Faster Argmin on Floats

Faster Argmin on Floats(algorithmiker.github.io)

22 points by return_to_monke 241 days ago | 11 comments

why_only_15 240 days ago |

This trick is very useful on Nvidia GPUs for calculating mins and maxes in some cases, e.g. atomic mins (better u32 support than f32) or warp-wide mins with `redux.sync` (only supports u32, not f32).

teo_zero 240 days ago |

I had expected something about algorithms, not Rust-specific implementations.

why_only_15 240 days ago | |

doing a u32 compare instead of an f32 compare is not rust-specific or indeed CPU-specific.

TheDudeMan 240 days ago |

How fast if you write a for loop and keep track of the index and value of the smallest (possibly treating them as ints)?

nine_k 240 days ago | |

I hazard to guess that it would be the same, because the compiler would produce a loop out of .iter(), would expose the loop index via .enumerate(), and would keep track of that index in .min_by(). I suppose the lambda would be inlined, maybe even along with comparisons.

I wonder could that be made faster by using AVX instructions; they allow to find the minimum value among several u32 values, but not immediately its index.

shoo 240 days ago | | |

Even without AVX it seems possible to do better than a naive C style for loop argmax by manually unrolling the loop a bit and maintaining multiple accumulators

e.g. using 4 accumulators instead of 1 accumulator in the naive for loop gives me around a 15%-20% speedup (Not using rust, extremely scalar terrible naive C code via g++ with -funroll-all-loops -march=native -O3)

if we're expressing argmax via the obvious C style naive for loop, or a functional reduce, with a single accumulator, we've forcing a chain dependency that isn't really part of the problem. but if we don't care which argmax-ing index we get (if there are multiple minimal elements in the array) then instead of evaluating the reductions in a single rigid chain bound by a single accumulator, we can break the chain and get our hardware to do more work in parallel, even if we're only single threaded.

anonymoushn is doing something much cleverer again using intrinsics but there's still that idea of "how do we break the dependency chain between different operations so the cpu can kick them off in parallel"

anonymoushn 240 days ago | | |

you can have some vector registers n_acc, ns, idx_acc, idxs, then you can do

  // (initialize ns and idxs by reading from the array
  //  and adding the apropriate constant to the old value of idxs.)
  n_acc = min(n_acc, ns);
  const is_new_min = eq(n_acc, ns);
  idx_acc = blend(idx_acc, idxs, is_new_min);

Edit: I wrote this with min, eq, blend but you can actually use cmpgt, min, blend to avoid having a dependency chain through all three instructions. I am just used to using min, eq, blend because of working on unsigned values that don't have cmpgt

you can consult the list of toys here: https://www.intel.com/content/www/us/en/docs/intrinsics-guid...

TinkersW 240 days ago | | |

Yes this is fairly easy to write in AVX, and you can track the index also, honestly the code is cleaner and nicer to read than this mildly obfuscated rust.

TheDudeMan 239 days ago | | |

But how is that slower than sorting the list?!

meisel 240 days ago |

Another speed up method here would be using simd, although it would be interesting to see in the assembly if it was auto-vectorized already.

This reminds me of a trick to sort floats faster, even if they have negatives, nans, and inf: map each float to a sortable int version of itself where one can compare them as ints (the precise mapping depending on how you want to order stuff like Nan). The one time conversion is fast and will pay off for the lg(n) comparisons. Then after sorting, map them back.

// (initialize ns and idxs by reading from the array // and adding the apropriate constant to the old value of idxs.) n_acc = min(n_acc, ns); const is_new_min = eq(n_acc, ns); idx_acc = blend(idx_acc, idxs, is_new_min);