3 ms·

I'd also love to see such comparisons. In SimSIMD, if AVX-512FP16 is available, I use FP16 for most I8/U8 operations, but can't speak about division. Overall,

• AlotOfReading 2y ago
  Don't have time to figure out the actual numbers myself, but here's an example doing the same for various transcendental functions: https://github.com/J-Montgomery/hacky_float_math/blob/623ee9f13da8343dda2af36c9a1bb9decca1fa04/softmax.cc#L34 https://github.com/J-Montgomery/hacky_float_math/blob/623ee9... a*(1.xxx/b) = a*(-1*1.xxx*log2(b)), which means you should be able to do a*(fma(b, magic, constant)) with appropriate conversions on either side. Should work in 32 bits for u8s.
• AlotOfReading 2y ago
  Put in a couple hours to see how well it worked. The approximately correct form is slightly faster than just doing an FP division without proper rounding. uint8_t magic_divide(uint8_t a, uint8_t b) { float x = static_cast<float>(b); int i = 0x7eb504f3 - std::bit_cast<int>(x); float reciprocal = std::bit_cast<float>(i); return a*1.94285123f*reciprocal*(-x*reciprocal+1.43566f); } No errors, ~20 cycles latency on skylake by uiCA. You can optimize it a bit further by approximating the newton raphson step though: uint8_t approx_magic_divide(uint8_t a, uint8_t b) { float x = static_cast<float>(b); int i = 0x7eb504f3 - std::bit_cast<int>(x); float reciprocal = std::bit_cast<float>(i); reciprocal = 1.385356f*reciprocal; return a*reciprocal; } Slightly off when a is a multiple of b, but approximately correct. 15.5 cycles on skylake because of the dependency chain.