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

- old
+ new

@@ -1,121 +1,392 @@ -# Float objects represent inexact real numbers using the native architecture's -# double-precision floating point representation. +# <!-- rdoc-file=numeric.c --> +# A Float object represents a sometimes-inexact real number using the native +# architecture's double-precision floating point representation. # # Floating point has a different arithmetic and is an inexact number. So you # should know its esoteric system. See following: # -# * http://docs.sun.com/source/806-3568/ncg_goldberg.html +# * https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html # * https://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_impre # cise -# * http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems +# * https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems # # +# You can create a Float object explicitly with: +# +# * A [floating-point +# literal](doc/syntax/literals_rdoc.html#label-Float+Literals). +# +# +# You can convert certain objects to Floats with: +# +# * Method [Float](Kernel.html#method-i-Float). +# +# +# ## What's Here +# +# First, what's elsewhere. Class Float: +# +# * Inherits from [class +# Numeric](Numeric.html#class-Numeric-label-What-27s+Here). +# +# +# Here, class Float provides methods for: +# +# * [Querying](#class-Float-label-Querying) +# * [Comparing](#class-Float-label-Comparing) +# * [Converting](#class-Float-label-Converting) +# +# +# ### Querying +# +# #finite? +# : Returns whether `self` is finite. +# +# #hash +# : Returns the integer hash code for `self`. +# +# #infinite? +# : Returns whether `self` is infinite. +# +# #nan? +# : Returns whether `self` is a NaN (not-a-number). +# +# +# +# ### Comparing +# +# [<](#method-i-3C) +# : Returns whether `self` is less than the given value. +# +# [<=](#method-i-3C-3D) +# : Returns whether `self` is less than or equal to the given value. +# +# [<=>](#method-i-3C-3D-3E) +# : Returns a number indicating whether `self` is less than, equal to, or +# greater than the given value. +# +# [==](#method-i-3D-3D) (aliased as #=== and #eql>) +# : Returns whether `self` is equal to the given value. +# +# [>](#method-i-3E) +# : Returns whether `self` is greater than the given value. +# +# [>=](#method-i-3E-3D) +# : Returns whether `self` is greater than or equal to the given value. +# +# +# +# ### Converting +# +# #% (aliased as #modulo) +# : Returns `self` modulo the given value. +# +# #* +# : Returns the product of `self` and the given value. +# +# [**](#method-i-2A-2A) +# : Returns the value of `self` raised to the power of the given value. +# +# #+ +# : Returns the sum of `self` and the given value. +# +# #- +# : Returns the difference of `self` and the given value. +# +# [/](#method-i-2F) +# : Returns the quotient of `self` and the given value. +# +# #ceil +# : Returns the smallest number greater than or equal to `self`. +# +# #coerce +# : Returns a 2-element array containing the given value converted to a +# Float and `self` +# +# #divmod +# : Returns a 2-element array containing the quotient and remainder +# results of dividing `self` by the given value. +# +# #fdiv +# : Returns the Float result of dividing `self` by the given value. +# +# #floor +# : Returns the greatest number smaller than or equal to `self`. +# +# #next_float +# : Returns the next-larger representable Float. +# +# #prev_float +# : Returns the next-smaller representable Float. +# +# #quo +# : Returns the quotient from dividing `self` by the given value. +# +# #round +# : Returns `self` rounded to the nearest value, to a given precision. +# +# #to_i (aliased as #to_int) +# : Returns `self` truncated to an Integer. +# +# #to_s (aliased as #inspect) +# : Returns a string containing the place-value representation of `self` +# in the given radix. +# +# #truncate +# : Returns `self` truncated to a given precision. +# class Float < Numeric public - # Returns the modulo after division of `float` by `other`. + # <!-- + # rdoc-file=numeric.c + # - self % other -> float + # --> + # Returns `self` modulo `other` as a float. # - # 6543.21.modulo(137) #=> 104.21000000000004 - # 6543.21.modulo(137.24) #=> 92.92999999999961 + # For float `f` and real number `r`, these expressions are equivalent: # + # f % r + # f-r*(f/r).floor + # f.divmod(r)[1] + # + # See Numeric#divmod. + # + # Examples: + # + # 10.0 % 2 # => 0.0 + # 10.0 % 3 # => 1.0 + # 10.0 % 4 # => 2.0 + # + # 10.0 % -2 # => 0.0 + # 10.0 % -3 # => -2.0 + # 10.0 % -4 # => -2.0 + # + # 10.0 % 4.0 # => 2.0 + # 10.0 % Rational(4, 1) # => 2.0 + # + # Float#modulo is an alias for Float#%. + # def %: (Integer) -> Float | (Float) -> Float | (Rational) -> Float | (Numeric) -> Numeric - # Returns a new Float which is the product of `float` and `other`. + # <!-- + # rdoc-file=numeric.c + # - self * other -> numeric + # --> + # Returns a new Float which is the product of `self` and `other`: # + # f = 3.14 + # f * 2 # => 6.28 + # f * 2.0 # => 6.28 + # f * Rational(1, 2) # => 1.57 + # f * Complex(2, 0) # => (6.28+0.0i) + # def *: (Complex) -> Complex | (Numeric) -> Float - # Raises `float` to the power of `other`. + # <!-- + # rdoc-file=numeric.c + # - self ** other -> numeric + # --> + # Raises `self` to the power of `other`: # - # 2.0**3 #=> 8.0 + # f = 3.14 + # f ** 2 # => 9.8596 + # f ** -2 # => 0.1014239928597509 + # f ** 2.1 # => 11.054834900588839 + # f ** Rational(2, 1) # => 9.8596 + # f ** Complex(2, 0) # => (9.8596+0i) # def **: (Complex) -> Complex | (Numeric) -> Float - # Returns a new Float which is the sum of `float` and `other`. + # <!-- + # rdoc-file=numeric.c + # - self + other -> numeric + # --> + # Returns a new Float which is the sum of `self` and `other`: # + # f = 3.14 + # f + 1 # => 4.140000000000001 + # f + 1.0 # => 4.140000000000001 + # f + Rational(1, 1) # => 4.140000000000001 + # f + Complex(1, 0) # => (4.140000000000001+0i) + # def +: (Complex) -> Complex | (Numeric) -> Float def +@: () -> Float - # Returns a new Float which is the difference of `float` and `other`. + # <!-- + # rdoc-file=numeric.c + # - self - other -> numeric + # --> + # Returns a new Float which is the difference of `self` and `other`: # + # f = 3.14 + # f - 1 # => 2.14 + # f - 1.0 # => 2.14 + # f - Rational(1, 1) # => 2.14 + # f - Complex(1, 0) # => (2.14+0i) + # def -: (Complex) -> Complex | (Numeric) -> Float + # <!-- + # rdoc-file=numeric.rb + # - -float -> float + # --> # Returns `float`, negated. # def -@: () -> Float - # Returns a new Float which is the result of dividing `float` by `other`. + # <!-- + # rdoc-file=numeric.c + # - self / other -> numeric + # --> + # Returns a new Float which is the result of dividing `self` by `other`: # + # f = 3.14 + # f / 2 # => 1.57 + # f / 2.0 # => 1.57 + # f / Rational(2, 1) # => 1.57 + # f / Complex(2, 0) # => (1.57+0.0i) + # def /: (Complex) -> Complex | (Numeric) -> Float - # Returns `true` if `float` is less than `real`. + # <!-- + # rdoc-file=numeric.c + # - self < other -> true or false + # --> + # Returns `true` if `self` is numerically less than `other`: # - # The result of `NaN < NaN` is undefined, so an implementation-dependent value - # is returned. + # 2.0 < 3 # => true + # 2.0 < 3.0 # => true + # 2.0 < Rational(3, 1) # => true + # 2.0 < 2.0 # => false # + # `Float::NAN < Float::NAN` returns an implementation-dependent value. + # def <: (Numeric) -> bool - # Returns `true` if `float` is less than or equal to `real`. + # <!-- + # rdoc-file=numeric.c + # - self <= other -> true or false + # --> + # Returns `true` if `self` is numerically less than or equal to `other`: # - # The result of `NaN <= NaN` is undefined, so an implementation-dependent value - # is returned. + # 2.0 <= 3 # => true + # 2.0 <= 3.0 # => true + # 2.0 <= Rational(3, 1) # => true + # 2.0 <= 2.0 # => true + # 2.0 <= 1.0 # => false # + # `Float::NAN <= Float::NAN` returns an implementation-dependent value. + # def <=: (Numeric) -> bool - # Returns -1, 0, or +1 depending on whether `float` is less than, equal to, or - # greater than `real`. This is the basis for the tests in the Comparable module. + # <!-- + # rdoc-file=numeric.c + # - self <=> other -> -1, 0, +1, or nil + # --> + # Returns a value that depends on the numeric relation between `self` and + # `other`: # - # The result of `NaN <=> NaN` is undefined, so an implementation-dependent value - # is returned. + # * -1, if `self` is less than `other`. + # * 0, if `self` is equal to `other`. + # * 1, if `self` is greater than `other`. + # * `nil`, if the two values are incommensurate. # - # `nil` is returned if the two values are incomparable. # + # Examples: + # + # 2.0 <=> 2 # => 0 + # 2.0 <=> 2.0 # => 0 + # 2.0 <=> Rational(2, 1) # => 0 + # 2.0 <=> Complex(2, 0) # => 0 + # 2.0 <=> 1.9 # => 1 + # 2.0 <=> 2.1 # => -1 + # 2.0 <=> 'foo' # => nil + # + # This is the basis for the tests in the Comparable module. + # + # `Float::NAN <=> Float::NAN` returns an implementation-dependent value. + # def <=>: (Numeric) -> Integer? - # Returns `true` only if `obj` has the same value as `float`. Contrast this with - # Float#eql?, which requires `obj` to be a Float. + # <!-- + # rdoc-file=numeric.c + # - self == other -> true or false + # --> + # Returns `true` if `other` has the same value as `self`, `false` otherwise: # - # 1.0 == 1 #=> true + # 2.0 == 2 # => true + # 2.0 == 2.0 # => true + # 2.0 == Rational(2, 1) # => true + # 2.0 == Complex(2, 0) # => true # - # The result of `NaN == NaN` is undefined, so an implementation-dependent value - # is returned. + # `Float::NAN == Float::NAN` returns an implementation-dependent value. # + # Related: Float#eql? (requires `other` to be a Float). + # def ==: (untyped) -> bool - # Returns `true` only if `obj` has the same value as `float`. Contrast this with - # Float#eql?, which requires `obj` to be a Float. + # <!-- rdoc-file=numeric.c --> + # Returns `true` if `other` has the same value as `self`, `false` otherwise: # - # 1.0 == 1 #=> true + # 2.0 == 2 # => true + # 2.0 == 2.0 # => true + # 2.0 == Rational(2, 1) # => true + # 2.0 == Complex(2, 0) # => true # - # The result of `NaN == NaN` is undefined, so an implementation-dependent value - # is returned. + # `Float::NAN == Float::NAN` returns an implementation-dependent value. # + # Related: Float#eql? (requires `other` to be a Float). + # def ===: (untyped) -> bool - # Returns `true` if `float` is greater than `real`. + # <!-- + # rdoc-file=numeric.c + # - self > other -> true or false + # --> + # Returns `true` if `self` is numerically greater than `other`: # - # The result of `NaN > NaN` is undefined, so an implementation-dependent value - # is returned. + # 2.0 > 1 # => true + # 2.0 > 1.0 # => true + # 2.0 > Rational(1, 2) # => true + # 2.0 > 2.0 # => false # + # `Float::NAN > Float::NAN` returns an implementation-dependent value. + # def >: (Numeric) -> bool - # Returns `true` if `float` is greater than or equal to `real`. + # <!-- + # rdoc-file=numeric.c + # - self >= other -> true or false + # --> + # Returns `true` if `self` is numerically greater than or equal to `other`: # - # The result of `NaN >= NaN` is undefined, so an implementation-dependent value - # is returned. + # 2.0 >= 1 # => true + # 2.0 >= 1.0 # => true + # 2.0 >= Rational(1, 2) # => true + # 2.0 >= 2.0 # => true + # 2.0 >= 2.1 # => false # + # `Float::NAN >= Float::NAN` returns an implementation-dependent value. + # def >=: (Numeric) -> bool + # <!-- + # rdoc-file=numeric.rb + # - float.abs -> float + # - float.magnitude -> float + # --> # Returns the absolute value of `float`. # # (-34.56).abs #=> 34.56 # -34.56.abs #=> 34.56 # 34.56.abs #=> 34.56 @@ -124,143 +395,215 @@ # def abs: () -> Float def abs2: () -> Float + # <!-- rdoc-file=complex.c --> # Returns 0 if the value is positive, pi otherwise. # def angle: () -> (Integer | Float) + # <!-- + # rdoc-file=complex.c + # - flo.arg -> 0 or float + # - flo.angle -> 0 or float + # - flo.phase -> 0 or float + # --> # Returns 0 if the value is positive, pi otherwise. # alias arg angle - # Returns the smallest number greater than or equal to `float` with a precision - # of `ndigits` decimal digits (default: 0). + # <!-- + # rdoc-file=numeric.c + # - ceil(ndigits = 0) -> float or integer + # --> + # Returns the smallest number greater than or equal to `self` with a precision + # of `ndigits` decimal digits. # - # When the precision is negative, the returned value is an integer with at least - # `ndigits.abs` trailing zeros. + # When `ndigits` is positive, returns a float with `ndigits` digits after the + # decimal point (as available): # - # Returns a floating point number when `ndigits` is positive, otherwise returns - # an integer. + # f = 12345.6789 + # f.ceil(1) # => 12345.7 + # f.ceil(3) # => 12345.679 + # f = -12345.6789 + # f.ceil(1) # => -12345.6 + # f.ceil(3) # => -12345.678 # - # 1.2.ceil #=> 2 - # 2.0.ceil #=> 2 - # (-1.2).ceil #=> -1 - # (-2.0).ceil #=> -2 + # When `ndigits` is non-positive, returns an integer with at least `ndigits.abs` + # trailing zeros: # - # 1.234567.ceil(2) #=> 1.24 - # 1.234567.ceil(3) #=> 1.235 - # 1.234567.ceil(4) #=> 1.2346 - # 1.234567.ceil(5) #=> 1.23457 + # f = 12345.6789 + # f.ceil(0) # => 12346 + # f.ceil(-3) # => 13000 + # f = -12345.6789 + # f.ceil(0) # => -12345 + # f.ceil(-3) # => -12000 # - # 34567.89.ceil(-5) #=> 100000 - # 34567.89.ceil(-4) #=> 40000 - # 34567.89.ceil(-3) #=> 35000 - # 34567.89.ceil(-2) #=> 34600 - # 34567.89.ceil(-1) #=> 34570 - # 34567.89.ceil(0) #=> 34568 - # 34567.89.ceil(1) #=> 34567.9 - # 34567.89.ceil(2) #=> 34567.89 - # 34567.89.ceil(3) #=> 34567.89 - # - # Note that the limited precision of floating point arithmetic might lead to + # Note that the limited precision of floating-point arithmetic may lead to # surprising results: # # (2.1 / 0.7).ceil #=> 4 (!) # + # Related: Float#floor. + # def ceil: () -> Integer | (int digits) -> (Integer | Float) - # Returns an array with both `numeric` and `float` represented as Float objects. + # <!-- + # rdoc-file=numeric.c + # - coerce(other) -> array + # --> + # Returns a 2-element array containing `other` converted to a Float and `self`: # - # This is achieved by converting `numeric` to a Float. + # f = 3.14 # => 3.14 + # f.coerce(2) # => [2.0, 3.14] + # f.coerce(2.0) # => [2.0, 3.14] + # f.coerce(Rational(1, 2)) # => [0.5, 3.14] + # f.coerce(Complex(1, 0)) # => [1.0, 3.14] # - # 1.2.coerce(3) #=> [3.0, 1.2] - # 2.5.coerce(1.1) #=> [1.1, 2.5] + # Raises an exception if a type conversion fails. # - def coerce: (Numeric) -> [Float, Float] + def coerce: (Numeric) -> [ Float, Float ] def conj: () -> Float def conjugate: () -> Float + # <!-- + # rdoc-file=rational.c + # - flo.denominator -> integer + # --> # Returns the denominator (always positive). The result is machine dependent. # # See also Float#numerator. # def denominator: () -> Integer def div: (Numeric) -> Integer - # See Numeric#divmod. + # <!-- + # rdoc-file=numeric.c + # - divmod(other) -> array + # --> + # Returns a 2-element array `[q, r]`, where # - # 42.0.divmod(6) #=> [7, 0.0] - # 42.0.divmod(5) #=> [8, 2.0] + # q = (self/other).floor # Quotient + # r = self % other # Remainder # - def divmod: (Numeric) -> [Numeric, Numeric] + # Examples: + # + # 11.0.divmod(4) # => [2, 3.0] + # 11.0.divmod(-4) # => [-3, -1.0] + # -11.0.divmod(4) # => [-3, 1.0] + # -11.0.divmod(-4) # => [2, -3.0] + # + # 12.0.divmod(4) # => [3, 0.0] + # 12.0.divmod(-4) # => [-3, 0.0] + # -12.0.divmod(4) # => [-3, -0.0] + # -12.0.divmod(-4) # => [3, -0.0] + # + # 13.0.divmod(4.0) # => [3, 1.0] + # 13.0.divmod(Rational(4, 1)) # => [3, 1.0] + # + def divmod: (Numeric) -> [ Numeric, Numeric ] def dup: () -> self - # Returns `true` only if `obj` is a Float with the same value as `float`. - # Contrast this with Float#==, which performs type conversions. + # <!-- + # rdoc-file=numeric.c + # - eql?(other) -> true or false + # --> + # Returns `true` if `other` is a Float with the same value as `self`, `false` + # otherwise: # - # 1.0.eql?(1) #=> false + # 2.0.eql?(2.0) # => true + # 2.0.eql?(1.0) # => false + # 2.0.eql?(1) # => false + # 2.0.eql?(Rational(2, 1)) # => false + # 2.0.eql?(Complex(2, 0)) # => false # - # The result of `NaN.eql?(NaN)` is undefined, so an implementation-dependent - # value is returned. + # `Float::NAN.eql?(Float::NAN)` returns an implementation-dependent value. # + # Related: Float#== (performs type conversions). + # def eql?: (untyped) -> bool - # Returns `float / numeric`, same as Float#/. + # <!-- rdoc-file=numeric.c --> + # Returns the quotient from dividing `self` by `other`: # + # f = 3.14 + # f.quo(2) # => 1.57 + # f.quo(-2) # => -1.57 + # f.quo(Rational(2, 1)) # => 1.57 + # f.quo(Complex(2, 0)) # => (1.57+0.0i) + # + # Float#fdiv is an alias for Float#quo. + # def fdiv: (Complex) -> Complex | (Numeric) -> Float - # Returns `true` if `float` is a valid IEEE floating point number, i.e. it is - # not infinite and Float#nan? is `false`. + # <!-- + # rdoc-file=numeric.c + # - finite? -> true or false + # --> + # Returns `true` if `self` is not `Infinity`, `-Infinity`, or `Nan`, `false` + # otherwise: # + # f = 2.0 # => 2.0 + # f.finite? # => true + # f = 1.0/0.0 # => Infinity + # f.finite? # => false + # f = -1.0/0.0 # => -Infinity + # f.finite? # => false + # f = 0.0/0.0 # => NaN + # f.finite? # => false + # def finite?: () -> bool - # Returns the largest number less than or equal to `float` with a precision of - # `ndigits` decimal digits (default: 0). + # <!-- + # rdoc-file=numeric.c + # - floor(ndigits = 0) -> float or integer + # --> + # Returns the largest number less than or equal to `self` with a precision of + # `ndigits` decimal digits. # - # When the precision is negative, the returned value is an integer with at least - # `ndigits.abs` trailing zeros. + # When `ndigits` is positive, returns a float with `ndigits` digits after the + # decimal point (as available): # - # Returns a floating point number when `ndigits` is positive, otherwise returns - # an integer. + # f = 12345.6789 + # f.floor(1) # => 12345.6 + # f.floor(3) # => 12345.678 + # f = -12345.6789 + # f.floor(1) # => -12345.7 + # f.floor(3) # => -12345.679 # - # 1.2.floor #=> 1 - # 2.0.floor #=> 2 - # (-1.2).floor #=> -2 - # (-2.0).floor #=> -2 + # When `ndigits` is non-positive, returns an integer with at least `ndigits.abs` + # trailing zeros: # - # 1.234567.floor(2) #=> 1.23 - # 1.234567.floor(3) #=> 1.234 - # 1.234567.floor(4) #=> 1.2345 - # 1.234567.floor(5) #=> 1.23456 + # f = 12345.6789 + # f.floor(0) # => 12345 + # f.floor(-3) # => 12000 + # f = -12345.6789 + # f.floor(0) # => -12346 + # f.floor(-3) # => -13000 # - # 34567.89.floor(-5) #=> 0 - # 34567.89.floor(-4) #=> 30000 - # 34567.89.floor(-3) #=> 34000 - # 34567.89.floor(-2) #=> 34500 - # 34567.89.floor(-1) #=> 34560 - # 34567.89.floor(0) #=> 34567 - # 34567.89.floor(1) #=> 34567.8 - # 34567.89.floor(2) #=> 34567.89 - # 34567.89.floor(3) #=> 34567.89 - # - # Note that the limited precision of floating point arithmetic might lead to + # Note that the limited precision of floating-point arithmetic may lead to # surprising results: # # (0.3 / 0.1).floor #=> 2 (!) # + # Related: Float#ceil. + # def floor: () -> Integer | (int digits) -> (Integer | Numeric) - # Returns a hash code for this float. + # <!-- + # rdoc-file=numeric.c + # - hash -> integer + # --> + # Returns the integer hash value for `self`. # # See also Object#hash. # def hash: () -> Integer @@ -268,171 +611,241 @@ def imag: () -> Integer def imaginary: () -> Integer - # Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, - # or `+Infinity`. + # <!-- + # rdoc-file=numeric.c + # - infinite? -> -1, 1, or nil + # --> + # Returns: # - # (0.0).infinite? #=> nil - # (-1.0/0.0).infinite? #=> -1 - # (+1.0/0.0).infinite? #=> 1 + # * 1, if `self` is `Infinity`. + # * -1 if `self` is `-Infinity`. + # * `nil`, otherwise. # + # + # Examples: + # + # f = 1.0/0.0 # => Infinity + # f.infinite? # => 1 + # f = -1.0/0.0 # => -Infinity + # f.infinite? # => -1 + # f = 1.0 # => 1.0 + # f.infinite? # => nil + # f = 0.0/0.0 # => NaN + # f.infinite? # => nil + # def infinite?: () -> Integer? + # <!-- rdoc-file=numeric.c --> + # Returns a string containing a representation of `self`; depending of the value + # of `self`, the string representation may contain: + # + # * A fixed-point number. + # * A number in "scientific notation" (containing an exponent). + # * 'Infinity'. + # * '-Infinity'. + # * 'NaN' (indicating not-a-number). + # + # 3.14.to_s # => "3.14" (10.1**50).to_s # => + # "1.644631821843879e+50" (10.1**500).to_s # => "Infinity" + # (-10.1**500).to_s # => "-Infinity" (0.0/0.0).to_s # => "NaN" + # alias inspect to_s def integer?: () -> bool - # Returns the absolute value of `float`. + # <!-- + # rdoc-file=numeric.rb + # - magnitude() + # --> # - # (-34.56).abs #=> 34.56 - # -34.56.abs #=> 34.56 - # 34.56.abs #=> 34.56 - # - # Float#magnitude is an alias for Float#abs. - # alias magnitude abs - # Returns the modulo after division of `float` by `other`. + # <!-- rdoc-file=numeric.c --> + # Returns `self` modulo `other` as a float. # - # 6543.21.modulo(137) #=> 104.21000000000004 - # 6543.21.modulo(137.24) #=> 92.92999999999961 + # For float `f` and real number `r`, these expressions are equivalent: # + # f % r + # f-r*(f/r).floor + # f.divmod(r)[1] + # + # See Numeric#divmod. + # + # Examples: + # + # 10.0 % 2 # => 0.0 + # 10.0 % 3 # => 1.0 + # 10.0 % 4 # => 2.0 + # + # 10.0 % -2 # => 0.0 + # 10.0 % -3 # => -2.0 + # 10.0 % -4 # => -2.0 + # + # 10.0 % 4.0 # => 2.0 + # 10.0 % Rational(4, 1) # => 2.0 + # + # Float#modulo is an alias for Float#%. + # def modulo: (Numeric) -> Float - # Returns `true` if `float` is an invalid IEEE floating point number. + # <!-- + # rdoc-file=numeric.c + # - nan? -> true or false + # --> + # Returns `true` if `self` is a NaN, `false` otherwise. # - # a = -1.0 #=> -1.0 - # a.nan? #=> false - # a = 0.0/0.0 #=> NaN - # a.nan? #=> true + # f = -1.0 #=> -1.0 + # f.nan? #=> false + # f = 0.0/0.0 #=> NaN + # f.nan? #=> true # def nan?: () -> bool + # <!-- + # rdoc-file=numeric.rb + # - float.negative? -> true or false + # --> # Returns `true` if `float` is less than 0. # def negative?: () -> bool - # Returns the next representable floating point number. + # <!-- + # rdoc-file=numeric.c + # - next_float -> float + # --> + # Returns the next-larger representable Float. # - # Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY. + # These examples show the internally stored values (64-bit hexadecimal) for each + # Float `f` and for the corresponding `f.next_float`: # - # Float::NAN.next_float is Float::NAN. + # f = 0.0 # 0x0000000000000000 + # f.next_float # 0x0000000000000001 # - # For example: + # f = 0.01 # 0x3f847ae147ae147b + # f.next_float # 0x3f847ae147ae147c # - # 0.01.next_float #=> 0.010000000000000002 - # 1.0.next_float #=> 1.0000000000000002 - # 100.0.next_float #=> 100.00000000000001 + # In the remaining examples here, the output is shown in the usual way (result + # `to_s`): # - # 0.01.next_float - 0.01 #=> 1.734723475976807e-18 - # 1.0.next_float - 1.0 #=> 2.220446049250313e-16 - # 100.0.next_float - 100.0 #=> 1.4210854715202004e-14 + # 0.01.next_float # => 0.010000000000000002 + # 1.0.next_float # => 1.0000000000000002 + # 100.0.next_float # => 100.00000000000001 # - # f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float } - # #=> 0x1.47ae147ae147bp-7 0.01 - # # 0x1.47ae147ae147cp-7 0.010000000000000002 - # # 0x1.47ae147ae147dp-7 0.010000000000000004 - # # 0x1.47ae147ae147ep-7 0.010000000000000005 - # # 0x1.47ae147ae147fp-7 0.010000000000000007 - # # 0x1.47ae147ae148p-7 0.010000000000000009 - # # 0x1.47ae147ae1481p-7 0.01000000000000001 - # # 0x1.47ae147ae1482p-7 0.010000000000000012 - # # 0x1.47ae147ae1483p-7 0.010000000000000014 - # # 0x1.47ae147ae1484p-7 0.010000000000000016 - # # 0x1.47ae147ae1485p-7 0.010000000000000018 - # # 0x1.47ae147ae1486p-7 0.01000000000000002 - # # 0x1.47ae147ae1487p-7 0.010000000000000021 - # # 0x1.47ae147ae1488p-7 0.010000000000000023 - # # 0x1.47ae147ae1489p-7 0.010000000000000024 - # # 0x1.47ae147ae148ap-7 0.010000000000000026 - # # 0x1.47ae147ae148bp-7 0.010000000000000028 - # # 0x1.47ae147ae148cp-7 0.01000000000000003 - # # 0x1.47ae147ae148dp-7 0.010000000000000031 - # # 0x1.47ae147ae148ep-7 0.010000000000000033 + # f = 0.01 + # (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float } # - # f = 0.0 - # 100.times { f += 0.1 } - # f #=> 9.99999999999998 # should be 10.0 in the ideal world. - # 10-f #=> 1.9539925233402755e-14 # the floating point error. - # 10.0.next_float-10 #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place). - # (10-f)/(10.0.next_float-10) #=> 11.0 # the error is 11 ulp. - # (10-f)/(10*Float::EPSILON) #=> 8.8 # approximation of the above. - # "%a" % 10 #=> "0x1.4p+3" - # "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp. + # Output: # + # 0 0x1.47ae147ae147bp-7 0.01 + # 1 0x1.47ae147ae147cp-7 0.010000000000000002 + # 2 0x1.47ae147ae147dp-7 0.010000000000000004 + # 3 0x1.47ae147ae147ep-7 0.010000000000000005 + # + # f = 0.0; 100.times { f += 0.1 } + # f # => 9.99999999999998 # should be 10.0 in the ideal world. + # 10-f # => 1.9539925233402755e-14 # the floating point error. + # 10.0.next_float-10 # => 1.7763568394002505e-15 # 1 ulp (unit in the last place). + # (10-f)/(10.0.next_float-10) # => 11.0 # the error is 11 ulp. + # (10-f)/(10*Float::EPSILON) # => 8.8 # approximation of the above. + # "%a" % 10 # => "0x1.4p+3" + # "%a" % f # => "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp. + # + # Related: Float#prev_float + # def next_float: () -> Float def nonzero?: () -> self? + # <!-- + # rdoc-file=rational.c + # - flo.numerator -> integer + # --> # Returns the numerator. The result is machine dependent. # # n = 0.3.numerator #=> 5404319552844595 # d = 0.3.denominator #=> 18014398509481984 # n.fdiv(d) #=> 0.3 # # See also Float#denominator. # def numerator: () -> Integer + # <!-- rdoc-file=complex.c --> # Returns 0 if the value is positive, pi otherwise. # alias phase angle def polar: () -> [ Float, Integer | Float ] + # <!-- + # rdoc-file=numeric.rb + # - float.positive? -> true or false + # --> # Returns `true` if `float` is greater than 0. # def positive?: () -> bool - # Returns the previous representable floating point number. + # <!-- + # rdoc-file=numeric.c + # - float.prev_float -> float + # --> + # Returns the next-smaller representable Float. # - # (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is - # -Float::INFINITY. + # These examples show the internally stored values (64-bit hexadecimal) for each + # Float `f` and for the corresponding `f.pev_float`: # - # Float::NAN.prev_float is Float::NAN. + # f = 5e-324 # 0x0000000000000001 + # f.prev_float # 0x0000000000000000 # - # For example: + # f = 0.01 # 0x3f847ae147ae147b + # f.prev_float # 0x3f847ae147ae147a # - # 0.01.prev_float #=> 0.009999999999999998 - # 1.0.prev_float #=> 0.9999999999999999 - # 100.0.prev_float #=> 99.99999999999999 + # In the remaining examples here, the output is shown in the usual way (result + # `to_s`): # - # 0.01 - 0.01.prev_float #=> 1.734723475976807e-18 - # 1.0 - 1.0.prev_float #=> 1.1102230246251565e-16 - # 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14 + # 0.01.prev_float # => 0.009999999999999998 + # 1.0.prev_float # => 0.9999999999999999 + # 100.0.prev_float # => 99.99999999999999 # - # f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float } - # #=> 0x1.47ae147ae147bp-7 0.01 - # # 0x1.47ae147ae147ap-7 0.009999999999999998 - # # 0x1.47ae147ae1479p-7 0.009999999999999997 - # # 0x1.47ae147ae1478p-7 0.009999999999999995 - # # 0x1.47ae147ae1477p-7 0.009999999999999993 - # # 0x1.47ae147ae1476p-7 0.009999999999999992 - # # 0x1.47ae147ae1475p-7 0.00999999999999999 - # # 0x1.47ae147ae1474p-7 0.009999999999999988 - # # 0x1.47ae147ae1473p-7 0.009999999999999986 - # # 0x1.47ae147ae1472p-7 0.009999999999999985 - # # 0x1.47ae147ae1471p-7 0.009999999999999983 - # # 0x1.47ae147ae147p-7 0.009999999999999981 - # # 0x1.47ae147ae146fp-7 0.00999999999999998 - # # 0x1.47ae147ae146ep-7 0.009999999999999978 - # # 0x1.47ae147ae146dp-7 0.009999999999999976 - # # 0x1.47ae147ae146cp-7 0.009999999999999974 - # # 0x1.47ae147ae146bp-7 0.009999999999999972 - # # 0x1.47ae147ae146ap-7 0.00999999999999997 - # # 0x1.47ae147ae1469p-7 0.009999999999999969 - # # 0x1.47ae147ae1468p-7 0.009999999999999967 + # f = 0.01 + # (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float } # + # Output: + # + # 0 0x1.47ae147ae147bp-7 0.01 + # 1 0x1.47ae147ae147ap-7 0.009999999999999998 + # 2 0x1.47ae147ae1479p-7 0.009999999999999997 + # 3 0x1.47ae147ae1478p-7 0.009999999999999995 + # + # Related: Float#next_float. + # def prev_float: () -> Float - # Returns `float / numeric`, same as Float#/. + # <!-- + # rdoc-file=numeric.c + # - quo(other) -> numeric + # --> + # Returns the quotient from dividing `self` by `other`: # + # f = 3.14 + # f.quo(2) # => 1.57 + # f.quo(-2) # => -1.57 + # f.quo(Rational(2, 1)) # => 1.57 + # f.quo(Complex(2, 0)) # => (1.57+0.0i) + # + # Float#fdiv is an alias for Float#quo. + # def quo: (Complex) -> Complex | (Numeric) -> Float + # <!-- + # rdoc-file=rational.c + # - flt.rationalize([eps]) -> rational + # --> # Returns a simpler approximation of the value (flt-|eps| <= result <= # flt+|eps|). If the optional argument `eps` is not given, it will be chosen # automatically. # # 0.3.rationalize #=> (3/10) @@ -451,99 +864,118 @@ alias rectangular rect def remainder: (Numeric) -> Float - # Returns `float` rounded to the nearest value with a precision of `ndigits` - # decimal digits (default: 0). + # <!-- + # rdoc-file=numeric.c + # - round(ndigits = 0, half: :up]) -> integer or float + # --> + # Returns `self` rounded to the nearest value with a precision of `ndigits` + # decimal digits. # - # When the precision is negative, the returned value is an integer with at least - # `ndigits.abs` trailing zeros. + # When `ndigits` is non-negative, returns a float with `ndigits` after the + # decimal point (as available): # - # Returns a floating point number when `ndigits` is positive, otherwise returns - # an integer. + # f = 12345.6789 + # f.round(1) # => 12345.7 + # f.round(3) # => 12345.679 + # f = -12345.6789 + # f.round(1) # => -12345.7 + # f.round(3) # => -12345.679 # - # 1.4.round #=> 1 - # 1.5.round #=> 2 - # 1.6.round #=> 2 - # (-1.5).round #=> -2 + # When `ndigits` is negative, returns an integer with at least `ndigits.abs` + # trailing zeros: # - # 1.234567.round(2) #=> 1.23 - # 1.234567.round(3) #=> 1.235 - # 1.234567.round(4) #=> 1.2346 - # 1.234567.round(5) #=> 1.23457 + # f = 12345.6789 + # f.round(0) # => 12346 + # f.round(-3) # => 12000 + # f = -12345.6789 + # f.round(0) # => -12346 + # f.round(-3) # => -12000 # - # 34567.89.round(-5) #=> 0 - # 34567.89.round(-4) #=> 30000 - # 34567.89.round(-3) #=> 35000 - # 34567.89.round(-2) #=> 34600 - # 34567.89.round(-1) #=> 34570 - # 34567.89.round(0) #=> 34568 - # 34567.89.round(1) #=> 34567.9 - # 34567.89.round(2) #=> 34567.89 - # 34567.89.round(3) #=> 34567.89 + # If keyword argument `half` is given, and `self` is equidistant from the two + # candidate values, the rounding is according to the given `half` value: # - # If the optional `half` keyword argument is given, numbers that are half-way - # between two possible rounded values will be rounded according to the specified - # tie-breaking `mode`: + # * `:up` or `nil`: round away from zero: # - # * `:up` or `nil`: round half away from zero (default) - # * `:down`: round half toward zero - # * `:even`: round half toward the nearest even number + # 2.5.round(half: :up) # => 3 + # 3.5.round(half: :up) # => 4 + # (-2.5).round(half: :up) # => -3 # - # 2.5.round(half: :up) #=> 3 - # 2.5.round(half: :down) #=> 2 - # 2.5.round(half: :even) #=> 2 - # 3.5.round(half: :up) #=> 4 - # 3.5.round(half: :down) #=> 3 - # 3.5.round(half: :even) #=> 4 - # (-2.5).round(half: :up) #=> -3 - # (-2.5).round(half: :down) #=> -2 - # (-2.5).round(half: :even) #=> -2 + # * `:down`: round toward zero: # + # 2.5.round(half: :down) # => 2 + # 3.5.round(half: :down) # => 3 + # (-2.5).round(half: :down) # => -2 + # + # * `:even`: round toward the candidate whose last nonzero digit is even: + # + # 2.5.round(half: :even) # => 2 + # 3.5.round(half: :even) # => 4 + # (-2.5).round(half: :even) # => -2 + # + # + # Raises and exception if the value for `half` is invalid. + # + # Related: Float#truncate. + # def round: (?half: :up | :down | :even) -> Integer | (int digits, ?half: :up | :down | :even) -> (Integer | Float) def step: (?Numeric limit, ?Numeric step) { (Float) -> void } -> self | (?Numeric limit, ?Numeric step) -> Enumerator[Float, self] | (?by: Numeric, ?to: Numeric) { (Float) -> void } -> self | (?by: Numeric, ?to: Numeric) -> Enumerator[Float, self] def to_c: () -> Complex + # <!-- + # rdoc-file=numeric.rb + # - float.to_f -> self + # --> # Since `float` is already a Float, returns `self`. # def to_f: () -> Float - # Returns the `float` truncated to an Integer. + # <!-- + # rdoc-file=numeric.c + # - to_i -> integer + # --> + # Returns `self` truncated to an Integer. # - # 1.2.to_i #=> 1 - # (-1.2).to_i #=> -1 + # 1.2.to_i # => 1 + # (-1.2).to_i # => -1 # - # Note that the limited precision of floating point arithmetic might lead to + # Note that the limited precision of floating-point arithmetic may lead to # surprising results: # - # (0.3 / 0.1).to_i #=> 2 (!) + # (0.3 / 0.1).to_i # => 2 (!) # - # #to_int is an alias for #to_i. + # Float#to_int is an alias for Float#to_i. # def to_i: () -> Integer - # Returns the `float` truncated to an Integer. + # <!-- rdoc-file=numeric.c --> + # Returns `self` truncated to an Integer. # - # 1.2.to_i #=> 1 - # (-1.2).to_i #=> -1 + # 1.2.to_i # => 1 + # (-1.2).to_i # => -1 # - # Note that the limited precision of floating point arithmetic might lead to + # Note that the limited precision of floating-point arithmetic may lead to # surprising results: # - # (0.3 / 0.1).to_i #=> 2 (!) + # (0.3 / 0.1).to_i # => 2 (!) # - # #to_int is an alias for #to_i. + # Float#to_int is an alias for Float#to_i. # alias to_int to_i + # <!-- + # rdoc-file=rational.c + # - flt.to_r -> rational + # --> # Returns the value as a rational. # # 2.0.to_r #=> (2/1) # 2.5.to_r #=> (5/2) # -0.75.to_r #=> (-3/4) @@ -558,112 +990,156 @@ # # See also Float#rationalize. # def to_r: () -> Rational - # Returns a string containing a representation of `self`. As well as a fixed or - # exponential form of the `float`, the call may return `NaN`, `Infinity`, and - # `-Infinity`. + # <!-- + # rdoc-file=numeric.c + # - to_s -> string + # --> + # Returns a string containing a representation of `self`; depending of the value + # of `self`, the string representation may contain: # + # * A fixed-point number. + # * A number in "scientific notation" (containing an exponent). + # * 'Infinity'. + # * '-Infinity'. + # * 'NaN' (indicating not-a-number). + # + # 3.14.to_s # => "3.14" (10.1**50).to_s # => + # "1.644631821843879e+50" (10.1**500).to_s # => "Infinity" + # (-10.1**500).to_s # => "-Infinity" (0.0/0.0).to_s # => "NaN" + # def to_s: () -> String - # Returns `float` truncated (toward zero) to a precision of `ndigits` decimal - # digits (default: 0). + # <!-- + # rdoc-file=numeric.c + # - truncate(ndigits = 0) -> float or integer + # --> + # Returns `self` truncated (toward zero) to a precision of `ndigits` decimal + # digits. # - # When the precision is negative, the returned value is an integer with at least - # `ndigits.abs` trailing zeros. + # When `ndigits` is positive, returns a float with `ndigits` digits after the + # decimal point (as available): # - # Returns a floating point number when `ndigits` is positive, otherwise returns - # an integer. + # f = 12345.6789 + # f.truncate(1) # => 12345.6 + # f.truncate(3) # => 12345.678 + # f = -12345.6789 + # f.truncate(1) # => -12345.6 + # f.truncate(3) # => -12345.678 # - # 2.8.truncate #=> 2 - # (-2.8).truncate #=> -2 - # 1.234567.truncate(2) #=> 1.23 - # 34567.89.truncate(-2) #=> 34500 + # When `ndigits` is negative, returns an integer with at least `ndigits.abs` + # trailing zeros: # - # Note that the limited precision of floating point arithmetic might lead to + # f = 12345.6789 + # f.truncate(0) # => 12345 + # f.truncate(-3) # => 12000 + # f = -12345.6789 + # f.truncate(0) # => -12345 + # f.truncate(-3) # => -12000 + # + # Note that the limited precision of floating-point arithmetic may lead to # surprising results: # # (0.3 / 0.1).truncate #=> 2 (!) # + # Related: Float#round. + # def truncate: () -> Integer | (Integer ndigits) -> (Integer | Float) + # <!-- + # rdoc-file=numeric.rb + # - float.zero? -> true or false + # --> # Returns `true` if `float` is 0.0. # def zero?: () -> bool end +# <!-- rdoc-file=numeric.c --> # The minimum number of significant decimal digits in a double-precision # floating point. # # Usually defaults to 15. # Float::DIG: Integer +# <!-- rdoc-file=numeric.c --> # The difference between 1 and the smallest double-precision floating point # number greater than 1. # # Usually defaults to 2.2204460492503131e-16. # Float::EPSILON: Float +# <!-- rdoc-file=numeric.c --> # An expression representing positive infinity. # Float::INFINITY: Float +# <!-- rdoc-file=numeric.c --> # The number of base digits for the `double` data type. # # Usually defaults to 53. # Float::MANT_DIG: Integer +# <!-- rdoc-file=numeric.c --> # The largest possible integer in a double-precision floating point number. # # Usually defaults to 1.7976931348623157e+308. # Float::MAX: Float +# <!-- rdoc-file=numeric.c --> # The largest positive exponent in a double-precision floating point where 10 # raised to this power minus 1. # # Usually defaults to 308. # Float::MAX_10_EXP: Integer +# <!-- rdoc-file=numeric.c --> # The largest possible exponent value in a double-precision floating point. # # Usually defaults to 1024. # Float::MAX_EXP: Integer +# <!-- rdoc-file=numeric.c --> # The smallest positive normalized number in a double-precision floating point. # # Usually defaults to 2.2250738585072014e-308. # # If the platform supports denormalized numbers, there are numbers between zero # and Float::MIN. 0.0.next_float returns the smallest positive floating point # number including denormalized numbers. # Float::MIN: Float +# <!-- rdoc-file=numeric.c --> # The smallest negative exponent in a double-precision floating point where 10 # raised to this power minus 1. # # Usually defaults to -307. # Float::MIN_10_EXP: Integer +# <!-- rdoc-file=numeric.c --> # The smallest possible exponent value in a double-precision floating point. # # Usually defaults to -1021. # Float::MIN_EXP: Integer +# <!-- rdoc-file=numeric.c --> # An expression representing a value which is "not a number". # Float::NAN: Float +# <!-- rdoc-file=numeric.c --> # The base of the floating point, or number of unique digits used to represent # the number. # # Usually defaults to 2 on most systems, which would represent a base-10 # decimal.