src/jpeg/jidctflt.c

   1 /*
   2  * jidctflt.c
   3  *
   4  * Copyright (C) 1994-1998, 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 floating-point implementation of the
   9  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
  10  * must also perform dequantization of the input coefficients.
  11  *
  12  * This implementation should be more accurate than either of the integer
  13  * IDCT implementations.  However, it may not give the same results on all
  14  * machines because of differences in roundoff behavior.  Speed will depend
  15  * on the hardware's floating point capacity.
  16  *
  17  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
  18  * on each row (or vice versa, but it's more convenient to emit a row at
  19  * a time).  Direct algorithms are also available, but they are much more
  20  * complex and seem not to be any faster when reduced to code.
  21  *
  22  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
  23  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
  24  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
  25  * JPEG textbook (see REFERENCES section in file README).  The following code
  26  * is based directly on figure 4-8 in P&M.
  27  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
  28  * possible to arrange the computation so that many of the multiplies are
  29  * simple scalings of the final outputs.  These multiplies can then be
  30  * folded into the multiplications or divisions by the JPEG quantization
  31  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
  32  * to be done in the DCT itself.
  33  * The primary disadvantage of this method is that with a fixed-point
  34  * implementation, accuracy is lost due to imprecise representation of the
  35  * scaled quantization values.  However, that problem does not arise if
  36  * we use floating point arithmetic.
  37  */
  38
  39 #define JPEG_INTERNALS
  40 #include "jinclude.h"
  41 #include "jpeglib.h"
  42 #include "jdct.h"               /* Private declarations for DCT subsystem */
  43
  44 #ifdef DCT_FLOAT_SUPPORTED
  45
  46
  47 /*
  48  * This module is specialized to the case DCTSIZE = 8.
  49  */
  50
  51 #if DCTSIZE != 8
  52   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  53 #endif
  54
  55
  56 /* Dequantize a coefficient by multiplying it by the multiplier-table
  57  * entry; produce a float result.
  58  */
  59
  60 #define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval))
  61
  62
  63 /*
  64  * Perform dequantization and inverse DCT on one block of coefficients.
  65  */
  66
  67 GLOBAL(void)
  68 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
  69                  JCOEFPTR coef_block,
  70                  JSAMPARRAY output_buf, JDIMENSION output_col)
  71 {
  72   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  73   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
  74   FAST_FLOAT z5, z10, z11, z12, z13;
  75   JCOEFPTR inptr;
  76   FLOAT_MULT_TYPE * quantptr;
  77   FAST_FLOAT * wsptr;
  78   JSAMPROW outptr;
  79   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
  80   int ctr;
  81   FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
  82   SHIFT_TEMPS
  83
  84   /* Pass 1: process columns from input, store into work array. */
  85
  86   inptr = coef_block;
  87   quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
  88   wsptr = workspace;
  89   for (ctr = DCTSIZE; ctr > 0; ctr--) {
  90     /* Due to quantization, we will usually find that many of the input
  91      * coefficients are zero, especially the AC terms.  We can exploit this
  92      * by short-circuiting the IDCT calculation for any column in which all
  93      * the AC terms are zero.  In that case each output is equal to the
  94      * DC coefficient (with scale factor as needed).
  95      * With typical images and quantization tables, half or more of the
  96      * column DCT calculations can be simplified this way.
  97      */
  98
  99     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
 100         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
 101         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
 102         inptr[DCTSIZE*7] == 0) {
 103       /* AC terms all zero */
 104       FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 105
 106       wsptr[DCTSIZE*0] = dcval;
 107       wsptr[DCTSIZE*1] = dcval;
 108       wsptr[DCTSIZE*2] = dcval;
 109       wsptr[DCTSIZE*3] = dcval;
 110       wsptr[DCTSIZE*4] = dcval;
 111       wsptr[DCTSIZE*5] = dcval;
 112       wsptr[DCTSIZE*6] = dcval;
 113       wsptr[DCTSIZE*7] = dcval;
 114
 115       inptr++;                  /* advance pointers to next column */
 116       quantptr++;
 117       wsptr++;
 118       continue;
 119     }
 120
 121     /* Even part */
 122
 123     tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
 124     tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
 125     tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
 126     tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
 127
 128     tmp10 = tmp0 + tmp2;        /* phase 3 */
 129     tmp11 = tmp0 - tmp2;
 130
 131     tmp13 = tmp1 + tmp3;        /* phases 5-3 */
 132     tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
 133
 134     tmp0 = tmp10 + tmp13;       /* phase 2 */
 135     tmp3 = tmp10 - tmp13;
 136     tmp1 = tmp11 + tmp12;
 137     tmp2 = tmp11 - tmp12;
 138
 139     /* Odd part */
 140
 141     tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
 142     tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
 143     tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
 144     tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
 145
 146     z13 = tmp6 + tmp5;          /* phase 6 */
 147     z10 = tmp6 - tmp5;
 148     z11 = tmp4 + tmp7;
 149     z12 = tmp4 - tmp7;
 150
 151     tmp7 = z11 + z13;           /* phase 5 */
 152     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
 153
 154     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
 155     tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
 156     tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
 157
 158     tmp6 = tmp12 - tmp7;        /* phase 2 */
 159     tmp5 = tmp11 - tmp6;
 160     tmp4 = tmp10 + tmp5;
 161
 162     wsptr[DCTSIZE*0] = tmp0 + tmp7;
 163     wsptr[DCTSIZE*7] = tmp0 - tmp7;
 164     wsptr[DCTSIZE*1] = tmp1 + tmp6;
 165     wsptr[DCTSIZE*6] = tmp1 - tmp6;
 166     wsptr[DCTSIZE*2] = tmp2 + tmp5;
 167     wsptr[DCTSIZE*5] = tmp2 - tmp5;
 168     wsptr[DCTSIZE*4] = tmp3 + tmp4;
 169     wsptr[DCTSIZE*3] = tmp3 - tmp4;
 170
 171     inptr++;                    /* advance pointers to next column */
 172     quantptr++;
 173     wsptr++;
 174   }
 175
 176   /* Pass 2: process rows from work array, store into output array. */
 177   /* Note that we must descale the results by a factor of 8 == 2**3. */
 178
 179   wsptr = workspace;
 180   for (ctr = 0; ctr < DCTSIZE; ctr++) {
 181     outptr = output_buf[ctr] + output_col;
 182     /* Rows of zeroes can be exploited in the same way as we did with columns.
 183      * However, the column calculation has created many nonzero AC terms, so
 184      * the simplification applies less often (typically 5% to 10% of the time).
 185      * And testing floats for zero is relatively expensive, so we don't bother.
 186      */
 187
 188     /* Even part */
 189
 190     tmp10 = wsptr[0] + wsptr[4];
 191     tmp11 = wsptr[0] - wsptr[4];
 192
 193     tmp13 = wsptr[2] + wsptr[6];
 194     tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
 195
 196     tmp0 = tmp10 + tmp13;
 197     tmp3 = tmp10 - tmp13;
 198     tmp1 = tmp11 + tmp12;
 199     tmp2 = tmp11 - tmp12;
 200
 201     /* Odd part */
 202
 203     z13 = wsptr[5] + wsptr[3];
 204     z10 = wsptr[5] - wsptr[3];
 205     z11 = wsptr[1] + wsptr[7];
 206     z12 = wsptr[1] - wsptr[7];
 207
 208     tmp7 = z11 + z13;
 209     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
 210
 211     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
 212     tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
 213     tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
 214
 215     tmp6 = tmp12 - tmp7;
 216     tmp5 = tmp11 - tmp6;
 217     tmp4 = tmp10 + tmp5;
 218
 219     /* Final output stage: scale down by a factor of 8 and range-limit */
 220
 221     outptr[0] = range_limit[(int) DESCALE((JPEG_INT32) (tmp0 + tmp7), 3)
 222                             & RANGE_MASK];
 223     outptr[7] = range_limit[(int) DESCALE((JPEG_INT32) (tmp0 - tmp7), 3)
 224                             & RANGE_MASK];
 225     outptr[1] = range_limit[(int) DESCALE((JPEG_INT32) (tmp1 + tmp6), 3)
 226                             & RANGE_MASK];
 227     outptr[6] = range_limit[(int) DESCALE((JPEG_INT32) (tmp1 - tmp6), 3)
 228                             & RANGE_MASK];
 229     outptr[2] = range_limit[(int) DESCALE((JPEG_INT32) (tmp2 + tmp5), 3)
 230                             & RANGE_MASK];
 231     outptr[5] = range_limit[(int) DESCALE((JPEG_INT32) (tmp2 - tmp5), 3)
 232                             & RANGE_MASK];
 233     outptr[4] = range_limit[(int) DESCALE((JPEG_INT32) (tmp3 + tmp4), 3)
 234                             & RANGE_MASK];
 235     outptr[3] = range_limit[(int) DESCALE((JPEG_INT32) (tmp3 - tmp4), 3)
 236                             & RANGE_MASK];
 237
 238     wsptr += DCTSIZE;           /* advance pointer to next row */
 239   }
 240 }
 241
 242 #endif /* DCT_FLOAT_SUPPORTED */