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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 
73 #if 1 //def USE_ACCURATE_ROUNDING
74 #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
75 #else
76 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
77 #endif
78 
79 
80 /*
81  * This module is specialized to the case DCTSIZE = 8.
82  */
83 
84 #if DCTSIZE != 8
85 #error "Sorry, this code only copes with 8x8 DCTs."
86 #endif
87 
88 
89 /*
90  * The poop on this scaling stuff is as follows:
91  *
92  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
93  * larger than the true DCT outputs. The final outputs are therefore
94  * a factor of N larger than desired; since N=8 this can be cured by
95  * a simple right shift at the end of the algorithm. The advantage of
96  * this arrangement is that we save two multiplications per 1-D DCT,
97  * because the y0 and y4 outputs need not be divided by sqrt(N).
98  * In the IJG code, this factor of 8 is removed by the quantization step
99  * (in jcdctmgr.c), NOT in this module.
100  *
101  * We have to do addition and subtraction of the integer inputs, which
102  * is no problem, and multiplication by fractional constants, which is
103  * a problem to do in integer arithmetic. We multiply all the constants
104  * by CONST_SCALE and convert them to integer constants (thus retaining
105  * CONST_BITS bits of precision in the constants). After doing a
106  * multiplication we have to divide the product by CONST_SCALE, with proper
107  * rounding, to produce the correct output. This division can be done
108  * cheaply as a right shift of CONST_BITS bits. We postpone shifting
109  * as long as possible so that partial sums can be added together with
110  * full fractional precision.
111  *
112  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
113  * they are represented to better-than-integral precision. These outputs
114  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
115  * with the recommended scaling. (For 12-bit sample data, the intermediate
116  * array is int32_t anyway.)
117  *
118  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
119  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
120  * shows that the values given below are the most effective.
121  */
122 
123 #undef CONST_BITS
124 #undef PASS1_BITS
125 #undef OUT_SHIFT
126 
127 #if BITS_IN_JSAMPLE == 8
128 #define CONST_BITS 13
129 #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
130 #define OUT_SHIFT PASS1_BITS
131 #else
132 #define CONST_BITS 13
133 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
134 #define OUT_SHIFT (PASS1_BITS + 1)
135 #endif
136 
137 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
138  * causing a lot of useless floating-point operations at run time.
139  * To get around this we use the following pre-calculated constants.
140  * If you change CONST_BITS you may want to add appropriate values.
141  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
142  */
143 
144 #if CONST_BITS == 13
145 #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
146 #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
147 #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
148 #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
149 #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
150 #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
151 #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
152 #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
153 #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
154 #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
155 #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
156 #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
157 #else
158 #define FIX_0_298631336 FIX(0.298631336)
159 #define FIX_0_390180644 FIX(0.390180644)
160 #define FIX_0_541196100 FIX(0.541196100)
161 #define FIX_0_765366865 FIX(0.765366865)
162 #define FIX_0_899976223 FIX(0.899976223)
163 #define FIX_1_175875602 FIX(1.175875602)
164 #define FIX_1_501321110 FIX(1.501321110)
165 #define FIX_1_847759065 FIX(1.847759065)
166 #define FIX_1_961570560 FIX(1.961570560)
167 #define FIX_2_053119869 FIX(2.053119869)
168 #define FIX_2_562915447 FIX(2.562915447)
169 #define FIX_3_072711026 FIX(3.072711026)
170 #endif
171 
172 
173 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
174  * For 8-bit samples with the recommended scaling, all the variable
175  * and constant values involved are no more than 16 bits wide, so a
176  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
177  * For 12-bit samples, a full 32-bit multiplication will be needed.
178  */
179 
180 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
181 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
182 #else
183 #define MULTIPLY(var,const) ((var) * (const))
184 #endif
185 
186 
187 static av_always_inline void FUNC(row_fdct)(int16_t *data)
188 {
189  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
190  int tmp10, tmp11, tmp12, tmp13;
191  int z1, z2, z3, z4, z5;
192  int16_t *dataptr;
193  int ctr;
194 
195  /* Pass 1: process rows. */
196  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
197  /* furthermore, we scale the results by 2**PASS1_BITS. */
198 
199  dataptr = data;
200  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
201  tmp0 = dataptr[0] + dataptr[7];
202  tmp7 = dataptr[0] - dataptr[7];
203  tmp1 = dataptr[1] + dataptr[6];
204  tmp6 = dataptr[1] - dataptr[6];
205  tmp2 = dataptr[2] + dataptr[5];
206  tmp5 = dataptr[2] - dataptr[5];
207  tmp3 = dataptr[3] + dataptr[4];
208  tmp4 = dataptr[3] - dataptr[4];
209 
210  /* Even part per LL&M figure 1 --- note that published figure is faulty;
211  * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
212  */
213 
214  tmp10 = tmp0 + tmp3;
215  tmp13 = tmp0 - tmp3;
216  tmp11 = tmp1 + tmp2;
217  tmp12 = tmp1 - tmp2;
218 
219  dataptr[0] = (int16_t) ((tmp10 + tmp11) * (1 << PASS1_BITS));
220  dataptr[4] = (int16_t) ((tmp10 - tmp11) * (1 << PASS1_BITS));
221 
222  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
223  dataptr[2] = (int16_t) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
225  dataptr[6] = (int16_t) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
227 
228  /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
229  * cK represents cos(K*pi/16).
230  * i0..i3 in the paper are tmp4..tmp7 here.
231  */
232 
233  z1 = tmp4 + tmp7;
234  z2 = tmp5 + tmp6;
235  z3 = tmp4 + tmp6;
236  z4 = tmp5 + tmp7;
237  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
238 
239  tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
240  tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
241  tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
242  tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
243  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
244  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
245  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
246  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
247 
248  z3 += z5;
249  z4 += z5;
250 
251  dataptr[7] = (int16_t) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
252  dataptr[5] = (int16_t) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
253  dataptr[3] = (int16_t) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
254  dataptr[1] = (int16_t) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
255 
256  dataptr += DCTSIZE; /* advance pointer to next row */
257  }
258 }
259 
260 /*
261  * Perform the forward DCT on one block of samples.
262  */
263 
264 GLOBAL(void)
266 {
267  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
268  int tmp10, tmp11, tmp12, tmp13;
269  int z1, z2, z3, z4, z5;
270  int16_t *dataptr;
271  int ctr;
272 
273  FUNC(row_fdct)(data);
274 
275  /* Pass 2: process columns.
276  * We remove the PASS1_BITS scaling, but leave the results scaled up
277  * by an overall factor of 8.
278  */
279 
280  dataptr = data;
281  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
282  tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
283  tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
284  tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
285  tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
286  tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
287  tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
288  tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
289  tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
290 
291  /* Even part per LL&M figure 1 --- note that published figure is faulty;
292  * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
293  */
294 
295  tmp10 = tmp0 + tmp3;
296  tmp13 = tmp0 - tmp3;
297  tmp11 = tmp1 + tmp2;
298  tmp12 = tmp1 - tmp2;
299 
300  dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
301  dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
302 
303  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
304  dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
306  dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
308 
309  /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
310  * cK represents cos(K*pi/16).
311  * i0..i3 in the paper are tmp4..tmp7 here.
312  */
313 
314  z1 = tmp4 + tmp7;
315  z2 = tmp5 + tmp6;
316  z3 = tmp4 + tmp6;
317  z4 = tmp5 + tmp7;
318  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
319 
320  tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
321  tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
322  tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
323  tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
324  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
325  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
326  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
327  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
328 
329  z3 += z5;
330  z4 += z5;
331 
332  dataptr[DCTSIZE*7] = DESCALE(tmp4 + z1 + z3, CONST_BITS + OUT_SHIFT);
333  dataptr[DCTSIZE*5] = DESCALE(tmp5 + z2 + z4, CONST_BITS + OUT_SHIFT);
334  dataptr[DCTSIZE*3] = DESCALE(tmp6 + z2 + z3, CONST_BITS + OUT_SHIFT);
335  dataptr[DCTSIZE*1] = DESCALE(tmp7 + z1 + z4, CONST_BITS + OUT_SHIFT);
336 
337  dataptr++; /* advance pointer to next column */
338  }
339 }
340 
341 /*
342  * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
343  * on the rows and then, instead of doing even and odd, part on the columns
344  * you do even part two times.
345  */
346 GLOBAL(void)
348 {
349  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
350  int tmp10, tmp11, tmp12, tmp13;
351  int z1;
352  int16_t *dataptr;
353  int ctr;
354 
355  FUNC(row_fdct)(data);
356 
357  /* Pass 2: process columns.
358  * We remove the PASS1_BITS scaling, but leave the results scaled up
359  * by an overall factor of 8.
360  */
361 
362  dataptr = data;
363  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
364  tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
365  tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
366  tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
367  tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
368  tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
369  tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
370  tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
371  tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
372 
373  tmp10 = tmp0 + tmp3;
374  tmp11 = tmp1 + tmp2;
375  tmp12 = tmp1 - tmp2;
376  tmp13 = tmp0 - tmp3;
377 
378  dataptr[DCTSIZE*0] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
379  dataptr[DCTSIZE*4] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
380 
381  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
382  dataptr[DCTSIZE*2] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
384  dataptr[DCTSIZE*6] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
386 
387  tmp10 = tmp4 + tmp7;
388  tmp11 = tmp5 + tmp6;
389  tmp12 = tmp5 - tmp6;
390  tmp13 = tmp4 - tmp7;
391 
392  dataptr[DCTSIZE*1] = DESCALE(tmp10 + tmp11, OUT_SHIFT);
393  dataptr[DCTSIZE*5] = DESCALE(tmp10 - tmp11, OUT_SHIFT);
394 
395  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
396  dataptr[DCTSIZE*3] = DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
398  dataptr[DCTSIZE*7] = DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
400 
401  dataptr++; /* advance pointer to next column */
402  }
403 }