JezK
Edit File: math.rbs
# <!-- 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) # # 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 # 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) # # -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] # 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) # # Codomain: [-1, 1] # # 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) # # Math.exp(0) #=> 1.0 # 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 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] # 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 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.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) # # Math.log10(1) #=> 0.0 # 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) # # Math.log2(1) #=> 0.0 # Math.log2(2) #=> 1.0 # 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) # # Codomain: [-1, 1] # # 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) # # 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] # # 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. # 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) # # 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: # # Math.acos(42) # # *produces:* # # Math::DomainError: Numerical argument is out of domain - "acos" # class Math::DomainError < StandardError end