compiler/libjpeg/main/jidctfst.c

   1 /*
   2     $Id$
   3 */
   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
 171 JGLOBAL(void)
 172 jpeg_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 */