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

  For the implementation strategy, see
  https://eprint.iacr.org/2017/793.pdf
*/
// 20221230 djb: split these arrays into separate .c files
// 20221230 djb: rename powers array as fft_powers
// 20221230 djb: rename consts array as fft_consts
// 20221230 djb: rename s array as fft_scalars_2x
// 20221230 djb: add linker lines

// linker define fft
// linker use vec_mul
// linker use fft_scalars_2x fft_consts fft_powers

#include "fft.h"
#include "fft_scalars_2x.h"
#include "fft_consts.h"
#include "fft_powers.h"

#include "transpose.h"

#include <stdint.h>

/* input: in, polynomial in bitsliced form */
/* output: in, result of applying the radix conversions on in */
static void radix_conversions(vec in[][GFBITS])
{
	int i, j, k;

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

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

		for (i = 0; i < GFBITS; i++)
		for (k = 4; k >= j; k--)
		{
			in[0][i] ^= (in[0][i] & mask[k][0]) >> (1 << k);
			in[0][i] ^= (in[0][i] & mask[k][1]) >> (1 << k);
			in[1][i] ^= (in[1][i] & mask[k][0]) >> (1 << k);
			in[1][i] ^= (in[1][i] & mask[k][1]) >> (1 << k);
		}

		if (j < 5)
		{
			vec_mul(in[0], in[0], fft_scalars_2x[j][0]);
			vec_mul(in[1], in[1], fft_scalars_2x[j][1]);
		}
	}
}

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

	vec tmp[ GFBITS ];
	vec pre[8][ GFBITS ];
	vec buf[128];

	uint64_t consts_ptr = 2;

	const unsigned char reversal[128] = 
	{ 
	  0, 64, 32, 96, 16, 80, 48, 112, 
	  8, 72, 40, 104, 24, 88, 56, 120, 
	  4, 68, 36, 100, 20, 84, 52, 116, 
	  12, 76, 44, 108, 28, 92, 60, 124, 
	  2, 66, 34, 98, 18, 82, 50, 114, 
	  10, 74, 42, 106, 26, 90, 58, 122, 
	  6, 70, 38, 102, 22, 86, 54, 118, 
	  14, 78, 46, 110, 30, 94, 62, 126, 
	  1, 65, 33, 97, 17, 81, 49, 113, 
	  9, 73, 41, 105, 25, 89, 57, 121, 
	  5, 69, 37, 101, 21, 85, 53, 117, 
	  13, 77, 45, 109, 29, 93, 61, 125, 
	  3, 67, 35, 99, 19, 83, 51, 115, 
	  11, 75, 43, 107, 27, 91, 59, 123, 
	  7, 71, 39, 103, 23, 87, 55, 119, 
	  15, 79, 47, 111, 31, 95, 63, 127
	};

	const uint16_t beta[7] = {2522, 7827, 7801, 8035, 6897, 8167, 3476};

	//

	for (i = 0; i < 7; i++)
	{
		for (j = 0; j < GFBITS; j++)
		{
			pre[i][j] = (beta[i] >> j) & 1; 
			pre[i][j] = -pre[i][j];
		}

		vec_mul(pre[i], in[1], pre[i]);
	}

	for (i = 0; i < GFBITS; i++)
	{
		buf[0] = in[0][i];             

		buf[1] = buf[0] ^ pre[0][i];      buf[32] = in[0][i] ^ pre[5][i];
		buf[3] = buf[1] ^ pre[1][i];      buf[96] = buf[32] ^ pre[6][i];
                                              buf[97] = buf[96] ^ pre[0][i];
		buf[2] = in[0][i] ^ pre[1][i];  buf[99] = buf[97] ^ pre[1][i];
		buf[6] = buf[2] ^ pre[2][i];      buf[98] = buf[99] ^ pre[0][i];
		buf[7] = buf[6] ^ pre[0][i];      buf[102] = buf[98] ^ pre[2][i];
		buf[5] = buf[7] ^ pre[1][i];      buf[103] = buf[102] ^ pre[0][i];
                                              buf[101] = buf[103] ^ pre[1][i];
		buf[4] = in[0][i] ^ pre[2][i];  buf[100] = buf[101] ^ pre[0][i];
		buf[12] = buf[4] ^ pre[3][i];     buf[108] = buf[100] ^ pre[3][i];
		buf[13] = buf[12] ^ pre[0][i];    buf[109] = buf[108] ^ pre[0][i];
		buf[15] = buf[13] ^ pre[1][i];    buf[111] = buf[109] ^ pre[1][i];
		buf[14] = buf[15] ^ pre[0][i];    buf[110] = buf[111] ^ pre[0][i];
		buf[10] = buf[14] ^ pre[2][i];    buf[106] = buf[110] ^ pre[2][i];
		buf[11] = buf[10] ^ pre[0][i];    buf[107] = buf[106] ^ pre[0][i];
		buf[9] = buf[11] ^ pre[1][i];     buf[105] = buf[107] ^ pre[1][i];
                                              buf[104] = buf[105] ^ pre[0][i];
		buf[8] = in[0][i] ^ pre[3][i];  buf[120] = buf[104] ^ pre[4][i];
		buf[24] = buf[8] ^ pre[4][i];     buf[121] = buf[120] ^ pre[0][i];
		buf[25] = buf[24] ^ pre[0][i];    buf[123] = buf[121] ^ pre[1][i];
		buf[27] = buf[25] ^ pre[1][i];    buf[122] = buf[123] ^ pre[0][i];
		buf[26] = buf[27] ^ pre[0][i];    buf[126] = buf[122] ^ pre[2][i];
		buf[30] = buf[26] ^ pre[2][i];    buf[127] = buf[126] ^ pre[0][i];
		buf[31] = buf[30] ^ pre[0][i];    buf[125] = buf[127] ^ pre[1][i];
		buf[29] = buf[31] ^ pre[1][i];    buf[124] = buf[125] ^ pre[0][i];
		buf[28] = buf[29] ^ pre[0][i];    buf[116] = buf[124] ^ pre[3][i];
		buf[20] = buf[28] ^ pre[3][i];    buf[117] = buf[116] ^ pre[0][i];
		buf[21] = buf[20] ^ pre[0][i];    buf[119] = buf[117] ^ pre[1][i];
		buf[23] = buf[21] ^ pre[1][i];    buf[118] = buf[119] ^ pre[0][i];
		buf[22] = buf[23] ^ pre[0][i];    buf[114] = buf[118] ^ pre[2][i];
		buf[18] = buf[22] ^ pre[2][i];    buf[115] = buf[114] ^ pre[0][i];
		buf[19] = buf[18] ^ pre[0][i];    buf[113] = buf[115] ^ pre[1][i];
		buf[17] = buf[19] ^ pre[1][i];    buf[112] = buf[113] ^ pre[0][i];
                                              buf[80] = buf[112] ^ pre[5][i];
		buf[16] = in[0][i] ^ pre[4][i]; buf[81] = buf[80] ^ pre[0][i];
		buf[48] = buf[16] ^ pre[5][i];    buf[83] = buf[81] ^ pre[1][i];
		buf[49] = buf[48] ^ pre[0][i];    buf[82] = buf[83] ^ pre[0][i];
		buf[51] = buf[49] ^ pre[1][i];    buf[86] = buf[82] ^ pre[2][i];
		buf[50] = buf[51] ^ pre[0][i];    buf[87] = buf[86] ^ pre[0][i];
		buf[54] = buf[50] ^ pre[2][i];    buf[85] = buf[87] ^ pre[1][i];
		buf[55] = buf[54] ^ pre[0][i];    buf[84] = buf[85] ^ pre[0][i];
		buf[53] = buf[55] ^ pre[1][i];    buf[92] = buf[84] ^ pre[3][i];
		buf[52] = buf[53] ^ pre[0][i];    buf[93] = buf[92] ^ pre[0][i];
		buf[60] = buf[52] ^ pre[3][i];    buf[95] = buf[93] ^ pre[1][i];
		buf[61] = buf[60] ^ pre[0][i];    buf[94] = buf[95] ^ pre[0][i];
		buf[63] = buf[61] ^ pre[1][i];    buf[90] = buf[94] ^ pre[2][i];
		buf[62] = buf[63] ^ pre[0][i];    buf[91] = buf[90] ^ pre[0][i];
		buf[58] = buf[62] ^ pre[2][i];    buf[89] = buf[91] ^ pre[1][i];
		buf[59] = buf[58] ^ pre[0][i];    buf[88] = buf[89] ^ pre[0][i];
		buf[57] = buf[59] ^ pre[1][i];    buf[72] = buf[88] ^ pre[4][i];
		buf[56] = buf[57] ^ pre[0][i];    buf[73] = buf[72] ^ pre[0][i];
		buf[40] = buf[56] ^ pre[4][i];    buf[75] = buf[73] ^ pre[1][i];
		buf[41] = buf[40] ^ pre[0][i];    buf[74] = buf[75] ^ pre[0][i];
		buf[43] = buf[41] ^ pre[1][i];    buf[78] = buf[74] ^ pre[2][i];
		buf[42] = buf[43] ^ pre[0][i];    buf[79] = buf[78] ^ pre[0][i];
		buf[46] = buf[42] ^ pre[2][i];    buf[77] = buf[79] ^ pre[1][i];
		buf[47] = buf[46] ^ pre[0][i];    buf[76] = buf[77] ^ pre[0][i];
		buf[45] = buf[47] ^ pre[1][i];    buf[68] = buf[76] ^ pre[3][i];
		buf[44] = buf[45] ^ pre[0][i];    buf[69] = buf[68] ^ pre[0][i];
		buf[36] = buf[44] ^ pre[3][i];    buf[71] = buf[69] ^ pre[1][i];
		buf[37] = buf[36] ^ pre[0][i];    buf[70] = buf[71] ^ pre[0][i];
		buf[39] = buf[37] ^ pre[1][i];    buf[66] = buf[70] ^ pre[2][i];
		buf[38] = buf[39] ^ pre[0][i];    buf[67] = buf[66] ^ pre[0][i];
		buf[34] = buf[38] ^ pre[2][i];    buf[65] = buf[67] ^ pre[1][i];
		buf[35] = buf[34] ^ pre[0][i];                                     
		buf[33] = buf[35] ^ pre[1][i];    buf[64] = in[0][i] ^ pre[6][i];

		transpose_64x64(buf +  0, buf +  0);
		transpose_64x64(buf + 64, buf + 64);
	
		for (j = 0; j < 128; j++)
			out[ reversal[j] ][i] = buf[j];
	}

	for (i = 1; i <= 6; i++)
	{
		s = 1 << i;

		for (j = 0; j < 128; j += 2*s)
		for (k = j; k < j+s; k++)
		{
			vec_mul(tmp, out[k+s], fft_consts[ consts_ptr + (k-j) ]);

			for (b = 0; b < GFBITS; b++) out[k  ][b] ^= tmp[b];
			for (b = 0; b < GFBITS; b++) out[k+s][b] ^= out[k][b];
		}

		consts_ptr += (1 << i);
	}

	// adding the part contributed by x^128
	
	for (i = 0; i < 128; i++)
	for (b = 0; b < GFBITS; b++) 
		out[i][b] ^= fft_powers[i][b];
}

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