/src/libressl/crypto/bn/bn_mul.c

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/* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 jsing Exp $ */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */

#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif

#include <assert.h>
#include <stdio.h>
#include <string.h>

#include <openssl/opensslconf.h>

#include "bn_lcl.h"

#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
/* Here follows specialised variants of bn_add_words() and
   bn_sub_words().  They have the property performing operations on
   arrays of different sizes.  The sizes of those arrays is expressed through
   cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
   which is the delta between the two lengths, calculated as len(a)-len(b).
   All lengths are the number of BN_ULONGs...  For the operations that require
   a result array as parameter, it must have the length cl+abs(dl).
   These functions should probably end up in bn_asm.c as soon as there are
   assembler counterparts for the systems that use assembler files.  */

BN_ULONG
bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
    int dl)
{
  BN_ULONG c, t;

  assert(cl >= 0);
  c = bn_sub_words(r, a, b, cl);

  if (dl == 0)
    return c;

  r += cl;
  a += cl;
  b += cl;

  if (dl < 0) {
#ifdef BN_COUNT
    fprintf(stderr,
        "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n",
        cl, dl, c);
#endif
    for (;;) {
      t = b[0];
      r[0] = (0 - t - c) & BN_MASK2;
      if (t != 0)
        c = 1;
      if (++dl >= 0)
        break;

      t = b[1];
      r[1] = (0 - t - c) & BN_MASK2;
      if (t != 0)
        c = 1;
      if (++dl >= 0)
        break;

      t = b[2];
      r[2] = (0 - t - c) & BN_MASK2;
      if (t != 0)
        c = 1;
      if (++dl >= 0)
        break;

      t = b[3];
      r[3] = (0 - t - c) & BN_MASK2;
      if (t != 0)
        c = 1;
      if (++dl >= 0)
        break;

      b += 4;
      r += 4;
    }
  } else {
    int save_dl = dl;
#ifdef BN_COUNT
    fprintf(stderr,
        "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n",
        cl, dl, c);
#endif
    while (c) {
      t = a[0];
      r[0] = (t - c) & BN_MASK2;
      if (t != 0)
        c = 0;
      if (--dl <= 0)
        break;

      t = a[1];
      r[1] = (t - c) & BN_MASK2;
      if (t != 0)
        c = 0;
      if (--dl <= 0)
        break;

      t = a[2];
      r[2] = (t - c) & BN_MASK2;
      if (t != 0)
        c = 0;
      if (--dl <= 0)
        break;

      t = a[3];
      r[3] = (t - c) & BN_MASK2;
      if (t != 0)
        c = 0;
      if (--dl <= 0)
        break;

      save_dl = dl;
      a += 4;
      r += 4;
    }
    if (dl > 0) {
#ifdef BN_COUNT
      fprintf(stderr,
          "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
          cl, dl);
#endif
      if (save_dl > dl) {
        switch (save_dl - dl) {
        case 1:
          r[1] = a[1];
          if (--dl <= 0)
            break;
        case 2:
          r[2] = a[2];
          if (--dl <= 0)
            break;
        case 3:
          r[3] = a[3];
          if (--dl <= 0)
            break;
        }
        a += 4;
        r += 4;
      }
    }
    if (dl > 0) {
#ifdef BN_COUNT
      fprintf(stderr,
          "  bn_sub_part_words %d + %d (dl > 0, copy)\n",
          cl, dl);
#endif
      for (;;) {
        r[0] = a[0];
        if (--dl <= 0)
          break;
        r[1] = a[1];
        if (--dl <= 0)
          break;
        r[2] = a[2];
        if (--dl <= 0)
          break;
        r[3] = a[3];
        if (--dl <= 0)
          break;

        a += 4;
        r += 4;
      }
    }
  }
  return c;
}
#endif

BN_ULONG
bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
    int dl)
{
  BN_ULONG c, l, t;

  assert(cl >= 0);
  c = bn_add_words(r, a, b, cl);

  if (dl == 0)
    return c;

  r += cl;
  a += cl;
  b += cl;

  if (dl < 0) {
    int save_dl = dl;
#ifdef BN_COUNT
    fprintf(stderr,
        "  bn_add_part_words %d + %d (dl < 0, c = %d)\n",
        cl, dl, c);
#endif
    while (c) {
      l = (c + b[0]) & BN_MASK2;
      c = (l < c);
      r[0] = l;
      if (++dl >= 0)
        break;

      l = (c + b[1]) & BN_MASK2;
      c = (l < c);
      r[1] = l;
      if (++dl >= 0)
        break;

      l = (c + b[2]) & BN_MASK2;
      c = (l < c);
      r[2] = l;
      if (++dl >= 0)
        break;

      l = (c + b[3]) & BN_MASK2;
      c = (l < c);
      r[3] = l;
      if (++dl >= 0)
        break;

      save_dl = dl;
      b += 4;
      r += 4;
    }
    if (dl < 0) {
#ifdef BN_COUNT
      fprintf(stderr,
          "  bn_add_part_words %d + %d (dl < 0, c == 0)\n",
          cl, dl);
#endif
      if (save_dl < dl) {
        switch (dl - save_dl) {
        case 1:
          r[1] = b[1];
          if (++dl >= 0)
            break;
        case 2:
          r[2] = b[2];
          if (++dl >= 0)
            break;
        case 3:
          r[3] = b[3];
          if (++dl >= 0)
            break;
        }
        b += 4;
        r += 4;
      }
    }
    if (dl < 0) {
#ifdef BN_COUNT
      fprintf(stderr,
          "  bn_add_part_words %d + %d (dl < 0, copy)\n",
          cl, dl);
#endif
      for (;;) {
        r[0] = b[0];
        if (++dl >= 0)
          break;
        r[1] = b[1];
        if (++dl >= 0)
          break;
        r[2] = b[2];
        if (++dl >= 0)
          break;
        r[3] = b[3];
        if (++dl >= 0)
          break;

        b += 4;
        r += 4;
      }
    }
  } else {
    int save_dl = dl;
#ifdef BN_COUNT
    fprintf(stderr,
        "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
#endif
    while (c) {
      t = (a[0] + c) & BN_MASK2;
      c = (t < c);
      r[0] = t;
      if (--dl <= 0)
        break;

      t = (a[1] + c) & BN_MASK2;
      c = (t < c);
      r[1] = t;
      if (--dl <= 0)
        break;

      t = (a[2] + c) & BN_MASK2;
      c = (t < c);
      r[2] = t;
      if (--dl <= 0)
        break;

      t = (a[3] + c) & BN_MASK2;
      c = (t < c);
      r[3] = t;
      if (--dl <= 0)
        break;

      save_dl = dl;
      a += 4;
      r += 4;
    }
#ifdef BN_COUNT
    fprintf(stderr,
        "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
#endif
    if (dl > 0) {
      if (save_dl > dl) {
        switch (save_dl - dl) {
        case 1:
          r[1] = a[1];
          if (--dl <= 0)
            break;
        case 2:
          r[2] = a[2];
          if (--dl <= 0)
            break;
        case 3:
          r[3] = a[3];
          if (--dl <= 0)
            break;
        }
        a += 4;
        r += 4;
      }
    }
    if (dl > 0) {
#ifdef BN_COUNT
      fprintf(stderr,
          "  bn_add_part_words %d + %d (dl > 0, copy)\n",
          cl, dl);
#endif
      for (;;) {
        r[0] = a[0];
        if (--dl <= 0)
          break;
        r[1] = a[1];
        if (--dl <= 0)
          break;
        r[2] = a[2];
        if (--dl <= 0)
          break;
        r[3] = a[3];
        if (--dl <= 0)
          break;

        a += 4;
        r += 4;
      }
    }
  }
  return c;
}

#ifdef BN_RECURSION
/* Karatsuba recursive multiplication algorithm
 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */

/* r is 2*n2 words in size,
 * a and b are both n2 words in size.
 * n2 must be a power of 2.
 * We multiply and return the result.
 * t must be 2*n2 words in size
 * We calculate
 * a[0]*b[0]
 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 * a[1]*b[1]
 */
/* dnX may not be positive, but n2/2+dnX has to be */
void
bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna,
    int dnb, BN_ULONG *t)
{
  int n = n2 / 2, c1, c2;
  int tna = n + dna, tnb = n + dnb;
  unsigned int neg, zero;
  BN_ULONG ln, lo, *p;

# ifdef BN_COUNT
  fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
# endif
# ifdef BN_MUL_COMBA
#  if 0
  if (n2 == 4) {
    bn_mul_comba4(r, a, b);
    return;
  }
#  endif
  /* Only call bn_mul_comba 8 if n2 == 8 and the
   * two arrays are complete [steve]
   */
  if (n2 == 8 && dna == 0 && dnb == 0) {
    bn_mul_comba8(r, a, b);
    return;
  }
# endif /* BN_MUL_COMBA */
  /* Else do normal multiply */
  if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
    bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
    if ((dna + dnb) < 0)
      memset(&r[2*n2 + dna + dnb], 0,
          sizeof(BN_ULONG) * -(dna + dnb));
    return;
  }
  /* r=(a[0]-a[1])*(b[1]-b[0]) */
  c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
  c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n);
  zero = neg = 0;
  switch (c1 * 3 + c2) {
  case -4:
    bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
    bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
    break;
  case -3:
    zero = 1;
    break;
  case -2:
    bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
    bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
    neg = 1;
    break;
  case -1:
  case 0:
  case 1:
    zero = 1;
    break;
  case 2:
    bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
    bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
    neg = 1;
    break;
  case 3:
    zero = 1;
    break;
  case 4:
    bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
    bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
    break;
  }

# ifdef BN_MUL_COMBA
  if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
                 extra args to do this well */
  {
    if (!zero)
      bn_mul_comba4(&(t[n2]), t, &(t[n]));
    else
      memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));

    bn_mul_comba4(r, a, b);
    bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
  } else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
                take extra args to do this
                well */
  {
    if (!zero)
      bn_mul_comba8(&(t[n2]), t, &(t[n]));
    else
      memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));

    bn_mul_comba8(r, a, b);
    bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
  } else
# endif /* BN_MUL_COMBA */
  {
    p = &(t[n2 * 2]);
    if (!zero)
      bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
    else
      memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
    bn_mul_recursive(r, a, b, n, 0, 0, p);
    bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
  }

  /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
   * r[10] holds (a[0]*b[0])
   * r[32] holds (b[1]*b[1])
   */

  c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));

  if (neg) /* if t[32] is negative */
  {
    c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
  } else {
    /* Might have a carry */
    c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
  }

  /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
   * r[10] holds (a[0]*b[0])
   * r[32] holds (b[1]*b[1])
   * c1 holds the carry bits
   */
  c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
  if (c1) {
    p = &(r[n + n2]);
    lo= *p;
    ln = (lo + c1) & BN_MASK2;
    *p = ln;

    /* The overflow will stop before we over write
     * words we should not overwrite */
    if (ln < (BN_ULONG)c1) {
      do {
        p++;
        lo= *p;
        ln = (lo + 1) & BN_MASK2;
        *p = ln;
      } while (ln == 0);
    }
  }
}

/* n+tn is the word length
 * t needs to be n*4 is size, as does r */
/* tnX may not be negative but less than n */
void
bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,
    int tnb, BN_ULONG *t)
{
  int i, j, n2 = n * 2;
  int c1, c2, neg;
  BN_ULONG ln, lo, *p;

# ifdef BN_COUNT
  fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
      n, tna, n, tnb);
# endif
  if (n < 8) {
    bn_mul_normal(r, a, n + tna, b, n + tnb);
    return;
  }

  /* r=(a[0]-a[1])*(b[1]-b[0]) */
  c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
  c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
  neg = 0;
  switch (c1 * 3 + c2) {
  case -4:
    bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
    bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
    break;
  case -3:
    /* break; */
  case -2:
    bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
    bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
    neg = 1;
    break;
  case -1:
  case 0:
  case 1:
    /* break; */
  case 2:
    bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
    bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
    neg = 1;
    break;
  case 3:
    /* break; */
  case 4:
    bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
    bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
    break;
  }
    /* The zero case isn't yet implemented here. The speedup
       would probably be negligible. */
# if 0
  if (n == 4) {
    bn_mul_comba4(&(t[n2]), t, &(t[n]));
    bn_mul_comba4(r, a, b);
    bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
    memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
  } else
# endif
    if (n == 8) {
    bn_mul_comba8(&(t[n2]), t, &(t[n]));
    bn_mul_comba8(r, a, b);
    bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
    memset(&(r[n2 + tna + tnb]), 0,
        sizeof(BN_ULONG) * (n2 - tna - tnb));
  } else {
    p = &(t[n2*2]);
    bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
    bn_mul_recursive(r, a, b, n, 0, 0, p);
    i = n / 2;
    /* If there is only a bottom half to the number,
     * just do it */
    if (tna > tnb)
      j = tna - i;
    else
      j = tnb - i;
    if (j == 0) {
      bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
          i, tna - i, tnb - i, p);
      memset(&(r[n2 + i * 2]), 0,
          sizeof(BN_ULONG) * (n2 - i * 2));
    }
    else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
    {
      bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
          i, tna - i, tnb - i, p);
      memset(&(r[n2 + tna + tnb]), 0,
          sizeof(BN_ULONG) * (n2 - tna - tnb));
    }
    else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
    {
      memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
      if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
          tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
        bn_mul_normal(&(r[n2]), &(a[n]), tna,
            &(b[n]), tnb);
      } else {
        for (;;) {
          i /= 2;
          /* these simplified conditions work
           * exclusively because difference
           * between tna and tnb is 1 or 0 */
          if (i < tna || i < tnb) {
            bn_mul_part_recursive(&(r[n2]),
                &(a[n]), &(b[n]), i,
                tna - i, tnb - i, p);
            break;
          } else if (i == tna || i == tnb) {
            bn_mul_recursive(&(r[n2]),
                &(a[n]), &(b[n]), i,
                tna - i, tnb - i, p);
            break;
          }
        }
      }
    }
  }

  /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
   * r[10] holds (a[0]*b[0])
   * r[32] holds (b[1]*b[1])
   */

  c1 = (int)(bn_add_words(t, r,&(r[n2]), n2));

  if (neg) /* if t[32] is negative */
  {
    c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2));
  } else {
    /* Might have a carry */
    c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
  }

  /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
   * r[10] holds (a[0]*b[0])
   * r[32] holds (b[1]*b[1])
   * c1 holds the carry bits
   */
  c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
  if (c1) {
    p = &(r[n + n2]);
    lo= *p;
    ln = (lo + c1)&BN_MASK2;
    *p = ln;

    /* The overflow will stop before we over write
     * words we should not overwrite */
    if (ln < (BN_ULONG)c1) {
      do {
        p++;
        lo= *p;
        ln = (lo + 1) & BN_MASK2;
        *p = ln;
      } while (ln == 0);
    }
  }
}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 */
void
bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t)
{
  int n = n2 / 2;

# ifdef BN_COUNT
  fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2);
# endif

  bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
  if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
    bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
    bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
    bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
    bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
  } else {
    bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
    bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
    bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
    bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
  }
}

/* a and b must be the same size, which is n2.
 * r needs to be n2 words and t needs to be n2*2
 * l is the low words of the output.
 * t needs to be n2*3
 */
void
bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
    BN_ULONG *t)
{
  int i, n;
  int c1, c2;
  int neg, oneg, zero;
  BN_ULONG ll, lc, *lp, *mp;

# ifdef BN_COUNT
  fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2);
# endif
  n = n2 / 2;

  /* Calculate (al-ah)*(bh-bl) */
  neg = zero = 0;
  c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
  c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
  switch (c1 * 3 + c2) {
  case -4:
    bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
    bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
    break;
  case -3:
    zero = 1;
    break;
  case -2:
    bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
    bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
    neg = 1;
    break;
  case -1:
  case 0:
  case 1:
    zero = 1;
    break;
  case 2:
    bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
    bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
    neg = 1;
    break;
  case 3:
    zero = 1;
    break;
  case 4:
    bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
    bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
    break;
  }

  oneg = neg;
  /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
  /* r[10] = (a[1]*b[1]) */
# ifdef BN_MUL_COMBA
  if (n == 8) {
    bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
    bn_mul_comba8(r, &(a[n]), &(b[n]));
  } else
# endif
  {
    bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
    bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
  }

  /* s0 == low(al*bl)
   * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
   * We know s0 and s1 so the only unknown is high(al*bl)
   * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
   * high(al*bl) == s1 - (r[0]+l[0]+t[0])
   */
  if (l != NULL) {
    lp = &(t[n2 + n]);
    c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
  } else {
    c1 = 0;
    lp = &(r[0]);
  }

  if (neg)
    neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
  else {
    bn_add_words(&(t[n2]), lp, &(t[0]), n);
    neg = 0;
  }

  if (l != NULL) {
    bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
  } else {
    lp = &(t[n2 + n]);
    mp = &(t[n2]);
    for (i = 0; i < n; i++)
      lp[i] = ((~mp[i]) + 1) & BN_MASK2;
  }

  /* s[0] = low(al*bl)
   * t[3] = high(al*bl)
   * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
   * r[10] = (a[1]*b[1])
   */
  /* R[10] = al*bl
   * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
   * R[32] = ah*bh
   */
  /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
   * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
   * R[3]=r[1]+(carry/borrow)
   */
  if (l != NULL) {
    lp = &(t[n2]);
    c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
  } else {
    lp = &(t[n2 + n]);
    c1 = 0;
  }
  c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
  if (oneg)
    c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
  else
    c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));

  c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
  c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
  if (oneg)
    c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
  else
    c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));

  if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
  {
    i = 0;
    if (c1 > 0) {
      lc = c1;
      do {
        ll = (r[i] + lc) & BN_MASK2;
        r[i++] = ll;
        lc = (lc > ll);
      } while (lc);
    } else {
      lc = -c1;
      do {
        ll = r[i];
        r[i++] = (ll - lc) & BN_MASK2;
        lc = (lc > ll);
      } while (lc);
    }
  }
  if (c2 != 0) /* Add starting at r[1] */
  {
    i = n;
    if (c2 > 0) {
      lc = c2;
      do {
        ll = (r[i] + lc) & BN_MASK2;
        r[i++] = ll;
        lc = (lc > ll);
      } while (lc);
    } else {
      lc = -c2;
      do {
        ll = r[i];
        r[i++] = (ll - lc) & BN_MASK2;
        lc = (lc > ll);
      } while (lc);
    }
  }
}
#endif /* BN_RECURSION */

int
BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
  int ret = 0;
  int top, al, bl;
  BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
  int i;
#endif
#ifdef BN_RECURSION
  BIGNUM *t = NULL;
  int j = 0, k;
#endif

#ifdef BN_COUNT
  fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top);
#endif

  bn_check_top(a);
  bn_check_top(b);
  bn_check_top(r);

  al = a->top;
  bl = b->top;

  if ((al == 0) || (bl == 0)) {
    BN_zero(r);
    return (1);
  }
  top = al + bl;

  BN_CTX_start(ctx);
  if ((r == a) || (r == b)) {
    if ((rr = BN_CTX_get(ctx)) == NULL)
      goto err;
  } else
    rr = r;
  rr->neg = a->neg ^ b->neg;

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
  i = al - bl;
#endif
#ifdef BN_MUL_COMBA
  if (i == 0) {
# if 0
    if (al == 4) {
      if (bn_wexpand(rr, 8) == NULL)
        goto err;
      rr->top = 8;
      bn_mul_comba4(rr->d, a->d, b->d);
      goto end;
    }
# endif
    if (al == 8) {
      if (bn_wexpand(rr, 16) == NULL)
        goto err;
      rr->top = 16;
      bn_mul_comba8(rr->d, a->d, b->d);
      goto end;
    }
  }
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
  if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
    if (i >= -1 && i <= 1) {
      /* Find out the power of two lower or equal
         to the longest of the two numbers */
      if (i >= 0) {
        j = BN_num_bits_word((BN_ULONG)al);
      }
      if (i == -1) {
        j = BN_num_bits_word((BN_ULONG)bl);
      }
      j = 1 << (j - 1);
      assert(j <= al || j <= bl);
      k = j + j;
      if ((t = BN_CTX_get(ctx)) == NULL)
        goto err;
      if (al > j || bl > j) {
        if (bn_wexpand(t, k * 4) == NULL)
          goto err;
        if (bn_wexpand(rr, k * 4) == NULL)
          goto err;
        bn_mul_part_recursive(rr->d, a->d, b->d,
            j, al - j, bl - j, t->d);
      }
      else  /* al <= j || bl <= j */
      {
        if (bn_wexpand(t, k * 2) == NULL)
          goto err;
        if (bn_wexpand(rr, k * 2) == NULL)
          goto err;
        bn_mul_recursive(rr->d, a->d, b->d,
            j, al - j, bl - j, t->d);
      }
      rr->top = top;
      goto end;
    }
#if 0
    if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
      BIGNUM *tmp_bn = (BIGNUM *)b;
      if (bn_wexpand(tmp_bn, al) == NULL)
        goto err;
      tmp_bn->d[bl] = 0;
      bl++;
      i--;
    } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
      BIGNUM *tmp_bn = (BIGNUM *)a;
      if (bn_wexpand(tmp_bn, bl) == NULL)
        goto err;
      tmp_bn->d[al] = 0;
      al++;
      i++;
    }
    if (i == 0) {
      /* symmetric and > 4 */
      /* 16 or larger */
      j = BN_num_bits_word((BN_ULONG)al);
      j = 1 << (j - 1);
      k = j + j;
      if ((t = BN_CTX_get(ctx)) == NULL)
        goto err;
      if (al == j) /* exact multiple */
      {
        if (bn_wexpand(t, k * 2) == NULL)
          goto err;
        if (bn_wexpand(rr, k * 2) == NULL)
          goto err;
        bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
      } else {
        if (bn_wexpand(t, k * 4) == NULL)
          goto err;
        if (bn_wexpand(rr, k * 4) == NULL)
          goto err;
        bn_mul_part_recursive(rr->d, a->d, b->d,
            al - j, j, t->d);
      }
      rr->top = top;
      goto end;
    }
#endif
  }
#endif /* BN_RECURSION */
  if (bn_wexpand(rr, top) == NULL)
    goto err;
  rr->top = top;
  bn_mul_normal(rr->d, a->d, al, b->d, bl);

#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
  bn_correct_top(rr);
  if (r != rr)
    BN_copy(r, rr);
  ret = 1;
err:
  bn_check_top(r);
  BN_CTX_end(ctx);
  return (ret);
}

void
bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
{
  BN_ULONG *rr;

#ifdef BN_COUNT
  fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
#endif

  if (na < nb) {
    int itmp;
    BN_ULONG *ltmp;

    itmp = na;
    na = nb;
    nb = itmp;
    ltmp = a;
    a = b;
    b = ltmp;

  }
  rr = &(r[na]);
  if (nb <= 0) {
    (void)bn_mul_words(r, a, na, 0);
    return;
  } else
    rr[0] = bn_mul_words(r, a, na, b[0]);

  for (;;) {
    if (--nb <= 0)
      return;
    rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
    if (--nb <= 0)
      return;
    rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
    if (--nb <= 0)
      return;
    rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
    if (--nb <= 0)
      return;
    rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
    rr += 4;
    r += 4;
    b += 4;
  }
}

void
bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
{
#ifdef BN_COUNT
  fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
#endif
  bn_mul_words(r, a, n, b[0]);

  for (;;) {
    if (--n <= 0)
      return;
    bn_mul_add_words(&(r[1]), a, n, b[1]);
    if (--n <= 0)
      return;
    bn_mul_add_words(&(r[2]), a, n, b[2]);
    if (--n <= 0)
      return;
    bn_mul_add_words(&(r[3]), a, n, b[3]);
    if (--n <= 0)
      return;
    bn_mul_add_words(&(r[4]), a, n, b[4]);
    r += 4;
    b += 4;
  }
}

Coverage Report

Created: 2022-08-24 06:31