summaryrefslogtreecommitdiff
path: root/math.c
diff options
context:
space:
mode:
Diffstat (limited to 'math.c')
-rw-r--r--math.c1149
1 files changed, 910 insertions, 239 deletions
diff --git a/math.c b/math.c
index e37ec75b49..852620da20 100644
--- a/math.c
+++ b/math.c
@@ -3,159 +3,249 @@
math.c -
$Author$
- $Date$
created at: Tue Jan 25 14:12:56 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
-#include "ruby/ruby.h"
+#include "ruby/internal/config.h"
+
+#ifdef _MSC_VER
+# define _USE_MATH_DEFINES 1
+#endif
+
+#include <float.h>
#include <math.h>
-#include <errno.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) (x) = rb_Float(x)
-#define Need_Float2(x,y) do {\
- Need_Float(x);\
- Need_Float(y);\
-} while (0)
-
-static void
-domain_check(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
+ *
+ * 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 obj, VALUE y, VALUE x)
+math_atan2(VALUE unused_obj, VALUE y, VALUE x)
{
- Need_Float2(y, x);
- return DOUBLE2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_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 <i>x</i> (expressed in radians). Returns
- * -1..1.
+ * 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 obj, VALUE x)
+math_cos(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(cos(RFLOAT_VALUE(x)));
+ 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
+ *
+ * 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 obj, VALUE x)
+math_sin(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
-
- return DOUBLE2NUM(sin(RFLOAT_VALUE(x)));
+ 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
+ *
+ * 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 obj, VALUE x)
+math_tan(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
-
- return DOUBLE2NUM(tan(RFLOAT_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
- *
- * Computes the arc cosine of <i>x</i>. Returns 0..PI.
+ * 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 obj, VALUE x)
+math_acos(VALUE unused_obj, VALUE x)
{
- double d;
-
- Need_Float(x);
- errno = 0;
- d = acos(RFLOAT_VALUE(x));
- domain_check(d, "acos");
- return DOUBLE2NUM(d);
+ math_arc(x, acos)
}
/*
* call-seq:
- * Math.asin(x) => float
- *
- * Computes the arc sine of <i>x</i>. Returns 0..PI.
+ * 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 obj, VALUE x)
+math_asin(VALUE unused_obj, VALUE x)
{
- double d;
-
- Need_Float(x);
- errno = 0;
- d = asin(RFLOAT_VALUE(x));
- domain_check(d, "asin");
- return DOUBLE2NUM(d);
+ math_arc(x, asin)
}
/*
* call-seq:
- * Math.atan(x) => float
- *
- * Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
+ * 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 obj, VALUE x)
+math_atan(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(atan(RFLOAT_VALUE(x)));
+ return DBL2NUM(atan(Get_Double(x)));
}
#ifndef HAVE_COSH
@@ -168,17 +258,26 @@ cosh(double x)
/*
* call-seq:
- * Math.cosh(x) => float
- *
- * Computes the hyperbolic cosine of <i>x</i> (expressed in radians).
+ * 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 obj, VALUE x)
+math_cosh(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
-
- return DOUBLE2NUM(cosh(RFLOAT_VALUE(x)));
+ return DBL2NUM(cosh(Get_Double(x)));
}
#ifndef HAVE_SINH
@@ -191,106 +290,199 @@ sinh(double x)
/*
* call-seq:
- * Math.sinh(x) => float
- *
- * Computes the hyperbolic sine of <i>x</i> (expressed in
- * radians).
+ * 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 obj, VALUE x)
+math_sinh(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(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
- *
- * Computes the hyperbolic tangent of <i>x</i> (expressed in
- * radians).
+ * 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 obj, VALUE x)
+math_tanh(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(tanh(RFLOAT_VALUE(x)));
+ 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
+ *
+ * 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 obj, VALUE x)
+math_acosh(VALUE unused_obj, VALUE x)
{
double d;
- Need_Float(x);
- errno = 0;
- d = acosh(RFLOAT_VALUE(x));
- domain_check(d, "acosh");
- return DOUBLE2NUM(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
+ *
+ * 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 obj, VALUE x)
+math_asinh(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(asinh(RFLOAT_VALUE(x)));
+ 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
+ *
+ * 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 obj, VALUE x)
+math_atanh(VALUE unused_obj, VALUE x)
{
double d;
- Need_Float(x);
- errno = 0;
- d = atanh(RFLOAT_VALUE(x));
- domain_check(d, "atanh");
- return DOUBLE2NUM(d);
+ d = Get_Double(x);
+ domain_check_range(d, -1.0, +1.0, "atanh");
+ /* check for pole error */
+ if (d == -1.0) return DBL2NUM(-HUGE_VAL);
+ if (d == +1.0) return DBL2NUM(+HUGE_VAL);
+ return DBL2NUM(atanh(d));
}
/*
* call-seq:
- * Math.exp(x) => float
- *
- * Returns e**x.
+ * 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 obj, VALUE x)
+math_exp(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(exp(RFLOAT_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__
@@ -302,32 +494,110 @@ 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
+
+FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE));
+
/*
* call-seq:
- * Math.log(numeric) => float
- * Math.log(num,base) => float
- *
- * Returns the natural logarithm of <i>numeric</i>.
- * If additional second argument is given, it will be the base
- * of logarithm.
+ * 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, VALUE *argv)
+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;
-
- rb_scan_args(argc, argv, "11", &x, &base);
- Need_Float(x);
- errno = 0;
- d = log(RFLOAT_VALUE(x));
- if (!NIL_P(base)) {
- Need_Float(base);
- d /= log(RFLOAT_VALUE(base));
+ 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;
}
- domain_check(d, "log");
- return DOUBLE2NUM(d);
+ return DBL2NUM(d);
}
#ifndef log2
@@ -344,172 +614,561 @@ extern double log2(double);
/*
* call-seq:
- * Math.log2(numeric) => float
- *
- * Returns the base 2 logarithm of <i>numeric</i>.
+ * 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 obj, VALUE x)
+math_log2(VALUE unused_obj, VALUE x)
{
- double d;
+ size_t numbits;
+ double d = get_double_rshift(x, &numbits);
- Need_Float(x);
- errno = 0;
- d = log2(RFLOAT_VALUE(x));
- if (errno) {
- rb_sys_fail("log2");
- }
- return DOUBLE2NUM(d);
+ 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}[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 obj, VALUE 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_VALUE(x));
- domain_check(d, "log10");
- return DOUBLE2NUM(d);
+ return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */
}
/*
* call-seq:
- * Math.sqrt(numeric) => float
- *
- * Returns the non-negative square root of <i>numeric</i>.
+ * 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_sqrt(VALUE obj, VALUE x)
+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;
- Need_Float(x);
- errno = 0;
- d = sqrt(RFLOAT_VALUE(x));
- domain_check(d, "sqrt");
- return DOUBLE2NUM(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>.
- *
- * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
- * fraction * 2**exponent #=> 1234.0
+ * 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 obj, VALUE x)
+math_frexp(VALUE unused_obj, VALUE x)
{
double d;
int exp;
- Need_Float(x);
-
- d = frexp(RFLOAT_VALUE(x), &exp);
- return rb_assoc_new(DOUBLE2NUM(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>).
- *
- * fraction, exponent = Math.frexp(1234)
- * Math.ldexp(fraction, exponent) #=> 1234.0
+ * 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 obj, VALUE x, VALUE n)
+math_ldexp(VALUE unused_obj, VALUE x, VALUE n)
{
- Need_Float(x);
- return DOUBLE2NUM(ldexp(RFLOAT_VALUE(x), 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(3, 4) #=> 5.0
+ * 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_hypot(VALUE obj, VALUE x, VALUE y)
+math_erf(VALUE unused_obj, VALUE x)
{
- Need_Float2(x, y);
- return DOUBLE2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
+ return DBL2NUM(erf(Get_Double(x)));
}
/*
* call-seq:
- * Math.erf(x) => float
+ * 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.
*
- * Calculates the error function of x.
*/
static VALUE
-math_erf(VALUE obj, VALUE x)
+math_erfc(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(erf(RFLOAT_VALUE(x)));
+ return DBL2NUM(erfc(Get_Double(x)));
}
/*
* call-seq:
- * Math.erfc(x) => float
+ * 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.
*
- * Calculates the complementary error function of x.
*/
static VALUE
-math_erfc(VALUE obj, VALUE x)
+math_gamma(VALUE unused_obj, VALUE x)
{
- Need_Float(x);
- return DOUBLE2NUM(erfc(RFLOAT_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));
}
/*
- * The <code>Math</code> module contains module functions for basic
- * trigonometric and transcendental functions. See class
- * <code>Float</code> for a list of constants that
- * define Ruby's floating point accuracy.
- */
+ * 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
-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
- rb_define_const(rb_mMath, "PI", DOUBLE2NUM(M_PI));
-#else
- rb_define_const(rb_mMath, "PI", DOUBLE2NUM(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", DOUBLE2NUM(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", DOUBLE2NUM(exp(1.0)));
+ rb_define_const(rb_mMath, "E", DBL2NUM(exp(1.0)));
#endif
rb_define_module_function(rb_mMath, "atan2", math_atan2, 2);
@@ -530,10 +1189,13 @@ Init_Math(void)
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);
@@ -542,4 +1204,13 @@ Init_Math(void)
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);
}
generated by cgit v1.2.3 (git 2.25.1) at 2026-01-21 07:12:50 +0000