Oscar Smith

Why did `exp10` get 2x faster in Julia 1.6? One reason is, unlike most other languages, Julia doesn't use the operating system-provided implementations for math (Libm). This talk will be an overview of improvements in Julia's math library  since version 1.5, and areas for future improvements. We will cover will be computing optimal polynomials, table based implementations, and bit-hacking for peak performance.

In this talk we will cover the fundamental numerical techniques for implementing accurate and fast floating point functions. We will start with a brief review of how Floating Point math works. Then use the changes made to `exp` and friends (`exp2`, `exp10`, and  `expm1`) over the past two years as a demonstration for the main techniques of computing functions.

Specifically we will look at:
* Range reduction
* Polynomial kernels using the `Remez` algorithm
* Fast polynomial evaluation
* Table based methods
* Bit manipulation (to make everything fast)

We will also discuss how to test the accuracy of implementations using [FunctionAccuracyTests.jl](https://github.com/JuliaMath/FunctionAccuracyTests.jl), and areas for future improvements in Base and beyond. Present and future work areas optimized routines are the Bessel Functions, cumulative distribution functions, and optimized elementary functions for [DoubleFloats.jl](https://github.com/JuliaMath/DoubleFloats.jl), and PRs across the entire package ecosystem are always welcome.

Oscar Smith

Talks:

Optimizing Floating Point Math in Julia

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