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facf0c92e0
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149 lines
3.6 KiB
C
149 lines
3.6 KiB
C
/* mpn_mod_1s_2p (ap, n, b, cps)
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Divide (ap,,n) by b. Return the single-limb remainder.
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Requires that b < B / 2.
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Contributed to the GNU project by Torbjorn Granlund.
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Based on a suggestion by Peter L. Montgomery.
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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 GNU MP RELEASE.
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Copyright 2008-2010 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_mod_1s_2p_cps (mp_limb_t cps[5], mp_limb_t b)
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{
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mp_limb_t bi;
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mp_limb_t B1modb, B2modb, B3modb;
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int cnt;
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ASSERT (b <= (~(mp_limb_t) 0) / 2);
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count_leading_zeros (cnt, b);
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b <<= cnt;
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invert_limb (bi, b);
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cps[0] = bi;
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cps[1] = cnt;
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B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
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ASSERT (B1modb <= b); /* NB: not fully reduced mod b */
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cps[2] = B1modb >> cnt;
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udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);
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cps[3] = B2modb >> cnt;
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udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);
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cps[4] = B3modb >> cnt;
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#if WANT_ASSERT
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{
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int i;
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b = cps[2];
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for (i = 3; i <= 4; i++)
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{
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b += cps[i];
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ASSERT (b >= cps[i]);
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}
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}
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#endif
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}
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mp_limb_t
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mpn_mod_1s_2p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[5])
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{
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mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
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mp_limb_t B1modb, B2modb, B3modb;
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mp_size_t i;
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int cnt;
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ASSERT (n >= 1);
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B1modb = cps[2];
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B2modb = cps[3];
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B3modb = cps[4];
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if ((n & 1) != 0)
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{
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if (n == 1)
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{
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rl = ap[n - 1];
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bi = cps[0];
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cnt = cps[1];
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udiv_rnnd_preinv (r, rl >> (GMP_LIMB_BITS - cnt),
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rl << cnt, b, bi);
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return r >> cnt;
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}
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umul_ppmm (ph, pl, ap[n - 2], B1modb);
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add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
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umul_ppmm (rh, rl, ap[n - 1], B2modb);
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add_ssaaaa (rh, rl, rh, rl, ph, pl);
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n--;
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}
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else
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{
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rh = ap[n - 1];
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rl = ap[n - 2];
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}
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for (i = n - 4; i >= 0; i -= 2)
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{
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/* rr = ap[i] < B
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+ ap[i+1] * (B mod b) <= (B-1)(b-1)
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+ LO(rr) * (B^2 mod b) <= (B-1)(b-1)
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+ HI(rr) * (B^3 mod b) <= (B-1)(b-1)
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*/
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umul_ppmm (ph, pl, ap[i + 1], B1modb);
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add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
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umul_ppmm (ch, cl, rl, B2modb);
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add_ssaaaa (ph, pl, ph, pl, ch, cl);
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umul_ppmm (rh, rl, rh, B3modb);
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add_ssaaaa (rh, rl, rh, rl, ph, pl);
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}
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umul_ppmm (rh, cl, rh, B1modb);
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add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
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cnt = cps[1];
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bi = cps[0];
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r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
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udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
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return r >> cnt;
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}
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