compiler/libjpeg/main/jfdctint.c

   1 /*
   2     $Id$
   3 */
   4
   5 /*
   6  * jfdctint.c
   7  *
   8  * Copyright (C) 1991-1996, 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  * forward DCT (Discrete Cosine Transform).
  14  *
  15  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
  16  * on each column.  Direct algorithms are also available, but they are
  17  * much more complex and seem not to be any faster when reduced to code.
  18  *
  19  * This implementation is based on an algorithm described in
  20  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  21  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  22  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  23  * The primary algorithm described there uses 11 multiplies and 29 adds.
  24  * We use their alternate method with 12 multiplies and 32 adds.
  25  * The advantage of this method is that no data path contains more than one
  26  * multiplication; this allows a very simple and accurate implementation in
  27  * scaled fixed-point arithmetic, with a minimal number of shifts.
  28  */
  29
  30 #define JPEG_INTERNALS
  31 #include "jinclude.h"
  32 #include "jpeglib.h"
  33 #include "jdct.h"               /* Private declarations for DCT subsystem */
  34
  35 #ifdef DCT_ISLOW_SUPPORTED
  36
  37
  38 /*
  39  * This module is specialized to the case DCTSIZE = 8.
  40  */
  41
  42 #if DCTSIZE != 8
  43   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  44 #endif
  45
  46
  47 /*
  48  * The poop on this scaling stuff is as follows:
  49  *
  50  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  51  * larger than the true DCT outputs.  The final outputs are therefore
  52  * a factor of N larger than desired; since N=8 this can be cured by
  53  * a simple right shift at the end of the algorithm.  The advantage of
  54  * this arrangement is that we save two multiplications per 1-D DCT,
  55  * because the y0 and y4 outputs need not be divided by sqrt(N).
  56  * In the IJG code, this factor of 8 is removed by the quantization step
  57  * (in jcdctmgr.c), NOT in this module.
  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.  (For 12-bit sample data, the intermediate
  74  * array is INT32 anyway.)
  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 /*
 140  * Perform the forward DCT on one block of samples.
 141  */
 142
 143 JGLOBAL(void)
 144 jpeg_fdct_islow (DCTELEM * data)
 145 {
 146   INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 147   INT32 tmp10, tmp11, tmp12, tmp13;
 148   INT32 z1, z2, z3, z4, z5;
 149   DCTELEM *dataptr;
 150   int ctr;
 151   SHIFT_TEMPS
 152
 153   /* Pass 1: process rows. */
 154   /* Note results are scaled up by sqrt(8) compared to a true DCT; */
 155   /* furthermore, we scale the results by 2**PASS1_BITS. */
 156
 157   dataptr = data;
 158   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 159     tmp0 = dataptr[0] + dataptr[7];
 160     tmp7 = dataptr[0] - dataptr[7];
 161     tmp1 = dataptr[1] + dataptr[6];
 162     tmp6 = dataptr[1] - dataptr[6];
 163     tmp2 = dataptr[2] + dataptr[5];
 164     tmp5 = dataptr[2] - dataptr[5];
 165     tmp3 = dataptr[3] + dataptr[4];
 166     tmp4 = dataptr[3] - dataptr[4];
 167
 168     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 169      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 170      */
 171
 172     tmp10 = tmp0 + tmp3;
 173     tmp13 = tmp0 - tmp3;
 174     tmp11 = tmp1 + tmp2;
 175     tmp12 = tmp1 - tmp2;
 176
 177     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
 178     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
 179
 180     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 181     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 182                                    CONST_BITS-PASS1_BITS);
 183     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 184                                    CONST_BITS-PASS1_BITS);
 185
 186     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 187      * cK represents cos(K*pi/16).
 188      * i0..i3 in the paper are tmp4..tmp7 here.
 189      */
 190
 191     z1 = tmp4 + tmp7;
 192     z2 = tmp5 + tmp6;
 193     z3 = tmp4 + tmp6;
 194     z4 = tmp5 + tmp7;
 195     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 196
 197     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 198     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 199     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 200     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 201     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 202     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 203     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 204     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 205
 206     z3 += z5;
 207     z4 += z5;
 208
 209     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
 210     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
 211     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
 212     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
 213
 214     dataptr += DCTSIZE;         /* advance pointer to next row */
 215   }
 216
 217   /* Pass 2: process columns.
 218    * We remove the PASS1_BITS scaling, but leave the results scaled up
 219    * by an overall factor of 8.
 220    */
 221
 222   dataptr = data;
 223   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 224     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 225     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 226     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 227     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 228     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 229     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 230     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 231     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 232
 233     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 234      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 235      */
 236
 237     tmp10 = tmp0 + tmp3;
 238     tmp13 = tmp0 - tmp3;
 239     tmp11 = tmp1 + tmp2;
 240     tmp12 = tmp1 - tmp2;
 241
 242     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 243     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 244
 245     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 246     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 247                                            CONST_BITS+PASS1_BITS);
 248     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 249                                            CONST_BITS+PASS1_BITS);
 250
 251     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 252      * cK represents cos(K*pi/16).
 253      * i0..i3 in the paper are tmp4..tmp7 here.
 254      */
 255
 256     z1 = tmp4 + tmp7;
 257     z2 = tmp5 + tmp6;
 258     z3 = tmp4 + tmp6;
 259     z4 = tmp5 + tmp7;
 260     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 261
 262     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 263     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 264     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 265     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 266     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 267     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 268     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 269     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 270
 271     z3 += z5;
 272     z4 += z5;
 273
 274     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
 275                                            CONST_BITS+PASS1_BITS);
 276     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
 277                                            CONST_BITS+PASS1_BITS);
 278     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
 279                                            CONST_BITS+PASS1_BITS);
 280     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
 281                                            CONST_BITS+PASS1_BITS);
 282
 283     dataptr++;                  /* advance pointer to next column */
 284   }
 285 }
 286
 287 #endif /* DCT_ISLOW_SUPPORTED */