00001 /*
00002  * jfdctflt.c
00003  *
00004  * Copyright (C) 1994-1996, Thomas G. Lane.
00005  * This file is part of the Independent JPEG Group's software.
00006  * For conditions of distribution and use, see the accompanying README file.
00007  *
00008  * This file contains a floating-point implementation of the
00009  * forward DCT (Discrete Cosine Transform).
00010  *
00011  * This implementation should be more accurate than either of the integer
00012  * DCT implementations.  However, it may not give the same results on all
00013  * machines because of differences in roundoff behavior.  Speed will depend
00014  * on the hardware's floating point capacity.
00015  *
00016  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
00017  * on each column.  Direct algorithms are also available, but they are
00018  * much more complex and seem not to be any faster when reduced to code.
00019  *
00020  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
00021  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
00022  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
00023  * JPEG textbook (see REFERENCES section in file README).  The following code
00024  * is based directly on figure 4-8 in P&M.
00025  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
00026  * possible to arrange the computation so that many of the multiplies are
00027  * simple scalings of the final outputs.  These multiplies can then be
00028  * folded into the multiplications or divisions by the JPEG quantization
00029  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
00030  * to be done in the DCT itself.
00031  * The primary disadvantage of this method is that with a fixed-point
00032  * implementation, accuracy is lost due to imprecise representation of the
00033  * scaled quantization values.  However, that problem does not arise if
00034  * we use floating point arithmetic.
00035  */
00036 
00037 #define JPEG_INTERNALS
00038 #include "jinclude.h"
00039 #include "jpeglib.h"
00040 #include "jdct.h"               /* Private declarations for DCT subsystem */
00041 
00042 #ifdef DCT_FLOAT_SUPPORTED
00043 
00044 
00045 /*
00046  * This module is specialized to the case DCTSIZE = 8.
00047  */
00048 
00049 #if DCTSIZE != 8
00050   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
00051 #endif
00052 
00053 
00054 /*
00055  * Perform the forward DCT on one block of samples.
00056  */
00057 
00058 GLOBAL(void)
00059 jpeg_fdct_float (FAST_FLOAT * data)
00060 {
00061   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
00062   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
00063   FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
00064   FAST_FLOAT *dataptr;
00065   int ctr;
00066 
00067   /* Pass 1: process rows. */
00068 
00069   dataptr = data;
00070   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00071     tmp0 = dataptr[0] + dataptr[7];
00072     tmp7 = dataptr[0] - dataptr[7];
00073     tmp1 = dataptr[1] + dataptr[6];
00074     tmp6 = dataptr[1] - dataptr[6];
00075     tmp2 = dataptr[2] + dataptr[5];
00076     tmp5 = dataptr[2] - dataptr[5];
00077     tmp3 = dataptr[3] + dataptr[4];
00078     tmp4 = dataptr[3] - dataptr[4];
00079     
00080     /* Even part */
00081     
00082     tmp10 = tmp0 + tmp3;        /* phase 2 */
00083     tmp13 = tmp0 - tmp3;
00084     tmp11 = tmp1 + tmp2;
00085     tmp12 = tmp1 - tmp2;
00086     
00087     dataptr[0] = tmp10 + tmp11; /* phase 3 */
00088     dataptr[4] = tmp10 - tmp11;
00089     
00090     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
00091     dataptr[2] = tmp13 + z1;    /* phase 5 */
00092     dataptr[6] = tmp13 - z1;
00093     
00094     /* Odd part */
00095 
00096     tmp10 = tmp4 + tmp5;        /* phase 2 */
00097     tmp11 = tmp5 + tmp6;
00098     tmp12 = tmp6 + tmp7;
00099 
00100     /* The rotator is modified from fig 4-8 to avoid extra negations. */
00101     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
00102     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
00103     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
00104     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
00105 
00106     z11 = tmp7 + z3;            /* phase 5 */
00107     z13 = tmp7 - z3;
00108 
00109     dataptr[5] = z13 + z2;      /* phase 6 */
00110     dataptr[3] = z13 - z2;
00111     dataptr[1] = z11 + z4;
00112     dataptr[7] = z11 - z4;
00113 
00114     dataptr += DCTSIZE;         /* advance pointer to next row */
00115   }
00116 
00117   /* Pass 2: process columns. */
00118 
00119   dataptr = data;
00120   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00121     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
00122     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
00123     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
00124     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
00125     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
00126     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
00127     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
00128     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
00129     
00130     /* Even part */
00131     
00132     tmp10 = tmp0 + tmp3;        /* phase 2 */
00133     tmp13 = tmp0 - tmp3;
00134     tmp11 = tmp1 + tmp2;
00135     tmp12 = tmp1 - tmp2;
00136     
00137     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
00138     dataptr[DCTSIZE*4] = tmp10 - tmp11;
00139     
00140     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
00141     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
00142     dataptr[DCTSIZE*6] = tmp13 - z1;
00143     
00144     /* Odd part */
00145 
00146     tmp10 = tmp4 + tmp5;        /* phase 2 */
00147     tmp11 = tmp5 + tmp6;
00148     tmp12 = tmp6 + tmp7;
00149 
00150     /* The rotator is modified from fig 4-8 to avoid extra negations. */
00151     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
00152     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
00153     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
00154     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
00155 
00156     z11 = tmp7 + z3;            /* phase 5 */
00157     z13 = tmp7 - z3;
00158 
00159     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
00160     dataptr[DCTSIZE*3] = z13 - z2;
00161     dataptr[DCTSIZE*1] = z11 + z4;
00162     dataptr[DCTSIZE*7] = z11 - z4;
00163 
00164     dataptr++;                  /* advance pointer to next column */
00165   }
00166 }
00167 
00168 #endif /* DCT_FLOAT_SUPPORTED */