mpn_mod: add batched AVX2 Montgomery 4x4 matrix power - #2823
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Add an AVX2 batched-Montgomery kernel for 4x4 matrices over Z/nZ and use it for matrix powering. Numbers are stored as 31-bit limbs with the four output columns in the four AVX2 lanes; dot products sum their four products into a wide accumulator and reduce with a single Montgomery REDC (lazy reduction), valid for n < 2^246. The kernel is compile-time specialized on the limb count s = ceil((bits+2)/31), so work scales with the modulus size.
Brian-Heckel
marked this pull request as draft
September 2, 2026 04:32
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Interesting, but this is a lot of ad hoc code for one specific operation at one specific size. Some context is missing here: is there a particularly important application relying critically on 4x4 matrix powering with these bit sizes? This looks like it would be more useful if:
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Adds an AVX2 batched-Montgomery kernel for 4×4 matrices over
Z/nZand uses it to accelerate matrix powering (A^exp) calledmpn_mod_mat_mul_batched_mont. On a 4×4 power over an odd modulus it is faster (1.60x) than the current generic path (gr_mat_pow_ui, which uses classical multiplies for 4×4), with the largest gains at smaller moduli. It falls back to the generic path whenever it does not apply. The matrix multiplication shouldn't be used for a generic multiply since conversion to Montgomery form has been profiled to end up taking more time than classic matrix multiplication. Thempn_mod_mat_mul_batched_montis provided as a function but doesn't provide a speedup in itself. Tests and profiles are provided.I'm leaving this as a draft in case details or specifics need to be addressed before merging.
Claude was used in the development and implementation of this PR.