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.ijg
7 * file.
8 *
9 * This file contains a floating-point implementation of the
10 * forward DCT (Discrete Cosine Transform).
11 *
12 * This implementation should be more accurate than either of the integer
13 * DCT 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 DCT can be done by 1-D DCT on each row followed by 1-D DCT
18 * on each column. Direct algorithms are also available, but they are
19 * much more complex and seem not to be any faster when reduced to code.
20 *
21 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
22 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
23 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
24 * JPEG textbook (see REFERENCES section in file README.ijg). The following
25 * code is based directly on figure 4-8 in P&M.
26 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
27 * possible to arrange the computation so that many of the multiplies are
28 * simple scalings of the final outputs. These multiplies can then be
29 * folded into the multiplications or divisions by the JPEG quantization
30 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
31 * to be done in the DCT itself.
32 * The primary disadvantage of this method is that with a fixed-point
33 * implementation, accuracy is lost due to imprecise representation of the
34 * scaled quantization values. However, that problem does not arise if
35 * we use floating point arithmetic.
36 */
37
38#define JPEG_INTERNALS
39#include "jinclude.h"
40#include "jpeglib.h"
41#include "jdct.h" /* Private declarations for DCT subsystem */
42
43#ifdef DCT_FLOAT_SUPPORTED
44
45
46/*
47 * This module is specialized to the case DCTSIZE = 8.
48 */
49
50#if DCTSIZE != 8
51 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
52#endif
53
54
55/*
56 * Perform the forward DCT on one block of samples.
57 */
58
59GLOBAL(void)
60jpeg_fdct_float(FAST_FLOAT *data)
61{
62 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
63 FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
64 FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
65 FAST_FLOAT *dataptr;
66 int ctr;
67
68 /* Pass 1: process rows. */
69
70 dataptr = data;
71 for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
72 tmp0 = dataptr[0] + dataptr[7];
73 tmp7 = dataptr[0] - dataptr[7];
74 tmp1 = dataptr[1] + dataptr[6];
75 tmp6 = dataptr[1] - dataptr[6];
76 tmp2 = dataptr[2] + dataptr[5];
77 tmp5 = dataptr[2] - dataptr[5];
78 tmp3 = dataptr[3] + dataptr[4];
79 tmp4 = dataptr[3] - dataptr[4];
80
81 /* Even part */
82
83 tmp10 = tmp0 + tmp3; /* phase 2 */
84 tmp13 = tmp0 - tmp3;
85 tmp11 = tmp1 + tmp2;
86 tmp12 = tmp1 - tmp2;
87
88 dataptr[0] = tmp10 + tmp11; /* phase 3 */
89 dataptr[4] = tmp10 - tmp11;
90
91 z1 = (tmp12 + tmp13) * ((FAST_FLOAT)0.707106781); /* c4 */
92 dataptr[2] = tmp13 + z1; /* phase 5 */
93 dataptr[6] = tmp13 - z1;
94
95 /* Odd part */
96
97 tmp10 = tmp4 + tmp5; /* phase 2 */
98 tmp11 = tmp5 + tmp6;
99 tmp12 = tmp6 + tmp7;
100
101 /* The rotator is modified from fig 4-8 to avoid extra negations. */
102 z5 = (tmp10 - tmp12) * ((FAST_FLOAT)0.382683433); /* c6 */
103 z2 = ((FAST_FLOAT)0.541196100) * tmp10 + z5; /* c2-c6 */
104 z4 = ((FAST_FLOAT)1.306562965) * tmp12 + z5; /* c2+c6 */
105 z3 = tmp11 * ((FAST_FLOAT)0.707106781); /* c4 */
106
107 z11 = tmp7 + z3; /* phase 5 */
108 z13 = tmp7 - z3;
109
110 dataptr[5] = z13 + z2; /* phase 6 */
111 dataptr[3] = z13 - z2;
112 dataptr[1] = z11 + z4;
113 dataptr[7] = z11 - z4;
114
115 dataptr += DCTSIZE; /* advance pointer to next row */
116 }
117
118 /* Pass 2: process columns. */
119
120 dataptr = data;
121 for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
122 tmp0 = dataptr[DCTSIZE * 0] + dataptr[DCTSIZE * 7];
123 tmp7 = dataptr[DCTSIZE * 0] - dataptr[DCTSIZE * 7];
124 tmp1 = dataptr[DCTSIZE * 1] + dataptr[DCTSIZE * 6];
125 tmp6 = dataptr[DCTSIZE * 1] - dataptr[DCTSIZE * 6];
126 tmp2 = dataptr[DCTSIZE * 2] + dataptr[DCTSIZE * 5];
127 tmp5 = dataptr[DCTSIZE * 2] - dataptr[DCTSIZE * 5];
128 tmp3 = dataptr[DCTSIZE * 3] + dataptr[DCTSIZE * 4];
129 tmp4 = dataptr[DCTSIZE * 3] - dataptr[DCTSIZE * 4];
130
131 /* Even part */
132
133 tmp10 = tmp0 + tmp3; /* phase 2 */
134 tmp13 = tmp0 - tmp3;
135 tmp11 = tmp1 + tmp2;
136 tmp12 = tmp1 - tmp2;
137
138 dataptr[DCTSIZE * 0] = tmp10 + tmp11; /* phase 3 */
139 dataptr[DCTSIZE * 4] = tmp10 - tmp11;
140
141 z1 = (tmp12 + tmp13) * ((FAST_FLOAT)0.707106781); /* c4 */
142 dataptr[DCTSIZE * 2] = tmp13 + z1; /* phase 5 */
143 dataptr[DCTSIZE * 6] = tmp13 - z1;
144
145 /* Odd part */
146
147 tmp10 = tmp4 + tmp5; /* phase 2 */
148 tmp11 = tmp5 + tmp6;
149 tmp12 = tmp6 + tmp7;
150
151 /* The rotator is modified from fig 4-8 to avoid extra negations. */
152 z5 = (tmp10 - tmp12) * ((FAST_FLOAT)0.382683433); /* c6 */
153 z2 = ((FAST_FLOAT)0.541196100) * tmp10 + z5; /* c2-c6 */
154 z4 = ((FAST_FLOAT)1.306562965) * tmp12 + z5; /* c2+c6 */
155 z3 = tmp11 * ((FAST_FLOAT)0.707106781); /* c4 */
156
157 z11 = tmp7 + z3; /* phase 5 */
158 z13 = tmp7 - z3;
159
160 dataptr[DCTSIZE * 5] = z13 + z2; /* phase 6 */
161 dataptr[DCTSIZE * 3] = z13 - z2;
162 dataptr[DCTSIZE * 1] = z11 + z4;
163 dataptr[DCTSIZE * 7] = z11 - z4;
164
165 dataptr++; /* advance pointer to next column */
166 }
167}
168
169#endif /* DCT_FLOAT_SUPPORTED */
170