Expose algebraic floating point intrinsics
# Problem
A stable Rust implementation of a simple dot product is 8x slower than C++ on modern x86-64 CPUs. The root cause is an inability to let the compiler reorder floating point operations for better vectorization.
See https://github.com/calder/dot-bench for benchmarks. Measurements below were performed on a i7-10875H.
### C++: 10us ✅
With Clang 18.1.3 and `-O2 -march=haswell`:
<table>
<tr>
<th>C++</th>
<th>Assembly</th>
</tr>
<tr>
<td>
<pre lang="cc">
float dot(float *a, float *b, size_t len) {
#pragma clang fp reassociate(on)
float sum = 0.0;
for (size_t i = 0; i < len; ++i) {
sum += a[i] * b[i];
}
return sum;
}
</pre>
</td>
<td>
<img src="https://github.com/user-attachments/assets/739573c0-380a-4d84-9fd9-141343ce7e68" />
</td>
</tr>
</table>
### Nightly Rust: 10us ✅
With rustc 1.86.0-nightly (8239a37f9) and `-C opt-level=3 -C target-feature=+avx2,+fma`:
<table>
<tr>
<th>Rust</th>
<th>Assembly</th>
</tr>
<tr>
<td>
<pre lang="rust">
fn dot(a: &[f32], b: &[f32]) -> f32 {
let mut sum = 0.0;
for i in 0..a.len() {
sum = fadd_algebraic(sum, fmul_algebraic(a[i], b[i]));
}
sum
}
</pre>
</td>
<td>
<img src="https://github.com/user-attachments/assets/9dcf953a-2cd7-42f3-bc34-7117de4c5fb9" />
</td>
</tr>
</table>
### Stable Rust: 84us ❌
With rustc 1.84.1 (e71f9a9a9) and `-C opt-level=3 -C target-feature=+avx2,+fma`:
<table>
<tr>
<th>Rust</th>
<th>Assembly</th>
</tr>
<tr>
<td>
<pre lang="rust">
fn dot(a: &[f32], b: &[f32]) -> f32 {
let mut sum = 0.0;
for i in 0..a.len() {
sum += a[i] * b[i];
}
sum
}
</pre>
</td>
<td>
<img src="https://github.com/user-attachments/assets/936a1f7e-33e4-4ff8-a732-c3cdfe068dca" />
</td>
</tr>
</table>
# Proposed Change
Add `core::intrinsics::f*_algebraic` wrappers to `f16`, `f32`, `f64`, and `f128` gated on a new `float_algebraic` feature.
# Alternatives Considered
https://github.com/rust-lang/rust/issues/21690 has a lot of good discussion of various options for supporting fast math in Rust, but is still open a decade later because any choice that opts in more than individual operations is ultimately contrary to Rust's design principles.
In the mean time, processors have evolved and we're leaving major performance on the table by not supporting vectorization. We shouldn't make users choose between an unstable compiler and an 8x performance hit.
# References
* https://github.com/rust-lang/rust/issues/21690
* https://github.com/rust-lang/libs-team/issues/532
* https://github.com/rust-lang/rust/issues/136469
* https://github.com/calder/dot-bench
* https://www.felixcloutier.com/x86/vfmadd132ps:vfmadd213ps:vfmadd231ps
try-job: x86_64-gnu-nopt
try-job: x86_64-gnu-aux
2e4e196a5b