libavcodec/jfdctint.c

   1 /*
   2  * jfdctint.c
   3  *
   4  * This file is part of the Independent JPEG Group's software.
   5  *
   6  * The authors make NO WARRANTY or representation, either express or implied,
   7  * with respect to this software, its quality, accuracy, merchantability, or
   8  * fitness for a particular purpose.  This software is provided "AS IS", and
   9  * you, its user, assume the entire risk as to its quality and accuracy.
  10  *
  11  * This software is copyright (C) 1991-1996, Thomas G. Lane.
  12  * All Rights Reserved except as specified below.
  13  *
  14  * Permission is hereby granted to use, copy, modify, and distribute this
  15  * software (or portions thereof) for any purpose, without fee, subject to
  16  * these conditions:
  17  * (1) If any part of the source code for this software is distributed, then
  18  * this README file must be included, with this copyright and no-warranty
  19  * notice unaltered; and any additions, deletions, or changes to the original
  20  * files must be clearly indicated in accompanying documentation.
  21  * (2) If only executable code is distributed, then the accompanying
  22  * documentation must state that "this software is based in part on the work
  23  * of the Independent JPEG Group".
  24  * (3) Permission for use of this software is granted only if the user accepts
  25  * full responsibility for any undesirable consequences; the authors accept
  26  * NO LIABILITY for damages of any kind.
  27  *
  28  * These conditions apply to any software derived from or based on the IJG
  29  * code, not just to the unmodified library.  If you use our work, you ought
  30  * to acknowledge us.
  31  *
  32  * Permission is NOT granted for the use of any IJG author's name or company
  33  * name in advertising or publicity relating to this software or products
  34  * derived from it.  This software may be referred to only as "the Independent
  35  * JPEG Group's software".
  36  *
  37  * We specifically permit and encourage the use of this software as the basis
  38  * of commercial products, provided that all warranty or liability claims are
  39  * assumed by the product vendor.
  40  *
  41  * This file contains a slow-but-accurate integer implementation of the
  42  * forward DCT (Discrete Cosine Transform).
  43  *
  44  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
  45  * on each column.  Direct algorithms are also available, but they are
  46  * much more complex and seem not to be any faster when reduced to code.
  47  *
  48  * This implementation is based on an algorithm described in
  49  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  50  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  51  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  52  * The primary algorithm described there uses 11 multiplies and 29 adds.
  53  * We use their alternate method with 12 multiplies and 32 adds.
  54  * The advantage of this method is that no data path contains more than one
  55  * multiplication; this allows a very simple and accurate implementation in
  56  * scaled fixed-point arithmetic, with a minimal number of shifts.
  57  */
  58
  59 /**
  60  * @file libavcodec/jfdctint.c
  61  * Independent JPEG Group's slow & accurate dct.
  62  */
  63
  64 #include <stdlib.h>
  65 #include <stdio.h>
  66 #include "libavutil/common.h"
  67 #include "dsputil.h"
  68
  69 #define SHIFT_TEMPS
  70 #define DCTSIZE 8
  71 #define BITS_IN_JSAMPLE 8
  72 #define GLOBAL(x) x
  73 #define RIGHT_SHIFT(x, n) ((x) >> (n))
  74 #define MULTIPLY16C16(var,const) ((var)*(const))
  75
  76 #if 1 //def USE_ACCURATE_ROUNDING
  77 #define DESCALE(x,n)  RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
  78 #else
  79 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
  80 #endif
  81
  82
  83 /*
  84  * This module is specialized to the case DCTSIZE = 8.
  85  */
  86
  87 #if DCTSIZE != 8
  88   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  89 #endif
  90
  91
  92 /*
  93  * The poop on this scaling stuff is as follows:
  94  *
  95  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  96  * larger than the true DCT outputs.  The final outputs are therefore
  97  * a factor of N larger than desired; since N=8 this can be cured by
  98  * a simple right shift at the end of the algorithm.  The advantage of
  99  * this arrangement is that we save two multiplications per 1-D DCT,
 100  * because the y0 and y4 outputs need not be divided by sqrt(N).
 101  * In the IJG code, this factor of 8 is removed by the quantization step
 102  * (in jcdctmgr.c), NOT in this module.
 103  *
 104  * We have to do addition and subtraction of the integer inputs, which
 105  * is no problem, and multiplication by fractional constants, which is
 106  * a problem to do in integer arithmetic.  We multiply all the constants
 107  * by CONST_SCALE and convert them to integer constants (thus retaining
 108  * CONST_BITS bits of precision in the constants).  After doing a
 109  * multiplication we have to divide the product by CONST_SCALE, with proper
 110  * rounding, to produce the correct output.  This division can be done
 111  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 112  * as long as possible so that partial sums can be added together with
 113  * full fractional precision.
 114  *
 115  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 116  * they are represented to better-than-integral precision.  These outputs
 117  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 118  * with the recommended scaling.  (For 12-bit sample data, the intermediate
 119  * array is int32_t anyway.)
 120  *
 121  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 122  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 123  * shows that the values given below are the most effective.
 124  */
 125
 126 #if BITS_IN_JSAMPLE == 8
 127 #define CONST_BITS  13
 128 #define PASS1_BITS  4   /* set this to 2 if 16x16 multiplies are faster */
 129 #else
 130 #define CONST_BITS  13
 131 #define PASS1_BITS  1   /* lose a little precision to avoid overflow */
 132 #endif
 133
 134 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 135  * causing a lot of useless floating-point operations at run time.
 136  * To get around this we use the following pre-calculated constants.
 137  * If you change CONST_BITS you may want to add appropriate values.
 138  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 139  */
 140
 141 #if CONST_BITS == 13
 142 #define FIX_0_298631336  ((int32_t)  2446)      /* FIX(0.298631336) */
 143 #define FIX_0_390180644  ((int32_t)  3196)      /* FIX(0.390180644) */
 144 #define FIX_0_541196100  ((int32_t)  4433)      /* FIX(0.541196100) */
 145 #define FIX_0_765366865  ((int32_t)  6270)      /* FIX(0.765366865) */
 146 #define FIX_0_899976223  ((int32_t)  7373)      /* FIX(0.899976223) */
 147 #define FIX_1_175875602  ((int32_t)  9633)      /* FIX(1.175875602) */
 148 #define FIX_1_501321110  ((int32_t)  12299)     /* FIX(1.501321110) */
 149 #define FIX_1_847759065  ((int32_t)  15137)     /* FIX(1.847759065) */
 150 #define FIX_1_961570560  ((int32_t)  16069)     /* FIX(1.961570560) */
 151 #define FIX_2_053119869  ((int32_t)  16819)     /* FIX(2.053119869) */
 152 #define FIX_2_562915447  ((int32_t)  20995)     /* FIX(2.562915447) */
 153 #define FIX_3_072711026  ((int32_t)  25172)     /* FIX(3.072711026) */
 154 #else
 155 #define FIX_0_298631336  FIX(0.298631336)
 156 #define FIX_0_390180644  FIX(0.390180644)
 157 #define FIX_0_541196100  FIX(0.541196100)
 158 #define FIX_0_765366865  FIX(0.765366865)
 159 #define FIX_0_899976223  FIX(0.899976223)
 160 #define FIX_1_175875602  FIX(1.175875602)
 161 #define FIX_1_501321110  FIX(1.501321110)
 162 #define FIX_1_847759065  FIX(1.847759065)
 163 #define FIX_1_961570560  FIX(1.961570560)
 164 #define FIX_2_053119869  FIX(2.053119869)
 165 #define FIX_2_562915447  FIX(2.562915447)
 166 #define FIX_3_072711026  FIX(3.072711026)
 167 #endif
 168
 169
 170 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
 171  * For 8-bit samples with the recommended scaling, all the variable
 172  * and constant values involved are no more than 16 bits wide, so a
 173  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 174  * For 12-bit samples, a full 32-bit multiplication will be needed.
 175  */
 176
 177 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
 178 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
 179 #else
 180 #define MULTIPLY(var,const)  ((var) * (const))
 181 #endif
 182
 183
 184 static av_always_inline void row_fdct(DCTELEM * data){
 185   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 186   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 187   int_fast32_t z1, z2, z3, z4, z5;
 188   DCTELEM *dataptr;
 189   int ctr;
 190   SHIFT_TEMPS
 191
 192   /* Pass 1: process rows. */
 193   /* Note results are scaled up by sqrt(8) compared to a true DCT; */
 194   /* furthermore, we scale the results by 2**PASS1_BITS. */
 195
 196   dataptr = data;
 197   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 198     tmp0 = dataptr[0] + dataptr[7];
 199     tmp7 = dataptr[0] - dataptr[7];
 200     tmp1 = dataptr[1] + dataptr[6];
 201     tmp6 = dataptr[1] - dataptr[6];
 202     tmp2 = dataptr[2] + dataptr[5];
 203     tmp5 = dataptr[2] - dataptr[5];
 204     tmp3 = dataptr[3] + dataptr[4];
 205     tmp4 = dataptr[3] - dataptr[4];
 206
 207     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 208      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 209      */
 210
 211     tmp10 = tmp0 + tmp3;
 212     tmp13 = tmp0 - tmp3;
 213     tmp11 = tmp1 + tmp2;
 214     tmp12 = tmp1 - tmp2;
 215
 216     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
 217     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
 218
 219     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 220     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 221                                    CONST_BITS-PASS1_BITS);
 222     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 223                                    CONST_BITS-PASS1_BITS);
 224
 225     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 226      * cK represents cos(K*pi/16).
 227      * i0..i3 in the paper are tmp4..tmp7 here.
 228      */
 229
 230     z1 = tmp4 + tmp7;
 231     z2 = tmp5 + tmp6;
 232     z3 = tmp4 + tmp6;
 233     z4 = tmp5 + tmp7;
 234     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 235
 236     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 237     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 238     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 239     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 240     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 241     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 242     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 243     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 244
 245     z3 += z5;
 246     z4 += z5;
 247
 248     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
 249     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
 250     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
 251     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
 252
 253     dataptr += DCTSIZE;         /* advance pointer to next row */
 254   }
 255 }
 256
 257 /*
 258  * Perform the forward DCT on one block of samples.
 259  */
 260
 261 GLOBAL(void)
 262 ff_jpeg_fdct_islow (DCTELEM * data)
 263 {
 264   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 265   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 266   int_fast32_t z1, z2, z3, z4, z5;
 267   DCTELEM *dataptr;
 268   int ctr;
 269   SHIFT_TEMPS
 270
 271   row_fdct(data);
 272
 273   /* Pass 2: process columns.
 274    * We remove the PASS1_BITS scaling, but leave the results scaled up
 275    * by an overall factor of 8.
 276    */
 277
 278   dataptr = data;
 279   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 280     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 281     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 282     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 283     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 284     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 285     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 286     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 287     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 288
 289     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 290      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 291      */
 292
 293     tmp10 = tmp0 + tmp3;
 294     tmp13 = tmp0 - tmp3;
 295     tmp11 = tmp1 + tmp2;
 296     tmp12 = tmp1 - tmp2;
 297
 298     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 299     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 300
 301     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 302     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 303                                            CONST_BITS+PASS1_BITS);
 304     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 305                                            CONST_BITS+PASS1_BITS);
 306
 307     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 308      * cK represents cos(K*pi/16).
 309      * i0..i3 in the paper are tmp4..tmp7 here.
 310      */
 311
 312     z1 = tmp4 + tmp7;
 313     z2 = tmp5 + tmp6;
 314     z3 = tmp4 + tmp6;
 315     z4 = tmp5 + tmp7;
 316     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 317
 318     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 319     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 320     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 321     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 322     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 323     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 324     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 325     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 326
 327     z3 += z5;
 328     z4 += z5;
 329
 330     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
 331                                            CONST_BITS+PASS1_BITS);
 332     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
 333                                            CONST_BITS+PASS1_BITS);
 334     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
 335                                            CONST_BITS+PASS1_BITS);
 336     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
 337                                            CONST_BITS+PASS1_BITS);
 338
 339     dataptr++;                  /* advance pointer to next column */
 340   }
 341 }
 342
 343 /*
 344  * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
 345  * on the rows and then, instead of doing even and odd, part on the colums
 346  * you do even part two times.
 347  */
 348 GLOBAL(void)
 349 ff_fdct248_islow (DCTELEM * data)
 350 {
 351   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 352   int_fast32_t tmp10, tmp11, tmp12, tmp13;
 353   int_fast32_t z1;
 354   DCTELEM *dataptr;
 355   int ctr;
 356   SHIFT_TEMPS
 357
 358   row_fdct(data);
 359
 360   /* Pass 2: process columns.
 361    * We remove the PASS1_BITS scaling, but leave the results scaled up
 362    * by an overall factor of 8.
 363    */
 364
 365   dataptr = data;
 366   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 367      tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
 368      tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
 369      tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
 370      tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
 371      tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
 372      tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
 373      tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
 374      tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
 375
 376      tmp10 = tmp0 + tmp3;
 377      tmp11 = tmp1 + tmp2;
 378      tmp12 = tmp1 - tmp2;
 379      tmp13 = tmp0 - tmp3;
 380
 381      dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 382      dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 383
 384      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 385      dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 386                                             CONST_BITS+PASS1_BITS);
 387      dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 388                                             CONST_BITS+PASS1_BITS);
 389
 390      tmp10 = tmp4 + tmp7;
 391      tmp11 = tmp5 + tmp6;
 392      tmp12 = tmp5 - tmp6;
 393      tmp13 = tmp4 - tmp7;
 394
 395      dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 396      dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 397
 398      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 399      dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 400                                             CONST_BITS+PASS1_BITS);
 401      dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 402                                             CONST_BITS+PASS1_BITS);
 403
 404      dataptr++;                 /* advance pointer to next column */
 405   }
 406 }