release/src/router/dropbear/libtommath/bn_mp_karatsuba_mul.c

   1 #include <tommath.h>
   2 #ifdef BN_MP_KARATSUBA_MUL_C
   3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
   4  *
   5  * LibTomMath is a library that provides multiple-precision
   6  * integer arithmetic as well as number theoretic functionality.
   7  *
   8  * The library was designed directly after the MPI library by
   9  * Michael Fromberger but has been written from scratch with
  10  * additional optimizations in place.
  11  *
  12  * The library is free for all purposes without any express
  13  * guarantee it works.
  14  *
  15  * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
  16  */
  17
  18 /* c = |a| * |b| using Karatsuba Multiplication using
  19  * three half size multiplications
  20  *
  21  * Let B represent the radix [e.g. 2**DIGIT_BIT] and
  22  * let n represent half of the number of digits in
  23  * the min(a,b)
  24  *
  25  * a = a1 * B**n + a0
  26  * b = b1 * B**n + b0
  27  *
  28  * Then, a * b =>
  29    a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
  30  *
  31  * Note that a1b1 and a0b0 are used twice and only need to be
  32  * computed once.  So in total three half size (half # of
  33  * digit) multiplications are performed, a0b0, a1b1 and
  34  * (a1+b1)(a0+b0)
  35  *
  36  * Note that a multiplication of half the digits requires
  37  * 1/4th the number of single precision multiplications so in
  38  * total after one call 25% of the single precision multiplications
  39  * are saved.  Note also that the call to mp_mul can end up back
  40  * in this function if the a0, a1, b0, or b1 are above the threshold.
  41  * This is known as divide-and-conquer and leads to the famous
  42  * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
  43  * the standard O(N**2) that the baseline/comba methods use.
  44  * Generally though the overhead of this method doesn't pay off
  45  * until a certain size (N ~ 80) is reached.
  46  */
  47 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
  48 {
  49   mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
  50   int     B, err;
  51
  52   /* default the return code to an error */
  53   err = MP_MEM;
  54
  55   /* min # of digits */
  56   B = MIN (a->used, b->used);
  57
  58   /* now divide in two */
  59   B = B >> 1;
  60
  61   /* init copy all the temps */
  62   if (mp_init_size (&x0, B) != MP_OKAY)
  63     goto ERR;
  64   if (mp_init_size (&x1, a->used - B) != MP_OKAY)
  65     goto X0;
  66   if (mp_init_size (&y0, B) != MP_OKAY)
  67     goto X1;
  68   if (mp_init_size (&y1, b->used - B) != MP_OKAY)
  69     goto Y0;
  70
  71   /* init temps */
  72   if (mp_init_size (&t1, B * 2) != MP_OKAY)
  73     goto Y1;
  74   if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
  75     goto T1;
  76   if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
  77     goto X0Y0;
  78
  79   /* now shift the digits */
  80   x0.used = y0.used = B;
  81   x1.used = a->used - B;
  82   y1.used = b->used - B;
  83
  84   {
  85     register int x;
  86     register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
  87
  88     /* we copy the digits directly instead of using higher level functions
  89      * since we also need to shift the digits
  90      */
  91     tmpa = a->dp;
  92     tmpb = b->dp;
  93
  94     tmpx = x0.dp;
  95     tmpy = y0.dp;
  96     for (x = 0; x < B; x++) {
  97       *tmpx++ = *tmpa++;
  98       *tmpy++ = *tmpb++;
  99     }
 100
 101     tmpx = x1.dp;
 102     for (x = B; x < a->used; x++) {
 103       *tmpx++ = *tmpa++;
 104     }
 105
 106     tmpy = y1.dp;
 107     for (x = B; x < b->used; x++) {
 108       *tmpy++ = *tmpb++;
 109     }
 110   }
 111
 112   /* only need to clamp the lower words since by definition the
 113    * upper words x1/y1 must have a known number of digits
 114    */
 115   mp_clamp (&x0);
 116   mp_clamp (&y0);
 117
 118   /* now calc the products x0y0 and x1y1 */
 119   /* after this x0 is no longer required, free temp [x0==t2]! */
 120   if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
 121     goto X1Y1;          /* x0y0 = x0*y0 */
 122   if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
 123     goto X1Y1;          /* x1y1 = x1*y1 */
 124
 125   /* now calc x1+x0 and y1+y0 */
 126   if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
 127     goto X1Y1;          /* t1 = x1 - x0 */
 128   if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
 129     goto X1Y1;          /* t2 = y1 - y0 */
 130   if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
 131     goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
 132
 133   /* add x0y0 */
 134   if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
 135     goto X1Y1;          /* t2 = x0y0 + x1y1 */
 136   if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
 137     goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
 138
 139   /* shift by B */
 140   if (mp_lshd (&t1, B) != MP_OKAY)
 141     goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
 142   if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
 143     goto X1Y1;          /* x1y1 = x1y1 << 2*B */
 144
 145   if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
 146     goto X1Y1;          /* t1 = x0y0 + t1 */
 147   if (mp_add (&t1, &x1y1, c) != MP_OKAY)
 148     goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
 149
 150   /* Algorithm succeeded set the return code to MP_OKAY */
 151   err = MP_OKAY;
 152
 153 X1Y1:mp_clear (&x1y1);
 154 X0Y0:mp_clear (&x0y0);
 155 T1:mp_clear (&t1);
 156 Y1:mp_clear (&y1);
 157 Y0:mp_clear (&y0);
 158 X1:mp_clear (&x1);
 159 X0:mp_clear (&x0);
 160 ERR:
 161   return err;
 162 }
 163 #endif
 164
 165 /* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */
 166 /* $Revision: 1.5 $ */
 167 /* $Date: 2006/03/31 14:18:44 $ */