void _nmod_poly_compose_mod_horner(mp_ptr res, mp_srcptr f, long lenf, mp_srcptr g, mp_srcptr h, long lenh, nmod_t mod) { long i, len; mp_ptr t; if (lenh == 1) return; if (lenf == 1) { res[0] = f[0]; return; } if (lenh == 2) { res[0] = _nmod_poly_evaluate_nmod(f, lenf, g[0], mod); return; } len = lenh - 1; i = lenf - 1; t = _nmod_vec_init(len); _nmod_vec_scalar_mul_nmod(res, g, len, f[i], mod); i--; if (i >= 0) res[0] = nmod_add(res[0], f[i], mod); while (i > 0) { i--; _nmod_poly_mulmod(t, res, len, g, len, h, lenh, mod); _nmod_poly_add(res, t, len, f + i, 1, mod); } _nmod_vec_clear(t); }
void _nmod_poly_compose_divconquer(mp_ptr res, mp_srcptr poly1, long len1, mp_srcptr poly2, long len2, nmod_t mod) { long i, j, k, n; long * hlen, alloc, powlen; mp_ptr v, * h, pow, temp; if (len1 == 1) { res[0] = poly1[0]; return; } if (len2 == 1) { res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod); return; } if (len1 == 2) { _nmod_poly_compose_horner(res, poly1, len1, poly2, len2, mod); return; } /* Initialisation */ hlen = (long *) flint_malloc(((len1 + 1) / 2) * sizeof(long)); for (k = 1; (2 << k) < len1; k++) ; hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1; for (i = k - 1; i > 0; i--) { long hi = (len1 + (1 << i) - 1) / (1 << i); for (n = (hi + 1) / 2; n < hi; n++) hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1; } powlen = (1 << k) * (len2 - 1) + 1; alloc = 0; for (i = 0; i < (len1 + 1) / 2; i++) alloc += hlen[i]; v = _nmod_vec_init(alloc + 2 * powlen); h = (mp_ptr *) flint_malloc(((len1 + 1) / 2) * sizeof(mp_ptr)); h[0] = v; for (i = 0; i < (len1 - 1) / 2; i++) { h[i + 1] = h[i] + hlen[i]; hlen[i] = 0; } hlen[(len1 - 1) / 2] = 0; pow = v + alloc; temp = pow + powlen; /* Let's start the actual work */ for (i = 0, j = 0; i < len1 / 2; i++, j += 2) { if (poly1[j + 1] != 0L) { _nmod_vec_scalar_mul_nmod(h[i], poly2, len2, poly1[j + 1], mod); h[i][0] = n_addmod(h[i][0], poly1[j], mod.n); hlen[i] = len2; } else if (poly1[j] != 0L) { h[i][0] = poly1[j]; hlen[i] = 1; } } if ((len1 & 1L)) { if (poly1[j] != 0L) { h[i][0] = poly1[j]; hlen[i] = 1; } } _nmod_poly_mul(pow, poly2, len2, poly2, len2, mod); powlen = 2 * len2 - 1; for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2) { if (hlen[1] > 0) { long templen = powlen + hlen[1] - 1; _nmod_poly_mul(temp, pow, powlen, h[1], hlen[1], mod); _nmod_poly_add(h[0], temp, templen, h[0], hlen[0], mod); hlen[0] = FLINT_MAX(hlen[0], templen); } for (i = 1; i < n / 2; i++) { if (hlen[2*i + 1] > 0) { _nmod_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1], mod); hlen[i] = hlen[2*i + 1] + powlen - 1; } else hlen[i] = 0; _nmod_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i], mod); hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]); } if ((n & 1L)) { mpn_copyi(h[i], h[2*i], hlen[2*i]); hlen[i] = hlen[2*i]; } _nmod_poly_mul(temp, pow, powlen, pow, powlen, mod); powlen += powlen - 1; { mp_ptr t = pow; pow = temp; temp = t; } } _nmod_poly_mul(res, pow, powlen, h[1], hlen[1], mod); _nmod_vec_add(res, res, h[0], hlen[0], mod); _nmod_vec_clear(v); flint_free(h); flint_free(hlen); }
mp_limb_t nmod_poly_evaluate_nmod(const nmod_poly_t poly, mp_limb_t c) { return _nmod_poly_evaluate_nmod(poly->coeffs, poly->length, c, poly->mod); }
void _nmod_poly_compose_mod_brent_kung(mp_ptr res, mp_srcptr poly1, long len1, mp_srcptr poly2, mp_srcptr poly3, long len3, nmod_t mod) { nmod_mat_t A, B, C; mp_ptr t, h; long i, n, m; n = len3 - 1; if (len3 == 1) return; if (len1 == 1) { res[0] = poly1[0]; return; } if (len3 == 2) { res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod); return; } m = n_sqrt(n) + 1; nmod_mat_init(A, m, n, mod.n); nmod_mat_init(B, m, m, mod.n); nmod_mat_init(C, m, n, mod.n); h = _nmod_vec_init(n); t = _nmod_vec_init(n); /* Set rows of B to the segments of poly1 */ for (i = 0; i < len1 / m; i++) _nmod_vec_set(B->rows[i], poly1 + i*m, m); _nmod_vec_set(B->rows[i], poly1 + i*m, len1 % m); /* Set rows of A to powers of poly2 */ A->rows[0][0] = 1UL; _nmod_vec_set(A->rows[1], poly2, n); for (i = 2; i < m; i++) _nmod_poly_mulmod(A->rows[i], A->rows[i-1], n, poly2, n, poly3, len3, mod); nmod_mat_mul(C, B, A); /* Evaluate block composition using the Horner scheme */ _nmod_vec_set(res, C->rows[m - 1], n); _nmod_poly_mulmod(h, A->rows[m - 1], n, poly2, n, poly3, len3, mod); for (i = m - 2; i >= 0; i--) { _nmod_poly_mulmod(t, res, n, h, n, poly3, len3, mod); _nmod_poly_add(res, t, n, C->rows[i], n, mod); } _nmod_vec_clear(h); _nmod_vec_clear(t); nmod_mat_clear(A); nmod_mat_clear(B); nmod_mat_clear(C); }