DoubleFloats.jl

Math with 85+ accurate bits.

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> d64"0.2"
1.9999999999999999999999999999999937e-01

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))

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][discourse-tag-url]. 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][issues-url] if you encounter any problems. The [contributing page][contrib-url] has a few guidelines that should be followed when opening pull requests.

[contrib-url]: https://juliamath.github.io/DoubleFloats.jl/latest/man/contributing/ [discourse-tag-url]: https://discourse.julialang.org/tags/doublefloats [gitter-url]: https://gitter.im/juliamath/users

[docs-current-img]: https://img.shields.io/badge/docs-latest-blue.svg [docs-current-url]: https://juliamath.github.io/DoubleFloats.jl

[travis-img]: https://travis-ci.org/JuliaMath/DoubleFloats.jl.svg?branch=master [travis-url]: https://travis-ci.org/JuliaMath/DoubleFloats.jl

[appveyor-img]: https://ci.appveyor.com/api/projects/status/xx7nimfpnl1r4gx0?svg=true [appveyor-url]: https://ci.appveyor.com/project/JuliaMath/doublefloats-jl

[codecov-img]: https://codecov.io/gh/JuliaMath/DoubleFloats.jl/branch/master/graph/badge.svg [codecov-url]: https://codecov.io/gh/JuliaMath/DoubleFloats.jl

[issues-url]: https://github.com/JuliaMath/DoubleFloats.jl/issues

[pkg-1.0-img]: http://pkg.julialang.org/badges/DoubleFloats_1.0.svg [pkg-1.0-url]: http://pkg.julialang.org/?pkg=DoubleFloats&ver=1.0