src/jpeg/jfdctfst.c

   1 /*
   2  * jfdctfst.c
   3  *
   4  * Copyright (C) 1994-1996, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for
  16  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
  17  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
  18  * JPEG textbook (see REFERENCES section in file README).  The following code
  19  * is based directly on figure 4-8 in P&M.
  20  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
  21  * possible to arrange the computation so that many of the multiplies are
  22  * simple scalings of the final outputs.  These multiplies can then be
  23  * folded into the multiplications or divisions by the JPEG quantization
  24  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
  25  * to be done in the DCT itself.
  26  * The primary disadvantage of this method is that with fixed-point math,
  27  * accuracy is lost due to imprecise representation of the scaled
  28  * quantization values.  The smaller the quantization table entry, the less
  29  * precise the scaled value, so this implementation does worse with high-
  30  * quality-setting files than with low-quality ones.
  31  */
  32
  33 #define JPEG_INTERNALS
  34 #include "jinclude.h"
  35 #include "jpeglib.h"
  36 #include "jdct.h"               /* Private declarations for DCT subsystem */
  37
  38 #ifdef DCT_IFAST_SUPPORTED
  39
  40
  41 /*
  42  * This module is specialized to the case DCTSIZE = 8.
  43  */
  44
  45 #if DCTSIZE != 8
  46   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  47 #endif
  48
  49
  50 /* Scaling decisions are generally the same as in the LL&M algorithm;
  51  * see jfdctint.c for more details.  However, we choose to descale
  52  * (right shift) multiplication products as soon as they are formed,
  53  * rather than carrying additional fractional bits into subsequent additions.
  54  * This compromises accuracy slightly, but it lets us save a few shifts.
  55  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
  56  * everywhere except in the multiplications proper; this saves a good deal
  57  * of work on 16-bit-int machines.
  58  *
  59  * Again to save a few shifts, the intermediate results between pass 1 and
  60  * pass 2 are not upscaled, but are represented only to integral precision.
  61  *
  62  * A final compromise is to represent the multiplicative constants to only
  63  * 8 fractional bits, rather than 13.  This saves some shifting work on some
  64  * machines, and may also reduce the cost of multiplication (since there
  65  * are fewer one-bits in the constants).
  66  */
  67
  68 #define CONST_BITS  8
  69
  70
  71 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  72  * causing a lot of useless floating-point operations at run time.
  73  * To get around this we use the following pre-calculated constants.
  74  * If you change CONST_BITS you may want to add appropriate values.
  75  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  76  */
  77
  78 #if CONST_BITS == 8
  79 #define FIX_0_382683433  ((INT32)   98)         /* FIX(0.382683433) */
  80 #define FIX_0_541196100  ((INT32)  139)         /* FIX(0.541196100) */
  81 #define FIX_0_707106781  ((INT32)  181)         /* FIX(0.707106781) */
  82 #define FIX_1_306562965  ((INT32)  334)         /* FIX(1.306562965) */
  83 #else
  84 #define FIX_0_382683433  FIX(0.382683433)
  85 #define FIX_0_541196100  FIX(0.541196100)
  86 #define FIX_0_707106781  FIX(0.707106781)
  87 #define FIX_1_306562965  FIX(1.306562965)
  88 #endif
  89
  90
  91 /* We can gain a little more speed, with a further compromise in accuracy,
  92  * by omitting the addition in a descaling shift.  This yields an incorrectly
  93  * rounded result half the time...
  94  */
  95
  96 #ifndef USE_ACCURATE_ROUNDING
  97 #undef DESCALE
  98 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
  99 #endif
 100
 101
 102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
 103  * descale to yield a DCTELEM result.
 104  */
 105
 106 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
 107
 108
 109 /*
 110  * Perform the forward DCT on one block of samples.
 111  */
 112
 113 GLOBAL(void)
 114 jpeg_fdct_ifast (DCTELEM * data)
 115 {
 116   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 117   DCTELEM tmp10, tmp11, tmp12, tmp13;
 118   DCTELEM z1, z2, z3, z4, z5, z11, z13;
 119   DCTELEM *dataptr;
 120   int ctr;
 121   SHIFT_TEMPS
 122
 123   /* Pass 1: process rows. */
 124
 125   dataptr = data;
 126   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 127     tmp0 = dataptr[0] + dataptr[7];
 128     tmp7 = dataptr[0] - dataptr[7];
 129     tmp1 = dataptr[1] + dataptr[6];
 130     tmp6 = dataptr[1] - dataptr[6];
 131     tmp2 = dataptr[2] + dataptr[5];
 132     tmp5 = dataptr[2] - dataptr[5];
 133     tmp3 = dataptr[3] + dataptr[4];
 134     tmp4 = dataptr[3] - dataptr[4];
 135
 136     /* Even part */
 137
 138     tmp10 = tmp0 + tmp3;        /* phase 2 */
 139     tmp13 = tmp0 - tmp3;
 140     tmp11 = tmp1 + tmp2;
 141     tmp12 = tmp1 - tmp2;
 142
 143     dataptr[0] = tmp10 + tmp11; /* phase 3 */
 144     dataptr[4] = tmp10 - tmp11;
 145
 146     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
 147     dataptr[2] = tmp13 + z1;    /* phase 5 */
 148     dataptr[6] = tmp13 - z1;
 149
 150     /* Odd part */
 151
 152     tmp10 = tmp4 + tmp5;        /* phase 2 */
 153     tmp11 = tmp5 + tmp6;
 154     tmp12 = tmp6 + tmp7;
 155
 156     /* The rotator is modified from fig 4-8 to avoid extra negations. */
 157     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
 158     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
 159     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
 160     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
 161
 162     z11 = tmp7 + z3;            /* phase 5 */
 163     z13 = tmp7 - z3;
 164
 165     dataptr[5] = z13 + z2;      /* phase 6 */
 166     dataptr[3] = z13 - z2;
 167     dataptr[1] = z11 + z4;
 168     dataptr[7] = z11 - z4;
 169
 170     dataptr += DCTSIZE;         /* advance pointer to next row */
 171   }
 172
 173   /* Pass 2: process columns. */
 174
 175   dataptr = data;
 176   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 177     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 178     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 179     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 180     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 181     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 182     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 183     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 184     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 185
 186     /* Even part */
 187
 188     tmp10 = tmp0 + tmp3;        /* phase 2 */
 189     tmp13 = tmp0 - tmp3;
 190     tmp11 = tmp1 + tmp2;
 191     tmp12 = tmp1 - tmp2;
 192
 193     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
 194     dataptr[DCTSIZE*4] = tmp10 - tmp11;
 195
 196     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
 197     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
 198     dataptr[DCTSIZE*6] = tmp13 - z1;
 199
 200     /* Odd part */
 201
 202     tmp10 = tmp4 + tmp5;        /* phase 2 */
 203     tmp11 = tmp5 + tmp6;
 204     tmp12 = tmp6 + tmp7;
 205
 206     /* The rotator is modified from fig 4-8 to avoid extra negations. */
 207     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
 208     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
 209     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
 210     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
 211
 212     z11 = tmp7 + z3;            /* phase 5 */
 213     z13 = tmp7 - z3;
 214
 215     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
 216     dataptr[DCTSIZE*3] = z13 - z2;
 217     dataptr[DCTSIZE*1] = z11 + z4;
 218     dataptr[DCTSIZE*7] = z11 - z4;
 219
 220     dataptr++;                  /* advance pointer to next column */
 221   }
 222 }
 223
 224 #endif /* DCT_IFAST_SUPPORTED */