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

     1  /* mpn_powlo -- Compute R = U^E mod B^n, where B is the limb base.
     2  
     3  Copyright 2007-2009, 2012, 2015 Free Software Foundation, Inc.
     4  
     5  This file is part of the GNU MP Library.
     6  
     7  The GNU MP Library is free software; you can redistribute it and/or modify
     8  it under the terms of either:
     9  
    10    * the GNU Lesser General Public License as published by the Free
    11      Software Foundation; either version 3 of the License, or (at your
    12      option) any later version.
    13  
    14  or
    15  
    16    * the GNU General Public License as published by the Free Software
    17      Foundation; either version 2 of the License, or (at your option) any
    18      later version.
    19  
    20  or both in parallel, as here.
    21  
    22  The GNU MP Library is distributed in the hope that it will be useful, but
    23  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    24  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    25  for more details.
    26  
    27  You should have received copies of the GNU General Public License and the
    28  GNU Lesser General Public License along with the GNU MP Library.  If not,
    29  see https://www.gnu.org/licenses/.  */
    30  
    31  
    32  #include "gmp.h"
    33  #include "gmp-impl.h"
    34  #include "longlong.h"
    35  
    36  
    37  #define getbit(p,bi) \
    38    ((p[(bi - 1) / GMP_LIMB_BITS] >> (bi - 1) % GMP_LIMB_BITS) & 1)
    39  
    40  static inline mp_limb_t
    41  getbits (const mp_limb_t *p, mp_bitcnt_t bi, int nbits)
    42  {
    43    int nbits_in_r;
    44    mp_limb_t r;
    45    mp_size_t i;
    46  
    47    if (bi < nbits)
    48      {
    49        return p[0] & (((mp_limb_t) 1 << bi) - 1);
    50      }
    51    else
    52      {
    53        bi -= nbits;			/* bit index of low bit to extract */
    54        i = bi / GMP_NUMB_BITS;		/* word index of low bit to extract */
    55        bi %= GMP_NUMB_BITS;		/* bit index in low word */
    56        r = p[i] >> bi;			/* extract (low) bits */
    57        nbits_in_r = GMP_NUMB_BITS - bi;	/* number of bits now in r */
    58        if (nbits_in_r < nbits)		/* did we get enough bits? */
    59  	r += p[i + 1] << nbits_in_r;	/* prepend bits from higher word */
    60        return r & (((mp_limb_t ) 1 << nbits) - 1);
    61      }
    62  }
    63  
    64  static inline int
    65  win_size (mp_bitcnt_t eb)
    66  {
    67    int k;
    68    static mp_bitcnt_t x[] = {1,7,25,81,241,673,1793,4609,11521,28161,~(mp_bitcnt_t)0};
    69    ASSERT (eb > 1);
    70    for (k = 1; eb > x[k]; ++k)
    71      ;
    72    return k;
    73  }
    74  
    75  /* rp[n-1..0] = bp[n-1..0] ^ ep[en-1..0] mod B^n, B is the limb base.
    76     Requires that ep[en-1] is non-zero.
    77     Uses scratch space tp[3n-1..0], i.e., 3n words.  */
    78  /* We only use n words in the scratch space, we should pass tp + n to
    79     mullo/sqrlo as a temporary area, it is needed. */
    80  void
    81  mpn_powlo (mp_ptr rp, mp_srcptr bp,
    82  	   mp_srcptr ep, mp_size_t en,
    83  	   mp_size_t n, mp_ptr tp)
    84  {
    85    int cnt;
    86    mp_bitcnt_t ebi;
    87    int windowsize, this_windowsize;
    88    mp_limb_t expbits;
    89    mp_limb_t *pp, *this_pp, *last_pp;
    90    long i;
    91    TMP_DECL;
    92  
    93    ASSERT (en > 1 || (en == 1 && ep[0] > 1));
    94  
    95    TMP_MARK;
    96  
    97    MPN_SIZEINBASE_2EXP(ebi, ep, en, 1);
    98  
    99    windowsize = win_size (ebi);
   100    ASSERT (windowsize < ebi);
   101  
   102    pp = TMP_ALLOC_LIMBS ((n << (windowsize - 1)));
   103  
   104    this_pp = pp;
   105  
   106    MPN_COPY (this_pp, bp, n);
   107  
   108    /* Store b^2 in tp.  */
   109    mpn_sqrlo (tp, bp, n);
   110  
   111    /* Precompute odd powers of b and put them in the temporary area at pp.  */
   112    for (i = (1 << (windowsize - 1)) - 1; i > 0; i--)
   113      {
   114        last_pp = this_pp;
   115        this_pp += n;
   116        mpn_mullo_n (this_pp, last_pp, tp, n);
   117      }
   118  
   119    expbits = getbits (ep, ebi, windowsize);
   120  
   121    /* FIXME: for even expbits, we can init with a mullo. */
   122    count_trailing_zeros (cnt, expbits);
   123    ebi -= windowsize;
   124    ebi += cnt;
   125    expbits >>= cnt;
   126  
   127    MPN_COPY (rp, pp + n * (expbits >> 1), n);
   128  
   129    do
   130      {
   131        while (getbit (ep, ebi) == 0)
   132  	{
   133  	  mpn_sqrlo (tp, rp, n);
   134  	  MPN_COPY (rp, tp, n);
   135  	  if (--ebi == 0)
   136  	    goto done;
   137  	}
   138  
   139        /* The next bit of the exponent is 1.  Now extract the largest block of
   140  	 bits <= windowsize, and such that the least significant bit is 1.  */
   141  
   142        expbits = getbits (ep, ebi, windowsize);
   143        this_windowsize = windowsize;
   144        if (ebi < windowsize)
   145  	{
   146  	  this_windowsize -= windowsize - ebi;
   147  	  ebi = 0;
   148  	}
   149        else
   150  	ebi -= windowsize;
   151  
   152        count_trailing_zeros (cnt, expbits);
   153        this_windowsize -= cnt;
   154        ebi += cnt;
   155        expbits >>= cnt;
   156  
   157        while (this_windowsize > 1)
   158  	{
   159  	  mpn_sqrlo (tp, rp, n);
   160  	  mpn_sqrlo (rp, tp, n);
   161  	  this_windowsize -= 2;
   162  	}
   163  
   164        if (this_windowsize != 0)
   165  	mpn_sqrlo (tp, rp, n);
   166        else
   167  	MPN_COPY (tp, rp, n);
   168        
   169        mpn_mullo_n (rp, tp, pp + n * (expbits >> 1), n);
   170      } while (ebi != 0);
   171  
   172   done:
   173    TMP_FREE;
   174  }