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: