DoubleFloats.jl

Math with 85+ accurate bits.

Extended precision float and complex types

• N.B. Double64 is the most performant type ^β

Installation

pkg> add DoubleFloats

or

julia> using Pkg
julia> Pkg.add("DoubleFloats")

More Performant Than BigFloat

Comparing Double64 and BigFloat after setting BigFloat precision to 106 bits.

these results are from BenchmarkTools, on one machine

Examples

Double64, Double32, Double16

julia> using DoubleFloats

julia> dbl64 = sqrt(Double64(2)); 1 - dbl64 * inv(dbl64)
0.0
julia> dbl32 = sqrt(Double32(2)); 1 - dbl32 * inv(dbl32)
0.0
julia> dbl16 = sqrt(Double16(2)); 1 - dbl16 * inv(dbl16)
0.0

julia> typeof(ans) === Double16
true

note: floating-point constants must be used with care, they are evaluated as Float64 values before additional processing

julia> Double64(0.2)
2.0000000000000001110223024625156540e-01

julia> Double64(2)/10
1.9999999999999999999999999999999937e-01

julia> df64"0.2"
1.9999999999999999999999999999999937e-01

Complex functions

julia> x = ComplexDF64(sqrt(df64"2"), cbrt(df64"3"))
1.4142135623730951 + 1.4422495703074083im

julia> y = acosh(x)
1.402873733241199 + 0.8555178360714634im

julia> x - cosh(y)
7.395570986446986e-32 + 0.0im

show, string, parse

julia> using DoubleFloats

julia> x = sqrt(Double64(2)) / sqrt(Double64(6))
0.5773502691896257

julia> string(x)
"5.7735026918962576450914878050194151e-01"

julia> show(IOContext(Base.stdout,:compact=>false),x)
5.7735026918962576450914878050194151e-01

julia> showtyped(x)
Double64(0.5773502691896257, 3.3450280739356326e-17)

julia> showtyped(parse(Double64, stringtyped(x)))
Double64(0.5773502691896257, 3.3450280739356326e-17)

julia> Meta.parse(stringtyped(x))
:(Double64(0.5773502691896257, 3.3450280739356326e-17))

julia> x = ComplexDF32(sqrt(d32"2"), cbrt(d32"3"))
1.4142135 + 1.4422495im

julia> string(x)
"1.414213562373094 + 1.442249570307406im"

julia> stringtyped(x)
"ComplexDF32(Double32(1.4142135, 2.4203233e-8), Double32(1.4422495, 3.3793125e-8))"

golden ratio

julia> using DoubleFloats

julia> ϕ = Double32(MathConstants.golden)
1.61803398874989490
julia> phi = "1.61803398874989484820+"
julia> ϕ⁻¹ = inv(ϕ)
6.18033988749894902e-01

julia> ϕ == 1 + ϕ⁻¹
true
julia> ϕ === ϕ * ϕ⁻¹ + ϕ⁻¹
true

Questions

Usage questions can be posted on the Julia Discourse forum. Use the topic Numerics (a "Discipline") and a put the package name, DoubleFloats, in your question ("topic").

Contributions

Contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems. The contributing page has a few guidelines that should be followed when opening pull requests.

<a name="involvement">β</a>: If you want to get involved with moving Double32 performance forward, great. I would provide guidance. Otherwise, for most purposes you are better off using Float64 than Double32 (Float64 has more significant bits, wider exponent range, and is much faster).