1 /*
2 * jidctfst.c
3 *
4 * Copyright (C) 1994-1998, Thomas G. Lane.
5 * Modified 2015-2017 by Guido Vollbeding.
6 * This file is part of the Independent JPEG Group's software.
7 * For conditions of distribution and use, see the accompanying README file.
8 *
9 * This file contains a fast, not so accurate integer implementation of the
10 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
11 * must also perform dequantization of the input coefficients.
12 *
13 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
14 * on each row (or vice versa, but it's more convenient to emit a row at
15 * a time). Direct algorithms are also available, but they are much more
16 * complex and seem not to be any faster when reduced to code.
17 *
18 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
19 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
20 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
21 * JPEG textbook (see REFERENCES section in file README). The following code
22 * is based directly on figure 4-8 in P&M.
23 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
24 * possible to arrange the computation so that many of the multiplies are
25 * simple scalings of the final outputs. These multiplies can then be
26 * folded into the multiplications or divisions by the JPEG quantization
27 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
28 * to be done in the DCT itself.
29 * The primary disadvantage of this method is that with fixed-point math,
30 * accuracy is lost due to imprecise representation of the scaled
31 * quantization values. The smaller the quantization table entry, the less
32 * precise the scaled value, so this implementation does worse with high-
33 * quality-setting files than with low-quality ones.
34 */
35
36 #define JPEG_INTERNALS
37 #include "jinclude.h"
38 #include "jpeglib.h"
39 #include "jdct.h" /* Private declarations for DCT subsystem */
40
41 #ifdef DCT_IFAST_SUPPORTED
42
43
44 /*
45 * This module is specialized to the case DCTSIZE = 8.
46 */
47
48 #if DCTSIZE != 8
49 Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */
50 #endif
51
52
53 /* Scaling decisions are generally the same as in the LL&M algorithm;
54 * see jidctint.c for more details. However, we choose to descale
55 * (right shift) multiplication products as soon as they are formed,
56 * rather than carrying additional fractional bits into subsequent additions.
57 * This compromises accuracy slightly, but it lets us save a few shifts.
58 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
59 * everywhere except in the multiplications proper; this saves a good deal
60 * of work on 16-bit-int machines.
61 *
62 * The dequantized coefficients are not integers because the AA&N scaling
63 * factors have been incorporated. We represent them scaled up by PASS1_BITS,
64 * so that the first and second IDCT rounds have the same input scaling.
65 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
66 * avoid a descaling shift; this compromises accuracy rather drastically
67 * for small quantization table entries, but it saves a lot of shifts.
68 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
69 * so we use a much larger scaling factor to preserve accuracy.
70 *
71 * A final compromise is to represent the multiplicative constants to only
72 * 8 fractional bits, rather than 13. This saves some shifting work on some
73 * machines, and may also reduce the cost of multiplication (since there
74 * are fewer one-bits in the constants).
75 */
76
77 #if BITS_IN_JSAMPLE == 8
78 #define CONST_BITS 8
79 #define PASS1_BITS 2
80 #else
81 #define CONST_BITS 8
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 == 8
93 #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
94 #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
95 #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
96 #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
97 #else
98 #define FIX_1_082392200 FIX(1.082392200)
99 #define FIX_1_414213562 FIX(1.414213562)
100 #define FIX_1_847759065 FIX(1.847759065)
101 #define FIX_2_613125930 FIX(2.613125930)
102 #endif
103
104
105 /* We can gain a little more speed, with a further compromise in accuracy,
106 * by omitting the addition in a descaling shift. This yields an incorrectly
107 * rounded result half the time...
108 */
109
110 #ifndef USE_ACCURATE_ROUNDING
111 #undef DESCALE
112 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
113 #endif
114
115
116 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
117 * descale to yield a DCTELEM result.
118 */
119
120 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
121
122
123 /* Dequantize a coefficient by multiplying it by the multiplier-table
124 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
125 * multiplication will do. For 12-bit data, the multiplier table is
126 * declared INT32, so a 32-bit multiply will be used.
127 */
128
129 #if BITS_IN_JSAMPLE == 8
130 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
131 #else
132 #define DEQUANTIZE(coef,quantval) \
133 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
134 #endif
135
136
137 /*
138 * Perform dequantization and inverse DCT on one block of coefficients.
139 *
140 * cK represents cos(K*pi/16).
141 */
142
143 GLOBAL(void)
144 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
145 JCOEFPTR coef_block,
146 JSAMPARRAY output_buf, JDIMENSION output_col)
147 {
148 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
149 DCTELEM tmp10, tmp11, tmp12, tmp13;
150 DCTELEM z5, z10, z11, z12, z13;
151 JCOEFPTR inptr;
152 IFAST_MULT_TYPE * quantptr;
153 int * wsptr;
154 JSAMPROW outptr;
155 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
156 int ctr;
157 int workspace[DCTSIZE2]; /* buffers data between passes */
158 SHIFT_TEMPS /* for DESCALE */
159 ISHIFT_TEMPS /* for IRIGHT_SHIFT */
160
161 /* Pass 1: process columns from input, store into work array. */
162
163 inptr = coef_block;
164 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
165 wsptr = workspace;
166 for (ctr = DCTSIZE; ctr > 0; ctr--) {
167 /* Due to quantization, we will usually find that many of the input
168 * coefficients are zero, especially the AC terms. We can exploit this
169 * by short-circuiting the IDCT calculation for any column in which all
170 * the AC terms are zero. In that case each output is equal to the
171 * DC coefficient (with scale factor as needed).
172 * With typical images and quantization tables, half or more of the
173 * column DCT calculations can be simplified this way.
174 */
175
176 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
177 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
178 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
179 inptr[DCTSIZE*7] == 0) {
180 /* AC terms all zero */
181 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
182
183 wsptr[DCTSIZE*0] = dcval;
184 wsptr[DCTSIZE*1] = dcval;
185 wsptr[DCTSIZE*2] = dcval;
186 wsptr[DCTSIZE*3] = dcval;
187 wsptr[DCTSIZE*4] = dcval;
188 wsptr[DCTSIZE*5] = dcval;
189 wsptr[DCTSIZE*6] = dcval;
190 wsptr[DCTSIZE*7] = dcval;
191
192 inptr++; /* advance pointers to next column */
193 quantptr++;
194 wsptr++;
195 continue;
196 }
197
198 /* Even part */
199
200 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
201 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
202 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
203 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
204
205 tmp10 = tmp0 + tmp2; /* phase 3 */
206 tmp11 = tmp0 - tmp2;
207
208 tmp13 = tmp1 + tmp3; /* phases 5-3 */
209 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
210
211 tmp0 = tmp10 + tmp13; /* phase 2 */
212 tmp3 = tmp10 - tmp13;
213 tmp1 = tmp11 + tmp12;
214 tmp2 = tmp11 - tmp12;
215
216 /* Odd part */
217
218 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
219 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
220 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
221 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
222
223 z13 = tmp6 + tmp5; /* phase 6 */
224 z10 = tmp6 - tmp5;
225 z11 = tmp4 + tmp7;
226 z12 = tmp4 - tmp7;
227
228 tmp7 = z11 + z13; /* phase 5 */
229 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
230
231 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
232 tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */
233 tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */
234
235 tmp6 = tmp12 - tmp7; /* phase 2 */
236 tmp5 = tmp11 - tmp6;
237 tmp4 = tmp10 - tmp5;
238
239 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
240 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
241 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
242 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
243 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
244 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
245 wsptr[DCTSIZE*3] = (int) (tmp3 + tmp4);
246 wsptr[DCTSIZE*4] = (int) (tmp3 - tmp4);
247
248 inptr++; /* advance pointers to next column */
249 quantptr++;
250 wsptr++;
251 }
252
253 /* Pass 2: process rows from work array, store into output array.
254 * Note that we must descale the results by a factor of 8 == 2**3,
255 * and also undo the PASS1_BITS scaling.
256 */
257
258 wsptr = workspace;
259 for (ctr = 0; ctr < DCTSIZE; ctr++) {
260 outptr = output_buf[ctr] + output_col;
261
262 /* Add range center and fudge factor for final descale and range-limit. */
263 z5 = (DCTELEM) wsptr[0] +
264 ((((DCTELEM) RANGE_CENTER) << (PASS1_BITS+3)) +
265 (1 << (PASS1_BITS+2)));
266
267 /* Rows of zeroes can be exploited in the same way as we did with columns.
268 * However, the column calculation has created many nonzero AC terms, so
269 * the simplification applies less often (typically 5% to 10% of the time).
270 * On machines with very fast multiplication, it's possible that the
271 * test takes more time than it's worth. In that case this section
272 * may be commented out.
273 */
274
275 #ifndef NO_ZERO_ROW_TEST
276 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
277 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
278 /* AC terms all zero */
279 JSAMPLE dcval = range_limit[(int) IRIGHT_SHIFT(z5, PASS1_BITS+3)
280 & RANGE_MASK];
281
282 outptr[0] = dcval;
283 outptr[1] = dcval;
284 outptr[2] = dcval;
285 outptr[3] = dcval;
286 outptr[4] = dcval;
287 outptr[5] = dcval;
288 outptr[6] = dcval;
289 outptr[7] = dcval;
290
291 wsptr += DCTSIZE; /* advance pointer to next row */
292 continue;
293 }
294 #endif
295
296 /* Even part */
297
298 tmp10 = z5 + (DCTELEM) wsptr[4];
299 tmp11 = z5 - (DCTELEM) wsptr[4];
300
301 tmp13 = (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6];
302 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6],
303 FIX_1_414213562) - tmp13; /* 2*c4 */
304
305 tmp0 = tmp10 + tmp13;
306 tmp3 = tmp10 - tmp13;
307 tmp1 = tmp11 + tmp12;
308 tmp2 = tmp11 - tmp12;
309
310 /* Odd part */
311
312 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
313 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
314 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
315 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
316
317 tmp7 = z11 + z13; /* phase 5 */
318 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
319
320 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
321 tmp10 = z5 - MULTIPLY(z12, FIX_1_082392200); /* 2*(c2-c6) */
322 tmp12 = z5 - MULTIPLY(z10, FIX_2_613125930); /* 2*(c2+c6) */
323
324 tmp6 = tmp12 - tmp7; /* phase 2 */
325 tmp5 = tmp11 - tmp6;
326 tmp4 = tmp10 - tmp5;
327
328 /* Final output stage: scale down by a factor of 8 and range-limit */
329
330 outptr[0] = range_limit[(int) IRIGHT_SHIFT(tmp0 + tmp7, PASS1_BITS+3)
331 & RANGE_MASK];
332 outptr[7] = range_limit[(int) IRIGHT_SHIFT(tmp0 - tmp7, PASS1_BITS+3)
333 & RANGE_MASK];
334 outptr[1] = range_limit[(int) IRIGHT_SHIFT(tmp1 + tmp6, PASS1_BITS+3)
335 & RANGE_MASK];
336 outptr[6] = range_limit[(int) IRIGHT_SHIFT(tmp1 - tmp6, PASS1_BITS+3)
337 & RANGE_MASK];
338 outptr[2] = range_limit[(int) IRIGHT_SHIFT(tmp2 + tmp5, PASS1_BITS+3)
339 & RANGE_MASK];
340 outptr[5] = range_limit[(int) IRIGHT_SHIFT(tmp2 - tmp5, PASS1_BITS+3)
341 & RANGE_MASK];
342 outptr[3] = range_limit[(int) IRIGHT_SHIFT(tmp3 + tmp4, PASS1_BITS+3)
343 & RANGE_MASK];
344 outptr[4] = range_limit[(int) IRIGHT_SHIFT(tmp3 - tmp4, PASS1_BITS+3)
345 & RANGE_MASK];
346
347 wsptr += DCTSIZE; /* advance pointer to next row */
348 }
349 }
350
351 #endif /* DCT_IFAST_SUPPORTED */