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

/*************************************************
* Name:        power2round
*
* Description: For finite field element a, compute a0, a1 such that
*              a mod^+ Q = a1*2^D + a0 with -2^{D-1} < a0 <= 2^{D-1}.
*              Assumes a to be standard representative.
*
* Arguments:   - int32_t a: input element
*              - int32_t *a0: pointer to output element a0
*
* Returns a1.
**************************************************/
int32_t power2round(int32_t *a0, int32_t a)  {
    int32_t a1;

    a1 = (a + (1 << (D - 1)) - 1) >> D;
    *a0 = a - (a1 << D);
    return a1;
}

/*************************************************
* Name:        decompose
*
* Description: For finite field element a, compute high and low bits a0, a1 such
*              that a mod^+ Q = a1*ALPHA + a0 with -ALPHA/2 < a0 <= ALPHA/2 except
*              if a1 = (Q-1)/ALPHA where we set a1 = 0 and
*              -ALPHA/2 <= a0 = a mod^+ Q - Q < 0. Assumes a to be standard
*              representative.
*
* Arguments:   - int32_t a: input element
*              - int32_t *a0: pointer to output element a0
*
* Returns a1.
**************************************************/
int32_t decompose(int32_t *a0, int32_t a) {
    int32_t a1;

    a1  = (a + 127) >> 7;

    a1  = (a1 * 11275 + (1 << 23)) >> 24;
    a1 ^= ((43 - a1) >> 31) & a1;


    *a0  = a - a1 * 2 * GAMMA2;
    *a0 -= (((DILITHIUM_Q - 1) / 2 - *a0) >> 31) & DILITHIUM_Q;
    return a1;
}

/*************************************************
* Name:        make_hint
*
* Description: Compute hint bit indicating whether the low bits of the
*              input element overflow into the high bits.
*
* Arguments:   - int32_t a0: low bits of input element
*              - int32_t a1: high bits of input element
*
* Returns 1 if overflow.
**************************************************/
unsigned int make_hint(int32_t a0, int32_t a1) {
    if (a0 > GAMMA2 || a0 < -GAMMA2 || (a0 == -GAMMA2 && a1 != 0)) {
        return 1;
    }

    return 0;
}

/*************************************************
* Name:        use_hint
*
* Description: Correct high bits according to hint.
*
* Arguments:   - int32_t a: input element
*              - unsigned int hint: hint bit
*
* Returns corrected high bits.
**************************************************/
int32_t use_hint(int32_t a, unsigned int hint) {
    int32_t a0, a1;

    a1 = decompose(&a0, a);
    if (hint == 0) {
        return a1;
    }


    if (a0 > 0) {
        return (a1 == 43) ?  0 : a1 + 1;
    }
    return (a1 ==  0) ? 43 : a1 - 1;

}