Implementation-dependent reciprocal [sqrt] approximation instructions · Issue #4 · WebAssembly/relaxed-simd (original) (raw)

The proposal in WebAssembly/simd#1 includes these instructions:

• f32x4.reciprocalApproximation(a: v128) -> v128,
• f32x4.reciprocalSqrtApproximation(a: v128) -> v128,
• f64x2.reciprocalApproximation(a: v128) -> v128, and
• f64x2.reciprocalSqrtApproximation(a: v128) -> v128.

The corresponding scalar instructions are mentioned in the future features design document.

These instructions are available in the ARM, Intel, and MIPS SIMD instruction sets. They are typically implemented as table-driven piece-wise linear approximations on the interval [0.5; 1) or [0.25; 1) and then extended to the full exponent domain. However, the exact nature of the approximation is implementation-dependent, so different ISAs will get different results.

The approximations are either used as-is for low-precision graphics or physics code, or they are used as starting points and refined with one or more steps of Newton-Raphson.