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      1 /*
      2  * jfdctflt.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 floating-point implementation of the
      9  * forward DCT (Discrete Cosine Transform).
     10  *
     11  * This implementation should be more accurate than either of the integer
     12  * DCT implementations.  However, it may not give the same results on all
     13  * machines because of differences in roundoff behavior.  Speed will depend
     14  * on the hardware's floating point capacity.
     15  *
     16  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
     17  * on each column.  Direct algorithms are also available, but they are
     18  * much more complex and seem not to be any faster when reduced to code.
     19  *
     20  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
     21  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
     22  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
     23  * JPEG textbook (see REFERENCES section in file README).  The following code
     24  * is based directly on figure 4-8 in P&M.
     25  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
     26  * possible to arrange the computation so that many of the multiplies are
     27  * simple scalings of the final outputs.  These multiplies can then be
     28  * folded into the multiplications or divisions by the JPEG quantization
     29  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
     30  * to be done in the DCT itself.
     31  * The primary disadvantage of this method is that with a fixed-point
     32  * implementation, accuracy is lost due to imprecise representation of the
     33  * scaled quantization values.  However, that problem does not arise if
     34  * we use floating point arithmetic.
     35  */
     36 
     37 #define JPEG_INTERNALS
     38 #include "jinclude.h"
     39 #include "jpeglib.h"
     40 #include "jdct.h"		/* Private declarations for DCT subsystem */
     41 
     42 #ifdef DCT_FLOAT_SUPPORTED
     43 
     44 
     45 /*
     46  * This module is specialized to the case DCTSIZE = 8.
     47  */
     48 
     49 #if DCTSIZE != 8
     50   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
     51 #endif
     52 
     53 
     54 /*
     55  * Perform the forward DCT on one block of samples.
     56  */
     57 
     58 GLOBAL(void)
     59 jpeg_fdct_float (FAST_FLOAT * data)
     60 {
     61   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
     62   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
     63   FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
     64   FAST_FLOAT *dataptr;
     65   int ctr;
     66 
     67   /* Pass 1: process rows. */
     68 
     69   dataptr = data;
     70   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
     71     tmp0 = dataptr[0] + dataptr[7];
     72     tmp7 = dataptr[0] - dataptr[7];
     73     tmp1 = dataptr[1] + dataptr[6];
     74     tmp6 = dataptr[1] - dataptr[6];
     75     tmp2 = dataptr[2] + dataptr[5];
     76     tmp5 = dataptr[2] - dataptr[5];
     77     tmp3 = dataptr[3] + dataptr[4];
     78     tmp4 = dataptr[3] - dataptr[4];
     79 
     80     /* Even part */
     81 
     82     tmp10 = tmp0 + tmp3;	/* phase 2 */
     83     tmp13 = tmp0 - tmp3;
     84     tmp11 = tmp1 + tmp2;
     85     tmp12 = tmp1 - tmp2;
     86 
     87     dataptr[0] = tmp10 + tmp11; /* phase 3 */
     88     dataptr[4] = tmp10 - tmp11;
     89 
     90     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
     91     dataptr[2] = tmp13 + z1;	/* phase 5 */
     92     dataptr[6] = tmp13 - z1;
     93 
     94     /* Odd part */
     95 
     96     tmp10 = tmp4 + tmp5;	/* phase 2 */
     97     tmp11 = tmp5 + tmp6;
     98     tmp12 = tmp6 + tmp7;
     99 
    100     /* The rotator is modified from fig 4-8 to avoid extra negations. */
    101     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
    102     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
    103     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
    104     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
    105 
    106     z11 = tmp7 + z3;		/* phase 5 */
    107     z13 = tmp7 - z3;
    108 
    109     dataptr[5] = z13 + z2;	/* phase 6 */
    110     dataptr[3] = z13 - z2;
    111     dataptr[1] = z11 + z4;
    112     dataptr[7] = z11 - z4;
    113 
    114     dataptr += DCTSIZE;		/* advance pointer to next row */
    115   }
    116 
    117   /* Pass 2: process columns. */
    118 
    119   dataptr = data;
    120   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
    121     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
    122     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
    123     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
    124     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
    125     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
    126     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
    127     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
    128     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
    129 
    130     /* Even part */
    131 
    132     tmp10 = tmp0 + tmp3;	/* phase 2 */
    133     tmp13 = tmp0 - tmp3;
    134     tmp11 = tmp1 + tmp2;
    135     tmp12 = tmp1 - tmp2;
    136 
    137     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
    138     dataptr[DCTSIZE*4] = tmp10 - tmp11;
    139 
    140     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
    141     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
    142     dataptr[DCTSIZE*6] = tmp13 - z1;
    143 
    144     /* Odd part */
    145 
    146     tmp10 = tmp4 + tmp5;	/* phase 2 */
    147     tmp11 = tmp5 + tmp6;
    148     tmp12 = tmp6 + tmp7;
    149 
    150     /* The rotator is modified from fig 4-8 to avoid extra negations. */
    151     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
    152     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
    153     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
    154     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
    155 
    156     z11 = tmp7 + z3;		/* phase 5 */
    157     z13 = tmp7 - z3;
    158 
    159     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
    160     dataptr[DCTSIZE*3] = z13 - z2;
    161     dataptr[DCTSIZE*1] = z11 + z4;
    162     dataptr[DCTSIZE*7] = z11 - z4;
    163 
    164     dataptr++;			/* advance pointer to next column */
    165   }
    166 }
    167 
    168 #endif /* DCT_FLOAT_SUPPORTED */
    169