1 /* 2 * jidctfst.c 3 * 4 * Copyright (C) 1994-1998, Thomas G. Lane. 5 * Modified 2015-2017 by Guido Vollbeding. 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for 19 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 20 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 21 * JPEG textbook (see REFERENCES section in file README). The following code 22 * is based directly on figure 4-8 in P&M. 23 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 24 * possible to arrange the computation so that many of the multiplies are 25 * simple scalings of the final outputs. These multiplies can then be 26 * folded into the multiplications or divisions by the JPEG quantization 27 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 28 * to be done in the DCT itself. 29 * The primary disadvantage of this method is that with fixed-point math, 30 * accuracy is lost due to imprecise representation of the scaled 31 * quantization values. The smaller the quantization table entry, the less 32 * precise the scaled value, so this implementation does worse with high- 33 * quality-setting files than with low-quality ones. 34 */ 35 36 #define JPEG_INTERNALS 37 #include "jinclude.h" 38 #include "jpeglib.h" 39 #include "jdct.h" /* Private declarations for DCT subsystem */ 40 41 #ifdef DCT_IFAST_SUPPORTED 42 43 44 /* 45 * This module is specialized to the case DCTSIZE = 8. 46 */ 47 48 #if DCTSIZE != 8 49 Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */ 50 #endif 51 52 53 /* Scaling decisions are generally the same as in the LL&M algorithm; 54 * see jidctint.c for more details. However, we choose to descale 55 * (right shift) multiplication products as soon as they are formed, 56 * rather than carrying additional fractional bits into subsequent additions. 57 * This compromises accuracy slightly, but it lets us save a few shifts. 58 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 59 * everywhere except in the multiplications proper; this saves a good deal 60 * of work on 16-bit-int machines. 61 * 62 * The dequantized coefficients are not integers because the AA&N scaling 63 * factors have been incorporated. We represent them scaled up by PASS1_BITS, 64 * so that the first and second IDCT rounds have the same input scaling. 65 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 66 * avoid a descaling shift; this compromises accuracy rather drastically 67 * for small quantization table entries, but it saves a lot of shifts. 68 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 69 * so we use a much larger scaling factor to preserve accuracy. 70 * 71 * A final compromise is to represent the multiplicative constants to only 72 * 8 fractional bits, rather than 13. This saves some shifting work on some 73 * machines, and may also reduce the cost of multiplication (since there 74 * are fewer one-bits in the constants). 75 */ 76 77 #if BITS_IN_JSAMPLE == 8 78 #define CONST_BITS 8 79 #define PASS1_BITS 2 80 #else 81 #define CONST_BITS 8 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 == 8 93 #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */ 94 #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ 95 #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ 96 #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */ 97 #else 98 #define FIX_1_082392200 FIX(1.082392200) 99 #define FIX_1_414213562 FIX(1.414213562) 100 #define FIX_1_847759065 FIX(1.847759065) 101 #define FIX_2_613125930 FIX(2.613125930) 102 #endif 103 104 105 /* We can gain a little more speed, with a further compromise in accuracy, 106 * by omitting the addition in a descaling shift. This yields an incorrectly 107 * rounded result half the time... 108 */ 109 110 #ifndef USE_ACCURATE_ROUNDING 111 #undef DESCALE 112 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 113 #endif 114 115 116 /* Multiply a DCTELEM variable by an INT32 constant, and immediately 117 * descale to yield a DCTELEM result. 118 */ 119 120 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 121 122 123 /* Dequantize a coefficient by multiplying it by the multiplier-table 124 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 125 * multiplication will do. For 12-bit data, the multiplier table is 126 * declared INT32, so a 32-bit multiply will be used. 127 */ 128 129 #if BITS_IN_JSAMPLE == 8 130 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) 131 #else 132 #define DEQUANTIZE(coef,quantval) \ 133 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) 134 #endif 135 136 137 /* 138 * Perform dequantization and inverse DCT on one block of coefficients. 139 * 140 * cK represents cos(K*pi/16). 141 */ 142 143 GLOBAL(void) 144 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, 145 JCOEFPTR coef_block, 146 JSAMPARRAY output_buf, JDIMENSION output_col) 147 { 148 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 149 DCTELEM tmp10, tmp11, tmp12, tmp13; 150 DCTELEM z5, z10, z11, z12, z13; 151 JCOEFPTR inptr; 152 IFAST_MULT_TYPE * quantptr; 153 int * wsptr; 154 JSAMPROW outptr; 155 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 156 int ctr; 157 int workspace[DCTSIZE2]; /* buffers data between passes */ 158 SHIFT_TEMPS /* for DESCALE */ 159 ISHIFT_TEMPS /* for IRIGHT_SHIFT */ 160 161 /* Pass 1: process columns from input, store into work array. */ 162 163 inptr = coef_block; 164 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 165 wsptr = workspace; 166 for (ctr = DCTSIZE; ctr > 0; ctr--) { 167 /* Due to quantization, we will usually find that many of the input 168 * coefficients are zero, especially the AC terms. We can exploit this 169 * by short-circuiting the IDCT calculation for any column in which all 170 * the AC terms are zero. In that case each output is equal to the 171 * DC coefficient (with scale factor as needed). 172 * With typical images and quantization tables, half or more of the 173 * column DCT calculations can be simplified this way. 174 */ 175 176 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 177 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 178 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 179 inptr[DCTSIZE*7] == 0) { 180 /* AC terms all zero */ 181 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 182 183 wsptr[DCTSIZE*0] = dcval; 184 wsptr[DCTSIZE*1] = dcval; 185 wsptr[DCTSIZE*2] = dcval; 186 wsptr[DCTSIZE*3] = dcval; 187 wsptr[DCTSIZE*4] = dcval; 188 wsptr[DCTSIZE*5] = dcval; 189 wsptr[DCTSIZE*6] = dcval; 190 wsptr[DCTSIZE*7] = dcval; 191 192 inptr++; /* advance pointers to next column */ 193 quantptr++; 194 wsptr++; 195 continue; 196 } 197 198 /* Even part */ 199 200 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 201 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 202 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 203 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 204 205 tmp10 = tmp0 + tmp2; /* phase 3 */ 206 tmp11 = tmp0 - tmp2; 207 208 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 209 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ 210 211 tmp0 = tmp10 + tmp13; /* phase 2 */ 212 tmp3 = tmp10 - tmp13; 213 tmp1 = tmp11 + tmp12; 214 tmp2 = tmp11 - tmp12; 215 216 /* Odd part */ 217 218 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 219 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 220 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 221 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 222 223 z13 = tmp6 + tmp5; /* phase 6 */ 224 z10 = tmp6 - tmp5; 225 z11 = tmp4 + tmp7; 226 z12 = tmp4 - tmp7; 227 228 tmp7 = z11 + z13; /* phase 5 */ 229 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 230 231 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 232 tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */ 233 tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */ 234 235 tmp6 = tmp12 - tmp7; /* phase 2 */ 236 tmp5 = tmp11 - tmp6; 237 tmp4 = tmp10 - tmp5; 238 239 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 240 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 241 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 242 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 243 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 244 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 245 wsptr[DCTSIZE*3] = (int) (tmp3 + tmp4); 246 wsptr[DCTSIZE*4] = (int) (tmp3 - tmp4); 247 248 inptr++; /* advance pointers to next column */ 249 quantptr++; 250 wsptr++; 251 } 252 253 /* Pass 2: process rows from work array, store into output array. 254 * Note that we must descale the results by a factor of 8 == 2**3, 255 * and also undo the PASS1_BITS scaling. 256 */ 257 258 wsptr = workspace; 259 for (ctr = 0; ctr < DCTSIZE; ctr++) { 260 outptr = output_buf[ctr] + output_col; 261 262 /* Add range center and fudge factor for final descale and range-limit. */ 263 z5 = (DCTELEM) wsptr[0] + 264 ((((DCTELEM) RANGE_CENTER) << (PASS1_BITS+3)) + 265 (1 << (PASS1_BITS+2))); 266 267 /* Rows of zeroes can be exploited in the same way as we did with columns. 268 * However, the column calculation has created many nonzero AC terms, so 269 * the simplification applies less often (typically 5% to 10% of the time). 270 * On machines with very fast multiplication, it's possible that the 271 * test takes more time than it's worth. In that case this section 272 * may be commented out. 273 */ 274 275 #ifndef NO_ZERO_ROW_TEST 276 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 277 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 278 /* AC terms all zero */ 279 JSAMPLE dcval = range_limit[(int) IRIGHT_SHIFT(z5, PASS1_BITS+3) 280 & RANGE_MASK]; 281 282 outptr[0] = dcval; 283 outptr[1] = dcval; 284 outptr[2] = dcval; 285 outptr[3] = dcval; 286 outptr[4] = dcval; 287 outptr[5] = dcval; 288 outptr[6] = dcval; 289 outptr[7] = dcval; 290 291 wsptr += DCTSIZE; /* advance pointer to next row */ 292 continue; 293 } 294 #endif 295 296 /* Even part */ 297 298 tmp10 = z5 + (DCTELEM) wsptr[4]; 299 tmp11 = z5 - (DCTELEM) wsptr[4]; 300 301 tmp13 = (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]; 302 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], 303 FIX_1_414213562) - tmp13; /* 2*c4 */ 304 305 tmp0 = tmp10 + tmp13; 306 tmp3 = tmp10 - tmp13; 307 tmp1 = tmp11 + tmp12; 308 tmp2 = tmp11 - tmp12; 309 310 /* Odd part */ 311 312 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 313 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 314 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 315 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 316 317 tmp7 = z11 + z13; /* phase 5 */ 318 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 319 320 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 321 tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */ 322 tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */ 323 324 tmp6 = tmp12 - tmp7; /* phase 2 */ 325 tmp5 = tmp11 - tmp6; 326 tmp4 = tmp10 - tmp5; 327 328 /* Final output stage: scale down by a factor of 8 and range-limit */ 329 330 outptr[0] = range_limit[(int) IRIGHT_SHIFT(tmp0 + tmp7, PASS1_BITS+3) 331 & RANGE_MASK]; 332 outptr[7] = range_limit[(int) IRIGHT_SHIFT(tmp0 - tmp7, PASS1_BITS+3) 333 & RANGE_MASK]; 334 outptr[1] = range_limit[(int) IRIGHT_SHIFT(tmp1 + tmp6, PASS1_BITS+3) 335 & RANGE_MASK]; 336 outptr[6] = range_limit[(int) IRIGHT_SHIFT(tmp1 - tmp6, PASS1_BITS+3) 337 & RANGE_MASK]; 338 outptr[2] = range_limit[(int) IRIGHT_SHIFT(tmp2 + tmp5, PASS1_BITS+3) 339 & RANGE_MASK]; 340 outptr[5] = range_limit[(int) IRIGHT_SHIFT(tmp2 - tmp5, PASS1_BITS+3) 341 & RANGE_MASK]; 342 outptr[3] = range_limit[(int) IRIGHT_SHIFT(tmp3 + tmp4, PASS1_BITS+3) 343 & RANGE_MASK]; 344 outptr[4] = range_limit[(int) IRIGHT_SHIFT(tmp3 - tmp4, PASS1_BITS+3) 345 & RANGE_MASK]; 346 347 wsptr += DCTSIZE; /* advance pointer to next row */ 348 } 349 } 350 351 #endif /* DCT_IFAST_SUPPORTED */ 352