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

   1 /* Compute {up,n}^(-1) mod B^n.
   2
   3    Contributed to the GNU project by Torbjorn Granlund.
   4
   5    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   6    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   7    GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
   8
   9 Copyright (C) 2004-2007, 2009, 2012 Free Software Foundation, Inc.
  10
  11 This file is part of the GNU MP Library.
  12
  13 The GNU MP Library is free software; you can redistribute it and/or modify
  14 it under the terms of either:
  15
  16   * the GNU Lesser General Public License as published by the Free
  17     Software Foundation; either version 3 of the License, or (at your
  18     option) any later version.
  19
  20 or
  21
  22   * the GNU General Public License as published by the Free Software
  23     Foundation; either version 2 of the License, or (at your option) any
  24     later version.
  25
  26 or both in parallel, as here.
  27
  28 The GNU MP Library is distributed in the hope that it will be useful, but
  29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  30 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  31 for more details.
  32
  33 You should have received copies of the GNU General Public License and the
  34 GNU Lesser General Public License along with the GNU MP Library.  If not,
  35 see https://www.gnu.org/licenses/.  */
  36
  37 #include "gmp.h"
  38 #include "gmp-impl.h"
  39
  40
  41 /*
  42   r[k+1] = r[k] - r[k] * (u*r[k] - 1)
  43   r[k+1] = r[k] + r[k] - r[k]*(u*r[k])
  44 */
  45
  46 #if TUNE_PROGRAM_BUILD
  47 #define NPOWS \
  48  ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)))
  49 #else
  50 #define NPOWS \
  51  ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)) - LOG2C (BINV_NEWTON_THRESHOLD))
  52 #endif
  53
  54 mp_size_t
  55 mpn_binvert_itch (mp_size_t n)
  56 {
  57   mp_size_t itch_local = mpn_mulmod_bnm1_next_size (n);
  58   mp_size_t itch_out = mpn_mulmod_bnm1_itch (itch_local, n, (n + 1) >> 1);
  59   return itch_local + itch_out;
  60 }
  61
  62 void
  63 mpn_binvert (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr scratch)
  64 {
  65   mp_ptr xp;
  66   mp_size_t rn, newrn;
  67   mp_size_t sizes[NPOWS], *sizp;
  68   mp_limb_t di;
  69
  70   /* Compute the computation precisions from highest to lowest, leaving the
  71      base case size in 'rn'.  */
  72   sizp = sizes;
  73   for (rn = n; ABOVE_THRESHOLD (rn, BINV_NEWTON_THRESHOLD); rn = (rn + 1) >> 1)
  74     *sizp++ = rn;
  75
  76   xp = scratch;
  77
  78   /* Compute a base value of rn limbs.  */
  79   MPN_ZERO (xp, rn);
  80   xp[0] = 1;
  81   binvert_limb (di, up[0]);
  82   if (BELOW_THRESHOLD (rn, DC_BDIV_Q_THRESHOLD))
  83     mpn_sbpi1_bdiv_q (rp, xp, rn, up, rn, -di);
  84   else
  85     mpn_dcpi1_bdiv_q (rp, xp, rn, up, rn, -di);
  86
  87   /* Use Newton iterations to get the desired precision.  */
  88   for (; rn < n; rn = newrn)
  89     {
  90       mp_size_t m;
  91       newrn = *--sizp;
  92
  93       /* X <- UR. */
  94       m = mpn_mulmod_bnm1_next_size (newrn);
  95       mpn_mulmod_bnm1 (xp, m, up, newrn, rp, rn, xp + m);
  96       mpn_sub_1 (xp + m, xp, rn - (m - newrn), 1);
  97
  98       /* R = R(X/B^rn) */
  99       mpn_mullo_n (rp + rn, rp, xp + rn, newrn - rn);
 100       mpn_neg (rp + rn, rp + rn, newrn - rn);
 101     }
 102 }