зеркало из https://github.com/github/ruby.git
[DOC] Enhanced RDoc for Math module (#5837)
Revises intro.
Adds "What's Here".
Revises methods doc.
This commit is contained in:
Burdette Lamar
GitHub
Родитель
5701b4084e
Коммит
69c1145fa8
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@ -0,0 +1,117 @@
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\Module \Math provides methods for basic trigonometric,
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logarithmic, and transcendental functions, and for extracting roots.
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You can write its constants and method calls thus:
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Math::PI # => 3.141592653589793
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Math::E # => 2.718281828459045
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Math.sin(0.0) # => 0.0
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Math.cos(0.0) # => 1.0
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If you include module \Math, you can write simpler forms:
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include Math
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PI # => 3.141592653589793
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E # => 2.718281828459045
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sin(0.0) # => 0.0
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cos(0.0) # => 1.0
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For simplicity, the examples here assume:
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include Math
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INFINITY = Float::INFINITY
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The domains and ranges for the methods
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are denoted by open or closed intervals,
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using, respectively, parentheses or square brackets:
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- An open interval does not include the endpoints:
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(-INFINITY, INFINITY)
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- A closed interval includes the endpoints:
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[-1.0, 1.0]
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- A half-open interval includes one endpoint, but not the other:
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[1.0, INFINITY)
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Many values returned by \Math methods are numerical approximations.
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This is because many such values are, in mathematics,
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of infinite precision, while in numerical computation
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the precision is finite.
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Thus, in mathematics, <i>cos(π/2)</i> is exactly zero,
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but in our computation <tt>cos(PI/2)</tt> is a number very close to zero:
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cos(PI/2) # => 6.123031769111886e-17
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For very large and very small returned values,
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we have added formatted numbers for clarity:
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tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0
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tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001
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See class Float for the constants
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that affect Ruby's floating-point arithmetic.
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=== What's Here
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==== Trigonometric Functions
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- ::cos: Returns the cosine of the given argument.
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- ::sin: Returns the sine of the given argument.
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- ::tan: Returns the tangent of the given argument.
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==== Inverse Trigonometric Functions
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- ::acos: Returns the arc cosine of the given argument.
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- ::asin: Returns the arc sine of the given argument.
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- ::atan: Returns the arc tangent of the given argument.
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- ::atan2: Returns the arg tangent of two given arguments.
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==== Hyperbolic Trigonometric Functions
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- ::cosh: Returns the hyperbolic cosine of the given argument.
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- ::sinh: Returns the hyperbolic sine of the given argument.
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- ::tanh: Returns the hyperbolic tangent of the given argument.
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==== Inverse Hyperbolic Trigonometric Functions
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- ::acosh: Returns the inverse hyperbolic cosine of the given argument.
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- ::asinh: Returns the inverse hyperbolic sine of the given argument.
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- ::atanh: Returns the inverse hyperbolic tangent of the given argument.
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==== Exponentiation and Logarithmic Functions
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- ::exp: Returns the value of a given value raised to a given power.
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- ::log: Returns the logarithm of a given value in a given base.
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- ::log10: Returns the base 10 logarithm of the given argument.
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- ::log2: Returns the base 2 logarithm of the given argument.
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==== Fraction and Exponent Functions
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- ::frexp: Returns the fraction and exponent of the given argument.
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- ::ldexp: Returns the value for a given fraction and exponent.
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==== Root Functions
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- ::cbrt: Returns the cube root of the given argument.
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- ::sqrt: Returns the square root of the given argument.
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==== Error Functions
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- ::erf: Returns the value of the Gauss error function for the given argument.
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- ::erfc: Returns the value of the complementary error function
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for the given argument.
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==== Gamma Functions
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- ::gamma: Returns the value of the gamma function for the given argument.
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- ::lgamma: Returns the value of the logarithmic gamma function
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for the given argument.
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==== Hypotenuse Function
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- ::hypot: Returns <tt>sqrt(a**2 + b**2)</tt> for the given +a+ and +b+.
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560
math.c
560
math.c
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@ -40,31 +40,21 @@ VALUE rb_eMathDomainError;
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/*
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* call-seq:
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* Math.atan2(y, x) -> Float
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* Math.atan2(y, x) -> float
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*
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* Computes the arc tangent given +y+ and +x+.
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* Returns a Float in the range -PI..PI. Return value is a angle
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* in radians between the positive x-axis of cartesian plane
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* and the point given by the coordinates (+x+, +y+) on it.
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* Returns the {arc tangent}[https://en.wikipedia.org/wiki/Atan2] of +y+ and +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain of +y+: <tt>[-INFINITY, INFINITY]</tt>.
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* - Domain of +x+: <tt>[-INFINITY, INFINITY]</tt>.
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* - Range: <tt>[-PI, PI]</tt>.
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*
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* Codomain: [-PI, PI]
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* Examples:
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*
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* Math.atan2(-0.0, -1.0) #=> -3.141592653589793
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* Math.atan2(-1.0, -1.0) #=> -2.356194490192345
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* Math.atan2(-1.0, 0.0) #=> -1.5707963267948966
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* Math.atan2(-1.0, 1.0) #=> -0.7853981633974483
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* Math.atan2(-0.0, 1.0) #=> -0.0
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* Math.atan2(0.0, 1.0) #=> 0.0
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* Math.atan2(1.0, 1.0) #=> 0.7853981633974483
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* Math.atan2(1.0, 0.0) #=> 1.5707963267948966
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* Math.atan2(1.0, -1.0) #=> 2.356194490192345
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* Math.atan2(0.0, -1.0) #=> 3.141592653589793
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* Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483
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* Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345
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* Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483
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* Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345
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* atan2(-1.0, -1.0) # => -2.356194490192345 # -3*PI/4
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* atan2(-1.0, 0.0) # => -1.5707963267948966 # -PI/2
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* atan2(-1.0, 1.0) # => -0.7853981633974483 # -PI/4
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* atan2(0.0, -1.0) # => 3.141592653589793 # PI
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*
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*/
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@ -100,16 +90,22 @@ math_atan2(VALUE unused_obj, VALUE y, VALUE x)
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/*
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* call-seq:
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* Math.cos(x) -> Float
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* Math.cos(x) -> float
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*
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* Computes the cosine of +x+ (expressed in radians).
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* Returns a Float in the range -1.0..1.0.
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* Returns the
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* {cosine}[https://en.wikipedia.org/wiki/Sine_and_cosine] of +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>(-INFINITY, INFINITY)</tt>.
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* - Range: <tt>[-1.0, 1.0]</tt>.
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*
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* Codomain: [-1, 1]
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* Examples:
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*
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* Math.cos(Math::PI) #=> -1.0
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* cos(-PI) # => -1.0
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* cos(-PI/2) # => 6.123031769111886e-17 # 0.0000000000000001
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* cos(0.0) # => 1.0
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* cos(PI/2) # => 6.123031769111886e-17 # 0.0000000000000001
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* cos(PI) # => -1.0
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*
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*/
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@ -121,16 +117,22 @@ math_cos(VALUE unused_obj, VALUE x)
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/*
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* call-seq:
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* Math.sin(x) -> Float
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* Math.sin(x) -> float
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*
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* Computes the sine of +x+ (expressed in radians).
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* Returns a Float in the range -1.0..1.0.
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* Returns the
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* {sine}[https://en.wikipedia.org/wiki/Sine_and_cosine] of +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>(-INFINITY, INFINITY)</tt>.
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* - Range: <tt>[-1.0, 1.0]</tt>.
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*
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* Codomain: [-1, 1]
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* Examples:
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*
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* Math.sin(Math::PI/2) #=> 1.0
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* sin(-PI) # => -1.2246063538223773e-16 # -0.0000000000000001
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* sin(-PI/2) # => -1.0
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* sin(0.0) # => 0.0
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* sin(PI/2) # => 1.0
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* sin(PI) # => 1.2246063538223773e-16 # 0.0000000000000001
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*
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*/
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@ -143,15 +145,22 @@ math_sin(VALUE unused_obj, VALUE x)
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/*
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* call-seq:
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* Math.tan(x) -> Float
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* Math.tan(x) -> float
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*
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* Computes the tangent of +x+ (expressed in radians).
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* Returns the
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* {tangent}[https://en.wikipedia.org/wiki/Trigonometric_functions] of +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>(-INFINITY, INFINITY)</tt>.
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* - Range: <tt>(-INFINITY, INFINITY)</tt>.
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*
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* Codomain: (-INFINITY, INFINITY)
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* Examples:
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*
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* Math.tan(0) #=> 0.0
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* tan(-PI) # => 1.2246467991473532e-16 # -0.0000000000000001
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* tan(-PI/2) # => -1.633123935319537e+16 # -16331239353195370.0
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* tan(0.0) # => 0.0
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* tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0
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* tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001
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*
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*/
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@ -163,15 +172,18 @@ math_tan(VALUE unused_obj, VALUE x)
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/*
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* call-seq:
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* Math.acos(x) -> Float
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* Math.acos(x) -> float
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*
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* Computes the arc cosine of +x+. Returns 0..PI.
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* Returns the {arc cosine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+.
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*
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* Domain: [-1, 1]
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* - Domain: <tt>[-1, 1]</tt>.
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* - Range: <tt>[0, PI]</tt>.
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*
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* Codomain: [0, PI]
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* Examples:
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*
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* Math.acos(0) == Math::PI/2 #=> true
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* acos(-1.0) # => 3.141592653589793 # PI
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* acos(0.0) # => 1.5707963267948966 # PI/2
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* acos(1.0) # => 0.0
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*
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*/
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@ -187,15 +199,19 @@ math_acos(VALUE unused_obj, VALUE x)
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/*
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* call-seq:
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* Math.asin(x) -> Float
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* Math.asin(x) -> float
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*
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* Computes the arc sine of +x+. Returns -PI/2..PI/2.
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* Returns the {arc sine}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+.
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*
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* Domain: [-1, -1]
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* - Domain: <tt>[-1, -1]</tt>.
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* - Range: <tt>[-PI/2, PI/2]</tt>.
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*
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* Codomain: [-PI/2, PI/2]
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* Examples:
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*
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* asin(-1.0) # => -1.5707963267948966 # -PI/2
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* asin(0.0) # => 0.0
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* asin(1.0) # => 1.5707963267948966 # PI/2
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*
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* Math.asin(1) == Math::PI/2 #=> true
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*/
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static VALUE
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@ -212,13 +228,21 @@ math_asin(VALUE unused_obj, VALUE x)
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* call-seq:
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* Math.atan(x) -> Float
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*
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* Computes the arc tangent of +x+. Returns -PI/2..PI/2.
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* Returns the {arc tangent}[https://en.wikipedia.org/wiki/Inverse_trigonometric_functions] of +x+.
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
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* - Range: <tt>[-PI/2, PI/2] </tt>.
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*
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* Codomain: (-PI/2, PI/2)
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* Examples:
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*
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* atan(-INFINITY) # => -1.5707963267948966 # -PI2
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* atan(-PI) # => -1.2626272556789115
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* atan(-PI/2) # => -1.0038848218538872
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* atan(0.0) # => 0.0
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* atan(PI/2) # => 1.0038848218538872
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* atan(PI) # => 1.2626272556789115
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* atan(INFINITY) # => 1.5707963267948966 # PI/2
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*
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* Math.atan(0) #=> 0.0
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*/
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static VALUE
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@ -237,15 +261,19 @@ cosh(double x)
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/*
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* call-seq:
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* Math.cosh(x) -> Float
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* Math.cosh(x) -> float
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*
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* Computes the hyperbolic cosine of +x+ (expressed in radians).
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* Returns the {hyperbolic cosine}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
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* - Range: <tt>[1, INFINITY]</tt>.
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*
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* Codomain: [1, INFINITY)
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* Examples:
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*
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* Math.cosh(0) #=> 1.0
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* cosh(-INFINITY) # => Infinity
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* cosh(0.0) # => 1.0
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* cosh(INFINITY) # => Infinity
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*
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*/
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@ -265,15 +293,19 @@ sinh(double x)
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/*
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* call-seq:
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* Math.sinh(x) -> Float
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* Math.sinh(x) -> float
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*
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* Computes the hyperbolic sine of +x+ (expressed in radians).
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* Returns the {hyperbolic sine}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+
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* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
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||||
* - Range: <tt>[-INFINITY, INFINITY]</tt>.
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*
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* Codomain: (-INFINITY, INFINITY)
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* Examples:
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*
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* Math.sinh(0) #=> 0.0
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* sinh(-INFINITY) # => -Infinity
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* sinh(0.0) # => 0.0
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* sinh(INFINITY) # => Infinity
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*
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*/
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@ -300,15 +332,19 @@ tanh(double x)
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/*
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* call-seq:
|
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* Math.tanh(x) -> Float
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* Math.tanh(x) -> float
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*
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* Computes the hyperbolic tangent of +x+ (expressed in radians).
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* Returns the {hyperbolic tangent}[https://en.wikipedia.org/wiki/Hyperbolic_functions] of +x+
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||||
* in {radians}[https://en.wikipedia.org/wiki/Trigonometric_functions#Radians_versus_degrees].
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*
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* Domain: (-INFINITY, INFINITY)
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* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
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||||
* - Range: <tt>[-1, 1]</tt>.
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*
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* Codomain: (-1, 1)
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* Examples:
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*
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||||
* Math.tanh(0) #=> 0.0
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* tanh(-INFINITY) # => -1.0
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||||
* tanh(0.0) # => 0.0
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* tanh(INFINITY) # => 1.0
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*
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*/
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@ -320,15 +356,17 @@ math_tanh(VALUE unused_obj, VALUE x)
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/*
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* call-seq:
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||||
* Math.acosh(x) -> Float
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* Math.acosh(x) -> float
|
||||
*
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||||
* Computes the inverse hyperbolic cosine of +x+.
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||||
* Returns the {inverse hyperbolic cosine}[https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions] of +x+.
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||||
*
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||||
* Domain: [1, INFINITY)
|
||||
* - Domain: <tt>[1, INFINITY]</tt>.
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||||
* - Range: <tt>[0, INFINITY]</tt>.
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||||
*
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||||
* Codomain: [0, INFINITY)
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* Examples:
|
||||
*
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* Math.acosh(1) #=> 0.0
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||||
* acosh(1.0) # => 0.0
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||||
* acosh(INFINITY) # => Infinity
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*
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||||
*/
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@ -344,15 +382,18 @@ math_acosh(VALUE unused_obj, VALUE x)
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/*
|
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* 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -364,15 +405,18 @@ 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -391,17 +435,22 @@ 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -432,22 +481,27 @@ 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -515,18 +569,19 @@ 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -545,17 +600,19 @@ 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -576,35 +633,23 @@ static VALUE rb_math_sqrt(VALUE x);
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.sqrt(x) -> Float
|
||||
* Math.sqrt(x) -> float
|
||||
*
|
||||
* Returns the non-negative square root of +x+.
|
||||
* Returns the principal (non-negative) {square root}[https://en.wikipedia.org/wiki/Square_root] of +x+.
|
||||
*
|
||||
* Domain: [0, INFINITY)
|
||||
* - Domain: <tt>[0, INFINITY]</tt>.
|
||||
* - Range: <tt>[0, INFINITY]</tt>.
|
||||
*
|
||||
* Codomain:[0, INFINITY)
|
||||
* Examples:
|
||||
*
|
||||
* 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]
|
||||
* 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
|
||||
*
|
||||
* 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
|
||||
|
|
@ -652,36 +697,26 @@ rb_math_sqrt(VALUE x)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.cbrt(x) -> Float
|
||||
* Math.cbrt(x) -> float
|
||||
*
|
||||
* Returns the cube root of +x+.
|
||||
* Returns the {cube root}[https://en.wikipedia.org/wiki/Cube_root] of +x+.
|
||||
*
|
||||
* Domain: (-INFINITY, INFINITY)
|
||||
* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
|
||||
* - Range: <tt>[-INFINITY, INFINITY]</tt>.
|
||||
*
|
||||
* Codomain: (-INFINITY, INFINITY)
|
||||
* Examples:
|
||||
*
|
||||
* -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]
|
||||
* 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
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -700,13 +735,30 @@ math_cbrt(VALUE unused_obj, VALUE x)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.frexp(x) -> [fraction, exponent]
|
||||
* Math.frexp(x) -> [fraction, exponent]
|
||||
*
|
||||
* Returns a two-element array containing the normalized fraction (a Float)
|
||||
* and exponent (an Integer) of +x+.
|
||||
* 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).
|
||||
*
|
||||
* fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11]
|
||||
* fraction * 2**exponent #=> 1234.0
|
||||
*/
|
||||
|
||||
static VALUE
|
||||
|
|
@ -721,12 +773,28 @@ math_frexp(VALUE unused_obj, VALUE x)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.ldexp(fraction, exponent) -> float
|
||||
* Math.ldexp(fraction, exponent) -> float
|
||||
*
|
||||
* Returns the value of +fraction+*(2**+exponent+).
|
||||
* 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).
|
||||
*
|
||||
* fraction, exponent = Math.frexp(1234)
|
||||
* Math.ldexp(fraction, exponent) #=> 1234.0
|
||||
*/
|
||||
|
||||
static VALUE
|
||||
|
|
@ -737,12 +805,27 @@ math_ldexp(VALUE unused_obj, VALUE x, VALUE n)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.hypot(x, y) -> Float
|
||||
* Math.hypot(a, b) -> float
|
||||
*
|
||||
* Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with
|
||||
* sides +x+ and +y+.
|
||||
* 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+.
|
||||
*
|
||||
* Math.hypot(3, 4) #=> 5.0
|
||||
*/
|
||||
|
||||
static VALUE
|
||||
|
|
@ -753,15 +836,20 @@ math_hypot(VALUE unused_obj, VALUE x, VALUE y)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.erf(x) -> Float
|
||||
* Math.erf(x) -> float
|
||||
*
|
||||
* Calculates the error function of +x+.
|
||||
* Returns the value of the {Gauss error function}[https://en.wikipedia.org/wiki/Error_function] for +x+.
|
||||
*
|
||||
* Domain: (-INFINITY, INFINITY)
|
||||
* - Domain: <tt>[-INFINITY, INFINITY]</tt>.
|
||||
* - Range: <tt>[-1, 1]</tt>.
|
||||
*
|
||||
* Codomain: (-1, 1)
|
||||
* Examples:
|
||||
*
|
||||
* Math.erf(0) #=> 0.0
|
||||
* erf(-INFINITY) # => -1.0
|
||||
* erf(0.0) # => 0.0
|
||||
* erf(INFINITY) # => 1.0
|
||||
*
|
||||
* Related: Math.erfc.
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -775,13 +863,18 @@ 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.
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -793,41 +886,26 @@ math_erfc(VALUE unused_obj, VALUE x)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.gamma(x) -> Float
|
||||
* Math.gamma(x) -> float
|
||||
*
|
||||
* Calculates the gamma function of x.
|
||||
* Returns the value of the {gamma function}[https://en.wikipedia.org/wiki/Gamma_function] for +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.
|
||||
* - Domain: <tt>(-INFINITY, INFINITY]</tt> excluding negative integers.
|
||||
* - Range: <tt>[-INFINITY, INFINITY]</tt>.
|
||||
*
|
||||
* 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]
|
||||
* 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.
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -884,15 +962,39 @@ math_gamma(VALUE unused_obj, VALUE x)
|
|||
|
||||
/*
|
||||
* call-seq:
|
||||
* Math.lgamma(x) -> [float, -1 or 1]
|
||||
* Math.lgamma(x) -> [float, -1 or 1]
|
||||
*
|
||||
* Calculates the logarithmic gamma of +x+ and the sign of gamma of +x+.
|
||||
* Returns a 2-element array equivalent to:
|
||||
*
|
||||
* 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.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
|
||||
*
|
||||
* Math.lgamma(0) #=> [Infinity, 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]
|
||||
*
|
||||
* 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.
|
||||
*
|
||||
*/
|
||||
|
||||
|
|
@ -962,12 +1064,8 @@ 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.
|
||||
*/
|
||||
|
||||
|
||||
|
|
|
|||
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