4 * This file is part of the Independent JPEG Group's software.
6 * The authors make NO WARRANTY or representation, either express or implied,
7 * with respect to this software, its quality, accuracy, merchantability, or
8 * fitness for a particular purpose. This software is provided "AS IS", and
9 * you, its user, assume the entire risk as to its quality and accuracy.
11 * This software is copyright (C) 1991-1996, Thomas G. Lane.
12 * All Rights Reserved except as specified below.
14 * Permission is hereby granted to use, copy, modify, and distribute this
15 * software (or portions thereof) for any purpose, without fee, subject to
17 * (1) If any part of the source code for this software is distributed, then
18 * this README file must be included, with this copyright and no-warranty
19 * notice unaltered; and any additions, deletions, or changes to the original
20 * files must be clearly indicated in accompanying documentation.
21 * (2) If only executable code is distributed, then the accompanying
22 * documentation must state that "this software is based in part on the work
23 * of the Independent JPEG Group".
24 * (3) Permission for use of this software is granted only if the user accepts
25 * full responsibility for any undesirable consequences; the authors accept
26 * NO LIABILITY for damages of any kind.
28 * These conditions apply to any software derived from or based on the IJG
29 * code, not just to the unmodified library. If you use our work, you ought
32 * Permission is NOT granted for the use of any IJG author's name or company
33 * name in advertising or publicity relating to this software or products
34 * derived from it. This software may be referred to only as "the Independent
35 * JPEG Group's software".
37 * We specifically permit and encourage the use of this software as the basis
38 * of commercial products, provided that all warranty or liability claims are
39 * assumed by the product vendor.
41 * This file contains a slow-but-accurate integer implementation of the
42 * forward DCT (Discrete Cosine Transform).
44 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
45 * on each column. Direct algorithms are also available, but they are
46 * much more complex and seem not to be any faster when reduced to code.
48 * This implementation is based on an algorithm described in
49 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
50 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
51 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
52 * The primary algorithm described there uses 11 multiplies and 29 adds.
53 * We use their alternate method with 12 multiplies and 32 adds.
54 * The advantage of this method is that no data path contains more than one
55 * multiplication; this allows a very simple and accurate implementation in
56 * scaled fixed-point arithmetic, with a minimal number of shifts.
60 * @file libavcodec/jfdctint.c
61 * Independent JPEG Group's slow & accurate dct.
66 #include "libavutil/common.h"
70 #define BITS_IN_JSAMPLE 8
72 #define RIGHT_SHIFT(x, n) ((x) >> (n))
73 #define MULTIPLY16C16(var,const) ((var)*(const))
75 #if 1 //def USE_ACCURATE_ROUNDING
76 #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
78 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
83 * This module is specialized to the case DCTSIZE = 8.
87 Sorry
, this code only copes with
8x8 DCTs
. /* deliberate syntax err */
92 * The poop on this scaling stuff is as follows:
94 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
95 * larger than the true DCT outputs. The final outputs are therefore
96 * a factor of N larger than desired; since N=8 this can be cured by
97 * a simple right shift at the end of the algorithm. The advantage of
98 * this arrangement is that we save two multiplications per 1-D DCT,
99 * because the y0 and y4 outputs need not be divided by sqrt(N).
100 * In the IJG code, this factor of 8 is removed by the quantization step
101 * (in jcdctmgr.c), NOT in this module.
103 * We have to do addition and subtraction of the integer inputs, which
104 * is no problem, and multiplication by fractional constants, which is
105 * a problem to do in integer arithmetic. We multiply all the constants
106 * by CONST_SCALE and convert them to integer constants (thus retaining
107 * CONST_BITS bits of precision in the constants). After doing a
108 * multiplication we have to divide the product by CONST_SCALE, with proper
109 * rounding, to produce the correct output. This division can be done
110 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
111 * as long as possible so that partial sums can be added together with
112 * full fractional precision.
114 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
115 * they are represented to better-than-integral precision. These outputs
116 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
117 * with the recommended scaling. (For 12-bit sample data, the intermediate
118 * array is int32_t anyway.)
120 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
121 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
122 * shows that the values given below are the most effective.
125 #if BITS_IN_JSAMPLE == 8
126 #define CONST_BITS 13
127 #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
129 #define CONST_BITS 13
130 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
133 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
134 * causing a lot of useless floating-point operations at run time.
135 * To get around this we use the following pre-calculated constants.
136 * If you change CONST_BITS you may want to add appropriate values.
137 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
141 #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
142 #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
143 #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
144 #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
145 #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
146 #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
147 #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
148 #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
149 #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
150 #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
151 #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
152 #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
154 #define FIX_0_298631336 FIX(0.298631336)
155 #define FIX_0_390180644 FIX(0.390180644)
156 #define FIX_0_541196100 FIX(0.541196100)
157 #define FIX_0_765366865 FIX(0.765366865)
158 #define FIX_0_899976223 FIX(0.899976223)
159 #define FIX_1_175875602 FIX(1.175875602)
160 #define FIX_1_501321110 FIX(1.501321110)
161 #define FIX_1_847759065 FIX(1.847759065)
162 #define FIX_1_961570560 FIX(1.961570560)
163 #define FIX_2_053119869 FIX(2.053119869)
164 #define FIX_2_562915447 FIX(2.562915447)
165 #define FIX_3_072711026 FIX(3.072711026)
169 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
170 * For 8-bit samples with the recommended scaling, all the variable
171 * and constant values involved are no more than 16 bits wide, so a
172 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
173 * For 12-bit samples, a full 32-bit multiplication will be needed.
176 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
177 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
179 #define MULTIPLY(var,const) ((var) * (const))
183 static av_always_inline
void row_fdct(DCTELEM
* data
){
184 int_fast32_t tmp0
, tmp1
, tmp2
, tmp3
, tmp4
, tmp5
, tmp6
, tmp7
;
185 int_fast32_t tmp10
, tmp11
, tmp12
, tmp13
;
186 int_fast32_t z1
, z2
, z3
, z4
, z5
;
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. */
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];
205 /* Even part per LL&M figure 1 --- note that published figure is faulty;
206 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
214 dataptr
[0] = (DCTELEM
) ((tmp10
+ tmp11
) << PASS1_BITS
);
215 dataptr
[4] = (DCTELEM
) ((tmp10
- tmp11
) << PASS1_BITS
);
217 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_541196100
);
218 dataptr
[2] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp13
, FIX_0_765366865
),
219 CONST_BITS
-PASS1_BITS
);
220 dataptr
[6] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp12
, - FIX_1_847759065
),
221 CONST_BITS
-PASS1_BITS
);
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.
232 z5
= MULTIPLY(z3
+ z4
, FIX_1_175875602
); /* sqrt(2) * c3 */
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) */
246 dataptr
[7] = (DCTELEM
) DESCALE(tmp4
+ z1
+ z3
, CONST_BITS
-PASS1_BITS
);
247 dataptr
[5] = (DCTELEM
) DESCALE(tmp5
+ z2
+ z4
, CONST_BITS
-PASS1_BITS
);
248 dataptr
[3] = (DCTELEM
) DESCALE(tmp6
+ z2
+ z3
, CONST_BITS
-PASS1_BITS
);
249 dataptr
[1] = (DCTELEM
) DESCALE(tmp7
+ z1
+ z4
, CONST_BITS
-PASS1_BITS
);
251 dataptr
+= DCTSIZE
; /* advance pointer to next row */
256 * Perform the forward DCT on one block of samples.
260 ff_jpeg_fdct_islow (DCTELEM
* data
)
262 int_fast32_t tmp0
, tmp1
, tmp2
, tmp3
, tmp4
, tmp5
, tmp6
, tmp7
;
263 int_fast32_t tmp10
, tmp11
, tmp12
, tmp13
;
264 int_fast32_t z1
, z2
, z3
, z4
, z5
;
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.
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];
286 /* Even part per LL&M figure 1 --- note that published figure is faulty;
287 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
295 dataptr
[DCTSIZE
*0] = (DCTELEM
) DESCALE(tmp10
+ tmp11
, PASS1_BITS
);
296 dataptr
[DCTSIZE
*4] = (DCTELEM
) DESCALE(tmp10
- tmp11
, PASS1_BITS
);
298 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_541196100
);
299 dataptr
[DCTSIZE
*2] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp13
, FIX_0_765366865
),
300 CONST_BITS
+PASS1_BITS
);
301 dataptr
[DCTSIZE
*6] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp12
, - FIX_1_847759065
),
302 CONST_BITS
+PASS1_BITS
);
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.
313 z5
= MULTIPLY(z3
+ z4
, FIX_1_175875602
); /* sqrt(2) * c3 */
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) */
327 dataptr
[DCTSIZE
*7] = (DCTELEM
) DESCALE(tmp4
+ z1
+ z3
,
328 CONST_BITS
+PASS1_BITS
);
329 dataptr
[DCTSIZE
*5] = (DCTELEM
) DESCALE(tmp5
+ z2
+ z4
,
330 CONST_BITS
+PASS1_BITS
);
331 dataptr
[DCTSIZE
*3] = (DCTELEM
) DESCALE(tmp6
+ z2
+ z3
,
332 CONST_BITS
+PASS1_BITS
);
333 dataptr
[DCTSIZE
*1] = (DCTELEM
) DESCALE(tmp7
+ z1
+ z4
,
334 CONST_BITS
+PASS1_BITS
);
336 dataptr
++; /* advance pointer to next column */
341 * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
342 * on the rows and then, instead of doing even and odd, part on the colums
343 * you do even part two times.
346 ff_fdct248_islow (DCTELEM
* data
)
348 int_fast32_t tmp0
, tmp1
, tmp2
, tmp3
, tmp4
, tmp5
, tmp6
, tmp7
;
349 int_fast32_t tmp10
, tmp11
, tmp12
, tmp13
;
356 /* Pass 2: process columns.
357 * We remove the PASS1_BITS scaling, but leave the results scaled up
358 * by an overall factor of 8.
362 for (ctr
= DCTSIZE
-1; ctr
>= 0; ctr
--) {
363 tmp0
= dataptr
[DCTSIZE
*0] + dataptr
[DCTSIZE
*1];
364 tmp1
= dataptr
[DCTSIZE
*2] + dataptr
[DCTSIZE
*3];
365 tmp2
= dataptr
[DCTSIZE
*4] + dataptr
[DCTSIZE
*5];
366 tmp3
= dataptr
[DCTSIZE
*6] + dataptr
[DCTSIZE
*7];
367 tmp4
= dataptr
[DCTSIZE
*0] - dataptr
[DCTSIZE
*1];
368 tmp5
= dataptr
[DCTSIZE
*2] - dataptr
[DCTSIZE
*3];
369 tmp6
= dataptr
[DCTSIZE
*4] - dataptr
[DCTSIZE
*5];
370 tmp7
= dataptr
[DCTSIZE
*6] - dataptr
[DCTSIZE
*7];
377 dataptr
[DCTSIZE
*0] = (DCTELEM
) DESCALE(tmp10
+ tmp11
, PASS1_BITS
);
378 dataptr
[DCTSIZE
*4] = (DCTELEM
) DESCALE(tmp10
- tmp11
, PASS1_BITS
);
380 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_541196100
);
381 dataptr
[DCTSIZE
*2] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp13
, FIX_0_765366865
),
382 CONST_BITS
+PASS1_BITS
);
383 dataptr
[DCTSIZE
*6] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp12
, - FIX_1_847759065
),
384 CONST_BITS
+PASS1_BITS
);
391 dataptr
[DCTSIZE
*1] = (DCTELEM
) DESCALE(tmp10
+ tmp11
, PASS1_BITS
);
392 dataptr
[DCTSIZE
*5] = (DCTELEM
) DESCALE(tmp10
- tmp11
, PASS1_BITS
);
394 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_541196100
);
395 dataptr
[DCTSIZE
*3] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp13
, FIX_0_765366865
),
396 CONST_BITS
+PASS1_BITS
);
397 dataptr
[DCTSIZE
*7] = (DCTELEM
) DESCALE(z1
+ MULTIPLY(tmp12
, - FIX_1_847759065
),
398 CONST_BITS
+PASS1_BITS
);
400 dataptr
++; /* advance pointer to next column */