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/* PROLOG END TAG zYx */
#ifndef _FFT_1D_R2_H_
#define _FFT_1D_R2_H_ 1
#include "fft_1d.h"
/* fft_1d_r2
* ---------
* Performs a single precision, complex Fast Fourier Transform using
* the DFT (Discrete Fourier Transform) with radix-2 decimation in time.
* The input <in> is an array of complex numbers of length (1<<log2_size)
* entries. The result is returned in the array of complex numbers specified
* by <out>. Note: This routine can support an in-place transformation
* by specifying <in> and <out> to be the same array.
*
* This implementation utilizes the Cooley-Tukey algorithm consisting
* of <log2_size> stages. The basic operation is the butterfly.
*
* p --------------------------> P = p + q*Wi
* \ /
* \ /
* \ /
* \/
* /\
* / \
* / \
* ____ / \
* q --| Wi |-----------------> Q = p - q*Wi
* ----
*
* This routine also requires pre-computed twiddle values, W. W is an
* array of single precision complex numbers of length 1<<(log2_size-2)
* and is computed as follows:
*
* for (i=0; i<n/4; i++)
* W[i].real = cos(i * 2*PI/n);
* W[i].imag = -sin(i * 2*PI/n);
* }
*
* This array actually only contains the first half of the twiddle
* factors. Due for symmetry, the second half of the twiddle factors
* are implied and equal:
*
* for (i=0; i<n/4; i++)
* W[i+n/4].real = W[i].imag = sin(i * 2*PI/n);
* W[i+n/4].imag = -W[i].real = -cos(i * 2*PI/n);
* }
*
* Further symmetry allows one to generate the twiddle factor table
* using half the number of trig computations as follows:
*
* W[0].real = 1.0;
* W[0].imag = 0.0;
* for (i=1; i<n/4; i++)
* W[i].real = cos(i * 2*PI/n);
* W[n/4 - i].imag = -W[i].real;
* }
*
* The complex numbers are packed into quadwords as follows:
*
* quadword complex
* array element array elements
* -----------------------------------------------------
* i | real 2*i | imag 2*i | real 2*i+1 | imag 2*i+1 |
* -----------------------------------------------------
*
*/
static __inline void _fft_1d_r2(vector float *out, vector float *in, vector float *W, int log2_size)
{
int i, j, k;
int stage, offset;
int i_rev;
int n, n_2, n_4, n_8, n_16, n_3_16;
int w_stride, w_2stride, w_3stride, w_4stride;
int stride, stride_2, stride_4, stride_3_4;
vector float *W0, *W1, *W2, *W3;
vector float *re0, *re1, *re2, *re3;
vector float *im0, *im1, *im2, *im3;
vector float *in0, *in1, *in2, *in3, *in4, *in5, *in6, *in7;
vector float *out0, *out1, *out2, *out3;
vector float tmp0, tmp1;
vector float w0_re, w0_im, w1_re, w1_im;
vector float w0, w1, w2, w3;
vector float src_lo0, src_lo1, src_lo2, src_lo3;
vector float src_hi0, src_hi1, src_hi2, src_hi3;
vector float dst_lo0, dst_lo1, dst_lo2, dst_lo3;
vector float dst_hi0, dst_hi1, dst_hi2, dst_hi3;
vector float out_re_lo0, out_re_lo1, out_re_lo2, out_re_lo3;
vector float out_im_lo0, out_im_lo1, out_im_lo2, out_im_lo3;
vector float out_re_hi0, out_re_hi1, out_re_hi2, out_re_hi3;
vector float out_im_hi0, out_im_hi1, out_im_hi2, out_im_hi3;
vector float re_lo0, re_lo1, re_lo2, re_lo3;
vector float im_lo0, im_lo1, im_lo2, im_lo3;
vector float re_hi0, re_hi1, re_hi2, re_hi3;
vector float im_hi0, im_hi1, im_hi2, im_hi3;
vector float pq_lo0, pq_lo1, pq_lo2, pq_lo3;
vector float pq_hi0, pq_hi1, pq_hi2, pq_hi3;
vector float re[MAX_FFT_1D_SIZE/4], im[MAX_FFT_1D_SIZE/4]; /* real & imaginary working arrays */
vector float ppmm = (vector float) { 1.0f, 1.0f, -1.0f, -1.0f};
vector float pmmp = (vector float) { 1.0f, -1.0f, -1.0f, 1.0f};
vector unsigned char reverse;
vector unsigned char shuf_lo = (vector unsigned char) {
0, 1, 2, 3, 4, 5, 6, 7,
16,17,18,19, 20,21,22,23};
vector unsigned char shuf_hi = (vector unsigned char) {
8, 9,10,11, 12,13,14,15,
24,25,26,27, 28,29,30,31};
vector unsigned char shuf_0202 = (vector unsigned char) {
0, 1, 2, 3, 8, 9,10,11,
0, 1, 2, 3, 8, 9,10,11};
vector unsigned char shuf_1313 = (vector unsigned char) {
4, 5, 6, 7, 12,13,14,15,
4, 5, 6, 7, 12,13,14,15};
vector unsigned char shuf_0303 = (vector unsigned char) {
0, 1, 2, 3, 12,13,14,15,
0, 1, 2, 3, 12,13,14,15};
vector unsigned char shuf_1212 = (vector unsigned char) {
4, 5, 6, 7, 8, 9,10,11,
4, 5, 6, 7, 8, 9,10,11};
vector unsigned char shuf_0415 = (vector unsigned char) {
0, 1, 2, 3, 16,17,18,19,
4, 5, 6, 7, 20,21,22,23};
vector unsigned char shuf_2637 = (vector unsigned char) {
8, 9,10,11, 24,25,26,27,
12,13,14,15,28,29,30,31};
vector unsigned char shuf_0246 = (vector unsigned char) {
0, 1, 2, 3, 8, 9,10,11,
16,17,18,19,24,25,26,27};
vector unsigned char shuf_1357 = (vector unsigned char) {
4, 5, 6, 7, 12,13,14,15,
20,21,22,23,28,29,30,31};
n = 1 << log2_size;
n_2 = n >> 1;
n_4 = n >> 2;
n_8 = n >> 3;
n_16 = n >> 4;
n_3_16 = n_8 + n_16;
/* Compute a byte reverse shuffle pattern to be used to produce
* an address bit swap.
*/
reverse = spu_or(spu_slqwbyte(spu_splats((unsigned char)0x80), log2_size),
spu_rlmaskqwbyte(((vec_uchar16){15,14,13,12, 11,10,9,8,
7, 6, 5, 4, 3, 2,1,0}),
log2_size-16));
/* Perform the first 3 stages of the FFT. These stages differs from
* other stages in that the inputs are unscrambled and the data is
* reformated into parallel arrays (ie, seperate real and imaginary
* arrays). The term "unscramble" means the bit address reverse the
* data array. In addition, the first three stages have simple twiddle
* weighting factors.
* stage 1: (1, 0)
* stage 2: (1, 0) and (0, -1)
* stage 3: (1, 0), (0.707, -0.707), (0, -1), (-0.707, -0.707)
*
* The arrays are processed as two halves, simultaneously. The lo (first
* half) and hi (second half). This is done because the scramble
* shares source value between each half of the output arrays.
*/
i = 0;
i_rev = 0;
in0 = in;
in1 = in + n_8;
in2 = in + n_16;
in3 = in + n_3_16;
in4 = in + n_4;
in5 = in1 + n_4;
in6 = in2 + n_4;
in7 = in3 + n_4;
re0 = re;
re1 = re + n_8;
im0 = im;
im1 = im + n_8;
w0_re = (vector float) { 1.0f, INV_SQRT_2, 0.0f, -INV_SQRT_2};
w0_im = (vector float) { 0.0f, -INV_SQRT_2, -1.0f, -INV_SQRT_2};
do {
src_lo0 = in0[i_rev];
src_lo1 = in1[i_rev];
src_lo2 = in2[i_rev];
src_lo3 = in3[i_rev];
src_hi0 = in4[i_rev];
src_hi1 = in5[i_rev];
src_hi2 = in6[i_rev];
src_hi3 = in7[i_rev];
/* Perform scramble.
*/
dst_lo0 = spu_shuffle(src_lo0, src_hi0, shuf_lo);
dst_hi0 = spu_shuffle(src_lo0, src_hi0, shuf_hi);
dst_lo1 = spu_shuffle(src_lo1, src_hi1, shuf_lo);
dst_hi1 = spu_shuffle(src_lo1, src_hi1, shuf_hi);
dst_lo2 = spu_shuffle(src_lo2, src_hi2, shuf_lo);
dst_hi2 = spu_shuffle(src_lo2, src_hi2, shuf_hi);
dst_lo3 = spu_shuffle(src_lo3, src_hi3, shuf_lo);
dst_hi3 = spu_shuffle(src_lo3, src_hi3, shuf_hi);
/* Perform the stage 1 butterfly. The multiplier constant, ppmm,
* is used to control the sign of the operands since a single
* quadword contains both of P and Q valule of the butterfly.
*/
pq_lo0 = spu_madd(ppmm, dst_lo0, spu_rlqwbyte(dst_lo0, 8));
pq_hi0 = spu_madd(ppmm, dst_hi0, spu_rlqwbyte(dst_hi0, 8));
pq_lo1 = spu_madd(ppmm, dst_lo1, spu_rlqwbyte(dst_lo1, 8));
pq_hi1 = spu_madd(ppmm, dst_hi1, spu_rlqwbyte(dst_hi1, 8));
pq_lo2 = spu_madd(ppmm, dst_lo2, spu_rlqwbyte(dst_lo2, 8));
pq_hi2 = spu_madd(ppmm, dst_hi2, spu_rlqwbyte(dst_hi2, 8));
pq_lo3 = spu_madd(ppmm, dst_lo3, spu_rlqwbyte(dst_lo3, 8));
pq_hi3 = spu_madd(ppmm, dst_hi3, spu_rlqwbyte(dst_hi3, 8));
/* Perfrom the stage 2 butterfly. For this stage, the
* inputs pq are still interleaved (p.real, p.imag, q.real,
* q.imag), so we must first re-order the data into
* parallel arrays as well as perform the reorder
* associated with the twiddle W[n/4], which equals
* (0, -1).
*
* ie. (A, B) * (0, -1) => (B, -A)
*/
re_lo0 = spu_madd(ppmm,
spu_shuffle(pq_lo1, pq_lo1, shuf_0303),
spu_shuffle(pq_lo0, pq_lo0, shuf_0202));
im_lo0 = spu_madd(pmmp,
spu_shuffle(pq_lo1, pq_lo1, shuf_1212),
spu_shuffle(pq_lo0, pq_lo0, shuf_1313));
re_lo1 = spu_madd(ppmm,
spu_shuffle(pq_lo3, pq_lo3, shuf_0303),
spu_shuffle(pq_lo2, pq_lo2, shuf_0202));
im_lo1 = spu_madd(pmmp,
spu_shuffle(pq_lo3, pq_lo3, shuf_1212),
spu_shuffle(pq_lo2, pq_lo2, shuf_1313));
re_hi0 = spu_madd(ppmm,
spu_shuffle(pq_hi1, pq_hi1, shuf_0303),
spu_shuffle(pq_hi0, pq_hi0, shuf_0202));
im_hi0 = spu_madd(pmmp,
spu_shuffle(pq_hi1, pq_hi1, shuf_1212),
spu_shuffle(pq_hi0, pq_hi0, shuf_1313));
re_hi1 = spu_madd(ppmm,
spu_shuffle(pq_hi3, pq_hi3, shuf_0303),
spu_shuffle(pq_hi2, pq_hi2, shuf_0202));
im_hi1 = spu_madd(pmmp,
spu_shuffle(pq_hi3, pq_hi3, shuf_1212),
spu_shuffle(pq_hi2, pq_hi2, shuf_1313));
/* Perform stage 3 butterfly.
*/
FFT_1D_BUTTERFLY(re0[0], im0[0], re0[1], im0[1], re_lo0, im_lo0, re_lo1, im_lo1, w0_re, w0_im);
FFT_1D_BUTTERFLY(re1[0], im1[0], re1[1], im1[1], re_hi0, im_hi0, re_hi1, im_hi1, w0_re, w0_im);
re0 += 2;
re1 += 2;
im0 += 2;
im1 += 2;
i += 8;
i_rev = BIT_SWAP(i, reverse) / 2;
} while (i < n_2);
/* Process stages 4 to log2_size-2
*/
for (stage=4, stride=4; stage<log2_size-1; stage++, stride += stride) {
w_stride = n_2 >> stage;
w_2stride = n >> stage;
w_3stride = w_stride + w_2stride;
w_4stride = w_2stride + w_2stride;
W0 = W;
W1 = W + w_stride;
W2 = W + w_2stride;
W3 = W + w_3stride;
stride_2 = stride >> 1;
stride_4 = stride >> 2;
stride_3_4 = stride_2 + stride_4;
re0 = re; im0 = im;
re1 = re + stride_2; im1 = im + stride_2;
re2 = re + stride_4; im2 = im + stride_4;
re3 = re + stride_3_4; im3 = im + stride_3_4;
for (i=0, offset=0; i<stride_4; i++, offset += w_4stride) {
/* Compute the twiddle factors
*/
w0 = W0[offset];
w1 = W1[offset];
w2 = W2[offset];
w3 = W3[offset];
tmp0 = spu_shuffle(w0, w2, shuf_0415);
tmp1 = spu_shuffle(w1, w3, shuf_0415);
w0_re = spu_shuffle(tmp0, tmp1, shuf_0415);
w0_im = spu_shuffle(tmp0, tmp1, shuf_2637);
j = i;
k = i + stride;
do {
re_lo0 = re0[j]; im_lo0 = im0[j];
re_lo1 = re1[j]; im_lo1 = im1[j];
re_hi0 = re2[j]; im_hi0 = im2[j];
re_hi1 = re3[j]; im_hi1 = im3[j];
re_lo2 = re0[k]; im_lo2 = im0[k];
re_lo3 = re1[k]; im_lo3 = im1[k];
re_hi2 = re2[k]; im_hi2 = im2[k];
re_hi3 = re3[k]; im_hi3 = im3[k];
FFT_1D_BUTTERFLY (re0[j], im0[j], re1[j], im1[j], re_lo0, im_lo0, re_lo1, im_lo1, w0_re, w0_im);
FFT_1D_BUTTERFLY_HI(re2[j], im2[j], re3[j], im3[j], re_hi0, im_hi0, re_hi1, im_hi1, w0_re, w0_im);
FFT_1D_BUTTERFLY (re0[k], im0[k], re1[k], im1[k], re_lo2, im_lo2, re_lo3, im_lo3, w0_re, w0_im);
FFT_1D_BUTTERFLY_HI(re2[k], im2[k], re3[k], im3[k], re_hi2, im_hi2, re_hi3, im_hi3, w0_re, w0_im);
j += 2 * stride;
k += 2 * stride;
} while (j < n_4);
}
}
/* Process stage log2_size-1. This is identical to the stage processing above
* except for this stage the inner loop is only executed once so it is removed
* entirely.
*/
w_stride = n_2 >> stage;
w_2stride = n >> stage;
w_3stride = w_stride + w_2stride;
w_4stride = w_2stride + w_2stride;
stride_2 = stride >> 1;
stride_4 = stride >> 2;
stride_3_4 = stride_2 + stride_4;
re0 = re; im0 = im;
re1 = re + stride_2; im1 = im + stride_2;
re2 = re + stride_4; im2 = im + stride_4;
re3 = re + stride_3_4; im3 = im + stride_3_4;
for (i=0, offset=0; i<stride_4; i++, offset += w_4stride) {
/* Compute the twiddle factors
*/
w0 = W[offset];
w1 = W[offset + w_stride];
w2 = W[offset + w_2stride];
w3 = W[offset + w_3stride];
tmp0 = spu_shuffle(w0, w2, shuf_0415);
tmp1 = spu_shuffle(w1, w3, shuf_0415);
w0_re = spu_shuffle(tmp0, tmp1, shuf_0415);
w0_im = spu_shuffle(tmp0, tmp1, shuf_2637);
j = i;
k = i + stride;
re_lo0 = re0[j]; im_lo0 = im0[j];
re_lo1 = re1[j]; im_lo1 = im1[j];
re_hi0 = re2[j]; im_hi0 = im2[j];
re_hi1 = re3[j]; im_hi1 = im3[j];
re_lo2 = re0[k]; im_lo2 = im0[k];
re_lo3 = re1[k]; im_lo3 = im1[k];
re_hi2 = re2[k]; im_hi2 = im2[k];
re_hi3 = re3[k]; im_hi3 = im3[k];
FFT_1D_BUTTERFLY (re0[j], im0[j], re1[j], im1[j], re_lo0, im_lo0, re_lo1, im_lo1, w0_re, w0_im);
FFT_1D_BUTTERFLY_HI(re2[j], im2[j], re3[j], im3[j], re_hi0, im_hi0, re_hi1, im_hi1, w0_re, w0_im);
FFT_1D_BUTTERFLY (re0[k], im0[k], re1[k], im1[k], re_lo2, im_lo2, re_lo3, im_lo3, w0_re, w0_im);
FFT_1D_BUTTERFLY_HI(re2[k], im2[k], re3[k], im3[k], re_hi2, im_hi2, re_hi3, im_hi3, w0_re, w0_im);
}
/* Process the final stage (stage log2_size). For this stage,
* reformat the data from parallel arrays back into
* interleaved arrays,storing the result into <in>.
*
* This loop has been manually unrolled by 2 to improve
* dual issue rates and reduce stalls. This unrolling
* forces a minimum FFT size of 32.
*/
re0 = re;
re1 = re + n_8;
re2 = re + n_16;
re3 = re + n_3_16;
im0 = im;
im1 = im + n_8;
im2 = im + n_16;
im3 = im + n_3_16;
out0 = out;
out1 = out + n_4;
out2 = out + n_8;
out3 = out1 + n_8;
i = n_16;
do {
/* Fetch the twiddle factors
*/
w0 = W[0];
w1 = W[1];
w2 = W[2];
w3 = W[3];
W += 4;
w0_re = spu_shuffle(w0, w1, shuf_0246);
w0_im = spu_shuffle(w0, w1, shuf_1357);
w1_re = spu_shuffle(w2, w3, shuf_0246);
w1_im = spu_shuffle(w2, w3, shuf_1357);
/* Fetch the butterfly inputs, reals and imaginaries
*/
re_lo0 = re0[0]; im_lo0 = im0[0];
re_lo1 = re1[0]; im_lo1 = im1[0];
re_lo2 = re0[1]; im_lo2 = im0[1];
re_lo3 = re1[1]; im_lo3 = im1[1];
re_hi0 = re2[0]; im_hi0 = im2[0];
re_hi1 = re3[0]; im_hi1 = im3[0];
re_hi2 = re2[1]; im_hi2 = im2[1];
re_hi3 = re3[1]; im_hi3 = im3[1];
re0 += 2; im0 += 2;
re1 += 2; im1 += 2;
re2 += 2; im2 += 2;
re3 += 2; im3 += 2;
/* Perform the butterflys
*/
FFT_1D_BUTTERFLY (out_re_lo0, out_im_lo0, out_re_lo1, out_im_lo1, re_lo0, im_lo0, re_lo1, im_lo1, w0_re, w0_im);
FFT_1D_BUTTERFLY (out_re_lo2, out_im_lo2, out_re_lo3, out_im_lo3, re_lo2, im_lo2, re_lo3, im_lo3, w1_re, w1_im);
FFT_1D_BUTTERFLY_HI(out_re_hi0, out_im_hi0, out_re_hi1, out_im_hi1, re_hi0, im_hi0, re_hi1, im_hi1, w0_re, w0_im);
FFT_1D_BUTTERFLY_HI(out_re_hi2, out_im_hi2, out_re_hi3, out_im_hi3, re_hi2, im_hi2, re_hi3, im_hi3, w1_re, w1_im);
/* Interleave the results and store them into the output buffers (ie,
* the original input buffers.
*/
out0[0] = spu_shuffle(out_re_lo0, out_im_lo0, shuf_0415);
out0[1] = spu_shuffle(out_re_lo0, out_im_lo0, shuf_2637);
out0[2] = spu_shuffle(out_re_lo2, out_im_lo2, shuf_0415);
out0[3] = spu_shuffle(out_re_lo2, out_im_lo2, shuf_2637);
out1[0] = spu_shuffle(out_re_lo1, out_im_lo1, shuf_0415);
out1[1] = spu_shuffle(out_re_lo1, out_im_lo1, shuf_2637);
out1[2] = spu_shuffle(out_re_lo3, out_im_lo3, shuf_0415);
out1[3] = spu_shuffle(out_re_lo3, out_im_lo3, shuf_2637);
out2[0] = spu_shuffle(out_re_hi0, out_im_hi0, shuf_0415);
out2[1] = spu_shuffle(out_re_hi0, out_im_hi0, shuf_2637);
out2[2] = spu_shuffle(out_re_hi2, out_im_hi2, shuf_0415);
out2[3] = spu_shuffle(out_re_hi2, out_im_hi2, shuf_2637);
out3[0] = spu_shuffle(out_re_hi1, out_im_hi1, shuf_0415);
out3[1] = spu_shuffle(out_re_hi1, out_im_hi1, shuf_2637);
out3[2] = spu_shuffle(out_re_hi3, out_im_hi3, shuf_0415);
out3[3] = spu_shuffle(out_re_hi3, out_im_hi3, shuf_2637);
out0 += 4;
out1 += 4;
out2 += 4;
out3 += 4;
i -= 2;
} while (i);
}
#endif /* _FFT_1D_R2_H_ */