diff options
Diffstat (limited to 'math.c')
| -rw-r--r-- | math.c | 742 |
1 files changed, 425 insertions, 317 deletions
@@ -26,13 +26,6 @@ #include "internal/object.h" #include "internal/vm.h" -#if defined(HAVE_SIGNBIT) && defined(__GNUC__) && defined(__sun) && \ - !defined(signbit) - extern int signbit(double); -#endif - -#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM) - VALUE rb_mMath; VALUE rb_eMathDomainError; @@ -47,31 +40,21 @@ VALUE rb_eMathDomainError; /* * call-seq: - * Math.atan2(y, x) -> Float - * - * Computes the arc tangent given +y+ and +x+. - * Returns a Float in the range -PI..PI. Return value is a angle - * in radians between the positive x-axis of cartesian plane - * and the point given by the coordinates (+x+, +y+) on it. - * - * Domain: (-INFINITY, INFINITY) - * - * Codomain: [-PI, PI] - * - * Math.atan2(-0.0, -1.0) #=> -3.141592653589793 - * Math.atan2(-1.0, -1.0) #=> -2.356194490192345 - * Math.atan2(-1.0, 0.0) #=> -1.5707963267948966 - * Math.atan2(-1.0, 1.0) #=> -0.7853981633974483 - * Math.atan2(-0.0, 1.0) #=> -0.0 - * Math.atan2(0.0, 1.0) #=> 0.0 - * Math.atan2(1.0, 1.0) #=> 0.7853981633974483 - * Math.atan2(1.0, 0.0) #=> 1.5707963267948966 - * Math.atan2(1.0, -1.0) #=> 2.356194490192345 - * Math.atan2(0.0, -1.0) #=> 3.141592653589793 - * Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483 - * Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345 - * Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483 - * Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345 + * 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 * */ @@ -82,23 +65,23 @@ math_atan2(VALUE unused_obj, VALUE y, VALUE x) dx = Get_Double(x); dy = Get_Double(y); if (dx == 0.0 && dy == 0.0) { - if (!signbit(dx)) - return DBL2NUM(dy); + if (!signbit(dx)) + return DBL2NUM(dy); if (!signbit(dy)) - return DBL2NUM(M_PI); - return DBL2NUM(-M_PI); + 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); - } + /* 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)); @@ -107,16 +90,22 @@ math_atan2(VALUE unused_obj, VALUE y, VALUE x) /* * 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. + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>[-1.0, 1.0]</tt>. * - * Codomain: [-1, 1] + * Examples: * - * Math.cos(Math::PI) #=> -1.0 + * 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 * */ @@ -128,16 +117,22 @@ math_cos(VALUE unused_obj, VALUE 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. + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>[-1.0, 1.0]</tt>. * - * Codomain: [-1, 1] + * Examples: * - * Math.sin(Math::PI/2) #=> 1.0 + * 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 * */ @@ -150,15 +145,22 @@ math_sin(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.tan(x) -> Float + * Math.tan(x) -> float * - * Computes the tangent of +x+ (expressed in radians). + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>(-INFINITY, INFINITY)</tt>. + * - Range: <tt>(-INFINITY, INFINITY)</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.tan(0) #=> 0.0 + * 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 * */ @@ -168,64 +170,77 @@ 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 + * Math.acos(x) -> float * - * Computes the arc cosine of +x+. Returns 0..PI. + * Returns the {arc cosine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+. * - * Domain: [-1, 1] + * - Domain: <tt>[-1, 1]</tt>. + * - Range: <tt>[0, PI]</tt>. * - * Codomain: [0, PI] + * Examples: * - * Math.acos(0) == Math::PI/2 #=> true + * 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) { - double d; - - d = Get_Double(x); - domain_check_range(d, -1.0, 1.0, "acos"); - return DBL2NUM(acos(d)); + math_arc(x, acos) } /* * call-seq: - * Math.asin(x) -> Float + * Math.asin(x) -> float * - * Computes the arc sine of +x+. Returns -PI/2..PI/2. + * Returns the {arc sine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+. * - * Domain: [-1, -1] + * - Domain: <tt>[-1, -1]</tt>. + * - Range: <tt>[-PI/2, PI/2]</tt>. * - * Codomain: [-PI/2, PI/2] + * Examples: + * + * asin(-1.0) # => -1.5707963267948966 # -PI/2 + * asin(0.0) # => 0.0 + * asin(1.0) # => 1.5707963267948966 # PI/2 * - * Math.asin(1) == Math::PI/2 #=> true */ static VALUE math_asin(VALUE unused_obj, VALUE x) { - double d; - - d = Get_Double(x); - domain_check_range(d, -1.0, 1.0, "asin"); - return DBL2NUM(asin(d)); + math_arc(x, asin) } /* * call-seq: * Math.atan(x) -> Float * - * Computes the arc tangent of +x+. Returns -PI/2..PI/2. + * 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>. * - * Domain: (-INFINITY, INFINITY) + * Examples: * - * Codomain: (-PI/2, PI/2) + * 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 * - * Math.atan(0) #=> 0.0 */ static VALUE @@ -244,15 +259,19 @@ cosh(double x) /* * call-seq: - * Math.cosh(x) -> Float + * Math.cosh(x) -> float * - * Computes the hyperbolic cosine of +x+ (expressed in radians). + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[1, INFINITY]</tt>. * - * Codomain: [1, INFINITY) + * Examples: * - * Math.cosh(0) #=> 1.0 + * cosh(-INFINITY) # => Infinity + * cosh(0.0) # => 1.0 + * cosh(INFINITY) # => Infinity * */ @@ -272,15 +291,19 @@ sinh(double x) /* * call-seq: - * Math.sinh(x) -> Float + * Math.sinh(x) -> float * - * Computes the hyperbolic sine of +x+ (expressed in radians). + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.sinh(0) #=> 0.0 + * sinh(-INFINITY) # => -Infinity + * sinh(0.0) # => 0.0 + * sinh(INFINITY) # => Infinity * */ @@ -307,15 +330,19 @@ tanh(double x) /* * call-seq: - * Math.tanh(x) -> Float + * Math.tanh(x) -> float * - * Computes the hyperbolic tangent of +x+ (expressed in radians). + * 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: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-1, 1]</tt>. * - * Codomain: (-1, 1) + * Examples: * - * Math.tanh(0) #=> 0.0 + * tanh(-INFINITY) # => -1.0 + * tanh(0.0) # => 0.0 + * tanh(INFINITY) # => 1.0 * */ @@ -327,15 +354,17 @@ math_tanh(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.acosh(x) -> Float + * Math.acosh(x) -> float * - * Computes the inverse hyperbolic cosine of +x+. + * Returns the {inverse hyperbolic cosine}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. * - * Domain: [1, INFINITY) + * - Domain: <tt>[1, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. * - * Codomain: [0, INFINITY) + * Examples: * - * Math.acosh(1) #=> 0.0 + * acosh(1.0) # => 0.0 + * acosh(INFINITY) # => Infinity * */ @@ -351,15 +380,18 @@ math_acosh(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.asinh(x) -> Float + * Math.asinh(x) -> float * - * Computes the inverse hyperbolic sine of +x+. + * Returns the {inverse hyperbolic sine}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. * - * Domain: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.asinh(1) #=> 0.881373587019543 + * asinh(-INFINITY) # => -Infinity + * asinh(0.0) # => 0.0 + * asinh(INFINITY) # => Infinity * */ @@ -371,15 +403,18 @@ math_asinh(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.atanh(x) -> Float + * Math.atanh(x) -> float * - * Computes the inverse hyperbolic tangent of +x+. + * Returns the {inverse hyperbolic tangent}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+. * - * Domain: (-1, 1) + * - Domain: <tt>[-1, 1]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.atanh(1) #=> Infinity + * atanh(-1.0) # => -Infinity + * atanh(0.0) # => 0.0 + * atanh(1.0) # => Infinity * */ @@ -398,17 +433,22 @@ math_atanh(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.exp(x) -> Float + * Math.exp(x) -> float * - * Returns e**x. + * Returns +e+ raised to the +x+ power. * - * Domain: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. * - * Codomain: (0, INFINITY) + * Examples: * - * Math.exp(0) #=> 1.0 - * Math.exp(1) #=> 2.718281828459045 - * Math.exp(1.5) #=> 4.4816890703380645 + * 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 * */ @@ -434,27 +474,31 @@ math_exp(VALUE unused_obj, VALUE x) # define M_LN10 2.30258509299404568401799145468436421 #endif -static double math_log1(VALUE x); FUNC_MINIMIZED(static VALUE math_log(int, const VALUE *, VALUE)); /* * call-seq: - * Math.log(x) -> Float - * Math.log(x, base) -> Float + * Math.log(x, base = Math::E) -> 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). + * Returns the base +base+ {logarithm}[https://en.wikipedia.org/wiki/Logarithm] of +x+. * - * Domain: (0, INFINITY) + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY)]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * 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 + * 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 * */ @@ -464,20 +508,6 @@ math_log(int argc, const VALUE *argv, VALUE unused_obj) return rb_math_log(argc, argv); } -VALUE -rb_math_log(int argc, const VALUE *argv) -{ - VALUE x, base; - double d; - - rb_scan_args(argc, argv, "11", &x, &base); - d = math_log1(x); - if (argc == 2) { - d /= math_log1(base); - } - return DBL2NUM(d); -} - static double get_double_rshift(VALUE x, size_t *pnumbits) { @@ -489,23 +519,58 @@ get_double_rshift(VALUE x, size_t *pnumbits) x = rb_big_rshift(x, SIZET2NUM(numbits)); } else { - numbits = 0; + numbits = 0; } *pnumbits = numbits; return Get_Double(x); } static double -math_log1(VALUE x) +math_log_split(VALUE x, size_t *numbits) { - size_t numbits; - double d = get_double_rshift(x, &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 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; - return log(d) + numbits * M_LN2; /* log(d * 2 ** 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 @@ -522,18 +587,19 @@ extern double log2(double); /* * call-seq: - * Math.log2(x) -> Float + * Math.log2(x) -> float * - * Returns the base 2 logarithm of +x+. + * Returns the base 2 {logarithm}[https://en.wikipedia.org/wiki/Logarithm] of +x+. * - * Domain: (0, INFINITY) + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.log2(1) #=> 0.0 - * Math.log2(2) #=> 1.0 - * Math.log2(32768) #=> 15.0 - * Math.log2(65536) #=> 16.0 + * log2(0.0) # => -Infinity + * log2(1.0) # => 0.0 + * log2(2.0) # => 1.0 + * log2(INFINITY) # => Infinity * */ @@ -552,17 +618,19 @@ math_log2(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.log10(x) -> Float + * Math.log10(x) -> float * - * Returns the base 10 logarithm of +x+. + * Returns the base 10 {logarithm}[https://en.wikipedia.org/wiki/Logarithm] of +x+. * - * Domain: (0, INFINITY) + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[-INFINITY, INFINITY]</tt>. * - * Codomain: (-INFINITY, INFINITY) + * Examples: * - * Math.log10(1) #=> 0.0 - * Math.log10(10) #=> 1.0 - * Math.log10(10**100) #=> 100.0 + * log10(0.0) # => -Infinity + * log10(1.0) # => 0.0 + * log10(10.0) # => 1.0 + * log10(INFINITY) # => Infinity * */ @@ -583,35 +651,23 @@ static VALUE rb_math_sqrt(VALUE x); /* * call-seq: - * Math.sqrt(x) -> Float - * - * Returns the non-negative square root of +x+. - * - * Domain: [0, INFINITY) + * Math.sqrt(x) -> float * - * Codomain:[0, INFINITY) + * Returns the principal (non-negative) {square root}[https://en.wikipedia.org/wiki/Square_root] of +x+. * - * 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] + * - Domain: <tt>[0, INFINITY]</tt>. + * - Range: <tt>[0, INFINITY]</tt>. * - * Note that the limited precision of floating point arithmetic - * might lead to surprising results: + * Examples: * - * Math.sqrt(10**46).to_i #=> 99999999999999991611392 (!) + * 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 * - * See also BigDecimal#sqrt and Integer.sqrt. */ static VALUE @@ -620,20 +676,19 @@ math_sqrt(VALUE unused_obj, VALUE x) return rb_math_sqrt(x); } -#define f_boolcast(x) ((x) ? Qtrue : Qfalse) inline static VALUE f_negative_p(VALUE x) { if (FIXNUM_P(x)) - return f_boolcast(FIX2LONG(x) < 0); + return RBOOL(FIX2LONG(x) < 0); return rb_funcall(x, '<', 1, INT2FIX(0)); } inline static VALUE f_signbit(VALUE x) { - if (RB_TYPE_P(x, T_FLOAT)) { + if (RB_FLOAT_TYPE_P(x)) { double f = RFLOAT_VALUE(x); - return f_boolcast(!isnan(f) && signbit(f)); + return RBOOL(!isnan(f) && signbit(f)); } return f_negative_p(x); } @@ -644,13 +699,13 @@ 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)); + 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"); @@ -660,36 +715,26 @@ rb_math_sqrt(VALUE x) /* * call-seq: - * Math.cbrt(x) -> Float - * - * Returns the cube root of +x+. - * - * Domain: (-INFINITY, INFINITY) - * - * Codomain: (-INFINITY, INFINITY) - * - * -9.upto(9) {|x| - * p [x, Math.cbrt(x), Math.cbrt(x)**3] - * } - * #=> [-9, -2.0800838230519, -9.0] - * # [-8, -2.0, -8.0] - * # [-7, -1.91293118277239, -7.0] - * # [-6, -1.81712059283214, -6.0] - * # [-5, -1.7099759466767, -5.0] - * # [-4, -1.5874010519682, -4.0] - * # [-3, -1.44224957030741, -3.0] - * # [-2, -1.25992104989487, -2.0] - * # [-1, -1.0, -1.0] - * # [0, 0.0, 0.0] - * # [1, 1.0, 1.0] - * # [2, 1.25992104989487, 2.0] - * # [3, 1.44224957030741, 3.0] - * # [4, 1.5874010519682, 4.0] - * # [5, 1.7099759466767, 5.0] - * # [6, 1.81712059283214, 6.0] - * # [7, 1.91293118277239, 7.0] - * # [8, 2.0, 8.0] - * # [9, 2.0800838230519, 9.0] + * 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 * */ @@ -700,7 +745,7 @@ math_cbrt(VALUE unused_obj, VALUE 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; + r = (2.0 * r + (f / r / r)) / 3.0; } #endif return DBL2NUM(r); @@ -708,13 +753,30 @@ math_cbrt(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.frexp(x) -> [fraction, exponent] + * 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]. * - * Returns a two-element array containing the normalized fraction (a Float) - * and exponent (an Integer) of +x+. + * - 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). * - * fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] - * fraction * 2**exponent #=> 1234.0 */ static VALUE @@ -729,12 +791,28 @@ math_frexp(VALUE unused_obj, VALUE x) /* * call-seq: - * Math.ldexp(fraction, exponent) -> float + * 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). * - * Returns the value of +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]. + * + * 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). * - * fraction, exponent = Math.frexp(1234) - * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE @@ -745,12 +823,27 @@ math_ldexp(VALUE unused_obj, VALUE x, VALUE n) /* * call-seq: - * Math.hypot(x, y) -> Float + * 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>. * - * Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with - * sides +x+ and +y+. + * 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+. * - * Math.hypot(3, 4) #=> 5.0 */ static VALUE @@ -761,15 +854,20 @@ math_hypot(VALUE unused_obj, VALUE x, VALUE y) /* * call-seq: - * Math.erf(x) -> Float + * Math.erf(x) -> float + * + * Returns the value of the {Gauss error function}[https://en.wikipedia.org/wiki/Error_function] for +x+. * - * Calculates the error function of +x+. + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[-1, 1]</tt>. * - * Domain: (-INFINITY, INFINITY) + * Examples: * - * Codomain: (-1, 1) + * erf(-INFINITY) # => -1.0 + * erf(0.0) # => 0.0 + * erf(INFINITY) # => 1.0 * - * Math.erf(0) #=> 0.0 + * Related: Math.erfc. * */ @@ -783,13 +881,18 @@ math_erf(VALUE unused_obj, VALUE x) * call-seq: * Math.erfc(x) -> Float * - * Calculates the complementary error function of x. + * Returns the value of the {complementary error function}[https://en.wikipedia.org/wiki/Error_function#Complementary_error_function] for +x+. * - * Domain: (-INFINITY, INFINITY) + * - Domain: <tt>[-INFINITY, INFINITY]</tt>. + * - Range: <tt>[0, 2]</tt>. * - * Codomain: (0, 2) + * Examples: * - * Math.erfc(0) #=> 1.0 + * erfc(-INFINITY) # => 2.0 + * erfc(0.0) # => 1.0 + * erfc(INFINITY) # => 0.0 + * + * Related: Math.erf. * */ @@ -801,41 +904,26 @@ math_erfc(VALUE unused_obj, VALUE 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] + * 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. * */ @@ -875,32 +963,56 @@ math_gamma(VALUE unused_obj, VALUE x) d = Get_Double(x); /* check for domain error */ if (isinf(d)) { - if (signbit(d)) domain_error("gamma"); - return DBL2NUM(HUGE_VAL); + if (signbit(d)) domain_error("gamma"); + return DBL2NUM(HUGE_VAL); } if (d == 0.0) { - return signbit(d) ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL); + 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]); - } + 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] + * 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 {logarithmic gamma function}[https://en.wikipedia.org/wiki/Gamma_function#The_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] * - * Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+. + * lgamma(1.0) # => [0.0, 1] + * lgamma(2.0) # => [0.0, 1] + * lgamma(3.0) # => [0.6931471805599436, 1] + * lgamma(4.0) # => [1.7917594692280545, 1] * - * 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. + * 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] * - * Math.lgamma(0) #=> [Infinity, 1] + * Related: Math.gamma. * */ @@ -913,12 +1025,12 @@ math_lgamma(VALUE unused_obj, VALUE x) 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 (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); + 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)); @@ -970,12 +1082,8 @@ exp1(sqrt) /* * Document-class: Math * - * The Math module contains module functions for basic - * trigonometric and transcendental functions. See class - * Float for a list of constants that - * define Ruby's floating point accuracy. + * :include: doc/math/math.rdoc * - * Domains and codomains are given only for real (not complex) numbers. */ |