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 */
175