src/jpeg/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 #define JPEG_INTERNALS
  27 #include "jinclude.h"
  28 #include "jpeglib.h"
  29 #include "jdct.h"               /* Private declarations for DCT subsystem */
  30
  31 #ifdef DCT_ISLOW_SUPPORTED
  32
  33
  34 /*
  35  * This module is specialized to the case DCTSIZE = 8.
  36  */
  37
  38 #if DCTSIZE != 8
  39   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  40 #endif
  41
  42
  43 /*
  44  * The poop on this scaling stuff is as follows:
  45  *
  46  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  47  * larger than the true DCT outputs.  The final outputs are therefore
  48  * a factor of N larger than desired; since N=8 this can be cured by
  49  * a simple right shift at the end of the algorithm.  The advantage of
  50  * this arrangement is that we save two multiplications per 1-D DCT,
  51  * because the y0 and y4 outputs need not be divided by sqrt(N).
  52  * In the IJG code, this factor of 8 is removed by the quantization step
  53  * (in jcdctmgr.c), NOT in this module.
  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.  (For 12-bit sample data, the intermediate
  70  * array is INT32 anyway.)
  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 /*
 136  * Perform the forward DCT on one block of samples.
 137  */
 138
 139 GLOBAL(void)
 140 jpeg_fdct_islow (DCTELEM * data)
 141 {
 142   JPEG_INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 143   JPEG_INT32 tmp10, tmp11, tmp12, tmp13;
 144   JPEG_INT32 z1, z2, z3, z4, z5;
 145   DCTELEM *dataptr;
 146   int ctr;
 147   SHIFT_TEMPS
 148
 149   /* Pass 1: process rows. */
 150   /* Note results are scaled up by sqrt(8) compared to a true DCT; */
 151   /* furthermore, we scale the results by 2**PASS1_BITS. */
 152
 153   dataptr = data;
 154   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 155     tmp0 = dataptr[0] + dataptr[7];
 156     tmp7 = dataptr[0] - dataptr[7];
 157     tmp1 = dataptr[1] + dataptr[6];
 158     tmp6 = dataptr[1] - dataptr[6];
 159     tmp2 = dataptr[2] + dataptr[5];
 160     tmp5 = dataptr[2] - dataptr[5];
 161     tmp3 = dataptr[3] + dataptr[4];
 162     tmp4 = dataptr[3] - dataptr[4];
 163
 164     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 165      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 166      */
 167
 168     tmp10 = tmp0 + tmp3;
 169     tmp13 = tmp0 - tmp3;
 170     tmp11 = tmp1 + tmp2;
 171     tmp12 = tmp1 - tmp2;
 172
 173     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
 174     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
 175
 176     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 177     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 178                                    CONST_BITS-PASS1_BITS);
 179     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 180                                    CONST_BITS-PASS1_BITS);
 181
 182     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 183      * cK represents cos(K*pi/16).
 184      * i0..i3 in the paper are tmp4..tmp7 here.
 185      */
 186
 187     z1 = tmp4 + tmp7;
 188     z2 = tmp5 + tmp6;
 189     z3 = tmp4 + tmp6;
 190     z4 = tmp5 + tmp7;
 191     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 192
 193     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 194     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 195     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 196     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 197     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 198     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 199     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 200     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 201
 202     z3 += z5;
 203     z4 += z5;
 204
 205     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
 206     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
 207     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
 208     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
 209
 210     dataptr += DCTSIZE;         /* advance pointer to next row */
 211   }
 212
 213   /* Pass 2: process columns.
 214    * We remove the PASS1_BITS scaling, but leave the results scaled up
 215    * by an overall factor of 8.
 216    */
 217
 218   dataptr = data;
 219   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 220     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 221     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 222     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 223     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 224     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 225     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 226     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 227     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 228
 229     /* Even part per LL&M figure 1 --- note that published figure is faulty;
 230      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
 231      */
 232
 233     tmp10 = tmp0 + tmp3;
 234     tmp13 = tmp0 - tmp3;
 235     tmp11 = tmp1 + tmp2;
 236     tmp12 = tmp1 - tmp2;
 237
 238     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
 239     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
 240
 241     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
 242     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
 243                                            CONST_BITS+PASS1_BITS);
 244     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
 245                                            CONST_BITS+PASS1_BITS);
 246
 247     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
 248      * cK represents cos(K*pi/16).
 249      * i0..i3 in the paper are tmp4..tmp7 here.
 250      */
 251
 252     z1 = tmp4 + tmp7;
 253     z2 = tmp5 + tmp6;
 254     z3 = tmp4 + tmp6;
 255     z4 = tmp5 + tmp7;
 256     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
 257
 258     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
 259     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
 260     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
 261     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
 262     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
 263     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
 264     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
 265     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
 266
 267     z3 += z5;
 268     z4 += z5;
 269
 270     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
 271                                            CONST_BITS+PASS1_BITS);
 272     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
 273                                            CONST_BITS+PASS1_BITS);
 274     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
 275                                            CONST_BITS+PASS1_BITS);
 276     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
 277                                            CONST_BITS+PASS1_BITS);
 278
 279     dataptr++;                  /* advance pointer to next column */
 280   }
 281 }
 282
 283 #endif /* DCT_ISLOW_SUPPORTED */