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