1 /* 2 * jidctfst.c 3 * 4 * This file was part of the Independent JPEG Group's software: 5 * Copyright (C) 1994-1998, Thomas G. Lane. 6 * libjpeg-turbo Modifications: 7 * Copyright (C) 2015, D. R. Commander. 8 * For conditions of distribution and use, see the accompanying README.ijg 9 * file. 10 * 11 * This file contains a fast, not so accurate integer implementation of the 12 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine 13 * must also perform dequantization of the input coefficients. 14 * 15 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 16 * on each row (or vice versa, but it's more convenient to emit a row at 17 * a time). Direct algorithms are also available, but they are much more 18 * complex and seem not to be any faster when reduced to code. 19 * 20 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 21 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 22 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 23 * JPEG textbook (see REFERENCES section in file README.ijg). The following 24 * code is based directly on figure 4-8 in P&M. 25 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 26 * possible to arrange the computation so that many of the multiplies are 27 * simple scalings of the final outputs. These multiplies can then be 28 * folded into the multiplications or divisions by the JPEG quantization 29 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 30 * to be done in the DCT itself. 31 * The primary disadvantage of this method is that with fixed-point math, 32 * accuracy is lost due to imprecise representation of the scaled 33 * quantization values. The smaller the quantization table entry, the less 34 * precise the scaled value, so this implementation does worse with high- 35 * quality-setting files than with low-quality ones. 36 */ 37 38 #define JPEG_INTERNALS 39 #include "jinclude.h" 40 #include "jpeglib.h" 41 #include "jdct.h" /* Private declarations for DCT subsystem */ 42 43 #ifdef DCT_IFAST_SUPPORTED 44 45 46 /* 47 * This module is specialized to the case DCTSIZE = 8. 48 */ 49 50 #if DCTSIZE != 8 51 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 52 #endif 53 54 55 /* Scaling decisions are generally the same as in the LL&M algorithm; 56 * see jidctint.c for more details. However, we choose to descale 57 * (right shift) multiplication products as soon as they are formed, 58 * rather than carrying additional fractional bits into subsequent additions. 59 * This compromises accuracy slightly, but it lets us save a few shifts. 60 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 61 * everywhere except in the multiplications proper; this saves a good deal 62 * of work on 16-bit-int machines. 63 * 64 * The dequantized coefficients are not integers because the AA&N scaling 65 * factors have been incorporated. We represent them scaled up by PASS1_BITS, 66 * so that the first and second IDCT rounds have the same input scaling. 67 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 68 * avoid a descaling shift; this compromises accuracy rather drastically 69 * for small quantization table entries, but it saves a lot of shifts. 70 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 71 * so we use a much larger scaling factor to preserve accuracy. 72 * 73 * A final compromise is to represent the multiplicative constants to only 74 * 8 fractional bits, rather than 13. This saves some shifting work on some 75 * machines, and may also reduce the cost of multiplication (since there 76 * are fewer one-bits in the constants). 77 */ 78 79 #if BITS_IN_JSAMPLE == 8 80 #define CONST_BITS 8 81 #define PASS1_BITS 2 82 #else 83 #define CONST_BITS 8 84 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 85 #endif 86 87 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 88 * causing a lot of useless floating-point operations at run time. 89 * To get around this we use the following pre-calculated constants. 90 * If you change CONST_BITS you may want to add appropriate values. 91 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 92 */ 93 94 #if CONST_BITS == 8 95 #define FIX_1_082392200 ((JLONG) 277) /* FIX(1.082392200) */ 96 #define FIX_1_414213562 ((JLONG) 362) /* FIX(1.414213562) */ 97 #define FIX_1_847759065 ((JLONG) 473) /* FIX(1.847759065) */ 98 #define FIX_2_613125930 ((JLONG) 669) /* FIX(2.613125930) */ 99 #else 100 #define FIX_1_082392200 FIX(1.082392200) 101 #define FIX_1_414213562 FIX(1.414213562) 102 #define FIX_1_847759065 FIX(1.847759065) 103 #define FIX_2_613125930 FIX(2.613125930) 104 #endif 105 106 107 /* We can gain a little more speed, with a further compromise in accuracy, 108 * by omitting the addition in a descaling shift. This yields an incorrectly 109 * rounded result half the time... 110 */ 111 112 #ifndef USE_ACCURATE_ROUNDING 113 #undef DESCALE 114 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 115 #endif 116 117 118 /* Multiply a DCTELEM variable by an JLONG constant, and immediately 119 * descale to yield a DCTELEM result. 120 */ 121 122 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 123 124 125 /* Dequantize a coefficient by multiplying it by the multiplier-table 126 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 127 * multiplication will do. For 12-bit data, the multiplier table is 128 * declared JLONG, so a 32-bit multiply will be used. 129 */ 130 131 #if BITS_IN_JSAMPLE == 8 132 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) 133 #else 134 #define DEQUANTIZE(coef,quantval) \ 135 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) 136 #endif 137 138 139 /* Like DESCALE, but applies to a DCTELEM and produces an int. 140 * We assume that int right shift is unsigned if JLONG right shift is. 141 */ 142 143 #ifdef RIGHT_SHIFT_IS_UNSIGNED 144 #define ISHIFT_TEMPS DCTELEM ishift_temp; 145 #if BITS_IN_JSAMPLE == 8 146 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ 147 #else 148 #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ 149 #endif 150 #define IRIGHT_SHIFT(x,shft) \ 151 ((ishift_temp = (x)) < 0 ? \ 152 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ 153 (ishift_temp >> (shft))) 154 #else 155 #define ISHIFT_TEMPS 156 #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) 157 #endif 158 159 #ifdef USE_ACCURATE_ROUNDING 160 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) 161 #else 162 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) 163 #endif 164 165 166 /* 167 * Perform dequantization and inverse DCT on one block of coefficients. 168 */ 169 170 GLOBAL(void) 171 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info *compptr, 172 JCOEFPTR coef_block, 173 JSAMPARRAY output_buf, JDIMENSION output_col) 174 { 175 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 176 DCTELEM tmp10, tmp11, tmp12, tmp13; 177 DCTELEM z5, z10, z11, z12, z13; 178 JCOEFPTR inptr; 179 IFAST_MULT_TYPE *quantptr; 180 int *wsptr; 181 JSAMPROW outptr; 182 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 183 int ctr; 184 int workspace[DCTSIZE2]; /* buffers data between passes */ 185 SHIFT_TEMPS /* for DESCALE */ 186 ISHIFT_TEMPS /* for IDESCALE */ 187 188 /* Pass 1: process columns from input, store into work array. */ 189 190 inptr = coef_block; 191 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 192 wsptr = workspace; 193 for (ctr = DCTSIZE; ctr > 0; ctr--) { 194 /* Due to quantization, we will usually find that many of the input 195 * coefficients are zero, especially the AC terms. We can exploit this 196 * by short-circuiting the IDCT calculation for any column in which all 197 * the AC terms are zero. In that case each output is equal to the 198 * DC coefficient (with scale factor as needed). 199 * With typical images and quantization tables, half or more of the 200 * column DCT calculations can be simplified this way. 201 */ 202 203 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 204 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 205 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 206 inptr[DCTSIZE*7] == 0) { 207 /* AC terms all zero */ 208 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 209 210 wsptr[DCTSIZE*0] = dcval; 211 wsptr[DCTSIZE*1] = dcval; 212 wsptr[DCTSIZE*2] = dcval; 213 wsptr[DCTSIZE*3] = dcval; 214 wsptr[DCTSIZE*4] = dcval; 215 wsptr[DCTSIZE*5] = dcval; 216 wsptr[DCTSIZE*6] = dcval; 217 wsptr[DCTSIZE*7] = dcval; 218 219 inptr++; /* advance pointers to next column */ 220 quantptr++; 221 wsptr++; 222 continue; 223 } 224 225 /* Even part */ 226 227 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 228 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 229 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 230 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 231 232 tmp10 = tmp0 + tmp2; /* phase 3 */ 233 tmp11 = tmp0 - tmp2; 234 235 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 236 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ 237 238 tmp0 = tmp10 + tmp13; /* phase 2 */ 239 tmp3 = tmp10 - tmp13; 240 tmp1 = tmp11 + tmp12; 241 tmp2 = tmp11 - tmp12; 242 243 /* Odd part */ 244 245 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 246 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 247 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 248 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 249 250 z13 = tmp6 + tmp5; /* phase 6 */ 251 z10 = tmp6 - tmp5; 252 z11 = tmp4 + tmp7; 253 z12 = tmp4 - tmp7; 254 255 tmp7 = z11 + z13; /* phase 5 */ 256 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 257 258 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 259 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 260 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 261 262 tmp6 = tmp12 - tmp7; /* phase 2 */ 263 tmp5 = tmp11 - tmp6; 264 tmp4 = tmp10 + tmp5; 265 266 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 267 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 268 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 269 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 270 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 271 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 272 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); 273 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); 274 275 inptr++; /* advance pointers to next column */ 276 quantptr++; 277 wsptr++; 278 } 279 280 /* Pass 2: process rows from work array, store into output array. */ 281 /* Note that we must descale the results by a factor of 8 == 2**3, */ 282 /* and also undo the PASS1_BITS scaling. */ 283 284 wsptr = workspace; 285 for (ctr = 0; ctr < DCTSIZE; ctr++) { 286 outptr = output_buf[ctr] + output_col; 287 /* Rows of zeroes can be exploited in the same way as we did with columns. 288 * However, the column calculation has created many nonzero AC terms, so 289 * the simplification applies less often (typically 5% to 10% of the time). 290 * On machines with very fast multiplication, it's possible that the 291 * test takes more time than it's worth. In that case this section 292 * may be commented out. 293 */ 294 295 #ifndef NO_ZERO_ROW_TEST 296 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 297 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 298 /* AC terms all zero */ 299 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) 300 & RANGE_MASK]; 301 302 outptr[0] = dcval; 303 outptr[1] = dcval; 304 outptr[2] = dcval; 305 outptr[3] = dcval; 306 outptr[4] = dcval; 307 outptr[5] = dcval; 308 outptr[6] = dcval; 309 outptr[7] = dcval; 310 311 wsptr += DCTSIZE; /* advance pointer to next row */ 312 continue; 313 } 314 #endif 315 316 /* Even part */ 317 318 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); 319 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); 320 321 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); 322 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) 323 - tmp13; 324 325 tmp0 = tmp10 + tmp13; 326 tmp3 = tmp10 - tmp13; 327 tmp1 = tmp11 + tmp12; 328 tmp2 = tmp11 - tmp12; 329 330 /* Odd part */ 331 332 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 333 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 334 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 335 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 336 337 tmp7 = z11 + z13; /* phase 5 */ 338 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 339 340 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 341 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 342 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 343 344 tmp6 = tmp12 - tmp7; /* phase 2 */ 345 tmp5 = tmp11 - tmp6; 346 tmp4 = tmp10 + tmp5; 347 348 /* Final output stage: scale down by a factor of 8 and range-limit */ 349 350 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) 351 & RANGE_MASK]; 352 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) 353 & RANGE_MASK]; 354 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) 355 & RANGE_MASK]; 356 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) 357 & RANGE_MASK]; 358 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) 359 & RANGE_MASK]; 360 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) 361 & RANGE_MASK]; 362 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) 363 & RANGE_MASK]; 364 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) 365 & RANGE_MASK]; 366 367 wsptr += DCTSIZE; /* advance pointer to next row */ 368 } 369 } 370 371 #endif /* DCT_IFAST_SUPPORTED */ 372
