libs/jpeg/jidctfst.c

   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 */