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
58GLOBAL(void)
59jpeg_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