text: /*
   * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
   *
   * Licensed under the OpenSSL license (the "License").  You may not use
   * this file except in compliance with the License.  You can obtain a copy
   * in the file LICENSE in the source distribution or at
   * https://www.openssl.org/source/license.html
   */
  
  #include "internal/cryptlib.h"
  #include "bn_lcl.h"
  
  /* r must not be a */
  /*
   * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
   */
  int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
  {
      int max, al;
      int ret = 0;
      BIGNUM *tmp, *rr;
  
      bn_check_top(a);
  
      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) {
  #ifndef BN_SQR_COMBA
          BN_ULONG t[8];
          bn_sqr_normal(rr->d, a->d, 4, t);
  #else
          bn_sqr_comba4(rr->d, a->d);
  #endif
      } else if (al == 8) {
  #ifndef BN_SQR_COMBA
          BN_ULONG t[16];
          bn_sqr_normal(rr->d, a->d, 8, t);
  #else
          bn_sqr_comba8(rr->d, a->d);
  #endif
      } else {
  #if defined(BN_RECURSION)
          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);
              }
          }
  #else
          if (bn_wexpand(tmp, max) == NULL)
              goto err;
          bn_sqr_normal(rr->d, a->d, al, tmp->d);
  #endif
      }
  
      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 (r != rr && BN_copy(r, rr) == NULL)
          goto err;
  
      ret = 1;
   err:
      bn_check_top(rr);
      bn_check_top(tmp);
      BN_CTX_end(ctx);
      return (ret);
  }
  
  /* tmp must have 2*n words */
  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);
  }
  
  #ifdef BN_RECURSION
  /*-
   * 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]
   */
  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) {
  # ifndef BN_SQR_COMBA
          bn_sqr_normal(r, a, 4, t);
  # else
          bn_sqr_comba4(r, a);
  # endif
          return;
      } else if (n2 == 8) {
  # ifndef BN_SQR_COMBA
          bn_sqr_normal(r, a, 8, t);
  # else
          bn_sqr_comba8(r, a);
  # endif
          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
          memset(&t[n2], 0, sizeof(*t) * n2);
      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);
          }
      }
  }
  #endif
  