/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is library that provides for multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library is designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@iahu.ca, http://libtommath.iahu.ca
 */
#include <tommath.h>

/* fast squaring
 *
 * This is the comba method where the columns of the product are computed first
 * then the carries are computed.  This has the effect of making a very simple
 * inner loop that is executed the most
 *
 * W2 represents the outer products and W the inner.  
 *
 * A further optimizations is made because the inner products are of the form
 * "A * B * 2".  The *2 part does not need to be computed until the end which is
 * good because 64-bit shifts are slow!
 *
 *
 */
int
fast_s_mp_sqr (mp_int * a, mp_int * b)
{
  int       olduse, newused, res, ix, pa;
  mp_word   W2[512], W[512];

  pa = a->used;
  newused = pa + pa + 1;
  if (b->alloc < newused) {
    if ((res = mp_grow (b, newused)) != MP_OKAY) {
      return res;
    }
  }

  /* zero temp buffer (columns) 
   * Note that there are two buffers.  Since squaring requires
   * a outter and inner product and the inner product requires 
   * computing a product and doubling it (a relatively expensive
   * op to perform n^2 times if you don't have to) the inner and
   * outer products are computed in different buffers.  This way
   * the inner product can be doubled using n doublings instead of
   * n^2
   */
  memset (W, 0,  newused * sizeof (mp_word));
  memset (W2, 0, newused * sizeof (mp_word));

  /* This computes the inner product.  To simplify the inner N^2 loop
   * the multiplication by two is done afterwards in the N loop.
   */
  for (ix = 0; ix < pa; ix++) {
     /* compute the outer product */
    W2[ix + ix] += ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);

    {
      register mp_digit tmpx, *tmpy;
      register mp_word *_W;
      register int iy;

      /* copy of left side */
      tmpx = a->dp[ix];

      /* alias for right side */
      tmpy = a->dp + (ix + 1);

      /* the column to store the result in */
      _W = W + (ix + ix + 1);

      /* inner products */
      for (iy = ix + 1; iy < pa; iy++) {
	*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
      }
    }
  }

  /* setup dest */
  olduse = b->used;
  b->used = newused;

  /* double first value, since the inner products are half of what they should be */
  W[0] += W[0] + W2[0];

  /* now compute digits */
  for (ix = 1; ix < newused; ix++) {
    /* double/add next digit */
    W[ix] += W[ix] + W2[ix];

    W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
    b->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
  }
  b->dp[(newused) - 1] = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));

  /* clear high */
  for (; ix < olduse; ix++) {
    b->dp[ix] = 0;
  }

  /* fix the sign (since we no longer make a fresh temp) */
  b->sign = MP_ZPOS;

  mp_clamp (b);
  return MP_OKAY;
}