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Diff for /OpenXM_contrib/gmp/mpz/Attic/powm.c between version 1.1.1.1 and 1.1.1.3

version 1.1.1.1, 2000/01/10 15:35:27 version 1.1.1.3, 2003/08/25 16:06:33
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 /* mpz_powm(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.  /* mpz_powm(res,base,exp,mod) -- Set RES to (base**exp) mod MOD.
   
 Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc.  Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002 Free Software
   Foundation, Inc.  Contributed by Paul Zimmermann.
   
 This file is part of the GNU MP Library.  This file is part of the GNU MP Library.
   
 The GNU MP Library is free software; you can redistribute it and/or modify  The GNU MP Library is free software; you can redistribute it and/or modify
 it under the terms of the GNU Library General Public License as published by  it under the terms of the GNU Lesser General Public License as published by
 the Free Software Foundation; either version 2 of the License, or (at your  the Free Software Foundation; either version 2.1 of the License, or (at your
 option) any later version.  option) any later version.
   
 The GNU MP Library is distributed in the hope that it will be useful, but  The GNU MP Library is distributed in the hope that it will be useful, but
 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
 License for more details.  License for more details.
   
 You should have received a copy of the GNU Library General Public License  You should have received a copy of the GNU Lesser General Public License
 along with the GNU MP Library; see the file COPYING.LIB.  If not, write to  along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,  the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 MA 02111-1307, USA. */  MA 02111-1307, USA. */
   
   
 #include "gmp.h"  #include "gmp.h"
 #include "gmp-impl.h"  #include "gmp-impl.h"
 #include "longlong.h"  #include "longlong.h"
   #ifdef BERKELEY_MP
   #include "mp.h"
   #endif
   
 #ifndef BERKELEY_MP  
 void  /* Set c <- tp/R^n mod m.
 #if __STDC__     tp should have space for 2*n+1 limbs; clobber its most significant limb. */
 mpz_powm (mpz_ptr res, mpz_srcptr base, mpz_srcptr exp, mpz_srcptr mod)  #if ! WANT_REDC_GLOBAL
 #else  static
 mpz_powm (res, base, exp, mod)  
      mpz_ptr res;  
      mpz_srcptr base;  
      mpz_srcptr exp;  
      mpz_srcptr mod;  
 #endif  #endif
 #else /* BERKELEY_MP */  
 void  void
 #if __STDC__  redc (mp_ptr cp, mp_srcptr mp, mp_size_t n, mp_limb_t Nprim, mp_ptr tp)
 pow (mpz_srcptr base, mpz_srcptr exp, mpz_srcptr mod, mpz_ptr res)  
 #else  
 pow (base, exp, mod, res)  
      mpz_srcptr base;  
      mpz_srcptr exp;  
      mpz_srcptr mod;  
      mpz_ptr res;  
 #endif  
 #endif /* BERKELEY_MP */  
 {  {
   mp_ptr rp, ep, mp, bp;    mp_limb_t cy;
   mp_size_t esize, msize, bsize, rsize;    mp_limb_t q;
   mp_size_t size;    mp_size_t j;
   int mod_shift_cnt;  
   int negative_result;    tp[2 * n] = 0;                /* carry guard */
   mp_limb_t *free_me = NULL;  
   size_t free_me_size;    for (j = 0; j < n; j++)
       {
         q = tp[0] * Nprim;
         cy = mpn_addmul_1 (tp, mp, n, q);
         mpn_incr_u (tp + n, cy);
         tp++;
       }
   
     if (tp[n] != 0)
       mpn_sub_n (cp, tp, mp, n);
     else
       MPN_COPY (cp, tp, n);
   }
   
   /* Compute t = a mod m, a is defined by (ap,an), m is defined by (mp,mn), and
      t is defined by (tp,mn).  */
   static void
   reduce (mp_ptr tp, mp_srcptr ap, mp_size_t an, mp_srcptr mp, mp_size_t mn)
   {
     mp_ptr qp;
   TMP_DECL (marker);    TMP_DECL (marker);
   
   esize = ABS (exp->_mp_size);    TMP_MARK (marker);
   msize = ABS (mod->_mp_size);    qp = TMP_ALLOC_LIMBS (an - mn + 1);
   size = 2 * msize;  
   
   rp = res->_mp_d;    mpn_tdiv_qr (qp, tp, 0L, ap, an, mp, mn);
   ep = exp->_mp_d;  
   
   if (msize == 0)    TMP_FREE (marker);
     msize = 1 / msize;          /* provoke a signal */  }
   
   if (esize == 0)  #if REDUCE_EXPONENT
   /* Return the group order of the ring mod m.  */
   static mp_limb_t
   phi (mp_limb_t t)
   {
     mp_limb_t d, m, go;
   
     go = 1;
   
     if (t % 2 == 0)
     {      {
       /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0        t = t / 2;
          depending on if MOD equals 1.  */        while (t % 2 == 0)
       rp[0] = 1;          {
       res->_mp_size = (msize == 1 && (mod->_mp_d)[0] == 1) ? 0 : 1;            go *= 2;
       return;            t = t / 2;
           }
     }      }
     for (d = 3;; d += 2)
       {
         m = d - 1;
         for (;;)
           {
             unsigned long int q = t / d;
             if (q < d)
               {
                 if (t <= 1)
                   return go;
                 if (t == d)
                   return go * m;
                 return go * (t - 1);
               }
             if (t != q * d)
               break;
             go *= m;
             m = d;
             t = q;
           }
       }
   }
   #endif
   
   /* average number of calls to redc for an exponent of n bits
      with the sliding window algorithm of base 2^k: the optimal is
      obtained for the value of k which minimizes 2^(k-1)+n/(k+1):
   
      n\k    4     5     6     7     8
      128    156*  159   171   200   261
      256    309   307*  316   343   403
      512    617   607*  610   632   688
      1024   1231  1204  1195* 1207  1256
      2048   2461  2399  2366  2360* 2396
      4096   4918  4787  4707  4665* 4670
   */
   
   
   /* Use REDC instead of usual reduction for sizes < POWM_THRESHOLD.  In REDC
      each modular multiplication costs about 2*n^2 limbs operations, whereas
      using usual reduction it costs 3*K(n), where K(n) is the cost of a
      multiplication using Karatsuba, and a division is assumed to cost 2*K(n),
      for example using Burnikel-Ziegler's algorithm. This gives a theoretical
      threshold of a*SQR_KARATSUBA_THRESHOLD, with a=(3/2)^(1/(2-ln(3)/ln(2))) ~
      2.66.  */
   /* For now, also disable REDC when MOD is even, as the inverse can't handle
      that.  At some point, we might want to make the code faster for that case,
      perhaps using CRR.  */
   
   #ifndef POWM_THRESHOLD
   #define POWM_THRESHOLD  ((8 * SQR_KARATSUBA_THRESHOLD) / 3)
   #endif
   
   #define HANDLE_NEGATIVE_EXPONENT 1
   #undef REDUCE_EXPONENT
   
   void
   #ifndef BERKELEY_MP
   mpz_powm (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m)
   #else /* BERKELEY_MP */
   pow (mpz_srcptr b, mpz_srcptr e, mpz_srcptr m, mpz_ptr r)
   #endif /* BERKELEY_MP */
   {
     mp_ptr xp, tp, qp, gp, this_gp;
     mp_srcptr bp, ep, mp;
     mp_size_t bn, es, en, mn, xn;
     mp_limb_t invm, c;
     unsigned long int enb;
     mp_size_t i, K, j, l, k;
     int m_zero_cnt, e_zero_cnt;
     int sh;
     int use_redc;
   #if HANDLE_NEGATIVE_EXPONENT
     mpz_t new_b;
   #endif
   #if REDUCE_EXPONENT
     mpz_t new_e;
   #endif
     TMP_DECL (marker);
   
     mp = PTR(m);
     mn = ABSIZ (m);
     if (mn == 0)
       DIVIDE_BY_ZERO;
   
   TMP_MARK (marker);    TMP_MARK (marker);
   
   /* Normalize MOD (i.e. make its most significant bit set) as required by    es = SIZ (e);
      mpn_divmod.  This will make the intermediate values in the calculation    if (es <= 0)
      slightly larger, but the correct result is obtained after a final      {
      reduction using the original MOD value.  */        if (es == 0)
           {
             /* Exponent is zero, result is 1 mod m, i.e., 1 or 0 depending on if
                m equals 1.  */
             SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1;
             PTR(r)[0] = 1;
             TMP_FREE (marker);    /* we haven't really allocated anything here */
             return;
           }
   #if HANDLE_NEGATIVE_EXPONENT
         MPZ_TMP_INIT (new_b, mn + 1);
   
   mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);        if (! mpz_invert (new_b, b, m))
   count_leading_zeros (mod_shift_cnt, mod->_mp_d[msize - 1]);          DIVIDE_BY_ZERO;
   if (mod_shift_cnt != 0)        b = new_b;
     mpn_lshift (mp, mod->_mp_d, msize, mod_shift_cnt);        es = -es;
   else  #else
     MPN_COPY (mp, mod->_mp_d, msize);        DIVIDE_BY_ZERO;
   #endif
       }
     en = es;
   
   bsize = ABS (base->_mp_size);  #if REDUCE_EXPONENT
   if (bsize > msize)    /* Reduce exponent by dividing it by phi(m) when m small.  */
     if (mn == 1 && mp[0] < 0x7fffffffL && en * GMP_NUMB_BITS > 150)
     {      {
       /* The base is larger than the module.  Reduce it.  */        MPZ_TMP_INIT (new_e, 2);
         mpz_mod_ui (new_e, e, phi (mp[0]));
         e = new_e;
       }
   #endif
   
       /* Allocate (BSIZE + 1) with space for remainder and quotient.    use_redc = mn < POWM_THRESHOLD && mp[0] % 2 != 0;
          (The quotient is (bsize - msize + 1) limbs.)  */    if (use_redc)
       bp = (mp_ptr) TMP_ALLOC ((bsize + 1) * BYTES_PER_MP_LIMB);      {
       MPN_COPY (bp, base->_mp_d, bsize);        /* invm = -1/m mod 2^BITS_PER_MP_LIMB, must have m odd */
       /* We don't care about the quotient, store it above the remainder,        modlimb_invert (invm, mp[0]);
          at BP + MSIZE.  */        invm = -invm;
       mpn_divmod (bp + msize, bp, bsize, mp, msize);  
       bsize = msize;  
       /* Canonicalize the base, since we are going to multiply with it  
          quite a few times.  */  
       MPN_NORMALIZE (bp, bsize);  
     }      }
   else    else
     bp = base->_mp_d;  
   
   if (bsize == 0)  
     {      {
       res->_mp_size = 0;        /* Normalize m (i.e. make its most significant bit set) as required by
       TMP_FREE (marker);           division functions below.  */
       return;        count_leading_zeros (m_zero_cnt, mp[mn - 1]);
         m_zero_cnt -= GMP_NAIL_BITS;
         if (m_zero_cnt != 0)
           {
             mp_ptr new_mp;
             new_mp = TMP_ALLOC_LIMBS (mn);
             mpn_lshift (new_mp, mp, mn, m_zero_cnt);
             mp = new_mp;
           }
     }      }
   
   if (res->_mp_alloc < size)    /* Determine optimal value of k, the number of exponent bits we look at
        at a time.  */
     count_leading_zeros (e_zero_cnt, PTR(e)[en - 1]);
     e_zero_cnt -= GMP_NAIL_BITS;
     enb = en * GMP_NUMB_BITS - e_zero_cnt; /* number of bits of exponent */
     k = 1;
     K = 2;
     while (2 * enb > K * (2 + k * (3 + k)))
     {      {
       /* We have to allocate more space for RES.  If any of the input        k++;
          parameters are identical to RES, defer deallocation of the old        K *= 2;
          space.  */      }
   
       if (rp == ep || rp == mp || rp == bp)    tp = TMP_ALLOC_LIMBS (2 * mn + 1);
     qp = TMP_ALLOC_LIMBS (mn + 1);
   
     gp = __GMP_ALLOCATE_FUNC_LIMBS (K / 2 * mn);
   
     /* Compute x*R^n where R=2^BITS_PER_MP_LIMB.  */
     bn = ABSIZ (b);
     bp = PTR(b);
     /* Handle |b| >= m by computing b mod m.  FIXME: It is not strictly necessary
        for speed or correctness to do this when b and m have the same number of
        limbs, perhaps remove mpn_cmp call.  */
     if (bn > mn || (bn == mn && mpn_cmp (bp, mp, mn) >= 0))
       {
         /* Reduce possibly huge base while moving it to gp[0].  Use a function
            call to reduce, since we don't want the quotient allocation to
            live until function return.  */
         if (use_redc)
         {          {
           free_me = rp;            reduce (tp + mn, bp, bn, mp, mn);     /* b mod m */
           free_me_size = res->_mp_alloc;            MPN_ZERO (tp, mn);
             mpn_tdiv_qr (qp, gp, 0L, tp, 2 * mn, mp, mn); /* unnormnalized! */
         }          }
       else        else
         (*_mp_free_func) (rp, res->_mp_alloc * BYTES_PER_MP_LIMB);          {
             reduce (gp, bp, bn, mp, mn);
       rp = (mp_ptr) (*_mp_allocate_func) (size * BYTES_PER_MP_LIMB);          }
       res->_mp_alloc = size;  
       res->_mp_d = rp;  
     }      }
   else    else
     {      {
       /* Make BASE, EXP and MOD not overlap with RES.  */        /* |b| < m.  We pad out operands to become mn limbs,  which simplifies
       if (rp == bp)           the rest of the function, but slows things down when the |b| << m.  */
         if (use_redc)
         {          {
           /* RES and BASE are identical.  Allocate temp. space for BASE.  */            MPN_ZERO (tp, mn);
           bp = (mp_ptr) TMP_ALLOC (bsize * BYTES_PER_MP_LIMB);            MPN_COPY (tp + mn, bp, bn);
           MPN_COPY (bp, rp, bsize);            MPN_ZERO (tp + mn + bn, mn - bn);
             mpn_tdiv_qr (qp, gp, 0L, tp, 2 * mn, mp, mn);
         }          }
       if (rp == ep)        else
         {          {
           /* RES and EXP are identical.  Allocate temp. space for EXP.  */            MPN_COPY (gp, bp, bn);
           ep = (mp_ptr) TMP_ALLOC (esize * BYTES_PER_MP_LIMB);            MPN_ZERO (gp + bn, mn - bn);
           MPN_COPY (ep, rp, esize);  
         }          }
       if (rp == mp)  
         {  
           /* RES and MOD are identical.  Allocate temporary space for MOD.  */  
           mp = (mp_ptr) TMP_ALLOC (msize * BYTES_PER_MP_LIMB);  
           MPN_COPY (mp, rp, msize);  
         }  
     }      }
   
   MPN_COPY (rp, bp, bsize);    /* Compute xx^i for odd g < 2^i.  */
   rsize = bsize;  
   
   {    xp = TMP_ALLOC_LIMBS (mn);
     mp_size_t i;    mpn_sqr_n (tp, gp, mn);
     mp_ptr xp = (mp_ptr) TMP_ALLOC (2 * (msize + 1) * BYTES_PER_MP_LIMB);    if (use_redc)
     int c;      redc (xp, mp, mn, invm, tp);                /* xx = x^2*R^n */
     mp_limb_t e;    else
     mp_limb_t carry_limb;      mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
     this_gp = gp;
     for (i = 1; i < K / 2; i++)
       {
         mpn_mul_n (tp, this_gp, xp, mn);
         this_gp += mn;
         if (use_redc)
           redc (this_gp, mp, mn, invm, tp);       /* g[i] = x^(2i+1)*R^n */
         else
           mpn_tdiv_qr (qp, this_gp, 0L, tp, 2 * mn, mp, mn);
       }
   
     negative_result = (ep[0] & 1) && base->_mp_size < 0;    /* Start the real stuff.  */
     ep = PTR (e);
     i = en - 1;                           /* current index */
     c = ep[i];                            /* current limb */
     sh = GMP_NUMB_BITS - e_zero_cnt;      /* significant bits in ep[i] */
     sh -= k;                              /* index of lower bit of ep[i] to take into account */
     if (sh < 0)
       {                                   /* k-sh extra bits are needed */
         if (i > 0)
           {
             i--;
             c <<= (-sh);
             sh += GMP_NUMB_BITS;
             c |= ep[i] >> sh;
           }
       }
     else
       c >>= sh;
   
     i = esize - 1;    for (j = 0; c % 2 == 0; j++)
     e = ep[i];      c >>= 1;
     count_leading_zeros (c, e);  
     e = (e << c) << 1;          /* shift the exp bits to the left, lose msb */  
     c = BITS_PER_MP_LIMB - 1 - c;  
   
     /* Main loop.    MPN_COPY (xp, gp + mn * (c >> 1), mn);
     while (--j >= 0)
       {
         mpn_sqr_n (tp, xp, mn);
         if (use_redc)
           redc (xp, mp, mn, invm, tp);
         else
           mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
       }
   
        Make the result be pointed to alternately by XP and RP.  This    while (i > 0 || sh > 0)
        helps us avoid block copying, which would otherwise be necessary      {
        with the overlap restrictions of mpn_divmod.  With 50% probability        c = ep[i];
        the result after this loop will be in the area originally pointed        l = k;                            /* number of bits treated */
        by RP (==RES->_mp_d), and with 50% probability in the area originally        sh -= l;
        pointed to by XP.  */        if (sh < 0)
           {
             if (i > 0)
               {
                 i--;
                 c <<= (-sh);
                 sh += GMP_NUMB_BITS;
                 c |= ep[i] >> sh;
               }
             else
               {
                 l += sh;                  /* last chunk of bits from e; l < k */
               }
           }
         else
           c >>= sh;
         c &= ((mp_limb_t) 1 << l) - 1;
   
     for (;;)        /* This while loop implements the sliding window improvement--loop while
       {           the most significant bit of c is zero, squaring xx as we go. */
         while (c != 0)        while ((c >> (l - 1)) == 0 && (i > 0 || sh > 0))
           {          {
             mp_ptr tp;            mpn_sqr_n (tp, xp, mn);
             mp_size_t xsize;            if (use_redc)
               redc (xp, mp, mn, invm, tp);
             else
               mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
             if (sh != 0)
               {
                 sh--;
                 c = (c << 1) + ((ep[i] >> sh) & 1);
               }
             else
               {
                 i--;
                 sh = GMP_NUMB_BITS - 1;
                 c = (c << 1) + (ep[i] >> sh);
               }
           }
   
             mpn_mul_n (xp, rp, rp, rsize);        /* Replace xx by xx^(2^l)*x^c.  */
             xsize = 2 * rsize;        if (c != 0)
             if (xsize > msize)          {
               {            for (j = 0; c % 2 == 0; j++)
                 mpn_divmod (xp + msize, xp, xsize, mp, msize);              c >>= 1;
                 xsize = msize;  
               }  
   
             tp = rp; rp = xp; xp = tp;            /* c0 = c * 2^j, i.e. xx^(2^l)*x^c = (A^(2^(l - j))*c)^(2^j) */
             rsize = xsize;            l -= j;
             while (--l >= 0)
               {
                 mpn_sqr_n (tp, xp, mn);
                 if (use_redc)
                   redc (xp, mp, mn, invm, tp);
                 else
                   mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
               }
             mpn_mul_n (tp, xp, gp + mn * (c >> 1), mn);
             if (use_redc)
               redc (xp, mp, mn, invm, tp);
             else
               mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
           }
         else
           j = l;                          /* case c=0 */
         while (--j >= 0)
           {
             mpn_sqr_n (tp, xp, mn);
             if (use_redc)
               redc (xp, mp, mn, invm, tp);
             else
               mpn_tdiv_qr (qp, xp, 0L, tp, 2 * mn, mp, mn);
           }
       }
   
             if ((mp_limb_signed_t) e < 0)    if (use_redc)
               {      {
                 mpn_mul (xp, rp, rsize, bp, bsize);        /* Convert back xx to xx/R^n.  */
                 xsize = rsize + bsize;        MPN_COPY (tp, xp, mn);
                 if (xsize > msize)        MPN_ZERO (tp + mn, mn);
                   {        redc (xp, mp, mn, invm, tp);
                     mpn_divmod (xp + msize, xp, xsize, mp, msize);        if (mpn_cmp (xp, mp, mn) >= 0)
                     xsize = msize;          mpn_sub_n (xp, xp, mp, mn);
                   }      }
     else
       {
         if (m_zero_cnt != 0)
           {
             mp_limb_t cy;
             cy = mpn_lshift (tp, xp, mn, m_zero_cnt);
             tp[mn] = cy;
             mpn_tdiv_qr (qp, xp, 0L, tp, mn + (cy != 0), mp, mn);
             mpn_rshift (xp, xp, mn, m_zero_cnt);
           }
       }
     xn = mn;
     MPN_NORMALIZE (xp, xn);
   
                 tp = rp; rp = xp; xp = tp;    if ((ep[0] & 1) && SIZ(b) < 0 && xn != 0)
                 rsize = xsize;  
               }  
             e <<= 1;  
             c--;  
           }  
   
         i--;  
         if (i < 0)  
           break;  
         e = ep[i];  
         c = BITS_PER_MP_LIMB;  
       }  
   
     /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT  
        steps.  Adjust the result by reducing it with the original MOD.  
   
        Also make sure the result is put in RES->_mp_d (where it already  
        might be, see above).  */  
   
     if (mod_shift_cnt != 0)  
       {  
         carry_limb = mpn_lshift (res->_mp_d, rp, rsize, mod_shift_cnt);  
         rp = res->_mp_d;  
         if (carry_limb != 0)  
           {  
             rp[rsize] = carry_limb;  
             rsize++;  
           }  
       }  
     else  
       {  
         MPN_COPY (res->_mp_d, rp, rsize);  
         rp = res->_mp_d;  
       }  
   
     if (rsize >= msize)  
       {  
         mpn_divmod (rp + msize, rp, rsize, mp, msize);  
         rsize = msize;  
       }  
   
     /* Remove any leading zero words from the result.  */  
     if (mod_shift_cnt != 0)  
       mpn_rshift (rp, rp, rsize, mod_shift_cnt);  
     MPN_NORMALIZE (rp, rsize);  
   }  
   
   if (negative_result && rsize != 0)  
     {      {
       if (mod_shift_cnt != 0)        mp = PTR(m);                    /* want original, unnormalized m */
         mpn_rshift (mp, mp, msize, mod_shift_cnt);        mpn_sub (xp, mp, mn, xp, xn);
       mpn_sub (rp, mp, msize, rp, rsize);        xn = mn;
       rsize = msize;        MPN_NORMALIZE (xp, xn);
       MPN_NORMALIZE (rp, rsize);  
     }      }
   res->_mp_size = rsize;    MPZ_REALLOC (r, xn);
     SIZ (r) = xn;
     MPN_COPY (PTR(r), xp, xn);
   
   if (free_me != NULL)    __GMP_FREE_FUNC_LIMBS (gp, K / 2 * mn);
     (*_mp_free_func) (free_me, free_me_size * BYTES_PER_MP_LIMB);  
   TMP_FREE (marker);    TMP_FREE (marker);
 }  }
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  Added in v.1.1.1.3
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