/* ====================================================================

 * 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

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 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in

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 *    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/)"

 *

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 *    endorse or promote products derived from this software without

 *    prior written permission. For written permission, please contact

 *    openssl-core@openssl.org.

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 * 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.

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 * 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

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 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED

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 * ====================================================================

 *

 * 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;

}