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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 #define JPEG_INTERNALS | |
34 #include "jinclude.h" | |
35 #include "jpeglib.h" | |
36 #include "jdct.h" /* Private declarations for DCT subsystem */ | |
37 | |
38 #ifdef DCT_IFAST_SUPPORTED | |
39 | |
40 | |
41 /* | |
42 * This module is specialized to the case DCTSIZE = 8. | |
43 */ | |
44 | |
45 #if DCTSIZE != 8 | |
46 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ | |
47 #endif | |
48 | |
49 | |
50 /* Scaling decisions are generally the same as in the LL&M algorithm; | |
51 * see jfdctint.c for more details. However, we choose to descale | |
52 * (right shift) multiplication products as soon as they are formed, | |
53 * rather than carrying additional fractional bits into subsequent additions. | |
54 * This compromises accuracy slightly, but it lets us save a few shifts. | |
55 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) | |
56 * everywhere except in the multiplications proper; this saves a good deal | |
57 * of work on 16-bit-int machines. | |
58 * | |
59 * Again to save a few shifts, the intermediate results between pass 1 and | |
60 * pass 2 are not upscaled, but are represented only to integral precision. | |
61 * | |
62 * A final compromise is to represent the multiplicative constants to only | |
63 * 8 fractional bits, rather than 13. This saves some shifting work on some | |
64 * machines, and may also reduce the cost of multiplication (since there | |
65 * are fewer one-bits in the constants). | |
66 */ | |
67 | |
68 #define CONST_BITS 8 | |
69 | |
70 | |
71 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus | |
72 * causing a lot of useless floating-point operations at run time. | |
73 * To get around this we use the following pre-calculated constants. | |
74 * If you change CONST_BITS you may want to add appropriate values. | |
75 * (With a reasonable C compiler, you can just rely on the FIX() macro...) | |
76 */ | |
77 | |
78 #if CONST_BITS == 8 | |
79 #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ | |
80 #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ | |
81 #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ | |
82 #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ | |
83 #else | |
84 #define FIX_0_382683433 FIX(0.382683433) | |
85 #define FIX_0_541196100 FIX(0.541196100) | |
86 #define FIX_0_707106781 FIX(0.707106781) | |
87 #define FIX_1_306562965 FIX(1.306562965) | |
88 #endif | |
89 | |
90 | |
91 /* We can gain a little more speed, with a further compromise in accuracy, | |
92 * by omitting the addition in a descaling shift. This yields an incorrectly | |
93 * rounded result half the time... | |
94 */ | |
95 | |
96 #ifndef USE_ACCURATE_ROUNDING | |
97 #undef DESCALE | |
98 #define DESCALE(x,n) RIGHT_SHIFT(x, n) | |
99 #endif | |
100 | |
101 | |
102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately | |
103 * descale to yield a DCTELEM result. | |
104 */ | |
105 | |
106 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) | |
107 | |
108 | |
109 /* | |
110 * Perform the forward DCT on one block of samples. | |
111 */ | |
112 | |
113 GLOBAL(void) | |
114 jpeg_fdct_ifast (DCTELEM * data) | |
115 { | |
116 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; | |
117 DCTELEM tmp10, tmp11, tmp12, tmp13; | |
118 DCTELEM z1, z2, z3, z4, z5, z11, z13; | |
119 DCTELEM *dataptr; | |
120 int ctr; | |
121 SHIFT_TEMPS | |
122 | |
123 /* Pass 1: process rows. */ | |
124 | |
125 dataptr = data; | |
126 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
127 tmp0 = dataptr[0] + dataptr[7]; | |
128 tmp7 = dataptr[0] - dataptr[7]; | |
129 tmp1 = dataptr[1] + dataptr[6]; | |
130 tmp6 = dataptr[1] - dataptr[6]; | |
131 tmp2 = dataptr[2] + dataptr[5]; | |
132 tmp5 = dataptr[2] - dataptr[5]; | |
133 tmp3 = dataptr[3] + dataptr[4]; | |
134 tmp4 = dataptr[3] - dataptr[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[0] = tmp10 + tmp11; /* phase 3 */ | |
144 dataptr[4] = tmp10 - tmp11; | |
145 | |
146 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |
147 dataptr[2] = tmp13 + z1; /* phase 5 */ | |
148 dataptr[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 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |
158 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |
159 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |
160 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |
161 | |
162 z11 = tmp7 + z3; /* phase 5 */ | |
163 z13 = tmp7 - z3; | |
164 | |
165 dataptr[5] = z13 + z2; /* phase 6 */ | |
166 dataptr[3] = z13 - z2; | |
167 dataptr[1] = z11 + z4; | |
168 dataptr[7] = z11 - z4; | |
169 | |
170 dataptr += DCTSIZE; /* advance pointer to next row */ | |
171 } | |
172 | |
173 /* Pass 2: process columns. */ | |
174 | |
175 dataptr = data; | |
176 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
177 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; | |
178 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; | |
179 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; | |
180 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; | |
181 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; | |
182 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; | |
183 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; | |
184 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; | |
185 | |
186 /* Even part */ | |
187 | |
188 tmp10 = tmp0 + tmp3; /* phase 2 */ | |
189 tmp13 = tmp0 - tmp3; | |
190 tmp11 = tmp1 + tmp2; | |
191 tmp12 = tmp1 - tmp2; | |
192 | |
193 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ | |
194 dataptr[DCTSIZE*4] = tmp10 - tmp11; | |
195 | |
196 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |
197 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ | |
198 dataptr[DCTSIZE*6] = tmp13 - z1; | |
199 | |
200 /* Odd part */ | |
201 | |
202 tmp10 = tmp4 + tmp5; /* phase 2 */ | |
203 tmp11 = tmp5 + tmp6; | |
204 tmp12 = tmp6 + tmp7; | |
205 | |
206 /* The rotator is modified from fig 4-8 to avoid extra negations. */ | |
207 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |
208 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |
209 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |
210 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |
211 | |
212 z11 = tmp7 + z3; /* phase 5 */ | |
213 z13 = tmp7 - z3; | |
214 | |
215 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ | |
216 dataptr[DCTSIZE*3] = z13 - z2; | |
217 dataptr[DCTSIZE*1] = z11 + z4; | |
218 dataptr[DCTSIZE*7] = z11 - z4; | |
219 | |
220 dataptr++; /* advance pointer to next column */ | |
221 } | |
222 } | |
223 | |
224 #endif /* DCT_IFAST_SUPPORTED */ | |
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