void _fmpz_poly_compose_divconquer(fmpz * res, const fmpz * poly1, long len1, const fmpz * poly2, long len2) { long i, j, k, n; long *hlen, alloc, powlen; fmpz *v, **h, *pow, *temp; if (len1 == 1) { fmpz_set(res, poly1); return; } if (len2 == 1) { _fmpz_poly_evaluate_fmpz(res, poly1, len1, poly2); return; } if (len1 == 2) { _fmpz_poly_compose_horner(res, poly1, len1, poly2, len2); return; } /* Initialisation */ hlen = (long *) 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 = _fmpz_vec_init(alloc + 2 * powlen); h = (fmpz **) malloc(((len1 + 1) / 2) * sizeof(fmpz *)); 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) { _fmpz_vec_scalar_mul_fmpz(h[i], poly2, len2, poly1 + j + 1); fmpz_add(h[i], h[i], poly1 + j); hlen[i] = len2; } else if (poly1[j] != 0L) { fmpz_set(h[i], poly1 + j); hlen[i] = 1; } } if ((len1 & 1L)) { if (poly1[j] != 0L) { fmpz_set(h[i], poly1 + j); hlen[i] = 1; } } _fmpz_poly_mul(pow, poly2, len2, poly2, len2); 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; _fmpz_poly_mul(temp, pow, powlen, h[1], hlen[1]); _fmpz_poly_add(h[0], temp, templen, h[0], hlen[0]); hlen[0] = FLINT_MAX(hlen[0], templen); } for (i = 1; i < n / 2; i++) { if (hlen[2*i + 1] > 0) { _fmpz_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1]); hlen[i] = hlen[2*i + 1] + powlen - 1; } else hlen[i] = 0; _fmpz_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i]); hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]); } if ((n & 1L)) { _fmpz_vec_set(h[i], h[2*i], hlen[2*i]); hlen[i] = hlen[2*i]; } _fmpz_poly_mul(temp, pow, powlen, pow, powlen); powlen += powlen - 1; { fmpz * t = pow; pow = temp; temp = t; } } _fmpz_poly_mul(res, pow, powlen, h[1], hlen[1]); _fmpz_vec_add(res, res, h[0], hlen[0]); _fmpz_vec_clear(v, alloc + 2 * powlen); free(h); free(hlen); }
void _padic_poly_sub(fmpz *rop, slong *val, slong N, const fmpz *op1, slong val1, slong len1, slong N1, const fmpz *op2, slong val2, slong len2, slong N2, const padic_ctx_t ctx) { const slong len = FLINT_MAX(len1, len2); *val = FLINT_MIN(val1, val2); if (val1 == val2) { _fmpz_poly_sub(rop, op1, len1, op2, len2); _padic_poly_canonicalise(rop, val, len, ctx->p); } else { fmpz_t x; fmpz_init(x); if (val1 < val2) /* F := p^g (G - p^{h-g} H) */ { fmpz_pow_ui(x, ctx->p, val2 - val1); if (rop == op1) { _fmpz_vec_zero(rop + len1, len2 - len1); _fmpz_vec_scalar_submul_fmpz(rop, op2, len2, x); } else { _fmpz_vec_scalar_mul_fmpz(rop, op2, len2, x); _fmpz_vec_neg(rop, rop, len2); _fmpz_poly_add(rop, op1, len1, rop, len2); } } else /* F := p^h (p^(g-h) G - H) */ { fmpz_pow_ui(x, ctx->p, val1 - val2); if (rop == op2) { _fmpz_vec_neg(rop, op2, len2); _fmpz_vec_zero(rop + len2, len1 - len2); _fmpz_vec_scalar_addmul_fmpz(rop, op1, len1, x); } else { _fmpz_vec_scalar_mul_fmpz(rop, op1, len1, x); _fmpz_poly_sub(rop, rop, len1, op2, len2); } } fmpz_clear(x); } /* Reduce */ if (N - *val > 0) { fmpz_t pow; int alloc; alloc = _padic_ctx_pow_ui(pow, N - *val, ctx); if (N >= N1 && N >= N2) { slong i; for (i = 0; i < len; i++) if (fmpz_sgn(rop + i) < 0) fmpz_add(rop + i, rop + i, pow); } else { _fmpz_vec_scalar_mod_fmpz(rop, rop, len, pow); } if (alloc) fmpz_clear(pow); } else { _fmpz_vec_zero(rop, len); *val = 0; } }