void fft64_2way( void *a )
{
__m256i* const A = a;
register __m256i X0, X1, X2, X3, X4, X5, X6, X7;
#define X(i) X##i
X0 = A[0];
X1 = A[1];
X2 = A[2];
X3 = A[3];
X4 = A[4];
X5 = A[5];
X6 = A[6];
X7 = A[7];
#define DO_REDUCE(i) X(i) = REDUCE( X(i) )
// Begin with 8 parallels DIF FFT_8
//
// FFT_8 using w=4 as 8th root of unity
// Unrolled decimation in frequency (DIF) radix-2 NTT.
// Output data is in revbin_permuted order.
static const int w[] = {0, 2, 4, 6};
// __m256i *Twiddle = (__m256i*)FFT64_Twiddle;
#define BUTTERFLY_0( i,j ) \
do { \
__m256i v = X(j); \
X(j) = _mm256_add_epi16( X(i), X(j) ); \
X(i) = _mm256_sub_epi16( X(i), v ); \
} while(0)
#define BUTTERFLY_N( i,j,n ) \
do { \
__m256i v = X(j); \
X(j) = _mm256_add_epi16( X(i), X(j) ); \
X(i) = _mm256_slli_epi16( _mm256_sub_epi16( X(i), v ), w[n] ); \
} while(0)
BUTTERFLY_0( 0, 4 );
BUTTERFLY_N( 1, 5, 1 );
BUTTERFLY_N( 2, 6, 2 );
BUTTERFLY_N( 3, 7, 3 );
DO_REDUCE( 2 );
DO_REDUCE( 3 );
BUTTERFLY_0( 0, 2 );
BUTTERFLY_0( 4, 6 );
BUTTERFLY_N( 1, 3, 2 );
BUTTERFLY_N( 5, 7, 2 );
DO_REDUCE( 1 );
BUTTERFLY_0( 0, 1 );
BUTTERFLY_0( 2, 3 );
BUTTERFLY_0( 4, 5 );
BUTTERFLY_0( 6, 7 );
/* We don't need to reduce X(7) */
DO_REDUCE_FULL_S( 0 );
DO_REDUCE_FULL_S( 1 );
DO_REDUCE_FULL_S( 2 );
DO_REDUCE_FULL_S( 3 );
DO_REDUCE_FULL_S( 4 );
DO_REDUCE_FULL_S( 5 );
DO_REDUCE_FULL_S( 6 );
#undef BUTTERFLY_0
#undef BUTTERFLY_N
// Multiply by twiddle factors
X(6) = _mm256_mullo_epi16( X(6), FFT64_Twiddle[0].m256i );
X(5) = _mm256_mullo_epi16( X(5), FFT64_Twiddle[1].m256i );
X(4) = _mm256_mullo_epi16( X(4), FFT64_Twiddle[2].m256i );
X(3) = _mm256_mullo_epi16( X(3), FFT64_Twiddle[3].m256i );
X(2) = _mm256_mullo_epi16( X(2), FFT64_Twiddle[4].m256i );
X(1) = _mm256_mullo_epi16( X(1), FFT64_Twiddle[5].m256i );
X(0) = _mm256_mullo_epi16( X(0), FFT64_Twiddle[6].m256i );
// Transpose the FFT state with a revbin order permutation
// on the rows and the column.
// This will make the full FFT_64 in order.
#define INTERLEAVE(i,j) \
do { \
__m256i t1= X(i); \
__m256i t2= X(j); \
X(i) = _mm256_unpacklo_epi16( t1, t2 ); \
X(j) = _mm256_unpackhi_epi16( t1, t2 ); \
} while(0)
INTERLEAVE( 1, 0 );
INTERLEAVE( 3, 2 );
INTERLEAVE( 5, 4 );
INTERLEAVE( 7, 6 );
INTERLEAVE( 2, 0 );
INTERLEAVE( 3, 1 );
INTERLEAVE( 6, 4 );
INTERLEAVE( 7, 5 );
INTERLEAVE( 4, 0 );
INTERLEAVE( 5, 1 );
INTERLEAVE( 6, 2 );
INTERLEAVE( 7, 3 );
#undef INTERLEAVE
//Finish with 8 parallels DIT FFT_8
//FFT_8 using w=4 as 8th root of unity
// Unrolled decimation in time (DIT) radix-2 NTT.
// Input data is in revbin_permuted order.
#define BUTTERFLY_0( i,j ) \
do { \
__m256i u = X(j); \
X(j) = _mm256_sub_epi16( X(j), X(i) ); \
X(i) = _mm256_add_epi16( u, X(i) ); \
} while(0)
#define BUTTERFLY_N( i,j,n ) \
do { \
__m256i u = X(j); \
X(i) = _mm256_slli_epi16( X(i), w[n] ); \
X(j) = _mm256_sub_epi16( X(j), X(i) ); \
X(i) = _mm256_add_epi16( u, X(i) ); \
} while(0)
DO_REDUCE( 0 );
DO_REDUCE( 1 );
DO_REDUCE( 2 );
DO_REDUCE( 3 );
DO_REDUCE( 4 );
DO_REDUCE( 5 );
DO_REDUCE( 6 );
DO_REDUCE( 7 );
BUTTERFLY_0( 0, 1 );
BUTTERFLY_0( 2, 3 );
BUTTERFLY_0( 4, 5 );
BUTTERFLY_0( 6, 7 );
BUTTERFLY_0( 0, 2 );
BUTTERFLY_0( 4, 6 );
BUTTERFLY_N( 1, 3, 2 );
BUTTERFLY_N( 5, 7, 2 );
DO_REDUCE( 3 );
BUTTERFLY_0( 0, 4 );
BUTTERFLY_N( 1, 5, 1 );
BUTTERFLY_N( 2, 6, 2 );
BUTTERFLY_N( 3, 7, 3 );
DO_REDUCE_FULL_S( 0 );
DO_REDUCE_FULL_S( 1 );
DO_REDUCE_FULL_S( 2 );
DO_REDUCE_FULL_S( 3 );
DO_REDUCE_FULL_S( 4 );
DO_REDUCE_FULL_S( 5 );
DO_REDUCE_FULL_S( 6 );
DO_REDUCE_FULL_S( 7 );
#undef BUTTERFLY
A[0] = X0;
A[1] = X1;
A[2] = X2;
A[3] = X3;
A[4] = X4;
A[5] = X5;
A[6] = X6;
A[7] = X7;
#undef X
}
void fft64(void *a) {
v16* const A = a;
register v16 X0, X1, X2, X3, X4, X5, X6, X7;
#define X(i) X##i
X0 = A[0];
X1 = A[1];
X2 = A[2];
X3 = A[3];
X4 = A[4];
X5 = A[5];
X6 = A[6];
X7 = A[7];
#define DO_REDUCE(i) \
X(i) = REDUCE(X(i))
/*
* Begin with 8 parallels DIF FFT_8
*
* FFT_8 using w=4 as 8th root of unity
* Unrolled decimation in frequency (DIF) radix-2 NTT.
* Output data is in revbin_permuted order.
*/
#define wn0 0
#define wn1 2
#define wn2 4
#define wn3 6
#define BUTTERFLY(i,j,n) \
do { \
v16 u= X(i); \
v16 v= X(j); \
X(i) = v16_add(u, v); \
if (n) \
X(j) = v16_shift_l(v16_sub(u, v), XCAT(wn,n)); \
else \
X(j) = v16_sub(u, v); \
} while(0)
BUTTERFLY(0, 4, 0);
BUTTERFLY(1, 5, 1);
BUTTERFLY(2, 6, 2);
BUTTERFLY(3, 7, 3);
DO_REDUCE(5);
DO_REDUCE(6);
DO_REDUCE(7);
BUTTERFLY(0, 2, 0);
BUTTERFLY(4, 6, 0);
BUTTERFLY(1, 3, 2);
BUTTERFLY(5, 7, 2);
BUTTERFLY(0, 1, 0);
BUTTERFLY(2, 3, 0);
BUTTERFLY(4, 5, 0);
BUTTERFLY(6, 7, 0);
/* We don't need to reduce X(0) */
DO_REDUCE_FULL_S(1);
DO_REDUCE_FULL_S(2);
DO_REDUCE_FULL_S(3);
DO_REDUCE_FULL_S(4);
DO_REDUCE_FULL_S(5);
DO_REDUCE_FULL_S(6);
DO_REDUCE_FULL_S(7);
#undef BUTTERFLY
/*
* Multiply by twiddle factors
*/
X(1) = v16_mul(X(1), FFT64_Twiddle[0].v16);
X(2) = v16_mul(X(2), FFT64_Twiddle[1].v16);
X(3) = v16_mul(X(3), FFT64_Twiddle[2].v16);
X(4) = v16_mul(X(4), FFT64_Twiddle[3].v16);
X(5) = v16_mul(X(5), FFT64_Twiddle[4].v16);
X(6) = v16_mul(X(6), FFT64_Twiddle[5].v16);
X(7) = v16_mul(X(7), FFT64_Twiddle[6].v16);
/*
* Transpose the FFT state with a revbin order permutation
* on the rows and the column.
* This will make the full FFT_64 in order.
*/
#ifdef v16_interleave_inplace
#define INTERLEAVE(i,j) v16_interleave_inplace(X(i), X(j))
#else
#define INTERLEAVE(i,j) \
do { \
v16 t1= X(i); \
v16 t2= X(j); \
X(i) = v16_interleavel(t1, t2); \
X(j) = v16_interleaveh(t1, t2); \
} while(0)
#endif
INTERLEAVE(0, 1);
INTERLEAVE(2, 3);
INTERLEAVE(4, 5);
INTERLEAVE(6, 7);
INTERLEAVE(0, 2);
INTERLEAVE(1, 3);
INTERLEAVE(4, 6);
INTERLEAVE(5, 7);
INTERLEAVE(0, 4);
INTERLEAVE(1, 5);
INTERLEAVE(2, 6);
INTERLEAVE(3, 7);
#undef INTERLEAVE
/*
* Finish with 8 parallels DIT FFT_8
*
* FFT_8 using w=4 as 8th root of unity
* Unrolled decimation in time (DIT) radix-2 NTT.
* Intput data is in revbin_permuted order.
*/
#define BUTTERFLY(i,j,n) \
do { \
v16 u= X(i); \
v16 v= X(j); \
if (n) \
v = v16_shift_l(v, XCAT(wn,n)); \
X(i) = v16_add(u, v); \
X(j) = v16_sub(u, v); \
} while(0)
DO_REDUCE(0);
DO_REDUCE(1);
DO_REDUCE(2);
DO_REDUCE(3);
DO_REDUCE(4);
DO_REDUCE(5);
DO_REDUCE(6);
DO_REDUCE(7);
BUTTERFLY(0, 1, 0);
BUTTERFLY(2, 3, 0);
BUTTERFLY(4, 5, 0);
BUTTERFLY(6, 7, 0);
BUTTERFLY(0, 2, 0);
BUTTERFLY(4, 6, 0);
BUTTERFLY(1, 3, 2);
BUTTERFLY(5, 7, 2);
DO_REDUCE(7);
BUTTERFLY(0, 4, 0);
BUTTERFLY(1, 5, 1);
BUTTERFLY(2, 6, 2);
BUTTERFLY(3, 7, 3);
DO_REDUCE_FULL_S(0);
DO_REDUCE_FULL_S(1);
DO_REDUCE_FULL_S(2);
DO_REDUCE_FULL_S(3);
DO_REDUCE_FULL_S(4);
DO_REDUCE_FULL_S(5);
DO_REDUCE_FULL_S(6);
DO_REDUCE_FULL_S(7);
#undef BUTTERFLY
A[0] = X0;
A[1] = X1;
A[2] = X2;
A[3] = X3;
A[4] = X4;
A[5] = X5;
A[6] = X6;
A[7] = X7;
#undef X
}