jfdctint.c@ 10184

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1	/*
2	* jfdctint.c
3	*
4	* Copyright (C) 1991-1996, Thomas G. Lane.
5	* This file is part of the Independent JPEG Group's software.
6	* For conditions of distribution and use, see the accompanying README file.
7	*
8	* This file contains a slow-but-accurate integer implementation of the
9	* forward DCT (Discrete Cosine Transform).
10	*
11	* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
12	* on each column. Direct algorithms are also available, but they are
13	* much more complex and seem not to be any faster when reduced to code.
14	*
15	* This implementation is based on an algorithm described in
16	* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
17	* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
18	* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
19	* The primary algorithm described there uses 11 multiplies and 29 adds.
20	* We use their alternate method with 12 multiplies and 32 adds.
21	* The advantage of this method is that no data path contains more than one
22	* multiplication; this allows a very simple and accurate implementation in
23	* scaled fixed-point arithmetic, with a minimal number of shifts.
24	*/
25
26	/**
27	* @file jfdctint.c
28	* Independent JPEG Group's slow & accurate dct.
29	*/
30
31	#include <stdlib.h>
32	#include <stdio.h>
33	#include "common.h"
34	#include "dsputil.h"
35
36	#define SHIFT_TEMPS
37	#define DCTSIZE 8
38	#define BITS_IN_JSAMPLE 8
39	#define GLOBAL(x) x
40	#define RIGHT_SHIFT(x, n) ((x) >> (n))
41	#define MULTIPLY16C16(var,const) ((var)*(const))
42
43	#if 1 //def USE_ACCURATE_ROUNDING
44	#define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
45	#else
46	#define DESCALE(x,n) RIGHT_SHIFT(x, n)
47	#endif
48
49
50	/*
51	* This module is specialized to the case DCTSIZE = 8.
52	*/
53
54	#if DCTSIZE != 8
55	Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
56	#endif
57
58
59	/*
60	* The poop on this scaling stuff is as follows:
61	*
62	* Each 1-D DCT step produces outputs which are a factor of sqrt(N)
63	* larger than the true DCT outputs. The final outputs are therefore
64	* a factor of N larger than desired; since N=8 this can be cured by
65	* a simple right shift at the end of the algorithm. The advantage of
66	* this arrangement is that we save two multiplications per 1-D DCT,
67	* because the y0 and y4 outputs need not be divided by sqrt(N).
68	* In the IJG code, this factor of 8 is removed by the quantization step
69	* (in jcdctmgr.c), NOT in this module.
70	*
71	* We have to do addition and subtraction of the integer inputs, which
72	* is no problem, and multiplication by fractional constants, which is
73	* a problem to do in integer arithmetic. We multiply all the constants
74	* by CONST_SCALE and convert them to integer constants (thus retaining
75	* CONST_BITS bits of precision in the constants). After doing a
76	* multiplication we have to divide the product by CONST_SCALE, with proper
77	* rounding, to produce the correct output. This division can be done
78	* cheaply as a right shift of CONST_BITS bits. We postpone shifting
79	* as long as possible so that partial sums can be added together with
80	* full fractional precision.
81	*
82	* The outputs of the first pass are scaled up by PASS1_BITS bits so that
83	* they are represented to better-than-integral precision. These outputs
84	* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
85	* with the recommended scaling. (For 12-bit sample data, the intermediate
86	* array is int32_t anyway.)
87	*
88	* To avoid overflow of the 32-bit intermediate results in pass 2, we must
89	* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
90	* shows that the values given below are the most effective.
91	*/
92
93	#if BITS_IN_JSAMPLE == 8
94	#define CONST_BITS 13
95	#define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
96	#else
97	#define CONST_BITS 13
98	#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
99	#endif
100
101	/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
102	* causing a lot of useless floating-point operations at run time.
103	* To get around this we use the following pre-calculated constants.
104	* If you change CONST_BITS you may want to add appropriate values.
105	* (With a reasonable C compiler, you can just rely on the FIX() macro...)
106	*/
107
108	#if CONST_BITS == 13
109	#define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
110	#define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
111	#define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
112	#define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
113	#define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
114	#define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
115	#define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
116	#define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
117	#define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
118	#define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
119	#define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
120	#define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
121	#else
122	#define FIX_0_298631336 FIX(0.298631336)
123	#define FIX_0_390180644 FIX(0.390180644)
124	#define FIX_0_541196100 FIX(0.541196100)
125	#define FIX_0_765366865 FIX(0.765366865)
126	#define FIX_0_899976223 FIX(0.899976223)
127	#define FIX_1_175875602 FIX(1.175875602)
128	#define FIX_1_501321110 FIX(1.501321110)
129	#define FIX_1_847759065 FIX(1.847759065)
130	#define FIX_1_961570560 FIX(1.961570560)
131	#define FIX_2_053119869 FIX(2.053119869)
132	#define FIX_2_562915447 FIX(2.562915447)
133	#define FIX_3_072711026 FIX(3.072711026)
134	#endif
135
136
137	/* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
138	* For 8-bit samples with the recommended scaling, all the variable
139	* and constant values involved are no more than 16 bits wide, so a
140	* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
141	* For 12-bit samples, a full 32-bit multiplication will be needed.
142	*/
143
144	#if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
145	#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
146	#else
147	#define MULTIPLY(var,const) ((var) * (const))
148	#endif
149
150
151	static always_inline void row_fdct(DCTELEM * data){
152	int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
153	int_fast32_t tmp10, tmp11, tmp12, tmp13;
154	int_fast32_t z1, z2, z3, z4, z5;
155	DCTELEM *dataptr;
156	int ctr;
157	SHIFT_TEMPS
158
159	/* Pass 1: process rows. */
160	/* Note results are scaled up by sqrt(8) compared to a true DCT; */
161	/* furthermore, we scale the results by 2*PASS1_BITS. /
162
163	dataptr = data;
164	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
165	tmp0 = dataptr[0] + dataptr[7];
166	tmp7 = dataptr[0] - dataptr[7];
167	tmp1 = dataptr[1] + dataptr[6];
168	tmp6 = dataptr[1] - dataptr[6];
169	tmp2 = dataptr[2] + dataptr[5];
170	tmp5 = dataptr[2] - dataptr[5];
171	tmp3 = dataptr[3] + dataptr[4];
172	tmp4 = dataptr[3] - dataptr[4];
173
174	/* Even part per LL&M figure 1 --- note that published figure is faulty;
175	* rotator "sqrt(2)c1" should be "sqrt(2)c6".
176	*/
177
178	tmp10 = tmp0 + tmp3;
179	tmp13 = tmp0 - tmp3;
180	tmp11 = tmp1 + tmp2;
181	tmp12 = tmp1 - tmp2;
182
183	dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
184	dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
185
186	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
187	dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
188	CONST_BITS-PASS1_BITS);
189	dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
190	CONST_BITS-PASS1_BITS);
191
192	/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
193	* cK represents cos(K*pi/16).
194	* i0..i3 in the paper are tmp4..tmp7 here.
195	*/
196
197	z1 = tmp4 + tmp7;
198	z2 = tmp5 + tmp6;
199	z3 = tmp4 + tmp6;
200	z4 = tmp5 + tmp7;
201	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
202
203	tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
204	tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
205	tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
206	tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
207	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
208	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
209	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
210	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
211
212	z3 += z5;
213	z4 += z5;
214
215	dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
216	dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
217	dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
218	dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
219
220	dataptr += DCTSIZE; /* advance pointer to next row */
221	}
222	}
223
224	/*
225	* Perform the forward DCT on one block of samples.
226	*/
227
228	GLOBAL(void)
229	ff_jpeg_fdct_islow (DCTELEM * data)
230	{
231	int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
232	int_fast32_t tmp10, tmp11, tmp12, tmp13;
233	int_fast32_t z1, z2, z3, z4, z5;
234	DCTELEM *dataptr;
235	int ctr;
236	SHIFT_TEMPS
237
238	row_fdct(data);
239
240	/* Pass 2: process columns.
241	* We remove the PASS1_BITS scaling, but leave the results scaled up
242	* by an overall factor of 8.
243	*/
244
245	dataptr = data;
246	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
247	tmp0 = dataptr[DCTSIZE0] + dataptr[DCTSIZE7];
248	tmp7 = dataptr[DCTSIZE0] - dataptr[DCTSIZE7];
249	tmp1 = dataptr[DCTSIZE1] + dataptr[DCTSIZE6];
250	tmp6 = dataptr[DCTSIZE1] - dataptr[DCTSIZE6];
251	tmp2 = dataptr[DCTSIZE2] + dataptr[DCTSIZE5];
252	tmp5 = dataptr[DCTSIZE2] - dataptr[DCTSIZE5];
253	tmp3 = dataptr[DCTSIZE3] + dataptr[DCTSIZE4];
254	tmp4 = dataptr[DCTSIZE3] - dataptr[DCTSIZE4];
255
256	/* Even part per LL&M figure 1 --- note that published figure is faulty;
257	* rotator "sqrt(2)c1" should be "sqrt(2)c6".
258	*/
259
260	tmp10 = tmp0 + tmp3;
261	tmp13 = tmp0 - tmp3;
262	tmp11 = tmp1 + tmp2;
263	tmp12 = tmp1 - tmp2;
264
265	dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
266	dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
267
268	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
269	dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
270	CONST_BITS+PASS1_BITS);
271	dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
272	CONST_BITS+PASS1_BITS);
273
274	/* Odd part per figure 8 --- note paper omits factor of sqrt(2).
275	* cK represents cos(K*pi/16).
276	* i0..i3 in the paper are tmp4..tmp7 here.
277	*/
278
279	z1 = tmp4 + tmp7;
280	z2 = tmp5 + tmp6;
281	z3 = tmp4 + tmp6;
282	z4 = tmp5 + tmp7;
283	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
284
285	tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
286	tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
287	tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
288	tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
289	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
290	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
291	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
292	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
293
294	z3 += z5;
295	z4 += z5;
296
297	dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
298	CONST_BITS+PASS1_BITS);
299	dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
300	CONST_BITS+PASS1_BITS);
301	dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
302	CONST_BITS+PASS1_BITS);
303	dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
304	CONST_BITS+PASS1_BITS);
305
306	dataptr++; /* advance pointer to next column */
307	}
308	}
309
310	/*
311	* The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
312	* on the rows and then, instead of doing even and odd, part on the colums
313	* you do even part two times.
314	*/
315	GLOBAL(void)
316	ff_fdct248_islow (DCTELEM * data)
317	{
318	int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
319	int_fast32_t tmp10, tmp11, tmp12, tmp13;
320	int_fast32_t z1;
321	DCTELEM *dataptr;
322	int ctr;
323	SHIFT_TEMPS
324
325	row_fdct(data);
326
327	/* Pass 2: process columns.
328	* We remove the PASS1_BITS scaling, but leave the results scaled up
329	* by an overall factor of 8.
330	*/
331
332	dataptr = data;
333	for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
334	tmp0 = dataptr[DCTSIZE0] + dataptr[DCTSIZE1];
335	tmp1 = dataptr[DCTSIZE2] + dataptr[DCTSIZE3];
336	tmp2 = dataptr[DCTSIZE4] + dataptr[DCTSIZE5];
337	tmp3 = dataptr[DCTSIZE6] + dataptr[DCTSIZE7];
338	tmp4 = dataptr[DCTSIZE0] - dataptr[DCTSIZE1];
339	tmp5 = dataptr[DCTSIZE2] - dataptr[DCTSIZE3];
340	tmp6 = dataptr[DCTSIZE4] - dataptr[DCTSIZE5];
341	tmp7 = dataptr[DCTSIZE6] - dataptr[DCTSIZE7];
342
343	tmp10 = tmp0 + tmp3;
344	tmp11 = tmp1 + tmp2;
345	tmp12 = tmp1 - tmp2;
346	tmp13 = tmp0 - tmp3;
347
348	dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
349	dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
350
351	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
352	dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
353	CONST_BITS+PASS1_BITS);
354	dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
355	CONST_BITS+PASS1_BITS);
356
357	tmp10 = tmp4 + tmp7;
358	tmp11 = tmp5 + tmp6;
359	tmp12 = tmp5 - tmp6;
360	tmp13 = tmp4 - tmp7;
361
362	dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
363	dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
364
365	z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
366	dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
367	CONST_BITS+PASS1_BITS);
368	dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
369	CONST_BITS+PASS1_BITS);
370
371	dataptr++; /* advance pointer to next column */
372	}
373	}

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