1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
|
/*
* jidctfst.c
*
* Copyright (C) 1994-1998, Thomas G. Lane.
* This file is part of the Independent JPEG Group's software.
* For conditions of distribution and use, see the accompanying README file.
*
* This file tqcontains a fast, not so accurate integer implementation of the
* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
* must also perform dequantization of the input coefficients.
*
* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
* on each row (or vice versa, but it's more convenient to emit a row at
* a time). Direct algorithms are also available, but they are much more
* complex and seem not to be any faster when reduced to code.
*
* This implementation is based on Arai, Agui, and Nakajima's algorithm for
* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
* Japanese, but the algorithm is described in the Pennebaker & Mitchell
* JPEG textbook (see REFERENCES section in file README). The following code
* is based directly on figure 4-8 in P&M.
* While an 8-point DCT cannot be done in less than 11 multiplies, it is
* possible to arrange the computation so that many of the multiplies are
* simple scalings of the final outputs. These multiplies can then be
* folded into the multiplications or divisions by the JPEG quantization
* table entries. The AA&N method leaves only 5 multiplies and 29 adds
* to be done in the DCT itself.
* The primary disadvantage of this method is that with fixed-point math,
* accuracy is lost due to imprecise representation of the scaled
* quantization values. The smaller the quantization table entry, the less
* precise the scaled value, so this implementation does worse with high-
* quality-setting files than with low-quality ones.
*/
#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
#ifdef DCT_IFAST_SUPPORTED
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/* Scaling decisions are generally the same as in the LL&M algorithm;
* see jidctint.c for more details. However, we choose to descale
* (right shift) multiplication products as soon as they are formed,
* rather than carrying additional fractional bits into subsequent additions.
* This compromises accuracy slightly, but it lets us save a few shifts.
* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
* everywhere except in the multiplications proper; this saves a good deal
* of work on 16-bit-int machines.
*
* The dequantized coefficients are not integers because the AA&N scaling
* factors have been incorporated. We represent them scaled up by PASS1_BITS,
* so that the first and second IDCT rounds have the same input scaling.
* For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
* avoid a descaling shift; this compromises accuracy rather drastically
* for small quantization table entries, but it saves a lot of shifts.
* For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
* so we use a much larger scaling factor to preserve accuracy.
*
* A final compromise is to represent the multiplicative constants to only
* 8 fractional bits, rather than 13. This saves some shifting work on some
* machines, and may also reduce the cost of multiplication (since there
* are fewer one-bits in the constants).
*/
#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 8
#define PASS1_BITS 2
#else
#define CONST_BITS 8
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#endif
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
* causing a lot of useless floating-point operations at run time.
* To get around this we use the following pre-calculated constants.
* If you change CONST_BITS you may want to add appropriate values.
* (With a reasonable C compiler, you can just rely on the FIX() macro...)
*/
#if CONST_BITS == 8
#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
#else
#define FIX_1_082392200 FIX(1.082392200)
#define FIX_1_414213562 FIX(1.414213562)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_2_613125930 FIX(2.613125930)
#endif
/* We can gain a little more speed, with a further compromise in accuracy,
* by omitting the addition in a descaling shift. This yields an incorrectly
* rounded result half the time...
*/
#ifndef USE_ACCURATE_ROUNDING
#undef DESCALE
#define DESCALE(x,n) RIGHT_SHIFT(x, n)
#endif
/* Multiply a DCTELEM variable by an INT32 constant, and immediately
* descale to yield a DCTELEM result.
*/
#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
/* Dequantize a coefficient by multiplying it by the multiplier-table
* entry; produce a DCTELEM result. For 8-bit data a 16x16->16
* multiplication will do. For 12-bit data, the multiplier table is
* declared INT32, so a 32-bit multiply will be used.
*/
#if BITS_IN_JSAMPLE == 8
#define DETQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
#else
#define DETQUANTIZE(coef,quantval) \
DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
#endif
/* Like DESCALE, but applies to a DCTELEM and produces an int.
* We assume that int right shift is unsigned if INT32 right shift is.
*/
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define ISHIFT_TEMPS DCTELEM ishift_temp;
#if BITS_IN_JSAMPLE == 8
#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
#else
#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
#endif
#define IRIGHT_SHIFT(x,shft) \
((ishift_temp = (x)) < 0 ? \
(ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
(ishift_temp >> (shft)))
#else
#define ISHIFT_TEMPS
#define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
#endif
#ifdef USE_ACCURATE_ROUNDING
#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
#else
#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
#endif
/*
* Perform dequantization and inverse DCT on one block of coefficients.
*/
GLOBAL(void)
jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
JCOEFPTR coef_block,
JSAMPARRAY output_buf, JDIMENSION output_col)
{
DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
DCTELEM tmp10, tmp11, tmp12, tmp13;
DCTELEM z5, z10, z11, z12, z13;
JCOEFPTR inptr;
IFAST_MULT_TYPE * quantptr;
int * wsptr;
JSAMPROW outptr;
JSAMPLE *range_limit = IDCT_range_limit(cinfo);
int ctr;
int workspace[DCTSIZE2]; /* buffers data between passes */
SHIFT_TEMPS /* for DESCALE */
ISHIFT_TEMPS /* for IDESCALE */
/* Pass 1: process columns from input, store into work array. */
inptr = coef_block;
quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
wsptr = workspace;
for (ctr = DCTSIZE; ctr > 0; ctr--) {
/* Due to quantization, we will usually tqfind that many of the input
* coefficients are zero, especially the AC terms. We can exploit this
* by short-circuiting the IDCT calculation for any column in which all
* the AC terms are zero. In that case each output is equal to the
* DC coefficient (with scale factor as needed).
* With typical images and quantization tables, half or more of the
* column DCT calculations can be simplified this way.
*/
if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
inptr[DCTSIZE*7] == 0) {
/* AC terms all zero */
int dcval = (int) DETQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
wsptr[DCTSIZE*0] = dcval;
wsptr[DCTSIZE*1] = dcval;
wsptr[DCTSIZE*2] = dcval;
wsptr[DCTSIZE*3] = dcval;
wsptr[DCTSIZE*4] = dcval;
wsptr[DCTSIZE*5] = dcval;
wsptr[DCTSIZE*6] = dcval;
wsptr[DCTSIZE*7] = dcval;
inptr++; /* advance pointers to next column */
quantptr++;
wsptr++;
continue;
}
/* Even part */
tmp0 = DETQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
tmp1 = DETQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
tmp2 = DETQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
tmp3 = DETQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
tmp10 = tmp0 + tmp2; /* phase 3 */
tmp11 = tmp0 - tmp2;
tmp13 = tmp1 + tmp3; /* phases 5-3 */
tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
tmp0 = tmp10 + tmp13; /* phase 2 */
tmp3 = tmp10 - tmp13;
tmp1 = tmp11 + tmp12;
tmp2 = tmp11 - tmp12;
/* Odd part */
tmp4 = DETQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
tmp5 = DETQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
tmp6 = DETQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
tmp7 = DETQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
z13 = tmp6 + tmp5; /* phase 6 */
z10 = tmp6 - tmp5;
z11 = tmp4 + tmp7;
z12 = tmp4 - tmp7;
tmp7 = z11 + z13; /* phase 5 */
tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
tmp6 = tmp12 - tmp7; /* phase 2 */
tmp5 = tmp11 - tmp6;
tmp4 = tmp10 + tmp5;
wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
inptr++; /* advance pointers to next column */
quantptr++;
wsptr++;
}
/* Pass 2: process rows from work array, store into output array. */
/* Note that we must descale the results by a factor of 8 == 2**3, */
/* and also undo the PASS1_BITS scaling. */
wsptr = workspace;
for (ctr = 0; ctr < DCTSIZE; ctr++) {
outptr = output_buf[ctr] + output_col;
/* Rows of zeroes can be exploited in the same way as we did with columns.
* However, the column calculation has created many nonzero AC terms, so
* the simplification applies less often (typically 5% to 10% of the time).
* On machines with very fast multiplication, it's possible that the
* test takes more time than it's worth. In that case this section
* may be commented out.
*/
#ifndef NO_ZERO_ROW_TEST
if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
/* AC terms all zero */
JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
& RANGE_MASK];
outptr[0] = dcval;
outptr[1] = dcval;
outptr[2] = dcval;
outptr[3] = dcval;
outptr[4] = dcval;
outptr[5] = dcval;
outptr[6] = dcval;
outptr[7] = dcval;
wsptr += DCTSIZE; /* advance pointer to next row */
continue;
}
#endif
/* Even part */
tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
- tmp13;
tmp0 = tmp10 + tmp13;
tmp3 = tmp10 - tmp13;
tmp1 = tmp11 + tmp12;
tmp2 = tmp11 - tmp12;
/* Odd part */
z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
tmp7 = z11 + z13; /* phase 5 */
tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
tmp6 = tmp12 - tmp7; /* phase 2 */
tmp5 = tmp11 - tmp6;
tmp4 = tmp10 + tmp5;
/* Final output stage: scale down by a factor of 8 and range-limit */
outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
& RANGE_MASK];
outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
& RANGE_MASK];
outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
& RANGE_MASK];
outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
& RANGE_MASK];
outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
& RANGE_MASK];
outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
& RANGE_MASK];
outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
& RANGE_MASK];
outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
& RANGE_MASK];
wsptr += DCTSIZE; /* advance pointer to next row */
}
}
#endif /* DCT_IFAST_SUPPORTED */
|
