text: /* 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 <CCryptoBoringSSL_bn.h>
  
  #include <assert.h>
  #include <stdlib.h>
  #include <string.h>
  
  #include <CCryptoBoringSSL_err.h>
  #include <CCryptoBoringSSL_mem.h>
  #include <CCryptoBoringSSL_type_check.h>
  
  #include "internal.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_abs_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                               size_t num, BN_ULONG *tmp) {
    BN_ULONG borrow = bn_sub_words(tmp, a, b, num);
    bn_sub_words(r, b, a, num);
    bn_select_words(r, 0 - borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);
  }
  
  static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na,
                            const BN_ULONG *b, size_t nb) {
    if (na < nb) {
      size_t itmp = na;
      na = nb;
      nb = itmp;
      const BN_ULONG *ltmp = a;
      a = b;
      b = ltmp;
    }
    BN_ULONG *rr = &(r[na]);
    if (nb == 0) {
      OPENSSL_memset(r, 0, na * sizeof(BN_ULONG));
      return;
    }
    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;
        if (t != 0) {
          c = 1;
        }
        if (++dl >= 0) {
          break;
        }
  
        t = b[1];
        r[1] = 0 - t - c;
        if (t != 0) {
          c = 1;
        }
        if (++dl >= 0) {
          break;
        }
  
        t = b[2];
        r[2] = 0 - t - c;
        if (t != 0) {
          c = 1;
        }
        if (++dl >= 0) {
          break;
        }
  
        t = b[3];
        r[3] = 0 - t - c;
        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;
        if (t != 0) {
          c = 0;
        }
        if (--dl <= 0) {
          break;
        }
  
        t = a[1];
        r[1] = t - c;
        if (t != 0) {
          c = 0;
        }
        if (--dl <= 0) {
          break;
        }
  
        t = a[2];
        r[2] = t - c;
        if (t != 0) {
          c = 0;
        }
        if (--dl <= 0) {
          break;
        }
  
        t = a[3];
        r[3] = t - c;
        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;
              }
              OPENSSL_FALLTHROUGH;
            case 2:
              r[2] = a[2];
              if (--dl <= 0) {
                break;
              }
              OPENSSL_FALLTHROUGH;
            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
  
  // bn_abs_sub_part_words computes |r| = |a| - |b|, storing the absolute value
  // and returning a mask of all ones if the result was negative and all zeros if
  // the result was positive. |cl| and |dl| follow the |bn_sub_part_words| calling
  // convention.
  //
  // TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention
  // is confusing. The trouble is 32-bit x86 implements |bn_sub_part_words| in
  // assembly, but we can probably just delete it?
  static BN_ULONG bn_abs_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
                                        const BN_ULONG *b, int cl, int dl,
                                        BN_ULONG *tmp) {
    BN_ULONG borrow = bn_sub_part_words(tmp, a, b, cl, dl);
    bn_sub_part_words(r, b, a, cl, -dl);
    int r_len = cl + (dl < 0 ? -dl : dl);
    borrow = 0 - borrow;
    bn_select_words(r, borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, r_len);
    return borrow;
  }
  
  int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                           BN_CTX *ctx) {
    int cl = a->width < b->width ? a->width : b->width;
    int dl = a->width - b->width;
    int r_len = a->width < b->width ? b->width : a->width;
    BN_CTX_start(ctx);
    BIGNUM *tmp = BN_CTX_get(ctx);
    int ok = tmp != NULL &&
             bn_wexpand(r, r_len) &&
             bn_wexpand(tmp, r_len);
    if (ok) {
      bn_abs_sub_part_words(r->d, a->d, b->d, cl, dl, tmp->d);
      r->width = r_len;
    }
    BN_CTX_end(ctx);
    return ok;
  }
  
  // Karatsuba recursive multiplication algorithm
  // (cf. Knuth, The Art of Computer Programming, Vol. 2)
  
  // bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has
  // length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and
  // |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have
  // -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and
  // -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0.
  //
  // TODO(davidben): Simplify and |size_t| the calling convention around lengths
  // here.
  static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                               int n2, int dna, int dnb, BN_ULONG *t) {
    // |n2| is a power of two.
    assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
    // Check |dna| and |dnb| are in range.
    assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dna && dna <= 0);
    assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dnb && dnb <= 0);
  
    // 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;
    }
  
    // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|.
    // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
    // for recursive calls.
    // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
    // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
    //
    //   a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
    //
    // Note that we know |n| >= |BN_MUL_RECURSIVE_SIZE_NORMAL|/2 above, so
    // |tna| and |tnb| are non-negative.
    int n = n2 / 2, tna = n + dna, tnb = n + dnb;
  
    // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
    // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
    // themselves store the absolute value.
    BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
    neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
  
    // Compute:
    // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
    // r0,r1 = a0 * b0
    // r2,r3 = a1 * b1
    if (n == 4 && dna == 0 && dnb == 0) {
      bn_mul_comba4(&t[n2], t, &t[n]);
  
      bn_mul_comba4(r, a, b);
      bn_mul_comba4(&r[n2], &a[n], &b[n]);
    } else if (n == 8 && dna == 0 && dnb == 0) {
      bn_mul_comba8(&t[n2], t, &t[n]);
  
      bn_mul_comba8(r, a, b);
      bn_mul_comba8(&r[n2], &a[n], &b[n]);
    } else {
      BN_ULONG *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);
      bn_mul_recursive(&r[n2], &a[n], &b[n], n, dna, dnb, p);
    }
  
    // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
    BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
  
    // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
    // The second term is stored as the absolute value, so we do this with a
    // constant-time select.
    BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
    BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
    bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
    OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
                          "crypto_word_t is too small");
    c = constant_time_select_w(neg, c_neg, c_pos);
  
    // We now have our three components. Add them together.
    // r1,r2,c = r1,r2 + t2,t3,c
    c += bn_add_words(&r[n], &r[n], &t[n2], n2);
  
    // Propagate the carry bit to the end.
    for (int i = n + n2; i < n2 + n2; i++) {
      BN_ULONG old = r[i];
      r[i] = old + c;
      c = r[i] < old;
    }
  
    // The product should fit without carries.
    assert(c == 0);
  }
  
  // bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r|
  // has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and
  // |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have
  // 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most
  // one.
  //
  // TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a|
  // and |b|.
  static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,
                                    const BN_ULONG *b, int n, int tna, int tnb,
                                    BN_ULONG *t) {
    // |n| is a power of two.
    assert(n != 0 && (n & (n - 1)) == 0);
    // Check |tna| and |tnb| are in range.
    assert(0 <= tna && tna < n);
    assert(0 <= tnb && tnb < n);
    assert(-1 <= tna - tnb && tna - tnb <= 1);
  
    int n2 = n * 2;
    if (n < 8) {
      bn_mul_normal(r, a, n + tna, b, n + tnb);
      OPENSSL_memset(r + n2 + tna + tnb, 0, n2 - tna - tnb);
      return;
    }
  
    // Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|. |a1|
    // and |b1| have size |tna| and |tnb|, respectively.
    // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
    // for recursive calls.
    // Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
    // to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
    //
    //   a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
  
    // t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
    // their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
    // themselves store the absolute value.
    BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
    neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
  
    // Compute:
    // t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
    // r0,r1 = a0 * b0
    // r2,r3 = a1 * b1
    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);
      // |bn_mul_normal| only writes |tna| + |tna| words. Zero the rest.
      OPENSSL_memset(&r[n2 + tna + tnb], 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
    } else {
      BN_ULONG *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);
  
      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 {
        int i = n;
        for (;;) {
          i /= 2;
          if (i < tna || i < tnb) {
            // E.g., n == 16, i == 8 and tna == 11. |tna| and |tnb| are within one
            // of each other, so if |tna| is larger and tna > i, then we know
            // tnb >= i, and this call is valid.
            bn_mul_part_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
            break;
          }
          if (i == tna || i == tnb) {
            // If there is only a bottom half to the number, just do it. We know
            // the larger of |tna - i| and |tnb - i| is zero. The other is zero or
            // -1 by because of |tna| and |tnb| differ by at most one.
            bn_mul_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
            break;
          }
  
          // This loop will eventually terminate when |i| falls below
          // |BN_MUL_RECURSIVE_SIZE_NORMAL| because we know one of |tna| and |tnb|
          // exceeds that.
        }
      }
    }
  
    // t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
    BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
  
    // t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
    // The second term is stored as the absolute value, so we do this with a
    // constant-time select.
    BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
    BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
    bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
    OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
                          "crypto_word_t is too small");
    c = constant_time_select_w(neg, c_neg, c_pos);
  
    // We now have our three components. Add them together.
    // r1,r2,c = r1,r2 + t2,t3,c
    c += bn_add_words(&r[n], &r[n], &t[n2], n2);
  
    // Propagate the carry bit to the end.
    for (int i = n + n2; i < n2 + n2; i++) {
      BN_ULONG old = r[i];
      r[i] = old + c;
      c = r[i] < old;
    }
  
    // The product should fit without carries.
    assert(c == 0);
  }
  
  // bn_mul_impl implements |BN_mul| and |bn_mul_consttime|. Note this function
  // breaks |BIGNUM| invariants and may return a negative zero. This is handled by
  // the callers.
  static int bn_mul_impl(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                         BN_CTX *ctx) {
    int al = a->width;
    int bl = b->width;
    if (al == 0 || bl == 0) {
      BN_zero(r);
      return 1;
    }
  
    int ret = 0;
    BIGNUM *rr;
    BN_CTX_start(ctx);
    if (r == a || r == b) {
      rr = BN_CTX_get(ctx);
      if (rr == NULL) {
        goto err;
      }
    } else {
      rr = r;
    }
    rr->neg = a->neg ^ b->neg;
  
    int i = al - bl;
    if (i == 0) {
      if (al == 8) {
        if (!bn_wexpand(rr, 16)) {
          goto err;
        }
        rr->width = 16;
        bn_mul_comba8(rr->d, a->d, b->d);
        goto end;
      }
    }
  
    int top = al + bl;
    static const int kMulNormalSize = 16;
    if (al >= kMulNormalSize && bl >= kMulNormalSize) {
      if (-1 <= i && i <= 1) {
        // Find the larger power of two less than or equal to the larger length.
        int j;
        if (i >= 0) {
          j = BN_num_bits_word((BN_ULONG)al);
        } else {
          j = BN_num_bits_word((BN_ULONG)bl);
        }
        j = 1 << (j - 1);
        assert(j <= al || j <= bl);
        BIGNUM *t = BN_CTX_get(ctx);
        if (t == NULL) {
          goto err;
        }
        if (al > j || bl > j) {
          // We know |al| and |bl| are at most one from each other, so if al > j,
          // bl >= j, and vice versa. Thus we can use |bn_mul_part_recursive|.
          assert(al >= j && bl >= j);
          if (!bn_wexpand(t, j * 8) ||
              !bn_wexpand(rr, j * 4)) {
            goto err;
          }
          bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
        } else {
          // al <= j && bl <= j. Additionally, we know j <= al or j <= bl, so one
          // of al - j or bl - j is zero. The other, by the bound on |i| above, is
          // zero or -1. Thus, we can use |bn_mul_recursive|.
          if (!bn_wexpand(t, j * 4) ||
              !bn_wexpand(rr, j * 2)) {
            goto err;
          }
          bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
        }
        rr->width = top;
        goto end;
      }
    }
  
    if (!bn_wexpand(rr, top)) {
      goto err;
    }
    rr->width = top;
    bn_mul_normal(rr->d, a->d, al, b->d, bl);
  
  end:
    if (r != rr && !BN_copy(r, rr)) {
      goto err;
    }
    ret = 1;
  
  err:
    BN_CTX_end(ctx);
    return ret;
  }
  
  int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
    if (!bn_mul_impl(r, a, b, ctx)) {
      return 0;
    }
  
    // This additionally fixes any negative zeros created by |bn_mul_impl|.
    bn_set_minimal_width(r);
    return 1;
  }
  
  int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
    // Prevent negative zeros.
    if (a->neg || b->neg) {
      OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
      return 0;
    }
  
    return bn_mul_impl(r, a, b, ctx);
  }
  
  void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
                    const BN_ULONG *b, size_t num_b) {
    if (num_r != num_a + num_b) {
      abort();
    }
    // TODO(davidben): Should this call |bn_mul_comba4| too? |BN_mul| does not
    // hit that code.
    if (num_a == 8 && num_b == 8) {
      bn_mul_comba8(r, a, b);
    } else {
      bn_mul_normal(r, a, num_a, b, num_b);
    }
  }
  
  // tmp must have 2*n words
  static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n,
                            BN_ULONG *tmp) {
    if (n == 0) {
      return;
    }
  
    size_t max = n * 2;
    const BN_ULONG *ap = a;
    BN_ULONG *rp = r;
    rp[0] = rp[max - 1] = 0;
    rp++;
  
    // Compute the contribution of a[i] * a[j] for all i < j.
    if (n > 1) {
      ap++;
      rp[n - 1] = bn_mul_words(rp, ap, n - 1, ap[-1]);
      rp += 2;
    }
    if (n > 2) {
      for (size_t i = n - 2; i > 0; i--) {
        ap++;
        rp[i] = bn_mul_add_words(rp, ap, i, ap[-1]);
        rp += 2;
      }
    }
  
    // The final result fits in |max| words, so none of the following operations
    // will overflow.
  
    // Double |r|, giving the contribution of a[i] * a[j] for all i != j.
    bn_add_words(r, r, r, max);
  
    // Add in the contribution of a[i] * a[i] for all i.
    bn_sqr_words(tmp, a, n);
    bn_add_words(r, r, tmp, max);
  }
  
  // bn_sqr_recursive sets |r| to |a|^2, using |t| as scratch space. |r| has
  // length 2*|n2|, |a| has length |n2|, and |t| has length 4*|n2|. |n2| must be
  // a power of two.
  static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, size_t n2,
                               BN_ULONG *t) {
    // |n2| is a power of two.
    assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
  
    if (n2 == 4) {
      bn_sqr_comba4(r, a);
      return;
    }
    if (n2 == 8) {
      bn_sqr_comba8(r, a);
      return;
    }
    if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
      bn_sqr_normal(r, a, n2, t);
      return;
    }
  
    // Split |a| into a0,a1, each of size |n|.
    // Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
    // for recursive calls.
    // Split |r| into r0,r1,r2,r3. We must contribute a0^2 to r0,r1, 2*a0*a1 to
    // r1,r2, and a1^2 to r2,r3.
    size_t n = n2 / 2;
    BN_ULONG *t_recursive = &t[n2 * 2];
  
    // t0 = |a0 - a1|.
    bn_abs_sub_words(t, a, &a[n], n, &t[n]);
    // t2,t3 = t0^2 = |a0 - a1|^2 = a0^2 - 2*a0*a1 + a1^2
    bn_sqr_recursive(&t[n2], t, n, t_recursive);
  
    // r0,r1 = a0^2
    bn_sqr_recursive(r, a, n, t_recursive);
  
    // r2,r3 = a1^2
    bn_sqr_recursive(&r[n2], &a[n], n, t_recursive);
  
    // t0,t1,c = r0,r1 + r2,r3 = a0^2 + a1^2
    BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
    // t2,t3,c = t0,t1,c - t2,t3 = 2*a0*a1
    c -= bn_sub_words(&t[n2], t, &t[n2], n2);
  
    // We now have our three components. Add them together.
    // r1,r2,c = r1,r2 + t2,t3,c
    c += bn_add_words(&r[n], &r[n], &t[n2], n2);
  
    // Propagate the carry bit to the end.
    for (size_t i = n + n2; i < n2 + n2; i++) {
      BN_ULONG old = r[i];
      r[i] = old + c;
      c = r[i] < old;
    }
  
    // The square should fit without carries.
    assert(c == 0);
  }
  
  int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
    if (!bn->width) {
      return 1;
    }
  
    if (w == 0) {
      BN_zero(bn);
      return 1;
    }
  
    BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->width, w);
    if (ll) {
      if (!bn_wexpand(bn, bn->width + 1)) {
        return 0;
      }
      bn->d[bn->width++] = ll;
    }
  
    return 1;
  }
  
  int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
    int al = a->width;
    if (al <= 0) {
      r->width = 0;
      r->neg = 0;
      return 1;
    }
  
    int ret = 0;
    BN_CTX_start(ctx);
    BIGNUM *rr = (a != r) ? r : BN_CTX_get(ctx);
    BIGNUM *tmp = BN_CTX_get(ctx);
    if (!rr || !tmp) {
      goto err;
    }
  
    int max = 2 * al;  // Non-zero (from above)
    if (!bn_wexpand(rr, max)) {
      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 {
        // If |al| is a power of two, we can use |bn_sqr_recursive|.
        if (al != 0 && (al & (al - 1)) == 0) {
          if (!bn_wexpand(tmp, al * 4)) {
            goto err;
          }
          bn_sqr_recursive(rr->d, a->d, al, tmp->d);
        } else {
          if (!bn_wexpand(tmp, max)) {
            goto err;
          }
          bn_sqr_normal(rr->d, a->d, al, tmp->d);
        }
      }
    }
  
    rr->neg = 0;
    rr->width = max;
  
    if (rr != r && !BN_copy(r, rr)) {
      goto err;
    }
    ret = 1;
  
  err:
    BN_CTX_end(ctx);
    return ret;
  }
  
  int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
    if (!bn_sqr_consttime(r, a, ctx)) {
      return 0;
    }
  
    bn_set_minimal_width(r);
    return 1;
  }
  
  void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) {
    if (num_r != 2 * num_a || num_a > BN_SMALL_MAX_WORDS) {
      abort();
    }
    if (num_a == 4) {
      bn_sqr_comba4(r, a);
    } else if (num_a == 8) {
      bn_sqr_comba8(r, a);
    } else {
      BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
      bn_sqr_normal(r, a, num_a, tmp);
      OPENSSL_cleanse(tmp, 2 * num_a * sizeof(BN_ULONG));
    }
  }
  