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