rename: MathConst => Irrational #11922
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@@ -535,3 +535,6 @@ end | |
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| const UnionType = Union | ||
| export UnionType | ||
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| const MathConst = Irrational | ||
| export MathConst | ||
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@@ -70,7 +70,7 @@ export | |
| LinSpace, | ||
| LocalProcess, | ||
| LowerTriangular, | ||
| Irrational, | ||
| Matrix, | ||
| MergeSort, | ||
| Nullable, | ||
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| # This file is a part of Julia. License is MIT: http://julialang.org/license | ||
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| ## general machinery for irrational mathematical constants | ||
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| immutable Irrational{sym} <: Real end | ||
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| show{sym}(io::IO, x::Irrational{sym}) = print(io, "$sym = $(string(float(x))[1:15])...") | ||
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| promote_rule{s}(::Type{Irrational{s}}, ::Type{Float32}) = Float32 | ||
| promote_rule{s,t}(::Type{Irrational{s}}, ::Type{Irrational{t}}) = Float64 | ||
| promote_rule{s,T<:Number}(::Type{Irrational{s}}, ::Type{T}) = promote_type(Float64,T) | ||
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| convert(::Type{FloatingPoint}, x::Irrational) = Float64(x) | ||
| convert(::Type{Float16}, x::Irrational) = Float16(Float32(x)) | ||
| convert{T<:Real}(::Type{Complex{T}}, x::Irrational) = convert(Complex{T}, convert(T,x)) | ||
| convert{T<:Integer}(::Type{Rational{T}}, x::Irrational) = convert(Rational{T}, Float64(x)) | ||
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| @generated function call{T<:Union{Float32,Float64},s}(t::Type{T},c::Irrational{s},r::RoundingMode) | ||
| f = T(big(c()),r()) | ||
| :($f) | ||
| end | ||
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| =={s}(::Irrational{s}, ::Irrational{s}) = true | ||
| ==(::Irrational, ::Irrational) = false | ||
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| # Irationals are not rational, so unequal to everything else | ||
| ==(x::Irrational, y::Real) = false | ||
| ==(x::Real, y::Irrational) = false | ||
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| # Irrational vs FloatingPoint | ||
| <(x::Irrational, y::Float64) = Float64(x,RoundUp) <= y | ||
| <(x::Float64, y::Irrational) = x <= Float64(y,RoundDown) | ||
| <(x::Irrational, y::Float32) = Float32(x,RoundUp) <= y | ||
| <(x::Float32, y::Irrational) = x <= Float32(y,RoundDown) | ||
| <(x::Irrational, y::Float16) = Float32(x,RoundUp) <= y | ||
| <(x::Float16, y::Irrational) = x <= Float32(y,RoundDown) | ||
| <(x::Irrational, y::BigFloat) = with_bigfloat_precision(precision(y)+32) do | ||
| big(x) < y | ||
| end | ||
| <(x::BigFloat, y::Irrational) = with_bigfloat_precision(precision(x)+32) do | ||
| x < big(y) | ||
| end | ||
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| <=(x::Irrational,y::FloatingPoint) = x < y | ||
| <=(x::FloatingPoint,y::Irrational) = x < y | ||
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| # Irrational vs Rational | ||
| @generated function <{T}(x::Irrational, y::Rational{T}) | ||
| bx = big(x()) | ||
| bx < 0 && T <: Unsigned && return true | ||
| rx = rationalize(T,bx,tol=0) | ||
| rx < bx ? :($rx < y) : :($rx <= y) | ||
| end | ||
| @generated function <{T}(x::Rational{T}, y::Irrational) | ||
| by = big(y()) | ||
| by < 0 && T <: Unsigned && return false | ||
| ry = rationalize(T,by,tol=0) | ||
| ry < by ? :(x <= $ry) : :(x < $ry) | ||
| end | ||
| <(x::Irrational, y::Rational{BigInt}) = big(x) < y | ||
| <(x::Rational{BigInt}, y::Irrational) = x < big(y) | ||
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| <=(x::Irrational,y::Rational) = x < y | ||
| <=(x::Rational,y::Irrational) = x < y | ||
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| hash(x::Irrational, h::UInt) = 3*object_id(x) - h | ||
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| -(x::Irrational) = -Float64(x) | ||
| for op in Symbol[:+, :-, :*, :/, :^] | ||
| @eval $op(x::Irrational, y::Irrational) = $op(Float64(x),Float64(y)) | ||
| end | ||
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| macro irrational(sym, val, def) | ||
| esym = esc(sym) | ||
| qsym = esc(Expr(:quote, sym)) | ||
| bigconvert = isa(def,Symbol) ? quote | ||
| function Base.convert(::Type{BigFloat}, ::Irrational{$qsym}) | ||
| c = BigFloat() | ||
| ccall(($(string("mpfr_const_", def)), :libmpfr), | ||
| Cint, (Ptr{BigFloat}, Int32), | ||
| &c, MPFR.ROUNDING_MODE[end]) | ||
| return c | ||
| end | ||
| end : quote | ||
| Base.convert(::Type{BigFloat}, ::Irrational{$qsym}) = $(esc(def)) | ||
| end | ||
| quote | ||
| const $esym = Irrational{$qsym}() | ||
| $bigconvert | ||
| Base.convert(::Type{Float64}, ::Irrational{$qsym}) = $val | ||
| Base.convert(::Type{Float32}, ::Irrational{$qsym}) = $(Float32(val)) | ||
| @assert isa(big($esym), BigFloat) | ||
| @assert Float64($esym) == Float64(big($esym)) | ||
| @assert Float32($esym) == Float32(big($esym)) | ||
| end | ||
| end | ||
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| big(x::Irrational) = convert(BigFloat,x) | ||
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| ## specific irriational mathematical constants | ||
|
There was a problem hiding this comment. typo here: "irriational" -> "irrational". |
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| @irrational π 3.14159265358979323846 pi | ||
| @irrational e 2.71828182845904523536 exp(big(1)) | ||
| @irrational γ 0.57721566490153286061 euler | ||
| @irrational catalan 0.91596559417721901505 catalan | ||
| @irrational φ 1.61803398874989484820 (1+sqrt(big(5)))/2 | ||
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| # aliases | ||
| const pi = π | ||
| const eu = e | ||
| const eulergamma = γ | ||
| const golden = φ | ||
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| # special behaviors | ||
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| # use exp for e^x or e.^x, as in | ||
| # ^(::Irrational{:e}, x::Number) = exp(x) | ||
| # .^(::Irrational{:e}, x) = exp(x) | ||
| # but need to loop over types to prevent ambiguity with generic rules for ^(::Number, x) etc. | ||
| for T in (Irrational, Rational, Integer, Number) | ||
| ^(::Irrational{:e}, x::T) = exp(x) | ||
| end | ||
| for T in (Range, BitArray, SparseMatrixCSC, StridedArray, AbstractArray) | ||
| .^(::Irrational{:e}, x::T) = exp(x) | ||
| end | ||
| ^(::Irrational{:e}, x::AbstractMatrix) = expm(x) | ||
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| log(::Irrational{:e}) = 1 # use 1 to correctly promote expressions like log(x)/log(e) | ||
| log(::Irrational{:e}, x) = log(x) | ||
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| # align along = for nice Array printing | ||
| function alignment(x::Irrational) | ||
| m = match(r"^(.*?)(=.*)$", sprint(showcompact_lim, x)) | ||
| m == nothing ? (length(sprint(showcompact_lim, x)), 0) : | ||
| (length(m.captures[1]), length(m.captures[2])) | ||
| end | ||
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Typo: Irationals is missing an "r". Also, I'm not sure I fully understand this comment. The beginning is redundant and the ending is kinda vague (especially since technically irrationals are reals).