Crate safeeft [−] [src]
Safe and branchless error-free transformation algorithms for floating point numbers.
Abstract
Error-free transformation (EFT) algorithms for floating point numbers are those
conserve mathematical equality between input and output.
For example, twosum
by D. E. Knuth[1] is an EFT algorithm that conserves
summation of two floating point numbers with non-overlapping property:
(a,b) = twosum(x,y), a+b=x+y, 0.5ulp(a) >= b
.
fn twosum(x: f64, y: f64) -> (f64, f64) { let sum = x + y; let tmp = sum - x; (sum, (x - (sum - tmp)) + (y - tmp))
But in practical, especially with IEEE 754 Std. floating point arithmetic[4], there were several cases which broke equality and M. Kashiwagi[3] fixed it using branch.
This crate provides safe and branchless EFT impllementations for twosum
, split
and twoproduct
[2]. The word "safe" means "if output is representable with
normal/subnormal floating point number, the algorithm is mathematically correct."
Accerelation
With nightly compiler and x86 cpu supporting fma
, you can accelerate some algorithms
using a use-fma
feature gate:
$ RUSTFLAGS='-C target-feature=+fma' cargo build --features use-fma
References
- D. E. Knuth, "The Art of Computer Programming", vol. 2. Addison-Wesley, Reading, MA, 3rd edition, 1998.
- T. J. Dekker, "A Floating-Point Technique for Extending the Available Precision", Numer. Math. 18(3), 224-242, 1971.
- M. Kashiwagi, "Emulation of Rounded Arithmetic in Rounding to Nearest(Japanese only)", NAS2014, 2014.
- American National Standards Institute and Institute of Electrical and Electronic Engineers, "IEEE Standard for Binary Floating-Point Arithmetic", ANSI/IEEE Standard 754-2008, 2008.
Traits
FloatEFT |
Functions
fasttwosum | |
safesplit_branch | |
safesplit_straight | |
safetwoproduct_branch | |
safetwoproduct_straight | |
safetwosum_branch | |
safetwosum_straight | |
split | |
twoproduct | |
twosum |