1/*
2 * jidctred.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 inverse-DCT routines that produce reduced-size output:
12 * either 4x4, 2x2, or 1x1 pixels from an 8x8 DCT block.
13 *
14 * The implementation is based on the Loeffler, Ligtenberg and Moschytz (LL&M)
15 * algorithm used in jidctint.c. We simply replace each 8-to-8 1-D IDCT step
16 * with an 8-to-4 step that produces the four averages of two adjacent outputs
17 * (or an 8-to-2 step producing two averages of four outputs, for 2x2 output).
18 * These steps were derived by computing the corresponding values at the end
19 * of the normal LL&M code, then simplifying as much as possible.
20 *
21 * 1x1 is trivial: just take the DC coefficient divided by 8.
22 *
23 * See jidctint.c for additional comments.
24 */
25
26#define JPEG_INTERNALS
27#include "jinclude.h"
28#include "jpeglib.h"
29#include "jdct.h" /* Private declarations for DCT subsystem */
30
31#ifdef IDCT_SCALING_SUPPORTED
32
33
34/*
35 * This module is specialized to the case DCTSIZE = 8.
36 */
37
38#if DCTSIZE != 8
39 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
40#endif
41
42
43/* Scaling is the same as in jidctint.c. */
44
45#if BITS_IN_JSAMPLE == 8
46#define CONST_BITS 13
47#define PASS1_BITS 2
48#else
49#define CONST_BITS 13
50#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
51#endif
52
53/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
54 * causing a lot of useless floating-point operations at run time.
55 * To get around this we use the following pre-calculated constants.
56 * If you change CONST_BITS you may want to add appropriate values.
57 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
58 */
59
60#if CONST_BITS == 13
61#define FIX_0_211164243 ((JLONG) 1730) /* FIX(0.211164243) */
62#define FIX_0_509795579 ((JLONG) 4176) /* FIX(0.509795579) */
63#define FIX_0_601344887 ((JLONG) 4926) /* FIX(0.601344887) */
64#define FIX_0_720959822 ((JLONG) 5906) /* FIX(0.720959822) */
65#define FIX_0_765366865 ((JLONG) 6270) /* FIX(0.765366865) */
66#define FIX_0_850430095 ((JLONG) 6967) /* FIX(0.850430095) */
67#define FIX_0_899976223 ((JLONG) 7373) /* FIX(0.899976223) */
68#define FIX_1_061594337 ((JLONG) 8697) /* FIX(1.061594337) */
69#define FIX_1_272758580 ((JLONG) 10426) /* FIX(1.272758580) */
70#define FIX_1_451774981 ((JLONG) 11893) /* FIX(1.451774981) */
71#define FIX_1_847759065 ((JLONG) 15137) /* FIX(1.847759065) */
72#define FIX_2_172734803 ((JLONG) 17799) /* FIX(2.172734803) */
73#define FIX_2_562915447 ((JLONG) 20995) /* FIX(2.562915447) */
74#define FIX_3_624509785 ((JLONG) 29692) /* FIX(3.624509785) */
75#else
76#define FIX_0_211164243 FIX(0.211164243)
77#define FIX_0_509795579 FIX(0.509795579)
78#define FIX_0_601344887 FIX(0.601344887)
79#define FIX_0_720959822 FIX(0.720959822)
80#define FIX_0_765366865 FIX(0.765366865)
81#define FIX_0_850430095 FIX(0.850430095)
82#define FIX_0_899976223 FIX(0.899976223)
83#define FIX_1_061594337 FIX(1.061594337)
84#define FIX_1_272758580 FIX(1.272758580)
85#define FIX_1_451774981 FIX(1.451774981)
86#define FIX_1_847759065 FIX(1.847759065)
87#define FIX_2_172734803 FIX(2.172734803)
88#define FIX_2_562915447 FIX(2.562915447)
89#define FIX_3_624509785 FIX(3.624509785)
90#endif
91
92
93/* Multiply a JLONG variable by a JLONG constant to yield a JLONG result.
94 * For 8-bit samples with the recommended scaling, all the variable
95 * and constant values involved are no more than 16 bits wide, so a
96 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
97 * For 12-bit samples, a full 32-bit multiplication will be needed.
98 */
99
100#if BITS_IN_JSAMPLE == 8
101#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
102#else
103#define MULTIPLY(var,const) ((var) * (const))
104#endif
105
106
107/* Dequantize a coefficient by multiplying it by the multiplier-table
108 * entry; produce an int result. In this module, both inputs and result
109 * are 16 bits or less, so either int or short multiply will work.
110 */
111
112#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
113
114
115/*
116 * Perform dequantization and inverse DCT on one block of coefficients,
117 * producing a reduced-size 4x4 output block.
118 */
119
120GLOBAL(void)
121jpeg_idct_4x4 (j_decompress_ptr cinfo, jpeg_component_info *compptr,
122 JCOEFPTR coef_block,
123 JSAMPARRAY output_buf, JDIMENSION output_col)
124{
125 JLONG tmp0, tmp2, tmp10, tmp12;
126 JLONG z1, z2, z3, z4;
127 JCOEFPTR inptr;
128 ISLOW_MULT_TYPE *quantptr;
129 int *wsptr;
130 JSAMPROW outptr;
131 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
132 int ctr;
133 int workspace[DCTSIZE*4]; /* buffers data between passes */
134 SHIFT_TEMPS
135
136 /* Pass 1: process columns from input, store into work array. */
137
138 inptr = coef_block;
139 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
140 wsptr = workspace;
141 for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
142 /* Don't bother to process column 4, because second pass won't use it */
143 if (ctr == DCTSIZE-4)
144 continue;
145 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
146 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*5] == 0 &&
147 inptr[DCTSIZE*6] == 0 && inptr[DCTSIZE*7] == 0) {
148 /* AC terms all zero; we need not examine term 4 for 4x4 output */
149 int dcval = LEFT_SHIFT(DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]),
150 PASS1_BITS);
151
152 wsptr[DCTSIZE*0] = dcval;
153 wsptr[DCTSIZE*1] = dcval;
154 wsptr[DCTSIZE*2] = dcval;
155 wsptr[DCTSIZE*3] = dcval;
156
157 continue;
158 }
159
160 /* Even part */
161
162 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
163 tmp0 = LEFT_SHIFT(tmp0, CONST_BITS+1);
164
165 z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
166 z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
167
168 tmp2 = MULTIPLY(z2, FIX_1_847759065) + MULTIPLY(z3, - FIX_0_765366865);
169
170 tmp10 = tmp0 + tmp2;
171 tmp12 = tmp0 - tmp2;
172
173 /* Odd part */
174
175 z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
176 z2 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
177 z3 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
178 z4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
179
180 tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
181 + MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
182 + MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
183 + MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */
184
185 tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
186 + MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
187 + MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
188 + MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */
189
190 /* Final output stage */
191
192 wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp2, CONST_BITS-PASS1_BITS+1);
193 wsptr[DCTSIZE*3] = (int) DESCALE(tmp10 - tmp2, CONST_BITS-PASS1_BITS+1);
194 wsptr[DCTSIZE*1] = (int) DESCALE(tmp12 + tmp0, CONST_BITS-PASS1_BITS+1);
195 wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 - tmp0, CONST_BITS-PASS1_BITS+1);
196 }
197
198 /* Pass 2: process 4 rows from work array, store into output array. */
199
200 wsptr = workspace;
201 for (ctr = 0; ctr < 4; ctr++) {
202 outptr = output_buf[ctr] + output_col;
203 /* It's not clear whether a zero row test is worthwhile here ... */
204
205#ifndef NO_ZERO_ROW_TEST
206 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 &&
207 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
208 /* AC terms all zero */
209 JSAMPLE dcval = range_limit[(int) DESCALE((JLONG) wsptr[0], PASS1_BITS+3)
210 & RANGE_MASK];
211
212 outptr[0] = dcval;
213 outptr[1] = dcval;
214 outptr[2] = dcval;
215 outptr[3] = dcval;
216
217 wsptr += DCTSIZE; /* advance pointer to next row */
218 continue;
219 }
220#endif
221
222 /* Even part */
223
224 tmp0 = LEFT_SHIFT((JLONG) wsptr[0], CONST_BITS+1);
225
226 tmp2 = MULTIPLY((JLONG) wsptr[2], FIX_1_847759065)
227 + MULTIPLY((JLONG) wsptr[6], - FIX_0_765366865);
228
229 tmp10 = tmp0 + tmp2;
230 tmp12 = tmp0 - tmp2;
231
232 /* Odd part */
233
234 z1 = (JLONG) wsptr[7];
235 z2 = (JLONG) wsptr[5];
236 z3 = (JLONG) wsptr[3];
237 z4 = (JLONG) wsptr[1];
238
239 tmp0 = MULTIPLY(z1, - FIX_0_211164243) /* sqrt(2) * (c3-c1) */
240 + MULTIPLY(z2, FIX_1_451774981) /* sqrt(2) * (c3+c7) */
241 + MULTIPLY(z3, - FIX_2_172734803) /* sqrt(2) * (-c1-c5) */
242 + MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * (c5+c7) */
243
244 tmp2 = MULTIPLY(z1, - FIX_0_509795579) /* sqrt(2) * (c7-c5) */
245 + MULTIPLY(z2, - FIX_0_601344887) /* sqrt(2) * (c5-c1) */
246 + MULTIPLY(z3, FIX_0_899976223) /* sqrt(2) * (c3-c7) */
247 + MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */
248
249 /* Final output stage */
250
251 outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp2,
252 CONST_BITS+PASS1_BITS+3+1)
253 & RANGE_MASK];
254 outptr[3] = range_limit[(int) DESCALE(tmp10 - tmp2,
255 CONST_BITS+PASS1_BITS+3+1)
256 & RANGE_MASK];
257 outptr[1] = range_limit[(int) DESCALE(tmp12 + tmp0,
258 CONST_BITS+PASS1_BITS+3+1)
259 & RANGE_MASK];
260 outptr[2] = range_limit[(int) DESCALE(tmp12 - tmp0,
261 CONST_BITS+PASS1_BITS+3+1)
262 & RANGE_MASK];
263
264 wsptr += DCTSIZE; /* advance pointer to next row */
265 }
266}
267
268
269/*
270 * Perform dequantization and inverse DCT on one block of coefficients,
271 * producing a reduced-size 2x2 output block.
272 */
273
274GLOBAL(void)
275jpeg_idct_2x2 (j_decompress_ptr cinfo, jpeg_component_info *compptr,
276 JCOEFPTR coef_block,
277 JSAMPARRAY output_buf, JDIMENSION output_col)
278{
279 JLONG tmp0, tmp10, z1;
280 JCOEFPTR inptr;
281 ISLOW_MULT_TYPE *quantptr;
282 int *wsptr;
283 JSAMPROW outptr;
284 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
285 int ctr;
286 int workspace[DCTSIZE*2]; /* buffers data between passes */
287 SHIFT_TEMPS
288
289 /* Pass 1: process columns from input, store into work array. */
290
291 inptr = coef_block;
292 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
293 wsptr = workspace;
294 for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
295 /* Don't bother to process columns 2,4,6 */
296 if (ctr == DCTSIZE-2 || ctr == DCTSIZE-4 || ctr == DCTSIZE-6)
297 continue;
298 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*3] == 0 &&
299 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*7] == 0) {
300 /* AC terms all zero; we need not examine terms 2,4,6 for 2x2 output */
301 int dcval = LEFT_SHIFT(DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]),
302 PASS1_BITS);
303
304 wsptr[DCTSIZE*0] = dcval;
305 wsptr[DCTSIZE*1] = dcval;
306
307 continue;
308 }
309
310 /* Even part */
311
312 z1 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
313 tmp10 = LEFT_SHIFT(z1, CONST_BITS+2);
314
315 /* Odd part */
316
317 z1 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
318 tmp0 = MULTIPLY(z1, - FIX_0_720959822); /* sqrt(2) * (c7-c5+c3-c1) */
319 z1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
320 tmp0 += MULTIPLY(z1, FIX_0_850430095); /* sqrt(2) * (-c1+c3+c5+c7) */
321 z1 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
322 tmp0 += MULTIPLY(z1, - FIX_1_272758580); /* sqrt(2) * (-c1+c3-c5-c7) */
323 z1 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
324 tmp0 += MULTIPLY(z1, FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */
325
326 /* Final output stage */
327
328 wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp0, CONST_BITS-PASS1_BITS+2);
329 wsptr[DCTSIZE*1] = (int) DESCALE(tmp10 - tmp0, CONST_BITS-PASS1_BITS+2);
330 }
331
332 /* Pass 2: process 2 rows from work array, store into output array. */
333
334 wsptr = workspace;
335 for (ctr = 0; ctr < 2; ctr++) {
336 outptr = output_buf[ctr] + output_col;
337 /* It's not clear whether a zero row test is worthwhile here ... */
338
339#ifndef NO_ZERO_ROW_TEST
340 if (wsptr[1] == 0 && wsptr[3] == 0 && wsptr[5] == 0 && wsptr[7] == 0) {
341 /* AC terms all zero */
342 JSAMPLE dcval = range_limit[(int) DESCALE((JLONG) wsptr[0], PASS1_BITS+3)
343 & RANGE_MASK];
344
345 outptr[0] = dcval;
346 outptr[1] = dcval;
347
348 wsptr += DCTSIZE; /* advance pointer to next row */
349 continue;
350 }
351#endif
352
353 /* Even part */
354
355 tmp10 = LEFT_SHIFT((JLONG) wsptr[0], CONST_BITS+2);
356
357 /* Odd part */
358
359 tmp0 = MULTIPLY((JLONG) wsptr[7], - FIX_0_720959822) /* sqrt(2) * (c7-c5+c3-c1) */
360 + MULTIPLY((JLONG) wsptr[5], FIX_0_850430095) /* sqrt(2) * (-c1+c3+c5+c7) */
361 + MULTIPLY((JLONG) wsptr[3], - FIX_1_272758580) /* sqrt(2) * (-c1+c3-c5-c7) */
362 + MULTIPLY((JLONG) wsptr[1], FIX_3_624509785); /* sqrt(2) * (c1+c3+c5+c7) */
363
364 /* Final output stage */
365
366 outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp0,
367 CONST_BITS+PASS1_BITS+3+2)
368 & RANGE_MASK];
369 outptr[1] = range_limit[(int) DESCALE(tmp10 - tmp0,
370 CONST_BITS+PASS1_BITS+3+2)
371 & RANGE_MASK];
372
373 wsptr += DCTSIZE; /* advance pointer to next row */
374 }
375}
376
377
378/*
379 * Perform dequantization and inverse DCT on one block of coefficients,
380 * producing a reduced-size 1x1 output block.
381 */
382
383GLOBAL(void)
384jpeg_idct_1x1 (j_decompress_ptr cinfo, jpeg_component_info *compptr,
385 JCOEFPTR coef_block,
386 JSAMPARRAY output_buf, JDIMENSION output_col)
387{
388 int dcval;
389 ISLOW_MULT_TYPE *quantptr;
390 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
391 SHIFT_TEMPS
392
393 /* We hardly need an inverse DCT routine for this: just take the
394 * average pixel value, which is one-eighth of the DC coefficient.
395 */
396 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
397 dcval = DEQUANTIZE(coef_block[0], quantptr[0]);
398 dcval = (int) DESCALE((JLONG) dcval, 3);
399
400 output_buf[0][output_col] = range_limit[dcval & RANGE_MASK];
401}
402
403#endif /* IDCT_SCALING_SUPPORTED */
404