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| 1 : | Isibaar | 1989 | /***************************************************************************** |
| 2 : | * | ||
| 3 : | * XVID MPEG-4 VIDEO CODEC | ||
| 4 : | * - Forward DCT - | ||
| 5 : | * | ||
| 6 : | * Copyright (C) 2006-2011 Xvid Solutions GmbH | ||
| 7 : | * | ||
| 8 : | * This program is free software ; you can redistribute it and/or modify | ||
| 9 : | * it under the terms of the GNU General Public License as published by | ||
| 10 : | * the Free Software Foundation ; either version 2 of the License, or | ||
| 11 : | * (at your option) any later version. | ||
| 12 : | * | ||
| 13 : | * This program is distributed in the hope that it will be useful, | ||
| 14 : | * but WITHOUT ANY WARRANTY ; without even the implied warranty of | ||
| 15 : | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| 16 : | * GNU General Public License for more details. | ||
| 17 : | * | ||
| 18 : | * You should have received a copy of the GNU General Public License | ||
| 19 : | * along with this program ; if not, write to the Free Software | ||
| 20 : | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 21 : | * | ||
| 22 : | * $Id$ | ||
| 23 : | * | ||
| 24 : | ****************************************************************************/ | ||
| 25 : | |||
| 26 : | Isibaar | 1979 | /* |
| 27 : | * Authors: Skal | ||
| 28 : | * | ||
| 29 : | * "Fast and precise" LLM implementation of FDCT/IDCT, where | ||
| 30 : | * rotations are decomposed using: | ||
| 31 : | * tmp = (x+y).cos t | ||
| 32 : | * x' = tmp + y.(sin t - cos t) | ||
| 33 : | * y' = tmp - x.(sin t + cos t) | ||
| 34 : | * | ||
| 35 : | * See details at the end of this file... | ||
| 36 : | * | ||
| 37 : | * Reference (e.g.): | ||
| 38 : | * Loeffler C., Ligtenberg A., and Moschytz C.S.: | ||
| 39 : | * Practical Fast 1D DCT Algorithm with Eleven Multiplications, | ||
| 40 : | * Proc. ICASSP 1989, 988-991. | ||
| 41 : | * | ||
| 42 : | * IEEE-1180-like error specs for FDCT: | ||
| 43 : | * Peak error: 1.0000 | ||
| 44 : | * Peak MSE: 0.0340 | ||
| 45 : | * Overall MSE: 0.0200 | ||
| 46 : | * Peak ME: 0.0191 | ||
| 47 : | * Overall ME: -0.0033 | ||
| 48 : | * | ||
| 49 : | ********************************************************/ | ||
| 50 : | |||
| 51 : | #include "fdct.h" | ||
| 52 : | |||
| 53 : | /* function pointer */ | ||
| 54 : | fdctFuncPtr fdct; | ||
| 55 : | |||
| 56 : | /* | ||
| 57 : | ////////////////////////////////////////////////////////// | ||
| 58 : | */ | ||
| 59 : | |||
| 60 : | #define BUTF(a, b, tmp) \ | ||
| 61 : | (tmp) = (a)+(b); \ | ||
| 62 : | (b) = (a)-(b); \ | ||
| 63 : | (a) = (tmp) | ||
| 64 : | |||
| 65 : | #define LOAD_BUTF(m1, m2, a, b, tmp, S) \ | ||
| 66 : | (m1) = (S)[(a)] + (S)[(b)]; \ | ||
| 67 : | (m2) = (S)[(a)] - (S)[(b)] | ||
| 68 : | |||
| 69 : | #define ROTATE(m1,m2,c,k1,k2,tmp,Fix,Rnd) \ | ||
| 70 : | (tmp) = ( (m1) + (m2) )*(c); \ | ||
| 71 : | (m1) *= k1; \ | ||
| 72 : | (m2) *= k2; \ | ||
| 73 : | (tmp) += (Rnd); \ | ||
| 74 : | (m1) = ((m1)+(tmp))>>(Fix); \ | ||
| 75 : | (m2) = ((m2)+(tmp))>>(Fix); | ||
| 76 : | |||
| 77 : | #define ROTATE2(m1,m2,c,k1,k2,tmp) \ | ||
| 78 : | (tmp) = ( (m1) + (m2) )*(c); \ | ||
| 79 : | (m1) *= k1; \ | ||
| 80 : | (m2) *= k2; \ | ||
| 81 : | (m1) = (m1)+(tmp); \ | ||
| 82 : | (m2) = (m2)+(tmp); | ||
| 83 : | |||
| 84 : | #define ROTATE0(m1,m2,c,k1,k2,tmp) \ | ||
| 85 : | (m1) = ( (m2) )*(c); \ | ||
| 86 : | (m2) = (m2)*k2+(m1); | ||
| 87 : | |||
| 88 : | #define SHIFTL(x,n) ((x)<<(n)) | ||
| 89 : | #define SHIFTR(x, n) ((x)>>(n)) | ||
| 90 : | #define HALF(n) (1<<((n)-1)) | ||
| 91 : | |||
| 92 : | #define IPASS 3 | ||
| 93 : | #define FPASS 2 | ||
| 94 : | #define FIX 16 | ||
| 95 : | |||
| 96 : | #if 1 | ||
| 97 : | |||
| 98 : | #define ROT6_C 35468 | ||
| 99 : | #define ROT6_SmC 50159 | ||
| 100 : | #define ROT6_SpC 121095 | ||
| 101 : | #define ROT17_C 77062 | ||
| 102 : | #define ROT17_SmC 25571 | ||
| 103 : | #define ROT17_SpC 128553 | ||
| 104 : | #define ROT37_C 58981 | ||
| 105 : | #define ROT37_SmC 98391 | ||
| 106 : | #define ROT37_SpC 19571 | ||
| 107 : | #define ROT13_C 167963 | ||
| 108 : | #define ROT13_SmC 134553 | ||
| 109 : | #define ROT13_SpC 201373 | ||
| 110 : | |||
| 111 : | #else | ||
| 112 : | |||
| 113 : | #include <math.h> | ||
| 114 : | #define FX(x) ( (int)floor((x)*(1<<FIX) + .5 ) ) | ||
| 115 : | |||
| 116 : | static const double c1 = cos(1.*M_PI/16); | ||
| 117 : | static const double c2 = cos(2.*M_PI/16); | ||
| 118 : | static const double c3 = cos(3.*M_PI/16); | ||
| 119 : | static const double c4 = cos(4.*M_PI/16); | ||
| 120 : | static const double c5 = cos(5.*M_PI/16); | ||
| 121 : | static const double c6 = cos(6.*M_PI/16); | ||
| 122 : | static const double c7 = cos(7.*M_PI/16); | ||
| 123 : | |||
| 124 : | static const int ROT6_C = FX(c2-c6); // 0.541 | ||
| 125 : | static const int ROT6_SmC = FX(2*c6); // 0.765 | ||
| 126 : | static const int ROT6_SpC = FX(2*c2); // 1.847 | ||
| 127 : | |||
| 128 : | static const int ROT17_C = FX(c1+c7); // 1.175 | ||
| 129 : | static const int ROT17_SmC = FX(2*c7); // 0.390 | ||
| 130 : | static const int ROT17_SpC = FX(2*c1); // 1.961 | ||
| 131 : | |||
| 132 : | static const int ROT37_C = FX((c3-c7)/c4); // 0.899 | ||
| 133 : | static const int ROT37_SmC = FX(2*(c5+c7)); // 1.501 | ||
| 134 : | static const int ROT37_SpC = FX(2*(c1-c3)); // 0.298 | ||
| 135 : | |||
| 136 : | static const int ROT13_C = FX((c1+c3)/c4); // 2.562 | ||
| 137 : | static const int ROT13_SmC = FX(2*(c3+c7)); // 2.053 | ||
| 138 : | static const int ROT13_SpC = FX(2*(c1+c5)); // 3.072 | ||
| 139 : | |||
| 140 : | #endif | ||
| 141 : | |||
| 142 : | /* | ||
| 143 : | ////////////////////////////////////////////////////////// | ||
| 144 : | // Forward transform | ||
| 145 : | */ | ||
| 146 : | |||
| 147 : | void fdct_int32( short *const In ) | ||
| 148 : | { | ||
| 149 : | short *pIn; | ||
| 150 : | int i; | ||
| 151 : | |||
| 152 : | pIn = In; | ||
| 153 : | for(i=8; i>0; --i) | ||
| 154 : | { | ||
| 155 : | int mm0, mm1, mm2, mm3, mm4, mm5, mm6, mm7, Spill; | ||
| 156 : | |||
| 157 : | // even | ||
| 158 : | |||
| 159 : | LOAD_BUTF(mm1,mm6, 1, 6, mm0, pIn); | ||
| 160 : | LOAD_BUTF(mm2,mm5, 2, 5, mm0, pIn); | ||
| 161 : | LOAD_BUTF(mm3,mm4, 3, 4, mm0, pIn); | ||
| 162 : | LOAD_BUTF(mm0,mm7, 0, 7, Spill, pIn); | ||
| 163 : | |||
| 164 : | BUTF(mm1, mm2, Spill); | ||
| 165 : | BUTF(mm0, mm3, Spill); | ||
| 166 : | |||
| 167 : | ROTATE(mm3, mm2, ROT6_C, ROT6_SmC, -ROT6_SpC, Spill, FIX-FPASS, HALF(FIX-FPASS)); | ||
| 168 : | pIn[2] = mm3; | ||
| 169 : | pIn[6] = mm2; | ||
| 170 : | |||
| 171 : | BUTF(mm0, mm1, Spill); | ||
| 172 : | pIn[0] = SHIFTL(mm0, FPASS); | ||
| 173 : | pIn[4] = SHIFTL(mm1, FPASS); | ||
| 174 : | |||
| 175 : | |||
| 176 : | // odd | ||
| 177 : | |||
| 178 : | mm3 = mm5 + mm7; | ||
| 179 : | mm2 = mm4 + mm6; | ||
| 180 : | ROTATE(mm2, mm3, ROT17_C, -ROT17_SpC, -ROT17_SmC, mm0, FIX-FPASS, HALF(FIX-FPASS)); | ||
| 181 : | ROTATE(mm4, mm7, -ROT37_C, ROT37_SpC, ROT37_SmC, mm0, FIX-FPASS, HALF(FIX-FPASS)); | ||
| 182 : | mm7 += mm3; | ||
| 183 : | mm4 += mm2; | ||
| 184 : | pIn[1] = mm7; | ||
| 185 : | pIn[7] = mm4; | ||
| 186 : | |||
| 187 : | ROTATE(mm5, mm6, -ROT13_C, ROT13_SmC, ROT13_SpC, mm0, FIX-FPASS, HALF(FIX-FPASS)); | ||
| 188 : | mm5 += mm3; | ||
| 189 : | mm6 += mm2; | ||
| 190 : | pIn[3] = mm6; | ||
| 191 : | pIn[5] = mm5; | ||
| 192 : | |||
| 193 : | pIn += 8; | ||
| 194 : | } | ||
| 195 : | |||
| 196 : | pIn = In; | ||
| 197 : | for(i=8; i>0; --i) | ||
| 198 : | { | ||
| 199 : | int mm0, mm1, mm2, mm3, mm4, mm5, mm6, mm7, Spill; | ||
| 200 : | |||
| 201 : | // even | ||
| 202 : | |||
| 203 : | LOAD_BUTF(mm1,mm6, 1*8, 6*8, mm0, pIn); | ||
| 204 : | LOAD_BUTF(mm2,mm5, 2*8, 5*8, mm0, pIn); | ||
| 205 : | BUTF(mm1, mm2, mm0); | ||
| 206 : | |||
| 207 : | LOAD_BUTF(mm3,mm4, 3*8, 4*8, mm0, pIn); | ||
| 208 : | LOAD_BUTF(mm0,mm7, 0*8, 7*8, Spill, pIn); | ||
| 209 : | BUTF(mm0, mm3, Spill); | ||
| 210 : | |||
| 211 : | ROTATE(mm3, mm2, ROT6_C, ROT6_SmC, -ROT6_SpC, Spill, 0, HALF(FIX+FPASS+3)); | ||
| 212 : | pIn[2*8] = (int16_t)SHIFTR(mm3,FIX+FPASS+3); | ||
| 213 : | pIn[6*8] = (int16_t)SHIFTR(mm2,FIX+FPASS+3); | ||
| 214 : | |||
| 215 : | mm0 += HALF(FPASS+3) - 1; | ||
| 216 : | BUTF(mm0, mm1, Spill); | ||
| 217 : | pIn[0*8] = (int16_t)SHIFTR(mm0, FPASS+3); | ||
| 218 : | pIn[4*8] = (int16_t)SHIFTR(mm1, FPASS+3); | ||
| 219 : | |||
| 220 : | // odd | ||
| 221 : | |||
| 222 : | mm3 = mm5 + mm7; | ||
| 223 : | mm2 = mm4 + mm6; | ||
| 224 : | |||
| 225 : | ROTATE(mm2, mm3, ROT17_C, -ROT17_SpC, -ROT17_SmC, mm0, 0, HALF(FIX+FPASS+3)); | ||
| 226 : | ROTATE2(mm4, mm7, -ROT37_C, ROT37_SpC, ROT37_SmC, mm0); | ||
| 227 : | mm7 += mm3; | ||
| 228 : | mm4 += mm2; | ||
| 229 : | pIn[7*8] = (int16_t)SHIFTR(mm4,FIX+FPASS+3); | ||
| 230 : | pIn[1*8] = (int16_t)SHIFTR(mm7,FIX+FPASS+3); | ||
| 231 : | |||
| 232 : | ROTATE2(mm5, mm6, -ROT13_C, ROT13_SmC, ROT13_SpC, mm0); | ||
| 233 : | mm5 += mm3; | ||
| 234 : | mm6 += mm2; | ||
| 235 : | pIn[5*8] = (int16_t)SHIFTR(mm5,FIX+FPASS+3); | ||
| 236 : | pIn[3*8] = (int16_t)SHIFTR(mm6,FIX+FPASS+3); | ||
| 237 : | |||
| 238 : | pIn++; | ||
| 239 : | } | ||
| 240 : | } | ||
| 241 : | #undef FIX | ||
| 242 : | #undef FPASS | ||
| 243 : | #undef IPASS | ||
| 244 : | |||
| 245 : | #undef BUTF | ||
| 246 : | #undef LOAD_BUTF | ||
| 247 : | #undef ROTATE | ||
| 248 : | #undef ROTATE2 | ||
| 249 : | #undef SHIFTL | ||
| 250 : | #undef SHIFTR | ||
| 251 : | |||
| 252 : | ////////////////////////////////////////////////////////// | ||
| 253 : | // - Data flow schematics for FDCT - | ||
| 254 : | // Output is scaled by 2.sqrt(2) | ||
| 255 : | // Initial butterflies (in0/in7, etc.) are not fully depicted. | ||
| 256 : | // Note: Rot6 coeffs are multiplied by sqrt(2). | ||
| 257 : | ////////////////////////////////////////////////////////// | ||
| 258 : | /* | ||
| 259 : | <---------Stage1 =even part=-----------> | ||
| 260 : | |||
| 261 : | in3 mm3 +_____.___-___________.____* out6 | ||
| 262 : | x \ / | | ||
| 263 : | in4 mm4 \ | | ||
| 264 : | / \ | | ||
| 265 : | in0 mm0 +_____o___+__.___-___ | ___* out4 | ||
| 266 : | x \ / | | ||
| 267 : | in7 mm7 \ (Rot6) | ||
| 268 : | / \ | | ||
| 269 : | in1 mm1 +_____o___+__o___+___ | ___* out0 | ||
| 270 : | x \ / | | ||
| 271 : | in6 mm6 / | | ||
| 272 : | / \ | | ||
| 273 : | in2 mm2 +_____.___-___________o____* out2 | ||
| 274 : | x | ||
| 275 : | in5 mm5 | ||
| 276 : | |||
| 277 : | <---------Stage2 =odd part=----------------> | ||
| 278 : | |||
| 279 : | mm7*___._________.___-___[xSqrt2]___* out3 | ||
| 280 : | | \ / | ||
| 281 : | (Rot3) \ | ||
| 282 : | | / \ | ||
| 283 : | mm5*__ | ___o____o___+___.___-______* out7 | ||
| 284 : | | | \ / | ||
| 285 : | | (Rot1) \ | ||
| 286 : | | | / \ | ||
| 287 : | mm6*__ |____.____o___+___o___+______* out1 | ||
| 288 : | | \ / | ||
| 289 : | | / | ||
| 290 : | | / \ | ||
| 291 : | mm4*___o_________.___-___[xSqrt2]___* out5 | ||
| 292 : | |||
| 293 : | |||
| 294 : | |||
| 295 : | Alternative schematics for stage 2: | ||
| 296 : | ----------------------------------- | ||
| 297 : | |||
| 298 : | mm7 *___[xSqrt2]____o___+____o_______* out1 | ||
| 299 : | \ / | | ||
| 300 : | / (Rot1) | ||
| 301 : | / \ | | ||
| 302 : | mm6 *____o___+______.___-___ | __.___* out5 | ||
| 303 : | \ / | | | ||
| 304 : | / | | | ||
| 305 : | / \ | | | ||
| 306 : | mm5 *____.___-______.___-____.__ | __* out7 | ||
| 307 : | \ / | | ||
| 308 : | \ (Rot3) | ||
| 309 : | / \ | | ||
| 310 : | mm4 *___[xSqrt2]____o___+________o___* out3 | ||
| 311 : | |||
| 312 : | */ |
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