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
170GLOBAL(void)
171jpeg_idct_ifast(j_decompress_ptr cinfo, jpeg_component_info *compptr,
172 JCOEFPTR coef_block, JSAMPARRAY output_buf,
173 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 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 inptr = coef_block;
191 quantptr = (IFAST_MULT_TYPE *)compptr->dct_table;
192 wsptr = workspace;
193 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 if (inptr[DCTSIZE * 1] == 0 && inptr[DCTSIZE * 2] == 0 &&
204 inptr[DCTSIZE * 3] == 0 && inptr[DCTSIZE * 4] == 0 &&
205 inptr[DCTSIZE * 5] == 0 && inptr[DCTSIZE * 6] == 0 &&
206 inptr[DCTSIZE * 7] == 0) {
207 /* AC terms all zero */
208 int dcval = (int)DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]);
209
210 wsptr[DCTSIZE * 0] = dcval;
211 wsptr[DCTSIZE * 1] = dcval;
212 wsptr[DCTSIZE * 2] = dcval;
213 wsptr[DCTSIZE * 3] = dcval;
214 wsptr[DCTSIZE * 4] = dcval;
215 wsptr[DCTSIZE * 5] = dcval;
216 wsptr[DCTSIZE * 6] = dcval;
217 wsptr[DCTSIZE * 7] = dcval;
218
219 inptr++; /* advance pointers to next column */
220 quantptr++;
221 wsptr++;
222 continue;
223 }
224
225 /* Even part */
226
227 tmp0 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]);
228 tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2]);
229 tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4]);
230 tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6]);
231
232 tmp10 = tmp0 + tmp2; /* phase 3 */
233 tmp11 = tmp0 - tmp2;
234
235 tmp13 = tmp1 + tmp3; /* phases 5-3 */
236 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
237
238 tmp0 = tmp10 + tmp13; /* phase 2 */
239 tmp3 = tmp10 - tmp13;
240 tmp1 = tmp11 + tmp12;
241 tmp2 = tmp11 - tmp12;
242
243 /* Odd part */
244
245 tmp4 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1]);
246 tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3]);
247 tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5]);
248 tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7]);
249
250 z13 = tmp6 + tmp5; /* phase 6 */
251 z10 = tmp6 - tmp5;
252 z11 = tmp4 + tmp7;
253 z12 = tmp4 - tmp7;
254
255 tmp7 = z11 + z13; /* phase 5 */
256 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
257
258 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
259 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
260 tmp12 = MULTIPLY(z10, -FIX_2_613125930) + z5; /* -2*(c2+c6) */
261
262 tmp6 = tmp12 - tmp7; /* phase 2 */
263 tmp5 = tmp11 - tmp6;
264 tmp4 = tmp10 + tmp5;
265
266 wsptr[DCTSIZE * 0] = (int)(tmp0 + tmp7);
267 wsptr[DCTSIZE * 7] = (int)(tmp0 - tmp7);
268 wsptr[DCTSIZE * 1] = (int)(tmp1 + tmp6);
269 wsptr[DCTSIZE * 6] = (int)(tmp1 - tmp6);
270 wsptr[DCTSIZE * 2] = (int)(tmp2 + tmp5);
271 wsptr[DCTSIZE * 5] = (int)(tmp2 - tmp5);
272 wsptr[DCTSIZE * 4] = (int)(tmp3 + tmp4);
273 wsptr[DCTSIZE * 3] = (int)(tmp3 - tmp4);
274
275 inptr++; /* advance pointers to next column */
276 quantptr++;
277 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 wsptr = workspace;
285 for (ctr = 0; ctr < DCTSIZE; ctr++) {
286 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 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
297 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
298 /* AC terms all zero */
299 JSAMPLE dcval =
300 range_limit[IDESCALE(wsptr[0], PASS1_BITS + 3) & RANGE_MASK];
301
302 outptr[0] = dcval;
303 outptr[1] = dcval;
304 outptr[2] = dcval;
305 outptr[3] = dcval;
306 outptr[4] = dcval;
307 outptr[5] = dcval;
308 outptr[6] = dcval;
309 outptr[7] = dcval;
310
311 wsptr += DCTSIZE; /* advance pointer to next row */
312 continue;
313 }
314#endif
315
316 /* Even part */
317
318 tmp10 = ((DCTELEM)wsptr[0] + (DCTELEM)wsptr[4]);
319 tmp11 = ((DCTELEM)wsptr[0] - (DCTELEM)wsptr[4]);
320
321 tmp13 = ((DCTELEM)wsptr[2] + (DCTELEM)wsptr[6]);
322 tmp12 =
323 MULTIPLY((DCTELEM)wsptr[2] - (DCTELEM)wsptr[6], FIX_1_414213562) - tmp13;
324
325 tmp0 = tmp10 + tmp13;
326 tmp3 = tmp10 - tmp13;
327 tmp1 = tmp11 + tmp12;
328 tmp2 = tmp11 - tmp12;
329
330 /* Odd part */
331
332 z13 = (DCTELEM)wsptr[5] + (DCTELEM)wsptr[3];
333 z10 = (DCTELEM)wsptr[5] - (DCTELEM)wsptr[3];
334 z11 = (DCTELEM)wsptr[1] + (DCTELEM)wsptr[7];
335 z12 = (DCTELEM)wsptr[1] - (DCTELEM)wsptr[7];
336
337 tmp7 = z11 + z13; /* phase 5 */
338 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
339
340 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
341 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
342 tmp12 = MULTIPLY(z10, -FIX_2_613125930) + z5; /* -2*(c2+c6) */
343
344 tmp6 = tmp12 - tmp7; /* phase 2 */
345 tmp5 = tmp11 - tmp6;
346 tmp4 = tmp10 + tmp5;
347
348 /* Final output stage: scale down by a factor of 8 and range-limit */
349
350 outptr[0] =
351 range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS + 3) & RANGE_MASK];
352 outptr[7] =
353 range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS + 3) & RANGE_MASK];
354 outptr[1] =
355 range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS + 3) & RANGE_MASK];
356 outptr[6] =
357 range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS + 3) & RANGE_MASK];
358 outptr[2] =
359 range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS + 3) & RANGE_MASK];
360 outptr[5] =
361 range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS + 3) & RANGE_MASK];
362 outptr[4] =
363 range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS + 3) & RANGE_MASK];
364 outptr[3] =
365 range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS + 3) & RANGE_MASK];
366
367 wsptr += DCTSIZE; /* advance pointer to next row */
368 }
369}
370
371#endif /* DCT_IFAST_SUPPORTED */
372