stdlib/builtin/float.rbs in rbs-0.13.1 vs stdlib/builtin/float.rbs in rbs-0.14.0

- old
+ new

@@ -1,338 +1,338 @@ # Float objects represent inexact real numbers 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://github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#floats_impre # cise # * http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems -# -# +# +# class Float < Numeric public # Returns the modulo after division of `float` by `other`. - # + # # 6543.21.modulo(137) #=> 104.21000000000004 # 6543.21.modulo(137.24) #=> 92.92999999999961 - # + # def %: (Integer) -> Float | (Float) -> Float | (Rational) -> Float | (Numeric) -> Numeric # Returns a new Float which is the product of `float` and `other`. - # + # def *: (Complex) -> Complex | (Numeric) -> Float # Raises `float` to the power of `other`. - # + # # 2.0**3 #=> 8.0 - # + # def **: (Complex) -> Complex | (Numeric) -> Float # Returns a new Float which is the sum of `float` and `other`. - # + # def +: (Complex) -> Complex | (Numeric) -> Float def +@: () -> Float # Returns a new Float which is the difference of `float` and `other`. - # + # def -: (Complex) -> Complex | (Numeric) -> Float # Returns `float`, negated. - # + # def -@: () -> Float # Returns a new Float which is the result of dividing `float` by `other`. - # + # def /: (Complex) -> Complex | (Numeric) -> Float # Returns `true` if `float` is less than `real`. - # + # # The result of `NaN < NaN` is undefined, so an implementation-dependent value # is returned. - # + # def <: (Numeric) -> bool # Returns `true` if `float` is less than or equal to `real`. - # + # # The result of `NaN <= NaN` is undefined, so an implementation-dependent value # is returned. - # + # 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. - # + # # The result of `NaN <=> NaN` is undefined, so an implementation-dependent value # is returned. - # + # # `nil` is returned if the two values are incomparable. - # + # 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. - # + # # 1.0 == 1 #=> true - # + # # The result of `NaN == NaN` is undefined, so an implementation-dependent value # is returned. - # + # 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. - # + # # 1.0 == 1 #=> true - # + # # The result of `NaN == NaN` is undefined, so an implementation-dependent value # is returned. - # + # def ===: (untyped) -> bool # Returns `true` if `float` is greater than `real`. - # + # # The result of `NaN > NaN` is undefined, so an implementation-dependent value # is returned. - # + # def >: (Numeric) -> bool # Returns `true` if `float` is greater than or equal to `real`. - # + # # The result of `NaN >= NaN` is undefined, so an implementation-dependent value # is returned. - # + # def >=: (Numeric) -> bool # Returns the absolute value of `float`. - # + # # (-34.56).abs #=> 34.56 # -34.56.abs #=> 34.56 # 34.56.abs #=> 34.56 - # + # # Float#magnitude is an alias for Float#abs. - # + # def abs: () -> Float def abs2: () -> Float # Returns 0 if the value is positive, pi otherwise. - # + # def angle: () -> (Integer | 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). - # + # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. - # + # # Returns a floating point number when `ndigits` is positive, otherwise returns # an integer. - # + # # 1.2.ceil #=> 2 # 2.0.ceil #=> 2 # (-1.2).ceil #=> -1 # (-2.0).ceil #=> -2 - # + # # 1.234567.ceil(2) #=> 1.24 # 1.234567.ceil(3) #=> 1.235 # 1.234567.ceil(4) #=> 1.2346 # 1.234567.ceil(5) #=> 1.23457 - # + # # 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 # surprising results: - # + # # (2.1 / 0.7).ceil #=> 4 (!) - # + # def ceil: () -> Integer | (int digits) -> (Integer | Float) def clone: (?freeze: bool) -> self # Returns an array with both `numeric` and `float` represented as Float objects. - # + # # This is achieved by converting `numeric` to a Float. - # + # # 1.2.coerce(3) #=> [3.0, 1.2] # 2.5.coerce(1.1) #=> [1.1, 2.5] - # + # def coerce: (Numeric) -> [Numeric, Numeric] def conj: () -> Float def conjugate: () -> Float # Returns the denominator (always positive). The result is machine dependent. - # + # # See also Float#numerator. - # + # def denominator: () -> Integer def div: (Numeric) -> Integer # See Numeric#divmod. - # + # # 42.0.divmod(6) #=> [7, 0.0] # 42.0.divmod(5) #=> [8, 2.0] - # + # 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. - # + # # 1.0.eql?(1) #=> false - # + # # The result of `NaN.eql?(NaN)` is undefined, so an implementation-dependent # value is returned. - # + # def eql?: (untyped) -> bool # Returns `float / numeric`, same as Float#/. - # + # 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`. - # + # def finite?: () -> bool # Returns the largest number less than or equal to `float` with a precision of # `ndigits` decimal digits (default: 0). - # + # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. - # + # # Returns a floating point number when `ndigits` is positive, otherwise returns # an integer. - # + # # 1.2.floor #=> 1 # 2.0.floor #=> 2 # (-1.2).floor #=> -2 # (-2.0).floor #=> -2 - # + # # 1.234567.floor(2) #=> 1.23 # 1.234567.floor(3) #=> 1.234 # 1.234567.floor(4) #=> 1.2345 # 1.234567.floor(5) #=> 1.23456 - # + # # 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 # surprising results: - # + # # (0.3 / 0.1).floor #=> 2 (!) - # + # def floor: () -> Integer | (int digits) -> (Integer | Numeric) # Returns a hash code for this float. - # + # # See also Object#hash. - # + # def hash: () -> Integer def i: () -> Complex def imag: () -> Integer def imaginary: () -> Integer # Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, # or `+Infinity`. - # + # # (0.0).infinite? #=> nil # (-1.0/0.0).infinite? #=> -1 # (+1.0/0.0).infinite? #=> 1 - # + # def infinite?: () -> Integer? alias inspect to_s def integer?: () -> bool # Returns the absolute value of `float`. - # + # # (-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`. - # + # # 6543.21.modulo(137) #=> 104.21000000000004 # 6543.21.modulo(137.24) #=> 92.92999999999961 - # + # def modulo: (Numeric) -> Float # Returns `true` if `float` is an invalid IEEE floating point number. - # + # # a = -1.0 #=> -1.0 # a.nan? #=> false # a = 0.0/0.0 #=> NaN # a.nan? #=> true - # + # def nan?: () -> bool # Returns `true` if `float` is less than 0. - # + # def negative?: () -> bool # Returns the next representable floating point number. - # + # # Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY. - # + # # Float::NAN.next_float is Float::NAN. - # + # # For example: - # + # # 0.01.next_float #=> 0.010000000000000002 # 1.0.next_float #=> 1.0000000000000002 # 100.0.next_float #=> 100.00000000000001 - # + # # 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 - # + # # 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 @@ -350,62 +350,62 @@ # # 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 = 0.0 # 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. - # + # def next_float: () -> Float def nonzero?: () -> self? # 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 # Returns 0 if the value is positive, pi otherwise. - # + # alias phase angle def polar: () -> [ Float, Integer | Float ] # Returns `true` if `float` is greater than 0. - # + # def positive?: () -> bool # Returns the previous representable floating point number. - # + # # (-Float::MAX).prev_float and (-Float::INFINITY).prev_float is # -Float::INFINITY. - # + # # Float::NAN.prev_float is Float::NAN. - # + # # For example: - # + # # 0.01.prev_float #=> 0.009999999999999998 # 1.0.prev_float #=> 0.9999999999999999 # 100.0.prev_float #=> 99.99999999999999 - # + # # 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 - # + # # 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 @@ -423,28 +423,28 @@ # # 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 - # + # def prev_float: () -> Float # Returns `float / numeric`, same as Float#/. - # + # def quo: (Complex) -> Complex | (Numeric) -> Float # 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) # 1.333.rationalize #=> (1333/1000) # 1.333.rationalize(0.01) #=> (4/3) - # + # # See also Float#to_r. - # + # def rationalize: (?Numeric eps) -> Rational def real: () -> Float def real?: () -> true @@ -455,55 +455,55 @@ def remainder: (Numeric) -> Float # Returns `float` rounded to the nearest value with a precision of `ndigits` # decimal digits (default: 0). - # + # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. - # + # # Returns a floating point number when `ndigits` is positive, otherwise returns # an integer. - # + # # 1.4.round #=> 1 # 1.5.round #=> 2 # 1.6.round #=> 2 # (-1.5).round #=> -2 - # + # # 1.234567.round(2) #=> 1.23 # 1.234567.round(3) #=> 1.235 # 1.234567.round(4) #=> 1.2346 # 1.234567.round(5) #=> 1.23457 - # + # # 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 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 half away from zero (default) # * `:down`: round half toward zero # * `:even`: round half toward the nearest even number - # + # # 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 - # + # 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] @@ -511,186 +511,186 @@ | (?by: Numeric, ?to: Numeric) -> Enumerator[Float, self] def to_c: () -> Complex # Since `float` is already a Float, returns `self`. - # + # def to_f: () -> Float # Returns the `float` truncated to an Integer. - # + # # 1.2.to_i #=> 1 # (-1.2).to_i #=> -1 - # + # # Note that the limited precision of floating point arithmetic might lead to # surprising results: - # + # # (0.3 / 0.1).to_i #=> 2 (!) - # + # # #to_int is an alias for #to_i. - # + # def to_i: () -> Integer # Returns the `float` truncated to an Integer. - # + # # 1.2.to_i #=> 1 # (-1.2).to_i #=> -1 - # + # # Note that the limited precision of floating point arithmetic might lead to # surprising results: - # + # # (0.3 / 0.1).to_i #=> 2 (!) - # + # # #to_int is an alias for #to_i. - # + # alias to_int to_i # Returns the value as a rational. - # + # # 2.0.to_r #=> (2/1) # 2.5.to_r #=> (5/2) # -0.75.to_r #=> (-3/4) # 0.0.to_r #=> (0/1) # 0.3.to_r #=> (5404319552844595/18014398509481984) - # + # # NOTE: 0.3.to_r isn't the same as "0.3".to_r. The latter is equivalent to # "3/10".to_r, but the former isn't so. - # + # # 0.3.to_r == 3/10r #=> false # "0.3".to_r == 3/10r #=> true - # + # # 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`. - # + # def to_s: () -> String # Returns `float` truncated (toward zero) to a precision of `ndigits` decimal # digits (default: 0). - # + # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. - # + # # Returns a floating point number when `ndigits` is positive, otherwise returns # an integer. - # + # # 2.8.truncate #=> 2 # (-2.8).truncate #=> -2 # 1.234567.truncate(2) #=> 1.23 # 34567.89.truncate(-2) #=> 34500 - # + # # Note that the limited precision of floating point arithmetic might lead to # surprising results: - # + # # (0.3 / 0.1).truncate #=> 2 (!) - # + # def truncate: () -> Integer | (Integer ndigits) -> (Integer | Float) # Returns `true` if `float` is 0.0. - # + # def zero?: () -> bool end # The minimum number of significant decimal digits in a double-precision # floating point. -# +# # Usually defaults to 15. -# +# Float::DIG: Integer # The difference between 1 and the smallest double-precision floating point # number greater than 1. -# +# # Usually defaults to 2.2204460492503131e-16. -# +# Float::EPSILON: Float # An expression representing positive infinity. -# +# Float::INFINITY: Float # The number of base digits for the `double` data type. -# +# # Usually defaults to 53. -# +# Float::MANT_DIG: Integer # The largest possible integer in a double-precision floating point number. -# +# # Usually defaults to 1.7976931348623157e+308. -# +# Float::MAX: Float # 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 # The largest possible exponent value in a double-precision floating point. -# +# # Usually defaults to 1024. -# +# Float::MAX_EXP: Integer # 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 # 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 # The smallest possible exponent value in a double-precision floating point. -# +# # Usually defaults to -1021. -# +# Float::MIN_EXP: Integer # An expression representing a value which is "not a number". -# +# Float::NAN: Float # 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. -# +# Float::RADIX: Integer # Deprecated, do not use. -# +# # Represents the rounding mode for floating point addition at the start time. -# +# # Usually defaults to 1, rounding to the nearest number. -# +# # Other modes include: -# +# # -1 # : Indeterminable # 0 # : Rounding towards zero # 1 # : Rounding to the nearest number # 2 # : Rounding towards positive infinity # 3 # : Rounding towards negative infinity -# -# +# +# Float::ROUNDS: Integer