source/libs/gmp/gmp-src/mpn/generic/mod_34lsub1.c

   1 /* mpn_mod_34lsub1 -- remainder modulo 2^(GMP_NUMB_BITS*3/4)-1.
   2
   3    THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
   4    CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
   5    FUTURE GNU MP RELEASES.
   6
   7 Copyright 2000-2002 Free Software Foundation, Inc.
   8
   9 This file is part of the GNU MP Library.
  10
  11 The GNU MP Library is free software; you can redistribute it and/or modify
  12 it under the terms of either:
  13
  14   * the GNU Lesser General Public License as published by the Free
  15     Software Foundation; either version 3 of the License, or (at your
  16     option) any later version.
  17
  18 or
  19
  20   * the GNU General Public License as published by the Free Software
  21     Foundation; either version 2 of the License, or (at your option) any
  22     later version.
  23
  24 or both in parallel, as here.
  25
  26 The GNU MP Library is distributed in the hope that it will be useful, but
  27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  28 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  29 for more details.
  30
  31 You should have received copies of the GNU General Public License and the
  32 GNU Lesser General Public License along with the GNU MP Library.  If not,
  33 see https://www.gnu.org/licenses/.  */
  34
  35
  36 #include "gmp.h"
  37 #include "gmp-impl.h"
  38
  39
  40 /* Calculate a remainder from {p,n} divided by 2^(GMP_NUMB_BITS*3/4)-1.
  41    The remainder is not fully reduced, it's any limb value congruent to
  42    {p,n} modulo that divisor.
  43
  44    This implementation is only correct when GMP_NUMB_BITS is a multiple of
  45    4.
  46
  47    FIXME: If GMP_NAIL_BITS is some silly big value during development then
  48    it's possible the carry accumulators c0,c1,c2 could overflow.
  49
  50    General notes:
  51
  52    The basic idea is to use a set of N accumulators (N=3 in this case) to
  53    effectively get a remainder mod 2^(GMP_NUMB_BITS*N)-1 followed at the end
  54    by a reduction to GMP_NUMB_BITS*N/M bits (M=4 in this case) for a
  55    remainder mod 2^(GMP_NUMB_BITS*N/M)-1.  N and M are chosen to give a good
  56    set of small prime factors in 2^(GMP_NUMB_BITS*N/M)-1.
  57
  58    N=3 M=4 suits GMP_NUMB_BITS==32 and GMP_NUMB_BITS==64 quite well, giving
  59    a few more primes than a single accumulator N=1 does, and for no extra
  60    cost (assuming the processor has a decent number of registers).
  61
  62    For strange nailified values of GMP_NUMB_BITS the idea would be to look
  63    for what N and M give good primes.  With GMP_NUMB_BITS not a power of 2
  64    the choices for M may be opened up a bit.  But such things are probably
  65    best done in separate code, not grafted on here.  */
  66
  67 #if GMP_NUMB_BITS % 4 == 0
  68
  69 #define B1  (GMP_NUMB_BITS / 4)
  70 #define B2  (B1 * 2)
  71 #define B3  (B1 * 3)
  72
  73 #define M1  ((CNST_LIMB(1) << B1) - 1)
  74 #define M2  ((CNST_LIMB(1) << B2) - 1)
  75 #define M3  ((CNST_LIMB(1) << B3) - 1)
  76
  77 #define LOW0(n)      ((n) & M3)
  78 #define HIGH0(n)     ((n) >> B3)
  79
  80 #define LOW1(n)      (((n) & M2) << B1)
  81 #define HIGH1(n)     ((n) >> B2)
  82
  83 #define LOW2(n)      (((n) & M1) << B2)
  84 #define HIGH2(n)     ((n) >> B1)
  85
  86 #define PARTS0(n)    (LOW0(n) + HIGH0(n))
  87 #define PARTS1(n)    (LOW1(n) + HIGH1(n))
  88 #define PARTS2(n)    (LOW2(n) + HIGH2(n))
  89
  90 #define ADD(c,a,val)                    \
  91   do {                                  \
  92     mp_limb_t  new_c;                   \
  93     ADDC_LIMB (new_c, a, a, val);       \
  94     (c) += new_c;                       \
  95   } while (0)
  96
  97 mp_limb_t
  98 mpn_mod_34lsub1 (mp_srcptr p, mp_size_t n)
  99 {
 100   mp_limb_t  c0 = 0;
 101   mp_limb_t  c1 = 0;
 102   mp_limb_t  c2 = 0;
 103   mp_limb_t  a0, a1, a2;
 104
 105   ASSERT (n >= 1);
 106   ASSERT (n/3 < GMP_NUMB_MAX);
 107
 108   a0 = a1 = a2 = 0;
 109   c0 = c1 = c2 = 0;
 110
 111   while ((n -= 3) >= 0)
 112     {
 113       ADD (c0, a0, p[0]);
 114       ADD (c1, a1, p[1]);
 115       ADD (c2, a2, p[2]);
 116       p += 3;
 117     }
 118
 119   if (n != -3)
 120     {
 121       ADD (c0, a0, p[0]);
 122       if (n != -2)
 123         ADD (c1, a1, p[1]);
 124     }
 125
 126   return
 127     PARTS0 (a0) + PARTS1 (a1) + PARTS2 (a2)
 128     + PARTS1 (c0) + PARTS2 (c1) + PARTS0 (c2);
 129 }
 130
 131 #endif