#include "gf.h"

static inline uint8_t gf256v_reduce_u32(uint32_t a) {
    // https://godbolt.org/z/7hirMb
    uint16_t *aa = (uint16_t *) (&a);
    uint16_t r = aa[0] ^ aa[1];
    uint8_t *rr = (uint8_t *) (&r);
    return rr[0] ^ rr[1];
}

//// gf4 := gf2[x]/x^2+x+1
static inline uint8_t gf4_mul_2(uint8_t a) {
    uint8_t r = (uint8_t) (a << 1);
    r ^= (uint8_t) ((a >> 1) * 7);
    return r;
}

static inline uint8_t gf4_mul(uint8_t a, uint8_t b) {
    uint8_t r = (uint8_t) (a * (b & 1));
    return r ^ (uint8_t)(gf4_mul_2(a) * (b >> 1));
}

static inline uint8_t gf4_squ(uint8_t a) {
    return a ^ (a >> 1);
}

static inline uint32_t gf4v_mul_2_u32(uint32_t a) {
    uint32_t bit0 = a & 0x55555555;
    uint32_t bit1 = a & 0xaaaaaaaa;
    return (bit0 << 1) ^ bit1 ^ (bit1 >> 1);
}

static inline uint32_t gf4v_mul_u32(uint32_t a, uint8_t b) {
    uint32_t bit0_b = ((uint32_t) 0) - ((uint32_t)(b & 1));
    uint32_t bit1_b = ((uint32_t) 0) - ((uint32_t)((b >> 1) & 1));
    return (a & bit0_b) ^ (bit1_b & gf4v_mul_2_u32(a));
}

static inline uint32_t _gf4v_mul_u32_u32(uint32_t a0, uint32_t a1, uint32_t b0, uint32_t b1) {
    uint32_t c0 = a0 & b0;
    uint32_t c2 = a1 & b1;
    uint32_t c1_ = (a0 ^ a1) & (b0 ^ b1);
    return ((c1_ ^ c0) << 1) ^ c0 ^ c2;
}

uint8_t PQCLEAN_RAINBOWIACLASSIC_CLEAN_gf16_is_nonzero(uint8_t a) {
    unsigned a4 = a & 0xf;
    unsigned r = ((unsigned) 0) - a4;
    r >>= 4;
    return r & 1;
}

//// gf16 := gf4[y]/y^2+y+x
static inline uint8_t gf16_mul(uint8_t a, uint8_t b) {
    uint8_t a0 = a & 3;
    uint8_t a1 = (a >> 2);
    uint8_t b0 = b & 3;
    uint8_t b1 = (b >> 2);
    uint8_t a0b0 = gf4_mul(a0, b0);
    uint8_t a1b1 = gf4_mul(a1, b1);
    uint8_t a0b1_a1b0 = gf4_mul(a0 ^ a1, b0 ^ b1) ^ a0b0 ^ a1b1;
    uint8_t a1b1_x2 = gf4_mul_2(a1b1);
    return (uint8_t) ((a0b1_a1b0 ^ a1b1) << 2 ^ a0b0 ^ a1b1_x2);
}

static inline uint8_t gf16_squ(uint8_t a) {
    uint8_t a0 = a & 3;
    uint8_t a1 = (a >> 2);
    a1 = gf4_squ(a1);
    uint8_t a1squ_x2 = gf4_mul_2(a1);
    return (uint8_t)((a1 << 2) ^ a1squ_x2 ^ gf4_squ(a0));
}

uint8_t PQCLEAN_RAINBOWIACLASSIC_CLEAN_gf16_inv(uint8_t a) {
    uint8_t a2 = gf16_squ(a);
    uint8_t a4 = gf16_squ(a2);
    uint8_t a8 = gf16_squ(a4);
    uint8_t a6 = gf16_mul(a4, a2);
    return gf16_mul(a8, a6);
}

// gf16 := gf4[y]/y^2+y+x

uint32_t PQCLEAN_RAINBOWIACLASSIC_CLEAN_gf16v_mul_u32(uint32_t a, uint8_t b) {
    uint32_t axb0 = gf4v_mul_u32(a, b);
    uint32_t axb1 = gf4v_mul_u32(a, b >> 2);
    uint32_t a0b1 = (axb1 << 2) & 0xcccccccc;
    uint32_t a1b1 = axb1 & 0xcccccccc;
    uint32_t a1b1_2 = a1b1 >> 2;

    return axb0 ^ a0b1 ^ a1b1 ^ gf4v_mul_2_u32(a1b1_2);
}

static inline uint32_t _gf16v_mul_u32_u32(uint32_t a0, uint32_t a1, uint32_t a2, uint32_t a3, uint32_t b0, uint32_t b1, uint32_t b2, uint32_t b3) {
    uint32_t c0 = _gf4v_mul_u32_u32(a0, a1, b0, b1);
    uint32_t c1_ = _gf4v_mul_u32_u32(a0 ^ a2, a1 ^ a3, b0 ^ b2, b1 ^ b3);

    uint32_t c2_0 = a2 & b2;
    uint32_t c2_2 = a3 & b3;
    uint32_t c2_1_ = (a2 ^ a3) & (b2 ^ b3);
    uint32_t c2_r0 = c2_0 ^ c2_2;
    uint32_t c2_r1 = c2_0 ^ c2_1_;
    // GF(4) x2: (bit0<<1)^bit1^(bit1>>1);
    return ((c1_ ^ c0) << 2) ^ c0 ^ (c2_r0 << 1) ^ c2_r1 ^ (c2_r1 << 1);
}

uint32_t PQCLEAN_RAINBOWIACLASSIC_CLEAN_gf16v_mul_u32_u32(uint32_t a, uint32_t b) {
    uint32_t a0 = a & 0x11111111;
    uint32_t a1 = (a >> 1) & 0x11111111;
    uint32_t a2 = (a >> 2) & 0x11111111;
    uint32_t a3 = (a >> 3) & 0x11111111;
    uint32_t b0 = b & 0x11111111;
    uint32_t b1 = (b >> 1) & 0x11111111;
    uint32_t b2 = (b >> 2) & 0x11111111;
    uint32_t b3 = (b >> 3) & 0x11111111;

    return _gf16v_mul_u32_u32(a0, a1, a2, a3, b0, b1, b2, b3);
}

uint8_t PQCLEAN_RAINBOWIACLASSIC_CLEAN_gf16v_reduce_u32(uint32_t a) {
    uint8_t r256 = gf256v_reduce_u32(a);
    return (uint8_t)((r256 & 0xf) ^ (r256 >> 4));
}