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DoubleFloats

math with more good bits

Readme

DoubleFloats.jl

Math with 85+ accurate bits.


Build Status

Documentation

  • Currentmost recently tagged version of the documentation.

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-30 1.0e-30
acos 1.0e-30 1.0e-29
atan 1.0e-31 1.0e-30
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 notes
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-24 1.0e-28 near asymptote
asin 1.0e-30 1.0e-30
acos 1.0e-30 1.0e-29
atan 1.0e-31 1.0e-30
sinh 1.0e-30 1.0e-31
cosh 1.0e-30 1.0e-31
tanh 1.0e-31 1.0e-31
asinh 1.0e-31 1.0e-31

Installation

pkg> add DoubleFloats

or

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

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
typed value computed value ~abs(golden - computed)
MathConstants.golden 1.61803_39887_49894_84820_45868+ 0.0
Float64(MathConstants.golden) 1.61803_39887_49895 1.5e-16
Double32(MathConstants.golden) 1.61803_39887_49894_90 5.2e-17

Performance

Double64 relative to BigFloat

op speedup
+ 11x
* 18x
\ 7x
trig 3x-6x
  • results from testing with BenchmarkTools on one machine
  • BigFloat precision was set to 106 bits, for fair comparison

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 and Contributions

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 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.

First Commit

01/26/2018

Last Touched

2 days ago

Commits

1936 commits