psoftfloat-rs

Software implementation of half-precision floating point numbers according to IEEE 754. Not all operations are supported. Only round to nearest, ties to even is implemented. Note that this implementation does not generate floating-point exception flags for underflow etc.

WARNING

This implementation is for educational purposes only. It is explicitly not optimized for speed, but readability.

Usage

use soft_float::SoftFloat16;

fn main() {
    let x = SoftFloat16::from_bits(0x4198); // 2.796875
    let y = SoftFloat16::from_bits(0xb180); // -0.171875
    let z = x * y;

    assert!(SoftFloat16::to_bits(z) == 0xb7b1);

    println!("{} * {} = {}", f32::from(x), f32::from(y), f32::from(z)); // print via `f32`
}

Testing

You can execute a couple of special test cases via

$ cd soft_float
$ cargo test

This is particularly helpful during development, but doesn't exactly proof correctness of the implementation.

For half-precision floats, we can actually test them all. By default, these exhaustive tests are ignored, but you can execute them via

$ cd soft_float
$ cargo test -- --ignored

Furthermore, we use the Berkeley TestFloat programs to verify the implementation. Exception flags are merely copied over from the testfloat_gen output. You can execute the tests by

$ cd tests
$ make

Resources

• https://en.wikipedia.org/wiki/Half-precision_floating-point_format
• https://float.exposed/
• https://numeral-systems.com/ieee-754-add/
• https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
• https://ciechanow.ski/exposing-floating-point/
• https://www.sci.utah.edu/~beiwang/teaching/cs6210-fall-2016/BonusLecture4.pdf
• https://www.cs.utexas.edu/~byoung/cs429/slides4-fp.pdf
• https://github.com/starkat99/half-rs/blob/main/src/binary16/arch.rs
• https://randomascii.wordpress.com/2014/01/27/theres-only-four-billion-floatsso-test-them-all/
• https://www.netlib.org/fp/
• https://www.eigentales.com/Floating-Point/
• https://pages.cs.wisc.edu/~david/courses/cs552/S12/handouts/guardbits.pdf
• https://github.com/koute/softfloat
• https://github.com/823984418/const_soft_float
• https://github.com/skeeto/scratch/blob/master/misc/float16.c
• https://cs.stackexchange.com/questions/80668/simple-algorithm-for-ieee-754-division-on-8-bit-cpu
• https://link.springer.com/book/10.1007/978-3-319-76526-6
• https://simonv.fr/TypesConvert/?integers
• https://www.sciencedirect.com/book/9781558607989/digital-arithmetic