compiler/libjpeg/main/jidctint.c

   1 /*
   2     $Id$
   3 */
   4
   5 /*
   6  * jidctint.c
   7  *
   8  * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in
  22  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  23  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  24  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  25  * The primary algorithm described there uses 11 multiplies and 29 adds.
  26  * We use their alternate method with 12 multiplies and 32 adds.
  27  * The advantage of this method is that no data path contains more than one
  28  * multiplication; this allows a very simple and accurate implementation in
  29  * scaled fixed-point arithmetic, with a minimal number of shifts.
  30  */
  31
  32 #define JPEG_INTERNALS
  33 #include "jinclude.h"
  34 #include "jpeglib.h"
  35 #include "jdct.h"               /* Private declarations for DCT subsystem */
  36
  37 #ifdef DCT_ISLOW_SUPPORTED
  38
  39
  40 /*
  41  * This module is specialized to the case DCTSIZE = 8.
  42  */
  43
  44 #if DCTSIZE != 8
  45   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  46 #endif
  47
  48
  49 /*
  50  * The poop on this scaling stuff is as follows:
  51  *
  52  * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
  53  * larger than the true IDCT outputs.  The final outputs are therefore
  54  * a factor of N larger than desired; since N=8 this can be cured by
  55  * a simple right shift at the end of the algorithm.  The advantage of
  56  * this arrangement is that we save two multiplications per 1-D IDCT,
  57  * because the y0 and y4 inputs need not be divided by sqrt(N).
  58  *
  59  * We have to do addition and subtraction of the integer inputs, which
  60  * is no problem, and multiplication by fractional constants, which is
  61  * a problem to do in integer arithmetic.  We multiply all the constants
  62  * by CONST_SCALE and convert them to integer constants (thus retaining
  63  * CONST_BITS bits of precision in the constants).  After doing a
  64  * multiplication we have to divide the product by CONST_SCALE, with proper
  65  * rounding, to produce the correct output.  This division can be done
  66  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
  67  * as long as possible so that partial sums can be added together with
  68  * full fractional precision.
  69  *
  70  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
  71  * they are represented to better-than-integral precision.  These outputs
  72  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
  73  * with the recommended scaling.  (To scale up 12-bit sample data further, an
  74  * intermediate INT32 array would be needed.)
  75  *
  76  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
  77  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
  78  * shows that the values given below are the most effective.
  79  */
  80
  81 #if BITS_IN_JSAMPLE == 8
  82 #define CONST_BITS  13
  83 #define PASS1_BITS  2
  84 #else
  85 #define CONST_BITS  13
  86 #define PASS1_BITS  1           /* lose a little precision to avoid overflow */
  87 #endif
  88
  89 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  90  * causing a lot of useless floating-point operations at run time.
  91  * To get around this we use the following pre-calculated constants.
  92  * If you change CONST_BITS you may want to add appropriate values.
  93  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  94  */
  95
  96 #if CONST_BITS == 13
  97 #define FIX_0_298631336  ((INT32)  2446)        /* FIX(0.298631336) */
  98 #define FIX_0_390180644  ((INT32)  3196)        /* FIX(0.390180644) */
  99 #define FIX_0_541196100  ((INT32)  4433)        /* FIX(0.541196100) */
 100 #define FIX_0_765366865  ((INT32)  6270)        /* FIX(0.765366865) */
 101 #define FIX_0_899976223  ((INT32)  7373)        /* FIX(0.899976223) */
 102 #define FIX_1_175875602  ((INT32)  9633)        /* FIX(1.175875602) */
 103 #define FIX_1_501321110  ((INT32)  12299)       /* FIX(1.501321110) */
 104 #define FIX_1_847759065  ((INT32)  15137)       /* FIX(1.847759065) */
 105 #define FIX_1_961570560  ((INT32)  16069)       /* FIX(1.961570560) */
 106 #define FIX_2_053119869  ((INT32)  16819)       /* FIX(2.053119869) */
 107 #define FIX_2_562915447  ((INT32)  20995)       /* FIX(2.562915447) */
 108 #define FIX_3_072711026  ((INT32)  25172)       /* FIX(3.072711026) */
 109 #else
 110 #define FIX_0_298631336  FIX(0.298631336)
 111 #define FIX_0_390180644  FIX(0.390180644)
 112 #define FIX_0_541196100  FIX(0.541196100)
 113 #define FIX_0_765366865  FIX(0.765366865)
 114 #define FIX_0_899976223  FIX(0.899976223)
 115 #define FIX_1_175875602  FIX(1.175875602)
 116 #define FIX_1_501321110  FIX(1.501321110)
 117 #define FIX_1_847759065  FIX(1.847759065)
 118 #define FIX_1_961570560  FIX(1.961570560)
 119 #define FIX_2_053119869  FIX(2.053119869)
 120 #define FIX_2_562915447  FIX(2.562915447)
 121 #define FIX_3_072711026  FIX(3.072711026)
 122 #endif
 123
 124
 125 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 126  * For 8-bit samples with the recommended scaling, all the variable
 127  * and constant values involved are no more than 16 bits wide, so a
 128  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 129  * For 12-bit samples, a full 32-bit multiplication will be needed.
 130  */
 131
 132 #if BITS_IN_JSAMPLE == 8
 133 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
 134 #else
 135 #define MULTIPLY(var,const)  ((var) * (const))
 136 #endif
 137
 138
 139 /* Dequantize a coefficient by multiplying it by the multiplier-table
 140  * entry; produce an int result.  In this module, both inputs and result
 141  * are 16 bits or less, so either int or short multiply will work.
 142  */
 143
 144 #define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))
 145
 146
 147 /*
 148  * Perform dequantization and inverse DCT on one block of coefficients.
 149  */
 150
 151 JGLOBAL(void)
 152 jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
 153                  JCOEFPTR coef_block,
 154                  JSAMPARRAY output_buf, JDIMENSION output_col)
 155 {
 156   INT32 tmp0, tmp1, tmp2, tmp3;
 157   INT32 tmp10, tmp11, tmp12, tmp13;
 158   INT32 z1, z2, z3, z4, z5;
 159   JCOEFPTR inptr;
 160   ISLOW_MULT_TYPE * quantptr;
 161   int * wsptr;
 162   JSAMPROW outptr;
 163   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
 164   int ctr;
 165   int workspace[DCTSIZE2];      /* buffers data between passes */
 166   SHIFT_TEMPS
 167
 168   /* Pass 1: process columns from input, store into work array. */
 169   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
 170   /* furthermore, we scale the results by 2**PASS1_BITS. */
 171
 172   inptr = coef_block;
 173   quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
 174   wsptr = workspace;
 175   for (ctr = DCTSIZE; ctr > 0; ctr--) {
 176     /* Due to quantization, we will usually find that many of the input
 177      * coefficients are zero, especially the AC terms.  We can exploit this
 178      * by short-circuiting the IDCT calculation for any column in which all
 179      * the AC terms are zero.  In that case each output is equal to the
 180      * DC coefficient (with scale factor as needed).
 181      * With typical images and quantization tables, half or more of the
 182      * column DCT calculations can be simplified this way.
 183      */
 184
 185     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
 186         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
 187         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
 188         inptr[DCTSIZE*7] == 0) {
 189       /* AC terms all zero */
 190       int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
 191
 192       wsptr[DCTSIZE*0] = dcval;
 193       wsptr[DCTSIZE*1] = dcval;
 194       wsptr[DCTSIZE*2] = dcval;
 195       wsptr[DCTSIZE*3] = dcval;
 196       wsptr[DCTSIZE*4] = dcval;
 197       wsptr[DCTSIZE*5] = dcval;
 198       wsptr[DCTSIZE*6] = dcval;
 199       wsptr[DCTSIZE*7] = dcval;
 200
 201       inptr++;                  /* advance pointers to next column */
 202       quantptr++;
 203       wsptr++;
 204       continue;
 205     }
 206
 207     /* Even part: reverse the even part of the forward DCT. */
 208     /* The rotator is sqrt(2)*c(-6). */
 209
 210     z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
 211     z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
 212
 213     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
 214     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
 215     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
 216
 217     z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 218     z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
 219
 220     tmp0 = (z2 + z3) << CONST_BITS;
 221     tmp1 = (z2 - z3) << CONST_BITS;
 222
 223     tmp10 = tmp0 + tmp3;
 224     tmp13 = tmp0 - tmp3;
 225     tmp11 = tmp1 + tmp2;
 226     tmp12 = tmp1 - tmp2;
 227
 228     /* Odd part per figure 8; the matrix is unitary and hence its
 229      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
 230      */
 231
 232     tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
 233     tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
 234     tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
 235     tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
 236
 237     z1 = tmp0 + tmp3;
 238     z2 = tmp1 + tmp2;
 239     z3 = tmp0 + tmp2;
 240     z4 = tmp1 + tmp3;
 241     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 242
 243     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 244     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 245     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 246     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 247     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 248     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 249     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 250     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 251
 252     z3 += z5;
 253     z4 += z5;
 254
 255     tmp0 += z1 + z3;
 256     tmp1 += z2 + z4;
 257     tmp2 += z2 + z3;
 258     tmp3 += z1 + z4;
 259
 260     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
 261
 262     wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
 263     wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
 264     wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
 265     wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
 266     wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
 267     wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
 268     wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
 269     wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
 270
 271     inptr++;                    /* advance pointers to next column */
 272     quantptr++;
 273     wsptr++;
 274   }
 275
 276   /* Pass 2: process rows from work array, store into output array. */
 277   /* Note that we must descale the results by a factor of 8 == 2**3, */
 278   /* and also undo the PASS1_BITS scaling. */
 279
 280   wsptr = workspace;
 281   for (ctr = 0; ctr < DCTSIZE; ctr++) {
 282     outptr = output_buf[ctr] + output_col;
 283     /* Rows of zeroes can be exploited in the same way as we did with columns.
 284      * However, the column calculation has created many nonzero AC terms, so
 285      * the simplification applies less often (typically 5% to 10% of the time).
 286      * On machines with very fast multiplication, it's possible that the
 287      * test takes more time than it's worth.  In that case this section
 288      * may be commented out.
 289      */
 290
 291 #ifndef NO_ZERO_ROW_TEST
 292     if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
 293         wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
 294       /* AC terms all zero */
 295       JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
 296                                   & RANGE_MASK];
 297
 298       outptr[0] = dcval;
 299       outptr[1] = dcval;
 300       outptr[2] = dcval;
 301       outptr[3] = dcval;
 302       outptr[4] = dcval;
 303       outptr[5] = dcval;
 304       outptr[6] = dcval;
 305       outptr[7] = dcval;
 306
 307       wsptr += DCTSIZE;         /* advance pointer to next row */
 308       continue;
 309     }
 310 #endif
 311
 312     /* Even part: reverse the even part of the forward DCT. */
 313     /* The rotator is sqrt(2)*c(-6). */
 314
 315     z2 = (INT32) wsptr[2];
 316     z3 = (INT32) wsptr[6];
 317
 318     z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
 319     tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
 320     tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
 321
 322     tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
 323     tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
 324
 325     tmp10 = tmp0 + tmp3;
 326     tmp13 = tmp0 - tmp3;
 327     tmp11 = tmp1 + tmp2;
 328     tmp12 = tmp1 - tmp2;
 329
 330     /* Odd part per figure 8; the matrix is unitary and hence its
 331      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
 332      */
 333
 334     tmp0 = (INT32) wsptr[7];
 335     tmp1 = (INT32) wsptr[5];
 336     tmp2 = (INT32) wsptr[3];
 337     tmp3 = (INT32) wsptr[1];
 338
 339     z1 = tmp0 + tmp3;
 340     z2 = tmp1 + tmp2;
 341     z3 = tmp0 + tmp2;
 342     z4 = tmp1 + tmp3;
 343     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 344
 345     tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 346     tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 347     tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 348     tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 349     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 350     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 351     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 352     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 353
 354     z3 += z5;
 355     z4 += z5;
 356
 357     tmp0 += z1 + z3;
 358     tmp1 += z2 + z4;
 359     tmp2 += z2 + z3;
 360     tmp3 += z1 + z4;
 361
 362     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
 363
 364     outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
 365                                           CONST_BITS+PASS1_BITS+3)
 366                             & RANGE_MASK];
 367     outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
 368                                           CONST_BITS+PASS1_BITS+3)
 369                             & RANGE_MASK];
 370     outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
 371                                           CONST_BITS+PASS1_BITS+3)
 372                             & RANGE_MASK];
 373     outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
 374                                           CONST_BITS+PASS1_BITS+3)
 375                             & RANGE_MASK];
 376     outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
 377                                           CONST_BITS+PASS1_BITS+3)
 378                             & RANGE_MASK];
 379     outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
 380                                           CONST_BITS+PASS1_BITS+3)
 381                             & RANGE_MASK];
 382     outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
 383                                           CONST_BITS+PASS1_BITS+3)
 384                             & RANGE_MASK];
 385     outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
 386                                           CONST_BITS+PASS1_BITS+3)
 387                             & RANGE_MASK];
 388
 389     wsptr += DCTSIZE;           /* advance pointer to next row */
 390   }
 391 }
 392
 393 #endif /* DCT_ISLOW_SUPPORTED */