invert.c
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上传日期:2022-08-06
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- /* invert.c -- Compute floor((B^{2n}-1)/U) - B^n.
- Contributed to the GNU project by Marco Bodrato.
- THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
- SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
- GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
- Copyright (C) 2007, 2009, 2010 Free Software Foundation, Inc.
- This file is part of the GNU MP Library.
- The GNU MP Library is free software; you can redistribute it and/or modify
- it under the terms of the GNU Lesser General Public License as published by
- the Free Software Foundation; either version 3 of the License, or (at your
- option) any later version.
- The GNU MP Library 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 Lesser General Public
- License for more details.
- You should have received a copy of the GNU Lesser General Public License
- along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- /* FIXME: Remove NULL and TMP_*, as soon as all the callers properly
- allocate and pass the scratch to the function. */
- #include <stdlib.h> /* for NULL */
- #include "gmp.h"
- #include "gmp-impl.h"
- #include "longlong.h"
- void
- mpn_invert (mp_ptr ip, mp_srcptr dp, mp_size_t n, mp_ptr scratch)
- {
- ASSERT (n > 0);
- ASSERT (dp[n-1] & GMP_NUMB_HIGHBIT);
- ASSERT (! MPN_OVERLAP_P (ip, n, dp, n));
- ASSERT (! MPN_OVERLAP_P (ip, n, scratch, mpn_invertappr_itch(n)));
- ASSERT (! MPN_OVERLAP_P (dp, n, scratch, mpn_invertappr_itch(n)));
- if (n == 1)
- invert_limb (*ip, *dp);
- else {
- TMP_DECL;
- TMP_MARK;
- if (scratch == NULL)
- scratch = TMP_ALLOC_LIMBS (mpn_invert_itch (n));
- if (BELOW_THRESHOLD (n, INV_APPR_THRESHOLD))
- {
- /* Maximum scratch needed by this branch: 2*n */
- mp_size_t i;
- mp_ptr xp;
- xp = scratch; /* 2 * n limbs */
- for (i = n - 1; i >= 0; i--)
- xp[i] = GMP_NUMB_MAX;
- mpn_com (xp + n, dp, n);
- if (n == 2) {
- mpn_divrem_2 (ip, 0, xp, 4, dp);
- } else {
- gmp_pi1_t inv;
- invert_pi1 (inv, dp[n-1], dp[n-2]);
- /* FIXME: should we use dcpi1_div_q, for big sizes? */
- mpn_sbpi1_div_q (ip, xp, 2 * n, dp, n, inv.inv32);
- }
- }
- else { /* Use approximated inverse; correct the result if needed. */
- mp_limb_t e; /* The possible error in the approximate inverse */
- ASSERT ( mpn_invert_itch (n) >= mpn_invertappr_itch (n) );
- e = mpn_ni_invertappr (ip, dp, n, scratch);
- if (e) { /* Assume the error can only be "0" (no error) or "1". */
- /* Code to detect and correct the "off by one" approximation. */
- mpn_mul_n (scratch, ip, dp, n);
- ASSERT_NOCARRY (mpn_add_n (scratch + n, scratch + n, dp, n));
- if (! mpn_add (scratch, scratch, 2*n, dp, n))
- MPN_INCR_U (ip, n, 1); /* The value was wrong, correct it. */
- }
- }
- TMP_FREE;
- }
- }