#include "reduce.h"
#include "params.h"
#include <stdint.h>

/*************************************************
 * Name:        montgomery_reduce
 *
 * Description: For finite field element a with 0 <= a <= Q*2^32,
 *              compute r \equiv a*2^{-32} (mod Q) such that 0 <= r < 2*Q.
 *
 * Arguments:   - uint64_t: finite field element a
 *
 * Returns r.
 **************************************************/
uint32_t PQCLEAN_DILITHIUMIII_CLEAN_montgomery_reduce(uint64_t a) {
    uint64_t t;

    t = a * QINV;
    t &= (1ULL << 32) - 1;
    t *= Q;
    t = a + t;
    t >>= 32;
    return t;
}

/*************************************************
 * Name:        reduce32
 *
 * Description: For finite field element a, compute r \equiv a (mod Q)
 *              such that 0 <= r < 2*Q.
 *
 * Arguments:   - uint32_t: finite field element a
 *
 * Returns r.
 **************************************************/
uint32_t PQCLEAN_DILITHIUMIII_CLEAN_reduce32(uint32_t a) {
    uint32_t t;

    t = a & 0x7FFFFF;
    a >>= 23;
    t += (a << 13) - a;
    return t;
}

/*************************************************
 * Name:        csubq
 *
 * Description: Subtract Q if input coefficient is bigger than Q.
 *
 * Arguments:   - uint32_t: finite field element a
 *
 * Returns r.
 **************************************************/
uint32_t PQCLEAN_DILITHIUMIII_CLEAN_csubq(uint32_t a) {
    a -= Q;
    a += ((int32_t)a >> 31) & Q;
    return a;
}

/*************************************************
 * Name:        freeze
 *
 * Description: For finite field element a, compute standard
 *              representative r = a mod Q.
 *
 * Arguments:   - uint32_t: finite field element a
 *
 * Returns r.
 **************************************************/
uint32_t PQCLEAN_DILITHIUMIII_CLEAN_freeze(uint32_t a) {
    a = PQCLEAN_DILITHIUMIII_CLEAN_reduce32(a);
    a = PQCLEAN_DILITHIUMIII_CLEAN_csubq(a);
    return a;
}