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Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 1216 |
1 files changed, 1216 insertions, 0 deletions
diff --git a/math.c b/math.c new file mode 100644 index 0000000000..852620da20 --- /dev/null +++ b/math.c @@ -0,0 +1,1216 @@ +/********************************************************************** + + 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 <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 + * + * Returns the {arc tangent}[https://en.wikipedia.org/wiki/Atan2] of +y+ and +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain of +y+: <tt>[-INFINITY, INFINITY]</tt>. + * - Domain of +x+: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-PI, PI]</tt>. + * + * Examples: + * + * atan2(-1.0, -1.0) # => -2.356194490192345 # -3*PI/4 + * atan2(-1.0, 0.0) # => -1.5707963267948966 # -PI/2 + * atan2(-1.0, 1.0) # => -0.7853981633974483 # -PI/4 + * atan2(0.0, -1.0) # => 3.141592653589793 # PI + * + */ + +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 + * + * Returns the + * {cosine}[https://en.wikipedia.org/wiki/Sine_and_cosine] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>[-1.0, 1.0]</tt>. + * + * Examples: + * + * cos(-PI) # => -1.0 + * cos(-PI/2) # => 6.123031769111886e-17 # 0.0000000000000001 + * cos(0.0) # => 1.0 + * cos(PI/2) # => 6.123031769111886e-17 # 0.0000000000000001 + * cos(PI) # => -1.0 + * + */ + +static VALUE +math_cos(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(cos(Get_Double(x))); +} + +/* + * call-seq: + * Math.sin(x) -> float + * + * Returns the + * {sine}[https://en.wikipedia.org/wiki/Sine_and_cosine] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>[-1.0, 1.0]</tt>. + * + * Examples: + * + * sin(-PI) # => -1.2246063538223773e-16 # -0.0000000000000001 + * sin(-PI/2) # => -1.0 + * sin(0.0) # => 0.0 + * sin(PI/2) # => 1.0 + * sin(PI) # => 1.2246063538223773e-16 # 0.0000000000000001 + * + */ + +static VALUE +math_sin(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(sin(Get_Double(x))); +} + + +/* + * call-seq: + * Math.tan(x) -> float + * + * Returns the + * {tangent}[https://en.wikipedia.org/wiki/Trigonometric_functions] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>(-INFINITY, INFINITY)</tt>. + * + * Examples: + * + * tan(-PI) # => 1.2246467991473532e-16 # -0.0000000000000001 + * tan(-PI/2) # => -1.633123935319537e+16 # -16331239353195370.0 + * tan(0.0) # => 0.0 + * tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0 + * tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001 + * + */ + +static VALUE +math_tan(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(tan(Get_Double(x))); +} + +#define math_arc(num, func) \ + double d; \ + d = Get_Double((num)); \ + domain_check_range(d, -1.0, 1.0, #func); \ + return DBL2NUM(func(d)); + +/* + * call-seq: + * Math.acos(x) -> float + * + * Returns the {arc cosine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+. + * + * - Domain: <tt>[-1, 1]</tt>. + * - Range: <tt>[0, PI]</tt>. + * + * Examples: + * + * acos(-1.0) # => 3.141592653589793 # PI + * acos(0.0) # => 1.5707963267948966 # PI/2 + * acos(1.0) # => 0.0 + * + */ + +static VALUE +math_acos(VALUE unused_obj, VALUE x) +{ + math_arc(x, acos) +} + +/* + * call-seq: + * Math.asin(x) -> float + * + * Returns the {arc sine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+. + * + * - Domain: <tt>[-1, -1]</tt>. + * - Range: <tt>[-PI/2, PI/2]</tt>. + * + * Examples: + * + * asin(-1.0) # => -1.5707963267948966 # -PI/2 + * asin(0.0) # => 0.0 + * asin(1.0) # => 1.5707963267948966 # PI/2 + * + */ + +static VALUE +math_asin(VALUE unused_obj, VALUE x) +{ + math_arc(x, asin) +} + +/* + * call-seq: + * Math.atan(x) -> Float + * + * Returns the {arc tangent}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-PI/2, PI/2] </tt>. + * + * Examples: + * + * atan(-INFINITY) # => -1.5707963267948966 # -PI2 + * atan(-PI) # => -1.2626272556789115 + * atan(-PI/2) # => -1.0038848218538872 + * atan(0.0) # => 0.0 + * atan(PI/2) # => 1.0038848218538872 + * atan(PI) # => 1.2626272556789115 + * atan(INFINITY) # => 1.5707963267948966 # PI/2 + * + */ + +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 + * + * Returns the {hyperbolic cosine}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[1, INFINITY]</tt>. + * + * Examples: + * + * cosh(-INFINITY) # => Infinity + * cosh(0.0) # => 1.0 + * cosh(INFINITY) # => Infinity + * + */ + +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 + * + * Returns the {hyperbolic sine}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * sinh(-INFINITY) # => -Infinity + * sinh(0.0) # => 0.0 + * sinh(INFINITY) # => Infinity + * + */ + +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 + * + * Returns the {hyperbolic tangent}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+ + * in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees]. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-1, 1]</tt>. + * + * Examples: + * + * tanh(-INFINITY) # => -1.0 + * tanh(0.0) # => 0.0 + * tanh(INFINITY) # => 1.0 + * + */ + +static VALUE +math_tanh(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(tanh(Get_Double(x))); +} + +/* + * call-seq: + * Math.acosh(x) -> float + * + * Returns the {inverse hyperbolic cosine}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. + * + * - Domain: <tt>[1, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. + * + * Examples: + * + * acosh(1.0) # => 0.0 + * acosh(INFINITY) # => Infinity + * + */ + +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 + * + * Returns the {inverse hyperbolic sine}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * asinh(-INFINITY) # => -Infinity + * asinh(0.0) # => 0.0 + * asinh(INFINITY) # => Infinity + * + */ + +static VALUE +math_asinh(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(asinh(Get_Double(x))); +} + +/* + * call-seq: + * Math.atanh(x) -> float + * + * Returns the {inverse hyperbolic tangent}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. + * + * - Domain: <tt>[-1, 1]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * atanh(-1.0) # => -Infinity + * atanh(0.0) # => 0.0 + * atanh(1.0) # => 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+ raised to the +x+ power. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. + * + * Examples: + * + * exp(-INFINITY) # => 0.0 + * exp(-1.0) # => 0.36787944117144233 # 1.0/E + * exp(0.0) # => 1.0 + * exp(0.5) # => 1.6487212707001282 # sqrt(E) + * exp(1.0) # => 2.718281828459045 # E + * exp(2.0) # => 7.38905609893065 # E**2 + * exp(INFINITY) # => Infinity + * + */ + +static VALUE +math_exp(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(exp(Get_Double(x))); +} + +/* + * call-seq: + * Math.expm1(x) -> float + * + * Returns "exp(x) - 1", +e+ raised to the +x+ power, minus 1. + * + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-1.0, INFINITY]</tt>. + * + * Examples: + * + * expm1(-INFINITY) # => 0.0 + * expm1(-1.0) # => -0.6321205588285577 # 1.0/E - 1 + * expm1(0.0) # => 0.0 + * expm1(0.5) # => 0.6487212707001282 # sqrt(E) - 1 + * expm1(1.0) # => 1.718281828459045 # E - 1 + * expm1(2.0) # => 6.38905609893065 # E**2 - 1 + * expm1(INFINITY) # => Infinity + * + */ + +static VALUE +math_expm1(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(expm1(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 + +FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE)); + +/* + * call-seq: + * Math.log(x, base = Math::E) -> Float + * + * Returns the base +base+ {logarithm}[https://en.wikipedia.org/wiki/Logarithm] of +x+. + * + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY)]</tt>. + * + * Examples: + * + * log(0.0) # => -Infinity + * log(1.0) # => 0.0 + * log(E) # => 1.0 + * log(INFINITY) # => Infinity + * + * log(0.0, 2.0) # => -Infinity + * log(1.0, 2.0) # => 0.0 + * log(2.0, 2.0) # => 1.0 + * + * log(0.0, 10.0) # => -Infinity + * log(1.0, 10.0) # => 0.0 + * log(10.0, 10.0) # => 1.0 + * + */ + +static VALUE +math_log(int argc, const VALUE *argv, VALUE unused_obj) +{ + return rb_math_log(argc, argv); +} + +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_log_split(VALUE x, size_t *numbits) +{ + double d = get_double_rshift(x, numbits); + + domain_check_min(d, 0.0, "log"); + return d; +} + +#if defined(log2) || defined(HAVE_LOG2) +# define log_intermediate log2 +#else +# define log_intermediate log10 +double log2(double x); +#endif + +VALUE +rb_math_log(int argc, const VALUE *argv) +{ + VALUE x, base; + double d; + size_t numbits; + + argc = rb_scan_args(argc, argv, "11", &x, &base); + d = math_log_split(x, &numbits); + if (argc == 2) { + size_t numbits_2; + double b = math_log_split(base, &numbits_2); + /* check for pole error */ + if (d == 0.0) { + // Already DomainError if b < 0.0 + return b ? DBL2NUM(-HUGE_VAL) : DBL2NUM(NAN); + } + else if (b == 0.0) { + return DBL2NUM(-0.0); + } + d = log_intermediate(d) / log_intermediate(b); + d += (numbits - numbits_2) / log2(b); + } + else { + /* check for pole error */ + if (d == 0.0) return DBL2NUM(-HUGE_VAL); + d = log(d); + d += numbits * M_LN2; + } + return DBL2NUM(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}[https://en.wikipedia.org/wiki/Logarithm] of +x+. + * + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * log2(0.0) # => -Infinity + * log2(1.0) # => 0.0 + * log2(2.0) # => 1.0 + * log2(INFINITY) # => Infinity + * + */ + +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}[https://en.wikipedia.org/wiki/Logarithm] of +x+. + * + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * log10(0.0) # => -Infinity + * log10(1.0) # => 0.0 + * log10(10.0) # => 1.0 + * log10(INFINITY) # => Infinity + * + */ + +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) */ +} + +/* + * call-seq: + * Math.log1p(x) -> float + * + * Returns "log(x + 1)", the base E {logarithm}[https://en.wikipedia.org/wiki/Logarithm] of (+x+ + 1). + * + * - Domain: <tt>[-1, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * log1p(-1.0) # => -Infinity + * log1p(0.0) # => 0.0 + * log1p(E - 1) # => 1.0 + * log1p(INFINITY) # => Infinity + * + */ + +static VALUE +math_log1p(VALUE unused_obj, VALUE x) +{ + size_t numbits; + double d = get_double_rshift(x, &numbits); + + if (numbits != 0) { + x = rb_big_plus(x, INT2FIX(1)); + d = math_log_split(x, &numbits); + /* check for pole error */ + if (d == 0.0) return DBL2NUM(-HUGE_VAL); + d = log(d); + d += numbits * M_LN2; + return DBL2NUM(d); + } + + domain_check_min(d, -1.0, "log1p"); + /* check for pole error */ + if (d == -1.0) return DBL2NUM(-HUGE_VAL); + + return DBL2NUM(log1p(d)); /* log10(d * 2 ** numbits) */ +} + +static VALUE rb_math_sqrt(VALUE x); + +/* + * call-seq: + * Math.sqrt(x) -> float + * + * Returns the principal (non-negative) {square root}[https://en.wikipedia.org/wiki/Square_root] of +x+. + * + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. + * + * Examples: + * + * sqrt(0.0) # => 0.0 + * sqrt(0.5) # => 0.7071067811865476 + * sqrt(1.0) # => 1.0 + * sqrt(2.0) # => 1.4142135623730951 + * sqrt(4.0) # => 2.0 + * sqrt(9.0) # => 3.0 + * sqrt(INFINITY) # => Infinity + * + */ + +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}[https://en.wikipedia.org/wiki/Cube_root] of +x+. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * cbrt(-INFINITY) # => -Infinity + * cbrt(-27.0) # => -3.0 + * cbrt(-8.0) # => -2.0 + * cbrt(-2.0) # => -1.2599210498948732 + * cbrt(1.0) # => 1.0 + * cbrt(0.0) # => 0.0 + * cbrt(1.0) # => 1.0 + * cbrt(2.0) # => 1.2599210498948732 + * cbrt(8.0) # => 2.0 + * cbrt(27.0) # => 3.0 + * cbrt(INFINITY) # => Infinity + * + */ + +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 2-element array containing the normalized signed float +fraction+ + * and integer +exponent+ of +x+ such that: + * + * x = fraction * 2**exponent + * + * See {IEEE 754 double-precision binary floating-point format: binary64}[https://en.wikipedia.org/wiki/Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64]. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * frexp(-INFINITY) # => [-Infinity, -1] + * frexp(-2.0) # => [-0.5, 2] + * frexp(-1.0) # => [-0.5, 1] + * frexp(0.0) # => [0.0, 0] + * frexp(1.0) # => [0.5, 1] + * frexp(2.0) # => [0.5, 2] + * frexp(INFINITY) # => [Infinity, -1] + * + * Related: Math.ldexp (inverse of Math.frexp). + * + */ + +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 <tt>fraction * 2**exponent</tt>. + * + * - Domain of +fraction+: <tt>[0.0, 1.0)</tt>. + * - Domain of +exponent+: <tt>[0, 1024]</tt> + * (larger values are equivalent to 1024). + * + * See {IEEE 754 double-precision binary floating-point format: binary64}[https://en.wikipedia.org/wiki/Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64]. + * + * Examples: + * + * ldexp(-INFINITY, -1) # => -Infinity + * ldexp(-0.5, 2) # => -2.0 + * ldexp(-0.5, 1) # => -1.0 + * ldexp(0.0, 0) # => 0.0 + * ldexp(-0.5, 1) # => 1.0 + * ldexp(-0.5, 2) # => 2.0 + * ldexp(INFINITY, -1) # => Infinity + * + * Related: Math.frexp (inverse of Math.ldexp). + * + */ + +static VALUE +math_ldexp(VALUE unused_obj, VALUE x, VALUE n) +{ + return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n))); +} + +/* + * call-seq: + * Math.hypot(a, b) -> float + * + * Returns <tt>sqrt(a**2 + b**2)</tt>, + * which is the length of the longest side +c+ (the hypotenuse) + * of the right triangle whose other sides have lengths +a+ and +b+. + * + * - Domain of +a+: <tt>[-INFINITY, INFINITY]</tt>. + * - Domain of +ab: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. + * + * Examples: + * + * hypot(0.0, 1.0) # => 1.0 + * hypot(1.0, 1.0) # => 1.4142135623730951 # sqrt(2.0) + * hypot(3.0, 4.0) # => 5.0 + * hypot(5.0, 12.0) # => 13.0 + * hypot(1.0, sqrt(3.0)) # => 1.9999999999999998 # Near 2.0 + * + * Note that if either argument is +INFINITY+ or <tt>-INFINITY</tt>, + * the result is +Infinity+. + * + */ + +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 + * + * Returns the value of the {Gauss error function}[https://en.wikipedia.org/wiki/Error_function] for +x+. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-1, 1]</tt>. + * + * Examples: + * + * erf(-INFINITY) # => -1.0 + * erf(0.0) # => 0.0 + * erf(INFINITY) # => 1.0 + * + * Related: Math.erfc. + * + */ + +static VALUE +math_erf(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(erf(Get_Double(x))); +} + +/* + * call-seq: + * Math.erfc(x) -> Float + * + * Returns the value of the {complementary error function}[https://en.wikipedia.org/wiki/Error_function#Complementary_error_function] for +x+. + * + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[0, 2]</tt>. + * + * Examples: + * + * erfc(-INFINITY) # => 2.0 + * erfc(0.0) # => 1.0 + * erfc(INFINITY) # => 0.0 + * + * Related: Math.erf. + * + */ + +static VALUE +math_erfc(VALUE unused_obj, VALUE x) +{ + return DBL2NUM(erfc(Get_Double(x))); +} + +/* + * call-seq: + * Math.gamma(x) -> float + * + * Returns the value of the {gamma function}[https://en.wikipedia.org/wiki/Gamma_function] for +x+. + * + * - Domain: <tt>(-INFINITY, INFINITY]</tt> excluding negative integers. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. + * + * Examples: + * + * gamma(-2.5) # => -0.9453087204829431 + * gamma(-1.5) # => 2.3632718012073513 + * gamma(-0.5) # => -3.5449077018110375 + * gamma(0.0) # => Infinity + * gamma(1.0) # => 1.0 + * gamma(2.0) # => 1.0 + * gamma(3.0) # => 2.0 + * gamma(4.0) # => 6.0 + * gamma(5.0) # => 24.0 + * + * Related: Math.lgamma. + * + */ + +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] + * + * Returns a 2-element array equivalent to: + * + * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1] + * + * See {log gamma function}[https://en.wikipedia.org/wiki/Gamma_function#Log-gamma_function]. + * + * - Domain: <tt>(-INFINITY, INFINITY]</tt>. + * - Range of first element: <tt>(-INFINITY, INFINITY]</tt>. + * - Second element is -1 or 1. + * + * Examples: + * + * lgamma(-4.0) # => [Infinity, -1] + * lgamma(-3.0) # => [Infinity, -1] + * lgamma(-2.0) # => [Infinity, -1] + * lgamma(-1.0) # => [Infinity, -1] + * lgamma(0.0) # => [Infinity, 1] + * + * lgamma(1.0) # => [0.0, 1] + * lgamma(2.0) # => [0.0, 1] + * lgamma(3.0) # => [0.6931471805599436, 1] + * lgamma(4.0) # => [1.7917594692280545, 1] + * + * lgamma(-2.5) # => [-0.05624371649767279, -1] + * lgamma(-1.5) # => [0.8600470153764797, 1] + * lgamma(-0.5) # => [1.265512123484647, -1] + * lgamma(0.5) # => [0.5723649429247004, 1] + * lgamma(1.5) # => [-0.12078223763524676, 1] + * lgamma(2.5) # => [0.2846828704729205, 1] + * + * Related: Math.gamma. + * + */ + +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 + * + * :include: doc/math/math.rdoc + * + */ + + +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, "expm1", math_expm1, 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, "log1p", math_log1p, 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); +} |