1/* 2 * reserved comment block 3 * DO NOT REMOVE OR ALTER! 4 */ 5/* 6 * jidctfst.c 7 * 8 * Copyright (C) 1994-1998, Thomas G. Lane. 9 * This file is part of the Independent JPEG Group's software. 10 * For conditions of distribution and use, see the accompanying README file. 11 * 12 * This file contains a fast, not so accurate integer implementation of the 13 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine 14 * must also perform dequantization of the input coefficients. 15 * 16 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 17 * on each row (or vice versa, but it's more convenient to emit a row at 18 * a time). Direct algorithms are also available, but they are much more 19 * complex and seem not to be any faster when reduced to code. 20 * 21 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 22 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 23 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 24 * JPEG textbook (see REFERENCES section in file README). The following code 25 * is based directly on figure 4-8 in P&M. 26 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 27 * possible to arrange the computation so that many of the multiplies are 28 * simple scalings of the final outputs. These multiplies can then be 29 * folded into the multiplications or divisions by the JPEG quantization 30 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 31 * to be done in the DCT itself. 32 * The primary disadvantage of this method is that with fixed-point math, 33 * accuracy is lost due to imprecise representation of the scaled 34 * quantization values. The smaller the quantization table entry, the less 35 * precise the scaled value, so this implementation does worse with high- 36 * quality-setting files than with low-quality ones. 37 */ 38 39#define JPEG_INTERNALS 40#include "jinclude.h" 41#include "jpeglib.h" 42#include "jdct.h" /* Private declarations for DCT subsystem */ 43 44#ifdef DCT_IFAST_SUPPORTED 45 46 47/* 48 * This module is specialized to the case DCTSIZE = 8. 49 */ 50 51#if DCTSIZE != 8 52 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 53#endif 54 55 56/* Scaling decisions are generally the same as in the LL&M algorithm; 57 * see jidctint.c for more details. However, we choose to descale 58 * (right shift) multiplication products as soon as they are formed, 59 * rather than carrying additional fractional bits into subsequent additions. 60 * This compromises accuracy slightly, but it lets us save a few shifts. 61 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 62 * everywhere except in the multiplications proper; this saves a good deal 63 * of work on 16-bit-int machines. 64 * 65 * The dequantized coefficients are not integers because the AA&N scaling 66 * factors have been incorporated. We represent them scaled up by PASS1_BITS, 67 * so that the first and second IDCT rounds have the same input scaling. 68 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 69 * avoid a descaling shift; this compromises accuracy rather drastically 70 * for small quantization table entries, but it saves a lot of shifts. 71 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 72 * so we use a much larger scaling factor to preserve accuracy. 73 * 74 * A final compromise is to represent the multiplicative constants to only 75 * 8 fractional bits, rather than 13. This saves some shifting work on some 76 * machines, and may also reduce the cost of multiplication (since there 77 * are fewer one-bits in the constants). 78 */ 79 80#if BITS_IN_JSAMPLE == 8 81#define CONST_BITS 8 82#define PASS1_BITS 2 83#else 84#define CONST_BITS 8 85#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 86#endif 87 88/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 89 * causing a lot of useless floating-point operations at run time. 90 * To get around this we use the following pre-calculated constants. 91 * If you change CONST_BITS you may want to add appropriate values. 92 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 93 */ 94 95#if CONST_BITS == 8 96#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */ 97#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */ 98#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */ 99#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */ 100#else 101#define FIX_1_082392200 FIX(1.082392200) 102#define FIX_1_414213562 FIX(1.414213562) 103#define FIX_1_847759065 FIX(1.847759065) 104#define FIX_2_613125930 FIX(2.613125930) 105#endif 106 107 108/* We can gain a little more speed, with a further compromise in accuracy, 109 * by omitting the addition in a descaling shift. This yields an incorrectly 110 * rounded result half the time... 111 */ 112 113#ifndef USE_ACCURATE_ROUNDING 114#undef DESCALE 115#define DESCALE(x,n) RIGHT_SHIFT(x, n) 116#endif 117 118 119/* Multiply a DCTELEM variable by an INT32 constant, and immediately 120 * descale to yield a DCTELEM result. 121 */ 122 123#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 124 125 126/* Dequantize a coefficient by multiplying it by the multiplier-table 127 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 128 * multiplication will do. For 12-bit data, the multiplier table is 129 * declared INT32, so a 32-bit multiply will be used. 130 */ 131 132#if BITS_IN_JSAMPLE == 8 133#define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval)) 134#else 135#define DEQUANTIZE(coef,quantval) \ 136 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) 137#endif 138 139 140/* Like DESCALE, but applies to a DCTELEM and produces an int. 141 * We assume that int right shift is unsigned if INT32 right shift is. 142 */ 143 144#ifdef RIGHT_SHIFT_IS_UNSIGNED 145#define ISHIFT_TEMPS DCTELEM ishift_temp; 146#if BITS_IN_JSAMPLE == 8 147#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ 148#else 149#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ 150#endif 151#define IRIGHT_SHIFT(x,shft) \ 152 ((ishift_temp = (x)) < 0 ? \ 153 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ 154 (ishift_temp >> (shft))) 155#else 156#define ISHIFT_TEMPS 157#define IRIGHT_SHIFT(x,shft) ((x) >> (shft)) 158#endif 159 160#ifdef USE_ACCURATE_ROUNDING 161#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) 162#else 163#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n)) 164#endif 165 166 167/* 168 * Perform dequantization and inverse DCT on one block of coefficients. 169 */ 170 171GLOBAL(void) 172jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, 173 JCOEFPTR coef_block, 174 JSAMPARRAY output_buf, JDIMENSION output_col) 175{ 176 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 177 DCTELEM tmp10, tmp11, tmp12, tmp13; 178 DCTELEM z5, z10, z11, z12, z13; 179 JCOEFPTR inptr; 180 IFAST_MULT_TYPE * quantptr; 181 int * wsptr; 182 JSAMPROW outptr; 183 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 184 int ctr; 185 int workspace[DCTSIZE2]; /* buffers data between passes */ 186 SHIFT_TEMPS /* for DESCALE */ 187 ISHIFT_TEMPS /* for IDESCALE */ 188 189 /* Pass 1: process columns from input, store into work array. */ 190 191 inptr = coef_block; 192 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 193 wsptr = workspace; 194 for (ctr = DCTSIZE; ctr > 0; ctr--) { 195 /* Due to quantization, we will usually find that many of the input 196 * coefficients are zero, especially the AC terms. We can exploit this 197 * by short-circuiting the IDCT calculation for any column in which all 198 * the AC terms are zero. In that case each output is equal to the 199 * DC coefficient (with scale factor as needed). 200 * With typical images and quantization tables, half or more of the 201 * column DCT calculations can be simplified this way. 202 */ 203 204 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 205 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 206 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 207 inptr[DCTSIZE*7] == 0) { 208 /* AC terms all zero */ 209 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 210 211 wsptr[DCTSIZE*0] = dcval; 212 wsptr[DCTSIZE*1] = dcval; 213 wsptr[DCTSIZE*2] = dcval; 214 wsptr[DCTSIZE*3] = dcval; 215 wsptr[DCTSIZE*4] = dcval; 216 wsptr[DCTSIZE*5] = dcval; 217 wsptr[DCTSIZE*6] = dcval; 218 wsptr[DCTSIZE*7] = dcval; 219 220 inptr++; /* advance pointers to next column */ 221 quantptr++; 222 wsptr++; 223 continue; 224 } 225 226 /* Even part */ 227 228 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 229 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 230 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 231 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 232 233 tmp10 = tmp0 + tmp2; /* phase 3 */ 234 tmp11 = tmp0 - tmp2; 235 236 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 237 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ 238 239 tmp0 = tmp10 + tmp13; /* phase 2 */ 240 tmp3 = tmp10 - tmp13; 241 tmp1 = tmp11 + tmp12; 242 tmp2 = tmp11 - tmp12; 243 244 /* Odd part */ 245 246 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 247 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 248 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 249 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 250 251 z13 = tmp6 + tmp5; /* phase 6 */ 252 z10 = tmp6 - tmp5; 253 z11 = tmp4 + tmp7; 254 z12 = tmp4 - tmp7; 255 256 tmp7 = z11 + z13; /* phase 5 */ 257 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 258 259 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 260 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 261 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 262 263 tmp6 = tmp12 - tmp7; /* phase 2 */ 264 tmp5 = tmp11 - tmp6; 265 tmp4 = tmp10 + tmp5; 266 267 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 268 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 269 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 270 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 271 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 272 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 273 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); 274 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4); 275 276 inptr++; /* advance pointers to next column */ 277 quantptr++; 278 wsptr++; 279 } 280 281 /* Pass 2: process rows from work array, store into output array. */ 282 /* Note that we must descale the results by a factor of 8 == 2**3, */ 283 /* and also undo the PASS1_BITS scaling. */ 284 285 wsptr = workspace; 286 for (ctr = 0; ctr < DCTSIZE; ctr++) { 287 outptr = output_buf[ctr] + output_col; 288 /* Rows of zeroes can be exploited in the same way as we did with columns. 289 * However, the column calculation has created many nonzero AC terms, so 290 * the simplification applies less often (typically 5% to 10% of the time). 291 * On machines with very fast multiplication, it's possible that the 292 * test takes more time than it's worth. In that case this section 293 * may be commented out. 294 */ 295 296#ifndef NO_ZERO_ROW_TEST 297 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 298 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 299 /* AC terms all zero */ 300 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) 301 & RANGE_MASK]; 302 303 outptr[0] = dcval; 304 outptr[1] = dcval; 305 outptr[2] = dcval; 306 outptr[3] = dcval; 307 outptr[4] = dcval; 308 outptr[5] = dcval; 309 outptr[6] = dcval; 310 outptr[7] = dcval; 311 312 wsptr += DCTSIZE; /* advance pointer to next row */ 313 continue; 314 } 315#endif 316 317 /* Even part */ 318 319 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); 320 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); 321 322 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); 323 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) 324 - tmp13; 325 326 tmp0 = tmp10 + tmp13; 327 tmp3 = tmp10 - tmp13; 328 tmp1 = tmp11 + tmp12; 329 tmp2 = tmp11 - tmp12; 330 331 /* Odd part */ 332 333 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 334 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 335 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 336 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 337 338 tmp7 = z11 + z13; /* phase 5 */ 339 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 340 341 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 342 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 343 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 344 345 tmp6 = tmp12 - tmp7; /* phase 2 */ 346 tmp5 = tmp11 - tmp6; 347 tmp4 = tmp10 + tmp5; 348 349 /* Final output stage: scale down by a factor of 8 and range-limit */ 350 351 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) 352 & RANGE_MASK]; 353 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) 354 & RANGE_MASK]; 355 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) 356 & RANGE_MASK]; 357 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) 358 & RANGE_MASK]; 359 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) 360 & RANGE_MASK]; 361 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) 362 & RANGE_MASK]; 363 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) 364 & RANGE_MASK]; 365 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) 366 & RANGE_MASK]; 367 368 wsptr += DCTSIZE; /* advance pointer to next row */ 369 } 370} 371 372#endif /* DCT_IFAST_SUPPORTED */ 373