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 0 : 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 0 : dataptr = data;
126 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
127 0 : tmp0 = dataptr[0] + dataptr[7];
128 0 : tmp7 = dataptr[0] - dataptr[7];
129 0 : tmp1 = dataptr[1] + dataptr[6];
130 0 : tmp6 = dataptr[1] - dataptr[6];
131 0 : tmp2 = dataptr[2] + dataptr[5];
132 0 : tmp5 = dataptr[2] - dataptr[5];
133 0 : tmp3 = dataptr[3] + dataptr[4];
134 0 : tmp4 = dataptr[3] - dataptr[4];
135 :
136 : /* Even part */
137 :
138 0 : tmp10 = tmp0 + tmp3; /* phase 2 */
139 0 : tmp13 = tmp0 - tmp3;
140 0 : tmp11 = tmp1 + tmp2;
141 0 : tmp12 = tmp1 - tmp2;
142 :
143 0 : dataptr[0] = tmp10 + tmp11; /* phase 3 */
144 0 : dataptr[4] = tmp10 - tmp11;
145 :
146 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
147 0 : dataptr[2] = tmp13 + z1; /* phase 5 */
148 0 : dataptr[6] = tmp13 - z1;
149 :
150 : /* Odd part */
151 :
152 0 : tmp10 = tmp4 + tmp5; /* phase 2 */
153 0 : tmp11 = tmp5 + tmp6;
154 0 : tmp12 = tmp6 + tmp7;
155 :
156 : /* The rotator is modified from fig 4-8 to avoid extra negations. */
157 0 : z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
158 0 : z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
159 0 : z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
160 0 : z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
161 :
162 0 : z11 = tmp7 + z3; /* phase 5 */
163 0 : z13 = tmp7 - z3;
164 :
165 0 : dataptr[5] = z13 + z2; /* phase 6 */
166 0 : dataptr[3] = z13 - z2;
167 0 : dataptr[1] = z11 + z4;
168 0 : dataptr[7] = z11 - z4;
169 :
170 0 : dataptr += DCTSIZE; /* advance pointer to next row */
171 : }
172 :
173 : /* Pass 2: process columns. */
174 :
175 0 : dataptr = data;
176 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
177 0 : tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
178 0 : tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
179 0 : tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
180 0 : tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
181 0 : tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
182 0 : tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
183 0 : tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
184 0 : tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
185 :
186 : /* Even part */
187 :
188 0 : tmp10 = tmp0 + tmp3; /* phase 2 */
189 0 : tmp13 = tmp0 - tmp3;
190 0 : tmp11 = tmp1 + tmp2;
191 0 : tmp12 = tmp1 - tmp2;
192 :
193 0 : dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
194 0 : dataptr[DCTSIZE*4] = tmp10 - tmp11;
195 :
196 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
197 0 : dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
198 0 : dataptr[DCTSIZE*6] = tmp13 - z1;
199 :
200 : /* Odd part */
201 :
202 0 : tmp10 = tmp4 + tmp5; /* phase 2 */
203 0 : tmp11 = tmp5 + tmp6;
204 0 : tmp12 = tmp6 + tmp7;
205 :
206 : /* The rotator is modified from fig 4-8 to avoid extra negations. */
207 0 : z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
208 0 : z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
209 0 : z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
210 0 : z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
211 :
212 0 : z11 = tmp7 + z3; /* phase 5 */
213 0 : z13 = tmp7 - z3;
214 :
215 0 : dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
216 0 : dataptr[DCTSIZE*3] = z13 - z2;
217 0 : dataptr[DCTSIZE*1] = z11 + z4;
218 0 : dataptr[DCTSIZE*7] = z11 - z4;
219 :
220 0 : dataptr++; /* advance pointer to next column */
221 : }
222 0 : }
223 :
224 : #endif /* DCT_IFAST_SUPPORTED */
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