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