1 /* 2 * jidctfst.c 3 * 4 * Copyright (C) 1994, 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 #define IRIGHT_SHIFT(x,shft) \ 143 ((ishift_temp = (x)) < 0 ? \ 144 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (32-(shft))) : \ 145 (ishift_temp >> (shft))) 146 #else 147 #define ISHIFT_TEMPS 148 #define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) 149 #endif 150 151 #ifdef USE_ACCURATE_ROUNDING 152 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) 153 #else 154 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) 155 #endif 156 157 158 /* 159 * Perform dequantization and inverse DCT on one block of coefficients. 160 */ 161 162 GLOBAL void 163 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, 164 JCOEFPTR coef_block, 165 JSAMPARRAY output_buf, JDIMENSION output_col) 166 { 167 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 168 DCTELEM tmp10, tmp11, tmp12, tmp13; 169 DCTELEM z5, z10, z11, z12, z13; 170 JCOEFPTR inptr; 171 IFAST_MULT_TYPE * quantptr; 172 int * wsptr; 173 JSAMPROW outptr; 174 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 175 int ctr; 176 int workspace[DCTSIZE2]; /* buffers data between passes */ 177 SHIFT_TEMPS /* for DESCALE */ 178 ISHIFT_TEMPS /* for IDESCALE */ 179 180 /* Pass 1: process columns from input, store into work array. */ 181 182 inptr = coef_block; 183 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 184 wsptr = workspace; 185 for (ctr = DCTSIZE; ctr > 0; ctr--) { 186 /* Due to quantization, we will usually find that many of the input 187 * coefficients are zero, especially the AC terms. We can exploit this 188 * by short-circuiting the IDCT calculation for any column in which all 189 * the AC terms are zero. In that case each output is equal to the 190 * DC coefficient (with scale factor as needed). 191 * With typical images and quantization tables, half or more of the 192 * column DCT calculations can be simplified this way. 193 */ 194 195 if ((inptr[DCTSIZE*1] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] | 196 inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] | 197 inptr[DCTSIZE*7]) == 0) { 198 /* AC terms all zero */ 199 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 200 201 wsptr[DCTSIZE*0] = dcval; 202 wsptr[DCTSIZE*1] = dcval; 203 wsptr[DCTSIZE*2] = dcval; 204 wsptr[DCTSIZE*3] = dcval; 205 wsptr[DCTSIZE*4] = dcval; 206 wsptr[DCTSIZE*5] = dcval; 207 wsptr[DCTSIZE*6] = dcval; 208 wsptr[DCTSIZE*7] = dcval; 209 210 inptr++; /* advance pointers to next column */ 211 quantptr++; 212 wsptr++; 213 continue; 214 } 215 216 /* Even part */ 217 218 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 219 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 220 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 221 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 222 223 tmp10 = tmp0 + tmp2; /* phase 3 */ 224 tmp11 = tmp0 - tmp2; 225 226 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 227 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ 228 229 tmp0 = tmp10 + tmp13; /* phase 2 */ 230 tmp3 = tmp10 - tmp13; 231 tmp1 = tmp11 + tmp12; 232 tmp2 = tmp11 - tmp12; 233 234 /* Odd part */ 235 236 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 237 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 238 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 239 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 240 241 z13 = tmp6 + tmp5; /* phase 6 */ 242 z10 = tmp6 - tmp5; 243 z11 = tmp4 + tmp7; 244 z12 = tmp4 - tmp7; 245 246 tmp7 = z11 + z13; /* phase 5 */ 247 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 248 249 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 250 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 251 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 252 253 tmp6 = tmp12 - tmp7; /* phase 2 */ 254 tmp5 = tmp11 - tmp6; 255 tmp4 = tmp10 + tmp5; 256 257 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 258 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 259 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 260 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 261 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 262 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 263 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); 264 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); 265 266 inptr++; /* advance pointers to next column */ 267 quantptr++; 268 wsptr++; 269 } 270 271 /* Pass 2: process rows from work array, store into output array. */ 272 /* Note that we must descale the results by a factor of 8 == 2**3, */ 273 /* and also undo the PASS1_BITS scaling. */ 274 275 wsptr = workspace; 276 for (ctr = 0; ctr < DCTSIZE; ctr++) { 277 outptr = output_buf[ctr] + output_col; 278 /* Rows of zeroes can be exploited in the same way as we did with columns. 279 * However, the column calculation has created many nonzero AC terms, so 280 * the simplification applies less often (typically 5% to 10% of the time). 281 * On machines with very fast multiplication, it's possible that the 282 * test takes more time than it's worth. In that case this section 283 * may be commented out. 284 */ 285 286 #ifndef NO_ZERO_ROW_TEST 287 if ((wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] | 288 wsptr[7]) == 0) { 289 /* AC terms all zero */ 290 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) 291 & RANGE_MASK]; 292 293 outptr[0] = dcval; 294 outptr[1] = dcval; 295 outptr[2] = dcval; 296 outptr[3] = dcval; 297 outptr[4] = dcval; 298 outptr[5] = dcval; 299 outptr[6] = dcval; 300 outptr[7] = dcval; 301 302 wsptr += DCTSIZE; /* advance pointer to next row */ 303 continue; 304 } 305 #endif 306 307 /* Even part */ 308 309 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); 310 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); 311 312 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); 313 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) 314 - tmp13; 315 316 tmp0 = tmp10 + tmp13; 317 tmp3 = tmp10 - tmp13; 318 tmp1 = tmp11 + tmp12; 319 tmp2 = tmp11 - tmp12; 320 321 /* Odd part */ 322 323 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 324 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 325 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 326 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 327 328 tmp7 = z11 + z13; /* phase 5 */ 329 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 330 331 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 332 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 333 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 334 335 tmp6 = tmp12 - tmp7; /* phase 2 */ 336 tmp5 = tmp11 - tmp6; 337 tmp4 = tmp10 + tmp5; 338 339 /* Final output stage: scale down by a factor of 8 and range-limit */ 340 341 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) 342 & RANGE_MASK]; 343 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) 344 & RANGE_MASK]; 345 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) 346 & RANGE_MASK]; 347 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) 348 & RANGE_MASK]; 349 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) 350 & RANGE_MASK]; 351 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) 352 & RANGE_MASK]; 353 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) 354 & RANGE_MASK]; 355 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) 356 & RANGE_MASK]; 357 358 wsptr += DCTSIZE; /* advance pointer to next row */ 359 } 360 } 361 362 #endif /* DCT_IFAST_SUPPORTED */ 363