File Manager
# 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
# # 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 = 0.0
# 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
# # 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
#
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
def rect: () -> [ Float, Numeric ]
alias rectangular rect
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]
| (?by: Numeric, ?to: Numeric) { (Float) -> void } -> self
| (?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
File Manager Version 1.0, Coded By Lucas
Email: hehe@yahoo.com