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Precise bounds calculation for nfixed_mat_mul #2112

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merged 1 commit into from
Nov 28, 2024

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fredrik-johansson
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For each of

  • _nfixed_mat_mul
  • _nfixed_mat_mul_classical
  • _nfixed_mat_mul_waksman
  • _nfixed_mat_mul_strassen
  • _nfixed_complex_mat_mul

we implement a corresponding method that bounds the magnitudes of all intermediate results as well as the final error (in ulps).

The magnitude bound allows one to scale the inputs tightly while guaranteeing |x| < 1 for intermediate results so that no overflow is possible.

Also, thanks to the error bound, it will be possible to use nfixed methods for arb_t and acb_t matrix multiplication (not done in this PR).

@albinahlback This basically SLP error analysis, so you might want to give this code a careful look when you have time.

@fredrik-johansson fredrik-johansson merged commit 2f4594b into flintlib:main Nov 28, 2024
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2 participants