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ruby--ruby/math.c
卜部昌平 0e8219f591 make functions static 
These functions are used from within a compilation unit so we can
make them static, for better binary size.  This changeset reduces
the size of generated ruby binary from 26,590,128 bytes to
26,584,472 bytes on my macihne.
2019-11-19 12:36:19 +09:00

1033 lines
22 KiB
C
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/**********************************************************************
math.c -
$Author$
created at: Tue Jan 25 14:12:56 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#ifdef _MSC_VER
# define _USE_MATH_DEFINES 1
#endif
#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 Get_Double(x) rb_num_to_dbl(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 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);
/* check for domain error */
if (d < -1.0 || 1.0 < d) domain_error("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);
/* check for domain error */
if (d < -1.0 || 1.0 < d) domain_error("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);
/* check for domain error */
if (d < 1.0) domain_error("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);
/* check for domain error */
if (d < -1.0 || +1.0 < d) domain_error("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);
/* check for domain error */
if (d < 0.0) domain_error("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);
/* check for domain error */
if (d < 0.0) domain_error("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);
/* check for domain error */
if (d < 0.0) domain_error("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);
}
#define f_boolcast(x) ((x) ? Qtrue : Qfalse)
inline static VALUE
f_negative_p(VALUE x)
{
if (FIXNUM_P(x))
return f_boolcast(FIX2LONG(x) < 0);
return rb_funcall(x, '<', 1, INT2FIX(0));
}
inline static VALUE
f_signbit(VALUE x)
{
if (RB_TYPE_P(x, T_FLOAT)) {
double f = RFLOAT_VALUE(x);
return f_boolcast(!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);
/* check for domain error */
if (d < 0.0) domain_error("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)) {
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 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)) {
if (d < 0.0) domain_error("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 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 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 for Euler's number 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)
{
InitVM(Math);
}
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