libs/jpeg/jfdctfst.c

   1 /*
   2  * jfdctfst.c
   3  *
   4  * Copyright (C) 1994-1996, Thomas G. Lane.
   5  * Modified 2003-2017 by Guido Vollbeding.
   6  * This file is part of the Independent JPEG Group's software.
   7  * For conditions of distribution and use, see the accompanying README file.
   8  *
   9  * This file contains a fast, not so accurate integer implementation of the
  10  * forward DCT (Discrete Cosine Transform).
  11  *
  12  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
  13  * on each column.  Direct algorithms are also available, but they are
  14  * much more complex and seem not to be any faster when reduced to code.
  15  *
  16  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
  17  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
  18  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
  19  * JPEG textbook (see REFERENCES section in file README).  The following code
  20  * is based directly on figure 4-8 in P&M.
  21  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
  22  * possible to arrange the computation so that many of the multiplies are
  23  * simple scalings of the final outputs.  These multiplies can then be
  24  * folded into the multiplications or divisions by the JPEG quantization
  25  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
  26  * to be done in the DCT itself.
  27  * The primary disadvantage of this method is that with fixed-point math,
  28  * accuracy is lost due to imprecise representation of the scaled
  29  * quantization values.  The smaller the quantization table entry, the less
  30  * precise the scaled value, so this implementation does worse with high-
  31  * quality-setting files than with low-quality ones.
  32  */
  33
  34 #define JPEG_INTERNALS
  35 #include "jinclude.h"
  36 #include "jpeglib.h"
  37 #include "jdct.h"               /* Private declarations for DCT subsystem */
  38
  39 #ifdef DCT_IFAST_SUPPORTED
  40
  41
  42 /*
  43  * This module is specialized to the case DCTSIZE = 8.
  44  */
  45
  46 #if DCTSIZE != 8
  47   Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */
  48 #endif
  49
  50
  51 /* Scaling decisions are generally the same as in the LL&M algorithm;
  52  * see jfdctint.c for more details.  However, we choose to descale
  53  * (right shift) multiplication products as soon as they are formed,
  54  * rather than carrying additional fractional bits into subsequent additions.
  55  * This compromises accuracy slightly, but it lets us save a few shifts.
  56  * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
  57  * everywhere except in the multiplications proper; this saves a good deal
  58  * of work on 16-bit-int machines.
  59  *
  60  * Again to save a few shifts, the intermediate results between pass 1 and
  61  * pass 2 are not upscaled, but are represented only to integral precision.
  62  *
  63  * A final compromise is to represent the multiplicative constants to only
  64  * 8 fractional bits, rather than 13.  This saves some shifting work on some
  65  * machines, and may also reduce the cost of multiplication (since there
  66  * are fewer one-bits in the constants).
  67  */
  68
  69 #define CONST_BITS  8
  70
  71
  72 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  73  * causing a lot of useless floating-point operations at run time.
  74  * To get around this we use the following pre-calculated constants.
  75  * If you change CONST_BITS you may want to add appropriate values.
  76  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  77  */
  78
  79 #if CONST_BITS == 8
  80 #define FIX_0_382683433  ((INT32)   98)         /* FIX(0.382683433) */
  81 #define FIX_0_541196100  ((INT32)  139)         /* FIX(0.541196100) */
  82 #define FIX_0_707106781  ((INT32)  181)         /* FIX(0.707106781) */
  83 #define FIX_1_306562965  ((INT32)  334)         /* FIX(1.306562965) */
  84 #else
  85 #define FIX_0_382683433  FIX(0.382683433)
  86 #define FIX_0_541196100  FIX(0.541196100)
  87 #define FIX_0_707106781  FIX(0.707106781)
  88 #define FIX_1_306562965  FIX(1.306562965)
  89 #endif
  90
  91
  92 /* We can gain a little more speed, with a further compromise in accuracy,
  93  * by omitting the addition in a descaling shift.  This yields an incorrectly
  94  * rounded result half the time...
  95  */
  96
  97 #ifndef USE_ACCURATE_ROUNDING
  98 #undef DESCALE
  99 #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
 100 #endif
 101
 102
 103 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
 104  * descale to yield a DCTELEM result.
 105  */
 106
 107 #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
 108
 109
 110 /*
 111  * Perform the forward DCT on one block of samples.
 112  *
 113  * cK represents cos(K*pi/16).
 114  */
 115
 116 GLOBAL(void)
 117 jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
 118 {
 119   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
 120   DCTELEM tmp10, tmp11, tmp12, tmp13;
 121   DCTELEM z1, z2, z3, z4, z5, z11, z13;
 122   DCTELEM *dataptr;
 123   JSAMPROW elemptr;
 124   int ctr;
 125   SHIFT_TEMPS
 126
 127   /* Pass 1: process rows. */
 128
 129   dataptr = data;
 130   for (ctr = 0; ctr < DCTSIZE; ctr++) {
 131     elemptr = sample_data[ctr] + start_col;
 132
 133     /* Load data into workspace */
 134     tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);
 135     tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);
 136     tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);
 137     tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);
 138     tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);
 139     tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);
 140     tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);
 141     tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);
 142
 143     /* Even part */
 144
 145     tmp10 = tmp0 + tmp3;        /* phase 2 */
 146     tmp13 = tmp0 - tmp3;
 147     tmp11 = tmp1 + tmp2;
 148     tmp12 = tmp1 - tmp2;
 149
 150     /* Apply unsigned->signed conversion. */
 151     dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */
 152     dataptr[4] = tmp10 - tmp11;
 153
 154     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
 155     dataptr[2] = tmp13 + z1;    /* phase 5 */
 156     dataptr[6] = tmp13 - z1;
 157
 158     /* Odd part */
 159
 160     tmp10 = tmp4 + tmp5;        /* phase 2 */
 161     tmp11 = tmp5 + tmp6;
 162     tmp12 = tmp6 + tmp7;
 163
 164     /* The rotator is modified from fig 4-8 to avoid extra negations. */
 165     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
 166     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
 167     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
 168     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
 169
 170     z11 = tmp7 + z3;            /* phase 5 */
 171     z13 = tmp7 - z3;
 172
 173     dataptr[5] = z13 + z2;      /* phase 6 */
 174     dataptr[3] = z13 - z2;
 175     dataptr[1] = z11 + z4;
 176     dataptr[7] = z11 - z4;
 177
 178     dataptr += DCTSIZE;         /* advance pointer to next row */
 179   }
 180
 181   /* Pass 2: process columns. */
 182
 183   dataptr = data;
 184   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
 185     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
 186     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
 187     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
 188     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
 189     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
 190     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
 191     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
 192     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
 193
 194     /* Even part */
 195
 196     tmp10 = tmp0 + tmp3;        /* phase 2 */
 197     tmp13 = tmp0 - tmp3;
 198     tmp11 = tmp1 + tmp2;
 199     tmp12 = tmp1 - tmp2;
 200
 201     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
 202     dataptr[DCTSIZE*4] = tmp10 - tmp11;
 203
 204     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
 205     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
 206     dataptr[DCTSIZE*6] = tmp13 - z1;
 207
 208     /* Odd part */
 209
 210     tmp10 = tmp4 + tmp5;        /* phase 2 */
 211     tmp11 = tmp5 + tmp6;
 212     tmp12 = tmp6 + tmp7;
 213
 214     /* The rotator is modified from fig 4-8 to avoid extra negations. */
 215     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
 216     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
 217     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
 218     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
 219
 220     z11 = tmp7 + z3;            /* phase 5 */
 221     z13 = tmp7 - z3;
 222
 223     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
 224     dataptr[DCTSIZE*3] = z13 - z2;
 225     dataptr[DCTSIZE*1] = z11 + z4;
 226     dataptr[DCTSIZE*7] = z11 - z4;
 227
 228     dataptr++;                  /* advance pointer to next column */
 229   }
 230 }
 231
 232 #endif /* DCT_IFAST_SUPPORTED */