github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpn/generic/binvert.c (about)

     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  }