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fix incorrect folder name for julia-0.6.x

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Former-commit-id: ef2c7401e0876f22d2f7762d182cfbcd5a7d9c70
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mollusk
2018-06-11 03:28:36 -07:00
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julia-0.6.3/share/julia/base/number.jl Normal file
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# This file is a part of Julia. License is MIT: https://julialang.org/license
## generic operations on numbers ##
"""
isinteger(x) -> Bool
Test whether `x` is numerically equal to some integer.
```jldoctest
julia> isinteger(4.0)
true
```
"""
isinteger(x::Integer) = true
"""
iszero(x)
Return `true` if `x == zero(x)`; if `x` is an array, this checks whether
all of the elements of `x` are zero.
"""
iszero(x) = x == zero(x) # fallback method
size(x::Number) = ()
size(x::Number,d) = convert(Int,d)<1 ? throw(BoundsError()) : 1
indices(x::Number) = ()
indices(x::Number,d) = convert(Int,d)<1 ? throw(BoundsError()) : OneTo(1)
eltype(::Type{T}) where {T<:Number} = T
ndims(x::Number) = 0
ndims(::Type{<:Number}) = 0
length(x::Number) = 1
endof(x::Number) = 1
iteratorsize(::Type{<:Number}) = HasShape()
getindex(x::Number) = x
function getindex(x::Number, i::Integer)
@_inline_meta
@boundscheck i == 1 || throw(BoundsError())
x
end
function getindex(x::Number, I::Integer...)
@_inline_meta
@boundscheck all([i == 1 for i in I]) || throw(BoundsError())
x
end
first(x::Number) = x
last(x::Number) = x
copy(x::Number) = x # some code treats numbers as collection-like
"""
divrem(x, y)
The quotient and remainder from Euclidean division. Equivalent to `(div(x,y), rem(x,y))` or
`(x÷y, x%y)`.
```jldoctest
julia> divrem(3,7)
(0, 3)
julia> divrem(7,3)
(2, 1)
```
"""
divrem(x,y) = (div(x,y),rem(x,y))
"""
fldmod(x, y)
The floored quotient and modulus after division. Equivalent to `(fld(x,y), mod(x,y))`.
"""
fldmod(x,y) = (fld(x,y),mod(x,y))
signbit(x::Real) = x < 0
"""
sign(x)
Return zero if `x==0` and ``x/|x|`` otherwise (i.e., ±1 for real `x`).
"""
sign(x::Number) = x == 0 ? x/abs(oneunit(x)) : x/abs(x)
sign(x::Real) = ifelse(x < 0, oftype(one(x),-1), ifelse(x > 0, one(x), typeof(one(x))(x)))
sign(x::Unsigned) = ifelse(x > 0, one(x), oftype(one(x),0))
abs(x::Real) = ifelse(signbit(x), -x, x)
"""
abs2(x)
Squared absolute value of `x`.
```jldoctest
julia> abs2(-3)
9
```
"""
abs2(x::Real) = x*x
"""
flipsign(x, y)
Return `x` with its sign flipped if `y` is negative. For example `abs(x) = flipsign(x,x)`.
```jldoctest
julia> flipsign(5, 3)
5
julia> flipsign(5, -3)
-5
```
"""
flipsign(x::Real, y::Real) = ifelse(signbit(y), -x, x)
copysign(x::Real, y::Real) = ifelse(signbit(x)!=signbit(y), -x, x)
conj(x::Real) = x
transpose(x::Number) = x
ctranspose(x::Number) = conj(x)
inv(x::Number) = one(x)/x
angle(z::Real) = atan2(zero(z), z)
"""
widemul(x, y)
Multiply `x` and `y`, giving the result as a larger type.
```jldoctest
julia> widemul(Float32(3.), 4.)
1.200000000000000000000000000000000000000000000000000000000000000000000000000000e+01
```
"""
widemul(x::Number, y::Number) = widen(x)*widen(y)
start(x::Number) = false
next(x::Number, state) = (x, true)
done(x::Number, state) = state
isempty(x::Number) = false
in(x::Number, y::Number) = x == y
map(f, x::Number, ys::Number...) = f(x, ys...)
"""
zero(x)
Get the additive identity element for the type of `x` (`x` can also specify the type itself).
```jldoctest
julia> zero(1)
0
julia> zero(big"2.0")
0.000000000000000000000000000000000000000000000000000000000000000000000000000000
julia> zero(rand(2,2))
2×2 Array{Float64,2}:
0.0 0.0
0.0 0.0
```
"""
zero(x::Number) = oftype(x,0)
zero(::Type{T}) where {T<:Number} = convert(T,0)
"""
one(x)
one(T::type)
Return a multiplicative identity for `x`: a value such that
`one(x)*x == x*one(x) == x`. Alternatively `one(T)` can
take a type `T`, in which case `one` returns a multiplicative
identity for any `x` of type `T`.
If possible, `one(x)` returns a value of the same type as `x`,
and `one(T)` returns a value of type `T`. However, this may
not be the case for types representing dimensionful quantities
(e.g. time in days), since the multiplicative
identity must be dimensionless. In that case, `one(x)`
should return an identity value of the same precision
(and shape, for matrices) as `x`.
If you want a quantity that is of the same type as `x`, or of type `T`,
even if `x` is dimensionful, use [`oneunit`](@ref) instead.
```jldoctest
julia> one(3.7)
1.0
julia> one(Int)
1
julia> one(Dates.Day(1))
1
```
"""
one(::Type{T}) where {T<:Number} = convert(T,1)
one(x::T) where {T<:Number} = one(T)
# note that convert(T, 1) should throw an error if T is dimensionful,
# so this fallback definition should be okay.
"""
oneunit(x::T)
oneunit(T::Type)
Returns `T(one(x))`, where `T` is either the type of the argument or
(if a type is passed) the argument. This differs from [`one`](@ref) for
dimensionful quantities: `one` is dimensionless (a multiplicative identity)
while `oneunit` is dimensionful (of the same type as `x`, or of type `T`).
```jldoctest
julia> oneunit(3.7)
1.0
julia> oneunit(Dates.Day)
1 day
```
"""
oneunit(x::T) where {T} = T(one(x))
oneunit(::Type{T}) where {T} = T(one(T))
_default_type(::Type{Number}) = Int
"""
factorial(n)
Factorial of `n`. If `n` is an [`Integer`](@ref), the factorial is computed as an
integer (promoted to at least 64 bits). Note that this may overflow if `n` is not small,
but you can use `factorial(big(n))` to compute the result exactly in arbitrary precision.
If `n` is not an `Integer`, `factorial(n)` is equivalent to [`gamma(n+1)`](@ref).
```jldoctest
julia> factorial(6)
720
julia> factorial(21)
ERROR: OverflowError()
[...]
julia> factorial(21.0)
5.109094217170944e19
julia> factorial(big(21))
51090942171709440000
```
"""
factorial(x::Number) = gamma(x + 1) # fallback for x not Integer