+++ /dev/null
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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_ */
projects / debian / gnuradio / blobdiff