boringssl/crypto/bn/mul.c

/* 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.] */

#include <openssl/bn.h>

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

#include "internal.h"


#define BN_MUL_RECURSIVE_SIZE_NORMAL 16
#define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL


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

  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;
  }
}

#if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
/* 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.  */

static 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) {
    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;
    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) {
      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) {
      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;
}
#else
/* On other platforms the function is defined in asm. */
BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                           int cl, int dl);
#endif

/* 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 */
static 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;

  /* 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;
  }

  /* 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) {
      OPENSSL_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;
  }

  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 {
      OPENSSL_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 {
      OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
    }

    bn_mul_comba8(r, a, b);
    bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
  } else {
    p = &(t[n2 * 2]);
    if (!zero) {
      bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
    } else {
      OPENSSL_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 */
static 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;

  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;
  }

  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);
    OPENSSL_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);
      OPENSSL_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);
      OPENSSL_memset(&(r[n2 + tna + tnb]), 0,
                     sizeof(BN_ULONG) * (n2 - tna - tnb));
    } else {
      /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
      OPENSSL_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);
    }
  }
}

int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
  int ret = 0;
  int top, al, bl;
  BIGNUM *rr;
  int i;
  BIGNUM *t = NULL;
  int j = 0, k;

  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;

  i = al - bl;
  if (i == 0) {
    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;
    }
  }

  static const int kMulNormalSize = 16;
  if (al >= kMulNormalSize && bl >= kMulNormalSize) {
    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;
      t = BN_CTX_get(ctx);
      if (t == 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 (bn_wexpand(rr, top) == NULL) {
    goto err;
  }
  rr->top = top;
  bn_mul_normal(rr->d, a->d, al, b->d, bl);

end:
  bn_correct_top(rr);
  if (r != rr && !BN_copy(r, rr)) {
    goto err;
  }
  ret = 1;

err:
  BN_CTX_end(ctx);
  return ret;
}

/* tmp must have 2*n words */
static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) {
  int i, j, max;
  const BN_ULONG *ap;
  BN_ULONG *rp;

  max = n * 2;
  ap = a;
  rp = r;
  rp[0] = rp[max - 1] = 0;
  rp++;
  j = n;

  if (--j > 0) {
    ap++;
    rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
    rp += 2;
  }

  for (i = n - 2; i > 0; i--) {
    j--;
    ap++;
    rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
    rp += 2;
  }

  bn_add_words(r, r, r, max);

  /* There will not be a carry */

  bn_sqr_words(tmp, a, n);

  bn_add_words(r, r, tmp, max);
}

/* r is 2*n words in size,
 * a and b are both n words in size.    (There's not actually a 'b' here ...)
 * n must be a power of 2.
 * We multiply and return the result.
 * t must be 2*n 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]
 */
static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) {
  int n = n2 / 2;
  int zero, c1;
  BN_ULONG ln, lo, *p;

  if (n2 == 4) {
    bn_sqr_comba4(r, a);
    return;
  } else if (n2 == 8) {
    bn_sqr_comba8(r, a);
    return;
  }
  if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
    bn_sqr_normal(r, a, n2, t);
    return;
  }
  /* r=(a[0]-a[1])*(a[1]-a[0]) */
  c1 = bn_cmp_words(a, &(a[n]), n);
  zero = 0;
  if (c1 > 0) {
    bn_sub_words(t, a, &(a[n]), n);
  } else if (c1 < 0) {
    bn_sub_words(t, &(a[n]), a, n);
  } else {
    zero = 1;
  }

  /* The result will always be negative unless it is zero */
  p = &(t[n2 * 2]);

  if (!zero) {
    bn_sqr_recursive(&(t[n2]), t, n, p);
  } else {
    OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
  }
  bn_sqr_recursive(r, a, n, p);
  bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);

  /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
   * r[10] holds (a[0]*b[0])
   * r[32] holds (b[1]*b[1]) */

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

  /* t[32] is negative */
  c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));

  /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
   * r[10] holds (a[0]*a[0])
   * r[32] holds (a[1]*a[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);
    }
  }
}

int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
  BN_ULONG ll;

  w &= BN_MASK2;
  if (!bn->top) {
    return 1;
  }

  if (w == 0) {
    BN_zero(bn);
    return 1;
  }

  ll = bn_mul_words(bn->d, bn->d, bn->top, w);
  if (ll) {
    if (bn_wexpand(bn, bn->top + 1) == NULL) {
      return 0;
    }
    bn->d[bn->top++] = ll;
  }

  return 1;
}

int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
  int max, al;
  int ret = 0;
  BIGNUM *tmp, *rr;

  al = a->top;
  if (al <= 0) {
    r->top = 0;
    r->neg = 0;
    return 1;
  }

  BN_CTX_start(ctx);
  rr = (a != r) ? r : BN_CTX_get(ctx);
  tmp = BN_CTX_get(ctx);
  if (!rr || !tmp) {
    goto err;
  }

  max = 2 * al; /* Non-zero (from above) */
  if (bn_wexpand(rr, max) == NULL) {
    goto err;
  }

  if (al == 4) {
    bn_sqr_comba4(rr->d, a->d);
  } else if (al == 8) {
    bn_sqr_comba8(rr->d, a->d);
  } else {
    if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
      BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
      bn_sqr_normal(rr->d, a->d, al, t);
    } else {
      int j, k;

      j = BN_num_bits_word((BN_ULONG)al);
      j = 1 << (j - 1);
      k = j + j;
      if (al == j) {
        if (bn_wexpand(tmp, k * 2) == NULL) {
          goto err;
        }
        bn_sqr_recursive(rr->d, a->d, al, tmp->d);
      } else {
        if (bn_wexpand(tmp, max) == NULL) {
          goto err;
        }
        bn_sqr_normal(rr->d, a->d, al, tmp->d);
      }
    }
  }

  rr->neg = 0;
  /* If the most-significant half of the top word of 'a' is zero, then
   * the square of 'a' will max-1 words. */
  if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
    rr->top = max - 1;
  } else {
    rr->top = max;
  }

  if (rr != r && !BN_copy(r, rr)) {
    goto err;
  }
  ret = 1;

err:
  BN_CTX_end(ctx);
  return ret;
}