Robust32s

A more robust Float32 that preserves float performance.

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An old Rule-of-Thumb offers the simplest way to evade numerical embarrassment. Perform your compututations carrying somewhat more than twice the precision of your data and somewhat more than twice the precision of you seek in your results. This rule has long served statistics, optimization, root-finding, geometry, and differential equations. Rare exceptions exist, of course. (adapted from W. Kahan)

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This package implements that Rule-of-Thumb in a highly performant manner. To offer the desired performance, this package works with Float32 data and provides Float32 results. This is handled automatically. While you are working with Float32 data and obtaining Float32 results, all is well.

exports

• Robust32 a robust 32bit floating point type
• ComplexR32 a robust 32bit complex floating point type (named like ComplexF32)

installation

julia> using Pkg
julia> Pkg.add("Robust32s")

Basic Examples

using FloatR32s

julia> a, b = sqrt.(Float32.((2.0, 0.5)))
(1.4142135f0, 0.70710677f0)

julia> c = a * b    # product of Float32s
0.99999994f0

julia> a, b = sqrt.(Robust32.((2.0, 0.5)))
(1.4142135f0, 0.70710677f0)

julia> c = a * b    # product of FloatR32s
1.0f0

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".. the simplest way to evade numerical embarrassment is to perform computation carrying extravagantly more precision throughout than you think necessary, and pray that it is enough. Usually somewhat more than twice the precision you trust in the data and seek in the results is enough."

• W. Kahan, "How Futile are Mindless Assessments of Roundoff in Floating Point Computation", 2006