source: trunk/libjpeg/jfdctint.c @ 15

Last change on this file since 15 was 15, checked in by Eugene Romanenko, 16 years ago

needed libs update

File size: 11.1 KB
RevLine 
[15]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#define JPEG_INTERNALS
27#include "jinclude.h"
28#include "jpeglib.h"
29#include "jdct.h"               /* Private declarations for DCT subsystem */
30
31#ifdef DCT_ISLOW_SUPPORTED
32
33
34/*
35 * This module is specialized to the case DCTSIZE = 8.
36 */
37
38#if DCTSIZE != 8
39  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
40#endif
41
42
43/*
44 * The poop on this scaling stuff is as follows:
45 *
46 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
47 * larger than the true DCT outputs.  The final outputs are therefore
48 * a factor of N larger than desired; since N=8 this can be cured by
49 * a simple right shift at the end of the algorithm.  The advantage of
50 * this arrangement is that we save two multiplications per 1-D DCT,
51 * because the y0 and y4 outputs need not be divided by sqrt(N).
52 * In the IJG code, this factor of 8 is removed by the quantization step
53 * (in jcdctmgr.c), NOT in this module.
54 *
55 * We have to do addition and subtraction of the integer inputs, which
56 * is no problem, and multiplication by fractional constants, which is
57 * a problem to do in integer arithmetic.  We multiply all the constants
58 * by CONST_SCALE and convert them to integer constants (thus retaining
59 * CONST_BITS bits of precision in the constants).  After doing a
60 * multiplication we have to divide the product by CONST_SCALE, with proper
61 * rounding, to produce the correct output.  This division can be done
62 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
63 * as long as possible so that partial sums can be added together with
64 * full fractional precision.
65 *
66 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
67 * they are represented to better-than-integral precision.  These outputs
68 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
69 * with the recommended scaling.  (For 12-bit sample data, the intermediate
70 * array is INT32 anyway.)
71 *
72 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
73 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
74 * shows that the values given below are the most effective.
75 */
76
77#if BITS_IN_JSAMPLE == 8
78#define CONST_BITS  13
79#define PASS1_BITS  2
80#else
81#define CONST_BITS  13
82#define PASS1_BITS  1           /* lose a little precision to avoid overflow */
83#endif
84
85/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
86 * causing a lot of useless floating-point operations at run time.
87 * To get around this we use the following pre-calculated constants.
88 * If you change CONST_BITS you may want to add appropriate values.
89 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
90 */
91
92#if CONST_BITS == 13
93#define FIX_0_298631336  ((INT32)  2446)        /* FIX(0.298631336) */
94#define FIX_0_390180644  ((INT32)  3196)        /* FIX(0.390180644) */
95#define FIX_0_541196100  ((INT32)  4433)        /* FIX(0.541196100) */
96#define FIX_0_765366865  ((INT32)  6270)        /* FIX(0.765366865) */
97#define FIX_0_899976223  ((INT32)  7373)        /* FIX(0.899976223) */
98#define FIX_1_175875602  ((INT32)  9633)        /* FIX(1.175875602) */
99#define FIX_1_501321110  ((INT32)  12299)       /* FIX(1.501321110) */
100#define FIX_1_847759065  ((INT32)  15137)       /* FIX(1.847759065) */
101#define FIX_1_961570560  ((INT32)  16069)       /* FIX(1.961570560) */
102#define FIX_2_053119869  ((INT32)  16819)       /* FIX(2.053119869) */
103#define FIX_2_562915447  ((INT32)  20995)       /* FIX(2.562915447) */
104#define FIX_3_072711026  ((INT32)  25172)       /* FIX(3.072711026) */
105#else
106#define FIX_0_298631336  FIX(0.298631336)
107#define FIX_0_390180644  FIX(0.390180644)
108#define FIX_0_541196100  FIX(0.541196100)
109#define FIX_0_765366865  FIX(0.765366865)
110#define FIX_0_899976223  FIX(0.899976223)
111#define FIX_1_175875602  FIX(1.175875602)
112#define FIX_1_501321110  FIX(1.501321110)
113#define FIX_1_847759065  FIX(1.847759065)
114#define FIX_1_961570560  FIX(1.961570560)
115#define FIX_2_053119869  FIX(2.053119869)
116#define FIX_2_562915447  FIX(2.562915447)
117#define FIX_3_072711026  FIX(3.072711026)
118#endif
119
120
121/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
122 * For 8-bit samples with the recommended scaling, all the variable
123 * and constant values involved are no more than 16 bits wide, so a
124 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
125 * For 12-bit samples, a full 32-bit multiplication will be needed.
126 */
127
128#if BITS_IN_JSAMPLE == 8
129#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
130#else
131#define MULTIPLY(var,const)  ((var) * (const))
132#endif
133
134
135/*
136 * Perform the forward DCT on one block of samples.
137 */
138
139GLOBAL(void)
140jpeg_fdct_islow (DCTELEM * data)
141{
142  INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
143  INT32 tmp10, tmp11, tmp12, tmp13;
144  INT32 z1, z2, z3, z4, z5;
145  DCTELEM *dataptr;
146  int ctr;
147  SHIFT_TEMPS
148
149  /* Pass 1: process rows. */
150  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
151  /* furthermore, we scale the results by 2**PASS1_BITS. */
152
153  dataptr = data;
154  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
155    tmp0 = dataptr[0] + dataptr[7];
156    tmp7 = dataptr[0] - dataptr[7];
157    tmp1 = dataptr[1] + dataptr[6];
158    tmp6 = dataptr[1] - dataptr[6];
159    tmp2 = dataptr[2] + dataptr[5];
160    tmp5 = dataptr[2] - dataptr[5];
161    tmp3 = dataptr[3] + dataptr[4];
162    tmp4 = dataptr[3] - dataptr[4];
163   
164    /* Even part per LL&M figure 1 --- note that published figure is faulty;
165     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
166     */
167   
168    tmp10 = tmp0 + tmp3;
169    tmp13 = tmp0 - tmp3;
170    tmp11 = tmp1 + tmp2;
171    tmp12 = tmp1 - tmp2;
172   
173    dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
174    dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
175   
176    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
177    dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
178                                   CONST_BITS-PASS1_BITS);
179    dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
180                                   CONST_BITS-PASS1_BITS);
181   
182    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
183     * cK represents cos(K*pi/16).
184     * i0..i3 in the paper are tmp4..tmp7 here.
185     */
186   
187    z1 = tmp4 + tmp7;
188    z2 = tmp5 + tmp6;
189    z3 = tmp4 + tmp6;
190    z4 = tmp5 + tmp7;
191    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
192   
193    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
194    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
195    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
196    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
197    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
198    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
199    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
200    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
201   
202    z3 += z5;
203    z4 += z5;
204   
205    dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
206    dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
207    dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
208    dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
209   
210    dataptr += DCTSIZE;         /* advance pointer to next row */
211  }
212
213  /* Pass 2: process columns.
214   * We remove the PASS1_BITS scaling, but leave the results scaled up
215   * by an overall factor of 8.
216   */
217
218  dataptr = data;
219  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
220    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
221    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
222    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
223    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
224    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
225    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
226    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
227    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
228   
229    /* Even part per LL&M figure 1 --- note that published figure is faulty;
230     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
231     */
232   
233    tmp10 = tmp0 + tmp3;
234    tmp13 = tmp0 - tmp3;
235    tmp11 = tmp1 + tmp2;
236    tmp12 = tmp1 - tmp2;
237   
238    dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
239    dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
240   
241    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
242    dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
243                                           CONST_BITS+PASS1_BITS);
244    dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
245                                           CONST_BITS+PASS1_BITS);
246   
247    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
248     * cK represents cos(K*pi/16).
249     * i0..i3 in the paper are tmp4..tmp7 here.
250     */
251   
252    z1 = tmp4 + tmp7;
253    z2 = tmp5 + tmp6;
254    z3 = tmp4 + tmp6;
255    z4 = tmp5 + tmp7;
256    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
257   
258    tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
259    tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
260    tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
261    tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
262    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
263    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
264    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
265    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
266   
267    z3 += z5;
268    z4 += z5;
269   
270    dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
271                                           CONST_BITS+PASS1_BITS);
272    dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
273                                           CONST_BITS+PASS1_BITS);
274    dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
275                                           CONST_BITS+PASS1_BITS);
276    dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
277                                           CONST_BITS+PASS1_BITS);
278   
279    dataptr++;                  /* advance pointer to next column */
280  }
281}
282
283#endif /* DCT_ISLOW_SUPPORTED */
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