/*
  This file is for the Gao-Mateer FFT
  sse http://www.math.clemson.edu/~sgao/papers/GM10.pdf

  For the implementation strategy, see
  https://eprint.iacr.org/2017/793.pdf
*/

#include "fft.h"

#include "transpose.h"
#include "vec256.h"

#include <stdint.h>

/* input: in, polynomial in bitsliced form */
/* output: in, result of applying the radix conversions on in */
static void radix_conversions(vec128 *in) {
    int i, j, k;
    vec128 t;
    uint64_t v0, v1;

    const vec128 mask[5][2] = {
        {
            vec128_set2x(0x8888888888888888, 0x8888888888888888),
            vec128_set2x(0x4444444444444444, 0x4444444444444444)
        },
        {
            vec128_set2x(0xC0C0C0C0C0C0C0C0, 0xC0C0C0C0C0C0C0C0),
            vec128_set2x(0x3030303030303030, 0x3030303030303030)
        },
        {
            vec128_set2x(0xF000F000F000F000, 0xF000F000F000F000),
            vec128_set2x(0x0F000F000F000F00, 0x0F000F000F000F00)
        },
        {
            vec128_set2x(0xFF000000FF000000, 0xFF000000FF000000),
            vec128_set2x(0x00FF000000FF0000, 0x00FF000000FF0000)
        },
        {
            vec128_set2x(0xFFFF000000000000, 0xFFFF000000000000),
            vec128_set2x(0x0000FFFF00000000, 0x0000FFFF00000000)
        }
    };

    const vec128 s[5][GFBITS] = {
#include "scalars_2x.data"
    };

    //

    for (j = 0; j <= 5; j++) {
        for (i = 0; i < GFBITS; i++) {
            v1 = vec128_extract(in[i], 1);
            v1 ^= v1 >> 32;
            v0 = vec128_extract(in[i], 0);
            v0 ^= v1 << 32;
            in[i] = vec128_set2x(v0, v1);
        }

        for (i = 0; i < GFBITS; i++) {
            for (k = 4; k >= j; k--) {
                t = vec128_and(in[i], mask[k][0]);
                t = vec128_srl_2x(t, 1 << k);
                in[i] = vec128_xor(in[i], t);

                t = vec128_and(in[i], mask[k][1]);
                t = vec128_srl_2x(t, 1 << k);
                in[i] = vec128_xor(in[i], t);
            }
        }

        if (j < 5) {
            vec128_mul(in, in, s[j]);    // scaling
        }
    }
}

/* input: in, result of applying the radix conversions to the input polynomial */
/* output: out, evaluation results (by applying the FFT butterflies) */
static void butterflies(vec256 out[][ GFBITS ], vec128 *in) {
    int i, j, k, s, b;

    vec128 tmp[ GFBITS ];
    vec256 tmp0[ GFBITS ];
    vec256 tmp1[ GFBITS ];
    vec128 t[ GFBITS ];

    union {
        vec128 v[8][  GFBITS + 1    ];
        vec256 V[8][ (GFBITS + 1) / 2 ];
    } pre;

    union {
        vec128 v[64][ 2 ];
        vec256 V[64];
    } buf;

    uint64_t v0, v1;

    const vec256 consts[ 33 ][ GFBITS ] = {
#include "consts.data"
    };

    uint64_t consts_ptr = 2;

    const unsigned char reversal[64] = {
        0, 32, 16, 48,  8, 40, 24, 56,
        4, 36, 20, 52, 12, 44, 28, 60,
        2, 34, 18, 50, 10, 42, 26, 58,
        6, 38, 22, 54, 14, 46, 30, 62,
        1, 33, 17, 49,  9, 41, 25, 57,
        5, 37, 21, 53, 13, 45, 29, 61,
        3, 35, 19, 51, 11, 43, 27, 59,
        7, 39, 23, 55, 15, 47, 31, 63
    };

    const uint16_t beta[8] = {2522, 7827, 7801, 8035, 6897, 8167, 3476, 0};

    // boradcast

    for (j = 0; j < GFBITS; j++) {
        t[j] = vec128_unpack_high(in[j], in[j]);
    }

    for (i = 0; i < 8; i += 2) {
        for (j = 0; j < GFBITS; j++) {
            v0 = (beta[i + 0] >> j) & 1;
            v0 = -v0;
            v1 = (beta[i + 1] >> j) & 1;
            v1 = -v1;

            tmp[j] = vec128_set2x(v0, v1);
        }

        vec128_mul(tmp, t, tmp);

        for (j = 0; j < GFBITS; j++) {
            pre.v[i + 0][j] = vec128_unpack_low(tmp[j], tmp[j]);
            pre.v[i + 1][j] = vec128_unpack_high(tmp[j], tmp[j]);
        }
    }

    for (i = 0; i < GFBITS; i += 2) {
        if (i != GFBITS - 1) {
            buf.v[0][1] = vec128_unpack_low(in[i + 1], in[i + 1] ^ pre.v[6][i + 1]);
        }
        buf.v[0][0] = vec128_unpack_low(in[i + 0], in[i + 0] ^ pre.v[6][i + 0]);

#define xor vec256_xor

        buf.V[1] = xor(buf.V[0], pre.V[0][i / 2]);
        buf.V[16] = xor(buf.V[0], pre.V[4][i / 2]);
        buf.V[3] = xor(buf.V[1], pre.V[1][i / 2]);
        buf.V[48] = xor(buf.V[16], pre.V[5][i / 2]);
        buf.V[49] = xor(buf.V[48], pre.V[0][i / 2]);
        buf.V[2] = xor(buf.V[0], pre.V[1][i / 2]);
        buf.V[51] = xor(buf.V[49], pre.V[1][i / 2]);
        buf.V[6] = xor(buf.V[2], pre.V[2][i / 2]);
        buf.V[50] = xor(buf.V[51], pre.V[0][i / 2]);
        buf.V[7] = xor(buf.V[6], pre.V[0][i / 2]);
        buf.V[54] = xor(buf.V[50], pre.V[2][i / 2]);
        buf.V[5] = xor(buf.V[7], pre.V[1][i / 2]);
        buf.V[55] = xor(buf.V[54], pre.V[0][i / 2]);
        buf.V[53] = xor(buf.V[55], pre.V[1][i / 2]);
        buf.V[4] = xor(buf.V[0], pre.V[2][i / 2]);
        buf.V[52] = xor(buf.V[53], pre.V[0][i / 2]);
        buf.V[12] = xor(buf.V[4], pre.V[3][i / 2]);
        buf.V[60] = xor(buf.V[52], pre.V[3][i / 2]);
        buf.V[13] = xor(buf.V[12], pre.V[0][i / 2]);
        buf.V[61] = xor(buf.V[60], pre.V[0][i / 2]);
        buf.V[15] = xor(buf.V[13], pre.V[1][i / 2]);
        buf.V[63] = xor(buf.V[61], pre.V[1][i / 2]);
        buf.V[14] = xor(buf.V[15], pre.V[0][i / 2]);
        buf.V[62] = xor(buf.V[63], pre.V[0][i / 2]);
        buf.V[10] = xor(buf.V[14], pre.V[2][i / 2]);
        buf.V[58] = xor(buf.V[62], pre.V[2][i / 2]);
        buf.V[11] = xor(buf.V[10], pre.V[0][i / 2]);
        buf.V[59] = xor(buf.V[58], pre.V[0][i / 2]);
        buf.V[9] = xor(buf.V[11], pre.V[1][i / 2]);
        buf.V[57] = xor(buf.V[59], pre.V[1][i / 2]);
        buf.V[56] = xor(buf.V[57], pre.V[0][i / 2]);
        buf.V[8] = xor(buf.V[0], pre.V[3][i / 2]);
        buf.V[40] = xor(buf.V[56], pre.V[4][i / 2]);
        buf.V[24] = xor(buf.V[8], pre.V[4][i / 2]);
        buf.V[41] = xor(buf.V[40], pre.V[0][i / 2]);
        buf.V[25] = xor(buf.V[24], pre.V[0][i / 2]);
        buf.V[43] = xor(buf.V[41], pre.V[1][i / 2]);
        buf.V[27] = xor(buf.V[25], pre.V[1][i / 2]);
        buf.V[42] = xor(buf.V[43], pre.V[0][i / 2]);
        buf.V[26] = xor(buf.V[27], pre.V[0][i / 2]);
        buf.V[46] = xor(buf.V[42], pre.V[2][i / 2]);
        buf.V[30] = xor(buf.V[26], pre.V[2][i / 2]);
        buf.V[47] = xor(buf.V[46], pre.V[0][i / 2]);
        buf.V[31] = xor(buf.V[30], pre.V[0][i / 2]);
        buf.V[45] = xor(buf.V[47], pre.V[1][i / 2]);
        buf.V[29] = xor(buf.V[31], pre.V[1][i / 2]);
        buf.V[44] = xor(buf.V[45], pre.V[0][i / 2]);
        buf.V[28] = xor(buf.V[29], pre.V[0][i / 2]);
        buf.V[36] = xor(buf.V[44], pre.V[3][i / 2]);
        buf.V[20] = xor(buf.V[28], pre.V[3][i / 2]);
        buf.V[37] = xor(buf.V[36], pre.V[0][i / 2]);
        buf.V[21] = xor(buf.V[20], pre.V[0][i / 2]);
        buf.V[39] = xor(buf.V[37], pre.V[1][i / 2]);
        buf.V[23] = xor(buf.V[21], pre.V[1][i / 2]);
        buf.V[38] = xor(buf.V[39], pre.V[0][i / 2]);
        buf.V[22] = xor(buf.V[23], pre.V[0][i / 2]);
        buf.V[34] = xor(buf.V[38], pre.V[2][i / 2]);
        buf.V[18] = xor(buf.V[22], pre.V[2][i / 2]);
        buf.V[35] = xor(buf.V[34], pre.V[0][i / 2]);
        buf.V[19] = xor(buf.V[18], pre.V[0][i / 2]);
        buf.V[33] = xor(buf.V[35], pre.V[1][i / 2]);
        buf.V[17] = xor(buf.V[19], pre.V[1][i / 2]);
        buf.V[32] = xor(buf.V[33], pre.V[0][i / 2]);

#undef xor

        // transpose

        transpose_64x256_sp(buf.V);

        for (j = 0; j < 32; j++) {
            if (i != GFBITS - 1) {
                out[j][i + 1] = vec256_unpack_high(buf.V[ reversal[2 * j + 0] ], buf.V[ reversal[2 * j + 1] ]);
            }
            out[j][i + 0] = vec256_unpack_low (buf.V[ reversal[2 * j + 0] ], buf.V[ reversal[2 * j + 1] ]);
        }
    }

    // butterflies

    for (k = 0; k < 32; k += 2) {
        for (b = 0; b < GFBITS; b++) {
            tmp0[b] = vec256_unpack_low (out[k][b], out[k + 1][b]);
        }
        for (b = 0; b < GFBITS; b++) {
            tmp1[b] = vec256_unpack_high (out[k][b], out[k + 1][b]);
        }

        vec256_maa_asm(tmp0, tmp1, consts[1]);

        for (b = 0; b < GFBITS; b++) {
            out[k][b] = vec256_unpack_low (tmp0[b], tmp1[b]);
        }
        for (b = 0; b < GFBITS; b++) {
            out[k + 1][b] = vec256_unpack_high (tmp0[b], tmp1[b]);
        }
    }

    for (i = 0; i <= 4; i++) {
        s = 1 << i;

        for (j = 0; j < 32; j += 2 * s) {
            for (k = j; k < j + s; k++) {
                vec256_maa_asm(out[k], out[k + s], consts[ consts_ptr + (k - j) ]);
            }
        }

        consts_ptr += (1 << i);
    }
}

/* input: in, polynomial in bitsliced form */
/* output: out, bitsliced results of evaluating in all the field elements */
void fft(vec256 out[][GFBITS], vec128 *in) {
    radix_conversions(in);
    butterflies(out, in);
}