/*
  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
// 20221230 djb: add linker lines

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

#include "fft.h"
#include "fft_scalars.h"
#include "fft_consts.h"
#include "fft_powers.h"
#include "vec.h"

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

	const uint64_t mask[5][2] = 
	{
		{0x8888888888888888, 0x4444444444444444},
		{0xC0C0C0C0C0C0C0C0, 0x3030303030303030},
		{0xF000F000F000F000, 0x0F000F000F000F00},
		{0xFF000000FF000000, 0x00FF000000FF0000},
		{0xFFFF000000000000, 0x0000FFFF00000000}
	};

	//

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

		vec_mul(in, in, fft_scalars[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(uint64_t out[][ GFBITS ], uint64_t *in)
{
	int i, j, k, s, b;

	uint64_t tmp[ GFBITS ];
	uint64_t consts_ptr = 0;

	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
	};

	// boradcast

	for (j = 0; j < 64; j++)
	for (i = 0; i < GFBITS; i++)
	{
			out[j][i] = (in[i] >> reversal[j]) & 1;
			out[j][i] = -out[j][i];
	}

	// butterflies

	for (i = 0; i <= 5; i++)
	{
		s = 1 << i;

		for (j = 0; j < 64; 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^64
	
	for (i = 0; i < 64; i++)
	for (b = 0; b < GFBITS; b++) 
		out[i][b] ^= fft_powers[i][b];
	
}

void fft(vec out[][ GFBITS ], vec *in)
{
		radix_conversions(in);
		butterflies(out, in);
}