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

   1 /* mpn_bsqrtinv, compute r such that r^2 * y = 1 (mod 2^{b+1}).
   2
   3    Contributed to the GNU project by Martin Boij (as part of perfpow.c).
   4
   5 Copyright 2009, 2010, 2012, 2015 Free Software Foundation, Inc.
   6
   7 This file is part of the GNU MP Library.
   8
   9 The GNU MP Library is free software; you can redistribute it and/or modify
  10 it under the terms of either:
  11
  12   * the GNU Lesser General Public License as published by the Free
  13     Software Foundation; either version 3 of the License, or (at your
  14     option) any later version.
  15
  16 or
  17
  18   * the GNU General Public License as published by the Free Software
  19     Foundation; either version 2 of the License, or (at your option) any
  20     later version.
  21
  22 or both in parallel, as here.
  23
  24 The GNU MP Library is distributed in the hope that it will be useful, but
  25 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  26 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  27 for more details.
  28
  29 You should have received copies of the GNU General Public License and the
  30 GNU Lesser General Public License along with the GNU MP Library.  If not,
  31 see https://www.gnu.org/licenses/.  */
  32
  33 #include "gmp.h"
  34 #include "gmp-impl.h"
  35
  36 /* Compute r such that r^2 * y = 1 (mod 2^{b+1}).
  37    Return non-zero if such an integer r exists.
  38
  39    Iterates
  40      r' <-- (3r - r^3 y) / 2
  41    using Hensel lifting.  Since we divide by two, the Hensel lifting is
  42    somewhat degenerates.  Therefore, we lift from 2^b to 2^{b+1}-1.
  43
  44    FIXME:
  45      (1) Simplify to do precision book-keeping in limbs rather than bits.
  46
  47      (2) Rewrite iteration as
  48            r' <-- r - r (r^2 y - 1) / 2
  49          and take advantage of zero low part of r^2 y - 1.
  50
  51      (3) Use wrap-around trick.
  52
  53      (4) Use a small table to get starting value.
  54 */
  55 int
  56 mpn_bsqrtinv (mp_ptr rp, mp_srcptr yp, mp_bitcnt_t bnb, mp_ptr tp)
  57 {
  58   mp_ptr tp2;
  59   mp_size_t bn, order[GMP_LIMB_BITS + 1];
  60   int i, d;
  61
  62   ASSERT (bnb > 0);
  63
  64   bn = 1 + bnb / GMP_LIMB_BITS;
  65
  66   tp2 = tp + bn;
  67
  68   rp[0] = 1;
  69   if (bnb == 1)
  70     {
  71       if ((yp[0] & 3) != 1)
  72         return 0;
  73     }
  74   else
  75     {
  76       if ((yp[0] & 7) != 1)
  77         return 0;
  78
  79       d = 0;
  80       for (; bnb != 2; bnb = (bnb + 2) >> 1)
  81         order[d++] = bnb;
  82
  83       for (i = d - 1; i >= 0; i--)
  84         {
  85           bnb = order[i];
  86           bn = 1 + bnb / GMP_LIMB_BITS;
  87
  88           mpn_sqrlo (tp, rp, bn);
  89           mpn_mullo_n (tp2, rp, tp, bn); /* tp2 <- rp ^ 3 */
  90
  91           mpn_mul_1 (tp, rp, bn, 3);
  92
  93           mpn_mullo_n (rp, yp, tp2, bn);
  94
  95 #if HAVE_NATIVE_mpn_rsh1sub_n
  96           mpn_rsh1sub_n (rp, tp, rp, bn);
  97 #else
  98           mpn_sub_n (tp2, tp, rp, bn);
  99           mpn_rshift (rp, tp2, bn, 1);
 100 #endif
 101         }
 102     }
 103   return 1;
 104 }