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DoubleFloats

math with more good bits

https://github.com/juliamath/doublefloats.jl

Science Score: 54.0%

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    Low similarity (9.0%) to scientific vocabulary

Keywords

accuracy doubledouble extended-precision floating-point julia math performance precision

Keywords from Contributors

graphics optim unconstrained-optimization optimisation unconstrained-optimisation julia-package julialang pdes heterogeneous-parallel-programming ode
Last synced: 4 months ago · JSON representation ·

Repository

math with more good bits

Basic Info
  • Host: GitHub
  • Owner: JuliaMath
  • License: mit
  • Language: Julia
  • Default Branch: main
  • Homepage:
  • Size: 3.09 MB
Statistics
  • Stars: 165
  • Watchers: 9
  • Forks: 31
  • Open Issues: 17
  • Releases: 134
Topics
accuracy doubledouble extended-precision floating-point julia math performance precision
Created almost 8 years ago · Last pushed 5 months ago
Metadata Files
Readme License Citation

README.md

DoubleFloats.jl

Math with 85+ accurate bits.

Extended precision float and complex types

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

Build Status   Docs    Coverage Status    codecov    Package Downloads

Installation

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

More Performant Than Float128, BigFloat

these results are from BenchmarkTools, on one machine

There is another package, Quadmath.jl, which exports Float128 from GNU’s libquadmath. Float128s have 6 more significant bits than Double64s, and a much wider exponent range (Double64s exponents have the same range as Float64s). Big128 is BigFloat after setprecision(BigFloat, 128).

Benchmarking: vectors (v) of 1000 values and 50x50 matrices (m).

| | Double64 | Float128 | Big128 | | Double64 | Float128 | Big128 | |:----------|:----------:|:--------:|:--------:|:-----------|:--------:|:---------:|:-------:| |dot(v,v) | 1 | 3 | 7 | exp.(m) | 1 | 2 | 6 | |v .+ v | 1 | 7 | 16 | m * m | 1 | 3 | 9 | |v .* v | 1 | 12 | 25 | det(m) | 1 | 5 | 11 |

relative performance: smaller is faster, the larger number takes proportionately longer.

Examples

Double64, Double32, Double16

```julia 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 julia> Double64(0.2) 0.2 julia> showall(ans) 2.0000000000000001110223024625156540e-01

julia> Double64(2)/10 0.2 julia> showall(ans) 1.9999999999999999999999999999999937e-01

julia> df64"0.2" 0.2 julia> showall(ans) 1.9999999999999999999999999999999937e-01 ```

Complex functions

```julia

julia> x = ComplexDF64(sqrt(df64"2"), cbrt(df64"3")) 1.4142135623730951 + 1.4422495703074083im julia> showall(x) 1.4142135623730950488016887242096816 + 1.4422495703074083823216383107800998im

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

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

show, string, parse

```julia 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> showall(x) 0.5773502691896257645091487805019415

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(df32"2"), cbrt(df32"3")) 1.4142135 + 1.4422495im

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

julia> stringtyped(x) "ComplexD32(Double32(1.4142135, 2.4203233e-8), Double32(1.4422495, 3.3793125e-8))" ```

see https://juliamath.github.io/DoubleFloats.jl/stable/ for more information

Accuracy

results for f(x), x in 0..1

| function | abserr | relerr | |:--------:|:----------:|:----------:| | exp | 1.0e-31 | 1.0e-31 | | log | 1.0e-31 | 1.0e-31 | | | | | | sin | 1.0e-31 | 1.0e-31 | | cos | 1.0e-31 | 1.0e-31 | | tan | 1.0e-31 | 1.0e-31 | | | | | | asin | 1.0e-31 | 1.0e-31 | | acos | 1.0e-31 | 1.0e-31 | | atan | 1.0e-31 | 1.0e-31 | | | | | | sinh | 1.0e-31 | 1.0e-29 | | cosh | 1.0e-31 | 1.0e-31 | | tanh | 1.0e-31 | 1.0e-29 | | | | | | asinh | 1.0e-31 | 1.0e-29 | | atanh | 1.0e-31 | 1.0e-30 |

results for f(x), x in 1..2

| function | abserr | relerr | |:--------:|:----------:|:----------:| | exp | 1.0e-30 | 1.0e-31 | | log | 1.0e-31 | 1.0e-31 | | | | | | sin | 1.0e-31 | 1.0e-31 | | cos | 1.0e-31 | 1.0e-28 | | tan | 1.0e-30 | 1.0e-30 | | | | | | atan | 1.0e-31 | 1.0e-31 | | | | | | sinh | 1.0e-30 | 1.0e-31 | | cosh | 1.0e-30 | 1.0e-31 | | tanh | 1.0e-31 | 1.0e-28 | | | | | | asinh | 1.0e-31 | 1.0e-28 |

isapprox

  • isapprox uses this default rtol=eps(1.0)^(37/64).

Good Ways To Use This

In addition to simply using DoubleFloats and going from there, these two suggestions are easily managed and will go a long way in increasing the robustness of the work and reliability in the computational results.

If your input values are Float64s, map them to Double64s and proceed with your computation. Then unmap your output values as Float64s, do additional work using those Float64s. With Float32 inputs, used Double32s similarly. Where throughput is important, and your algorithms are well-understood, this approach be used with the numerically sensitive parts of your computation only. If you are doing that, be careful to map the inputs to those parts and unmap the outputs from those parts just as described above.

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.

β: 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).

Owner

  • Name: Julia Math
  • Login: JuliaMath
  • Kind: organization

Mathematics made easy in Julia

Citation (CITATION.cff) 

cff-version: 1.2.0
message: If you use this software, please cite it using these metadata.
title: DoubleFloats
abstract: A high-performance type for accurate extended precision math.
authors:
  - given-names: Jeffrey
    family-names: Sarnoff
    email: "jeffrey.sarnoff@gmail.com"
    affiliation: "Julia Innovator"
    orcid: "https://orcid.org/0000-0001-9159-1667"
  - name: "JuliaMath"
type: software
url: "https://juliamath.github.io/DoubleFloats.jl/stable"
repository-code: "https://github.com/JuliaMath/DoubleFloats.jl"
version: 1.2.2
date-released: 2022-06-25
license: MIT

GitHub Events

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  • Release event: 3
  • Issues event: 3
  • Watch event: 9
  • Delete event: 6
  • Issue comment event: 19
  • Push event: 11
  • Pull request review comment event: 1
  • Pull request review event: 1
  • Pull request event: 7
  • Fork event: 1
Last Year
  • Create event: 6
  • Commit comment event: 6
  • Release event: 3
  • Issues event: 3
  • Watch event: 9
  • Delete event: 6
  • Issue comment event: 19
  • Push event: 11
  • Pull request review comment event: 1
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Committers

Last synced: 8 months ago

All Time
  • Total Commits: 3,048
  • Total Committers: 38
  • Avg Commits per committer: 80.211
  • Development Distribution Score (DDS): 0.037
Past Year
  • Commits: 10
  • Committers: 5
  • Avg Commits per committer: 2.0
  • Development Distribution Score (DDS): 0.6
Top Committers
Name Email Commits
Jeffrey Sarnoff J****f 2,935
Sascha Timme s****e@g****m 13
Oscar Smith o****h@g****m 11
araujoms m****n@g****m 9
Dillon Daudert d****t@g****m 7
Neven Sajko s@p****m 6
David Gleich d****h@p****u 5
dependabot[bot] 4****] 5
t-bltg t****g@g****m 4
Simon Byrne s****e@g****m 4
Asbjørn Nilsen Riseth a****h@g****m 3
Kristoffer Carlsson k****9@g****m 3
Steven G. Johnson s****j@m****u 3
woclass g****t@w****n 3
yikait2 4****2 3
Antoine Levitt a****t@g****m 2
Benjamin Deonovic b****c@g****m 2
GregPlowman G****n 2
Hannes Uppman h****n@g****m 2
Harmen Stoppels h****s@g****m 2
Lilith Orion Hafner l****r@g****m 2
Michael F. Herbst i****o@m****m 2
Ralph A. Smith s****a@g****m 2
Zeke 6****t 2
klinemichael m****l@k****m 2
Hendrik Ranocha r****a 2
mtanneau m****u@g****m 1
github-actions[bot] 4****] 1
Yuping Luo r****u@g****m 1
Viral B. Shah V****h 1
and 8 more...
Committer Domains (Top 20 + Academic)
physics.ubc.ca: 1 chrisrackauckas.com: 1 chalmers.se: 1 control.lth.se: 1 klinesoftware.com: 1 michael-herbst.com: 1 wo-class.cn: 1 mit.edu: 1 purdue.edu: 1 purelymail.com: 1

Issues and Pull Requests

Last synced: 5 months ago

All Time
  • Total issues: 76
  • Total pull requests: 64
  • Average time to close issues: about 2 months
  • Average time to close pull requests: 27 days
  • Total issue authors: 58
  • Total pull request authors: 29
  • Average comments per issue: 6.08
  • Average comments per pull request: 2.33
  • Merged pull requests: 58
  • Bot issues: 0
  • Bot pull requests: 7
Past Year
  • Issues: 2
  • Pull requests: 6
  • Average time to close issues: N/A
  • Average time to close pull requests: 6 days
  • Issue authors: 2
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  • Average comments per issue: 3.0
  • Average comments per pull request: 2.67
  • Merged pull requests: 6
  • Bot issues: 0
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Top Authors
Issue Authors
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Pull Request Authors
  • JeffreySarnoff (14)
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Packages

  • Total packages: 1
  • Total downloads:
    • julia 730 total
  • Total dependent packages: 24
  • Total dependent repositories: 5
  • Total versions: 136
juliahub.com: DoubleFloats

math with more good bits

  • Versions: 136
  • Dependent Packages: 24
  • Dependent Repositories: 5
  • Downloads: 730 Total
Rankings
Dependent packages count: 3.3%
Dependent repos count: 4.6%
Average: 4.7%
Forks count: 5.4%
Stargazers count: 5.5%
Last synced: 5 months ago

Dependencies

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