1 /* 2 * jidctfst.c 3 * 4 * Copyright (C) 1994-1998, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for 18 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 19 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 20 * JPEG textbook (see REFERENCES section in file README). The following code 21 * is based directly on figure 4-8 in P&M. 22 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 23 * possible to arrange the computation so that many of the multiplies are 24 * simple scalings of the final outputs. These multiplies can then be 25 * folded into the multiplications or divisions by the JPEG quantization 26 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 27 * to be done in the DCT itself. 28 * The primary disadvantage of this method is that with fixed-point math, 29 * accuracy is lost due to imprecise representation of the scaled 30 * quantization values. The smaller the quantization table entry, the less 31 * precise the scaled value, so this implementation does worse with high- 32 * quality-setting files than with low-quality ones. 33 */ 34 35 #define JPEG_INTERNALS 36 #include "jinclude.h" 37 #include "jpeglib.h" 38 #include "jdct.h" /* Private declarations for DCT subsystem */ 39 40 #ifdef DCT_IFAST_SUPPORTED 41 42 43 /* 44 * This module is specialized to the case DCTSIZE = 8. 45 */ 46 47 #if DCTSIZE != 8 48 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 49 #endif 50 51 52 /* Scaling decisions are generally the same as in the LL&M algorithm; 53 * see jidctint.c for more details. However, we choose to descale 54 * (right shift) multiplication products as soon as they are formed, 55 * rather than carrying additional fractional bits into subsequent additions. 56 * This compromises accuracy slightly, but it lets us save a few shifts. 57 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 58 * everywhere except in the multiplications proper; this saves a good deal 59 * of work on 16-bit-int machines. 60 * 61 * The dequantized coefficients are not integers because the AA&N scaling 62 * factors have been incorporated. We represent them scaled up by PASS1_BITS, 63 * so that the first and second IDCT rounds have the same input scaling. 64 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 65 * avoid a descaling shift; this compromises accuracy rather drastically 66 * for small quantization table entries, but it saves a lot of shifts. 67 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 68 * so we use a much larger scaling factor to preserve accuracy. 69 * 70 * A final compromise is to represent the multiplicative constants to only 71 * 8 fractional bits, rather than 13. This saves some shifting work on some 72 * machines, and may also reduce the cost of multiplication (since there 73 * are fewer one-bits in the constants). 74 */ 75 76 #if BITS_IN_JSAMPLE == 8 77 #define CONST_BITS 8 78 #define PASS1_BITS 2 79 #else 80 #define CONST_BITS 8 81 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 82 #endif 83 84 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 85 * causing a lot of useless floating-point operations at run time. 86 * To get around this we use the following pre-calculated constants. 87 * If you change CONST_BITS you may want to add appropriate values. 88 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 89 */ 90 91 #if CONST_BITS == 8 92 #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */ 93 #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ 94 #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ 95 #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */ 96 #else 97 #define FIX_1_082392200 FIX(1.082392200) 98 #define FIX_1_414213562 FIX(1.414213562) 99 #define FIX_1_847759065 FIX(1.847759065) 100 #define FIX_2_613125930 FIX(2.613125930) 101 #endif 102 103 104 /* We can gain a little more speed, with a further compromise in accuracy, 105 * by omitting the addition in a descaling shift. This yields an incorrectly 106 * rounded result half the time... 107 */ 108 109 #ifndef USE_ACCURATE_ROUNDING 110 #undef DESCALE 111 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 112 #endif 113 114 115 /* Multiply a DCTELEM variable by an INT32 constant, and immediately 116 * descale to yield a DCTELEM result. 117 */ 118 119 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 120 121 122 /* Dequantize a coefficient by multiplying it by the multiplier-table 123 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 124 * multiplication will do. For 12-bit data, the multiplier table is 125 * declared INT32, so a 32-bit multiply will be used. 126 */ 127 128 #if BITS_IN_JSAMPLE == 8 129 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) 130 #else 131 #define DEQUANTIZE(coef,quantval) \ 132 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) 133 #endif 134 135 136 /* Like DESCALE, but applies to a DCTELEM and produces an int. 137 * We assume that int right shift is unsigned if INT32 right shift is. 138 */ 139 140 #ifdef RIGHT_SHIFT_IS_UNSIGNED 141 #define ISHIFT_TEMPS DCTELEM ishift_temp; 142 #if BITS_IN_JSAMPLE == 8 143 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ 144 #else 145 #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ 146 #endif 147 #define IRIGHT_SHIFT(x,shft) \ 148 ((ishift_temp = (x)) < 0 ? \ 149 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ 150 (ishift_temp >> (shft))) 151 #else 152 #define ISHIFT_TEMPS 153 #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) 154 #endif 155 156 #ifdef USE_ACCURATE_ROUNDING 157 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) 158 #else 159 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) 160 #endif 161 162 163 /* 164 * Perform dequantization and inverse DCT on one block of coefficients. 165 */ 166 167 GLOBAL(void) 168 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, 169 JCOEFPTR coef_block, 170 JSAMPARRAY output_buf, JDIMENSION output_col) 171 { 172 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 173 DCTELEM tmp10, tmp11, tmp12, tmp13; 174 DCTELEM z5, z10, z11, z12, z13; 175 JCOEFPTR inptr; 176 IFAST_MULT_TYPE * quantptr; 177 int * wsptr; 178 JSAMPROW outptr; 179 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 180 int ctr; 181 int workspace[DCTSIZE2]; /* buffers data between passes */ 182 SHIFT_TEMPS /* for DESCALE */ 183 ISHIFT_TEMPS /* for IDESCALE */ 184 185 /* Pass 1: process columns from input, store into work array. */ 186 187 inptr = coef_block; 188 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 189 wsptr = workspace; 190 for (ctr = DCTSIZE; ctr > 0; ctr--) { 191 /* Due to quantization, we will usually find that many of the input 192 * coefficients are zero, especially the AC terms. We can exploit this 193 * by short-circuiting the IDCT calculation for any column in which all 194 * the AC terms are zero. In that case each output is equal to the 195 * DC coefficient (with scale factor as needed). 196 * With typical images and quantization tables, half or more of the 197 * column DCT calculations can be simplified this way. 198 */ 199 200 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 201 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 202 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 203 inptr[DCTSIZE*7] == 0) { 204 /* AC terms all zero */ 205 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 206 207 wsptr[DCTSIZE*0] = dcval; 208 wsptr[DCTSIZE*1] = dcval; 209 wsptr[DCTSIZE*2] = dcval; 210 wsptr[DCTSIZE*3] = dcval; 211 wsptr[DCTSIZE*4] = dcval; 212 wsptr[DCTSIZE*5] = dcval; 213 wsptr[DCTSIZE*6] = dcval; 214 wsptr[DCTSIZE*7] = dcval; 215 216 inptr++; /* advance pointers to next column */ 217 quantptr++; 218 wsptr++; 219 continue; 220 } 221 222 /* Even part */ 223 224 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 225 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 226 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 227 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 228 229 tmp10 = tmp0 + tmp2; /* phase 3 */ 230 tmp11 = tmp0 - tmp2; 231 232 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 233 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ 234 235 tmp0 = tmp10 + tmp13; /* phase 2 */ 236 tmp3 = tmp10 - tmp13; 237 tmp1 = tmp11 + tmp12; 238 tmp2 = tmp11 - tmp12; 239 240 /* Odd part */ 241 242 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 243 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 244 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 245 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 246 247 z13 = tmp6 + tmp5; /* phase 6 */ 248 z10 = tmp6 - tmp5; 249 z11 = tmp4 + tmp7; 250 z12 = tmp4 - tmp7; 251 252 tmp7 = z11 + z13; /* phase 5 */ 253 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 254 255 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 256 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 257 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 258 259 tmp6 = tmp12 - tmp7; /* phase 2 */ 260 tmp5 = tmp11 - tmp6; 261 tmp4 = tmp10 + tmp5; 262 263 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 264 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 265 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 266 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 267 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 268 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 269 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); 270 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); 271 272 inptr++; /* advance pointers to next column */ 273 quantptr++; 274 wsptr++; 275 } 276 277 /* Pass 2: process rows from work array, store into output array. */ 278 /* Note that we must descale the results by a factor of 8 == 2**3, */ 279 /* and also undo the PASS1_BITS scaling. */ 280 281 wsptr = workspace; 282 for (ctr = 0; ctr < DCTSIZE; ctr++) { 283 outptr = output_buf[ctr] + output_col; 284 /* Rows of zeroes can be exploited in the same way as we did with columns. 285 * However, the column calculation has created many nonzero AC terms, so 286 * the simplification applies less often (typically 5% to 10% of the time). 287 * On machines with very fast multiplication, it's possible that the 288 * test takes more time than it's worth. In that case this section 289 * may be commented out. 290 */ 291 292 #ifndef NO_ZERO_ROW_TEST 293 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 294 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 295 /* AC terms all zero */ 296 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) 297 & RANGE_MASK]; 298 299 outptr[0] = dcval; 300 outptr[1] = dcval; 301 outptr[2] = dcval; 302 outptr[3] = dcval; 303 outptr[4] = dcval; 304 outptr[5] = dcval; 305 outptr[6] = dcval; 306 outptr[7] = dcval; 307 308 wsptr += DCTSIZE; /* advance pointer to next row */ 309 continue; 310 } 311 #endif 312 313 /* Even part */ 314 315 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); 316 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); 317 318 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); 319 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) 320 - tmp13; 321 322 tmp0 = tmp10 + tmp13; 323 tmp3 = tmp10 - tmp13; 324 tmp1 = tmp11 + tmp12; 325 tmp2 = tmp11 - tmp12; 326 327 /* Odd part */ 328 329 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 330 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 331 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 332 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 333 334 tmp7 = z11 + z13; /* phase 5 */ 335 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 336 337 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 338 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 339 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 340 341 tmp6 = tmp12 - tmp7; /* phase 2 */ 342 tmp5 = tmp11 - tmp6; 343 tmp4 = tmp10 + tmp5; 344 345 /* Final output stage: scale down by a factor of 8 and range-limit */ 346 347 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) 348 & RANGE_MASK]; 349 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) 350 & RANGE_MASK]; 351 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) 352 & RANGE_MASK]; 353 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) 354 & RANGE_MASK]; 355 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) 356 & RANGE_MASK]; 357 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) 358 & RANGE_MASK]; 359 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) 360 & RANGE_MASK]; 361 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) 362 & RANGE_MASK]; 363 364 wsptr += DCTSIZE; /* advance pointer to next row */ 365 } 366 } 367 368 #endif /* DCT_IFAST_SUPPORTED */ 369