALUE x)
- {
- return DBL2NUM(exp(Get_Double(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
- #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:
- * 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 unused_obj)
- {
- return rb_math_log(argc, argv);
- }
- VALUE
- rb_math_log(int argc, const VALUE *argv)
- {
- 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
- get_double_rshift(VALUE x, size_t *pnumbits)
- {
- 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;
- }
- *pnumbits = numbits;
- return Get_Double(x);
- }
- 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 (d == 0.0) return -HUGE_VAL;
- return log(d) + numbits * M_LN2; /* log(d * 2 ** numbits) */
- }
- #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 unused_obj, VALUE x)
- {
- size_t numbits;
- double d = get_double_rshift(x, &numbits);
- domain_check_min(d, 0.0, "log2");
- /* check for pole error */
- if (d == 0.0) return DBL2NUM(-HUGE_VAL);
- return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */
- }
- /*
- * 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 unused_obj, VALUE x)
- {
- size_t numbits;
- double d = get_double_rshift(x, &numbits);
- domain_check_min(d, 0.0, "log10");
- /* check for pole error */
- 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
- *
- * 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]
- *
- * 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 unused_obj, VALUE x)
- {
- return rb_math_sqrt(x);
- }
- 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));
- }
- /*
- * call-seq:
- * Math.cbrt(x) -> Float
- *
- * Returns the cube root of +x+.
- *
- * Domain: (-INFINITY, INFINITY)
- *
- * Codomain: (-INFINITY, 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 unused_obj, 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);
- }
- /*
- * call-seq:
- * Math.frexp(x) -> [fraction, exponent]
- *
- * Returns a two-element array containing the normalized fraction (a Float)
- * and exponent (an Integer) of +x+.
- *
- * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
- * fraction * 2**exponent #=> 1234.0
- */
- static VALUE
- math_frexp(VALUE unused_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 unused_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 unused_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 unused_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 unused_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 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
- * 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 unused_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. */
- };
- enum {NFACT_TABLE = numberof(fact_table)};
- double d;
- d = Get_Double(x);
- /* check for domain error */
- 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]);
- }
- }
- return DBL2NUM(tgamma(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 the same as
- * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
- * but avoids overflow by Math.gamma(x) for large x.
- *
- * Math.lgamma(0) #=> [Infinity, 1]
- *
- */
- static VALUE
- math_lgamma(VALUE unused_obj, VALUE x)
- {
- double d;
- int sign=1;
- VALUE v;
- d = Get_Double(x);
- /* check for domain error */
- if (isinf(d)) {
- if (signbit(d)) domain_error("lgamma");
- return rb_assoc_new(DBL2NUM(HUGE_VAL), INT2FIX(1));
- }
- 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));
- }
- #define exp1(n) \
- VALUE \
- rb_math_##n(VALUE x)\
- {\
- return math_##n(0, x);\
- }
- #define exp2(n) \
- VALUE \
- rb_math_##n(VALUE x, VALUE y)\
- {\
- return math_##n(0, x, y);\
- }
- exp2(atan2)
- exp1(cos)
- exp1(cosh)
- exp1(exp)
- exp2(hypot)
- 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
- InitVM_Math(void)
- {
- rb_mMath = rb_define_module("Math");
- rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError);
- /* Definition of the mathematical constant PI as a Float number. */
- rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI));
- #ifdef M_E
- /* 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)));
- #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)
- {
- InitVM(Math);
- }