Merge pull request #2441 from fredrik-johansson/bivar3

Kronecker substitution multiplication for ``gr_poly``

Author: fredrik-johansson

doc/source/gr_poly.rst

@@ -192,6 +192,14 @@ Multiplication algorithms
     Multiply using the classical (schoolbook) algorithm, performing
     a sequence of dot products.
 
+.. function:: int _gr_poly_mullow_bivariate_KS(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx)
+              int gr_poly_mullow_bivariate_KS(gr_poly_t res, const gr_poly_t poly1, const gr_poly_t poly2, slong n, gr_ctx_t ctx)
+
+    Assuming that the coefficients are polynomials of type ``gr_poly``,
+    reduce the bivariate product to a single univariate product using
+    Kronecker substitution. Returns ``GR_UNABLE`` if the elements are not
+    of type ``gr_poly``.
+
 .. function:: int _gr_poly_mullow_complex_reorder(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, int karatsuba, gr_ctx_t ctx, gr_ctx_t real_ctx)
               int gr_poly_mullow_complex_reorder(gr_poly_t res, const gr_poly_t poly1, const gr_poly_t poly2, slong n, int karatsuba, gr_ctx_t ctx, gr_ctx_t real_ctx)
 

src/gr/fmpz_poly.c

@@ -801,6 +801,18 @@ _gr_fmpz_poly_factor(fmpz_poly_t c, gr_vec_t factors, gr_vec_t exponents, gr_src
     return GR_SUCCESS;
 }
 
+#define MUL_KS_CUTOFF 5
+
+int
+_gr_fmpz_poly_gr_poly_mullow(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx)
+{
+    if (len1 < MUL_KS_CUTOFF || len2 < MUL_KS_CUTOFF || n < MUL_KS_CUTOFF)
+        return _gr_poly_mullow_classical(res, poly1, len1, poly2, len2, n, ctx);
+    else
+        return _gr_poly_mullow_bivariate_KS(res, poly1, len1, poly2, len2, n, ctx);
+}
+
+
 int _fmpz_poly_methods_initialized = 0;
 
 gr_static_method_table _fmpz_poly_methods;
@@ -892,6 +904,7 @@ gr_method_tab_input _fmpz_poly_methods_input[] =
     {GR_METHOD_RSQRT,           (gr_funcptr) _gr_fmpz_poly_rsqrt},
     {GR_METHOD_CANONICAL_ASSOCIATE,  (gr_funcptr) _gr_fmpz_poly_canonical_associate},
     {GR_METHOD_FACTOR,          (gr_funcptr) _gr_fmpz_poly_factor},
+    {GR_METHOD_POLY_MULLOW,     (gr_funcptr) _gr_fmpz_poly_gr_poly_mullow},
     {0,                         (gr_funcptr) NULL},
 };
 

src/gr/polynomial.c

@@ -673,6 +673,47 @@ polynomial_factor(gr_ptr c, gr_vec_t fac, gr_vec_t mult, const gr_poly_t pol, in
     return GR_FACTOR_OP(cctx, POLY_FACTOR)(c, fac, mult, pol, flags, cctx);
 }
 
+/* TODO: account for sparsity */
+#define MUL_KS_CUTOFF 5
+
+/* Don't do extremely deep recursive KS; the polynomials will
+   typically be too sparse, and we risk blowing up memory too. */
+#define MUL_KS_DEPTH_LIMIT 3
+
+/* Assume that the underlying polynomial ring has asymptotically
+   fast univariate multiplication if it overrides the default
+   multiplication routine. */
+
+static int
+want_KS(gr_ctx_t cctx, slong depth)
+{
+    if (cctx->methods[GR_METHOD_POLY_MULLOW] == (gr_funcptr) _gr_poly_mullow_generic)
+        return 0;
+
+    /* If the coefficients are polynomials, check the ground ring. */
+    if (depth > MUL_KS_DEPTH_LIMIT)
+        return 0;
+
+    if (cctx->which_ring == GR_CTX_GR_POLY)
+        return want_KS(POLYNOMIAL_ELEM_CTX(cctx), depth + 1);
+
+    return 1;
+}
+
+int
+_polynomial_gr_poly_mullow(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx)
+{
+    gr_ctx_struct * cctx = POLYNOMIAL_ELEM_CTX(ctx);
+
+    if (len1 < MUL_KS_CUTOFF || len2 < MUL_KS_CUTOFF || n < MUL_KS_CUTOFF)
+        return _gr_poly_mullow_classical(res, poly1, len1, poly2, len2, n, ctx);
+
+    if (!want_KS(cctx, 0))
+        return _gr_poly_mullow_classical(res, poly1, len1, poly2, len2, n, ctx);
+
+    return _gr_poly_mullow_bivariate_KS(res, poly1, len1, poly2, len2, n, ctx);
+}
+
 
 int _gr_poly_methods_initialized = 0;
 
@@ -760,6 +801,7 @@ gr_method_tab_input _gr_poly_methods_input[] =
     {GR_METHOD_GCD,         (gr_funcptr) polynomial_gcd},
 
     {GR_METHOD_FACTOR,      (gr_funcptr) polynomial_factor},
+    {GR_METHOD_POLY_MULLOW, (gr_funcptr) _polynomial_gr_poly_mullow},
 
     {0,                     (gr_funcptr) NULL},
 };

src/gr_poly.h

@@ -144,6 +144,9 @@ WARN_UNUSED_RESULT int gr_poly_mullow_classical(gr_poly_t res, const gr_poly_t p
 WARN_UNUSED_RESULT int _gr_poly_mullow_complex_reorder(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, int karatsuba, gr_ctx_t ctx, gr_ctx_t real_ctx);
 WARN_UNUSED_RESULT int gr_poly_mullow_complex_reorder(gr_poly_t res, const gr_poly_t poly1, const gr_poly_t poly2, slong n, int karatsuba, gr_ctx_t ctx, gr_ctx_t real_ctx);
 
+WARN_UNUSED_RESULT int _gr_poly_mullow_bivariate_KS(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx);
+WARN_UNUSED_RESULT int gr_poly_mullow_bivariate_KS(gr_poly_t res, const gr_poly_t poly1, const gr_poly_t poly2, slong n, gr_ctx_t ctx);
+
 WARN_UNUSED_RESULT int _gr_poly_mul_karatsuba(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, gr_ctx_t ctx);
 WARN_UNUSED_RESULT int gr_poly_mul_karatsuba(gr_poly_t res, const gr_poly_t poly1, const gr_poly_t poly2, gr_ctx_t ctx);
 WARN_UNUSED_RESULT int _gr_poly_mul_toom33(gr_ptr res, gr_srcptr poly1, slong len1, gr_srcptr poly2, slong len2, gr_ctx_t ctx);

src/gr_poly/mullow_bivariate_KS.c

@@ -0,0 +1,162 @@
+/*
+    Copyright (C) 2025 Fredrik Johansson
+
+    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 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include <string.h>
+#include "gr.h"
+#include "gr_vec.h"
+#include "gr_poly.h"
+
+int
+_gr_poly_mullow_bivariate_KS(gr_ptr res,
+    gr_srcptr poly1, slong len1,
+    gr_srcptr poly2, slong len2, slong n, gr_ctx_t ctx)
+{
+    slong i, l, max_len1, max_len2, inner_len;
+    gr_ctx_struct * cctx;
+    gr_ctx_t tmp_ctx;
+    const gr_poly_struct * ppoly1, * ppoly2;
+    gr_poly_struct * pres;
+    gr_ptr R, P1, P2, pp, tmp_zero;
+    slong csz;
+    int status = GR_SUCCESS;
+    int squaring;
+
+    /* Todo: other base types */
+    if (ctx->which_ring == GR_CTX_GR_POLY)
+    {
+        cctx = POLYNOMIAL_ELEM_CTX(ctx);
+    }
+    else if (ctx->which_ring == GR_CTX_FMPZ_POLY)
+    {
+        gr_ctx_init_fmpz(tmp_ctx);
+        cctx = tmp_ctx;
+    }
+    else
+        return GR_UNABLE;
+
+    csz = cctx->sizeof_elem;
+
+    len1 = FLINT_MIN(len1, n);
+    len2 = FLINT_MIN(len2, n);
+
+    squaring = (poly1 == poly2) && (len1 == len2);
+    ppoly1 = poly1;
+    ppoly2 = poly2;
+    pres = res;
+
+    max_len1 = 0;
+    max_len2 = 0;
+
+    for (i = 0; i < len1; i++)
+    {
+        l = ppoly1[i].length;
+        max_len1 = FLINT_MAX(l, max_len1);
+    }
+
+    if (squaring)
+    {
+        max_len2 = max_len1;
+    }
+    else
+    {
+        for (i = 0; i < len2; i++)
+        {
+            l = ppoly2[i].length;
+            max_len2 = FLINT_MAX(l, max_len2);
+        }
+    }
+
+    if (max_len1 == 0 || max_len2 == 0)
+        return _gr_vec_zero(res, n, ctx);
+
+    inner_len = max_len1 + max_len2 - 1;
+
+    GR_TMP_INIT_VEC(R, n * inner_len, cctx);
+    GR_TMP_INIT_VEC(tmp_zero, inner_len, cctx);
+    P1 = GR_TMP_ALLOC(len1 * inner_len * cctx->sizeof_elem);
+
+    if (squaring)
+        P2 = P1;
+    else
+        P2 = GR_TMP_ALLOC(len2 * inner_len * cctx->sizeof_elem);
+
+    for (i = 0; i < len1; i++)
+    {
+        l = ppoly1[i].length;
+        memcpy(GR_ENTRY(P1, i * inner_len, csz), ppoly1[i].coeffs, l * csz);
+        memcpy(GR_ENTRY(P1, i * inner_len + l, csz), tmp_zero, (inner_len - l) * csz);
+    }
+
+    if (!squaring)
+    {
+        for (i = 0; i < len2; i++)
+        {
+            l = ppoly2[i].length;
+            memcpy(GR_ENTRY(P2, i * inner_len, csz), ppoly2[i].coeffs, l * csz);
+            memcpy(GR_ENTRY(P2, i * inner_len + l, csz), tmp_zero, (inner_len - l) * csz);
+        }
+    }
+
+    status = _gr_poly_mullow(R, P1, len1 * inner_len, P2, len2 * inner_len, n * inner_len, cctx);
+
+    for (i = 0; i < n; i++)
+    {
+        l = inner_len;
+        pp = GR_ENTRY(R, i * inner_len, csz);
+        while (l > 0 && gr_is_zero(GR_ENTRY(pp, l - 1, csz), cctx) == T_TRUE)
+            l--;
+        gr_poly_fit_length(pres + i, l, cctx);
+        _gr_poly_set_length(pres + i, l, cctx);
+        _gr_vec_swap(pres[i].coeffs, pp, l, cctx);
+    }
+
+    GR_TMP_CLEAR_VEC(R, n * inner_len, cctx);
+    GR_TMP_CLEAR_VEC(tmp_zero, inner_len, cctx);
+    GR_TMP_FREE(P1, len1 * inner_len * cctx->sizeof_elem);
+    if (!squaring)
+        GR_TMP_FREE(P2, len2 * inner_len * cctx->sizeof_elem);
+
+    return status;
+}
+
+int
+gr_poly_mullow_bivariate_KS(gr_poly_t res, const gr_poly_t poly1,
+                                            const gr_poly_t poly2,
+                                                slong n, gr_ctx_t ctx)
+{
+    slong len_out;
+    int status;
+
+    if (poly1->length == 0 || poly2->length == 0 || n == 0)
+        return gr_poly_zero(res, ctx);
+
+    len_out = poly1->length + poly2->length - 1;
+    n = FLINT_MIN(n, len_out);
+
+    if (res == poly1 || res == poly2)
+    {
+        gr_poly_t t;
+        gr_poly_init2(t, n, ctx);
+        status = _gr_poly_mullow_bivariate_KS(t->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, ctx);
+        gr_poly_swap(res, t, ctx);
+        gr_poly_clear(t, ctx);
+    }
+    else
+    {
+        gr_poly_fit_length(res, n, ctx);
+        status = _gr_poly_mullow_bivariate_KS(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, ctx);
+    }
+
+    _gr_poly_set_length(res, n, ctx);
+    _gr_poly_normalise(res, ctx);
+    return status;
+}
+