diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 977 |
1 files changed, 739 insertions, 238 deletions
@@ -3,174 +3,233 @@ math.c - $Author$ - $Date$ created at: Tue Jan 25 14:12:56 JST 1994 - Copyright (C) 1993-2003 Yukihiro Matsumoto + Copyright (C) 1993-2007 Yukihiro Matsumoto **********************************************************************/ -#include "ruby.h" -#include <math.h> +#include "ruby/internal/config.h" + +#ifdef _MSC_VER +# define _USE_MATH_DEFINES 1 +#endif + #include <errno.h> +#include <float.h> +#include <math.h> -VALUE rb_mMath; +#include "internal.h" +#include "internal/bignum.h" +#include "internal/complex.h" +#include "internal/math.h" +#include "internal/object.h" +#include "internal/vm.h" -#define Need_Float(x) (x) = rb_Float(x) -#define Need_Float2(x,y) do {\ - Need_Float(x);\ - Need_Float(y);\ -} while (0) +VALUE rb_mMath; +VALUE rb_eMathDomainError; -static void -domain_check(x, msg) - double x; - char *msg; -{ - while(1) { - if (errno) { - rb_sys_fail(msg); - } - if (isnan(x)) { -#if defined(EDOM) - errno = EDOM; -#elif define(ERANGE) - errno = ERANGE; -#endif - continue; - } - break; - } -} +#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 <i>y</i> and <i>x</i>. Returns - * -PI..PI. - * + * 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(obj, y, x) - VALUE obj, x, y; +math_atan2(VALUE unused_obj, VALUE y, VALUE x) { - Need_Float2(y, x); - return rb_float_new(atan2(RFLOAT(y)->value, RFLOAT(x)->value)); + 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 <i>x</i> (expressed in radians). Returns - * -1..1. + * 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(obj, x) - VALUE obj, x; +math_cos(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(cos(RFLOAT(x)->value)); + return DBL2NUM(cos(Get_Double(x))); } /* * call-seq: - * Math.sin(x) => float - * - * Computes the sine of <i>x</i> (expressed in radians). Returns - * -1..1. + * 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(obj, x) - VALUE obj, x; +math_sin(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return rb_float_new(sin(RFLOAT(x)->value)); + return DBL2NUM(sin(Get_Double(x))); } /* * call-seq: - * Math.tan(x) => float - * - * Returns the tangent of <i>x</i> (expressed in radians). + * 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(obj, x) - VALUE obj, x; +math_tan(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return rb_float_new(tan(RFLOAT(x)->value)); + return DBL2NUM(tan(Get_Double(x))); } /* * call-seq: - * Math.acos(x) => float - * - * Computes the arc cosine of <i>x</i>. Returns 0..PI. + * 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(obj, x) - VALUE obj, x; +math_acos(VALUE unused_obj, VALUE x) { double d; - Need_Float(x); - errno = 0; - d = acos(RFLOAT(x)->value); - domain_check(d, "acos"); - return rb_float_new(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 <i>x</i>. Returns 0..PI. + * 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(obj, x) - VALUE obj, x; +math_asin(VALUE unused_obj, VALUE x) { double d; - Need_Float(x); - errno = 0; - d = asin(RFLOAT(x)->value); - domain_check(d, "asin"); - return rb_float_new(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 <i>x</i>. Returns -{PI/2} .. {PI/2}. + * 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(obj, x) - VALUE obj, x; +math_atan(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(atan(RFLOAT(x)->value)); + return DBL2NUM(atan(Get_Double(x))); } #ifndef HAVE_COSH double -cosh(x) - double x; +cosh(double x) { return (exp(x) + exp(-x)) / 2; } @@ -178,24 +237,27 @@ cosh(x) /* * call-seq: - * Math.cosh(x) => float - * - * Computes the hyperbolic cosine of <i>x</i> (expressed in radians). + * 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(obj, x) - VALUE obj, x; +math_cosh(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return rb_float_new(cosh(RFLOAT(x)->value)); + return DBL2NUM(cosh(Get_Double(x))); } #ifndef HAVE_SINH double -sinh(x) - double x; +sinh(double x) { return (exp(x) - exp(-x)) / 2; } @@ -203,113 +265,150 @@ sinh(x) /* * call-seq: - * Math.sinh(x) => float - * - * Computes the hyperbolic sine of <i>x</i> (expressed in - * radians). + * 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(obj, x) - VALUE obj, x; +math_sinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(sinh(RFLOAT(x)->value)); + return DBL2NUM(sinh(Get_Double(x))); } #ifndef HAVE_TANH double -tanh(x) - double x; +tanh(double x) { - return sinh(x) / cosh(x); +# if defined(HAVE_SINH) && defined(HAVE_COSH) + const double c = cosh(x); + if (!isinf(c)) return sinh(x) / c; +# else + const double e = exp(x+x); + if (!isinf(e)) return (e - 1) / (e + 1); +# endif + return x > 0 ? 1.0 : -1.0; } #endif /* * call-seq: - * Math.tanh() => float - * - * Computes the hyperbolic tangent of <i>x</i> (expressed in - * radians). + * 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(obj, x) - VALUE obj, x; +math_tanh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(tanh(RFLOAT(x)->value)); + return DBL2NUM(tanh(Get_Double(x))); } /* * call-seq: - * Math.acosh(x) => float - * - * Computes the inverse hyperbolic cosine of <i>x</i>. + * 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(obj, x) - VALUE obj, x; +math_acosh(VALUE unused_obj, VALUE x) { double d; - Need_Float(x); - errno = 0; - d = acosh(RFLOAT(x)->value); - domain_check(d, "acosh"); - return rb_float_new(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 <i>x</i>. + * 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(obj, x) - VALUE obj, x; +math_asinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(asinh(RFLOAT(x)->value)); + return DBL2NUM(asinh(Get_Double(x))); } /* * call-seq: - * Math.atanh(x) => float - * - * Computes the inverse hyperbolic tangent of <i>x</i>. + * 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(obj, x) - VALUE obj, x; +math_atanh(VALUE unused_obj, VALUE x) { double d; - Need_Float(x); - errno = 0; - d = atanh(RFLOAT(x)->value); - domain_check(d, "atanh"); - return rb_float_new(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 - * + * 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(obj, x) - VALUE obj, x; +math_exp(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(exp(RFLOAT(x)->value)); + return DBL2NUM(exp(Get_Double(x))); } #if defined __CYGWIN__ @@ -321,180 +420,571 @@ math_exp(obj, 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(numeric) => float - * - * Returns the natural logarithm of <i>numeric</i>. + * 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(obj, x) - VALUE obj, x; +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; - Need_Float(x); - errno = 0; - d = log(RFLOAT(x)->value); - domain_check(d, "log"); - return rb_float_new(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(numeric) => float - * - * Returns the base 10 logarithm of <i>numeric</i>. + * 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(obj, x) - VALUE obj, x; +math_log10(VALUE unused_obj, VALUE x) { - double d; + 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); - Need_Float(x); - errno = 0; - d = log10(RFLOAT(x)->value); - domain_check(d, "log10"); - return rb_float_new(d); + return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */ } +static VALUE rb_math_sqrt(VALUE x); + /* * call-seq: - * Math.sqrt(numeric) => float - * - * Returns the non-negative square root of <i>numeric</i>. + * 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(obj, x) - VALUE obj, x; +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; - Need_Float(x); - errno = 0; - d = sqrt(RFLOAT(x)->value); - domain_check(d, "sqrt"); - return rb_float_new(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.frexp(numeric) => [ fraction, exponent ] - * - * Returns a two-element array containing the normalized fraction (a - * <code>Float</code>) and exponent (a <code>Fixnum</code>) of - * <i>numeric</i>. - * + * 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(obj, x) - VALUE obj, x; +math_frexp(VALUE unused_obj, VALUE x) { double d; int exp; - Need_Float(x); - - d = frexp(RFLOAT(x)->value, &exp); - return rb_assoc_new(rb_float_new(d), INT2NUM(exp)); + d = frexp(Get_Double(x), &exp); + return rb_assoc_new(DBL2NUM(d), INT2NUM(exp)); } /* * call-seq: - * Math.ldexp(flt, int) -> float - * - * Returns the value of <i>flt</i>*(2**<i>int</i>). - * + * 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(obj, x, n) - VALUE obj, x, n; +math_ldexp(VALUE unused_obj, VALUE x, VALUE n) { - Need_Float(x); - return rb_float_new(ldexp(RFLOAT(x)->value, NUM2INT(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 <i>x</i> and <i>y</i>. - * + * 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(obj, x, y) - VALUE obj, x, y; +math_hypot(VALUE unused_obj, VALUE x, VALUE y) { - Need_Float2(x, y); - return rb_float_new(hypot(RFLOAT(x)->value, RFLOAT(y)->value)); + return DBL2NUM(hypot(Get_Double(x), Get_Double(y))); } /* * call-seq: - * Math.erf(x) => float + * Math.erf(x) -> Float + * + * Calculates the error function of +x+. + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-1, 1) + * + * Math.erf(0) #=> 0.0 * - * Calculates the error function of x. */ static VALUE -math_erf(obj, x) - VALUE obj, x; +math_erf(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(erf(RFLOAT(x)->value)); + return DBL2NUM(erf(Get_Double(x))); } /* * call-seq: - * Math.erfc(x) => float + * 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_erfc(obj, x) - VALUE obj, x; +math_lgamma(VALUE unused_obj, VALUE x) { - Need_Float(x); - return rb_float_new(erfc(RFLOAT(x)->value)); + 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 + + /* - * The <code>Math</code> module contains module functions for basic + * 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 - * <code>Float</code> for a list of constants that + * 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() +InitVM_Math(void) { rb_mMath = rb_define_module("Math"); + rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError); -#ifdef M_PI - rb_define_const(rb_mMath, "PI", rb_float_new(M_PI)); -#else - rb_define_const(rb_mMath, "PI", rb_float_new(atan(1.0)*4.0)); -#endif + /* Definition of the mathematical constant PI as a Float number. */ + rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI)); #ifdef M_E - rb_define_const(rb_mMath, "E", rb_float_new(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", rb_float_new(exp(1.0))); + rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0))); #endif rb_define_module_function(rb_mMath, "atan2", math_atan2, 2); @@ -515,9 +1005,11 @@ Init_Math() 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, "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); @@ -526,4 +1018,13 @@ Init_Math() 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); } |