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facf0c92e0
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87 lines
2.9 KiB
C
87 lines
2.9 KiB
C
/* invert.c -- Compute floor((B^{2n}-1)/U) - B^n.
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Contributed to the GNU project by Marco Bodrato.
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
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Copyright (C) 2007, 2009, 2010, 2012, 2014-2016 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#include "longlong.h"
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void
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mpn_invert (mp_ptr ip, mp_srcptr dp, mp_size_t n, mp_ptr scratch)
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{
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ASSERT (n > 0);
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ASSERT (dp[n-1] & GMP_NUMB_HIGHBIT);
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ASSERT (! MPN_OVERLAP_P (ip, n, dp, n));
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ASSERT (! MPN_OVERLAP_P (ip, n, scratch, mpn_invertappr_itch(n)));
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ASSERT (! MPN_OVERLAP_P (dp, n, scratch, mpn_invertappr_itch(n)));
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if (n == 1)
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invert_limb (*ip, *dp);
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else if (BELOW_THRESHOLD (n, INV_APPR_THRESHOLD))
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{
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/* Maximum scratch needed by this branch: 2*n */
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mp_ptr xp;
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xp = scratch; /* 2 * n limbs */
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/* n > 1 here */
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MPN_FILL (xp, n, GMP_NUMB_MAX);
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mpn_com (xp + n, dp, n);
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if (n == 2) {
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mpn_divrem_2 (ip, 0, xp, 4, dp);
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} else {
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gmp_pi1_t inv;
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invert_pi1 (inv, dp[n-1], dp[n-2]);
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/* FIXME: should we use dcpi1_div_q, for big sizes? */
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mpn_sbpi1_div_q (ip, xp, 2 * n, dp, n, inv.inv32);
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}
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}
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else { /* Use approximated inverse; correct the result if needed. */
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mp_limb_t e; /* The possible error in the approximate inverse */
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ASSERT ( mpn_invert_itch (n) >= mpn_invertappr_itch (n) );
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e = mpn_ni_invertappr (ip, dp, n, scratch);
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if (UNLIKELY (e)) { /* Assume the error can only be "0" (no error) or "1". */
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/* Code to detect and correct the "off by one" approximation. */
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mpn_mul_n (scratch, ip, dp, n);
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e = mpn_add_n (scratch, scratch, dp, n); /* FIXME: we only need e.*/
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if (LIKELY(e)) /* The high part can not give a carry by itself. */
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e = mpn_add_nc (scratch + n, scratch + n, dp, n, e); /* FIXME:e */
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/* If the value was wrong (no carry), correct it (increment). */
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e ^= CNST_LIMB (1);
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MPN_INCR_U (ip, n, e);
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}
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}
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}
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