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webrtc/modules/audio_processing/aec/main/source/aec_rdft.c
cduvivier@google.com 20cb6b684b Optimization of 'rftfsub': 
* scalar optimization, vectorization (including new file for SSE2 code
  and path selection mechanism).
* 0.5% AEC overall speedup for the straight C path.
* 3.0% AEC overall speedup for the SSE2 path.
Review URL: http://webrtc-codereview.appspot.com/46005

git-svn-id: http://webrtc.googlecode.com/svn/trunk@134 4adac7df-926f-26a2-2b94-8c16560cd09d
2011-06-30 01:22:19 +00:00

521 lines
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/*
* http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
* Copyright Takuya OOURA, 1996-2001
*
* You may use, copy, modify and distribute this code for any purpose (include
* commercial use) and without fee. Please refer to this package when you modify
* this code.
*
* Changes by the WebRTC authors:
* - Trivial type modifications.
* - Minimal code subset to do rdft of length 128.
* - Optimizations because of known length.
*
* All changes are covered by the WebRTC license and IP grant:
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be found
* in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
#include <math.h>
#include "aec_rdft.h"
#include "system_wrappers/interface/cpu_features_wrapper.h"
static void bitrv2_32or128(int n, int *ip, float *a) {
// n is 32 or 128
int j, j1, k, k1, m, m2;
float xr, xi, yr, yi;
ip[0] = 0;
{
int l = n;
m = 1;
while ((m << 3) < l) {
l >>= 1;
for (j = 0; j < m; j++) {
ip[m + j] = ip[j] + l;
}
m <<= 1;
}
}
m2 = 2 * m;
for (k = 0; k < m; k++) {
for (j = 0; j < k; j++) {
j1 = 2 * j + ip[k];
k1 = 2 * k + ip[j];
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += m2;
k1 += 2 * m2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += m2;
k1 -= m2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += m2;
k1 += 2 * m2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
j1 = 2 * k + m2 + ip[k];
k1 = j1 + m2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
}
static void makewt(int *ip, float *w) {
const int nw = 32;
int j, nwh;
float delta, x, y;
ip[0] = nw;
ip[1] = 1;
nwh = nw >> 1;
delta = atanf(1.0f) / nwh;
w[0] = 1;
w[1] = 0;
w[nwh] = cosf(delta * nwh);
w[nwh + 1] = w[nwh];
for (j = 2; j < nwh; j += 2) {
x = cosf(delta * j);
y = sinf(delta * j);
w[j] = x;
w[j + 1] = y;
w[nw - j] = y;
w[nw - j + 1] = x;
}
bitrv2_32or128(nw, ip + 2, w);
}
static void makect_32(int *ip, float *c) {
const int nc = 32;
int j, nch;
float delta;
ip[1] = nc;
nch = nc >> 1;
delta = atanf(1.0f) / nch;
c[0] = cosf(delta * nch);
c[nch] = 0.5f * c[0];
for (j = 1; j < nch; j++) {
c[j] = 0.5f * cosf(delta * j);
c[nc - j] = 0.5f * sinf(delta * j);
}
}
static void cft1st_128(float *a, float *w) {
const int n = 128;
int j, k1, k2;
float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
x0r = a[0] + a[2];
x0i = a[1] + a[3];
x1r = a[0] - a[2];
x1i = a[1] - a[3];
x2r = a[4] + a[6];
x2i = a[5] + a[7];
x3r = a[4] - a[6];
x3i = a[5] - a[7];
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[4] = x0r - x2r;
a[5] = x0i - x2i;
a[2] = x1r - x3i;
a[3] = x1i + x3r;
a[6] = x1r + x3i;
a[7] = x1i - x3r;
wk1r = w[2];
x0r = a[8] + a[10];
x0i = a[9] + a[11];
x1r = a[8] - a[10];
x1i = a[9] - a[11];
x2r = a[12] + a[14];
x2i = a[13] + a[15];
x3r = a[12] - a[14];
x3i = a[13] - a[15];
a[8] = x0r + x2r;
a[9] = x0i + x2i;
a[12] = x2i - x0i;
a[13] = x0r - x2r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[10] = wk1r * (x0r - x0i);
a[11] = wk1r * (x0r + x0i);
x0r = x3i + x1r;
x0i = x3r - x1i;
a[14] = wk1r * (x0i - x0r);
a[15] = wk1r * (x0i + x0r);
k1 = 0;
for (j = 16; j < n; j += 16) {
k1 += 2;
k2 = 2 * k1;
wk2r = w[k1];
wk2i = w[k1 + 1];
wk1r = w[k2];
wk1i = w[k2 + 1];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
x0r = a[j] + a[j + 2];
x0i = a[j + 1] + a[j + 3];
x1r = a[j] - a[j + 2];
x1i = a[j + 1] - a[j + 3];
x2r = a[j + 4] + a[j + 6];
x2i = a[j + 5] + a[j + 7];
x3r = a[j + 4] - a[j + 6];
x3i = a[j + 5] - a[j + 7];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j + 4] = wk2r * x0r - wk2i * x0i;
a[j + 5] = wk2r * x0i + wk2i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j + 2] = wk1r * x0r - wk1i * x0i;
a[j + 3] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j + 6] = wk3r * x0r - wk3i * x0i;
a[j + 7] = wk3r * x0i + wk3i * x0r;
wk1r = w[k2 + 2];
wk1i = w[k2 + 3];
wk3r = wk1r - 2 * wk2r * wk1i;
wk3i = 2 * wk2r * wk1r - wk1i;
x0r = a[j + 8] + a[j + 10];
x0i = a[j + 9] + a[j + 11];
x1r = a[j + 8] - a[j + 10];
x1i = a[j + 9] - a[j + 11];
x2r = a[j + 12] + a[j + 14];
x2i = a[j + 13] + a[j + 15];
x3r = a[j + 12] - a[j + 14];
x3i = a[j + 13] - a[j + 15];
a[j + 8] = x0r + x2r;
a[j + 9] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j + 12] = -wk2i * x0r - wk2r * x0i;
a[j + 13] = -wk2i * x0i + wk2r * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j + 10] = wk1r * x0r - wk1i * x0i;
a[j + 11] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j + 14] = wk3r * x0r - wk3i * x0i;
a[j + 15] = wk3r * x0i + wk3i * x0r;
}
}
static void cftmdl_128(int l, float *a, float *w) {
const int n = 128;
int j, j1, j2, j3, k, k1, k2, m, m2;
float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
m = l << 2;
for (j = 0; j < l; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = a[j + 1] + a[j1 + 1];
x1r = a[j] - a[j1];
x1i = a[j + 1] - a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
a[j2] = x0r - x2r;
a[j2 + 1] = x0i - x2i;
a[j1] = x1r - x3i;
a[j1 + 1] = x1i + x3r;
a[j3] = x1r + x3i;
a[j3 + 1] = x1i - x3r;
}
wk1r = w[2];
for (j = m; j < l + m; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = a[j + 1] + a[j1 + 1];
x1r = a[j] - a[j1];
x1i = a[j + 1] - a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
a[j2] = x2i - x0i;
a[j2 + 1] = x0r - x2r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j1] = wk1r * (x0r - x0i);
a[j1 + 1] = wk1r * (x0r + x0i);
x0r = x3i + x1r;
x0i = x3r - x1i;
a[j3] = wk1r * (x0i - x0r);
a[j3 + 1] = wk1r * (x0i + x0r);
}
k1 = 0;
m2 = 2 * m;
for (k = m2; k < n; k += m2) {
k1 += 2;
k2 = 2 * k1;
wk2r = w[k1];
wk2i = w[k1 + 1];
wk1r = w[k2];
wk1i = w[k2 + 1];
wk3r = wk1r - 2 * wk2i * wk1i;
wk3i = 2 * wk2i * wk1r - wk1i;
for (j = k; j < l + k; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = a[j + 1] + a[j1 + 1];
x1r = a[j] - a[j1];
x1i = a[j + 1] - a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j2] = wk2r * x0r - wk2i * x0i;
a[j2 + 1] = wk2r * x0i + wk2i * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j1] = wk1r * x0r - wk1i * x0i;
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3r * x0r - wk3i * x0i;
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
}
wk1r = w[k2 + 2];
wk1i = w[k2 + 3];
wk3r = wk1r - 2 * wk2r * wk1i;
wk3i = 2 * wk2r * wk1r - wk1i;
for (j = k + m; j < l + (k + m); j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = a[j + 1] + a[j1 + 1];
x1r = a[j] - a[j1];
x1i = a[j + 1] - a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
x0r -= x2r;
x0i -= x2i;
a[j2] = -wk2i * x0r - wk2r * x0i;
a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j1] = wk1r * x0r - wk1i * x0i;
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3r * x0r - wk3i * x0i;
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
}
}
}
static void cftfsub_128(float *a, float *w) {
int j, j1, j2, j3, l;
float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
cft1st_128(a, w);
cftmdl_128(8, a, w);
l = 32;
for (j = 0; j < l; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = a[j + 1] + a[j1 + 1];
x1r = a[j] - a[j1];
x1i = a[j + 1] - a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
a[j2] = x0r - x2r;
a[j2 + 1] = x0i - x2i;
a[j1] = x1r - x3i;
a[j1 + 1] = x1i + x3r;
a[j3] = x1r + x3i;
a[j3 + 1] = x1i - x3r;
}
}
static void cftbsub_128(float *a, float *w) {
int j, j1, j2, j3, l;
float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
cft1st_128(a, w);
cftmdl_128(8, a, w);
l = 32;
for (j = 0; j < l; j += 2) {
j1 = j + l;
j2 = j1 + l;
j3 = j2 + l;
x0r = a[j] + a[j1];
x0i = -a[j + 1] - a[j1 + 1];
x1r = a[j] - a[j1];
x1i = -a[j + 1] + a[j1 + 1];
x2r = a[j2] + a[j3];
x2i = a[j2 + 1] + a[j3 + 1];
x3r = a[j2] - a[j3];
x3i = a[j2 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i - x2i;
a[j2] = x0r - x2r;
a[j2 + 1] = x0i + x2i;
a[j1] = x1r - x3i;
a[j1 + 1] = x1i - x3r;
a[j3] = x1r + x3i;
a[j3 + 1] = x1i + x3r;
}
}
static void rftfsub_128_C(float *a, float *c) {
int j1, j2, k1, k2;
float wkr, wki, xr, xi, yr, yi;
for (j1 = 1, j2 = 2; j2 < 64; j1 += 1, j2 += 2) {
k2 = 128 - j2;
k1 = 32 - j1;
wkr = 0.5f - c[k1];
wki = c[j1];
xr = a[j2 + 0] - a[k2 + 0];
xi = a[j2 + 1] + a[k2 + 1];
yr = wkr * xr - wki * xi;
yi = wkr * xi + wki * xr;
a[j2 + 0] -= yr;
a[j2 + 1] -= yi;
a[k2 + 0] += yr;
a[k2 + 1] -= yi;
}
}
static void rftbsub_128(float *a, int nc, float *c) {
const int n = 128;
int j, k, kk, ks, m;
float wkr, wki, xr, xi, yr, yi;
a[1] = -a[1];
m = n >> 1;
ks = 2 * nc / m;
kk = 0;
for (j = 2; j < m; j += 2) {
k = n - j;
kk += ks;
wkr = 0.5f - c[nc - kk];
wki = c[kk];
xr = a[j] - a[k];
xi = a[j + 1] + a[k + 1];
yr = wkr * xr + wki * xi;
yi = wkr * xi - wki * xr;
a[j] -= yr;
a[j + 1] = yi - a[j + 1];
a[k] += yr;
a[k + 1] = yi - a[k + 1];
}
a[m + 1] = -a[m + 1];
}
void aec_rdft_128(int isgn, float *a, int *ip, float *w)
{
const int n = 128;
int nw, nc;
float xi;
nw = ip[0];
if (n > (nw << 2)) {
nw = n >> 2;
makewt(ip, w);
}
nc = ip[1];
if (n > (nc << 2)) {
nc = n >> 2;
makect_32(ip, w + nw);
}
if (isgn >= 0) {
bitrv2_32or128(n, ip + 2, a);
cftfsub_128(a, w);
rftfsub_128(a, w + nw);
xi = a[0] - a[1];
a[0] += a[1];
a[1] = xi;
} else {
a[1] = 0.5f * (a[0] - a[1]);
a[0] -= a[1];
rftbsub_128(a, nc, w + nw);
bitrv2_32or128(n, ip + 2, a);
cftbsub_128(a, w);
}
}
// code path selection
rftfsub_128_t rftfsub_128;
void aec_rdft_init(void) {
rftfsub_128 = rftfsub_128_C;
if (WebRtc_GetCPUInfo(kSSE2)) {
#if defined(__SSE2__)
aec_rdft_init_sse2();
#endif
}
}
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