1/* 2 * jfdctint.c 3 * 4 * This file is part of the Independent JPEG Group's software. 5 * 6 * The authors make NO WARRANTY or representation, either express or implied, 7 * with respect to this software, its quality, accuracy, merchantability, or 8 * fitness for a particular purpose. This software is provided "AS IS", and 9 * you, its user, assume the entire risk as to its quality and accuracy. 10 * 11 * This software is copyright (C) 1991-1996, Thomas G. Lane. 12 * All Rights Reserved except as specified below. 13 * 14 * Permission is hereby granted to use, copy, modify, and distribute this 15 * software (or portions thereof) for any purpose, without fee, subject to 16 * these conditions: 17 * (1) If any part of the source code for this software is distributed, then 18 * this README file must be included, with this copyright and no-warranty 19 * notice unaltered; and any additions, deletions, or changes to the original 20 * files must be clearly indicated in accompanying documentation. 21 * (2) If only executable code is distributed, then the accompanying 22 * documentation must state that "this software is based in part on the work 23 * of the Independent JPEG Group". 24 * (3) Permission for use of this software is granted only if the user accepts 25 * full responsibility for any undesirable consequences; the authors accept 26 * NO LIABILITY for damages of any kind. 27 * 28 * These conditions apply to any software derived from or based on the IJG 29 * code, not just to the unmodified library. If you use our work, you ought 30 * to acknowledge us. 31 * 32 * Permission is NOT granted for the use of any IJG author's name or company 33 * name in advertising or publicity relating to this software or products 34 * derived from it. This software may be referred to only as "the Independent 35 * JPEG Group's software". 36 * 37 * We specifically permit and encourage the use of this software as the basis 38 * of commercial products, provided that all warranty or liability claims are 39 * assumed by the product vendor. 40 * 41 * This file contains a slow-but-accurate integer implementation of the 42 * forward DCT (Discrete Cosine Transform). 43 * 44 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 45 * on each column. Direct algorithms are also available, but they are 46 * much more complex and seem not to be any faster when reduced to code. 47 * 48 * This implementation is based on an algorithm described in 49 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 50 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 51 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 52 * The primary algorithm described there uses 11 multiplies and 29 adds. 53 * We use their alternate method with 12 multiplies and 32 adds. 54 * The advantage of this method is that no data path contains more than one 55 * multiplication; this allows a very simple and accurate implementation in 56 * scaled fixed-point arithmetic, with a minimal number of shifts. 57 */ 58 59/** 60 * @file 61 * Independent JPEG Group's slow & accurate dct. 62 */ 63 64#include <stdlib.h> 65#include <stdio.h> 66#include "libavutil/common.h" 67#include "dsputil.h" 68 69#define DCTSIZE 8 70#define BITS_IN_JSAMPLE 8 71#define GLOBAL(x) x 72#define RIGHT_SHIFT(x, n) ((x) >> (n)) 73#define MULTIPLY16C16(var,const) ((var)*(const)) 74 75#if 1 //def USE_ACCURATE_ROUNDING 76#define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n) 77#else 78#define DESCALE(x,n) RIGHT_SHIFT(x, n) 79#endif 80 81 82/* 83 * This module is specialized to the case DCTSIZE = 8. 84 */ 85 86#if DCTSIZE != 8 87 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 88#endif 89 90 91/* 92 * The poop on this scaling stuff is as follows: 93 * 94 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 95 * larger than the true DCT outputs. The final outputs are therefore 96 * a factor of N larger than desired; since N=8 this can be cured by 97 * a simple right shift at the end of the algorithm. The advantage of 98 * this arrangement is that we save two multiplications per 1-D DCT, 99 * because the y0 and y4 outputs need not be divided by sqrt(N). 100 * In the IJG code, this factor of 8 is removed by the quantization step 101 * (in jcdctmgr.c), NOT in this module. 102 * 103 * We have to do addition and subtraction of the integer inputs, which 104 * is no problem, and multiplication by fractional constants, which is 105 * a problem to do in integer arithmetic. We multiply all the constants 106 * by CONST_SCALE and convert them to integer constants (thus retaining 107 * CONST_BITS bits of precision in the constants). After doing a 108 * multiplication we have to divide the product by CONST_SCALE, with proper 109 * rounding, to produce the correct output. This division can be done 110 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 111 * as long as possible so that partial sums can be added together with 112 * full fractional precision. 113 * 114 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 115 * they are represented to better-than-integral precision. These outputs 116 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 117 * with the recommended scaling. (For 12-bit sample data, the intermediate 118 * array is int32_t anyway.) 119 * 120 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 121 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 122 * shows that the values given below are the most effective. 123 */ 124 125#if BITS_IN_JSAMPLE == 8 126#define CONST_BITS 13 127#define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */ 128#else 129#define CONST_BITS 13 130#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 131#endif 132 133/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 134 * causing a lot of useless floating-point operations at run time. 135 * To get around this we use the following pre-calculated constants. 136 * If you change CONST_BITS you may want to add appropriate values. 137 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 138 */ 139 140#if CONST_BITS == 13 141#define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */ 142#define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */ 143#define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */ 144#define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */ 145#define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */ 146#define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */ 147#define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */ 148#define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */ 149#define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */ 150#define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */ 151#define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */ 152#define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */ 153#else 154#define FIX_0_298631336 FIX(0.298631336) 155#define FIX_0_390180644 FIX(0.390180644) 156#define FIX_0_541196100 FIX(0.541196100) 157#define FIX_0_765366865 FIX(0.765366865) 158#define FIX_0_899976223 FIX(0.899976223) 159#define FIX_1_175875602 FIX(1.175875602) 160#define FIX_1_501321110 FIX(1.501321110) 161#define FIX_1_847759065 FIX(1.847759065) 162#define FIX_1_961570560 FIX(1.961570560) 163#define FIX_2_053119869 FIX(2.053119869) 164#define FIX_2_562915447 FIX(2.562915447) 165#define FIX_3_072711026 FIX(3.072711026) 166#endif 167 168 169/* Multiply an int32_t variable by an int32_t constant to yield an int32_t result. 170 * For 8-bit samples with the recommended scaling, all the variable 171 * and constant values involved are no more than 16 bits wide, so a 172 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 173 * For 12-bit samples, a full 32-bit multiplication will be needed. 174 */ 175 176#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2 177#define MULTIPLY(var,const) MULTIPLY16C16(var,const) 178#else 179#define MULTIPLY(var,const) ((var) * (const)) 180#endif 181 182 183static av_always_inline void row_fdct(DCTELEM * data){ 184 int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 185 int_fast32_t tmp10, tmp11, tmp12, tmp13; 186 int_fast32_t z1, z2, z3, z4, z5; 187 DCTELEM *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] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); 215 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); 216 217 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 218 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 219 CONST_BITS-PASS1_BITS); 220 dataptr[6] = (DCTELEM) 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] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 247 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 248 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 249 dataptr[1] = (DCTELEM) 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 259GLOBAL(void) 260ff_jpeg_fdct_islow (DCTELEM * data) 261{ 262 int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 263 int_fast32_t tmp10, tmp11, tmp12, tmp13; 264 int_fast32_t z1, z2, z3, z4, z5; 265 DCTELEM *dataptr; 266 int ctr; 267 268 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] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 296 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 297 298 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 299 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 300 CONST_BITS+PASS1_BITS); 301 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 302 CONST_BITS+PASS1_BITS); 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] = (DCTELEM) DESCALE(tmp4 + z1 + z3, 328 CONST_BITS+PASS1_BITS); 329 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, 330 CONST_BITS+PASS1_BITS); 331 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, 332 CONST_BITS+PASS1_BITS); 333 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, 334 CONST_BITS+PASS1_BITS); 335 336 dataptr++; /* advance pointer to next column */ 337 } 338} 339 340/* 341 * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT 342 * on the rows and then, instead of doing even and odd, part on the colums 343 * you do even part two times. 344 */ 345GLOBAL(void) 346ff_fdct248_islow (DCTELEM * data) 347{ 348 int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 349 int_fast32_t tmp10, tmp11, tmp12, tmp13; 350 int_fast32_t z1; 351 DCTELEM *dataptr; 352 int ctr; 353 354 row_fdct(data); 355 356 /* Pass 2: process columns. 357 * We remove the PASS1_BITS scaling, but leave the results scaled up 358 * by an overall factor of 8. 359 */ 360 361 dataptr = data; 362 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 363 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1]; 364 tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3]; 365 tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5]; 366 tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7]; 367 tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1]; 368 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3]; 369 tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5]; 370 tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7]; 371 372 tmp10 = tmp0 + tmp3; 373 tmp11 = tmp1 + tmp2; 374 tmp12 = tmp1 - tmp2; 375 tmp13 = tmp0 - tmp3; 376 377 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 378 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 379 380 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 381 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 382 CONST_BITS+PASS1_BITS); 383 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 384 CONST_BITS+PASS1_BITS); 385 386 tmp10 = tmp4 + tmp7; 387 tmp11 = tmp5 + tmp6; 388 tmp12 = tmp5 - tmp6; 389 tmp13 = tmp4 - tmp7; 390 391 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 392 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 393 394 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 395 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 396 CONST_BITS+PASS1_BITS); 397 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 398 CONST_BITS+PASS1_BITS); 399 400 dataptr++; /* advance pointer to next column */ 401 } 402} 403