// Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved.

//

// Licensed under the Apache License, Version 2.0 (the "License");

// you may not use this file except in compliance with the License.

// You may obtain a copy of the License at

//

//     https://www.apache.org/licenses/LICENSE-2.0

//

// Unless required by applicable law or agreed to in writing, software

// distributed under the License is distributed on an "AS IS" BASIS,

// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.

// See the License for the specific language governing permissions and

// limitations under the License.

#include <openssl/bn.h>

#include <openssl/err.h>

#include "internal.h"

using namespace bssl;

// least significant word

#define BN_lsw(n) (((n)->width == 0) ? (BN_ULONG)0 : (n)->d[0])

int bssl::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;

  }

  BN_CTXScope scope(ctx);

  BIGNUM *A = BN_CTX_get(ctx);

  BIGNUM *B = BN_CTX_get(ctx);

  if (B == nullptr) {

    return -2;

  }

  if (!BN_copy(A, a) ||

      !BN_copy(B, b)) {

    return -2;

  }

  // 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).

  int ret = 1;

  while (1) {

    // Cohen's step 3:

    // B is positive and odd

    if (BN_is_zero(A)) {

      return BN_is_one(B) ? ret : 0;

    }

    // now A is non-zero

    int i = 0;

    while (!BN_is_bit_set(A, i)) {

      i++;

    }

    if (!BN_rshift(A, A, i)) {

      return -2;

    }

    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)) {

      return -2;

    }

    BIGNUM *tmp = A;

    A = B;

    B = tmp;

    tmp->neg = 0;

  }

}