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/*
* Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
*
* 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.
*/
/*
* fft.c
*
* Fast Fourier Transform
*
*/
#include "fft.h"
const WebRtc_Word16 kSortTabFft[240] = {
0, 60, 120, 180, 20, 80, 140, 200, 40, 100, 160, 220,
4, 64, 124, 184, 24, 84, 144, 204, 44, 104, 164, 224,
8, 68, 128, 188, 28, 88, 148, 208, 48, 108, 168, 228,
12, 72, 132, 192, 32, 92, 152, 212, 52, 112, 172, 232,
16, 76, 136, 196, 36, 96, 156, 216, 56, 116, 176, 236,
1, 61, 121, 181, 21, 81, 141, 201, 41, 101, 161, 221,
5, 65, 125, 185, 25, 85, 145, 205, 45, 105, 165, 225,
9, 69, 129, 189, 29, 89, 149, 209, 49, 109, 169, 229,
13, 73, 133, 193, 33, 93, 153, 213, 53, 113, 173, 233,
17, 77, 137, 197, 37, 97, 157, 217, 57, 117, 177, 237,
2, 62, 122, 182, 22, 82, 142, 202, 42, 102, 162, 222,
6, 66, 126, 186, 26, 86, 146, 206, 46, 106, 166, 226,
10, 70, 130, 190, 30, 90, 150, 210, 50, 110, 170, 230,
14, 74, 134, 194, 34, 94, 154, 214, 54, 114, 174, 234,
18, 78, 138, 198, 38, 98, 158, 218, 58, 118, 178, 238,
3, 63, 123, 183, 23, 83, 143, 203, 43, 103, 163, 223,
7, 67, 127, 187, 27, 87, 147, 207, 47, 107, 167, 227,
11, 71, 131, 191, 31, 91, 151, 211, 51, 111, 171, 231,
15, 75, 135, 195, 35, 95, 155, 215, 55, 115, 175, 235,
19, 79, 139, 199, 39, 99, 159, 219, 59, 119, 179, 239
};
/* Cosine table in Q14 */
const WebRtc_Word16 kCosTabFfftQ14[240] = {
16384, 16378, 16362, 16333, 16294, 16244, 16182, 16110, 16026, 15931, 15826, 15709,
15582, 15444, 15296, 15137, 14968, 14788, 14598, 14399, 14189, 13970, 13741, 13502,
13255, 12998, 12733, 12458, 12176, 11885, 11585, 11278, 10963, 10641, 10311, 9974,
9630, 9280, 8923, 8561, 8192, 7818, 7438, 7053, 6664, 6270, 5872, 5469,
5063, 4653, 4240, 3825, 3406, 2986, 2563, 2139, 1713, 1285, 857, 429,
0, -429, -857, -1285, -1713, -2139, -2563, -2986, -3406, -3825, -4240, -4653,
-5063, -5469, -5872, -6270, -6664, -7053, -7438, -7818, -8192, -8561, -8923, -9280,
-9630, -9974, -10311, -10641, -10963, -11278, -11585, -11885, -12176, -12458, -12733, -12998,
-13255, -13502, -13741, -13970, -14189, -14399, -14598, -14788, -14968, -15137, -15296, -15444,
-15582, -15709, -15826, -15931, -16026, -16110, -16182, -16244, -16294, -16333, -16362, -16378,
-16384, -16378, -16362, -16333, -16294, -16244, -16182, -16110, -16026, -15931, -15826, -15709,
-15582, -15444, -15296, -15137, -14968, -14788, -14598, -14399, -14189, -13970, -13741, -13502,
-13255, -12998, -12733, -12458, -12176, -11885, -11585, -11278, -10963, -10641, -10311, -9974,
-9630, -9280, -8923, -8561, -8192, -7818, -7438, -7053, -6664, -6270, -5872, -5469,
-5063, -4653, -4240, -3825, -3406, -2986, -2563, -2139, -1713, -1285, -857, -429,
0, 429, 857, 1285, 1713, 2139, 2563, 2986, 3406, 3825, 4240, 4653,
5063, 5469, 5872, 6270, 6664, 7053, 7438, 7818, 8192, 8561, 8923, 9280,
9630, 9974, 10311, 10641, 10963, 11278, 11585, 11885, 12176, 12458, 12733, 12998,
13255, 13502, 13741, 13970, 14189, 14399, 14598, 14788, 14968, 15137, 15296, 15444,
15582, 15709, 15826, 15931, 16026, 16110, 16182, 16244, 16294, 16333, 16362, 16378
};
/* Uses 16x16 mul, without rounding, which is faster. Uses WEBRTC_SPL_MUL_16_16_RSFT */
WebRtc_Word16 WebRtcIsacfix_FftRadix16Fastest(WebRtc_Word16 RexQx[], WebRtc_Word16 ImxQx[], WebRtc_Word16 iSign) {
WebRtc_Word16 dd, ee, ff, gg, hh, ii;
WebRtc_Word16 k0, k1, k2, k3, k4, kk;
WebRtc_Word16 tmp116, tmp216;
WebRtc_Word16 ccc1Q14, ccc2Q14, ccc3Q14, sss1Q14, sss2Q14, sss3Q14;
WebRtc_Word16 sss60Q14, ccc72Q14, sss72Q14;
WebRtc_Word16 aaQx, ajQx, akQx, ajmQx, ajpQx, akmQx, akpQx;
WebRtc_Word16 bbQx, bjQx, bkQx, bjmQx, bjpQx, bkmQx, bkpQx;
WebRtc_Word16 ReDATAQx[240], ImDATAQx[240];
sss60Q14 = kCosTabFfftQ14[20];
ccc72Q14 = kCosTabFfftQ14[48];
sss72Q14 = kCosTabFfftQ14[12];
if (iSign < 0) {
sss72Q14 = -sss72Q14;
sss60Q14 = -sss60Q14;
}
/* Complexity is: 10 cycles */
/* compute fourier transform */
// transform for factor of 4
for (kk=0; kk<60; kk++) {
k0 = kk;
k1 = k0 + 60;
k2 = k1 + 60;
k3 = k2 + 60;
akpQx = RexQx[k0] + RexQx[k2];
akmQx = RexQx[k0] - RexQx[k2];
ajpQx = RexQx[k1] + RexQx[k3];
ajmQx = RexQx[k1] - RexQx[k3];
bkpQx = ImxQx[k0] + ImxQx[k2];
bkmQx = ImxQx[k0] - ImxQx[k2];
bjpQx = ImxQx[k1] + ImxQx[k3];
bjmQx = ImxQx[k1] - ImxQx[k3];
RexQx[k0] = akpQx + ajpQx;
ImxQx[k0] = bkpQx + bjpQx;
ajpQx = akpQx - ajpQx;
bjpQx = bkpQx - bjpQx;
if (iSign < 0) {
akpQx = akmQx + bjmQx;
bkpQx = bkmQx - ajmQx;
akmQx -= bjmQx;
bkmQx += ajmQx;
} else {
akpQx = akmQx - bjmQx;
bkpQx = bkmQx + ajmQx;
akmQx += bjmQx;
bkmQx -= ajmQx;
}
ccc1Q14 = kCosTabFfftQ14[kk];
ccc2Q14 = kCosTabFfftQ14[WEBRTC_SPL_MUL_16_16(2, kk)];
ccc3Q14 = kCosTabFfftQ14[WEBRTC_SPL_MUL_16_16(3, kk)];
sss1Q14 = kCosTabFfftQ14[kk+60];
sss2Q14 = kCosTabFfftQ14[WEBRTC_SPL_MUL_16_16(2, kk)+60];
sss3Q14 = kCosTabFfftQ14[WEBRTC_SPL_MUL_16_16(3, kk)+60];
if (iSign==1) {
sss1Q14 = -sss1Q14;
sss2Q14 = -sss2Q14;
sss3Q14 = -sss3Q14;
}
//Do several multiplications like Q14*Q16>>14 = Q16
// RexQ16[k1] = akpQ16 * ccc1Q14 - bkpQ16 * sss1Q14;
// RexQ16[k2] = ajpQ16 * ccc2Q14 - bjpQ16 * sss2Q14;
// RexQ16[k3] = akmQ16 * ccc3Q14 - bkmQ16 * sss3Q14;
// ImxQ16[k1] = akpQ16 * sss1Q14 + bkpQ16 * ccc1Q14;
// ImxQ16[k2] = ajpQ16 * sss2Q14 + bjpQ16 * ccc2Q14;
// ImxQ16[k3] = akmQ16 * sss3Q14 + bkmQ16 * ccc3Q14;
RexQx[k1] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc1Q14, akpQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss1Q14, bkpQx, 14); // 6 non-mul + 2 mul cycles, i.e. 8 cycles (6+2*7=20 cycles if 16x32mul)
RexQx[k2] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, ajpQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, bjpQx, 14);
RexQx[k3] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc3Q14, akmQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss3Q14, bkmQx, 14);
ImxQx[k1] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss1Q14, akpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc1Q14, bkpQx, 14);
ImxQx[k2] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, ajpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, bjpQx, 14);
ImxQx[k3] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss3Q14, akmQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc3Q14, bkmQx, 14);
//This mul segment needs 6*8 = 48 cycles for 16x16 muls, but 6*20 = 120 cycles for 16x32 muls
}
/* Complexity is: 51+48 = 99 cycles for 16x16 muls, but 51+120 = 171 cycles for 16x32 muls*/
// transform for factor of 3
kk=0;
k1=20;
k2=40;
for (hh=0; hh<4; hh++) {
for (ii=0; ii<20; ii++) {
akQx = RexQx[kk];
bkQx = ImxQx[kk];
ajQx = RexQx[k1] + RexQx[k2];
bjQx = ImxQx[k1] + ImxQx[k2];
RexQx[kk] = akQx + ajQx;
ImxQx[kk] = bkQx + bjQx;
tmp116 = WEBRTC_SPL_RSHIFT_W16(ajQx, 1);
tmp216 = WEBRTC_SPL_RSHIFT_W16(bjQx, 1);
akQx = akQx - tmp116;
bkQx = bkQx - tmp216;
tmp116 = RexQx[k1] - RexQx[k2];
tmp216 = ImxQx[k1] - ImxQx[k2];
ajQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss60Q14, tmp116, 14); // Q14*Qx>>14 = Qx
bjQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss60Q14, tmp216, 14); // Q14*Qx>>14 = Qx
RexQx[k1] = akQx - bjQx;
RexQx[k2] = akQx + bjQx;
ImxQx[k1] = bkQx + ajQx;
ImxQx[k2] = bkQx - ajQx;
kk++;
k1++;
k2++;
}
/* Complexity : (31+6)*20 = 740 cycles for 16x16 muls, but (31+18)*20 = 980 cycles for 16x32 muls*/
kk=kk+40;
k1=k1+40;
k2=k2+40;
}
/* Complexity : 4*(740+3) = 2972 cycles for 16x16 muls, but 4*(980+3) = 3932 cycles for 16x32 muls*/
/* multiply by rotation factor for odd factor 3 or 5 (not for 4)
Same code (duplicated) for both ii=2 and ii=3 */
kk = 1;
ee = 0;
ff = 0;
for (gg=0; gg<19; gg++) {
kk += 20;
ff = ff+4;
for (hh=0; hh<2; hh++) {
ee = ff + (WebRtc_Word16)WEBRTC_SPL_MUL_16_16(hh, ff);
dd = ee + 60;
ccc2Q14 = kCosTabFfftQ14[ee];
sss2Q14 = kCosTabFfftQ14[dd];
if (iSign==1) {
sss2Q14 = -sss2Q14;
}
for (ii=0; ii<4; ii++) {
akQx = RexQx[kk];
bkQx = ImxQx[kk];
RexQx[kk] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, akQx, 14) - // Q14*Qx>>14 = Qx
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, bkQx, 14);
ImxQx[kk] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, akQx, 14) + // Q14*Qx>>14 = Qx
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, bkQx, 14);
kk += 60;
}
kk = kk - 220;
}
// Complexity: 2*(13+5+4*13+2) = 144 for 16x16 muls, but 2*(13+5+4*33+2) = 304 cycles for 16x32 muls
kk = kk - 59;
}
// Complexity: 19*144 = 2736 for 16x16 muls, but 19*304 = 5776 cycles for 16x32 muls
// transform for factor of 5
kk = 0;
ccc2Q14 = kCosTabFfftQ14[96];
sss2Q14 = kCosTabFfftQ14[84];
if (iSign==1) {
sss2Q14 = -sss2Q14;
}
for (hh=0; hh<4; hh++) {
for (ii=0; ii<12; ii++) {
k1 = kk + 4;
k2 = k1 + 4;
k3 = k2 + 4;
k4 = k3 + 4;
akpQx = RexQx[k1] + RexQx[k4];
akmQx = RexQx[k1] - RexQx[k4];
bkpQx = ImxQx[k1] + ImxQx[k4];
bkmQx = ImxQx[k1] - ImxQx[k4];
ajpQx = RexQx[k2] + RexQx[k3];
ajmQx = RexQx[k2] - RexQx[k3];
bjpQx = ImxQx[k2] + ImxQx[k3];
bjmQx = ImxQx[k2] - ImxQx[k3];
aaQx = RexQx[kk];
bbQx = ImxQx[kk];
RexQx[kk] = aaQx + akpQx + ajpQx;
ImxQx[kk] = bbQx + bkpQx + bjpQx;
akQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc72Q14, akpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, ajpQx, 14) + aaQx;
bkQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc72Q14, bkpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, bjpQx, 14) + bbQx;
ajQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss72Q14, akmQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, ajmQx, 14);
bjQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss72Q14, bkmQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, bjmQx, 14);
// 32+4*8=64 or 32+4*20=112
RexQx[k1] = akQx - bjQx;
RexQx[k4] = akQx + bjQx;
ImxQx[k1] = bkQx + ajQx;
ImxQx[k4] = bkQx - ajQx;
akQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, akpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc72Q14, ajpQx, 14) + aaQx;
bkQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, bkpQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc72Q14, bjpQx, 14) + bbQx;
ajQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, akmQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss72Q14, ajmQx, 14);
bjQx = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, bkmQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss72Q14, bjmQx, 14);
// 8+4*8=40 or 8+4*20=88
RexQx[k2] = akQx - bjQx;
RexQx[k3] = akQx + bjQx;
ImxQx[k2] = bkQx + ajQx;
ImxQx[k3] = bkQx - ajQx;
kk = k4 + 4;
}
// Complexity: 12*(64+40+10) = 1368 for 16x16 muls, but 12*(112+88+10) = 2520 cycles for 16x32 muls
kk -= 239;
}
// Complexity: 4*1368 = 5472 for 16x16 muls, but 4*2520 = 10080 cycles for 16x32 muls
/* multiply by rotation factor for odd factor 3 or 5 (not for 4)
Same code (duplicated) for both ii=2 and ii=3 */
kk = 1;
ee=0;
for (gg=0; gg<3; gg++) {
kk += 4;
dd = 12 + (WebRtc_Word16)WEBRTC_SPL_MUL_16_16(12, gg);
ff = 0;
for (hh=0; hh<4; hh++) {
ff = ff+dd;
ee = ff+60;
for (ii=0; ii<12; ii++) {
akQx = RexQx[kk];
bkQx = ImxQx[kk];
ccc2Q14 = kCosTabFfftQ14[ff];
sss2Q14 = kCosTabFfftQ14[ee];
if (iSign==1) {
sss2Q14 = -sss2Q14;
}
RexQx[kk] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, akQx, 14) -
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, bkQx, 14);
ImxQx[kk] = (WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(sss2Q14, akQx, 14) +
(WebRtc_Word16)WEBRTC_SPL_MUL_16_16_RSFT(ccc2Q14, bkQx, 14);
kk += 20;
}
kk = kk - 236;
// Complexity: 12*(12+12) = 288 for 16x16 muls, but 12*(12+32) = 528 cycles for 16x32 muls
}
kk = kk - 19;
// Complexity: 4*288+6 for 16x16 muls, but 4*528+6 cycles for 16x32 muls
}
// Complexity: 3*4*288+6 = 3462 for 16x16 muls, but 3*4*528+6 = 6342 cycles for 16x32 muls
// last transform for factor of 4 */
for (kk=0; kk<240; kk=kk+4) {
k1 = kk + 1;
k2 = k1 + 1;
k3 = k2 + 1;
akpQx = RexQx[kk] + RexQx[k2];
akmQx = RexQx[kk] - RexQx[k2];
ajpQx = RexQx[k1] + RexQx[k3];
ajmQx = RexQx[k1] - RexQx[k3];
bkpQx = ImxQx[kk] + ImxQx[k2];
bkmQx = ImxQx[kk] - ImxQx[k2];
bjpQx = ImxQx[k1] + ImxQx[k3];
bjmQx = ImxQx[k1] - ImxQx[k3];
RexQx[kk] = akpQx + ajpQx;
ImxQx[kk] = bkpQx + bjpQx;
ajpQx = akpQx - ajpQx;
bjpQx = bkpQx - bjpQx;
if (iSign < 0) {
akpQx = akmQx + bjmQx;
bkpQx = bkmQx - ajmQx;
akmQx -= bjmQx;
bkmQx += ajmQx;
} else {
akpQx = akmQx - bjmQx;
bkpQx = bkmQx + ajmQx;
akmQx += bjmQx;
bkmQx -= ajmQx;
}
RexQx[k1] = akpQx;
RexQx[k2] = ajpQx;
RexQx[k3] = akmQx;
ImxQx[k1] = bkpQx;
ImxQx[k2] = bjpQx;
ImxQx[k3] = bkmQx;
}
// Complexity: 60*45 = 2700 for 16x16 muls, but 60*45 = 2700 cycles for 16x32 muls
/* permute the results to normal order */
for (ii=0; ii<240; ii++) {
ReDATAQx[ii]=RexQx[ii];
ImDATAQx[ii]=ImxQx[ii];
}
// Complexity: 240*2=480 cycles
for (ii=0; ii<240; ii++) {
RexQx[ii]=ReDATAQx[kSortTabFft[ii]];
ImxQx[ii]=ImDATAQx[kSortTabFft[ii]];
}
// Complexity: 240*2*2=960 cycles
// Total complexity:
// 16x16 16x32
// Complexity: 10 10
// Complexity: 99 171
// Complexity: 2972 3932
// Complexity: 2736 5776
// Complexity: 5472 10080
// Complexity: 3462 6342
// Complexity: 2700 2700
// Complexity: 480 480
// Complexity: 960 960
// =======================
// 18891 30451
//
// If this FFT is called 2 time each frame, i.e. 67 times per second, it will correspond to
// a C54 complexity of 67*18891/1000000 = 1.27 MIPS with 16x16-muls, and 67*30451/1000000 =
// = 2.04 MIPS with 16x32-muls. Note that this routine somtimes is called 6 times during the
// encoding of a frame, i.e. the max complexity would be 7/2*1.27 = 4.4 MIPS for the 16x16 mul case.
return 0;
}
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