text: /* ====================================================================
   * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
   *
   * 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 above 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 acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
   *
   * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
   *    endorse or promote products derived from this software without
   *    prior written permission. For written permission, please contact
   *    openssl-core@openssl.org.
   *
   * 5. Products derived from this software may not be called "OpenSSL"
   *    nor may "OpenSSL" appear in their names without prior written
   *    permission of the OpenSSL Project.
   *
   * 6. Redistributions of any form whatsoever must retain the following
   *    acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
   *
   * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
   * EXPRESSED 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 OpenSSL PROJECT OR
   * ITS 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.
   * ====================================================================
   *
   * This product includes cryptographic software written by Eric Young
   * (eay@cryptsoft.com).  This product includes software written by Tim
   * Hudson (tjh@cryptsoft.com). */
  
  #include <openssl/bn.h>
  
  #include <openssl/err.h>
  
  #include "internal.h"
  
  
  // least significant word
  #define BN_lsw(n) (((n)->width == 0) ? (BN_ULONG) 0 : (n)->d[0])
  
  int bn_jacobi(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
    // In 'tab', only odd-indexed entries are relevant:
    // For any odd BIGNUM n,
    //     tab[BN_lsw(n) & 7]
    // is $(-1)^{(n^2-1)/8}$ (using TeX notation).
    // Note that the sign of n does not matter.
    static const int tab[8] = {0, 1, 0, -1, 0, -1, 0, 1};
  
    // The Jacobi symbol is only defined for odd modulus.
    if (!BN_is_odd(b)) {
      OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
      return -2;
    }
  
    // Require b be positive.
    if (BN_is_negative(b)) {
      OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
      return -2;
    }
  
    int ret = -2;
    BN_CTX_start(ctx);
    BIGNUM *A = BN_CTX_get(ctx);
    BIGNUM *B = BN_CTX_get(ctx);
    if (B == NULL) {
      goto end;
    }
  
    if (!BN_copy(A, a) ||
        !BN_copy(B, b)) {
      goto end;
    }
  
    // Adapted from logic to compute the Kronecker symbol, originally implemented
    // according to Henri Cohen, "A Course in Computational Algebraic Number
    // Theory" (algorithm 1.4.10).
  
    ret = 1;
  
    while (1) {
      // Cohen's step 3:
  
      // B is positive and odd
      if (BN_is_zero(A)) {
        ret = BN_is_one(B) ? ret : 0;
        goto end;
      }
  
      // now A is non-zero
      int i = 0;
      while (!BN_is_bit_set(A, i)) {
        i++;
      }
      if (!BN_rshift(A, A, i)) {
        ret = -2;
        goto end;
      }
      if (i & 1) {
        // i is odd
        // multiply 'ret' by  $(-1)^{(B^2-1)/8}$
        ret = ret * tab[BN_lsw(B) & 7];
      }
  
      // Cohen's step 4:
      // multiply 'ret' by  $(-1)^{(A-1)(B-1)/4}$
      if ((A->neg ? ~BN_lsw(A) : BN_lsw(A)) & BN_lsw(B) & 2) {
        ret = -ret;
      }
  
      // (A, B) := (B mod |A|, |A|)
      if (!BN_nnmod(B, B, A, ctx)) {
        ret = -2;
        goto end;
      }
      BIGNUM *tmp = A;
      A = B;
      B = tmp;
      tmp->neg = 0;
    }
  
  end:
    BN_CTX_end(ctx);
    return ret;
  }
  