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fmpz_mat_mul_waksman (code from PML)
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,131 @@ | ||
| /* | ||
| Copyright (C) 2024 Éric Schost | ||
| Copyright (C) 2024 Vincent Neiger | ||
| This file is part of FLINT. | ||
| FLINT is free software: you can redistribute it and/or modify it under | ||
| the terms of the GNU Lesser General Public License (LGPL) as published | ||
| by the Free Software Foundation; either version 2.1 of the License, or | ||
| (at your option) any later version. See <https://www.gnu.org/licenses/>. | ||
| */ | ||
|
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| #include "fmpz.h" | ||
| #include "fmpz_vec.h" | ||
| #include "fmpz_mat.h" | ||
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| /** ------------------------------------------------------------ */ | ||
| /** Waksman's algorithm for matrix multiplication */ | ||
| /** does n^3/2+O(n^2) products, but many additions */ | ||
| /** good for small matrices with large entries */ | ||
| /** ------------------------------------------------------------ */ | ||
| void fmpz_mat_mul_waksman(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B) | ||
| { | ||
| slong m = A->r; | ||
| slong n = B->r; | ||
| slong p = B->c; | ||
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| if (m == 0 || n == 0 || p == 0) | ||
| { | ||
| fmpz_mat_zero(C); | ||
| return; | ||
| } | ||
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| slong i, l, j, k; | ||
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| fmpz * Crow = _fmpz_vec_init(p + m); | ||
| fmpz * Ccol = Crow + p; | ||
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| slong np = n >> 1; | ||
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| fmpz_t val0, val1, val2, crow; | ||
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| fmpz_init(val0); | ||
| fmpz_init(val1); | ||
| fmpz_init(val2); | ||
| fmpz_init(crow); | ||
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| for (i = 0; i < p; i++) | ||
| fmpz_zero(Crow + i); | ||
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| for (i = 0; i < m; i++) | ||
| fmpz_zero(Ccol + i); | ||
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| for (i = 0; i < m; i++) | ||
| for (j = 0; j < p; j++) | ||
| fmpz_zero(fmpz_mat_entry(C, i, j)); | ||
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| for (j = 1; j <= np; j++) | ||
| { | ||
| slong j2 = (j << 1) - 1; | ||
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| for (k = 0; k < p; k++) | ||
| { | ||
| fmpz_add(val1, fmpz_mat_entry(A, 0, j2-1), fmpz_mat_entry(B, j2, k)); | ||
| fmpz_add(val2, fmpz_mat_entry(A, 0, j2), fmpz_mat_entry(B, j2-1, k)); | ||
| fmpz_addmul(fmpz_mat_entry(C, 0, k), val1, val2); | ||
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| fmpz_sub(val1, fmpz_mat_entry(A, 0, j2-1), fmpz_mat_entry(B, j2, k)); | ||
| fmpz_sub(val2, fmpz_mat_entry(A, 0, j2), fmpz_mat_entry(B, j2-1, k)); | ||
| fmpz_addmul(Crow + k, val1, val2); | ||
| } | ||
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| for (l = 1; l < m; l++) | ||
| { | ||
| fmpz_add(val1, fmpz_mat_entry(A, l, j2-1), fmpz_mat_entry(B, j2, 0)); | ||
| fmpz_add(val2, fmpz_mat_entry(A, l, j2), fmpz_mat_entry(B, j2-1, 0)); | ||
| fmpz_addmul(fmpz_mat_entry(C, l, 0), val1, val2); | ||
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| fmpz_sub(val1, fmpz_mat_entry(A, l, j2-1), fmpz_mat_entry(B, j2, 0)); | ||
| fmpz_sub(val2, fmpz_mat_entry(A, l, j2), fmpz_mat_entry(B, j2-1, 0)); | ||
| fmpz_addmul(Ccol + l, val1, val2); | ||
| } | ||
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| for (k = 1; k < p; k++) | ||
| { | ||
| for (l = 1; l < m; l++) | ||
| { | ||
| fmpz_add(val1, fmpz_mat_entry(A, l, j2-1), fmpz_mat_entry(B, j2, k)); | ||
| fmpz_add(val2, fmpz_mat_entry(A, l, j2), fmpz_mat_entry(B, j2-1, k)); | ||
| fmpz_addmul(fmpz_mat_entry(C, l, k), val1, val2); | ||
| } | ||
| } | ||
| } | ||
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| for (l = 1; l < m; l++) | ||
| { | ||
| fmpz_add(val1, Ccol + l, fmpz_mat_entry(C, l, 0)); | ||
| fmpz_tdiv_q_2exp(Ccol+ l, val1, 1); | ||
| fmpz_sub(fmpz_mat_entry(C, l, 0), fmpz_mat_entry(C, l, 0), Ccol + l); | ||
| } | ||
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| fmpz_add(val1, Crow, fmpz_mat_entry(C, 0, 0)); | ||
| fmpz_tdiv_q_2exp(val0, val1, 1); | ||
| fmpz_sub(fmpz_mat_entry(C, 0, 0), fmpz_mat_entry(C, 0, 0), val0); | ||
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| for (k = 1; k < p; k++) | ||
| { | ||
| fmpz_add(crow, Crow + k, fmpz_mat_entry(C, 0, k)); | ||
| fmpz_tdiv_q_2exp(val1, crow, 1); | ||
| fmpz_sub(fmpz_mat_entry(C, 0, k), fmpz_mat_entry(C, 0, k), val1); | ||
| fmpz_sub(crow, val1, val0); | ||
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| for (l = 1; l < m; l++) | ||
| { | ||
| fmpz_sub(val2, fmpz_mat_entry(C, l, k), crow); | ||
| fmpz_sub(fmpz_mat_entry(C, l, k), val2, Ccol + l); | ||
| } | ||
| } | ||
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| if ((n & 1) == 1) | ||
| for (l = 0; l < m; l++) | ||
| for (k = 0; k < p; k++) | ||
| fmpz_addmul(fmpz_mat_entry(C, l, k), fmpz_mat_entry(A, l, n-1), fmpz_mat_entry(B, n-1, k)); | ||
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| _fmpz_vec_clear(Crow, p + m); | ||
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| fmpz_clear(val0); | ||
| fmpz_clear(val1); | ||
| fmpz_clear(val2); | ||
| fmpz_clear(crow); | ||
| } |
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