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1 : chl 461 /*****************************************************************************
2 : Isibaar 3 *
3 : chl 461 * XVID MPEG-4 VIDEO CODEC
4 :     * - fast disrete cosine transformation - integer C version
5 : Isibaar 3 *
6 : chl 461 * These routines are from Independent JPEG Group's free JPEG software
7 :     * Copyright (C) 1991-1998, Thomas G. Lane (see the file README.IJG)
8 : Isibaar 3 *
9 : edgomez 649 * This file is part of XviD, a free MPEG-4 video encoder/decoder
10 : Isibaar 3 *
11 : edgomez 649 * XviD is free software; you can redistribute it and/or modify it
12 :     * under the terms of the GNU General Public License as published by
13 : chl 461 * the Free Software Foundation; either version 2 of the License, or
14 :     * (at your option) any later version.
15 : Isibaar 3 *
16 : chl 461 * This program is distributed in the hope that it will be useful,
17 :     * but WITHOUT ANY WARRANTY; without even the implied warranty of
18 :     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 :     * GNU General Public License for more details.
20 :     *
21 :     * You should have received a copy of the GNU General Public License
22 :     * along with this program; if not, write to the Free Software
23 :     * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 :     *
25 : edgomez 649 * Under section 8 of the GNU General Public License, the copyright
26 :     * holders of XVID explicitly forbid distribution in the following
27 :     * countries:
28 :     *
29 :     * - Japan
30 :     * - United States of America
31 :     *
32 :     * Linking XviD statically or dynamically with other modules is making a
33 :     * combined work based on XviD. Thus, the terms and conditions of the
34 :     * GNU General Public License cover the whole combination.
35 :     *
36 :     * As a special exception, the copyright holders of XviD give you
37 :     * permission to link XviD with independent modules that communicate with
38 :     * XviD solely through the VFW1.1 and DShow interfaces, regardless of the
39 :     * license terms of these independent modules, and to copy and distribute
40 :     * the resulting combined work under terms of your choice, provided that
41 :     * every copy of the combined work is accompanied by a complete copy of
42 :     * the source code of XviD (the version of XviD used to produce the
43 :     * combined work), being distributed under the terms of the GNU General
44 :     * Public License plus this exception. An independent module is a module
45 :     * which is not derived from or based on XviD.
46 :     *
47 :     * Note that people who make modified versions of XviD are not obligated
48 :     * to grant this special exception for their modified versions; it is
49 :     * their choice whether to do so. The GNU General Public License gives
50 :     * permission to release a modified version without this exception; this
51 :     * exception also makes it possible to release a modified version which
52 :     * carries forward this exception.
53 :     *
54 : edgomez 677 * $Id: fdct.c,v 1.5 2002-11-26 23:44:10 edgomez Exp $
55 : edgomez 649 *
56 : chl 461 *************************************************************************/
57 : Isibaar 3
58 :     /* This routine is a slow-but-accurate integer implementation of the
59 :     * forward DCT (Discrete Cosine Transform). Taken from the IJG software
60 :     *
61 :     * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
62 :     * on each column. Direct algorithms are also available, but they are
63 :     * much more complex and seem not to be any faster when reduced to code.
64 :     *
65 :     * This implementation is based on an algorithm described in
66 :     * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
67 :     * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
68 :     * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
69 :     * The primary algorithm described there uses 11 multiplies and 29 adds.
70 :     * We use their alternate method with 12 multiplies and 32 adds.
71 :     * The advantage of this method is that no data path contains more than one
72 :     * multiplication; this allows a very simple and accurate implementation in
73 :     * scaled fixed-point arithmetic, with a minimal number of shifts.
74 :     *
75 :     * The poop on this scaling stuff is as follows:
76 :     *
77 :     * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
78 :     * larger than the true DCT outputs. The final outputs are therefore
79 :     * a factor of N larger than desired; since N=8 this can be cured by
80 :     * a simple right shift at the end of the algorithm. The advantage of
81 :     * this arrangement is that we save two multiplications per 1-D DCT,
82 :     * because the y0 and y4 outputs need not be divided by sqrt(N).
83 :     * In the IJG code, this factor of 8 is removed by the quantization step
84 :     * (in jcdctmgr.c), here it is removed.
85 :     *
86 :     * We have to do addition and subtraction of the integer inputs, which
87 :     * is no problem, and multiplication by fractional constants, which is
88 :     * a problem to do in integer arithmetic. We multiply all the constants
89 :     * by CONST_SCALE and convert them to integer constants (thus retaining
90 :     * CONST_BITS bits of precision in the constants). After doing a
91 :     * multiplication we have to divide the product by CONST_SCALE, with proper
92 :     * rounding, to produce the correct output. This division can be done
93 :     * cheaply as a right shift of CONST_BITS bits. We postpone shifting
94 :     * as long as possible so that partial sums can be added together with
95 :     * full fractional precision.
96 :     *
97 :     * The outputs of the first pass are scaled up by PASS1_BITS bits so that
98 :     * they are represented to better-than-integral precision. These outputs
99 :     * require 8 + PASS1_BITS + 3 bits; this fits in a 16-bit word
100 :     * with the recommended scaling. (For 12-bit sample data, the intermediate
101 :     * array is INT32 anyway.)
102 :     *
103 :     * To avoid overflow of the 32-bit intermediate results in pass 2, we must
104 :     * have 8 + CONST_BITS + PASS1_BITS <= 26. Error analysis
105 :     * shows that the values given below are the most effective.
106 :     *
107 :     * We can gain a little more speed, with a further compromise in accuracy,
108 :     * by omitting the addition in a descaling shift. This yields an incorrectly
109 :     * rounded result half the time...
110 :     */
111 :    
112 :     #include "fdct.h"
113 :    
114 :     #define USE_ACCURATE_ROUNDING
115 :    
116 :     #define RIGHT_SHIFT(x, shft) ((x) >> (shft))
117 :    
118 :     #ifdef USE_ACCURATE_ROUNDING
119 :     #define ONE ((int) 1)
120 :     #define DESCALE(x, n) RIGHT_SHIFT((x) + (ONE << ((n) - 1)), n)
121 :     #else
122 :     #define DESCALE(x, n) RIGHT_SHIFT(x, n)
123 :     #endif
124 :    
125 :     #define CONST_BITS 13
126 :     #define PASS1_BITS 2
127 :    
128 :     #define FIX_0_298631336 ((int) 2446) /* FIX(0.298631336) */
129 :     #define FIX_0_390180644 ((int) 3196) /* FIX(0.390180644) */
130 :     #define FIX_0_541196100 ((int) 4433) /* FIX(0.541196100) */
131 :     #define FIX_0_765366865 ((int) 6270) /* FIX(0.765366865) */
132 :     #define FIX_0_899976223 ((int) 7373) /* FIX(0.899976223) */
133 :     #define FIX_1_175875602 ((int) 9633) /* FIX(1.175875602) */
134 :     #define FIX_1_501321110 ((int) 12299) /* FIX(1.501321110) */
135 :     #define FIX_1_847759065 ((int) 15137) /* FIX(1.847759065) */
136 :     #define FIX_1_961570560 ((int) 16069) /* FIX(1.961570560) */
137 :     #define FIX_2_053119869 ((int) 16819) /* FIX(2.053119869) */
138 :     #define FIX_2_562915447 ((int) 20995) /* FIX(2.562915447) */
139 :     #define FIX_3_072711026 ((int) 25172) /* FIX(3.072711026) */
140 :    
141 : edgomez 677 /* function pointer */
142 : Isibaar 3 fdctFuncPtr fdct;
143 :    
144 :     /*
145 :     * Perform an integer forward DCT on one block of samples.
146 :     */
147 :    
148 : edgomez 195 void
149 :     fdct_int32(short *const block)
150 : Isibaar 3 {
151 : edgomez 195 int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
152 :     int tmp10, tmp11, tmp12, tmp13;
153 :     int z1, z2, z3, z4, z5;
154 :     short *blkptr;
155 :     int *dataptr;
156 :     int data[64];
157 :     int i;
158 : Isibaar 3
159 : edgomez 195 /* Pass 1: process rows. */
160 :     /* Note results are scaled up by sqrt(8) compared to a true DCT; */
161 :     /* furthermore, we scale the results by 2**PASS1_BITS. */
162 : Isibaar 3
163 : edgomez 195 dataptr = data;
164 :     blkptr = block;
165 :     for (i = 0; i < 8; i++) {
166 :     tmp0 = blkptr[0] + blkptr[7];
167 :     tmp7 = blkptr[0] - blkptr[7];
168 :     tmp1 = blkptr[1] + blkptr[6];
169 :     tmp6 = blkptr[1] - blkptr[6];
170 :     tmp2 = blkptr[2] + blkptr[5];
171 :     tmp5 = blkptr[2] - blkptr[5];
172 :     tmp3 = blkptr[3] + blkptr[4];
173 :     tmp4 = blkptr[3] - blkptr[4];
174 : Isibaar 3
175 : edgomez 195 /* Even part per LL&M figure 1 --- note that published figure is faulty;
176 :     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
177 :     */
178 : Isibaar 3
179 : edgomez 195 tmp10 = tmp0 + tmp3;
180 :     tmp13 = tmp0 - tmp3;
181 :     tmp11 = tmp1 + tmp2;
182 :     tmp12 = tmp1 - tmp2;
183 : Isibaar 3
184 : edgomez 195 dataptr[0] = (tmp10 + tmp11) << PASS1_BITS;
185 :     dataptr[4] = (tmp10 - tmp11) << PASS1_BITS;
186 : Isibaar 3
187 : edgomez 195 z1 = (tmp12 + tmp13) * FIX_0_541196100;
188 :     dataptr[2] =
189 :     DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS - PASS1_BITS);
190 :     dataptr[6] =
191 :     DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS - PASS1_BITS);
192 : Isibaar 3
193 : edgomez 195 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
194 :     * cK represents cos(K*pi/16).
195 :     * i0..i3 in the paper are tmp4..tmp7 here.
196 :     */
197 : Isibaar 3
198 : edgomez 195 z1 = tmp4 + tmp7;
199 :     z2 = tmp5 + tmp6;
200 :     z3 = tmp4 + tmp6;
201 :     z4 = tmp5 + tmp7;
202 :     z5 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */
203 : Isibaar 3
204 : edgomez 195 tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */
205 :     tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */
206 :     tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */
207 :     tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */
208 :     z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */
209 :     z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */
210 :     z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */
211 :     z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */
212 : Isibaar 3
213 : edgomez 195 z3 += z5;
214 :     z4 += z5;
215 : Isibaar 3
216 : edgomez 195 dataptr[7] = DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);
217 :     dataptr[5] = DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);
218 :     dataptr[3] = DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);
219 :     dataptr[1] = DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);
220 : Isibaar 3
221 : edgomez 195 dataptr += 8; /* advance pointer to next row */
222 :     blkptr += 8;
223 :     }
224 : Isibaar 3
225 : edgomez 195 /* Pass 2: process columns.
226 :     * We remove the PASS1_BITS scaling, but leave the results scaled up
227 :     * by an overall factor of 8.
228 :     */
229 : Isibaar 3
230 : edgomez 195 dataptr = data;
231 :     for (i = 0; i < 8; i++) {
232 :     tmp0 = dataptr[0] + dataptr[56];
233 :     tmp7 = dataptr[0] - dataptr[56];
234 :     tmp1 = dataptr[8] + dataptr[48];
235 :     tmp6 = dataptr[8] - dataptr[48];
236 :     tmp2 = dataptr[16] + dataptr[40];
237 :     tmp5 = dataptr[16] - dataptr[40];
238 :     tmp3 = dataptr[24] + dataptr[32];
239 :     tmp4 = dataptr[24] - dataptr[32];
240 : Isibaar 3
241 : edgomez 195 /* Even part per LL&M figure 1 --- note that published figure is faulty;
242 :     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
243 :     */
244 : Isibaar 3
245 : edgomez 195 tmp10 = tmp0 + tmp3;
246 :     tmp13 = tmp0 - tmp3;
247 :     tmp11 = tmp1 + tmp2;
248 :     tmp12 = tmp1 - tmp2;
249 : Isibaar 3
250 : edgomez 195 dataptr[0] = DESCALE(tmp10 + tmp11, PASS1_BITS);
251 :     dataptr[32] = DESCALE(tmp10 - tmp11, PASS1_BITS);
252 : Isibaar 3
253 : edgomez 195 z1 = (tmp12 + tmp13) * FIX_0_541196100;
254 :     dataptr[16] =
255 :     DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS + PASS1_BITS);
256 :     dataptr[48] =
257 :     DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS + PASS1_BITS);
258 : Isibaar 3
259 : edgomez 195 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
260 :     * cK represents cos(K*pi/16).
261 :     * i0..i3 in the paper are tmp4..tmp7 here.
262 :     */
263 : Isibaar 3
264 : edgomez 195 z1 = tmp4 + tmp7;
265 :     z2 = tmp5 + tmp6;
266 :     z3 = tmp4 + tmp6;
267 :     z4 = tmp5 + tmp7;
268 :     z5 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */
269 : Isibaar 3
270 : edgomez 195 tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */
271 :     tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */
272 :     tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */
273 :     tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */
274 :     z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */
275 :     z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */
276 :     z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */
277 :     z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */
278 : Isibaar 3
279 : edgomez 195 z3 += z5;
280 :     z4 += z5;
281 : Isibaar 3
282 : edgomez 195 dataptr[56] = DESCALE(tmp4 + z1 + z3, CONST_BITS + PASS1_BITS);
283 :     dataptr[40] = DESCALE(tmp5 + z2 + z4, CONST_BITS + PASS1_BITS);
284 :     dataptr[24] = DESCALE(tmp6 + z2 + z3, CONST_BITS + PASS1_BITS);
285 :     dataptr[8] = DESCALE(tmp7 + z1 + z4, CONST_BITS + PASS1_BITS);
286 : Isibaar 3
287 : edgomez 195 dataptr++; /* advance pointer to next column */
288 :     }
289 :     /* descale */
290 :     for (i = 0; i < 64; i++)
291 :     block[i] = (short int) DESCALE(data[i], 3);
292 : Isibaar 3 }

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