Add fast approximate reciprocal methods for float vectors#204
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tomcur wants to merge 2 commits intolinebender:mainfrom
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Add fast approximate reciprocal methods for float vectors#204tomcur wants to merge 2 commits intolinebender:mainfrom
tomcur wants to merge 2 commits intolinebender:mainfrom
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x86 and AArch64 have instructions to calculate fast approximate reciprocals, and these can speed up some algorithms quite nicely (e.g. sprinkling this in Vello's `flatten_simd.rs` results in -4% flattening timings for GhostScript Tiger (actually landing that there requires a bit of thought whether the lowered precision is acceptable of course!). There is some detail here that this PR as-is doesn't attempt to solve. x86's `rcp` has about 12 bits of precision, AArch64's `vrecpe` about 8 bits. AArch64 has an additional instruction however, `vrecps`, to perform a Newton refinement step, which bumps the precision to 16 bits. That'd look something like the following. ```rust let x0 = vrecpeq_f32(a); x0 * vrecpsq_f32(a, x0); // calculates x0 * (2 - x0 * a), roughly doubling the precision of the `x0` estimate ``` Then, AVX512 introduces `rcp14`, which allows calculating to 14-bit precision with (I believe) the same performance as `rcp`, and extends support to `f64`. In any case, this method does the simplest thing of just exposing the cheapest hardware estimate, similar to e.g. Highway's `ApproximateReciprocal`.
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| } | ||
| #[inline(always)] | ||
| fn approximate_recip_f32x4(self, a: f32x4<Self>) -> f32x4<Self> { | ||
| self.splat_f32x4(1.0) / a |
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I haven't tried it, does division work without splatting? I think for mutliplication it works at least.
| } | ||
| #[inline(always)] | ||
| fn approximate_recip_f32x4(self, a: f32x4<Self>) -> f32x4<Self> { | ||
| self.div_f32x4(self.splat_f32x4(1.0), a) |
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Same comment as in fallback
| unsafe { _mm_sqrt_ps(a.into()).simd_into(self) } | ||
| } | ||
| #[inline(always)] | ||
| fn approximate_recip_f32x4(self, a: f32x4<Self>) -> f32x4<Self> { |
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I'm wondering whether we should just spell reciprocal out. But should be fine this way!
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Wondered the same thing, but decided to mirror e.g. f32::recip.
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x86 and AArch64 have instructions to calculate fast approximate reciprocals, and these can speed up some algorithms quite nicely (e.g. sprinkling this in Vello's
flatten_simd.rsresults in -4% flattening timings for GhostScript Tiger (actually landing that there requires a bit of thought whether the lowered precision is acceptable of course!)).There is some detail here that this PR as-is doesn't attempt to solve. x86's
rcphas about 12 bits of precision, AArch64'svrecpeabout 8 bits. AArch64 has an additional instruction however,vrecps, to perform a Newton refinement step, which bumps the precision to 16 bits. That'd look something like the following.Then, AVX512 introduces
rcp14, which allows calculating to 14-bit precision with (I believe) the same performance asrcp, and extends support tof64.In any case, this method does the simplest thing of just exposing the cheapest hardware estimate, similar to e.g. Highway's
ApproximateReciprocal.