core/math.rbs in rbs-2.0.0 vs core/math.rbs in rbs-2.1.0

- old
+ new

@@ -1,62 +1,87 @@ +# <!-- rdoc-file=math.c --> # 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. # # Domains and codomains are given only for real (not complex) numbers. # module Math + # <!-- + # rdoc-file=math.c + # - Math.acos(x) -> Float + # --> # Computes the arc cosine of `x`. Returns 0..PI. # # Domain: [-1, 1] # # Codomain: [0, PI] # # Math.acos(0) == Math::PI/2 #=> true # def self.acos: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.acosh(x) -> Float + # --> # Computes the inverse hyperbolic cosine of `x`. # # Domain: [1, INFINITY) # # Codomain: [0, INFINITY) # # Math.acosh(1) #=> 0.0 # def self.acosh: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.asin(x) -> Float + # --> # Computes the arc sine of `x`. Returns -PI/2..PI/2. # # Domain: [-1, -1] # # Codomain: [-PI/2, PI/2] # # Math.asin(1) == Math::PI/2 #=> true # def self.asin: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.asinh(x) -> Float + # --> # Computes the inverse hyperbolic sine of `x`. # # Domain: (-INFINITY, INFINITY) # # Codomain: (-INFINITY, INFINITY) # # Math.asinh(1) #=> 0.881373587019543 # def self.asinh: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.atan(x) -> Float + # --> # Computes the arc tangent of `x`. Returns -PI/2..PI/2. # # Domain: (-INFINITY, INFINITY) # # Codomain: (-PI/2, PI/2) # # Math.atan(0) #=> 0.0 # def self.atan: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - 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) @@ -78,20 +103,28 @@ # Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483 # Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345 # def self.atan2: (Numeric y, Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.atanh(x) -> Float + # --> # Computes the inverse hyperbolic tangent of `x`. # # Domain: (-1, 1) # # Codomain: (-INFINITY, INFINITY) # # Math.atanh(1) #=> Infinity # def self.atanh: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.cbrt(x) -> Float + # --> # Returns the cube root of `x`. # # Domain: (-INFINITY, INFINITY) # # Codomain: (-INFINITY, INFINITY) @@ -119,10 +152,14 @@ # # [8, 2.0, 8.0] # # [9, 2.0800838230519, 9.0] # def self.cbrt: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.cos(x) -> Float + # --> # Computes the cosine of `x` (expressed in radians). Returns a Float in the # range -1.0..1.0. # # Domain: (-INFINITY, INFINITY) # @@ -130,40 +167,56 @@ # # Math.cos(Math::PI) #=> -1.0 # def self.cos: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.cosh(x) -> Float + # --> # Computes the hyperbolic cosine of `x` (expressed in radians). # # Domain: (-INFINITY, INFINITY) # # Codomain: [1, INFINITY) # # Math.cosh(0) #=> 1.0 # def self.cosh: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.erf(x) -> Float + # --> # Calculates the error function of `x`. # # Domain: (-INFINITY, INFINITY) # # Codomain: (-1, 1) # # Math.erf(0) #=> 0.0 # def self.erf: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.erfc(x) -> Float + # --> # Calculates the complementary error function of x. # # Domain: (-INFINITY, INFINITY) # # Codomain: (0, 2) # # Math.erfc(0) #=> 1.0 # def self.erfc: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.exp(x) -> Float + # --> # Returns e**x. # # Domain: (-INFINITY, INFINITY) # # Codomain: (0, INFINITY) @@ -172,22 +225,30 @@ # Math.exp(1) #=> 2.718281828459045 # Math.exp(1.5) #=> 4.4816890703380645 # def self.exp: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.frexp(x) -> [fraction, exponent] + # --> # Returns a two-element array containing the normalized fraction (a Float) and # exponent (an Integer) of `x`. # # fraction, exponent = Math.frexp(1234) #=> [0.6025390625, 11] # fraction * 2**exponent #=> 1234.0 # def self.frexp: (Numeric x) -> [ Float, Integer ] + # <!-- + # rdoc-file=math.c + # - Math.gamma(x) -> Float + # --> # Calculates the gamma function of x. # - # Note that gamma(n) is same as fact(n-1) for integer n > 0. However gamma(n) - # returns float and can be an approximation. + # 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] @@ -216,37 +277,71 @@ # # [25, 6.204484017332391e+23, 620448401733239439360000] # # [26, 1.5511210043330954e+25, 15511210043330985984000000] # def self.gamma: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.hypot(x, y) -> Float + # --> # Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with # sides `x` and `y`. # # Math.hypot(3, 4) #=> 5.0 # def self.hypot: (Numeric x, Numeric y) -> Float + # <!-- + # rdoc-file=math.c + # - Math.ldexp(fraction, exponent) -> float + # --> # Returns the value of `fraction`*(2**`exponent`). # # fraction, exponent = Math.frexp(1234) # Math.ldexp(fraction, exponent) #=> 1234.0 # def self.ldexp: (Numeric fraction, Numeric exponent) -> Float + # <!-- + # rdoc-file=math.c + # - Math.lgamma(x) -> [float, -1 or 1] + # --> # Calculates the logarithmic gamma of `x` and the sign of gamma of `x`. # - # Math.lgamma(x) is same as + # Math.lgamma(x) is the same as # [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1] # - # but avoid overflow by Math.gamma(x) for large x. + # but avoids overflow by Math.gamma(x) for large x. # # Math.lgamma(0) #=> [Infinity, 1] # def self.lgamma: (Numeric x) -> [ Float, Integer ] + # <!-- + # rdoc-file=math.c + # - Math.log(x) -> Float + # - Math.log(x, base) -> Float + # --> + # Returns the logarithm of `x`. If additional second argument is given, it will + # be the base of logarithm. Otherwise it is `e` (for the natural logarithm). + # + # Domain: (0, INFINITY) + # + # Codomain: (-INFINITY, INFINITY) + # + # Math.log(0) #=> -Infinity + # Math.log(1) #=> 0.0 + # Math.log(Math::E) #=> 1.0 + # Math.log(Math::E**3) #=> 3.0 + # Math.log(12, 3) #=> 2.2618595071429146 + # def self.log: (Numeric x, ?Numeric base) -> Float + # <!-- + # rdoc-file=math.c + # - Math.log10(x) -> Float + # --> # Returns the base 10 logarithm of `x`. # # Domain: (0, INFINITY) # # Codomain: (-INFINITY, INFINITY) @@ -255,10 +350,14 @@ # Math.log10(10) #=> 1.0 # Math.log10(10**100) #=> 100.0 # def self.log10: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.log2(x) -> Float + # --> # Returns the base 2 logarithm of `x`. # # Domain: (0, INFINITY) # # Codomain: (-INFINITY, INFINITY) @@ -268,10 +367,14 @@ # Math.log2(32768) #=> 15.0 # Math.log2(65536) #=> 16.0 # def self.log2: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.sin(x) -> Float + # --> # Computes the sine of `x` (expressed in radians). Returns a Float in the range # -1.0..1.0. # # Domain: (-INFINITY, INFINITY) # @@ -279,20 +382,28 @@ # # Math.sin(Math::PI/2) #=> 1.0 # def self.sin: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.sinh(x) -> Float + # --> # Computes the hyperbolic sine of `x` (expressed in radians). # # Domain: (-INFINITY, INFINITY) # # Codomain: (-INFINITY, INFINITY) # # Math.sinh(0) #=> 0.0 # def self.sinh: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.sqrt(x) -> Float + # --> # Returns the non-negative square root of `x`. # # Domain: [0, INFINITY) # # Codomain:[0, INFINITY) @@ -319,20 +430,28 @@ # # See also BigDecimal#sqrt and Integer.sqrt. # def self.sqrt: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.tan(x) -> Float + # --> # Computes the tangent of `x` (expressed in radians). # # Domain: (-INFINITY, INFINITY) # # Codomain: (-INFINITY, INFINITY) # # Math.tan(0) #=> 0.0 # def self.tan: (Numeric x) -> Float + # <!-- + # rdoc-file=math.c + # - Math.tanh(x) -> Float + # --> # Computes the hyperbolic tangent of `x` (expressed in radians). # # Domain: (-INFINITY, INFINITY) # # Codomain: (-1, 1) @@ -340,20 +459,21 @@ # Math.tanh(0) #=> 0.0 # def self.tanh: (Numeric x) -> Float end +# <!-- rdoc-file=math.c --> # Definition of the mathematical constant E for Euler's number (e) as a Float # number. # -# Math::E: Float +# <!-- rdoc-file=math.c --> # Definition of the mathematical constant PI as a Float number. # -# Math::PI: Float +# <!-- rdoc-file=math.c --> # 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: