1/*
2 * jfdctint.c
3 *
4 * This file is part of the Independent JPEG Group's software.
5 *
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.
10 *
11 * This software is copyright (C) 1991-1996, Thomas G. Lane.
12 * All Rights Reserved except as specified below.
13 *
14 * Permission is hereby granted to use, copy, modify, and distribute this
15 * software (or portions thereof) for any purpose, without fee, subject to
16 * these conditions:
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.
27 *
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
30 * to acknowledge us.
31 *
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".
36 *
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.
40 *
41 * This file contains a slow-but-accurate integer implementation of the
42 * forward DCT (Discrete Cosine Transform).
43 *
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.
47 *
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.
57 */
58
59/**
60 * @file libavcodec/jfdctint.c
61 * Independent JPEG Group's slow & accurate dct.
62 */
63
64#include <stdlib.h>
65#include <stdio.h>
66#include "libavutil/common.h"
67#include "dsputil.h"
68
69#define SHIFT_TEMPS
70#define DCTSIZE 8
71#define BITS_IN_JSAMPLE 8
72#define GLOBAL(x) x
73#define RIGHT_SHIFT(x, n) ((x) >> (n))
74#define MULTIPLY16C16(var,const) ((var)*(const))
75
76#if 1 //def USE_ACCURATE_ROUNDING
77#define DESCALE(x,n)  RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
78#else
79#define DESCALE(x,n)  RIGHT_SHIFT(x, n)
80#endif
81
82
83/*
84 * This module is specialized to the case DCTSIZE = 8.
85 */
86
87#if DCTSIZE != 8
88  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
89#endif
90
91
92/*
93 * The poop on this scaling stuff is as follows:
94 *
95 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
96 * larger than the true DCT outputs.  The final outputs are therefore
97 * a factor of N larger than desired; since N=8 this can be cured by
98 * a simple right shift at the end of the algorithm.  The advantage of
99 * this arrangement is that we save two multiplications per 1-D DCT,
100 * because the y0 and y4 outputs need not be divided by sqrt(N).
101 * In the IJG code, this factor of 8 is removed by the quantization step
102 * (in jcdctmgr.c), NOT in this module.
103 *
104 * We have to do addition and subtraction of the integer inputs, which
105 * is no problem, and multiplication by fractional constants, which is
106 * a problem to do in integer arithmetic.  We multiply all the constants
107 * by CONST_SCALE and convert them to integer constants (thus retaining
108 * CONST_BITS bits of precision in the constants).  After doing a
109 * multiplication we have to divide the product by CONST_SCALE, with proper
110 * rounding, to produce the correct output.  This division can be done
111 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
112 * as long as possible so that partial sums can be added together with
113 * full fractional precision.
114 *
115 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
116 * they are represented to better-than-integral precision.  These outputs
117 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
118 * with the recommended scaling.  (For 12-bit sample data, the intermediate
119 * array is int32_t anyway.)
120 *
121 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
122 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
123 * shows that the values given below are the most effective.
124 */
125
126#if BITS_IN_JSAMPLE == 8
127#define CONST_BITS  13
128#define PASS1_BITS  4   /* set this to 2 if 16x16 multiplies are faster */
129#else
130#define CONST_BITS  13
131#define PASS1_BITS  1   /* lose a little precision to avoid overflow */
132#endif
133
134/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
135 * causing a lot of useless floating-point operations at run time.
136 * To get around this we use the following pre-calculated constants.
137 * If you change CONST_BITS you may want to add appropriate values.
138 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
139 */
140
141#if CONST_BITS == 13
142#define FIX_0_298631336  ((int32_t)  2446)      /* FIX(0.298631336) */
143#define FIX_0_390180644  ((int32_t)  3196)      /* FIX(0.390180644) */
144#define FIX_0_541196100  ((int32_t)  4433)      /* FIX(0.541196100) */
145#define FIX_0_765366865  ((int32_t)  6270)      /* FIX(0.765366865) */
146#define FIX_0_899976223  ((int32_t)  7373)      /* FIX(0.899976223) */
147#define FIX_1_175875602  ((int32_t)  9633)      /* FIX(1.175875602) */
148#define FIX_1_501321110  ((int32_t)  12299)     /* FIX(1.501321110) */
149#define FIX_1_847759065  ((int32_t)  15137)     /* FIX(1.847759065) */
150#define FIX_1_961570560  ((int32_t)  16069)     /* FIX(1.961570560) */
151#define FIX_2_053119869  ((int32_t)  16819)     /* FIX(2.053119869) */
152#define FIX_2_562915447  ((int32_t)  20995)     /* FIX(2.562915447) */
153#define FIX_3_072711026  ((int32_t)  25172)     /* FIX(3.072711026) */
154#else
155#define FIX_0_298631336  FIX(0.298631336)
156#define FIX_0_390180644  FIX(0.390180644)
157#define FIX_0_541196100  FIX(0.541196100)
158#define FIX_0_765366865  FIX(0.765366865)
159#define FIX_0_899976223  FIX(0.899976223)
160#define FIX_1_175875602  FIX(1.175875602)
161#define FIX_1_501321110  FIX(1.501321110)
162#define FIX_1_847759065  FIX(1.847759065)
163#define FIX_1_961570560  FIX(1.961570560)
164#define FIX_2_053119869  FIX(2.053119869)
165#define FIX_2_562915447  FIX(2.562915447)
166#define FIX_3_072711026  FIX(3.072711026)
167#endif
168
169
170/* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
171 * For 8-bit samples with the recommended scaling, all the variable
172 * and constant values involved are no more than 16 bits wide, so a
173 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
174 * For 12-bit samples, a full 32-bit multiplication will be needed.
175 */
176
177#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
178#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
179#else
180#define MULTIPLY(var,const)  ((var) * (const))
181#endif
182
183
184static av_always_inline void row_fdct(DCTELEM * data){
185  int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
186  int_fast32_t tmp10, tmp11, tmp12, tmp13;
187  int_fast32_t z1, z2, z3, z4, z5;
188  DCTELEM *dataptr;
189  int ctr;
190  SHIFT_TEMPS
191
192  /* Pass 1: process rows. */
193  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
194  /* furthermore, we scale the results by 2**PASS1_BITS. */
195
196  dataptr = data;
197  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
198    tmp0 = dataptr[0] + dataptr[7];
199    tmp7 = dataptr[0] - dataptr[7];
200    tmp1 = dataptr[1] + dataptr[6];
201    tmp6 = dataptr[1] - dataptr[6];
202    tmp2 = dataptr[2] + dataptr[5];
203    tmp5 = dataptr[2] - dataptr[5];
204    tmp3 = dataptr[3] + dataptr[4];
205    tmp4 = dataptr[3] - dataptr[4];
206
207    /* Even part per LL&M figure 1 --- note that published figure is faulty;
208     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
209     */
210
211    tmp10 = tmp0 + tmp3;
212    tmp13 = tmp0 - tmp3;
213    tmp11 = tmp1 + tmp2;
214    tmp12 = tmp1 - tmp2;
215
216    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
217    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
218
219    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
220    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
221                                   CONST_BITS-PASS1_BITS);
222    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
223                                   CONST_BITS-PASS1_BITS);
224
225    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
226     * cK represents cos(K*pi/16).
227     * i0..i3 in the paper are tmp4..tmp7 here.
228     */
229
230    z1 = tmp4 + tmp7;
231    z2 = tmp5 + tmp6;
232    z3 = tmp4 + tmp6;
233    z4 = tmp5 + tmp7;
234    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
235
236    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
237    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
238    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
239    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
240    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
241    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
242    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
243    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
244
245    z3 += z5;
246    z4 += z5;
247
248    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
249    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
250    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
251    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
252
253    dataptr += DCTSIZE;         /* advance pointer to next row */
254  }
255}
256
257/*
258 * Perform the forward DCT on one block of samples.
259 */
260
261GLOBAL(void)
262ff_jpeg_fdct_islow (DCTELEM * data)
263{
264  int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
265  int_fast32_t tmp10, tmp11, tmp12, tmp13;
266  int_fast32_t z1, z2, z3, z4, z5;
267  DCTELEM *dataptr;
268  int ctr;
269  SHIFT_TEMPS
270
271  row_fdct(data);
272
273  /* Pass 2: process columns.
274   * We remove the PASS1_BITS scaling, but leave the results scaled up
275   * by an overall factor of 8.
276   */
277
278  dataptr = data;
279  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
280    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
281    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
282    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
283    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
284    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
285    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
286    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
287    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
288
289    /* Even part per LL&M figure 1 --- note that published figure is faulty;
290     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
291     */
292
293    tmp10 = tmp0 + tmp3;
294    tmp13 = tmp0 - tmp3;
295    tmp11 = tmp1 + tmp2;
296    tmp12 = tmp1 - tmp2;
297
298    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
299    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
300
301    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
302    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
303                                           CONST_BITS+PASS1_BITS);
304    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
305                                           CONST_BITS+PASS1_BITS);
306
307    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
308     * cK represents cos(K*pi/16).
309     * i0..i3 in the paper are tmp4..tmp7 here.
310     */
311
312    z1 = tmp4 + tmp7;
313    z2 = tmp5 + tmp6;
314    z3 = tmp4 + tmp6;
315    z4 = tmp5 + tmp7;
316    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
317
318    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
319    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
320    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
321    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
322    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
323    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
324    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
325    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
326
327    z3 += z5;
328    z4 += z5;
329
330    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
331                                           CONST_BITS+PASS1_BITS);
332    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
333                                           CONST_BITS+PASS1_BITS);
334    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
335                                           CONST_BITS+PASS1_BITS);
336    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
337                                           CONST_BITS+PASS1_BITS);
338
339    dataptr++;                  /* advance pointer to next column */
340  }
341}
342
343/*
344 * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
345 * on the rows and then, instead of doing even and odd, part on the colums
346 * you do even part two times.
347 */
348GLOBAL(void)
349ff_fdct248_islow (DCTELEM * data)
350{
351  int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
352  int_fast32_t tmp10, tmp11, tmp12, tmp13;
353  int_fast32_t z1;
354  DCTELEM *dataptr;
355  int ctr;
356  SHIFT_TEMPS
357
358  row_fdct(data);
359
360  /* Pass 2: process columns.
361   * We remove the PASS1_BITS scaling, but leave the results scaled up
362   * by an overall factor of 8.
363   */
364
365  dataptr = data;
366  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
367     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
368     tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
369     tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
370     tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
371     tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
372     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
373     tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
374     tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
375
376     tmp10 = tmp0 + tmp3;
377     tmp11 = tmp1 + tmp2;
378     tmp12 = tmp1 - tmp2;
379     tmp13 = tmp0 - tmp3;
380
381     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
382     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
383
384     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
385     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
386                                            CONST_BITS+PASS1_BITS);
387     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
388                                            CONST_BITS+PASS1_BITS);
389
390     tmp10 = tmp4 + tmp7;
391     tmp11 = tmp5 + tmp6;
392     tmp12 = tmp5 - tmp6;
393     tmp13 = tmp4 - tmp7;
394
395     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
396     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
397
398     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
399     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
400                                            CONST_BITS+PASS1_BITS);
401     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
402                                            CONST_BITS+PASS1_BITS);
403
404     dataptr++;                 /* advance pointer to next column */
405  }
406}
407