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1 | /* |
2 | * jfdctfst.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 fast, not so accurate integer implementation of the | |
9 | * forward DCT (Discrete Cosine Transform). | |
10 | * | |
11 | * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT | |
12 | * on each column. Direct algorithms are also available, but they are | |
13 | * much more complex and seem not to be any faster when reduced to code. | |
14 | * | |
15 | * This implementation is based on Arai, Agui, and Nakajima's algorithm for | |
16 | * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in | |
17 | * Japanese, but the algorithm is described in the Pennebaker & Mitchell | |
18 | * JPEG textbook (see REFERENCES section in file README). The following code | |
19 | * is based directly on figure 4-8 in P&M. | |
20 | * While an 8-point DCT cannot be done in less than 11 multiplies, it is | |
21 | * possible to arrange the computation so that many of the multiplies are | |
22 | * simple scalings of the final outputs. These multiplies can then be | |
23 | * folded into the multiplications or divisions by the JPEG quantization | |
24 | * table entries. The AA&N method leaves only 5 multiplies and 29 adds | |
25 | * to be done in the DCT itself. | |
26 | * The primary disadvantage of this method is that with fixed-point math, | |
27 | * accuracy is lost due to imprecise representation of the scaled | |
28 | * quantization values. The smaller the quantization table entry, the less | |
29 | * precise the scaled value, so this implementation does worse with high- | |
30 | * quality-setting files than with low-quality ones. | |
31 | */ | |
32 | ||
33 | #include <stdlib.h> | |
34 | #include <stdio.h> | |
35 | #include "common.h" | |
36 | #include "dsputil.h" | |
37 | ||
38 | #define DCTSIZE 8 | |
39 | #define GLOBAL(x) x | |
40 | #define RIGHT_SHIFT(x, n) ((x) >> (n)) | |
41 | #define SHIFT_TEMPS | |
42 | ||
43 | /* | |
44 | * This module is specialized to the case DCTSIZE = 8. | |
45 | */ | |
46 | ||
47 | #if DCTSIZE != 8 | |
48 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ | |
49 | #endif | |
50 | ||
51 | ||
52 | /* Scaling decisions are generally the same as in the LL&M algorithm; | |
53 | * see jfdctint.c for more details. However, we choose to descale | |
54 | * (right shift) multiplication products as soon as they are formed, | |
55 | * rather than carrying additional fractional bits into subsequent additions. | |
56 | * This compromises accuracy slightly, but it lets us save a few shifts. | |
57 | * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) | |
58 | * everywhere except in the multiplications proper; this saves a good deal | |
59 | * of work on 16-bit-int machines. | |
60 | * | |
61 | * Again to save a few shifts, the intermediate results between pass 1 and | |
62 | * pass 2 are not upscaled, but are represented only to integral precision. | |
63 | * | |
64 | * A final compromise is to represent the multiplicative constants to only | |
65 | * 8 fractional bits, rather than 13. This saves some shifting work on some | |
66 | * machines, and may also reduce the cost of multiplication (since there | |
67 | * are fewer one-bits in the constants). | |
68 | */ | |
69 | ||
70 | #define CONST_BITS 8 | |
71 | ||
72 | ||
73 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus | |
74 | * causing a lot of useless floating-point operations at run time. | |
75 | * To get around this we use the following pre-calculated constants. | |
76 | * If you change CONST_BITS you may want to add appropriate values. | |
77 | * (With a reasonable C compiler, you can just rely on the FIX() macro...) | |
78 | */ | |
79 | ||
80 | #if CONST_BITS == 8 | |
81 | #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ | |
82 | #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ | |
83 | #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ | |
84 | #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ | |
85 | #else | |
86 | #define FIX_0_382683433 FIX(0.382683433) | |
87 | #define FIX_0_541196100 FIX(0.541196100) | |
88 | #define FIX_0_707106781 FIX(0.707106781) | |
89 | #define FIX_1_306562965 FIX(1.306562965) | |
90 | #endif | |
91 | ||
92 | ||
93 | /* We can gain a little more speed, with a further compromise in accuracy, | |
94 | * by omitting the addition in a descaling shift. This yields an incorrectly | |
95 | * rounded result half the time... | |
96 | */ | |
97 | ||
98 | #ifndef USE_ACCURATE_ROUNDING | |
99 | #undef DESCALE | |
100 | #define DESCALE(x,n) RIGHT_SHIFT(x, n) | |
101 | #endif | |
102 | ||
103 | ||
104 | /* Multiply a DCTELEM variable by an INT32 constant, and immediately | |
105 | * descale to yield a DCTELEM result. | |
106 | */ | |
107 | ||
108 | #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) | |
109 | ||
110 | ||
111 | /* | |
112 | * Perform the forward DCT on one block of samples. | |
113 | */ | |
114 | ||
115 | GLOBAL(void) | |
03c94ede | 116 | fdct_ifast (DCTELEM * data) |
de6d9b64 FB |
117 | { |
118 | DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; | |
119 | DCTELEM tmp10, tmp11, tmp12, tmp13; | |
120 | DCTELEM z1, z2, z3, z4, z5, z11, z13; | |
121 | DCTELEM *dataptr; | |
122 | int ctr; | |
123 | SHIFT_TEMPS | |
124 | ||
125 | /* Pass 1: process rows. */ | |
126 | ||
127 | dataptr = data; | |
128 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
129 | tmp0 = dataptr[0] + dataptr[7]; | |
130 | tmp7 = dataptr[0] - dataptr[7]; | |
131 | tmp1 = dataptr[1] + dataptr[6]; | |
132 | tmp6 = dataptr[1] - dataptr[6]; | |
133 | tmp2 = dataptr[2] + dataptr[5]; | |
134 | tmp5 = dataptr[2] - dataptr[5]; | |
135 | tmp3 = dataptr[3] + dataptr[4]; | |
136 | tmp4 = dataptr[3] - dataptr[4]; | |
137 | ||
138 | /* Even part */ | |
139 | ||
140 | tmp10 = tmp0 + tmp3; /* phase 2 */ | |
141 | tmp13 = tmp0 - tmp3; | |
142 | tmp11 = tmp1 + tmp2; | |
143 | tmp12 = tmp1 - tmp2; | |
144 | ||
145 | dataptr[0] = tmp10 + tmp11; /* phase 3 */ | |
146 | dataptr[4] = tmp10 - tmp11; | |
147 | ||
148 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |
149 | dataptr[2] = tmp13 + z1; /* phase 5 */ | |
150 | dataptr[6] = tmp13 - z1; | |
151 | ||
152 | /* Odd part */ | |
153 | ||
154 | tmp10 = tmp4 + tmp5; /* phase 2 */ | |
155 | tmp11 = tmp5 + tmp6; | |
156 | tmp12 = tmp6 + tmp7; | |
157 | ||
158 | /* The rotator is modified from fig 4-8 to avoid extra negations. */ | |
159 | z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |
160 | z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |
161 | z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |
162 | z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |
163 | ||
164 | z11 = tmp7 + z3; /* phase 5 */ | |
165 | z13 = tmp7 - z3; | |
166 | ||
167 | dataptr[5] = z13 + z2; /* phase 6 */ | |
168 | dataptr[3] = z13 - z2; | |
169 | dataptr[1] = z11 + z4; | |
170 | dataptr[7] = z11 - z4; | |
171 | ||
172 | dataptr += DCTSIZE; /* advance pointer to next row */ | |
173 | } | |
174 | ||
175 | /* Pass 2: process columns. */ | |
176 | ||
177 | dataptr = data; | |
178 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
179 | tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; | |
180 | tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; | |
181 | tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; | |
182 | tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; | |
183 | tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; | |
184 | tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; | |
185 | tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; | |
186 | tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; | |
187 | ||
188 | /* Even part */ | |
189 | ||
190 | tmp10 = tmp0 + tmp3; /* phase 2 */ | |
191 | tmp13 = tmp0 - tmp3; | |
192 | tmp11 = tmp1 + tmp2; | |
193 | tmp12 = tmp1 - tmp2; | |
194 | ||
195 | dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ | |
196 | dataptr[DCTSIZE*4] = tmp10 - tmp11; | |
197 | ||
198 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |
199 | dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ | |
200 | dataptr[DCTSIZE*6] = tmp13 - z1; | |
201 | ||
202 | /* Odd part */ | |
203 | ||
204 | tmp10 = tmp4 + tmp5; /* phase 2 */ | |
205 | tmp11 = tmp5 + tmp6; | |
206 | tmp12 = tmp6 + tmp7; | |
207 | ||
208 | /* The rotator is modified from fig 4-8 to avoid extra negations. */ | |
209 | z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |
210 | z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |
211 | z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |
212 | z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |
213 | ||
214 | z11 = tmp7 + z3; /* phase 5 */ | |
215 | z13 = tmp7 - z3; | |
216 | ||
217 | dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ | |
218 | dataptr[DCTSIZE*3] = z13 - z2; | |
219 | dataptr[DCTSIZE*1] = z11 + z4; | |
220 | dataptr[DCTSIZE*7] = z11 - z4; | |
221 | ||
222 | dataptr++; /* advance pointer to next column */ | |
223 | } | |
224 | } | |
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225 | |
226 | ||
227 | #undef GLOBAL | |
228 | #undef CONST_BITS | |
229 | #undef DESCALE | |
230 | #undef FIX_0_541196100 | |
231 | #undef FIX_1_306562965 |