1/* 2 * reserved comment block 3 * DO NOT REMOVE OR ALTER! 4 */ 5/* 6 * jidctint.c 7 * 8 * Copyright (C) 1991-1998, Thomas G. Lane. 9 * This file is part of the Independent JPEG Group's software. 10 * For conditions of distribution and use, see the accompanying README file. 11 * 12 * This file contains a slow-but-accurate integer implementation of the 13 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine 14 * must also perform dequantization of the input coefficients. 15 * 16 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 17 * on each row (or vice versa, but it's more convenient to emit a row at 18 * a time). Direct algorithms are also available, but they are much more 19 * complex and seem not to be any faster when reduced to code. 20 * 21 * This implementation is based on an algorithm described in 22 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 23 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 24 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 25 * The primary algorithm described there uses 11 multiplies and 29 adds. 26 * We use their alternate method with 12 multiplies and 32 adds. 27 * The advantage of this method is that no data path contains more than one 28 * multiplication; this allows a very simple and accurate implementation in 29 * scaled fixed-point arithmetic, with a minimal number of shifts. 30 */ 31 32#define JPEG_INTERNALS 33#include "jinclude.h" 34#include "jpeglib.h" 35#include "jdct.h" /* Private declarations for DCT subsystem */ 36 37#ifdef DCT_ISLOW_SUPPORTED 38 39 40/* 41 * This module is specialized to the case DCTSIZE = 8. 42 */ 43 44#if DCTSIZE != 8 45 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 46#endif 47 48 49/* 50 * The poop on this scaling stuff is as follows: 51 * 52 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N) 53 * larger than the true IDCT outputs. The final outputs are therefore 54 * a factor of N larger than desired; since N=8 this can be cured by 55 * a simple right shift at the end of the algorithm. The advantage of 56 * this arrangement is that we save two multiplications per 1-D IDCT, 57 * because the y0 and y4 inputs need not be divided by sqrt(N). 58 * 59 * We have to do addition and subtraction of the integer inputs, which 60 * is no problem, and multiplication by fractional constants, which is 61 * a problem to do in integer arithmetic. We multiply all the constants 62 * by CONST_SCALE and convert them to integer constants (thus retaining 63 * CONST_BITS bits of precision in the constants). After doing a 64 * multiplication we have to divide the product by CONST_SCALE, with proper 65 * rounding, to produce the correct output. This division can be done 66 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 67 * as long as possible so that partial sums can be added together with 68 * full fractional precision. 69 * 70 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 71 * they are represented to better-than-integral precision. These outputs 72 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 73 * with the recommended scaling. (To scale up 12-bit sample data further, an 74 * intermediate INT32 array would be needed.) 75 * 76 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 77 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 78 * shows that the values given below are the most effective. 79 */ 80 81#if BITS_IN_JSAMPLE == 8 82#define CONST_BITS 13 83#define PASS1_BITS 2 84#else 85#define CONST_BITS 13 86#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 87#endif 88 89/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 90 * causing a lot of useless floating-point operations at run time. 91 * To get around this we use the following pre-calculated constants. 92 * If you change CONST_BITS you may want to add appropriate values. 93 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 94 */ 95 96#if CONST_BITS == 13 97#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ 98#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ 99#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ 100#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ 101#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ 102#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ 103#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ 104#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ 105#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ 106#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ 107#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ 108#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ 109#else 110#define FIX_0_298631336 FIX(0.298631336) 111#define FIX_0_390180644 FIX(0.390180644) 112#define FIX_0_541196100 FIX(0.541196100) 113#define FIX_0_765366865 FIX(0.765366865) 114#define FIX_0_899976223 FIX(0.899976223) 115#define FIX_1_175875602 FIX(1.175875602) 116#define FIX_1_501321110 FIX(1.501321110) 117#define FIX_1_847759065 FIX(1.847759065) 118#define FIX_1_961570560 FIX(1.961570560) 119#define FIX_2_053119869 FIX(2.053119869) 120#define FIX_2_562915447 FIX(2.562915447) 121#define FIX_3_072711026 FIX(3.072711026) 122#endif 123 124 125/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. 126 * For 8-bit samples with the recommended scaling, all the variable 127 * and constant values involved are no more than 16 bits wide, so a 128 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 129 * For 12-bit samples, a full 32-bit multiplication will be needed. 130 */ 131 132#if BITS_IN_JSAMPLE == 8 133#define MULTIPLY(var,const) MULTIPLY16C16(var,const) 134#else 135#define MULTIPLY(var,const) ((var) * (const)) 136#endif 137 138 139/* Dequantize a coefficient by multiplying it by the multiplier-table 140 * entry; produce an int result. In this module, both inputs and result 141 * are 16 bits or less, so either int or short multiply will work. 142 */ 143 144#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval)) 145 146 147/* 148 * Perform dequantization and inverse DCT on one block of coefficients. 149 */ 150 151GLOBAL(void) 152jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr, 153 JCOEFPTR coef_block, 154 JSAMPARRAY output_buf, JDIMENSION output_col) 155{ 156 INT32 tmp0, tmp1, tmp2, tmp3; 157 INT32 tmp10, tmp11, tmp12, tmp13; 158 INT32 z1, z2, z3, z4, z5; 159 JCOEFPTR inptr; 160 ISLOW_MULT_TYPE * quantptr; 161 int * wsptr; 162 JSAMPROW outptr; 163 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 164 int ctr; 165 int workspace[DCTSIZE2]; /* buffers data between passes */ 166 SHIFT_TEMPS 167 168 /* Pass 1: process columns from input, store into work array. */ 169 /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ 170 /* furthermore, we scale the results by 2**PASS1_BITS. */ 171 172 inptr = coef_block; 173 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table; 174 wsptr = workspace; 175 for (ctr = DCTSIZE; ctr > 0; ctr--) { 176 /* Due to quantization, we will usually find that many of the input 177 * coefficients are zero, especially the AC terms. We can exploit this 178 * by short-circuiting the IDCT calculation for any column in which all 179 * the AC terms are zero. In that case each output is equal to the 180 * DC coefficient (with scale factor as needed). 181 * With typical images and quantization tables, half or more of the 182 * column DCT calculations can be simplified this way. 183 */ 184 185 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 186 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 187 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 188 inptr[DCTSIZE*7] == 0) { 189 /* AC terms all zero */ 190 int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS; 191 192 wsptr[DCTSIZE*0] = dcval; 193 wsptr[DCTSIZE*1] = dcval; 194 wsptr[DCTSIZE*2] = dcval; 195 wsptr[DCTSIZE*3] = dcval; 196 wsptr[DCTSIZE*4] = dcval; 197 wsptr[DCTSIZE*5] = dcval; 198 wsptr[DCTSIZE*6] = dcval; 199 wsptr[DCTSIZE*7] = dcval; 200 201 inptr++; /* advance pointers to next column */ 202 quantptr++; 203 wsptr++; 204 continue; 205 } 206 207 /* Even part: reverse the even part of the forward DCT. */ 208 /* The rotator is sqrt(2)*c(-6). */ 209 210 z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 211 z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 212 213 z1 = MULTIPLY(z2 + z3, FIX_0_541196100); 214 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); 215 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); 216 217 z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 218 z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 219 220 tmp0 = (z2 + z3) << CONST_BITS; 221 tmp1 = (z2 - z3) << CONST_BITS; 222 223 tmp10 = tmp0 + tmp3; 224 tmp13 = tmp0 - tmp3; 225 tmp11 = tmp1 + tmp2; 226 tmp12 = tmp1 - tmp2; 227 228 /* Odd part per figure 8; the matrix is unitary and hence its 229 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. 230 */ 231 232 tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 233 tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 234 tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 235 tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 236 237 z1 = tmp0 + tmp3; 238 z2 = tmp1 + tmp2; 239 z3 = tmp0 + tmp2; 240 z4 = tmp1 + tmp3; 241 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 242 243 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 244 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 245 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 246 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 247 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 248 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 249 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 250 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 251 252 z3 += z5; 253 z4 += z5; 254 255 tmp0 += z1 + z3; 256 tmp1 += z2 + z4; 257 tmp2 += z2 + z3; 258 tmp3 += z1 + z4; 259 260 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 261 262 wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); 263 wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); 264 wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); 265 wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); 266 wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); 267 wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); 268 wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); 269 wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); 270 271 inptr++; /* advance pointers to next column */ 272 quantptr++; 273 wsptr++; 274 } 275 276 /* Pass 2: process rows from work array, store into output array. */ 277 /* Note that we must descale the results by a factor of 8 == 2**3, */ 278 /* and also undo the PASS1_BITS scaling. */ 279 280 wsptr = workspace; 281 for (ctr = 0; ctr < DCTSIZE; ctr++) { 282 outptr = output_buf[ctr] + output_col; 283 /* Rows of zeroes can be exploited in the same way as we did with columns. 284 * However, the column calculation has created many nonzero AC terms, so 285 * the simplification applies less often (typically 5% to 10% of the time). 286 * On machines with very fast multiplication, it's possible that the 287 * test takes more time than it's worth. In that case this section 288 * may be commented out. 289 */ 290 291#ifndef NO_ZERO_ROW_TEST 292 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 293 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 294 /* AC terms all zero */ 295 JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3) 296 & RANGE_MASK]; 297 298 outptr[0] = dcval; 299 outptr[1] = dcval; 300 outptr[2] = dcval; 301 outptr[3] = dcval; 302 outptr[4] = dcval; 303 outptr[5] = dcval; 304 outptr[6] = dcval; 305 outptr[7] = dcval; 306 307 wsptr += DCTSIZE; /* advance pointer to next row */ 308 continue; 309 } 310#endif 311 312 /* Even part: reverse the even part of the forward DCT. */ 313 /* The rotator is sqrt(2)*c(-6). */ 314 315 z2 = (INT32) wsptr[2]; 316 z3 = (INT32) wsptr[6]; 317 318 z1 = MULTIPLY(z2 + z3, FIX_0_541196100); 319 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); 320 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); 321 322 tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS; 323 tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS; 324 325 tmp10 = tmp0 + tmp3; 326 tmp13 = tmp0 - tmp3; 327 tmp11 = tmp1 + tmp2; 328 tmp12 = tmp1 - tmp2; 329 330 /* Odd part per figure 8; the matrix is unitary and hence its 331 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. 332 */ 333 334 tmp0 = (INT32) wsptr[7]; 335 tmp1 = (INT32) wsptr[5]; 336 tmp2 = (INT32) wsptr[3]; 337 tmp3 = (INT32) wsptr[1]; 338 339 z1 = tmp0 + tmp3; 340 z2 = tmp1 + tmp2; 341 z3 = tmp0 + tmp2; 342 z4 = tmp1 + tmp3; 343 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 344 345 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 346 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 347 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 348 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 349 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 350 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 351 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 352 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 353 354 z3 += z5; 355 z4 += z5; 356 357 tmp0 += z1 + z3; 358 tmp1 += z2 + z4; 359 tmp2 += z2 + z3; 360 tmp3 += z1 + z4; 361 362 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 363 364 outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3, 365 CONST_BITS+PASS1_BITS+3) 366 & RANGE_MASK]; 367 outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3, 368 CONST_BITS+PASS1_BITS+3) 369 & RANGE_MASK]; 370 outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2, 371 CONST_BITS+PASS1_BITS+3) 372 & RANGE_MASK]; 373 outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2, 374 CONST_BITS+PASS1_BITS+3) 375 & RANGE_MASK]; 376 outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1, 377 CONST_BITS+PASS1_BITS+3) 378 & RANGE_MASK]; 379 outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1, 380 CONST_BITS+PASS1_BITS+3) 381 & RANGE_MASK]; 382 outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0, 383 CONST_BITS+PASS1_BITS+3) 384 & RANGE_MASK]; 385 outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0, 386 CONST_BITS+PASS1_BITS+3) 387 & RANGE_MASK]; 388 389 wsptr += DCTSIZE; /* advance pointer to next row */ 390 } 391} 392 393#endif /* DCT_ISLOW_SUPPORTED */ 394