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