https://gcc.gnu.org/bugzilla/show_bug.cgi?id=77776
Jakub Jelinek <jakub at gcc dot gnu.org> changed: What |Removed |Added ---------------------------------------------------------------------------- CC| |jakub at gcc dot gnu.org --- Comment #16 from Jakub Jelinek <jakub at gcc dot gnu.org> --- (In reply to Matthias Kretz (Vir) from comment #15) > Your implementation still needs to solve: > > 1. Loss of precision because of division & subsequent scaling by max. Users > comparing std::hypot(x, y, z) against a simple std::sqrt(x * x + y * y + z * > z) might wonder why they want to use std::hypot if it's less precise. > > 2. Relatively high cost (in latency and throughput) because of the three > divisions. You could replace it with scale = 1/max; x *= scale; ... But that > can reduce precision even further. > > 3. Summation of the x, y, and z squares isn't associative if you care about > precision. A high quality implementation needs to add the two lowest values > first. > > Here's a precise but inefficient implementation: > (https://compiler-explorer.com/z/ocGPnsYE3) > > template <typename T> > [[gnu::optimize("-fno-unsafe-math-optimizations")]] > T > hypot3(T x, T y, T z) > { > x = std::abs(x); > y = std::abs(y); > z = std::abs(z); > if (std::isinf(x) || std::isinf(y) || std::isinf(z)) > return std::__infinity_v<T>; > else if (std::isnan(x) || std::isnan(y) || std::isnan(z)) > return std::__quiet_NaN_v<T>; > else if (x == y && y == z) > return x * std::sqrt(T(3)); > else if (z == 0 && y == 0) > return x; > else if (x == 0 && z == 0) > return y; > else if (x == 0 && y == 0) > return z; > else > { > T hi = std::max(std::max(x, y), z); > T lo0 = std::min(std::max(x, y), z); > T lo1 = std::min(x, y); > int e = 0; > hi = std::frexp(hi, &e); > lo0 = std::ldexp(lo0, -e); > lo1 = std::ldexp(lo1, -e); > T lo = lo0 * lo0 + lo1 * lo1; > return std::ldexp(std::sqrt(hi * hi + lo), e); > } > } > > AFAIK > https://gcc.gnu.org/git/?p=gcc.git;a=blob;f=libstdc%2B%2B-v3/include/ > experimental/bits/simd_math.h;h=06e7b4496f9917f886f66fbd7629700dd17e55f9; > hb=HEAD#l1168 is a precise and efficient implementation. It also avoids > division altogether unless an input is subnormal. What glibc does there for the 2 argument hypot is after handling the non-finite cases finds the minimum and maximum and uses just normal multiplication, addition + sqrt for the common case where maximum isn't too large and minimum isn't too small. So, no need to use frexp/ldexp, just comparisons of hi above against sqrt of (max finite / 3), in that case scale by multiplying all 3 args by some appropriate scale constant, and similarly otherwise if lo1 is too small by some large scale.