FFmpeg
jfdctint_template.c
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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 }
FIX_1_175875602
#define FIX_1_175875602
Definition: jfdctint_template.c:145
data
const char data[16]
Definition: mxf.c:143
PASS1_BITS
#define PASS1_BITS
Definition: jfdctint_template.c:128
GLOBAL
#define GLOBAL(x)
Definition: jfdctint_template.c:69
ff_fdct248_islow
FUNC() ff_fdct248_islow(int16_t *data)
Definition: jfdctint_template.c:342
FIX_3_072711026
#define FIX_3_072711026
Definition: jfdctint_template.c:151
FIX_0_298631336
#define FIX_0_298631336
Definition: jfdctint_template.c:140
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#define FIX_0_765366865
Definition: jfdctint_template.c:143
bit_depth_template.c
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#define DESCALE(x, n)
Definition: jfdctint_template.c:72
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#define MULTIPLY(var, const)
Definition: jfdctint_template.c:178
FIX_1_961570560
#define FIX_1_961570560
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#define FIX_2_562915447
Definition: jfdctint_template.c:150
FIX_1_847759065
#define FIX_1_847759065
Definition: jfdctint_template.c:147
common.h
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#define av_always_inline
Definition: attributes.h:49
FIX_0_541196100
#define FIX_0_541196100
Definition: jfdctint_template.c:142
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#define DCTSIZE
Definition: jfdctint_template.c:67
FIX_0_899976223
#define FIX_0_899976223
Definition: jfdctint_template.c:144
row_fdct
static av_always_inline void FUNC() row_fdct(int16_t *data)
Definition: jfdctint_template.c:182
FUNC
#define FUNC(a)
Definition: bit_depth_template.c:104
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#define OUT_SHIFT
Definition: jfdctint_template.c:129
CONST_BITS
#define CONST_BITS
Definition: jfdctint_template.c:127
FIX_0_390180644
#define FIX_0_390180644
Definition: jfdctint_template.c:141
FIX_1_501321110
#define FIX_1_501321110
Definition: jfdctint_template.c:146
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FUNC() ff_jpeg_fdct_islow(int16_t *data)
Definition: jfdctint_template.c:260
FIX_2_053119869
#define FIX_2_053119869
Definition: jfdctint_template.c:149
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