metallic-rs

C math functions from scratch for Rust

This library is a successor to Metallic, my C library for WebAssembly started in 2017. Its most wanted feature turned out to be math functions I wrote from scratch, so I decided to rewrite them in Rust.

Assumptions

C libraries tend to have strict yet obsolete assumptions on math functions. For example, float functions dare not use double instructions for fear that the host does not support them. In this library, I assume all Rust primitive types are IEEE 754 compliant and native to the host. In other words, I assume the following instructions are available to floating-point types:

• Addition, subtraction, multiplication, division
• Square root (f32::sqrt)
• Fused multiply-add (f32::mul_add)
• Rounding instructions such as f32::trunc

The assumptions beyond the four basic arithmetic operations creates dependency on the Rust standard library.

Besides, I ignore the floating-point environment, which is not available in Rust. It is also mostly unused in C and C++ because it requires #pragma STDC FENV_ACCESS ON and compiler support.

Goals

• The functions should be faithfully rounded (error < 1 ulp).
• The functions should be about as fast as the system library.
• Try to make f32 functions faster than the system library.
• Avoid lookup tables to reduce memory usage, especially on WebAssembly.
  • This goal is not as important as the others. For example, a lookup table for trigonometric functions is required to achieve faithful rounding. See Payne–Hanek reduction for more details.

Non-goals

• I skip rounding functions such as rint, round, and trunc because
  • They are likely to be a single instruction on modern CPUs.
  • Rust already provides f32::round_ties_even, f32::round, f32::trunc, etc.
  • Their software implementations are slow and tedious, unlike fabs.

Milestones

• Real f32/float functions in <math.h>
• Complex f32/float functions in <complex.h>
• Real f64/double functions in <math.h>
• Complex f64/double functions in <complex.h>