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, JSAMPARRAY output_buf,
123 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],
150 quantptr[DCTSIZE * 0]), 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] =
193 (int)DESCALE(tmp10 + tmp2, CONST_BITS - PASS1_BITS + 1);
194 wsptr[DCTSIZE * 3] =
195 (int)DESCALE(tmp10 - tmp2, CONST_BITS - PASS1_BITS + 1);
196 wsptr[DCTSIZE * 1] =
197 (int)DESCALE(tmp12 + tmp0, CONST_BITS - PASS1_BITS + 1);
198 wsptr[DCTSIZE * 2] =
199 (int)DESCALE(tmp12 - tmp0, CONST_BITS - PASS1_BITS + 1);
200 }
201
202 /* Pass 2: process 4 rows from work array, store into output array. */
203
204 wsptr = workspace;
205 for (ctr = 0; ctr < 4; ctr++) {
206 outptr = output_buf[ctr] + output_col;
207 /* It's not clear whether a zero row test is worthwhile here ... */
208
209#ifndef NO_ZERO_ROW_TEST
210 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 &&
211 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
212 /* AC terms all zero */
213 JSAMPLE dcval = range_limit[(int)DESCALE((JLONG)wsptr[0],
214 PASS1_BITS + 3) & RANGE_MASK];
215
216 outptr[0] = dcval;
217 outptr[1] = dcval;
218 outptr[2] = dcval;
219 outptr[3] = dcval;
220
221 wsptr += DCTSIZE; /* advance pointer to next row */
222 continue;
223 }
224#endif
225
226 /* Even part */
227
228 tmp0 = LEFT_SHIFT((JLONG)wsptr[0], CONST_BITS + 1);
229
230 tmp2 = MULTIPLY((JLONG)wsptr[2], FIX_1_847759065) +
231 MULTIPLY((JLONG)wsptr[6], -FIX_0_765366865);
232
233 tmp10 = tmp0 + tmp2;
234 tmp12 = tmp0 - tmp2;
235
236 /* Odd part */
237
238 z1 = (JLONG)wsptr[7];
239 z2 = (JLONG)wsptr[5];
240 z3 = (JLONG)wsptr[3];
241 z4 = (JLONG)wsptr[1];
242
243 tmp0 = MULTIPLY(z1, -FIX_0_211164243) + /* sqrt(2) * ( c3-c1) */
244 MULTIPLY(z2, FIX_1_451774981) + /* sqrt(2) * ( c3+c7) */
245 MULTIPLY(z3, -FIX_2_172734803) + /* sqrt(2) * (-c1-c5) */
246 MULTIPLY(z4, FIX_1_061594337); /* sqrt(2) * ( c5+c7) */
247
248 tmp2 = MULTIPLY(z1, -FIX_0_509795579) + /* sqrt(2) * (c7-c5) */
249 MULTIPLY(z2, -FIX_0_601344887) + /* sqrt(2) * (c5-c1) */
250 MULTIPLY(z3, FIX_0_899976223) + /* sqrt(2) * (c3-c7) */
251 MULTIPLY(z4, FIX_2_562915447); /* sqrt(2) * (c1+c3) */
252
253 /* Final output stage */
254
255 outptr[0] = range_limit[(int)DESCALE(tmp10 + tmp2,
256 CONST_BITS + PASS1_BITS + 3 + 1) &
257 RANGE_MASK];
258 outptr[3] = range_limit[(int)DESCALE(tmp10 - tmp2,
259 CONST_BITS + PASS1_BITS + 3 + 1) &
260 RANGE_MASK];
261 outptr[1] = range_limit[(int)DESCALE(tmp12 + tmp0,
262 CONST_BITS + PASS1_BITS + 3 + 1) &
263 RANGE_MASK];
264 outptr[2] = range_limit[(int)DESCALE(tmp12 - tmp0,
265 CONST_BITS + PASS1_BITS + 3 + 1) &
266 RANGE_MASK];
267
268 wsptr += DCTSIZE; /* advance pointer to next row */
269 }
270}
271
272
273/*
274 * Perform dequantization and inverse DCT on one block of coefficients,
275 * producing a reduced-size 2x2 output block.
276 */
277
278GLOBAL(void)
279jpeg_idct_2x2(j_decompress_ptr cinfo, jpeg_component_info *compptr,
280 JCOEFPTR coef_block, JSAMPARRAY output_buf,
281 JDIMENSION output_col)
282{
283 JLONG tmp0, tmp10, z1;
284 JCOEFPTR inptr;
285 ISLOW_MULT_TYPE *quantptr;
286 int *wsptr;
287 JSAMPROW outptr;
288 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
289 int ctr;
290 int workspace[DCTSIZE * 2]; /* buffers data between passes */
291 SHIFT_TEMPS
292
293 /* Pass 1: process columns from input, store into work array. */
294
295 inptr = coef_block;
296 quantptr = (ISLOW_MULT_TYPE *)compptr->dct_table;
297 wsptr = workspace;
298 for (ctr = DCTSIZE; ctr > 0; inptr++, quantptr++, wsptr++, ctr--) {
299 /* Don't bother to process columns 2,4,6 */
300 if (ctr == DCTSIZE - 2 || ctr == DCTSIZE - 4 || ctr == DCTSIZE - 6)
301 continue;
302 if (inptr[DCTSIZE * 1] == 0 && inptr[DCTSIZE * 3] == 0 &&
303 inptr[DCTSIZE * 5] == 0 && inptr[DCTSIZE * 7] == 0) {
304 /* AC terms all zero; we need not examine terms 2,4,6 for 2x2 output */
305 int dcval = LEFT_SHIFT(DEQUANTIZE(inptr[DCTSIZE * 0],
306 quantptr[DCTSIZE * 0]), PASS1_BITS);
307
308 wsptr[DCTSIZE * 0] = dcval;
309 wsptr[DCTSIZE * 1] = dcval;
310
311 continue;
312 }
313
314 /* Even part */
315
316 z1 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]);
317 tmp10 = LEFT_SHIFT(z1, CONST_BITS + 2);
318
319 /* Odd part */
320
321 z1 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7]);
322 tmp0 = MULTIPLY(z1, -FIX_0_720959822); /* sqrt(2) * ( c7-c5+c3-c1) */
323 z1 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5]);
324 tmp0 += MULTIPLY(z1, FIX_0_850430095); /* sqrt(2) * (-c1+c3+c5+c7) */
325 z1 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3]);
326 tmp0 += MULTIPLY(z1, -FIX_1_272758580); /* sqrt(2) * (-c1+c3-c5-c7) */
327 z1 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1]);
328 tmp0 += MULTIPLY(z1, FIX_3_624509785); /* sqrt(2) * ( c1+c3+c5+c7) */
329
330 /* Final output stage */
331
332 wsptr[DCTSIZE * 0] =
333 (int)DESCALE(tmp10 + tmp0, CONST_BITS - PASS1_BITS + 2);
334 wsptr[DCTSIZE * 1] =
335 (int)DESCALE(tmp10 - tmp0, CONST_BITS - PASS1_BITS + 2);
336 }
337
338 /* Pass 2: process 2 rows from work array, store into output array. */
339
340 wsptr = workspace;
341 for (ctr = 0; ctr < 2; ctr++) {
342 outptr = output_buf[ctr] + output_col;
343 /* It's not clear whether a zero row test is worthwhile here ... */
344
345#ifndef NO_ZERO_ROW_TEST
346 if (wsptr[1] == 0 && wsptr[3] == 0 && wsptr[5] == 0 && wsptr[7] == 0) {
347 /* AC terms all zero */
348 JSAMPLE dcval = range_limit[(int)DESCALE((JLONG)wsptr[0],
349 PASS1_BITS + 3) & RANGE_MASK];
350
351 outptr[0] = dcval;
352 outptr[1] = dcval;
353
354 wsptr += DCTSIZE; /* advance pointer to next row */
355 continue;
356 }
357#endif
358
359 /* Even part */
360
361 tmp10 = LEFT_SHIFT((JLONG)wsptr[0], CONST_BITS + 2);
362
363 /* Odd part */
364
365 tmp0 = MULTIPLY((JLONG)wsptr[7], -FIX_0_720959822) + /* sqrt(2) * ( c7-c5+c3-c1) */
366 MULTIPLY((JLONG)wsptr[5], FIX_0_850430095) + /* sqrt(2) * (-c1+c3+c5+c7) */
367 MULTIPLY((JLONG)wsptr[3], -FIX_1_272758580) + /* sqrt(2) * (-c1+c3-c5-c7) */
368 MULTIPLY((JLONG)wsptr[1], FIX_3_624509785); /* sqrt(2) * ( c1+c3+c5+c7) */
369
370 /* Final output stage */
371
372 outptr[0] = range_limit[(int)DESCALE(tmp10 + tmp0,
373 CONST_BITS + PASS1_BITS + 3 + 2) &
374 RANGE_MASK];
375 outptr[1] = range_limit[(int)DESCALE(tmp10 - tmp0,
376 CONST_BITS + PASS1_BITS + 3 + 2) &
377 RANGE_MASK];
378
379 wsptr += DCTSIZE; /* advance pointer to next row */
380 }
381}
382
383
384/*
385 * Perform dequantization and inverse DCT on one block of coefficients,
386 * producing a reduced-size 1x1 output block.
387 */
388
389GLOBAL(void)
390jpeg_idct_1x1(j_decompress_ptr cinfo, jpeg_component_info *compptr,
391 JCOEFPTR coef_block, JSAMPARRAY output_buf,
392 JDIMENSION output_col)
393{
394 int dcval;
395 ISLOW_MULT_TYPE *quantptr;
396 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
397 SHIFT_TEMPS
398
399 /* We hardly need an inverse DCT routine for this: just take the
400 * average pixel value, which is one-eighth of the DC coefficient.
401 */
402 quantptr = (ISLOW_MULT_TYPE *)compptr->dct_table;
403 dcval = DEQUANTIZE(coef_block[0], quantptr[0]);
404 dcval = (int)DESCALE((JLONG)dcval, 3);
405
406 output_buf[0][output_col] = range_limit[dcval & RANGE_MASK];
407}
408
409#endif /* IDCT_SCALING_SUPPORTED */
410