Line data Source code
1 : /*
2 : * jidctfst.c
3 : *
4 : * This file was part of the Independent JPEG Group's software:
5 : * Copyright (C) 1994-1998, Thomas G. Lane.
6 : * libjpeg-turbo Modifications:
7 : * Copyright (C) 2015, D. R. Commander.
8 : * For conditions of distribution and use, see the accompanying README.ijg
9 : * file.
10 : *
11 : * This file contains a fast, not so accurate integer implementation of the
12 : * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
13 : * must also perform dequantization of the input coefficients.
14 : *
15 : * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
16 : * on each row (or vice versa, but it's more convenient to emit a row at
17 : * a time). Direct algorithms are also available, but they are much more
18 : * complex and seem not to be any faster when reduced to code.
19 : *
20 : * This implementation is based on Arai, Agui, and Nakajima's algorithm for
21 : * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
22 : * Japanese, but the algorithm is described in the Pennebaker & Mitchell
23 : * JPEG textbook (see REFERENCES section in file README.ijg). The following
24 : * code is based directly on figure 4-8 in P&M.
25 : * While an 8-point DCT cannot be done in less than 11 multiplies, it is
26 : * possible to arrange the computation so that many of the multiplies are
27 : * simple scalings of the final outputs. These multiplies can then be
28 : * folded into the multiplications or divisions by the JPEG quantization
29 : * table entries. The AA&N method leaves only 5 multiplies and 29 adds
30 : * to be done in the DCT itself.
31 : * The primary disadvantage of this method is that with fixed-point math,
32 : * accuracy is lost due to imprecise representation of the scaled
33 : * quantization values. The smaller the quantization table entry, the less
34 : * precise the scaled value, so this implementation does worse with high-
35 : * quality-setting files than with low-quality ones.
36 : */
37 :
38 : #define JPEG_INTERNALS
39 : #include "jinclude.h"
40 : #include "jpeglib.h"
41 : #include "jdct.h" /* Private declarations for DCT subsystem */
42 :
43 : #ifdef DCT_IFAST_SUPPORTED
44 :
45 :
46 : /*
47 : * This module is specialized to the case DCTSIZE = 8.
48 : */
49 :
50 : #if DCTSIZE != 8
51 : Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
52 : #endif
53 :
54 :
55 : /* Scaling decisions are generally the same as in the LL&M algorithm;
56 : * see jidctint.c for more details. However, we choose to descale
57 : * (right shift) multiplication products as soon as they are formed,
58 : * rather than carrying additional fractional bits into subsequent additions.
59 : * This compromises accuracy slightly, but it lets us save a few shifts.
60 : * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
61 : * everywhere except in the multiplications proper; this saves a good deal
62 : * of work on 16-bit-int machines.
63 : *
64 : * The dequantized coefficients are not integers because the AA&N scaling
65 : * factors have been incorporated. We represent them scaled up by PASS1_BITS,
66 : * so that the first and second IDCT rounds have the same input scaling.
67 : * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
68 : * avoid a descaling shift; this compromises accuracy rather drastically
69 : * for small quantization table entries, but it saves a lot of shifts.
70 : * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
71 : * so we use a much larger scaling factor to preserve accuracy.
72 : *
73 : * A final compromise is to represent the multiplicative constants to only
74 : * 8 fractional bits, rather than 13. This saves some shifting work on some
75 : * machines, and may also reduce the cost of multiplication (since there
76 : * are fewer one-bits in the constants).
77 : */
78 :
79 : #if BITS_IN_JSAMPLE == 8
80 : #define CONST_BITS 8
81 : #define PASS1_BITS 2
82 : #else
83 : #define CONST_BITS 8
84 : #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
85 : #endif
86 :
87 : /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
88 : * causing a lot of useless floating-point operations at run time.
89 : * To get around this we use the following pre-calculated constants.
90 : * If you change CONST_BITS you may want to add appropriate values.
91 : * (With a reasonable C compiler, you can just rely on the FIX() macro...)
92 : */
93 :
94 : #if CONST_BITS == 8
95 : #define FIX_1_082392200 ((JLONG) 277) /* FIX(1.082392200) */
96 : #define FIX_1_414213562 ((JLONG) 362) /* FIX(1.414213562) */
97 : #define FIX_1_847759065 ((JLONG) 473) /* FIX(1.847759065) */
98 : #define FIX_2_613125930 ((JLONG) 669) /* FIX(2.613125930) */
99 : #else
100 : #define FIX_1_082392200 FIX(1.082392200)
101 : #define FIX_1_414213562 FIX(1.414213562)
102 : #define FIX_1_847759065 FIX(1.847759065)
103 : #define FIX_2_613125930 FIX(2.613125930)
104 : #endif
105 :
106 :
107 : /* We can gain a little more speed, with a further compromise in accuracy,
108 : * by omitting the addition in a descaling shift. This yields an incorrectly
109 : * rounded result half the time...
110 : */
111 :
112 : #ifndef USE_ACCURATE_ROUNDING
113 : #undef DESCALE
114 : #define DESCALE(x,n) RIGHT_SHIFT(x, n)
115 : #endif
116 :
117 :
118 : /* Multiply a DCTELEM variable by an JLONG constant, and immediately
119 : * descale to yield a DCTELEM result.
120 : */
121 :
122 : #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
123 :
124 :
125 : /* Dequantize a coefficient by multiplying it by the multiplier-table
126 : * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
127 : * multiplication will do. For 12-bit data, the multiplier table is
128 : * declared JLONG, so a 32-bit multiply will be used.
129 : */
130 :
131 : #if BITS_IN_JSAMPLE == 8
132 : #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
133 : #else
134 : #define DEQUANTIZE(coef,quantval) \
135 : DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
136 : #endif
137 :
138 :
139 : /* Like DESCALE, but applies to a DCTELEM and produces an int.
140 : * We assume that int right shift is unsigned if JLONG right shift is.
141 : */
142 :
143 : #ifdef RIGHT_SHIFT_IS_UNSIGNED
144 : #define ISHIFT_TEMPS DCTELEM ishift_temp;
145 : #if BITS_IN_JSAMPLE == 8
146 : #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
147 : #else
148 : #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
149 : #endif
150 : #define IRIGHT_SHIFT(x,shft) \
151 : ((ishift_temp = (x)) < 0 ? \
152 : (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
153 : (ishift_temp >> (shft)))
154 : #else
155 : #define ISHIFT_TEMPS
156 : #define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
157 : #endif
158 :
159 : #ifdef USE_ACCURATE_ROUNDING
160 : #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
161 : #else
162 : #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
163 : #endif
164 :
165 :
166 : /*
167 : * Perform dequantization and inverse DCT on one block of coefficients.
168 : */
169 :
170 : GLOBAL(void)
171 0 : jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info *compptr,
172 : JCOEFPTR coef_block,
173 : JSAMPARRAY output_buf, JDIMENSION output_col)
174 : {
175 : DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
176 : DCTELEM tmp10, tmp11, tmp12, tmp13;
177 : DCTELEM z5, z10, z11, z12, z13;
178 : JCOEFPTR inptr;
179 : IFAST_MULT_TYPE *quantptr;
180 : int *wsptr;
181 : JSAMPROW outptr;
182 0 : JSAMPLE *range_limit = IDCT_range_limit(cinfo);
183 : int ctr;
184 : int workspace[DCTSIZE2]; /* buffers data between passes */
185 : SHIFT_TEMPS /* for DESCALE */
186 : ISHIFT_TEMPS /* for IDESCALE */
187 :
188 : /* Pass 1: process columns from input, store into work array. */
189 :
190 0 : inptr = coef_block;
191 0 : quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
192 0 : wsptr = workspace;
193 0 : for (ctr = DCTSIZE; ctr > 0; ctr--) {
194 : /* Due to quantization, we will usually find that many of the input
195 : * coefficients are zero, especially the AC terms. We can exploit this
196 : * by short-circuiting the IDCT calculation for any column in which all
197 : * the AC terms are zero. In that case each output is equal to the
198 : * DC coefficient (with scale factor as needed).
199 : * With typical images and quantization tables, half or more of the
200 : * column DCT calculations can be simplified this way.
201 : */
202 :
203 0 : if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
204 0 : inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
205 0 : inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
206 0 : inptr[DCTSIZE*7] == 0) {
207 : /* AC terms all zero */
208 0 : int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
209 :
210 0 : wsptr[DCTSIZE*0] = dcval;
211 0 : wsptr[DCTSIZE*1] = dcval;
212 0 : wsptr[DCTSIZE*2] = dcval;
213 0 : wsptr[DCTSIZE*3] = dcval;
214 0 : wsptr[DCTSIZE*4] = dcval;
215 0 : wsptr[DCTSIZE*5] = dcval;
216 0 : wsptr[DCTSIZE*6] = dcval;
217 0 : wsptr[DCTSIZE*7] = dcval;
218 :
219 0 : inptr++; /* advance pointers to next column */
220 0 : quantptr++;
221 0 : wsptr++;
222 0 : continue;
223 : }
224 :
225 : /* Even part */
226 :
227 0 : tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
228 0 : tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
229 0 : tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
230 0 : tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
231 :
232 0 : tmp10 = tmp0 + tmp2; /* phase 3 */
233 0 : tmp11 = tmp0 - tmp2;
234 :
235 0 : tmp13 = tmp1 + tmp3; /* phases 5-3 */
236 0 : tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
237 :
238 0 : tmp0 = tmp10 + tmp13; /* phase 2 */
239 0 : tmp3 = tmp10 - tmp13;
240 0 : tmp1 = tmp11 + tmp12;
241 0 : tmp2 = tmp11 - tmp12;
242 :
243 : /* Odd part */
244 :
245 0 : tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
246 0 : tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
247 0 : tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
248 0 : tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
249 :
250 0 : z13 = tmp6 + tmp5; /* phase 6 */
251 0 : z10 = tmp6 - tmp5;
252 0 : z11 = tmp4 + tmp7;
253 0 : z12 = tmp4 - tmp7;
254 :
255 0 : tmp7 = z11 + z13; /* phase 5 */
256 0 : tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
257 :
258 0 : z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
259 0 : tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
260 0 : tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
261 :
262 0 : tmp6 = tmp12 - tmp7; /* phase 2 */
263 0 : tmp5 = tmp11 - tmp6;
264 0 : tmp4 = tmp10 + tmp5;
265 :
266 0 : wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
267 0 : wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
268 0 : wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
269 0 : wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
270 0 : wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
271 0 : wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
272 0 : wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
273 0 : wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
274 :
275 0 : inptr++; /* advance pointers to next column */
276 0 : quantptr++;
277 0 : wsptr++;
278 : }
279 :
280 : /* Pass 2: process rows from work array, store into output array. */
281 : /* Note that we must descale the results by a factor of 8 == 2**3, */
282 : /* and also undo the PASS1_BITS scaling. */
283 :
284 0 : wsptr = workspace;
285 0 : for (ctr = 0; ctr < DCTSIZE; ctr++) {
286 0 : outptr = output_buf[ctr] + output_col;
287 : /* Rows of zeroes can be exploited in the same way as we did with columns.
288 : * However, the column calculation has created many nonzero AC terms, so
289 : * the simplification applies less often (typically 5% to 10% of the time).
290 : * On machines with very fast multiplication, it's possible that the
291 : * test takes more time than it's worth. In that case this section
292 : * may be commented out.
293 : */
294 :
295 : #ifndef NO_ZERO_ROW_TEST
296 0 : if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
297 0 : wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
298 : /* AC terms all zero */
299 0 : JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
300 0 : & RANGE_MASK];
301 :
302 0 : outptr[0] = dcval;
303 0 : outptr[1] = dcval;
304 0 : outptr[2] = dcval;
305 0 : outptr[3] = dcval;
306 0 : outptr[4] = dcval;
307 0 : outptr[5] = dcval;
308 0 : outptr[6] = dcval;
309 0 : outptr[7] = dcval;
310 :
311 0 : wsptr += DCTSIZE; /* advance pointer to next row */
312 0 : continue;
313 : }
314 : #endif
315 :
316 : /* Even part */
317 :
318 0 : tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
319 0 : tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
320 :
321 0 : tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
322 0 : tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
323 0 : - tmp13;
324 :
325 0 : tmp0 = tmp10 + tmp13;
326 0 : tmp3 = tmp10 - tmp13;
327 0 : tmp1 = tmp11 + tmp12;
328 0 : tmp2 = tmp11 - tmp12;
329 :
330 : /* Odd part */
331 :
332 0 : z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
333 0 : z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
334 0 : z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
335 0 : z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
336 :
337 0 : tmp7 = z11 + z13; /* phase 5 */
338 0 : tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
339 :
340 0 : z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
341 0 : tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
342 0 : tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
343 :
344 0 : tmp6 = tmp12 - tmp7; /* phase 2 */
345 0 : tmp5 = tmp11 - tmp6;
346 0 : tmp4 = tmp10 + tmp5;
347 :
348 : /* Final output stage: scale down by a factor of 8 and range-limit */
349 :
350 0 : outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
351 0 : & RANGE_MASK];
352 0 : outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
353 0 : & RANGE_MASK];
354 0 : outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
355 0 : & RANGE_MASK];
356 0 : outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
357 0 : & RANGE_MASK];
358 0 : outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
359 0 : & RANGE_MASK];
360 0 : outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
361 0 : & RANGE_MASK];
362 0 : outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
363 0 : & RANGE_MASK];
364 0 : outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
365 0 : & RANGE_MASK];
366 :
367 0 : wsptr += DCTSIZE; /* advance pointer to next row */
368 : }
369 0 : }
370 :
371 : #endif /* DCT_IFAST_SUPPORTED */
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