ALL: Add flint

external/flint-2.4.3/fmpz_poly/divremlow_divconquer_recursive.c

@@ -0,0 +1,151 @@
+/*=============================================================================
+
+    This file is part of FLINT.
+
+    FLINT is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    FLINT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with FLINT; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2008, 2009 William Hart
+    Copyright (C) 2010 Sebastian Pancratz
+
+******************************************************************************/
+
+#include <stdlib.h>
+#include <gmp.h>
+#include "flint.h"
+#include "fmpz.h"
+#include "fmpz_vec.h"
+#include "fmpz_poly.h"
+
+#define FLINT_DIVREMLOW_DIVCONQUER_CUTOFF  16
+
+void
+_fmpz_poly_divremlow_divconquer_recursive(fmpz * Q, fmpz * QB, 
+                                          const fmpz * A, const fmpz * B, slong lenB)
+{
+    if (lenB <= FLINT_DIVREMLOW_DIVCONQUER_CUTOFF)
+    {
+        _fmpz_poly_divrem_basecase(Q, QB, A, 2 * lenB - 1, B, lenB);
+        _fmpz_vec_sub(QB, A, QB, lenB - 1);
+    }
+    else
+    {
+        const slong n2 = lenB / 2;
+        const slong n1 = lenB - n2;
+
+        const fmpz * p1 = A + 2 * n2;
+        const fmpz * p2;
+        const fmpz * d1 = B + n2;
+        const fmpz * d2 = B;
+
+        fmpz * q1 = Q + n2;
+        fmpz * q2 = Q;
+
+        /*
+           Think of the top lenB coefficients of QB as temporary space; this 
+           code will not depend on {QB, lenB - 1} and W being adjacent
+         */
+
+        fmpz * W = QB + (lenB - 1);
+
+        fmpz *d1q1, *d2q1, *t, *d3q2, *d4q2;
+
+        /*
+           Set q1 to p1 div d1, a 2 n1 - 1 by n1 division, so q1 has length 
+           at most n1; {W, n1 - 1} is d1 * q1 is truncated to length n1 - 1
+         */
+
+        _fmpz_poly_divremlow_divconquer_recursive(q1, W, p1, d1, n1);
+
+        /* 
+           W is of length lenB, but we only care about the bottom n1 - 1 
+           coeffs, which we push up by n2 + 1, to the very top; we do this 
+           manually here instead of via _fmpz_vec_swap() because the source 
+           and destination arrays overlap
+         */
+
+        d1q1 = W + (n2 + 1);
+
+        {
+            slong i;
+            for (i = 0; i < n1 - 1; i++)
+                fmpz_swap(d1q1 + i, W + i);
+        }
+
+        /*
+           Compute d2q1 = d2 * q1, of length at most lenB - 1; we'll need the 
+           top n2 coeffs for t and the bottom n1 - 1 coeffs for QB
+         */
+
+        d2q1 = QB;
+
+        _fmpz_poly_mul(d2q1, q1, n1, d2, n2);
+
+        /*
+           Compute {t - (n2 - 1), 2 n2 - 1} to be the top 2 n2 - 1 coeffs of 
+
+               A / x^n2 - (d1q1 x^n2 + d2q1).
+
+           Note that actually the bottom n2 - 1 coeffs may be arbitrary
+         */
+
+        t = W + n1;
+
+        if (n1 == n2)
+            fmpz_zero(t);
+        _fmpz_vec_add(t, t, d2q1 + (n1 - 1), n2);
+        _fmpz_vec_neg(t, t, n2);
+        _fmpz_vec_add(t, t, A + (n1 + n2 - 1), n2);
+
+        p2 = t - (n2 - 1);
+
+        /*
+           Move {QB, n1 - 1} into the bottom coefficients of W, so that 
+           we can use {QB, 2 n2 - 1} as space in the next division
+         */
+
+        _fmpz_vec_swap(QB, W, n1 - 1);
+
+        /*
+           Compute q2 = t div {B + n1}, a 2 n2 - 1 by n2 division
+         */
+
+        d3q2 = QB;
+
+        _fmpz_poly_divremlow_divconquer_recursive(q2, d3q2, p2, B + n1, n2);
+
+        _fmpz_vec_swap(QB + n1, d3q2, n2 - 1);
+
+        if (lenB & WORD(1))
+            fmpz_zero(QB + n2);
+        _fmpz_vec_add(QB + n2, QB + n2, W, n1 - 1);
+
+        /*
+           Compute {d4q2, lenB - 1} as {B, n1} * {q2, n2}; then move the 
+           bottom n2 coeffs of this into {QB, n2}, and add the top n1 - 1 
+           coeffs to {QB + n2, n1 - 1}
+         */
+
+        d4q2 = W;
+
+        _fmpz_poly_mul(d4q2, B, n1, q2, n2);
+
+        _fmpz_vec_swap(QB, d4q2, n2);
+        _fmpz_vec_add(QB + n2, QB + n2, d4q2 + n2, n1 - 1);
+    }
+}
+