diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 757 |
1 files changed, 479 insertions, 278 deletions
@@ -9,36 +9,47 @@ **********************************************************************/ -#include "ruby/ruby.h" -#include "internal.h" -#include <math.h> -#include <errno.h> +#include "ruby/internal/config.h" -#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ - !defined(signbit) - extern int signbit(double); +#ifdef _MSC_VER +# define _USE_MATH_DEFINES 1 #endif -#define numberof(array) (int)(sizeof(array) / sizeof((array)[0])) +#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 Need_Float(x) do {if (!RB_TYPE_P(x, T_FLOAT)) {(x) = rb_to_float(x);}} while(0) -#define Need_Float2(x,y) do {\ - Need_Float(x);\ - Need_Float(y);\ -} while (0) +#define Get_Double(x) rb_num_to_dbl(x) #define domain_error(msg) \ - rb_raise(rb_eMathDomainError, "Numerical argument is out of domain - " #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 + * 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) * - * Computes the arc tangent given <i>y</i> and <i>x</i>. Returns - * -PI..PI. + * Codomain: [-PI, PI] * * Math.atan2(-0.0, -1.0) #=> -3.141592653589793 * Math.atan2(-1.0, -1.0) #=> -2.356194490192345 @@ -50,19 +61,19 @@ VALUE rb_eMathDomainError; * Math.atan2(1.0, 0.0) #=> 1.5707963267948966 * Math.atan2(1.0, -1.0) #=> 2.356194490192345 * Math.atan2(0.0, -1.0) #=> 3.141592653589793 + * Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483 + * Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345 + * Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483 + * Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345 * */ static VALUE -math_atan2(VALUE obj, VALUE y, VALUE x) +math_atan2(VALUE unused_obj, VALUE y, VALUE x) { -#ifndef M_PI -# define M_PI 3.14159265358979323846 -#endif double dx, dy; - Need_Float2(y, x); - dx = RFLOAT_VALUE(x); - dy = RFLOAT_VALUE(y); + dx = Get_Double(x); + dy = Get_Double(y); if (dx == 0.0 && dy == 0.0) { if (!signbit(dx)) return DBL2NUM(dy); @@ -70,110 +81,150 @@ math_atan2(VALUE obj, VALUE y, VALUE x) return DBL2NUM(M_PI); return DBL2NUM(-M_PI); } - if (isinf(dx) && isinf(dy)) domain_error("atan2"); +#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 + * 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 * - * Computes the cosine of <i>x</i> (expressed in radians). Returns - * -1..1. */ static VALUE -math_cos(VALUE obj, VALUE x) +math_cos(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(cos(RFLOAT_VALUE(x))); + return DBL2NUM(cos(Get_Double(x))); } /* * call-seq: - * Math.sin(x) -> float + * 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 * - * Computes the sine of <i>x</i> (expressed in radians). Returns - * -1..1. */ static VALUE -math_sin(VALUE obj, VALUE x) +math_sin(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return DBL2NUM(sin(RFLOAT_VALUE(x))); + return DBL2NUM(sin(Get_Double(x))); } /* * call-seq: - * Math.tan(x) -> float + * Math.tan(x) -> Float + * + * Computes the tangent of +x+ (expressed in radians). + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-INFINITY, INFINITY) + * + * Math.tan(0) #=> 0.0 * - * Returns the tangent of <i>x</i> (expressed in radians). */ static VALUE -math_tan(VALUE obj, VALUE x) +math_tan(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return DBL2NUM(tan(RFLOAT_VALUE(x))); + return DBL2NUM(tan(Get_Double(x))); } /* * call-seq: - * Math.acos(x) -> float + * 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 * - * Computes the arc cosine of <i>x</i>. Returns 0..PI. */ static VALUE -math_acos(VALUE obj, VALUE x) +math_acos(VALUE unused_obj, VALUE x) { - double d0, d; + double d; - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < -1.0 || 1.0 < d0) domain_error("acos"); - d = acos(d0); - return DBL2NUM(d); + d = Get_Double(x); + domain_check_range(d, -1.0, 1.0, "acos"); + return DBL2NUM(acos(d)); } /* * call-seq: - * Math.asin(x) -> float + * Math.asin(x) -> Float + * + * Computes the arc sine of +x+. Returns -PI/2..PI/2. + * + * Domain: [-1, -1] * - * Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}. + * Codomain: [-PI/2, PI/2] + * + * Math.asin(1) == Math::PI/2 #=> true */ static VALUE -math_asin(VALUE obj, VALUE x) +math_asin(VALUE unused_obj, VALUE x) { - double d0, d; + double d; - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < -1.0 || 1.0 < d0) domain_error("asin"); - d = asin(d0); - return DBL2NUM(d); + d = Get_Double(x); + domain_check_range(d, -1.0, 1.0, "asin"); + return DBL2NUM(asin(d)); } /* * call-seq: - * Math.atan(x) -> float + * Math.atan(x) -> Float + * + * Computes the arc tangent of +x+. Returns -PI/2..PI/2. * - * Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}. + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-PI/2, PI/2) + * + * Math.atan(0) #=> 0.0 */ static VALUE -math_atan(VALUE obj, VALUE x) +math_atan(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(atan(RFLOAT_VALUE(x))); + return DBL2NUM(atan(Get_Double(x))); } #ifndef HAVE_COSH @@ -186,17 +237,22 @@ cosh(double x) /* * call-seq: - * Math.cosh(x) -> float + * Math.cosh(x) -> Float + * + * Computes the hyperbolic cosine of +x+ (expressed in radians). + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: [1, INFINITY) + * + * Math.cosh(0) #=> 1.0 * - * Computes the hyperbolic cosine of <i>x</i> (expressed in radians). */ static VALUE -math_cosh(VALUE obj, VALUE x) +math_cosh(VALUE unused_obj, VALUE x) { - Need_Float(x); - - return DBL2NUM(cosh(RFLOAT_VALUE(x))); + return DBL2NUM(cosh(Get_Double(x))); } #ifndef HAVE_SINH @@ -209,105 +265,140 @@ sinh(double x) /* * call-seq: - * Math.sinh(x) -> float + * Math.sinh(x) -> Float + * + * Computes the hyperbolic sine of +x+ (expressed in radians). + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-INFINITY, INFINITY) + * + * Math.sinh(0) #=> 0.0 * - * Computes the hyperbolic sine of <i>x</i> (expressed in - * radians). */ static VALUE -math_sinh(VALUE obj, VALUE x) +math_sinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(sinh(RFLOAT_VALUE(x))); + return DBL2NUM(sinh(Get_Double(x))); } #ifndef HAVE_TANH double 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 + * Math.tanh(x) -> Float + * + * Computes the hyperbolic tangent of +x+ (expressed in radians). + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-1, 1) + * + * Math.tanh(0) #=> 0.0 * - * Computes the hyperbolic tangent of <i>x</i> (expressed in - * radians). */ static VALUE -math_tanh(VALUE obj, VALUE x) +math_tanh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(tanh(RFLOAT_VALUE(x))); + return DBL2NUM(tanh(Get_Double(x))); } /* * call-seq: - * Math.acosh(x) -> float + * Math.acosh(x) -> Float + * + * Computes the inverse hyperbolic cosine of +x+. + * + * Domain: [1, INFINITY) + * + * Codomain: [0, INFINITY) + * + * Math.acosh(1) #=> 0.0 * - * Computes the inverse hyperbolic cosine of <i>x</i>. */ static VALUE -math_acosh(VALUE obj, VALUE x) +math_acosh(VALUE unused_obj, VALUE x) { - double d0, d; + double d; - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 1.0) domain_error("acosh"); - d = acosh(d0); - return DBL2NUM(d); + d = Get_Double(x); + domain_check_min(d, 1.0, "acosh"); + return DBL2NUM(acosh(d)); } /* * call-seq: - * Math.asinh(x) -> float + * Math.asinh(x) -> Float + * + * Computes the inverse hyperbolic sine of +x+. + * + * Domain: (-INFINITY, INFINITY) + * + * Codomain: (-INFINITY, INFINITY) + * + * Math.asinh(1) #=> 0.881373587019543 * - * Computes the inverse hyperbolic sine of <i>x</i>. */ static VALUE -math_asinh(VALUE obj, VALUE x) +math_asinh(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(asinh(RFLOAT_VALUE(x))); + return DBL2NUM(asinh(Get_Double(x))); } /* * call-seq: - * Math.atanh(x) -> float + * Math.atanh(x) -> Float + * + * Computes the inverse hyperbolic tangent of +x+. + * + * Domain: (-1, 1) + * + * Codomain: (-INFINITY, INFINITY) + * + * Math.atanh(1) #=> Infinity * - * Computes the inverse hyperbolic tangent of <i>x</i>. */ static VALUE -math_atanh(VALUE obj, VALUE x) +math_atanh(VALUE unused_obj, VALUE x) { - double d0, d; + double d; - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < -1.0 || +1.0 < d0) domain_error("atanh"); + d = Get_Double(x); + domain_check_range(d, -1.0, +1.0, "atanh"); /* check for pole error */ - if (d0 == -1.0) return DBL2NUM(-INFINITY); - if (d0 == +1.0) return DBL2NUM(+INFINITY); - d = atanh(d0); - return DBL2NUM(d); + 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 @@ -315,10 +406,9 @@ math_atanh(VALUE obj, VALUE x) */ static VALUE -math_exp(VALUE obj, VALUE x) +math_exp(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(exp(RFLOAT_VALUE(x))); + return DBL2NUM(exp(Get_Double(x))); } #if defined __CYGWIN__ @@ -330,43 +420,87 @@ math_exp(VALUE obj, VALUE 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 - * Math.log(num,base) -> float + * Math.log(x) -> Float + * Math.log(x, base) -> Float * - * Returns the natural logarithm of <i>numeric</i>. + * Returns the logarithm of +x+. * If additional second argument is given, it will be the base - * of logarithm. + * 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 + * Math.log(12, 3) #=> 2.2618595071429146 * */ static VALUE -math_log(int argc, VALUE *argv) +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 d0, d; + double d; rb_scan_args(argc, argv, "11", &x, &base); - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log"); - /* check for pole error */ - if (d0 == 0.0) return DBL2NUM(-INFINITY); - d = log(d0); + d = math_log1(x); if (argc == 2) { - Need_Float(base); - d /= log(RFLOAT_VALUE(base)); + 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 @@ -381,9 +515,13 @@ extern double log2(double); /* * call-seq: - * Math.log2(numeric) -> float + * Math.log2(x) -> Float + * + * Returns the base 2 logarithm of +x+. + * + * Domain: (0, INFINITY) * - * Returns the base 2 logarithm of <i>numeric</i>. + * Codomain: (-INFINITY, INFINITY) * * Math.log2(1) #=> 0.0 * Math.log2(2) #=> 1.0 @@ -393,25 +531,27 @@ extern double log2(double); */ static VALUE -math_log2(VALUE obj, VALUE x) +math_log2(VALUE unused_obj, VALUE x) { - double d0, d; + size_t numbits; + double d = get_double_rshift(x, &numbits); - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log2"); + domain_check_min(d, 0.0, "log2"); /* check for pole error */ - if (d0 == 0.0) return DBL2NUM(-INFINITY); - d = log2(d0); - return DBL2NUM(d); + if (d == 0.0) return DBL2NUM(-HUGE_VAL); + + return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */ } /* * call-seq: - * Math.log10(numeric) -> float + * Math.log10(x) -> Float * - * Returns the base 10 logarithm of <i>numeric</i>. + * Returns the base 10 logarithm of +x+. + * + * Domain: (0, INFINITY) + * + * Codomain: (-INFINITY, INFINITY) * * Math.log10(1) #=> 0.0 * Math.log10(10) #=> 1.0 @@ -420,190 +560,244 @@ math_log2(VALUE obj, VALUE x) */ static VALUE -math_log10(VALUE obj, VALUE x) +math_log10(VALUE unused_obj, VALUE x) { - double d0, d; + size_t numbits; + double d = get_double_rshift(x, &numbits); - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("log10"); + domain_check_min(d, 0.0, "log10"); /* check for pole error */ - if (d0 == 0.0) return DBL2NUM(-INFINITY); - d = log10(d0); - return DBL2NUM(d); + 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(numeric) -> float + * Math.sqrt(x) -> Float + * + * Returns the non-negative square root of +x+. + * + * Domain: [0, INFINITY) * - * Returns the non-negative square root of <i>numeric</i>. + * 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] + * #=> [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 obj, VALUE x) +math_sqrt(VALUE unused_obj, VALUE x) { - double d0, d; + return rb_math_sqrt(x); +} - Need_Float(x); - d0 = RFLOAT_VALUE(x); - /* check for domain error */ - if (d0 < 0.0) domain_error("sqrt"); - if (d0 == 0.0) return DBL2NUM(0.0); - d = sqrt(d0); - return DBL2NUM(d); +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(numeric) -> float + * Math.cbrt(x) -> Float * - * Returns the cube root of <i>numeric</i>. + * 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] + * #=> [-9, -2.0800838230519, -9.0] + * # [-8, -2.0, -8.0] + * # [-7, -1.91293118277239, -7.0] + * # [-6, -1.81712059283214, -6.0] + * # [-5, -1.7099759466767, -5.0] + * # [-4, -1.5874010519682, -4.0] + * # [-3, -1.44224957030741, -3.0] + * # [-2, -1.25992104989487, -2.0] + * # [-1, -1.0, -1.0] + * # [0, 0.0, 0.0] + * # [1, 1.0, 1.0] + * # [2, 1.25992104989487, 2.0] + * # [3, 1.44224957030741, 3.0] + * # [4, 1.5874010519682, 4.0] + * # [5, 1.7099759466767, 5.0] + * # [6, 1.81712059283214, 6.0] + * # [7, 1.91293118277239, 7.0] + * # [8, 2.0, 8.0] + * # [9, 2.0800838230519, 9.0] * */ static VALUE -math_cbrt(VALUE obj, VALUE x) +math_cbrt(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(cbrt(RFLOAT_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(numeric) -> [ fraction, exponent ] + * Math.frexp(x) -> [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>. + * 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 obj, VALUE x) +math_frexp(VALUE unused_obj, VALUE x) { double d; int exp; - Need_Float(x); - - d = frexp(RFLOAT_VALUE(x), &exp); + d = frexp(Get_Double(x), &exp); return rb_assoc_new(DBL2NUM(d), INT2NUM(exp)); } /* * call-seq: - * Math.ldexp(flt, int) -> float + * Math.ldexp(fraction, exponent) -> float * - * Returns the value of <i>flt</i>*(2**<i>int</i>). + * Returns the value of +fraction+*(2**+exponent+). * * fraction, exponent = Math.frexp(1234) * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE -math_ldexp(VALUE obj, VALUE x, VALUE n) +math_ldexp(VALUE unused_obj, VALUE x, VALUE n) { - Need_Float(x); - return DBL2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n))); + return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n))); } /* * call-seq: - * Math.hypot(x, y) -> float + * 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>. + * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with + * sides +x+ and +y+. * * Math.hypot(3, 4) #=> 5.0 */ static VALUE -math_hypot(VALUE obj, VALUE x, VALUE y) +math_hypot(VALUE unused_obj, VALUE x, VALUE y) { - Need_Float2(x, y); - return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y))); + 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(VALUE obj, VALUE x) +math_erf(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(erf(RFLOAT_VALUE(x))); + 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 obj, VALUE x) +math_erfc(VALUE unused_obj, VALUE x) { - Need_Float(x); - return DBL2NUM(erfc(RFLOAT_VALUE(x))); + return DBL2NUM(erfc(Get_Double(x))); } /* * call-seq: - * Math.gamma(x) -> float + * Math.gamma(x) -> Float * * Calculates the gamma function of x. * - * Note that gamma(n) is same as fact(n-1) for integer n > 0. + * 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 @@ -638,7 +832,7 @@ math_erfc(VALUE obj, VALUE x) */ static VALUE -math_gamma(VALUE obj, VALUE x) +math_gamma(VALUE unused_obj, VALUE x) { static const double fact_table[] = { /* fact(0) */ 1.0, @@ -668,51 +862,57 @@ math_gamma(VALUE obj, VALUE x) * impossible to represent exactly in IEEE 754 double which have * 53bit mantissa. */ }; - double d0, d; - double intpart, fracpart; - Need_Float(x); - d0 = RFLOAT_VALUE(x); + enum {NFACT_TABLE = numberof(fact_table)}; + double d; + d = Get_Double(x); /* check for domain error */ - if (isinf(d0) && signbit(d0)) domain_error("gamma"); - fracpart = modf(d0, &intpart); - if (fracpart == 0.0) { - if (intpart < 0) domain_error("gamma"); - if (0 < intpart && - intpart - 1 < (double)numberof(fact_table)) { - return DBL2NUM(fact_table[(int)intpart - 1]); + 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]); } } - d = tgamma(d0); - return DBL2NUM(d); + 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. + * Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+. * - * Math.lgamma(x) is same as + * Math.lgamma(x) is the same as * [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1] - * but avoid overflow by Math.gamma(x) for large x. + * but avoids overflow by Math.gamma(x) for large x. + * + * Math.lgamma(0) #=> [Infinity, 1] + * */ static VALUE -math_lgamma(VALUE obj, VALUE x) +math_lgamma(VALUE unused_obj, VALUE x) { - double d0, d; + double d; int sign=1; VALUE v; - Need_Float(x); - d0 = RFLOAT_VALUE(x); + d = Get_Double(x); /* check for domain error */ - if (isinf(d0)) { - if (signbit(d0)) domain_error("lgamma"); - return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1)); + 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); } - d = lgamma_r(d0, &sign); - v = DBL2NUM(d); + v = DBL2NUM(lgamma_r(d, &sign)); return rb_assoc_new(v, INT2FIX(sign)); } @@ -721,14 +921,14 @@ math_lgamma(VALUE obj, VALUE x) VALUE \ rb_math_##n(VALUE x)\ {\ - return math_##n(rb_mMath, x);\ + return math_##n(0, x);\ } #define exp2(n) \ VALUE \ rb_math_##n(VALUE x, VALUE y)\ {\ - return math_##n(rb_mMath, x, y);\ + return math_##n(0, x, y);\ } exp2(atan2) @@ -736,16 +936,11 @@ exp1(cos) exp1(cosh) exp1(exp) exp2(hypot) - -VALUE -rb_math_log(int argc, VALUE *argv) -{ - return math_log(argc, argv); -} - exp1(sin) exp1(sinh) +#if 0 exp1(sqrt) +#endif /* @@ -767,26 +962,26 @@ exp1(sqrt) /* * Document-class: Math * - * The <code>Math</code> module contains module functions for basic + * 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(void) +InitVM_Math(void) { rb_mMath = rb_define_module("Math"); rb_eMathDomainError = rb_define_class_under(rb_mMath, "DomainError", rb_eStandardError); -#ifdef M_PI + /* Definition of the mathematical constant PI as a Float number. */ rb_define_const(rb_mMath, "PI", DBL2NUM(M_PI)); -#else - rb_define_const(rb_mMath, "PI", DBL2NUM(atan(1.0)*4.0)); -#endif #ifdef M_E + /* Definition of the mathematical constant E 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))); @@ -827,3 +1022,9 @@ Init_Math(void) 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); +} |