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      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((INT32) (tmp0 + tmp7), 3)
    222 			    & RANGE_MASK];
    223     outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
    224 			    & RANGE_MASK];
    225     outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
    226 			    & RANGE_MASK];
    227     outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
    228 			    & RANGE_MASK];
    229     outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
    230 			    & RANGE_MASK];
    231     outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
    232 			    & RANGE_MASK];
    233     outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
    234 			    & RANGE_MASK];
    235     outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
    236 			    & RANGE_MASK];
    237 
    238     wsptr += DCTSIZE;		/* advance pointer to next row */
    239   }
    240 }
    241 
    242 #endif /* DCT_FLOAT_SUPPORTED */
    243