1 /*
2 * jfdctflt.c
3 *
4 * Copyright (C) 1994-1996, Thomas G. Lane.
5 * Modified 2003-2009 by Guido Vollbeding.
6 * This file is part of the Independent JPEG Group's software.
7 * For conditions of distribution and use, see the accompanying README 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). The following code
25 * 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
59 GLOBAL(void)
60 jpeg_fdct_float (FAST_FLOAT * data, JSAMPARRAY sample_data, JDIMENSION start_col)
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 JSAMPROW elemptr;
67 int ctr;
68
69 /* Pass 1: process rows. */
70
71 dataptr = data;
72 for (ctr = 0; ctr < DCTSIZE; ctr++) {
73 elemptr = sample_data[ctr] + start_col;
74
75 /* Load data into workspace */
76 tmp0 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]));
77 tmp7 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]));
78 tmp1 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]));
79 tmp6 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]));
80 tmp2 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]));
81 tmp5 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]));
82 tmp3 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]));
83 tmp4 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]));
84
85 /* Even part */
86
87 tmp10 = tmp0 + tmp3; /* phase 2 */
88 tmp13 = tmp0 - tmp3;
89 tmp11 = tmp1 + tmp2;
90 tmp12 = tmp1 - tmp2;
91
92 /* Apply unsigned->signed conversion */
93 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */
94 dataptr[4] = tmp10 - tmp11;
95
96 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
97 dataptr[2] = tmp13 + z1; /* phase 5 */
98 dataptr[6] = tmp13 - z1;
99
100 /* Odd part */
101
102 tmp10 = tmp4 + tmp5; /* phase 2 */
103 tmp11 = tmp5 + tmp6;
104 tmp12 = tmp6 + tmp7;
105
106 /* The rotator is modified from fig 4-8 to avoid extra negations. */
107 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
108 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
109 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
110 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
111
112 z11 = tmp7 + z3; /* phase 5 */
113 z13 = tmp7 - z3;
114
115 dataptr[5] = z13 + z2; /* phase 6 */
116 dataptr[3] = z13 - z2;
117 dataptr[1] = z11 + z4;
118 dataptr[7] = z11 - z4;
119
120 dataptr += DCTSIZE; /* advance pointer to next row */
121 }
122
123 /* Pass 2: process columns. */
124
125 dataptr = data;
126 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
127 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
128 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
129 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
130 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
131 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
132 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
133 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
134 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
135
136 /* Even part */
137
138 tmp10 = tmp0 + tmp3; /* phase 2 */
139 tmp13 = tmp0 - tmp3;
140 tmp11 = tmp1 + tmp2;
141 tmp12 = tmp1 - tmp2;
142
143 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
144 dataptr[DCTSIZE*4] = tmp10 - tmp11;
145
146 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
147 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
148 dataptr[DCTSIZE*6] = tmp13 - z1;
149
150 /* Odd part */
151
152 tmp10 = tmp4 + tmp5; /* phase 2 */
153 tmp11 = tmp5 + tmp6;
154 tmp12 = tmp6 + tmp7;
155
156 /* The rotator is modified from fig 4-8 to avoid extra negations. */
157 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
158 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
159 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
160 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
161
162 z11 = tmp7 + z3; /* phase 5 */
163 z13 = tmp7 - z3;
164
165 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
166 dataptr[DCTSIZE*3] = z13 - z2;
167 dataptr[DCTSIZE*1] = z11 + z4;
168 dataptr[DCTSIZE*7] = z11 - z4;
169
170 dataptr++; /* advance pointer to next column */
171 }
172 }
173
174 #endif /* DCT_FLOAT_SUPPORTED */