source: trunk/libjpeg/jidctint.c @ 199

Last change on this file since 199 was 15, checked in by Eugene Romanenko, 16 years ago

needed libs update

File size: 14.8 KB
Line 
1/*
2 * jidctint.c
3 *
4 * Copyright (C) 1991-1998, 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 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
10 * must also perform dequantization of the input coefficients.
11 *
12 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
13 * on each row (or vice versa, but it's more convenient to emit a row at
14 * a time).  Direct algorithms are also available, but they are much more
15 * complex and seem not to be any faster when reduced to code.
16 *
17 * This implementation is based on an algorithm described in
18 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
19 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
20 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
21 * The primary algorithm described there uses 11 multiplies and 29 adds.
22 * We use their alternate method with 12 multiplies and 32 adds.
23 * The advantage of this method is that no data path contains more than one
24 * multiplication; this allows a very simple and accurate implementation in
25 * scaled fixed-point arithmetic, with a minimal number of shifts.
26 */
27
28#define JPEG_INTERNALS
29#include "jinclude.h"
30#include "jpeglib.h"
31#include "jdct.h"               /* Private declarations for DCT subsystem */
32
33#ifdef DCT_ISLOW_SUPPORTED
34
35
36/*
37 * This module is specialized to the case DCTSIZE = 8.
38 */
39
40#if DCTSIZE != 8
41  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
42#endif
43
44
45/*
46 * The poop on this scaling stuff is as follows:
47 *
48 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
49 * larger than the true IDCT outputs.  The final outputs are therefore
50 * a factor of N larger than desired; since N=8 this can be cured by
51 * a simple right shift at the end of the algorithm.  The advantage of
52 * this arrangement is that we save two multiplications per 1-D IDCT,
53 * because the y0 and y4 inputs need not be divided by sqrt(N).
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.  (To scale up 12-bit sample data further, an
70 * intermediate INT32 array would be needed.)
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/* Dequantize a coefficient by multiplying it by the multiplier-table
136 * entry; produce an int result.  In this module, both inputs and result
137 * are 16 bits or less, so either int or short multiply will work.
138 */
139
140#define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))
141
142
143/*
144 * Perform dequantization and inverse DCT on one block of coefficients.
145 */
146
147GLOBAL(void)
148jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
149                 JCOEFPTR coef_block,
150                 JSAMPARRAY output_buf, JDIMENSION output_col)
151{
152  INT32 tmp0, tmp1, tmp2, tmp3;
153  INT32 tmp10, tmp11, tmp12, tmp13;
154  INT32 z1, z2, z3, z4, z5;
155  JCOEFPTR inptr;
156  ISLOW_MULT_TYPE * quantptr;
157  int * wsptr;
158  JSAMPROW outptr;
159  JSAMPLE *range_limit = IDCT_range_limit(cinfo);
160  int ctr;
161  int workspace[DCTSIZE2];      /* buffers data between passes */
162  SHIFT_TEMPS
163
164  /* Pass 1: process columns from input, store into work array. */
165  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
166  /* furthermore, we scale the results by 2**PASS1_BITS. */
167
168  inptr = coef_block;
169  quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
170  wsptr = workspace;
171  for (ctr = DCTSIZE; ctr > 0; ctr--) {
172    /* Due to quantization, we will usually find that many of the input
173     * coefficients are zero, especially the AC terms.  We can exploit this
174     * by short-circuiting the IDCT calculation for any column in which all
175     * the AC terms are zero.  In that case each output is equal to the
176     * DC coefficient (with scale factor as needed).
177     * With typical images and quantization tables, half or more of the
178     * column DCT calculations can be simplified this way.
179     */
180   
181    if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
182        inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
183        inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
184        inptr[DCTSIZE*7] == 0) {
185      /* AC terms all zero */
186      int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
187     
188      wsptr[DCTSIZE*0] = dcval;
189      wsptr[DCTSIZE*1] = dcval;
190      wsptr[DCTSIZE*2] = dcval;
191      wsptr[DCTSIZE*3] = dcval;
192      wsptr[DCTSIZE*4] = dcval;
193      wsptr[DCTSIZE*5] = dcval;
194      wsptr[DCTSIZE*6] = dcval;
195      wsptr[DCTSIZE*7] = dcval;
196     
197      inptr++;                  /* advance pointers to next column */
198      quantptr++;
199      wsptr++;
200      continue;
201    }
202   
203    /* Even part: reverse the even part of the forward DCT. */
204    /* The rotator is sqrt(2)*c(-6). */
205   
206    z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
207    z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
208   
209    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
210    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
211    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
212   
213    z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
214    z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
215
216    tmp0 = (z2 + z3) << CONST_BITS;
217    tmp1 = (z2 - z3) << CONST_BITS;
218   
219    tmp10 = tmp0 + tmp3;
220    tmp13 = tmp0 - tmp3;
221    tmp11 = tmp1 + tmp2;
222    tmp12 = tmp1 - tmp2;
223   
224    /* Odd part per figure 8; the matrix is unitary and hence its
225     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
226     */
227   
228    tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
229    tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
230    tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
231    tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
232   
233    z1 = tmp0 + tmp3;
234    z2 = tmp1 + tmp2;
235    z3 = tmp0 + tmp2;
236    z4 = tmp1 + tmp3;
237    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
238   
239    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
240    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
241    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
242    tmp3 = MULTIPLY(tmp3, 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    tmp0 += z1 + z3;
252    tmp1 += z2 + z4;
253    tmp2 += z2 + z3;
254    tmp3 += z1 + z4;
255   
256    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
257   
258    wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
259    wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
260    wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
261    wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
262    wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
263    wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
264    wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
265    wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
266   
267    inptr++;                    /* advance pointers to next column */
268    quantptr++;
269    wsptr++;
270  }
271 
272  /* Pass 2: process rows from work array, store into output array. */
273  /* Note that we must descale the results by a factor of 8 == 2**3, */
274  /* and also undo the PASS1_BITS scaling. */
275
276  wsptr = workspace;
277  for (ctr = 0; ctr < DCTSIZE; ctr++) {
278    outptr = output_buf[ctr] + output_col;
279    /* Rows of zeroes can be exploited in the same way as we did with columns.
280     * However, the column calculation has created many nonzero AC terms, so
281     * the simplification applies less often (typically 5% to 10% of the time).
282     * On machines with very fast multiplication, it's possible that the
283     * test takes more time than it's worth.  In that case this section
284     * may be commented out.
285     */
286   
287#ifndef NO_ZERO_ROW_TEST
288    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
289        wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
290      /* AC terms all zero */
291      JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
292                                  & RANGE_MASK];
293     
294      outptr[0] = dcval;
295      outptr[1] = dcval;
296      outptr[2] = dcval;
297      outptr[3] = dcval;
298      outptr[4] = dcval;
299      outptr[5] = dcval;
300      outptr[6] = dcval;
301      outptr[7] = dcval;
302
303      wsptr += DCTSIZE;         /* advance pointer to next row */
304      continue;
305    }
306#endif
307   
308    /* Even part: reverse the even part of the forward DCT. */
309    /* The rotator is sqrt(2)*c(-6). */
310   
311    z2 = (INT32) wsptr[2];
312    z3 = (INT32) wsptr[6];
313   
314    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
315    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
316    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
317   
318    tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
319    tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
320   
321    tmp10 = tmp0 + tmp3;
322    tmp13 = tmp0 - tmp3;
323    tmp11 = tmp1 + tmp2;
324    tmp12 = tmp1 - tmp2;
325   
326    /* Odd part per figure 8; the matrix is unitary and hence its
327     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
328     */
329   
330    tmp0 = (INT32) wsptr[7];
331    tmp1 = (INT32) wsptr[5];
332    tmp2 = (INT32) wsptr[3];
333    tmp3 = (INT32) wsptr[1];
334   
335    z1 = tmp0 + tmp3;
336    z2 = tmp1 + tmp2;
337    z3 = tmp0 + tmp2;
338    z4 = tmp1 + tmp3;
339    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
340   
341    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
342    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
343    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
344    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
345    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
346    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
347    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
348    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
349   
350    z3 += z5;
351    z4 += z5;
352   
353    tmp0 += z1 + z3;
354    tmp1 += z2 + z4;
355    tmp2 += z2 + z3;
356    tmp3 += z1 + z4;
357   
358    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
359   
360    outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
361                                          CONST_BITS+PASS1_BITS+3)
362                            & RANGE_MASK];
363    outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
364                                          CONST_BITS+PASS1_BITS+3)
365                            & RANGE_MASK];
366    outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
367                                          CONST_BITS+PASS1_BITS+3)
368                            & RANGE_MASK];
369    outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
370                                          CONST_BITS+PASS1_BITS+3)
371                            & RANGE_MASK];
372    outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
373                                          CONST_BITS+PASS1_BITS+3)
374                            & RANGE_MASK];
375    outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
376                                          CONST_BITS+PASS1_BITS+3)
377                            & RANGE_MASK];
378    outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
379                                          CONST_BITS+PASS1_BITS+3)
380                            & RANGE_MASK];
381    outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
382                                          CONST_BITS+PASS1_BITS+3)
383                            & RANGE_MASK];
384   
385    wsptr += DCTSIZE;           /* advance pointer to next row */
386  }
387}
388
389#endif /* DCT_ISLOW_SUPPORTED */
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