src/jpeg/jidctint.c

   1 /*
   2  * jidctint.c
   3  *
   4  * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in
  18  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  19  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  20  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  21  * The primary algorithm described there uses 11 multiplies and 29 adds.
  22  * We use their alternate method with 12 multiplies and 32 adds.
  23  * The advantage of this method is that no data path contains more than one
  24  * multiplication; this allows a very simple and accurate implementation in
  25  * scaled fixed-point arithmetic, with a minimal number of shifts.
  26  */
  27
  28 #define JPEG_INTERNALS
  29 #include "jinclude.h"
  30 #include "jpeglib.h"
  31 #include "jdct.h"               /* Private declarations for DCT subsystem */
  32
  33 #ifdef DCT_ISLOW_SUPPORTED
  34
  35
  36 /*
  37  * This module is specialized to the case DCTSIZE = 8.
  38  */
  39
  40 #if DCTSIZE != 8
  41   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  42 #endif
  43
  44
  45 /*
  46  * The poop on this scaling stuff is as follows:
  47  *
  48  * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
  49  * larger than the true IDCT outputs.  The final outputs are therefore
  50  * a factor of N larger than desired; since N=8 this can be cured by
  51  * a simple right shift at the end of the algorithm.  The advantage of
  52  * this arrangement is that we save two multiplications per 1-D IDCT,
  53  * because the y0 and y4 inputs need not be divided by sqrt(N).
  54  *
  55  * We have to do addition and subtraction of the integer inputs, which
  56  * is no problem, and multiplication by fractional constants, which is
  57  * a problem to do in integer arithmetic.  We multiply all the constants
  58  * by CONST_SCALE and convert them to integer constants (thus retaining
  59  * CONST_BITS bits of precision in the constants).  After doing a
  60  * multiplication we have to divide the product by CONST_SCALE, with proper
  61  * rounding, to produce the correct output.  This division can be done
  62  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
  63  * as long as possible so that partial sums can be added together with
  64  * full fractional precision.
  65  *
  66  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
  67  * they are represented to better-than-integral precision.  These outputs
  68  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
  69  * with the recommended scaling.  (To scale up 12-bit sample data further, an
  70  * intermediate INT32 array would be needed.)
  71  *
  72  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
  73  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
  74  * shows that the values given below are the most effective.
  75  */
  76
  77 #if BITS_IN_JSAMPLE == 8
  78 #define CONST_BITS  13
  79 #define PASS1_BITS  2
  80 #else
  81 #define CONST_BITS  13
  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 == 13
  93 #define FIX_0_298631336  ((JPEG_INT32)  2446)   /* FIX(0.298631336) */
  94 #define FIX_0_390180644  ((JPEG_INT32)  3196)   /* FIX(0.390180644) */
  95 #define FIX_0_541196100  ((JPEG_INT32)  4433)   /* FIX(0.541196100) */
  96 #define FIX_0_765366865  ((JPEG_INT32)  6270)   /* FIX(0.765366865) */
  97 #define FIX_0_899976223  ((JPEG_INT32)  7373)   /* FIX(0.899976223) */
  98 #define FIX_1_175875602  ((JPEG_INT32)  9633)   /* FIX(1.175875602) */
  99 #define FIX_1_501321110  ((JPEG_INT32)  12299)  /* FIX(1.501321110) */
 100 #define FIX_1_847759065  ((JPEG_INT32)  15137)  /* FIX(1.847759065) */
 101 #define FIX_1_961570560  ((JPEG_INT32)  16069)  /* FIX(1.961570560) */
 102 #define FIX_2_053119869  ((JPEG_INT32)  16819)  /* FIX(2.053119869) */
 103 #define FIX_2_562915447  ((JPEG_INT32)  20995)  /* FIX(2.562915447) */
 104 #define FIX_3_072711026  ((JPEG_INT32)  25172)  /* FIX(3.072711026) */
 105 #else
 106 #define FIX_0_298631336  FIX(0.298631336)
 107 #define FIX_0_390180644  FIX(0.390180644)
 108 #define FIX_0_541196100  FIX(0.541196100)
 109 #define FIX_0_765366865  FIX(0.765366865)
 110 #define FIX_0_899976223  FIX(0.899976223)
 111 #define FIX_1_175875602  FIX(1.175875602)
 112 #define FIX_1_501321110  FIX(1.501321110)
 113 #define FIX_1_847759065  FIX(1.847759065)
 114 #define FIX_1_961570560  FIX(1.961570560)
 115 #define FIX_2_053119869  FIX(2.053119869)
 116 #define FIX_2_562915447  FIX(2.562915447)
 117 #define FIX_3_072711026  FIX(3.072711026)
 118 #endif
 119
 120
 121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 122  * For 8-bit samples with the recommended scaling, all the variable
 123  * and constant values involved are no more than 16 bits wide, so a
 124  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 125  * For 12-bit samples, a full 32-bit multiplication will be needed.
 126  */
 127
 128 #if BITS_IN_JSAMPLE == 8
 129 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
 130 #else
 131 #define MULTIPLY(var,const)  ((var) * (const))
 132 #endif
 133
 134
 135 /* Dequantize a coefficient by multiplying it by the multiplier-table
 136  * entry; produce an int result.  In this module, both inputs and result
 137  * are 16 bits or less, so either int or short multiply will work.
 138  */
 139
 140 #define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))
 141
 142
 143 /*
 144  * Perform dequantization and inverse DCT on one block of coefficients.
 145  */
 146
 147 GLOBAL(void)
 148 jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
 149                  JCOEFPTR coef_block,
 150                  JSAMPARRAY output_buf, JDIMENSION output_col)
 151 {
 152   JPEG_INT32 tmp0, tmp1, tmp2, tmp3;
 153   JPEG_INT32 tmp10, tmp11, tmp12, tmp13;
 154   JPEG_INT32 z1, z2, z3, z4, z5;
 155   JCOEFPTR inptr;
 156   ISLOW_MULT_TYPE * quantptr;
 157   int * wsptr;
 158   JSAMPROW outptr;
 159   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
 160   int ctr;
 161   int workspace[DCTSIZE2];      /* buffers data between passes */
 162   SHIFT_TEMPS
 163
 164   /* Pass 1: process columns from input, store into work array. */
 165   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
 166   /* furthermore, we scale the results by 2**PASS1_BITS. */
 167
 168   inptr = coef_block;
 169   quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
 170   wsptr = workspace;
 171   for (ctr = DCTSIZE; ctr > 0; ctr--) {
 172     /* Due to quantization, we will usually find that many of the input
 173      * coefficients are zero, especially the AC terms.  We can exploit this
 174      * by short-circuiting the IDCT calculation for any column in which all
 175      * the AC terms are zero.  In that case each output is equal to the
 176      * DC coefficient (with scale factor as needed).
 177      * With typical images and quantization tables, half or more of the
 178      * column DCT calculations can be simplified this way.
 179      */
 180
 181     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
 182         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
 183         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
 184         inptr[DCTSIZE*7] == 0) {
 185       /* AC terms all zero */
 186       int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
 187
 188       wsptr[DCTSIZE*0] = dcval;
 189       wsptr[DCTSIZE*1] = dcval;
 190       wsptr[DCTSIZE*2] = dcval;
 191       wsptr[DCTSIZE*3] = dcval;
 192       wsptr[DCTSIZE*4] = dcval;
 193       wsptr[DCTSIZE*5] = dcval;
 194       wsptr[DCTSIZE*6] = dcval;
 195       wsptr[DCTSIZE*7] = dcval;
 196
 197       inptr++;                  /* advance pointers to next column */
 198       quantptr++;
 199       wsptr++;
 200       continue;
 201     }
 202
 203     /* Even part: reverse the even part of the forward DCT. */
 204     /* The rotator is sqrt(2)*c(-6). */
 205
 206     z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
 207     z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
 208
 209     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
 210     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
 211     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
 212
 213     z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 214     z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
 215
 216     tmp0 = (z2 + z3) << CONST_BITS;
 217     tmp1 = (z2 - z3) << CONST_BITS;
 218
 219     tmp10 = tmp0 + tmp3;
 220     tmp13 = tmp0 - tmp3;
 221     tmp11 = tmp1 + tmp2;
 222     tmp12 = tmp1 - tmp2;
 223
 224     /* Odd part per figure 8; the matrix is unitary and hence its
 225      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
 226      */
 227
 228     tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
 229     tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
 230     tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
 231     tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
 232
 233     z1 = tmp0 + tmp3;
 234     z2 = tmp1 + tmp2;
 235     z3 = tmp0 + tmp2;
 236     z4 = tmp1 + tmp3;
 237     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 238
 239     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 240     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 241     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 242     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 243     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 244     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 245     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 246     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 247
 248     z3 += z5;
 249     z4 += z5;
 250
 251     tmp0 += z1 + z3;
 252     tmp1 += z2 + z4;
 253     tmp2 += z2 + z3;
 254     tmp3 += z1 + z4;
 255
 256     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
 257
 258     wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
 259     wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
 260     wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
 261     wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
 262     wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
 263     wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
 264     wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
 265     wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
 266
 267     inptr++;                    /* advance pointers to next column */
 268     quantptr++;
 269     wsptr++;
 270   }
 271
 272   /* Pass 2: process rows from work array, store into output array. */
 273   /* Note that we must descale the results by a factor of 8 == 2**3, */
 274   /* and also undo the PASS1_BITS scaling. */
 275
 276   wsptr = workspace;
 277   for (ctr = 0; ctr < DCTSIZE; ctr++) {
 278     outptr = output_buf[ctr] + output_col;
 279     /* Rows of zeroes can be exploited in the same way as we did with columns.
 280      * However, the column calculation has created many nonzero AC terms, so
 281      * the simplification applies less often (typically 5% to 10% of the time).
 282      * On machines with very fast multiplication, it's possible that the
 283      * test takes more time than it's worth.  In that case this section
 284      * may be commented out.
 285      */
 286
 287 #ifndef NO_ZERO_ROW_TEST
 288     if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
 289         wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
 290       /* AC terms all zero */
 291       JSAMPLE dcval = range_limit[(int) DESCALE((JPEG_INT32) wsptr[0], PASS1_BITS+3)
 292                                   & RANGE_MASK];
 293
 294       outptr[0] = dcval;
 295       outptr[1] = dcval;
 296       outptr[2] = dcval;
 297       outptr[3] = dcval;
 298       outptr[4] = dcval;
 299       outptr[5] = dcval;
 300       outptr[6] = dcval;
 301       outptr[7] = dcval;
 302
 303       wsptr += DCTSIZE;         /* advance pointer to next row */
 304       continue;
 305     }
 306 #endif
 307
 308     /* Even part: reverse the even part of the forward DCT. */
 309     /* The rotator is sqrt(2)*c(-6). */
 310
 311     z2 = (JPEG_INT32) wsptr[2];
 312     z3 = (JPEG_INT32) wsptr[6];
 313
 314     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
 315     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
 316     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
 317
 318     tmp0 = ((JPEG_INT32) wsptr[0] + (JPEG_INT32) wsptr[4]) << CONST_BITS;
 319     tmp1 = ((JPEG_INT32) wsptr[0] - (JPEG_INT32) wsptr[4]) << CONST_BITS;
 320
 321     tmp10 = tmp0 + tmp3;
 322     tmp13 = tmp0 - tmp3;
 323     tmp11 = tmp1 + tmp2;
 324     tmp12 = tmp1 - tmp2;
 325
 326     /* Odd part per figure 8; the matrix is unitary and hence its
 327      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
 328      */
 329
 330     tmp0 = (JPEG_INT32) wsptr[7];
 331     tmp1 = (JPEG_INT32) wsptr[5];
 332     tmp2 = (JPEG_INT32) wsptr[3];
 333     tmp3 = (JPEG_INT32) wsptr[1];
 334
 335     z1 = tmp0 + tmp3;
 336     z2 = tmp1 + tmp2;
 337     z3 = tmp0 + tmp2;
 338     z4 = tmp1 + tmp3;
 339     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 340
 341     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 342     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 343     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 344     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 345     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 346     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 347     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 348     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 349
 350     z3 += z5;
 351     z4 += z5;
 352
 353     tmp0 += z1 + z3;
 354     tmp1 += z2 + z4;
 355     tmp2 += z2 + z3;
 356     tmp3 += z1 + z4;
 357
 358     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
 359
 360     outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
 361                                           CONST_BITS+PASS1_BITS+3)
 362                             & RANGE_MASK];
 363     outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
 364                                           CONST_BITS+PASS1_BITS+3)
 365                             & RANGE_MASK];
 366     outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
 367                                           CONST_BITS+PASS1_BITS+3)
 368                             & RANGE_MASK];
 369     outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
 370                                           CONST_BITS+PASS1_BITS+3)
 371                             & RANGE_MASK];
 372     outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
 373                                           CONST_BITS+PASS1_BITS+3)
 374                             & RANGE_MASK];
 375     outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
 376                                           CONST_BITS+PASS1_BITS+3)
 377                             & RANGE_MASK];
 378     outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
 379                                           CONST_BITS+PASS1_BITS+3)
 380                             & RANGE_MASK];
 381     outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
 382                                           CONST_BITS+PASS1_BITS+3)
 383                             & RANGE_MASK];
 384
 385     wsptr += DCTSIZE;           /* advance pointer to next row */
 386   }
 387 }
 388
 389 #endif /* DCT_ISLOW_SUPPORTED */