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 0 : 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 0 : dataptr = data;
70 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
71 0 : tmp0 = dataptr[0] + dataptr[7];
72 0 : tmp7 = dataptr[0] - dataptr[7];
73 0 : tmp1 = dataptr[1] + dataptr[6];
74 0 : tmp6 = dataptr[1] - dataptr[6];
75 0 : tmp2 = dataptr[2] + dataptr[5];
76 0 : tmp5 = dataptr[2] - dataptr[5];
77 0 : tmp3 = dataptr[3] + dataptr[4];
78 0 : tmp4 = dataptr[3] - dataptr[4];
79 :
80 : /* Even part */
81 :
82 0 : tmp10 = tmp0 + tmp3; /* phase 2 */
83 0 : tmp13 = tmp0 - tmp3;
84 0 : tmp11 = tmp1 + tmp2;
85 0 : tmp12 = tmp1 - tmp2;
86 :
87 0 : dataptr[0] = tmp10 + tmp11; /* phase 3 */
88 0 : dataptr[4] = tmp10 - tmp11;
89 :
90 0 : z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
91 0 : dataptr[2] = tmp13 + z1; /* phase 5 */
92 0 : dataptr[6] = tmp13 - z1;
93 :
94 : /* Odd part */
95 :
96 0 : tmp10 = tmp4 + tmp5; /* phase 2 */
97 0 : tmp11 = tmp5 + tmp6;
98 0 : tmp12 = tmp6 + tmp7;
99 :
100 : /* The rotator is modified from fig 4-8 to avoid extra negations. */
101 0 : z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
102 0 : z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
103 0 : z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
104 0 : z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
105 :
106 0 : z11 = tmp7 + z3; /* phase 5 */
107 0 : z13 = tmp7 - z3;
108 :
109 0 : dataptr[5] = z13 + z2; /* phase 6 */
110 0 : dataptr[3] = z13 - z2;
111 0 : dataptr[1] = z11 + z4;
112 0 : dataptr[7] = z11 - z4;
113 :
114 0 : dataptr += DCTSIZE; /* advance pointer to next row */
115 : }
116 :
117 : /* Pass 2: process columns. */
118 :
119 0 : dataptr = data;
120 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
121 0 : tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
122 0 : tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
123 0 : tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
124 0 : tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
125 0 : tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
126 0 : tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
127 0 : tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
128 0 : tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
129 :
130 : /* Even part */
131 :
132 0 : tmp10 = tmp0 + tmp3; /* phase 2 */
133 0 : tmp13 = tmp0 - tmp3;
134 0 : tmp11 = tmp1 + tmp2;
135 0 : tmp12 = tmp1 - tmp2;
136 :
137 0 : dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
138 0 : dataptr[DCTSIZE*4] = tmp10 - tmp11;
139 :
140 0 : z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
141 0 : dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
142 0 : dataptr[DCTSIZE*6] = tmp13 - z1;
143 :
144 : /* Odd part */
145 :
146 0 : tmp10 = tmp4 + tmp5; /* phase 2 */
147 0 : tmp11 = tmp5 + tmp6;
148 0 : tmp12 = tmp6 + tmp7;
149 :
150 : /* The rotator is modified from fig 4-8 to avoid extra negations. */
151 0 : z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
152 0 : z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
153 0 : z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
154 0 : z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
155 :
156 0 : z11 = tmp7 + z3; /* phase 5 */
157 0 : z13 = tmp7 - z3;
158 :
159 0 : dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
160 0 : dataptr[DCTSIZE*3] = z13 - z2;
161 0 : dataptr[DCTSIZE*1] = z11 + z4;
162 0 : dataptr[DCTSIZE*7] = z11 - z4;
163 :
164 0 : dataptr++; /* advance pointer to next column */
165 : }
166 0 : }
167 :
168 : #endif /* DCT_FLOAT_SUPPORTED */
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