int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
                BN_RECP_CTX *recp, BN_CTX *ctx)
{
    int i, j, ret = 0;
    BIGNUM *a, *b, *d, *r;

    BN_CTX_start(ctx);
    a = BN_CTX_get(ctx);
    b = BN_CTX_get(ctx);
    if (dv != NULL)
        d = dv;
    else
        d = BN_CTX_get(ctx);
    if (rem != NULL)
        r = rem;
    else
        r = BN_CTX_get(ctx);
    if (a == NULL || b == NULL || d == NULL || r == NULL)
        goto err;

    if (BN_ucmp(m, &(recp->N)) < 0) {
        BN_zero(d);
        if (!BN_copy(r, m)) {
            BN_CTX_end(ctx);
            return 0;
        }
        BN_CTX_end(ctx);
        return (1);
    }

    /*
     * We want the remainder Given input of ABCDEF / ab we need multiply
     * ABCDEF by 3 digests of the reciprocal of ab
     */

    /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
    i = BN_num_bits(m);
    j = recp->num_bits << 1;
    if (j > i)
        i = j;

    /* Nr := round(2^i / N) */
    if (i != recp->shift)
        recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
    /* BN_reciprocal could have returned -1 for an error */
    if (recp->shift == -1)
        goto err;

    /*-
     * d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
     *    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
     *   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
     *    = |m/N|
     */
    if (!BN_rshift(a, m, recp->num_bits))
        goto err;
    if (!BN_mul(b, a, &(recp->Nr), ctx))
        goto err;
    if (!BN_rshift(d, b, i - recp->num_bits))
        goto err;
    d->neg = 0;

    if (!BN_mul(b, &(recp->N), d, ctx))
        goto err;
    if (!BN_usub(r, m, b))
        goto err;
    r->neg = 0;

    j = 0;
    while (BN_ucmp(r, &(recp->N)) >= 0) {
        if (j++ > 2) {
            BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL);
            goto err;
        }
        if (!BN_usub(r, r, &(recp->N)))
            goto err;
        if (!BN_add_word(d, 1))
            goto err;
    }

    r->neg = BN_is_zero(r) ? 0 : m->neg;
    d->neg = m->neg ^ recp->N.neg;
    ret = 1;
 err:
    BN_CTX_end(ctx);
    bn_check_top(dv);
    bn_check_top(rem);
    return (ret);
}