blob: 67fb77b5e12010f1c34d5c599c9d7e8c234e20a7
1 | /* |
2 | * This file is part of the Independent JPEG Group's software. |
3 | * |
4 | * The authors make NO WARRANTY or representation, either express or implied, |
5 | * with respect to this software, its quality, accuracy, merchantability, or |
6 | * fitness for a particular purpose. This software is provided "AS IS", and |
7 | * you, its user, assume the entire risk as to its quality and accuracy. |
8 | * |
9 | * This software is copyright (C) 1991-1996, Thomas G. Lane. |
10 | * All Rights Reserved except as specified below. |
11 | * |
12 | * Permission is hereby granted to use, copy, modify, and distribute this |
13 | * software (or portions thereof) for any purpose, without fee, subject to |
14 | * these conditions: |
15 | * (1) If any part of the source code for this software is distributed, then |
16 | * this README file must be included, with this copyright and no-warranty |
17 | * notice unaltered; and any additions, deletions, or changes to the original |
18 | * files must be clearly indicated in accompanying documentation. |
19 | * (2) If only executable code is distributed, then the accompanying |
20 | * documentation must state that "this software is based in part on the work |
21 | * of the Independent JPEG Group". |
22 | * (3) Permission for use of this software is granted only if the user accepts |
23 | * full responsibility for any undesirable consequences; the authors accept |
24 | * NO LIABILITY for damages of any kind. |
25 | * |
26 | * These conditions apply to any software derived from or based on the IJG |
27 | * code, not just to the unmodified library. If you use our work, you ought |
28 | * to acknowledge us. |
29 | * |
30 | * Permission is NOT granted for the use of any IJG author's name or company |
31 | * name in advertising or publicity relating to this software or products |
32 | * derived from it. This software may be referred to only as "the Independent |
33 | * JPEG Group's software". |
34 | * |
35 | * We specifically permit and encourage the use of this software as the basis |
36 | * of commercial products, provided that all warranty or liability claims are |
37 | * assumed by the product vendor. |
38 | * |
39 | * This file contains a slow-but-accurate integer implementation of the |
40 | * forward DCT (Discrete Cosine Transform). |
41 | * |
42 | * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT |
43 | * on each column. Direct algorithms are also available, but they are |
44 | * much more complex and seem not to be any faster when reduced to code. |
45 | * |
46 | * This implementation is based on an algorithm described in |
47 | * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT |
48 | * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, |
49 | * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. |
50 | * The primary algorithm described there uses 11 multiplies and 29 adds. |
51 | * We use their alternate method with 12 multiplies and 32 adds. |
52 | * The advantage of this method is that no data path contains more than one |
53 | * multiplication; this allows a very simple and accurate implementation in |
54 | * scaled fixed-point arithmetic, with a minimal number of shifts. |
55 | */ |
56 | |
57 | /** |
58 | * @file |
59 | * Independent JPEG Group's slow & accurate dct. |
60 | */ |
61 | |
62 | #include "libavutil/common.h" |
63 | #include "dct.h" |
64 | |
65 | #include "bit_depth_template.c" |
66 | |
67 | #define DCTSIZE 8 |
68 | #define BITS_IN_JSAMPLE BIT_DEPTH |
69 | #define GLOBAL(x) x |
70 | #define RIGHT_SHIFT(x, n) ((x) >> (n)) |
71 | #define MULTIPLY16C16(var,const) ((var)*(const)) |
72 | #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n) |
73 | |
74 | |
75 | /* |
76 | * This module is specialized to the case DCTSIZE = 8. |
77 | */ |
78 | |
79 | #if DCTSIZE != 8 |
80 | #error "Sorry, this code only copes with 8x8 DCTs." |
81 | #endif |
82 | |
83 | |
84 | /* |
85 | * The poop on this scaling stuff is as follows: |
86 | * |
87 | * Each 1-D DCT step produces outputs which are a factor of sqrt(N) |
88 | * larger than the true DCT outputs. The final outputs are therefore |
89 | * a factor of N larger than desired; since N=8 this can be cured by |
90 | * a simple right shift at the end of the algorithm. The advantage of |
91 | * this arrangement is that we save two multiplications per 1-D DCT, |
92 | * because the y0 and y4 outputs need not be divided by sqrt(N). |
93 | * In the IJG code, this factor of 8 is removed by the quantization step |
94 | * (in jcdctmgr.c), NOT in this module. |
95 | * |
96 | * We have to do addition and subtraction of the integer inputs, which |
97 | * is no problem, and multiplication by fractional constants, which is |
98 | * a problem to do in integer arithmetic. We multiply all the constants |
99 | * by CONST_SCALE and convert them to integer constants (thus retaining |
100 | * CONST_BITS bits of precision in the constants). After doing a |
101 | * multiplication we have to divide the product by CONST_SCALE, with proper |
102 | * rounding, to produce the correct output. This division can be done |
103 | * cheaply as a right shift of CONST_BITS bits. We postpone shifting |
104 | * as long as possible so that partial sums can be added together with |
105 | * full fractional precision. |
106 | * |
107 | * The outputs of the first pass are scaled up by PASS1_BITS bits so that |
108 | * they are represented to better-than-integral precision. These outputs |
109 | * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word |
110 | * with the recommended scaling. (For 12-bit sample data, the intermediate |
111 | * array is int32_t anyway.) |
112 | * |
113 | * To avoid overflow of the 32-bit intermediate results in pass 2, we must |
114 | * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis |
115 | * shows that the values given below are the most effective. |
116 | */ |
117 | |
118 | #undef CONST_BITS |
119 | #undef PASS1_BITS |
120 | #undef OUT_SHIFT |
121 | |
122 | #if BITS_IN_JSAMPLE == 8 |
123 | #define CONST_BITS 13 |
124 | #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */ |
125 | #define OUT_SHIFT PASS1_BITS |
126 | #else |
127 | #define CONST_BITS 13 |
128 | #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ |
129 | #define OUT_SHIFT (PASS1_BITS + 1) |
130 | #endif |
131 | |
132 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus |
133 | * causing a lot of useless floating-point operations at run time. |
134 | * To get around this we use the following pre-calculated constants. |
135 | * If you change CONST_BITS you may want to add appropriate values. |
136 | * (With a reasonable C compiler, you can just rely on the FIX() macro...) |
137 | */ |
138 | |
139 | #if CONST_BITS == 13 |
140 | #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */ |
141 | #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */ |
142 | #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */ |
143 | #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */ |
144 | #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */ |
145 | #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */ |
146 | #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */ |
147 | #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */ |
148 | #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */ |
149 | #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */ |
150 | #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */ |
151 | #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */ |
152 | #else |
153 | #define FIX_0_298631336 FIX(0.298631336) |
154 | #define FIX_0_390180644 FIX(0.390180644) |
155 | #define FIX_0_541196100 FIX(0.541196100) |
156 | #define FIX_0_765366865 FIX(0.765366865) |
157 | #define FIX_0_899976223 FIX(0.899976223) |
158 | #define FIX_1_175875602 FIX(1.175875602) |
159 | #define FIX_1_501321110 FIX(1.501321110) |
160 | #define FIX_1_847759065 FIX(1.847759065) |
161 | #define FIX_1_961570560 FIX(1.961570560) |
162 | #define FIX_2_053119869 FIX(2.053119869) |
163 | #define FIX_2_562915447 FIX(2.562915447) |
164 | #define FIX_3_072711026 FIX(3.072711026) |
165 | #endif |
166 | |
167 | |
168 | /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result. |
169 | * For 8-bit samples with the recommended scaling, all the variable |
170 | * and constant values involved are no more than 16 bits wide, so a |
171 | * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. |
172 | * For 12-bit samples, a full 32-bit multiplication will be needed. |
173 | */ |
174 | |
175 | #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2 |
176 | #define MULTIPLY(var,const) MULTIPLY16C16(var,const) |
177 | #else |
178 | #define MULTIPLY(var,const) ((var) * (const)) |
179 | #endif |
180 | |
181 | |
182 | static av_always_inline void FUNC(row_fdct)(int16_t *data) |
183 | { |
184 | int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
185 | int tmp10, tmp11, tmp12, tmp13; |
186 | int z1, z2, z3, z4, z5; |
187 | int16_t *dataptr; |
188 | int ctr; |
189 | |
190 | /* Pass 1: process rows. */ |
191 | /* Note results are scaled up by sqrt(8) compared to a true DCT; */ |
192 | /* furthermore, we scale the results by 2**PASS1_BITS. */ |
193 | |
194 | dataptr = data; |
195 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
196 | tmp0 = dataptr[0] + dataptr[7]; |
197 | tmp7 = dataptr[0] - dataptr[7]; |
198 | tmp1 = dataptr[1] + dataptr[6]; |
199 | tmp6 = dataptr[1] - dataptr[6]; |
200 | tmp2 = dataptr[2] + dataptr[5]; |
201 | tmp5 = dataptr[2] - dataptr[5]; |
202 | tmp3 = dataptr[3] + dataptr[4]; |
203 | tmp4 = dataptr[3] - dataptr[4]; |
204 | |
205 | /* Even part per LL&M figure 1 --- note that published figure is faulty; |
206 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". |
207 | */ |
208 | |
209 | tmp10 = tmp0 + tmp3; |
210 | tmp13 = tmp0 - tmp3; |
211 | tmp11 = tmp1 + tmp2; |
212 | tmp12 = tmp1 - tmp2; |
213 | |
214 | dataptr[0] = (int16_t) ((tmp10 + tmp11) * (1 << PASS1_BITS)); |
215 | dataptr[4] = (int16_t) ((tmp10 - tmp11) * (1 << PASS1_BITS)); |
216 | |
217 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |
218 | dataptr[2] = (int16_t) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |
219 | CONST_BITS-PASS1_BITS); |
220 | dataptr[6] = (int16_t) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |
221 | CONST_BITS-PASS1_BITS); |
222 | |
223 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2). |
224 | * cK represents cos(K*pi/16). |
225 | * i0..i3 in the paper are tmp4..tmp7 here. |
226 | */ |
227 | |
228 | z1 = tmp4 + tmp7; |
229 | z2 = tmp5 + tmp6; |
230 | z3 = tmp4 + tmp6; |
231 | z4 = tmp5 + tmp7; |
232 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ |
233 | |
234 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ |
235 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ |
236 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ |
237 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ |
238 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ |
239 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ |
240 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ |
241 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ |
242 | |
243 | z3 += z5; |
244 | z4 += z5; |
245 | |
246 | dataptr[7] = (int16_t) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); |
247 | dataptr[5] = (int16_t) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); |
248 | dataptr[3] = (int16_t) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); |
249 | dataptr[1] = (int16_t) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); |
250 | |
251 | dataptr += DCTSIZE; /* advance pointer to next row */ |
252 | } |
253 | } |
254 | |
255 | /* |
256 | * Perform the forward DCT on one block of samples. |
257 | */ |
258 | |
259 | GLOBAL(void) |
260 | FUNC(ff_jpeg_fdct_islow)(int16_t *data) |
261 | { |
262 | int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
263 | int tmp10, tmp11, tmp12, tmp13; |
264 | int z1, z2, z3, z4, z5; |
265 | int16_t *dataptr; |
266 | int ctr; |
267 | |
268 | FUNC(row_fdct)(data); |
269 | |
270 | /* Pass 2: process columns. |
271 | * We remove the PASS1_BITS scaling, but leave the results scaled up |
272 | * by an overall factor of 8. |
273 | */ |
274 | |
275 | dataptr = data; |
276 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
277 | tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; |
278 | tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; |
279 | tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; |
280 | tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; |
281 | tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; |
282 | tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; |
283 | tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; |
284 | tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; |
285 | |
286 | /* Even part per LL&M figure 1 --- note that published figure is faulty; |
287 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". |
288 | */ |
289 | |
290 | tmp10 = tmp0 + tmp3; |
291 | tmp13 = tmp0 - tmp3; |
292 | tmp11 = tmp1 + tmp2; |
293 | tmp12 = tmp1 - tmp2; |
294 | |
295 | dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT); |
296 | dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT); |
297 | |
298 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |
299 | dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |
300 | CONST_BITS + OUT_SHIFT); |
301 | dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |
302 | CONST_BITS + OUT_SHIFT); |
303 | |
304 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2). |
305 | * cK represents cos(K*pi/16). |
306 | * i0..i3 in the paper are tmp4..tmp7 here. |
307 | */ |
308 | |
309 | z1 = tmp4 + tmp7; |
310 | z2 = tmp5 + tmp6; |
311 | z3 = tmp4 + tmp6; |
312 | z4 = tmp5 + tmp7; |
313 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ |
314 | |
315 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ |
316 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ |
317 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ |
318 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ |
319 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ |
320 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ |
321 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ |
322 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ |
323 | |
324 | z3 += z5; |
325 | z4 += z5; |
326 | |
327 | dataptr[DCTSIZE*7] = DESCALE(tmp4 + z1 + z3, CONST_BITS + OUT_SHIFT); |
328 | dataptr[DCTSIZE*5] = DESCALE(tmp5 + z2 + z4, CONST_BITS + OUT_SHIFT); |
329 | dataptr[DCTSIZE*3] = DESCALE(tmp6 + z2 + z3, CONST_BITS + OUT_SHIFT); |
330 | dataptr[DCTSIZE*1] = DESCALE(tmp7 + z1 + z4, CONST_BITS + OUT_SHIFT); |
331 | |
332 | dataptr++; /* advance pointer to next column */ |
333 | } |
334 | } |
335 | |
336 | /* |
337 | * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT |
338 | * on the rows and then, instead of doing even and odd, part on the columns |
339 | * you do even part two times. |
340 | */ |
341 | GLOBAL(void) |
342 | FUNC(ff_fdct248_islow)(int16_t *data) |
343 | { |
344 | int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
345 | int tmp10, tmp11, tmp12, tmp13; |
346 | int z1; |
347 | int16_t *dataptr; |
348 | int ctr; |
349 | |
350 | FUNC(row_fdct)(data); |
351 | |
352 | /* Pass 2: process columns. |
353 | * We remove the PASS1_BITS scaling, but leave the results scaled up |
354 | * by an overall factor of 8. |
355 | */ |
356 | |
357 | dataptr = data; |
358 | for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { |
359 | tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1]; |
360 | tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3]; |
361 | tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5]; |
362 | tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7]; |
363 | tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1]; |
364 | tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3]; |
365 | tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5]; |
366 | tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7]; |
367 | |
368 | tmp10 = tmp0 + tmp3; |
369 | tmp11 = tmp1 + tmp2; |
370 | tmp12 = tmp1 - tmp2; |
371 | tmp13 = tmp0 - tmp3; |
372 | |
373 | dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT); |
374 | dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT); |
375 | |
376 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |
377 | dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |
378 | CONST_BITS+OUT_SHIFT); |
379 | dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |
380 | CONST_BITS+OUT_SHIFT); |
381 | |
382 | tmp10 = tmp4 + tmp7; |
383 | tmp11 = tmp5 + tmp6; |
384 | tmp12 = tmp5 - tmp6; |
385 | tmp13 = tmp4 - tmp7; |
386 | |
387 | dataptr[DCTSIZE*1] = DESCALE(tmp10 + tmp11, OUT_SHIFT); |
388 | dataptr[DCTSIZE*5] = DESCALE(tmp10 - tmp11, OUT_SHIFT); |
389 | |
390 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |
391 | dataptr[DCTSIZE*3] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |
392 | CONST_BITS + OUT_SHIFT); |
393 | dataptr[DCTSIZE*7] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |
394 | CONST_BITS + OUT_SHIFT); |
395 | |
396 | dataptr++; /* advance pointer to next column */ |
397 | } |
398 | } |
399 |