jfdctint_template.c (15669B)
1 /* 2 * This file is part of the Independent JPEG Group's software. 3 * 4 * The authors make NO WARRANTY or representation, either express or implied, 5 * with respect to this software, its quality, accuracy, merchantability, or 6 * fitness for a particular purpose. This software is provided "AS IS", and 7 * you, its user, assume the entire risk as to its quality and accuracy. 8 * 9 * This software is copyright (C) 1991-1996, Thomas G. Lane. 10 * All Rights Reserved except as specified below. 11 * 12 * Permission is hereby granted to use, copy, modify, and distribute this 13 * software (or portions thereof) for any purpose, without fee, subject to 14 * these conditions: 15 * (1) If any part of the source code for this software is distributed, then 16 * this README file must be included, with this copyright and no-warranty 17 * notice unaltered; and any additions, deletions, or changes to the original 18 * files must be clearly indicated in accompanying documentation. 19 * (2) If only executable code is distributed, then the accompanying 20 * documentation must state that "this software is based in part on the work 21 * of the Independent JPEG Group". 22 * (3) Permission for use of this software is granted only if the user accepts 23 * full responsibility for any undesirable consequences; the authors accept 24 * NO LIABILITY for damages of any kind. 25 * 26 * These conditions apply to any software derived from or based on the IJG 27 * code, not just to the unmodified library. If you use our work, you ought 28 * to acknowledge us. 29 * 30 * Permission is NOT granted for the use of any IJG author's name or company 31 * name in advertising or publicity relating to this software or products 32 * derived from it. This software may be referred to only as "the Independent 33 * JPEG Group's software". 34 * 35 * We specifically permit and encourage the use of this software as the basis 36 * of commercial products, provided that all warranty or liability claims are 37 * assumed by the product vendor. 38 * 39 * This file contains a slow-but-accurate integer implementation of the 40 * forward DCT (Discrete Cosine Transform). 41 * 42 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 43 * on each column. Direct algorithms are also available, but they are 44 * much more complex and seem not to be any faster when reduced to code. 45 * 46 * This implementation is based on an algorithm described in 47 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 48 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 49 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 50 * The primary algorithm described there uses 11 multiplies and 29 adds. 51 * We use their alternate method with 12 multiplies and 32 adds. 52 * The advantage of this method is that no data path contains more than one 53 * multiplication; this allows a very simple and accurate implementation in 54 * scaled fixed-point arithmetic, with a minimal number of shifts. 55 */ 56 57 /** 58 * @file 59 * Independent JPEG Group's slow & accurate dct. 60 */ 61 62 #include "libavutil/common.h" 63 #include "fdctdsp.h" 64 65 #include "bit_depth_template.c" 66 67 #define DCTSIZE 8 68 #define BITS_IN_JSAMPLE BIT_DEPTH 69 #define GLOBAL(x) x 70 #define RIGHT_SHIFT(x, n) ((x) >> (n)) 71 #define MULTIPLY16C16(var,const) ((var)*(const)) 72 #define DESCALE(x,n) RIGHT_SHIFT((int)(x) + (1 << ((n) - 1)), n) 73 74 75 /* 76 * This module is specialized to the case DCTSIZE = 8. 77 */ 78 79 #if DCTSIZE != 8 80 #error "Sorry, this code only copes with 8x8 DCTs." 81 #endif 82 83 84 /* 85 * The poop on this scaling stuff is as follows: 86 * 87 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 88 * larger than the true DCT outputs. The final outputs are therefore 89 * a factor of N larger than desired; since N=8 this can be cured by 90 * a simple right shift at the end of the algorithm. The advantage of 91 * this arrangement is that we save two multiplications per 1-D DCT, 92 * because the y0 and y4 outputs need not be divided by sqrt(N). 93 * In the IJG code, this factor of 8 is removed by the quantization step 94 * (in jcdctmgr.c), NOT in this module. 95 * 96 * We have to do addition and subtraction of the integer inputs, which 97 * is no problem, and multiplication by fractional constants, which is 98 * a problem to do in integer arithmetic. We multiply all the constants 99 * by CONST_SCALE and convert them to integer constants (thus retaining 100 * CONST_BITS bits of precision in the constants). After doing a 101 * multiplication we have to divide the product by CONST_SCALE, with proper 102 * rounding, to produce the correct output. This division can be done 103 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 104 * as long as possible so that partial sums can be added together with 105 * full fractional precision. 106 * 107 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 108 * they are represented to better-than-integral precision. These outputs 109 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 110 * with the recommended scaling. (For 12-bit sample data, the intermediate 111 * array is int32_t anyway.) 112 * 113 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 114 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 115 * shows that the values given below are the most effective. 116 */ 117 118 #undef CONST_BITS 119 #undef PASS1_BITS 120 #undef OUT_SHIFT 121 122 #if BITS_IN_JSAMPLE == 8 123 #define CONST_BITS 13 124 #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */ 125 #define OUT_SHIFT PASS1_BITS 126 #else 127 #define CONST_BITS 13 128 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 129 #define OUT_SHIFT (PASS1_BITS + 1) 130 #endif 131 132 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 133 * causing a lot of useless floating-point operations at run time. 134 * To get around this we use the following pre-calculated constants. 135 * If you change CONST_BITS you may want to add appropriate values. 136 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 137 */ 138 139 #if CONST_BITS == 13 140 #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */ 141 #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */ 142 #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */ 143 #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */ 144 #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */ 145 #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */ 146 #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */ 147 #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */ 148 #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */ 149 #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */ 150 #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */ 151 #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */ 152 #else 153 #define FIX_0_298631336 FIX(0.298631336) 154 #define FIX_0_390180644 FIX(0.390180644) 155 #define FIX_0_541196100 FIX(0.541196100) 156 #define FIX_0_765366865 FIX(0.765366865) 157 #define FIX_0_899976223 FIX(0.899976223) 158 #define FIX_1_175875602 FIX(1.175875602) 159 #define FIX_1_501321110 FIX(1.501321110) 160 #define FIX_1_847759065 FIX(1.847759065) 161 #define FIX_1_961570560 FIX(1.961570560) 162 #define FIX_2_053119869 FIX(2.053119869) 163 #define FIX_2_562915447 FIX(2.562915447) 164 #define FIX_3_072711026 FIX(3.072711026) 165 #endif 166 167 168 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result. 169 * For 8-bit samples with the recommended scaling, all the variable 170 * and constant values involved are no more than 16 bits wide, so a 171 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 172 * For 12-bit samples, a full 32-bit multiplication will be needed. 173 */ 174 175 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2 176 #define MULTIPLY(var,const) MULTIPLY16C16(var,const) 177 #else 178 #define MULTIPLY(var,const) (int)((var) * (unsigned)(const)) 179 #endif 180 181 182 static av_always_inline void FUNC(row_fdct)(int16_t *data) 183 { 184 int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 185 int tmp10, tmp11, tmp12, tmp13; 186 unsigned z1, z2, z3, z4, z5; 187 int16_t *dataptr; 188 int ctr; 189 190 /* Pass 1: process rows. */ 191 /* Note results are scaled up by sqrt(8) compared to a true DCT; */ 192 /* furthermore, we scale the results by 2**PASS1_BITS. */ 193 194 dataptr = data; 195 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 196 tmp0 = dataptr[0] + dataptr[7]; 197 tmp7 = dataptr[0] - dataptr[7]; 198 tmp1 = dataptr[1] + dataptr[6]; 199 tmp6 = dataptr[1] - dataptr[6]; 200 tmp2 = dataptr[2] + dataptr[5]; 201 tmp5 = dataptr[2] - dataptr[5]; 202 tmp3 = dataptr[3] + dataptr[4]; 203 tmp4 = dataptr[3] - dataptr[4]; 204 205 /* Even part per LL&M figure 1 --- note that published figure is faulty; 206 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 207 */ 208 209 tmp10 = tmp0 + tmp3; 210 tmp13 = tmp0 - tmp3; 211 tmp11 = tmp1 + tmp2; 212 tmp12 = tmp1 - tmp2; 213 214 dataptr[0] = (int16_t) ((tmp10 + tmp11) * (1 << PASS1_BITS)); 215 dataptr[4] = (int16_t) ((tmp10 - tmp11) * (1 << PASS1_BITS)); 216 217 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 218 dataptr[2] = (int16_t) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 219 CONST_BITS-PASS1_BITS); 220 dataptr[6] = (int16_t) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 221 CONST_BITS-PASS1_BITS); 222 223 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 224 * cK represents cos(K*pi/16). 225 * i0..i3 in the paper are tmp4..tmp7 here. 226 */ 227 228 z1 = tmp4 + tmp7; 229 z2 = tmp5 + tmp6; 230 z3 = tmp4 + tmp6; 231 z4 = tmp5 + tmp7; 232 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 233 234 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 235 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 236 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 237 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 238 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 239 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 240 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 241 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 242 243 z3 += z5; 244 z4 += z5; 245 246 dataptr[7] = (int16_t) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 247 dataptr[5] = (int16_t) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 248 dataptr[3] = (int16_t) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 249 dataptr[1] = (int16_t) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); 250 251 dataptr += DCTSIZE; /* advance pointer to next row */ 252 } 253 } 254 255 /* 256 * Perform the forward DCT on one block of samples. 257 */ 258 259 GLOBAL(void) 260 FUNC(ff_jpeg_fdct_islow)(int16_t *data) 261 { 262 int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 263 int tmp10, tmp11, tmp12, tmp13; 264 unsigned z1, z2, z3, z4, z5; 265 int16_t *dataptr; 266 int ctr; 267 268 FUNC(row_fdct)(data); 269 270 /* Pass 2: process columns. 271 * We remove the PASS1_BITS scaling, but leave the results scaled up 272 * by an overall factor of 8. 273 */ 274 275 dataptr = data; 276 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 277 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 278 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 279 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 280 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 281 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 282 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 283 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 284 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 285 286 /* Even part per LL&M figure 1 --- note that published figure is faulty; 287 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 288 */ 289 290 tmp10 = tmp0 + tmp3; 291 tmp13 = tmp0 - tmp3; 292 tmp11 = tmp1 + tmp2; 293 tmp12 = tmp1 - tmp2; 294 295 dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT); 296 dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT); 297 298 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 299 dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 300 CONST_BITS + OUT_SHIFT); 301 dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 302 CONST_BITS + OUT_SHIFT); 303 304 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 305 * cK represents cos(K*pi/16). 306 * i0..i3 in the paper are tmp4..tmp7 here. 307 */ 308 309 z1 = tmp4 + tmp7; 310 z2 = tmp5 + tmp6; 311 z3 = tmp4 + tmp6; 312 z4 = tmp5 + tmp7; 313 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 314 315 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 316 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 317 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 318 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 319 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 320 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 321 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 322 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 323 324 z3 += z5; 325 z4 += z5; 326 327 dataptr[DCTSIZE*7] = DESCALE(tmp4 + z1 + z3, CONST_BITS + OUT_SHIFT); 328 dataptr[DCTSIZE*5] = DESCALE(tmp5 + z2 + z4, CONST_BITS + OUT_SHIFT); 329 dataptr[DCTSIZE*3] = DESCALE(tmp6 + z2 + z3, CONST_BITS + OUT_SHIFT); 330 dataptr[DCTSIZE*1] = DESCALE(tmp7 + z1 + z4, CONST_BITS + OUT_SHIFT); 331 332 dataptr++; /* advance pointer to next column */ 333 } 334 } 335 336 /* 337 * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT 338 * on the rows and then, instead of doing even and odd, part on the columns 339 * you do even part two times. 340 */ 341 GLOBAL(void) 342 FUNC(ff_fdct248_islow)(int16_t *data) 343 { 344 int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 345 int tmp10, tmp11, tmp12, tmp13; 346 int z1; 347 int16_t *dataptr; 348 int ctr; 349 350 FUNC(row_fdct)(data); 351 352 /* Pass 2: process columns. 353 * We remove the PASS1_BITS scaling, but leave the results scaled up 354 * by an overall factor of 8. 355 */ 356 357 dataptr = data; 358 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 359 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1]; 360 tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3]; 361 tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5]; 362 tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7]; 363 tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1]; 364 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3]; 365 tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5]; 366 tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7]; 367 368 tmp10 = tmp0 + tmp3; 369 tmp11 = tmp1 + tmp2; 370 tmp12 = tmp1 - tmp2; 371 tmp13 = tmp0 - tmp3; 372 373 dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT); 374 dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT); 375 376 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 377 dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 378 CONST_BITS+OUT_SHIFT); 379 dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 380 CONST_BITS+OUT_SHIFT); 381 382 tmp10 = tmp4 + tmp7; 383 tmp11 = tmp5 + tmp6; 384 tmp12 = tmp5 - tmp6; 385 tmp13 = tmp4 - tmp7; 386 387 dataptr[DCTSIZE*1] = DESCALE(tmp10 + tmp11, OUT_SHIFT); 388 dataptr[DCTSIZE*5] = DESCALE(tmp10 - tmp11, OUT_SHIFT); 389 390 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 391 dataptr[DCTSIZE*3] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 392 CONST_BITS + OUT_SHIFT); 393 dataptr[DCTSIZE*7] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 394 CONST_BITS + OUT_SHIFT); 395 396 dataptr++; /* advance pointer to next column */ 397 } 398 }