niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1 | /* |
| 2 | * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html |
| 3 | * Copyright Takuya OOURA, 1996-2001 |
| 4 | * |
| 5 | * You may use, copy, modify and distribute this code for any purpose (include |
| 6 | * commercial use) and without fee. Please refer to this package when you modify |
| 7 | * this code. |
| 8 | * |
| 9 | * Changes: |
| 10 | * Trivial type modifications by the WebRTC authors. |
| 11 | */ |
| 12 | |
| 13 | /* |
| 14 | Fast Fourier/Cosine/Sine Transform |
| 15 | dimension :one |
| 16 | data length :power of 2 |
| 17 | decimation :frequency |
| 18 | radix :4, 2 |
| 19 | data :inplace |
| 20 | table :use |
| 21 | functions |
| 22 | cdft: Complex Discrete Fourier Transform |
| 23 | rdft: Real Discrete Fourier Transform |
| 24 | ddct: Discrete Cosine Transform |
| 25 | ddst: Discrete Sine Transform |
| 26 | dfct: Cosine Transform of RDFT (Real Symmetric DFT) |
| 27 | dfst: Sine Transform of RDFT (Real Anti-symmetric DFT) |
| 28 | function prototypes |
| 29 | void cdft(int, int, float *, int *, float *); |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 30 | void rdft(size_t, int, float *, size_t *, float *); |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 31 | void ddct(int, int, float *, int *, float *); |
| 32 | void ddst(int, int, float *, int *, float *); |
| 33 | void dfct(int, float *, float *, int *, float *); |
| 34 | void dfst(int, float *, float *, int *, float *); |
| 35 | |
| 36 | |
| 37 | -------- Complex DFT (Discrete Fourier Transform) -------- |
| 38 | [definition] |
| 39 | <case1> |
| 40 | X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n |
| 41 | <case2> |
| 42 | X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n |
| 43 | (notes: sum_j=0^n-1 is a summation from j=0 to n-1) |
| 44 | [usage] |
| 45 | <case1> |
| 46 | ip[0] = 0; // first time only |
| 47 | cdft(2*n, 1, a, ip, w); |
| 48 | <case2> |
| 49 | ip[0] = 0; // first time only |
| 50 | cdft(2*n, -1, a, ip, w); |
| 51 | [parameters] |
| 52 | 2*n :data length (int) |
| 53 | n >= 1, n = power of 2 |
| 54 | a[0...2*n-1] :input/output data (float *) |
| 55 | input data |
| 56 | a[2*j] = Re(x[j]), |
| 57 | a[2*j+1] = Im(x[j]), 0<=j<n |
| 58 | output data |
| 59 | a[2*k] = Re(X[k]), |
| 60 | a[2*k+1] = Im(X[k]), 0<=k<n |
| 61 | ip[0...*] :work area for bit reversal (int *) |
| 62 | length of ip >= 2+sqrt(n) |
| 63 | strictly, |
| 64 | length of ip >= |
| 65 | 2+(1<<(int)(log(n+0.5)/log(2))/2). |
| 66 | ip[0],ip[1] are pointers of the cos/sin table. |
| 67 | w[0...n/2-1] :cos/sin table (float *) |
| 68 | w[],ip[] are initialized if ip[0] == 0. |
| 69 | [remark] |
| 70 | Inverse of |
| 71 | cdft(2*n, -1, a, ip, w); |
| 72 | is |
| 73 | cdft(2*n, 1, a, ip, w); |
| 74 | for (j = 0; j <= 2 * n - 1; j++) { |
| 75 | a[j] *= 1.0 / n; |
| 76 | } |
| 77 | . |
| 78 | |
| 79 | |
| 80 | -------- Real DFT / Inverse of Real DFT -------- |
| 81 | [definition] |
| 82 | <case1> RDFT |
| 83 | R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2 |
| 84 | I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2 |
| 85 | <case2> IRDFT (excluding scale) |
| 86 | a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + |
| 87 | sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + |
| 88 | sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n |
| 89 | [usage] |
| 90 | <case1> |
| 91 | ip[0] = 0; // first time only |
| 92 | rdft(n, 1, a, ip, w); |
| 93 | <case2> |
| 94 | ip[0] = 0; // first time only |
| 95 | rdft(n, -1, a, ip, w); |
| 96 | [parameters] |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 97 | n :data length (size_t) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 98 | n >= 2, n = power of 2 |
| 99 | a[0...n-1] :input/output data (float *) |
| 100 | <case1> |
| 101 | output data |
| 102 | a[2*k] = R[k], 0<=k<n/2 |
| 103 | a[2*k+1] = I[k], 0<k<n/2 |
| 104 | a[1] = R[n/2] |
| 105 | <case2> |
| 106 | input data |
| 107 | a[2*j] = R[j], 0<=j<n/2 |
| 108 | a[2*j+1] = I[j], 0<j<n/2 |
| 109 | a[1] = R[n/2] |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 110 | ip[0...*] :work area for bit reversal (size_t *) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 111 | length of ip >= 2+sqrt(n/2) |
| 112 | strictly, |
| 113 | length of ip >= |
| 114 | 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| 115 | ip[0],ip[1] are pointers of the cos/sin table. |
| 116 | w[0...n/2-1] :cos/sin table (float *) |
| 117 | w[],ip[] are initialized if ip[0] == 0. |
| 118 | [remark] |
| 119 | Inverse of |
| 120 | rdft(n, 1, a, ip, w); |
| 121 | is |
| 122 | rdft(n, -1, a, ip, w); |
| 123 | for (j = 0; j <= n - 1; j++) { |
| 124 | a[j] *= 2.0 / n; |
| 125 | } |
| 126 | . |
| 127 | |
| 128 | |
| 129 | -------- DCT (Discrete Cosine Transform) / Inverse of DCT -------- |
| 130 | [definition] |
| 131 | <case1> IDCT (excluding scale) |
| 132 | C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n |
| 133 | <case2> DCT |
| 134 | C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n |
| 135 | [usage] |
| 136 | <case1> |
| 137 | ip[0] = 0; // first time only |
| 138 | ddct(n, 1, a, ip, w); |
| 139 | <case2> |
| 140 | ip[0] = 0; // first time only |
| 141 | ddct(n, -1, a, ip, w); |
| 142 | [parameters] |
| 143 | n :data length (int) |
| 144 | n >= 2, n = power of 2 |
| 145 | a[0...n-1] :input/output data (float *) |
| 146 | output data |
| 147 | a[k] = C[k], 0<=k<n |
| 148 | ip[0...*] :work area for bit reversal (int *) |
| 149 | length of ip >= 2+sqrt(n/2) |
| 150 | strictly, |
| 151 | length of ip >= |
| 152 | 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| 153 | ip[0],ip[1] are pointers of the cos/sin table. |
| 154 | w[0...n*5/4-1] :cos/sin table (float *) |
| 155 | w[],ip[] are initialized if ip[0] == 0. |
| 156 | [remark] |
| 157 | Inverse of |
| 158 | ddct(n, -1, a, ip, w); |
| 159 | is |
| 160 | a[0] *= 0.5; |
| 161 | ddct(n, 1, a, ip, w); |
| 162 | for (j = 0; j <= n - 1; j++) { |
| 163 | a[j] *= 2.0 / n; |
| 164 | } |
| 165 | . |
| 166 | |
| 167 | |
| 168 | -------- DST (Discrete Sine Transform) / Inverse of DST -------- |
| 169 | [definition] |
| 170 | <case1> IDST (excluding scale) |
| 171 | S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n |
| 172 | <case2> DST |
| 173 | S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n |
| 174 | [usage] |
| 175 | <case1> |
| 176 | ip[0] = 0; // first time only |
| 177 | ddst(n, 1, a, ip, w); |
| 178 | <case2> |
| 179 | ip[0] = 0; // first time only |
| 180 | ddst(n, -1, a, ip, w); |
| 181 | [parameters] |
| 182 | n :data length (int) |
| 183 | n >= 2, n = power of 2 |
| 184 | a[0...n-1] :input/output data (float *) |
| 185 | <case1> |
| 186 | input data |
| 187 | a[j] = A[j], 0<j<n |
| 188 | a[0] = A[n] |
| 189 | output data |
| 190 | a[k] = S[k], 0<=k<n |
| 191 | <case2> |
| 192 | output data |
| 193 | a[k] = S[k], 0<k<n |
| 194 | a[0] = S[n] |
| 195 | ip[0...*] :work area for bit reversal (int *) |
| 196 | length of ip >= 2+sqrt(n/2) |
| 197 | strictly, |
| 198 | length of ip >= |
| 199 | 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| 200 | ip[0],ip[1] are pointers of the cos/sin table. |
| 201 | w[0...n*5/4-1] :cos/sin table (float *) |
| 202 | w[],ip[] are initialized if ip[0] == 0. |
| 203 | [remark] |
| 204 | Inverse of |
| 205 | ddst(n, -1, a, ip, w); |
| 206 | is |
| 207 | a[0] *= 0.5; |
| 208 | ddst(n, 1, a, ip, w); |
| 209 | for (j = 0; j <= n - 1; j++) { |
| 210 | a[j] *= 2.0 / n; |
| 211 | } |
| 212 | . |
| 213 | |
| 214 | |
| 215 | -------- Cosine Transform of RDFT (Real Symmetric DFT) -------- |
| 216 | [definition] |
| 217 | C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n |
| 218 | [usage] |
| 219 | ip[0] = 0; // first time only |
| 220 | dfct(n, a, t, ip, w); |
| 221 | [parameters] |
| 222 | n :data length - 1 (int) |
| 223 | n >= 2, n = power of 2 |
| 224 | a[0...n] :input/output data (float *) |
| 225 | output data |
| 226 | a[k] = C[k], 0<=k<=n |
| 227 | t[0...n/2] :work area (float *) |
| 228 | ip[0...*] :work area for bit reversal (int *) |
| 229 | length of ip >= 2+sqrt(n/4) |
| 230 | strictly, |
| 231 | length of ip >= |
| 232 | 2+(1<<(int)(log(n/4+0.5)/log(2))/2). |
| 233 | ip[0],ip[1] are pointers of the cos/sin table. |
| 234 | w[0...n*5/8-1] :cos/sin table (float *) |
| 235 | w[],ip[] are initialized if ip[0] == 0. |
| 236 | [remark] |
| 237 | Inverse of |
| 238 | a[0] *= 0.5; |
| 239 | a[n] *= 0.5; |
| 240 | dfct(n, a, t, ip, w); |
| 241 | is |
| 242 | a[0] *= 0.5; |
| 243 | a[n] *= 0.5; |
| 244 | dfct(n, a, t, ip, w); |
| 245 | for (j = 0; j <= n; j++) { |
| 246 | a[j] *= 2.0 / n; |
| 247 | } |
| 248 | . |
| 249 | |
| 250 | |
| 251 | -------- Sine Transform of RDFT (Real Anti-symmetric DFT) -------- |
| 252 | [definition] |
| 253 | S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n |
| 254 | [usage] |
| 255 | ip[0] = 0; // first time only |
| 256 | dfst(n, a, t, ip, w); |
| 257 | [parameters] |
| 258 | n :data length + 1 (int) |
| 259 | n >= 2, n = power of 2 |
| 260 | a[0...n-1] :input/output data (float *) |
| 261 | output data |
| 262 | a[k] = S[k], 0<k<n |
| 263 | (a[0] is used for work area) |
| 264 | t[0...n/2-1] :work area (float *) |
| 265 | ip[0...*] :work area for bit reversal (int *) |
| 266 | length of ip >= 2+sqrt(n/4) |
| 267 | strictly, |
| 268 | length of ip >= |
| 269 | 2+(1<<(int)(log(n/4+0.5)/log(2))/2). |
| 270 | ip[0],ip[1] are pointers of the cos/sin table. |
| 271 | w[0...n*5/8-1] :cos/sin table (float *) |
| 272 | w[],ip[] are initialized if ip[0] == 0. |
| 273 | [remark] |
| 274 | Inverse of |
| 275 | dfst(n, a, t, ip, w); |
| 276 | is |
| 277 | dfst(n, a, t, ip, w); |
| 278 | for (j = 1; j <= n - 1; j++) { |
| 279 | a[j] *= 2.0 / n; |
| 280 | } |
| 281 | . |
| 282 | |
| 283 | |
| 284 | Appendix : |
| 285 | The cos/sin table is recalculated when the larger table required. |
| 286 | w[] and ip[] are compatible with all routines. |
| 287 | */ |
| 288 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 289 | #include <stddef.h> |
| 290 | |
| 291 | static void makewt(size_t nw, size_t *ip, float *w); |
| 292 | static void makect(size_t nc, size_t *ip, float *c); |
| 293 | static void bitrv2(size_t n, size_t *ip, float *a); |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 294 | #if 0 // Not used. |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 295 | static void bitrv2conj(int n, int *ip, float *a); |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 296 | #endif |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 297 | static void cftfsub(size_t n, float *a, float *w); |
| 298 | static void cftbsub(size_t n, float *a, float *w); |
| 299 | static void cft1st(size_t n, float *a, float *w); |
| 300 | static void cftmdl(size_t n, size_t l, float *a, float *w); |
| 301 | static void rftfsub(size_t n, float *a, size_t nc, float *c); |
| 302 | static void rftbsub(size_t n, float *a, size_t nc, float *c); |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 303 | #if 0 // Not used. |
| 304 | static void dctsub(int n, float *a, int nc, float *c) |
| 305 | static void dstsub(int n, float *a, int nc, float *c) |
| 306 | #endif |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 307 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 308 | |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 309 | #if 0 // Not used. |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 310 | void WebRtc_cdft(int n, int isgn, float *a, int *ip, float *w) |
| 311 | { |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 312 | if (n > (ip[0] << 2)) { |
| 313 | makewt(n >> 2, ip, w); |
| 314 | } |
| 315 | if (n > 4) { |
| 316 | if (isgn >= 0) { |
| 317 | bitrv2(n, ip + 2, a); |
| 318 | cftfsub(n, a, w); |
| 319 | } else { |
| 320 | bitrv2conj(n, ip + 2, a); |
| 321 | cftbsub(n, a, w); |
| 322 | } |
| 323 | } else if (n == 4) { |
| 324 | cftfsub(n, a, w); |
| 325 | } |
| 326 | } |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 327 | #endif |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 328 | |
| 329 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 330 | void WebRtc_rdft(size_t n, int isgn, float *a, size_t *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 331 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 332 | size_t nw, nc; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 333 | float xi; |
| 334 | |
| 335 | nw = ip[0]; |
| 336 | if (n > (nw << 2)) { |
| 337 | nw = n >> 2; |
| 338 | makewt(nw, ip, w); |
| 339 | } |
| 340 | nc = ip[1]; |
| 341 | if (n > (nc << 2)) { |
| 342 | nc = n >> 2; |
| 343 | makect(nc, ip, w + nw); |
| 344 | } |
| 345 | if (isgn >= 0) { |
| 346 | if (n > 4) { |
| 347 | bitrv2(n, ip + 2, a); |
| 348 | cftfsub(n, a, w); |
| 349 | rftfsub(n, a, nc, w + nw); |
| 350 | } else if (n == 4) { |
| 351 | cftfsub(n, a, w); |
| 352 | } |
| 353 | xi = a[0] - a[1]; |
| 354 | a[0] += a[1]; |
| 355 | a[1] = xi; |
| 356 | } else { |
| 357 | a[1] = 0.5f * (a[0] - a[1]); |
| 358 | a[0] -= a[1]; |
| 359 | if (n > 4) { |
| 360 | rftbsub(n, a, nc, w + nw); |
| 361 | bitrv2(n, ip + 2, a); |
| 362 | cftbsub(n, a, w); |
| 363 | } else if (n == 4) { |
| 364 | cftfsub(n, a, w); |
| 365 | } |
| 366 | } |
| 367 | } |
| 368 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 369 | #if 0 // Not used. |
| 370 | static void ddct(int n, int isgn, float *a, int *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 371 | { |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 372 | int j, nw, nc; |
| 373 | float xr; |
| 374 | |
| 375 | nw = ip[0]; |
| 376 | if (n > (nw << 2)) { |
| 377 | nw = n >> 2; |
| 378 | makewt(nw, ip, w); |
| 379 | } |
| 380 | nc = ip[1]; |
| 381 | if (n > nc) { |
| 382 | nc = n; |
| 383 | makect(nc, ip, w + nw); |
| 384 | } |
| 385 | if (isgn < 0) { |
| 386 | xr = a[n - 1]; |
| 387 | for (j = n - 2; j >= 2; j -= 2) { |
| 388 | a[j + 1] = a[j] - a[j - 1]; |
| 389 | a[j] += a[j - 1]; |
| 390 | } |
| 391 | a[1] = a[0] - xr; |
| 392 | a[0] += xr; |
| 393 | if (n > 4) { |
| 394 | rftbsub(n, a, nc, w + nw); |
| 395 | bitrv2(n, ip + 2, a); |
| 396 | cftbsub(n, a, w); |
| 397 | } else if (n == 4) { |
| 398 | cftfsub(n, a, w); |
| 399 | } |
| 400 | } |
| 401 | dctsub(n, a, nc, w + nw); |
| 402 | if (isgn >= 0) { |
| 403 | if (n > 4) { |
| 404 | bitrv2(n, ip + 2, a); |
| 405 | cftfsub(n, a, w); |
| 406 | rftfsub(n, a, nc, w + nw); |
| 407 | } else if (n == 4) { |
| 408 | cftfsub(n, a, w); |
| 409 | } |
| 410 | xr = a[0] - a[1]; |
| 411 | a[0] += a[1]; |
| 412 | for (j = 2; j < n; j += 2) { |
| 413 | a[j - 1] = a[j] - a[j + 1]; |
| 414 | a[j] += a[j + 1]; |
| 415 | } |
| 416 | a[n - 1] = xr; |
| 417 | } |
| 418 | } |
| 419 | |
| 420 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 421 | static void ddst(int n, int isgn, float *a, int *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 422 | { |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 423 | int j, nw, nc; |
| 424 | float xr; |
| 425 | |
| 426 | nw = ip[0]; |
| 427 | if (n > (nw << 2)) { |
| 428 | nw = n >> 2; |
| 429 | makewt(nw, ip, w); |
| 430 | } |
| 431 | nc = ip[1]; |
| 432 | if (n > nc) { |
| 433 | nc = n; |
| 434 | makect(nc, ip, w + nw); |
| 435 | } |
| 436 | if (isgn < 0) { |
| 437 | xr = a[n - 1]; |
| 438 | for (j = n - 2; j >= 2; j -= 2) { |
| 439 | a[j + 1] = -a[j] - a[j - 1]; |
| 440 | a[j] -= a[j - 1]; |
| 441 | } |
| 442 | a[1] = a[0] + xr; |
| 443 | a[0] -= xr; |
| 444 | if (n > 4) { |
| 445 | rftbsub(n, a, nc, w + nw); |
| 446 | bitrv2(n, ip + 2, a); |
| 447 | cftbsub(n, a, w); |
| 448 | } else if (n == 4) { |
| 449 | cftfsub(n, a, w); |
| 450 | } |
| 451 | } |
| 452 | dstsub(n, a, nc, w + nw); |
| 453 | if (isgn >= 0) { |
| 454 | if (n > 4) { |
| 455 | bitrv2(n, ip + 2, a); |
| 456 | cftfsub(n, a, w); |
| 457 | rftfsub(n, a, nc, w + nw); |
| 458 | } else if (n == 4) { |
| 459 | cftfsub(n, a, w); |
| 460 | } |
| 461 | xr = a[0] - a[1]; |
| 462 | a[0] += a[1]; |
| 463 | for (j = 2; j < n; j += 2) { |
| 464 | a[j - 1] = -a[j] - a[j + 1]; |
| 465 | a[j] -= a[j + 1]; |
| 466 | } |
| 467 | a[n - 1] = -xr; |
| 468 | } |
| 469 | } |
| 470 | |
| 471 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 472 | static void dfct(int n, float *a, float *t, int *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 473 | { |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 474 | int j, k, l, m, mh, nw, nc; |
| 475 | float xr, xi, yr, yi; |
| 476 | |
| 477 | nw = ip[0]; |
| 478 | if (n > (nw << 3)) { |
| 479 | nw = n >> 3; |
| 480 | makewt(nw, ip, w); |
| 481 | } |
| 482 | nc = ip[1]; |
| 483 | if (n > (nc << 1)) { |
| 484 | nc = n >> 1; |
| 485 | makect(nc, ip, w + nw); |
| 486 | } |
| 487 | m = n >> 1; |
| 488 | yi = a[m]; |
| 489 | xi = a[0] + a[n]; |
| 490 | a[0] -= a[n]; |
| 491 | t[0] = xi - yi; |
| 492 | t[m] = xi + yi; |
| 493 | if (n > 2) { |
| 494 | mh = m >> 1; |
| 495 | for (j = 1; j < mh; j++) { |
| 496 | k = m - j; |
| 497 | xr = a[j] - a[n - j]; |
| 498 | xi = a[j] + a[n - j]; |
| 499 | yr = a[k] - a[n - k]; |
| 500 | yi = a[k] + a[n - k]; |
| 501 | a[j] = xr; |
| 502 | a[k] = yr; |
| 503 | t[j] = xi - yi; |
| 504 | t[k] = xi + yi; |
| 505 | } |
| 506 | t[mh] = a[mh] + a[n - mh]; |
| 507 | a[mh] -= a[n - mh]; |
| 508 | dctsub(m, a, nc, w + nw); |
| 509 | if (m > 4) { |
| 510 | bitrv2(m, ip + 2, a); |
| 511 | cftfsub(m, a, w); |
| 512 | rftfsub(m, a, nc, w + nw); |
| 513 | } else if (m == 4) { |
| 514 | cftfsub(m, a, w); |
| 515 | } |
| 516 | a[n - 1] = a[0] - a[1]; |
| 517 | a[1] = a[0] + a[1]; |
| 518 | for (j = m - 2; j >= 2; j -= 2) { |
| 519 | a[2 * j + 1] = a[j] + a[j + 1]; |
| 520 | a[2 * j - 1] = a[j] - a[j + 1]; |
| 521 | } |
| 522 | l = 2; |
| 523 | m = mh; |
| 524 | while (m >= 2) { |
| 525 | dctsub(m, t, nc, w + nw); |
| 526 | if (m > 4) { |
| 527 | bitrv2(m, ip + 2, t); |
| 528 | cftfsub(m, t, w); |
| 529 | rftfsub(m, t, nc, w + nw); |
| 530 | } else if (m == 4) { |
| 531 | cftfsub(m, t, w); |
| 532 | } |
| 533 | a[n - l] = t[0] - t[1]; |
| 534 | a[l] = t[0] + t[1]; |
| 535 | k = 0; |
| 536 | for (j = 2; j < m; j += 2) { |
| 537 | k += l << 2; |
| 538 | a[k - l] = t[j] - t[j + 1]; |
| 539 | a[k + l] = t[j] + t[j + 1]; |
| 540 | } |
| 541 | l <<= 1; |
| 542 | mh = m >> 1; |
| 543 | for (j = 0; j < mh; j++) { |
| 544 | k = m - j; |
| 545 | t[j] = t[m + k] - t[m + j]; |
| 546 | t[k] = t[m + k] + t[m + j]; |
| 547 | } |
| 548 | t[mh] = t[m + mh]; |
| 549 | m = mh; |
| 550 | } |
| 551 | a[l] = t[0]; |
| 552 | a[n] = t[2] - t[1]; |
| 553 | a[0] = t[2] + t[1]; |
| 554 | } else { |
| 555 | a[1] = a[0]; |
| 556 | a[2] = t[0]; |
| 557 | a[0] = t[1]; |
| 558 | } |
| 559 | } |
| 560 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 561 | static void dfst(int n, float *a, float *t, int *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 562 | { |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 563 | int j, k, l, m, mh, nw, nc; |
| 564 | float xr, xi, yr, yi; |
| 565 | |
| 566 | nw = ip[0]; |
| 567 | if (n > (nw << 3)) { |
| 568 | nw = n >> 3; |
| 569 | makewt(nw, ip, w); |
| 570 | } |
| 571 | nc = ip[1]; |
| 572 | if (n > (nc << 1)) { |
| 573 | nc = n >> 1; |
| 574 | makect(nc, ip, w + nw); |
| 575 | } |
| 576 | if (n > 2) { |
| 577 | m = n >> 1; |
| 578 | mh = m >> 1; |
| 579 | for (j = 1; j < mh; j++) { |
| 580 | k = m - j; |
| 581 | xr = a[j] + a[n - j]; |
| 582 | xi = a[j] - a[n - j]; |
| 583 | yr = a[k] + a[n - k]; |
| 584 | yi = a[k] - a[n - k]; |
| 585 | a[j] = xr; |
| 586 | a[k] = yr; |
| 587 | t[j] = xi + yi; |
| 588 | t[k] = xi - yi; |
| 589 | } |
| 590 | t[0] = a[mh] - a[n - mh]; |
| 591 | a[mh] += a[n - mh]; |
| 592 | a[0] = a[m]; |
| 593 | dstsub(m, a, nc, w + nw); |
| 594 | if (m > 4) { |
| 595 | bitrv2(m, ip + 2, a); |
| 596 | cftfsub(m, a, w); |
| 597 | rftfsub(m, a, nc, w + nw); |
| 598 | } else if (m == 4) { |
| 599 | cftfsub(m, a, w); |
| 600 | } |
| 601 | a[n - 1] = a[1] - a[0]; |
| 602 | a[1] = a[0] + a[1]; |
| 603 | for (j = m - 2; j >= 2; j -= 2) { |
| 604 | a[2 * j + 1] = a[j] - a[j + 1]; |
| 605 | a[2 * j - 1] = -a[j] - a[j + 1]; |
| 606 | } |
| 607 | l = 2; |
| 608 | m = mh; |
| 609 | while (m >= 2) { |
| 610 | dstsub(m, t, nc, w + nw); |
| 611 | if (m > 4) { |
| 612 | bitrv2(m, ip + 2, t); |
| 613 | cftfsub(m, t, w); |
| 614 | rftfsub(m, t, nc, w + nw); |
| 615 | } else if (m == 4) { |
| 616 | cftfsub(m, t, w); |
| 617 | } |
| 618 | a[n - l] = t[1] - t[0]; |
| 619 | a[l] = t[0] + t[1]; |
| 620 | k = 0; |
| 621 | for (j = 2; j < m; j += 2) { |
| 622 | k += l << 2; |
| 623 | a[k - l] = -t[j] - t[j + 1]; |
| 624 | a[k + l] = t[j] - t[j + 1]; |
| 625 | } |
| 626 | l <<= 1; |
| 627 | mh = m >> 1; |
| 628 | for (j = 1; j < mh; j++) { |
| 629 | k = m - j; |
| 630 | t[j] = t[m + k] + t[m + j]; |
| 631 | t[k] = t[m + k] - t[m + j]; |
| 632 | } |
| 633 | t[0] = t[m + mh]; |
| 634 | m = mh; |
| 635 | } |
| 636 | a[l] = t[0]; |
| 637 | } |
| 638 | a[0] = 0; |
| 639 | } |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 640 | #endif // Not used. |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 641 | |
| 642 | |
| 643 | /* -------- initializing routines -------- */ |
| 644 | |
| 645 | |
| 646 | #include <math.h> |
| 647 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 648 | static void makewt(size_t nw, size_t *ip, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 649 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 650 | size_t j, nwh; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 651 | float delta, x, y; |
| 652 | |
| 653 | ip[0] = nw; |
| 654 | ip[1] = 1; |
| 655 | if (nw > 2) { |
| 656 | nwh = nw >> 1; |
Peter Kasting | b7e5054 | 2015-06-11 12:55:50 -0700 | [diff] [blame] | 657 | delta = atanf(1.0f) / nwh; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 658 | w[0] = 1; |
| 659 | w[1] = 0; |
| 660 | w[nwh] = (float)cos(delta * nwh); |
| 661 | w[nwh + 1] = w[nwh]; |
| 662 | if (nwh > 2) { |
| 663 | for (j = 2; j < nwh; j += 2) { |
| 664 | x = (float)cos(delta * j); |
| 665 | y = (float)sin(delta * j); |
| 666 | w[j] = x; |
| 667 | w[j + 1] = y; |
| 668 | w[nw - j] = y; |
| 669 | w[nw - j + 1] = x; |
| 670 | } |
| 671 | bitrv2(nw, ip + 2, w); |
| 672 | } |
| 673 | } |
| 674 | } |
| 675 | |
| 676 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 677 | static void makect(size_t nc, size_t *ip, float *c) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 678 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 679 | size_t j, nch; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 680 | float delta; |
| 681 | |
| 682 | ip[1] = nc; |
| 683 | if (nc > 1) { |
| 684 | nch = nc >> 1; |
Peter Kasting | b7e5054 | 2015-06-11 12:55:50 -0700 | [diff] [blame] | 685 | delta = atanf(1.0f) / nch; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 686 | c[0] = (float)cos(delta * nch); |
| 687 | c[nch] = 0.5f * c[0]; |
| 688 | for (j = 1; j < nch; j++) { |
| 689 | c[j] = 0.5f * (float)cos(delta * j); |
| 690 | c[nc - j] = 0.5f * (float)sin(delta * j); |
| 691 | } |
| 692 | } |
| 693 | } |
| 694 | |
| 695 | |
| 696 | /* -------- child routines -------- */ |
| 697 | |
| 698 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 699 | static void bitrv2(size_t n, size_t *ip, float *a) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 700 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 701 | size_t j, j1, k, k1, l, m, m2; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 702 | float xr, xi, yr, yi; |
| 703 | |
| 704 | ip[0] = 0; |
| 705 | l = n; |
| 706 | m = 1; |
| 707 | while ((m << 3) < l) { |
| 708 | l >>= 1; |
| 709 | for (j = 0; j < m; j++) { |
| 710 | ip[m + j] = ip[j] + l; |
| 711 | } |
| 712 | m <<= 1; |
| 713 | } |
| 714 | m2 = 2 * m; |
| 715 | if ((m << 3) == l) { |
| 716 | for (k = 0; k < m; k++) { |
| 717 | for (j = 0; j < k; j++) { |
| 718 | j1 = 2 * j + ip[k]; |
| 719 | k1 = 2 * k + ip[j]; |
| 720 | xr = a[j1]; |
| 721 | xi = a[j1 + 1]; |
| 722 | yr = a[k1]; |
| 723 | yi = a[k1 + 1]; |
| 724 | a[j1] = yr; |
| 725 | a[j1 + 1] = yi; |
| 726 | a[k1] = xr; |
| 727 | a[k1 + 1] = xi; |
| 728 | j1 += m2; |
| 729 | k1 += 2 * m2; |
| 730 | xr = a[j1]; |
| 731 | xi = a[j1 + 1]; |
| 732 | yr = a[k1]; |
| 733 | yi = a[k1 + 1]; |
| 734 | a[j1] = yr; |
| 735 | a[j1 + 1] = yi; |
| 736 | a[k1] = xr; |
| 737 | a[k1 + 1] = xi; |
| 738 | j1 += m2; |
| 739 | k1 -= m2; |
| 740 | xr = a[j1]; |
| 741 | xi = a[j1 + 1]; |
| 742 | yr = a[k1]; |
| 743 | yi = a[k1 + 1]; |
| 744 | a[j1] = yr; |
| 745 | a[j1 + 1] = yi; |
| 746 | a[k1] = xr; |
| 747 | a[k1 + 1] = xi; |
| 748 | j1 += m2; |
| 749 | k1 += 2 * m2; |
| 750 | xr = a[j1]; |
| 751 | xi = a[j1 + 1]; |
| 752 | yr = a[k1]; |
| 753 | yi = a[k1 + 1]; |
| 754 | a[j1] = yr; |
| 755 | a[j1 + 1] = yi; |
| 756 | a[k1] = xr; |
| 757 | a[k1 + 1] = xi; |
| 758 | } |
| 759 | j1 = 2 * k + m2 + ip[k]; |
| 760 | k1 = j1 + m2; |
| 761 | xr = a[j1]; |
| 762 | xi = a[j1 + 1]; |
| 763 | yr = a[k1]; |
| 764 | yi = a[k1 + 1]; |
| 765 | a[j1] = yr; |
| 766 | a[j1 + 1] = yi; |
| 767 | a[k1] = xr; |
| 768 | a[k1 + 1] = xi; |
| 769 | } |
| 770 | } else { |
| 771 | for (k = 1; k < m; k++) { |
| 772 | for (j = 0; j < k; j++) { |
| 773 | j1 = 2 * j + ip[k]; |
| 774 | k1 = 2 * k + ip[j]; |
| 775 | xr = a[j1]; |
| 776 | xi = a[j1 + 1]; |
| 777 | yr = a[k1]; |
| 778 | yi = a[k1 + 1]; |
| 779 | a[j1] = yr; |
| 780 | a[j1 + 1] = yi; |
| 781 | a[k1] = xr; |
| 782 | a[k1 + 1] = xi; |
| 783 | j1 += m2; |
| 784 | k1 += m2; |
| 785 | xr = a[j1]; |
| 786 | xi = a[j1 + 1]; |
| 787 | yr = a[k1]; |
| 788 | yi = a[k1 + 1]; |
| 789 | a[j1] = yr; |
| 790 | a[j1 + 1] = yi; |
| 791 | a[k1] = xr; |
| 792 | a[k1 + 1] = xi; |
| 793 | } |
| 794 | } |
| 795 | } |
| 796 | } |
| 797 | |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 798 | #if 0 // Not used. |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 799 | static void bitrv2conj(int n, int *ip, float *a) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 800 | { |
| 801 | int j, j1, k, k1, l, m, m2; |
| 802 | float xr, xi, yr, yi; |
| 803 | |
| 804 | ip[0] = 0; |
| 805 | l = n; |
| 806 | m = 1; |
| 807 | while ((m << 3) < l) { |
| 808 | l >>= 1; |
| 809 | for (j = 0; j < m; j++) { |
| 810 | ip[m + j] = ip[j] + l; |
| 811 | } |
| 812 | m <<= 1; |
| 813 | } |
| 814 | m2 = 2 * m; |
| 815 | if ((m << 3) == l) { |
| 816 | for (k = 0; k < m; k++) { |
| 817 | for (j = 0; j < k; j++) { |
| 818 | j1 = 2 * j + ip[k]; |
| 819 | k1 = 2 * k + ip[j]; |
| 820 | xr = a[j1]; |
| 821 | xi = -a[j1 + 1]; |
| 822 | yr = a[k1]; |
| 823 | yi = -a[k1 + 1]; |
| 824 | a[j1] = yr; |
| 825 | a[j1 + 1] = yi; |
| 826 | a[k1] = xr; |
| 827 | a[k1 + 1] = xi; |
| 828 | j1 += m2; |
| 829 | k1 += 2 * m2; |
| 830 | xr = a[j1]; |
| 831 | xi = -a[j1 + 1]; |
| 832 | yr = a[k1]; |
| 833 | yi = -a[k1 + 1]; |
| 834 | a[j1] = yr; |
| 835 | a[j1 + 1] = yi; |
| 836 | a[k1] = xr; |
| 837 | a[k1 + 1] = xi; |
| 838 | j1 += m2; |
| 839 | k1 -= m2; |
| 840 | xr = a[j1]; |
| 841 | xi = -a[j1 + 1]; |
| 842 | yr = a[k1]; |
| 843 | yi = -a[k1 + 1]; |
| 844 | a[j1] = yr; |
| 845 | a[j1 + 1] = yi; |
| 846 | a[k1] = xr; |
| 847 | a[k1 + 1] = xi; |
| 848 | j1 += m2; |
| 849 | k1 += 2 * m2; |
| 850 | xr = a[j1]; |
| 851 | xi = -a[j1 + 1]; |
| 852 | yr = a[k1]; |
| 853 | yi = -a[k1 + 1]; |
| 854 | a[j1] = yr; |
| 855 | a[j1 + 1] = yi; |
| 856 | a[k1] = xr; |
| 857 | a[k1 + 1] = xi; |
| 858 | } |
| 859 | k1 = 2 * k + ip[k]; |
| 860 | a[k1 + 1] = -a[k1 + 1]; |
| 861 | j1 = k1 + m2; |
| 862 | k1 = j1 + m2; |
| 863 | xr = a[j1]; |
| 864 | xi = -a[j1 + 1]; |
| 865 | yr = a[k1]; |
| 866 | yi = -a[k1 + 1]; |
| 867 | a[j1] = yr; |
| 868 | a[j1 + 1] = yi; |
| 869 | a[k1] = xr; |
| 870 | a[k1 + 1] = xi; |
| 871 | k1 += m2; |
| 872 | a[k1 + 1] = -a[k1 + 1]; |
| 873 | } |
| 874 | } else { |
| 875 | a[1] = -a[1]; |
| 876 | a[m2 + 1] = -a[m2 + 1]; |
| 877 | for (k = 1; k < m; k++) { |
| 878 | for (j = 0; j < k; j++) { |
| 879 | j1 = 2 * j + ip[k]; |
| 880 | k1 = 2 * k + ip[j]; |
| 881 | xr = a[j1]; |
| 882 | xi = -a[j1 + 1]; |
| 883 | yr = a[k1]; |
| 884 | yi = -a[k1 + 1]; |
| 885 | a[j1] = yr; |
| 886 | a[j1 + 1] = yi; |
| 887 | a[k1] = xr; |
| 888 | a[k1 + 1] = xi; |
| 889 | j1 += m2; |
| 890 | k1 += m2; |
| 891 | xr = a[j1]; |
| 892 | xi = -a[j1 + 1]; |
| 893 | yr = a[k1]; |
| 894 | yi = -a[k1 + 1]; |
| 895 | a[j1] = yr; |
| 896 | a[j1 + 1] = yi; |
| 897 | a[k1] = xr; |
| 898 | a[k1 + 1] = xi; |
| 899 | } |
| 900 | k1 = 2 * k + ip[k]; |
| 901 | a[k1 + 1] = -a[k1 + 1]; |
| 902 | a[k1 + m2 + 1] = -a[k1 + m2 + 1]; |
| 903 | } |
| 904 | } |
| 905 | } |
Peter Kasting | 728d903 | 2015-06-11 14:31:38 -0700 | [diff] [blame] | 906 | #endif |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 907 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 908 | static void cftfsub(size_t n, float *a, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 909 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 910 | size_t j, j1, j2, j3, l; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 911 | float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| 912 | |
| 913 | l = 2; |
| 914 | if (n > 8) { |
| 915 | cft1st(n, a, w); |
| 916 | l = 8; |
| 917 | while ((l << 2) < n) { |
| 918 | cftmdl(n, l, a, w); |
| 919 | l <<= 2; |
| 920 | } |
| 921 | } |
| 922 | if ((l << 2) == n) { |
| 923 | for (j = 0; j < l; j += 2) { |
| 924 | j1 = j + l; |
| 925 | j2 = j1 + l; |
| 926 | j3 = j2 + l; |
| 927 | x0r = a[j] + a[j1]; |
| 928 | x0i = a[j + 1] + a[j1 + 1]; |
| 929 | x1r = a[j] - a[j1]; |
| 930 | x1i = a[j + 1] - a[j1 + 1]; |
| 931 | x2r = a[j2] + a[j3]; |
| 932 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 933 | x3r = a[j2] - a[j3]; |
| 934 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 935 | a[j] = x0r + x2r; |
| 936 | a[j + 1] = x0i + x2i; |
| 937 | a[j2] = x0r - x2r; |
| 938 | a[j2 + 1] = x0i - x2i; |
| 939 | a[j1] = x1r - x3i; |
| 940 | a[j1 + 1] = x1i + x3r; |
| 941 | a[j3] = x1r + x3i; |
| 942 | a[j3 + 1] = x1i - x3r; |
| 943 | } |
| 944 | } else { |
| 945 | for (j = 0; j < l; j += 2) { |
| 946 | j1 = j + l; |
| 947 | x0r = a[j] - a[j1]; |
| 948 | x0i = a[j + 1] - a[j1 + 1]; |
| 949 | a[j] += a[j1]; |
| 950 | a[j + 1] += a[j1 + 1]; |
| 951 | a[j1] = x0r; |
| 952 | a[j1 + 1] = x0i; |
| 953 | } |
| 954 | } |
| 955 | } |
| 956 | |
| 957 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 958 | static void cftbsub(size_t n, float *a, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 959 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 960 | size_t j, j1, j2, j3, l; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 961 | float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| 962 | |
| 963 | l = 2; |
| 964 | if (n > 8) { |
| 965 | cft1st(n, a, w); |
| 966 | l = 8; |
| 967 | while ((l << 2) < n) { |
| 968 | cftmdl(n, l, a, w); |
| 969 | l <<= 2; |
| 970 | } |
| 971 | } |
| 972 | if ((l << 2) == n) { |
| 973 | for (j = 0; j < l; j += 2) { |
| 974 | j1 = j + l; |
| 975 | j2 = j1 + l; |
| 976 | j3 = j2 + l; |
| 977 | x0r = a[j] + a[j1]; |
| 978 | x0i = -a[j + 1] - a[j1 + 1]; |
| 979 | x1r = a[j] - a[j1]; |
| 980 | x1i = -a[j + 1] + a[j1 + 1]; |
| 981 | x2r = a[j2] + a[j3]; |
| 982 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 983 | x3r = a[j2] - a[j3]; |
| 984 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 985 | a[j] = x0r + x2r; |
| 986 | a[j + 1] = x0i - x2i; |
| 987 | a[j2] = x0r - x2r; |
| 988 | a[j2 + 1] = x0i + x2i; |
| 989 | a[j1] = x1r - x3i; |
| 990 | a[j1 + 1] = x1i - x3r; |
| 991 | a[j3] = x1r + x3i; |
| 992 | a[j3 + 1] = x1i + x3r; |
| 993 | } |
| 994 | } else { |
| 995 | for (j = 0; j < l; j += 2) { |
| 996 | j1 = j + l; |
| 997 | x0r = a[j] - a[j1]; |
| 998 | x0i = -a[j + 1] + a[j1 + 1]; |
| 999 | a[j] += a[j1]; |
| 1000 | a[j + 1] = -a[j + 1] - a[j1 + 1]; |
| 1001 | a[j1] = x0r; |
| 1002 | a[j1 + 1] = x0i; |
| 1003 | } |
| 1004 | } |
| 1005 | } |
| 1006 | |
| 1007 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1008 | static void cft1st(size_t n, float *a, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1009 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1010 | size_t j, k1, k2; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1011 | float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; |
| 1012 | float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| 1013 | |
| 1014 | x0r = a[0] + a[2]; |
| 1015 | x0i = a[1] + a[3]; |
| 1016 | x1r = a[0] - a[2]; |
| 1017 | x1i = a[1] - a[3]; |
| 1018 | x2r = a[4] + a[6]; |
| 1019 | x2i = a[5] + a[7]; |
| 1020 | x3r = a[4] - a[6]; |
| 1021 | x3i = a[5] - a[7]; |
| 1022 | a[0] = x0r + x2r; |
| 1023 | a[1] = x0i + x2i; |
| 1024 | a[4] = x0r - x2r; |
| 1025 | a[5] = x0i - x2i; |
| 1026 | a[2] = x1r - x3i; |
| 1027 | a[3] = x1i + x3r; |
| 1028 | a[6] = x1r + x3i; |
| 1029 | a[7] = x1i - x3r; |
| 1030 | wk1r = w[2]; |
| 1031 | x0r = a[8] + a[10]; |
| 1032 | x0i = a[9] + a[11]; |
| 1033 | x1r = a[8] - a[10]; |
| 1034 | x1i = a[9] - a[11]; |
| 1035 | x2r = a[12] + a[14]; |
| 1036 | x2i = a[13] + a[15]; |
| 1037 | x3r = a[12] - a[14]; |
| 1038 | x3i = a[13] - a[15]; |
| 1039 | a[8] = x0r + x2r; |
| 1040 | a[9] = x0i + x2i; |
| 1041 | a[12] = x2i - x0i; |
| 1042 | a[13] = x0r - x2r; |
| 1043 | x0r = x1r - x3i; |
| 1044 | x0i = x1i + x3r; |
| 1045 | a[10] = wk1r * (x0r - x0i); |
| 1046 | a[11] = wk1r * (x0r + x0i); |
| 1047 | x0r = x3i + x1r; |
| 1048 | x0i = x3r - x1i; |
| 1049 | a[14] = wk1r * (x0i - x0r); |
| 1050 | a[15] = wk1r * (x0i + x0r); |
| 1051 | k1 = 0; |
| 1052 | for (j = 16; j < n; j += 16) { |
| 1053 | k1 += 2; |
| 1054 | k2 = 2 * k1; |
| 1055 | wk2r = w[k1]; |
| 1056 | wk2i = w[k1 + 1]; |
| 1057 | wk1r = w[k2]; |
| 1058 | wk1i = w[k2 + 1]; |
| 1059 | wk3r = wk1r - 2 * wk2i * wk1i; |
| 1060 | wk3i = 2 * wk2i * wk1r - wk1i; |
| 1061 | x0r = a[j] + a[j + 2]; |
| 1062 | x0i = a[j + 1] + a[j + 3]; |
| 1063 | x1r = a[j] - a[j + 2]; |
| 1064 | x1i = a[j + 1] - a[j + 3]; |
| 1065 | x2r = a[j + 4] + a[j + 6]; |
| 1066 | x2i = a[j + 5] + a[j + 7]; |
| 1067 | x3r = a[j + 4] - a[j + 6]; |
| 1068 | x3i = a[j + 5] - a[j + 7]; |
| 1069 | a[j] = x0r + x2r; |
| 1070 | a[j + 1] = x0i + x2i; |
| 1071 | x0r -= x2r; |
| 1072 | x0i -= x2i; |
| 1073 | a[j + 4] = wk2r * x0r - wk2i * x0i; |
| 1074 | a[j + 5] = wk2r * x0i + wk2i * x0r; |
| 1075 | x0r = x1r - x3i; |
| 1076 | x0i = x1i + x3r; |
| 1077 | a[j + 2] = wk1r * x0r - wk1i * x0i; |
| 1078 | a[j + 3] = wk1r * x0i + wk1i * x0r; |
| 1079 | x0r = x1r + x3i; |
| 1080 | x0i = x1i - x3r; |
| 1081 | a[j + 6] = wk3r * x0r - wk3i * x0i; |
| 1082 | a[j + 7] = wk3r * x0i + wk3i * x0r; |
| 1083 | wk1r = w[k2 + 2]; |
| 1084 | wk1i = w[k2 + 3]; |
| 1085 | wk3r = wk1r - 2 * wk2r * wk1i; |
| 1086 | wk3i = 2 * wk2r * wk1r - wk1i; |
| 1087 | x0r = a[j + 8] + a[j + 10]; |
| 1088 | x0i = a[j + 9] + a[j + 11]; |
| 1089 | x1r = a[j + 8] - a[j + 10]; |
| 1090 | x1i = a[j + 9] - a[j + 11]; |
| 1091 | x2r = a[j + 12] + a[j + 14]; |
| 1092 | x2i = a[j + 13] + a[j + 15]; |
| 1093 | x3r = a[j + 12] - a[j + 14]; |
| 1094 | x3i = a[j + 13] - a[j + 15]; |
| 1095 | a[j + 8] = x0r + x2r; |
| 1096 | a[j + 9] = x0i + x2i; |
| 1097 | x0r -= x2r; |
| 1098 | x0i -= x2i; |
| 1099 | a[j + 12] = -wk2i * x0r - wk2r * x0i; |
| 1100 | a[j + 13] = -wk2i * x0i + wk2r * x0r; |
| 1101 | x0r = x1r - x3i; |
| 1102 | x0i = x1i + x3r; |
| 1103 | a[j + 10] = wk1r * x0r - wk1i * x0i; |
| 1104 | a[j + 11] = wk1r * x0i + wk1i * x0r; |
| 1105 | x0r = x1r + x3i; |
| 1106 | x0i = x1i - x3r; |
| 1107 | a[j + 14] = wk3r * x0r - wk3i * x0i; |
| 1108 | a[j + 15] = wk3r * x0i + wk3i * x0r; |
| 1109 | } |
| 1110 | } |
| 1111 | |
| 1112 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1113 | static void cftmdl(size_t n, size_t l, float *a, float *w) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1114 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1115 | size_t j, j1, j2, j3, k, k1, k2, m, m2; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1116 | float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i; |
| 1117 | float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| 1118 | |
| 1119 | m = l << 2; |
| 1120 | for (j = 0; j < l; j += 2) { |
| 1121 | j1 = j + l; |
| 1122 | j2 = j1 + l; |
| 1123 | j3 = j2 + l; |
| 1124 | x0r = a[j] + a[j1]; |
| 1125 | x0i = a[j + 1] + a[j1 + 1]; |
| 1126 | x1r = a[j] - a[j1]; |
| 1127 | x1i = a[j + 1] - a[j1 + 1]; |
| 1128 | x2r = a[j2] + a[j3]; |
| 1129 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 1130 | x3r = a[j2] - a[j3]; |
| 1131 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 1132 | a[j] = x0r + x2r; |
| 1133 | a[j + 1] = x0i + x2i; |
| 1134 | a[j2] = x0r - x2r; |
| 1135 | a[j2 + 1] = x0i - x2i; |
| 1136 | a[j1] = x1r - x3i; |
| 1137 | a[j1 + 1] = x1i + x3r; |
| 1138 | a[j3] = x1r + x3i; |
| 1139 | a[j3 + 1] = x1i - x3r; |
| 1140 | } |
| 1141 | wk1r = w[2]; |
| 1142 | for (j = m; j < l + m; j += 2) { |
| 1143 | j1 = j + l; |
| 1144 | j2 = j1 + l; |
| 1145 | j3 = j2 + l; |
| 1146 | x0r = a[j] + a[j1]; |
| 1147 | x0i = a[j + 1] + a[j1 + 1]; |
| 1148 | x1r = a[j] - a[j1]; |
| 1149 | x1i = a[j + 1] - a[j1 + 1]; |
| 1150 | x2r = a[j2] + a[j3]; |
| 1151 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 1152 | x3r = a[j2] - a[j3]; |
| 1153 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 1154 | a[j] = x0r + x2r; |
| 1155 | a[j + 1] = x0i + x2i; |
| 1156 | a[j2] = x2i - x0i; |
| 1157 | a[j2 + 1] = x0r - x2r; |
| 1158 | x0r = x1r - x3i; |
| 1159 | x0i = x1i + x3r; |
| 1160 | a[j1] = wk1r * (x0r - x0i); |
| 1161 | a[j1 + 1] = wk1r * (x0r + x0i); |
| 1162 | x0r = x3i + x1r; |
| 1163 | x0i = x3r - x1i; |
| 1164 | a[j3] = wk1r * (x0i - x0r); |
| 1165 | a[j3 + 1] = wk1r * (x0i + x0r); |
| 1166 | } |
| 1167 | k1 = 0; |
| 1168 | m2 = 2 * m; |
| 1169 | for (k = m2; k < n; k += m2) { |
| 1170 | k1 += 2; |
| 1171 | k2 = 2 * k1; |
| 1172 | wk2r = w[k1]; |
| 1173 | wk2i = w[k1 + 1]; |
| 1174 | wk1r = w[k2]; |
| 1175 | wk1i = w[k2 + 1]; |
| 1176 | wk3r = wk1r - 2 * wk2i * wk1i; |
| 1177 | wk3i = 2 * wk2i * wk1r - wk1i; |
| 1178 | for (j = k; j < l + k; j += 2) { |
| 1179 | j1 = j + l; |
| 1180 | j2 = j1 + l; |
| 1181 | j3 = j2 + l; |
| 1182 | x0r = a[j] + a[j1]; |
| 1183 | x0i = a[j + 1] + a[j1 + 1]; |
| 1184 | x1r = a[j] - a[j1]; |
| 1185 | x1i = a[j + 1] - a[j1 + 1]; |
| 1186 | x2r = a[j2] + a[j3]; |
| 1187 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 1188 | x3r = a[j2] - a[j3]; |
| 1189 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 1190 | a[j] = x0r + x2r; |
| 1191 | a[j + 1] = x0i + x2i; |
| 1192 | x0r -= x2r; |
| 1193 | x0i -= x2i; |
| 1194 | a[j2] = wk2r * x0r - wk2i * x0i; |
| 1195 | a[j2 + 1] = wk2r * x0i + wk2i * x0r; |
| 1196 | x0r = x1r - x3i; |
| 1197 | x0i = x1i + x3r; |
| 1198 | a[j1] = wk1r * x0r - wk1i * x0i; |
| 1199 | a[j1 + 1] = wk1r * x0i + wk1i * x0r; |
| 1200 | x0r = x1r + x3i; |
| 1201 | x0i = x1i - x3r; |
| 1202 | a[j3] = wk3r * x0r - wk3i * x0i; |
| 1203 | a[j3 + 1] = wk3r * x0i + wk3i * x0r; |
| 1204 | } |
| 1205 | wk1r = w[k2 + 2]; |
| 1206 | wk1i = w[k2 + 3]; |
| 1207 | wk3r = wk1r - 2 * wk2r * wk1i; |
| 1208 | wk3i = 2 * wk2r * wk1r - wk1i; |
| 1209 | for (j = k + m; j < l + (k + m); j += 2) { |
| 1210 | j1 = j + l; |
| 1211 | j2 = j1 + l; |
| 1212 | j3 = j2 + l; |
| 1213 | x0r = a[j] + a[j1]; |
| 1214 | x0i = a[j + 1] + a[j1 + 1]; |
| 1215 | x1r = a[j] - a[j1]; |
| 1216 | x1i = a[j + 1] - a[j1 + 1]; |
| 1217 | x2r = a[j2] + a[j3]; |
| 1218 | x2i = a[j2 + 1] + a[j3 + 1]; |
| 1219 | x3r = a[j2] - a[j3]; |
| 1220 | x3i = a[j2 + 1] - a[j3 + 1]; |
| 1221 | a[j] = x0r + x2r; |
| 1222 | a[j + 1] = x0i + x2i; |
| 1223 | x0r -= x2r; |
| 1224 | x0i -= x2i; |
| 1225 | a[j2] = -wk2i * x0r - wk2r * x0i; |
| 1226 | a[j2 + 1] = -wk2i * x0i + wk2r * x0r; |
| 1227 | x0r = x1r - x3i; |
| 1228 | x0i = x1i + x3r; |
| 1229 | a[j1] = wk1r * x0r - wk1i * x0i; |
| 1230 | a[j1 + 1] = wk1r * x0i + wk1i * x0r; |
| 1231 | x0r = x1r + x3i; |
| 1232 | x0i = x1i - x3r; |
| 1233 | a[j3] = wk3r * x0r - wk3i * x0i; |
| 1234 | a[j3 + 1] = wk3r * x0i + wk3i * x0r; |
| 1235 | } |
| 1236 | } |
| 1237 | } |
| 1238 | |
| 1239 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1240 | static void rftfsub(size_t n, float *a, size_t nc, float *c) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1241 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1242 | size_t j, k, kk, ks, m; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1243 | float wkr, wki, xr, xi, yr, yi; |
| 1244 | |
| 1245 | m = n >> 1; |
| 1246 | ks = 2 * nc / m; |
| 1247 | kk = 0; |
| 1248 | for (j = 2; j < m; j += 2) { |
| 1249 | k = n - j; |
| 1250 | kk += ks; |
| 1251 | wkr = 0.5f - c[nc - kk]; |
| 1252 | wki = c[kk]; |
| 1253 | xr = a[j] - a[k]; |
| 1254 | xi = a[j + 1] + a[k + 1]; |
| 1255 | yr = wkr * xr - wki * xi; |
| 1256 | yi = wkr * xi + wki * xr; |
| 1257 | a[j] -= yr; |
| 1258 | a[j + 1] -= yi; |
| 1259 | a[k] += yr; |
| 1260 | a[k + 1] -= yi; |
| 1261 | } |
| 1262 | } |
| 1263 | |
| 1264 | |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1265 | static void rftbsub(size_t n, float *a, size_t nc, float *c) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1266 | { |
Peter Kasting | dce40cf | 2015-08-24 14:52:23 -0700 | [diff] [blame] | 1267 | size_t j, k, kk, ks, m; |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1268 | float wkr, wki, xr, xi, yr, yi; |
| 1269 | |
| 1270 | a[1] = -a[1]; |
| 1271 | m = n >> 1; |
| 1272 | ks = 2 * nc / m; |
| 1273 | kk = 0; |
| 1274 | for (j = 2; j < m; j += 2) { |
| 1275 | k = n - j; |
| 1276 | kk += ks; |
| 1277 | wkr = 0.5f - c[nc - kk]; |
| 1278 | wki = c[kk]; |
| 1279 | xr = a[j] - a[k]; |
| 1280 | xi = a[j + 1] + a[k + 1]; |
| 1281 | yr = wkr * xr + wki * xi; |
| 1282 | yi = wkr * xi - wki * xr; |
| 1283 | a[j] -= yr; |
| 1284 | a[j + 1] = yi - a[j + 1]; |
| 1285 | a[k] += yr; |
| 1286 | a[k + 1] = yi - a[k + 1]; |
| 1287 | } |
| 1288 | a[m + 1] = -a[m + 1]; |
| 1289 | } |
| 1290 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 1291 | #if 0 // Not used. |
| 1292 | static void dctsub(int n, float *a, int nc, float *c) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1293 | { |
| 1294 | int j, k, kk, ks, m; |
| 1295 | float wkr, wki, xr; |
| 1296 | |
| 1297 | m = n >> 1; |
| 1298 | ks = nc / n; |
| 1299 | kk = 0; |
| 1300 | for (j = 1; j < m; j++) { |
| 1301 | k = n - j; |
| 1302 | kk += ks; |
| 1303 | wkr = c[kk] - c[nc - kk]; |
| 1304 | wki = c[kk] + c[nc - kk]; |
| 1305 | xr = wki * a[j] - wkr * a[k]; |
| 1306 | a[j] = wkr * a[j] + wki * a[k]; |
| 1307 | a[k] = xr; |
| 1308 | } |
| 1309 | a[m] *= c[0]; |
| 1310 | } |
| 1311 | |
| 1312 | |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 1313 | static void dstsub(int n, float *a, int nc, float *c) |
niklase@google.com | 470e71d | 2011-07-07 08:21:25 +0000 | [diff] [blame] | 1314 | { |
| 1315 | int j, k, kk, ks, m; |
| 1316 | float wkr, wki, xr; |
| 1317 | |
| 1318 | m = n >> 1; |
| 1319 | ks = nc / n; |
| 1320 | kk = 0; |
| 1321 | for (j = 1; j < m; j++) { |
| 1322 | k = n - j; |
| 1323 | kk += ks; |
| 1324 | wkr = c[kk] - c[nc - kk]; |
| 1325 | wki = c[kk] + c[nc - kk]; |
| 1326 | xr = wki * a[k] - wkr * a[j]; |
| 1327 | a[k] = wkr * a[k] + wki * a[j]; |
| 1328 | a[j] = xr; |
| 1329 | } |
| 1330 | a[m] *= c[0]; |
| 1331 | } |
pwestin@webrtc.org | f4d3b9d | 2011-12-22 12:33:08 +0000 | [diff] [blame] | 1332 | #endif // Not used. |