quicktime/ffmpeg/libavcodec/jfdctint.c

   1 /*
   2  * jfdctint.c
   3  *
   4  * Copyright (C) 1991-1996, 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  * forward DCT (Discrete Cosine Transform).
  10  *
  11  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
  12  * on each column.  Direct algorithms are also available, but they are
  13  * much more complex and seem not to be any faster when reduced to code.
  14  *
  15  * This implementation is based on an algorithm described in
  16  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  17  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  18  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  19  * The primary algorithm described there uses 11 multiplies and 29 adds.
  20  * We use their alternate method with 12 multiplies and 32 adds.
  21  * The advantage of this method is that no data path contains more than one
  22  * multiplication; this allows a very simple and accurate implementation in
  23  * scaled fixed-point arithmetic, with a minimal number of shifts.
  24  */
  25
  26 /**
  27  * @file jfdctint.c
  28  * Independent JPEG Group's slow & accurate dct.
  29  */
  30
  31 #include <stdlib.h>
  32 #include <stdio.h>
  33 #include "common.h"
  34 #include "dsputil.h"
  35
  36 #define SHIFT_TEMPS
  37 #define DCTSIZE 8
  38 #define BITS_IN_JSAMPLE 8
  39 #define GLOBAL(x) x
  40 #define RIGHT_SHIFT(x, n) ((x) >> (n))
  41 #define MULTIPLY16C16(var,const) ((var)*(const))
  42
  43 #if 1 //def USE_ACCURATE_ROUNDING
  44 #define DESCALE(x,n)  RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
  45 #else
  46 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
  47 #endif
  48
  49
  50 /*
  51  * This module is specialized to the case DCTSIZE = 8.
  52  */
  53
  54 #if DCTSIZE != 8
  55   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  56 #endif
  57
  58
  59 /*
  60  * The poop on this scaling stuff is as follows:
  61  *
  62  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  63  * larger than the true DCT outputs.  The final outputs are therefore
  64  * a factor of N larger than desired; since N=8 this can be cured by
  65  * a simple right shift at the end of the algorithm.  The advantage of
  66  * this arrangement is that we save two multiplications per 1-D DCT,
  67  * because the y0 and y4 outputs need not be divided by sqrt(N).
  68  * In the IJG code, this factor of 8 is removed by the quantization step
  69  * (in jcdctmgr.c), NOT in this module.
  70  *
  71  * We have to do addition and subtraction of the integer inputs, which
  72  * is no problem, and multiplication by fractional constants, which is
  73  * a problem to do in integer arithmetic.  We multiply all the constants
  74  * by CONST_SCALE and convert them to integer constants (thus retaining
  75  * CONST_BITS bits of precision in the constants).  After doing a
  76  * multiplication we have to divide the product by CONST_SCALE, with proper
  77  * rounding, to produce the correct output.  This division can be done
  78  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
  79  * as long as possible so that partial sums can be added together with
  80  * full fractional precision.
  81  *
  82  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
  83  * they are represented to better-than-integral precision.  These outputs
  84  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
  85  * with the recommended scaling.  (For 12-bit sample data, the intermediate
  86  * array is int32_t anyway.)
  87  *
  88  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
  89  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
  90  * shows that the values given below are the most effective.
  91  */
  92
  93 #if BITS_IN_JSAMPLE == 8
  94 #define CONST_BITS  13
  95 #define PASS1_BITS  4           /* set this to 2 if 16x16 multiplies are faster */
  96 #else
  97 #define CONST_BITS  13
  98 #define PASS1_BITS  1           /* lose a little precision to avoid overflow */
  99 #endif
 100
 101 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 102  * causing a lot of useless floating-point operations at run time.
 103  * To get around this we use the following pre-calculated constants.
 104  * If you change CONST_BITS you may want to add appropriate values.
 105  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 106  */
 107
 108 #if CONST_BITS == 13
 109 #define FIX_0_298631336  ((int32_t)  2446)      /* FIX(0.298631336) */
 110 #define FIX_0_390180644  ((int32_t)  3196)      /* FIX(0.390180644) */
 111 #define FIX_0_541196100  ((int32_t)  4433)      /* FIX(0.541196100) */
 112 #define FIX_0_765366865  ((int32_t)  6270)      /* FIX(0.765366865) */
 113 #define FIX_0_899976223  ((int32_t)  7373)      /* FIX(0.899976223) */
 114 #define FIX_1_175875602  ((int32_t)  9633)      /* FIX(1.175875602) */
 115 #define FIX_1_501321110  ((int32_t)  12299)     /* FIX(1.501321110) */
 116 #define FIX_1_847759065  ((int32_t)  15137)     /* FIX(1.847759065) */
 117 #define FIX_1_961570560  ((int32_t)  16069)     /* FIX(1.961570560) */
 118 #define FIX_2_053119869  ((int32_t)  16819)     /* FIX(2.053119869) */
 119 #define FIX_2_562915447  ((int32_t)  20995)     /* FIX(2.562915447) */
 120 #define FIX_3_072711026  ((int32_t)  25172)     /* FIX(3.072711026) */
 121 #else
 122 #define FIX_0_298631336  FIX(0.298631336)
 123 #define FIX_0_390180644  FIX(0.390180644)
 124 #define FIX_0_541196100  FIX(0.541196100)
 125 #define FIX_0_765366865  FIX(0.765366865)
 126 #define FIX_0_899976223  FIX(0.899976223)
 127 #define FIX_1_175875602  FIX(1.175875602)
 128 #define FIX_1_501321110  FIX(1.501321110)
 129 #define FIX_1_847759065  FIX(1.847759065)
 130 #define FIX_1_961570560  FIX(1.961570560)
 131 #define FIX_2_053119869  FIX(2.053119869)
 132 #define FIX_2_562915447  FIX(2.562915447)
 133 #define FIX_3_072711026  FIX(3.072711026)
 134 #endif
 135
 136
 137 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
 138  * For 8-bit samples with the recommended scaling, all the variable
 139  * and constant values involved are no more than 16 bits wide, so a
 140  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 141  * For 12-bit samples, a full 32-bit multiplication will be needed.
 142  */
 143
 144 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
 145 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
 146 #else
 147 #define MULTIPLY(var,const)  ((var) * (const))
 148 #endif
 149
 150
 151 static always_inline void row_fdct(DCTELEM * data){
 152   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 153   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 154   int_fast32_t z1, z2, z3, z4, z5;
 155   DCTELEM *dataptr;
 156   int ctr;
 157   SHIFT_TEMPS
 158
 159   /* Pass 1: process rows. */
 160   /* Note results are scaled up by sqrt(8) compared to a true DCT; */
 161   /* furthermore, we scale the results by 2**PASS1_BITS. */
 162
 163   dataptr = data;
 164   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 165     tmp0 = dataptr[0] + dataptr[7];
 166     tmp7 = dataptr[0] - dataptr[7];
 167     tmp1 = dataptr[1] + dataptr[6];
 168     tmp6 = dataptr[1] - dataptr[6];
 169     tmp2 = dataptr[2] + dataptr[5];
 170     tmp5 = dataptr[2] - dataptr[5];
 171     tmp3 = dataptr[3] + dataptr[4];
 172     tmp4 = dataptr[3] - dataptr[4];
 173
 174     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 175      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 176      */
 177
 178     tmp10 = tmp0 + tmp3;
 179     tmp13 = tmp0 - tmp3;
 180     tmp11 = tmp1 + tmp2;
 181     tmp12 = tmp1 - tmp2;
 182
 183     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
 184     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
 185
 186     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 187     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 188                                    CONST_BITS-PASS1_BITS);
 189     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 190                                    CONST_BITS-PASS1_BITS);
 191
 192     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 193      * cK represents cos(K*pi/16).
 194      * i0..i3 in the paper are tmp4..tmp7 here.
 195      */
 196
 197     z1 = tmp4 + tmp7;
 198     z2 = tmp5 + tmp6;
 199     z3 = tmp4 + tmp6;
 200     z4 = tmp5 + tmp7;
 201     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 202
 203     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 204     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 205     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 206     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 207     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 208     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 209     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 210     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 211
 212     z3 += z5;
 213     z4 += z5;
 214
 215     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
 216     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
 217     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
 218     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
 219
 220     dataptr += DCTSIZE;         /* advance pointer to next row */
 221   }
 222 }
 223
 224 /*
 225  * Perform the forward DCT on one block of samples.
 226  */
 227
 228 GLOBAL(void)
 229 ff_jpeg_fdct_islow (DCTELEM * data)
 230 {
 231   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 232   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 233   int_fast32_t z1, z2, z3, z4, z5;
 234   DCTELEM *dataptr;
 235   int ctr;
 236   SHIFT_TEMPS
 237
 238   row_fdct(data);
 239
 240   /* Pass 2: process columns.
 241    * We remove the PASS1_BITS scaling, but leave the results scaled up
 242    * by an overall factor of 8.
 243    */
 244
 245   dataptr = data;
 246   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 247     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 248     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 249     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 250     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 251     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 252     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 253     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 254     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 255
 256     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 257      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 258      */
 259
 260     tmp10 = tmp0 + tmp3;
 261     tmp13 = tmp0 - tmp3;
 262     tmp11 = tmp1 + tmp2;
 263     tmp12 = tmp1 - tmp2;
 264
 265     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 266     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 267
 268     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 269     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 270                                            CONST_BITS+PASS1_BITS);
 271     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 272                                            CONST_BITS+PASS1_BITS);
 273
 274     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 275      * cK represents cos(K*pi/16).
 276      * i0..i3 in the paper are tmp4..tmp7 here.
 277      */
 278
 279     z1 = tmp4 + tmp7;
 280     z2 = tmp5 + tmp6;
 281     z3 = tmp4 + tmp6;
 282     z4 = tmp5 + tmp7;
 283     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 284
 285     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 286     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 287     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 288     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 289     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 290     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 291     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 292     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 293
 294     z3 += z5;
 295     z4 += z5;
 296
 297     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
 298                                            CONST_BITS+PASS1_BITS);
 299     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
 300                                            CONST_BITS+PASS1_BITS);
 301     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
 302                                            CONST_BITS+PASS1_BITS);
 303     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
 304                                            CONST_BITS+PASS1_BITS);
 305
 306     dataptr++;                  /* advance pointer to next column */
 307   }
 308 }
 309
 310 /*
 311  * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
 312  * on the rows and then, instead of doing even and odd, part on the colums
 313  * you do even part two times.
 314  */
 315 GLOBAL(void)
 316 ff_fdct248_islow (DCTELEM * data)
 317 {
 318   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 319   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 320   int_fast32_t z1;
 321   DCTELEM *dataptr;
 322   int ctr;
 323   SHIFT_TEMPS
 324
 325   row_fdct(data);
 326
 327   /* Pass 2: process columns.
 328    * We remove the PASS1_BITS scaling, but leave the results scaled up
 329    * by an overall factor of 8.
 330    */
 331
 332   dataptr = data;
 333   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 334      tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
 335      tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
 336      tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
 337      tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
 338      tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
 339      tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
 340      tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
 341      tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
 342
 343      tmp10 = tmp0 + tmp3;
 344      tmp11 = tmp1 + tmp2;
 345      tmp12 = tmp1 - tmp2;
 346      tmp13 = tmp0 - tmp3;
 347
 348      dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 349      dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 350
 351      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 352      dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 353                                             CONST_BITS+PASS1_BITS);
 354      dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 355                                             CONST_BITS+PASS1_BITS);
 356
 357      tmp10 = tmp4 + tmp7;
 358      tmp11 = tmp5 + tmp6;
 359      tmp12 = tmp5 - tmp6;
 360      tmp13 = tmp4 - tmp7;
 361
 362      dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 363      dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 364
 365      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 366      dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 367                                             CONST_BITS+PASS1_BITS);
 368      dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 369                                             CONST_BITS+PASS1_BITS);
 370
 371      dataptr++;                 /* advance pointer to next column */
 372   }
 373 }