FLINT3.7.0-dev
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_fmpz_poly_mulmid_toom_scalar, _fmpz_poly_mulmid_toom_scalar_nmax, fmpz_poly_mulmid_toom_scalar

Synopsis#include <flint/fmpz_poly.h>
int _fmpz_poly_mulmid_toom_scalar(fmpz * res, const fmpz * poly1, slong len1, const fmpz * poly2, slong len2, slong nlo, slong nhi)source
int _fmpz_poly_mulmid_toom_scalar_nmax(fmpz * res, const fmpz * poly1, slong len1, const fmpz * poly2, slong len2, slong nlo, slong nhi, slong nmax)source
int fmpz_poly_mulmid_toom_scalar(fmpz_poly_t res, const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong nlo, slong nhi)source

Compute the middle product window [nlo,nhi)[\mathit{nlo}, \mathit{nhi}) as _fmpz_poly_mulmid, by Toom–Cook interpolation. With mm, nn the lengths of the operands after removing coefficients that cannot contribute and ww the length of the window, the number of coefficient multiplications is the sum of the two smallest of m,n,wm, n, w, minus one: either a full product of the trimmed operands, or, transposed, a middle product of the window against the shorter operand. Return 0, leaving res unchanged, when both routes exceed the length bound of _fmpz_poly_mul_toom_scalar_nmax.

The count is symmetric in the three lengths, as the transposition principle requires, and is optimal when the window touches an end of the product. A narrow window can be supported when the full product is not: four coefficients of a 16×1616 \times 16 product need 19 multiplications, the full product 31.

The underscore versions take the lengths in either order and require 0≤nlo<nhi≤len1+len2−10 \le \mathit{nlo} < \mathit{nhi} \le \mathit{len1} + \mathit{len2} - 1 and no overlap of res with the inputs.

Cite this page

The FLINT team, “_fmpz_poly_mulmid_toom_scalar, _fmpz_poly_mulmid_toom_scalar_nmax, fmpz_poly_mulmid_toom_scalar (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/_fmpz_poly_mulmid_toom_scalar.html (generated 2026-11-02).