1/*
2 * reserved comment block
3 * DO NOT REMOVE OR ALTER!
4 */
5/*
6 * jidctfst.c
7 *
8 * Copyright (C) 1994-1998, Thomas G. Lane.
9 * This file is part of the Independent JPEG Group's software.
10 * For conditions of distribution and use, see the accompanying README file.
11 *
12 * This file contains a fast, not so accurate integer implementation of the
13 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
14 * must also perform dequantization of the input coefficients.
15 *
16 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
17 * on each row (or vice versa, but it's more convenient to emit a row at
18 * a time). Direct algorithms are also available, but they are much more
19 * complex and seem not to be any faster when reduced to code.
20 *
21 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
22 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
23 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
24 * JPEG textbook (see REFERENCES section in file README). The following code
25 * is based directly on figure 4-8 in P&M.
26 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
27 * possible to arrange the computation so that many of the multiplies are
28 * simple scalings of the final outputs. These multiplies can then be
29 * folded into the multiplications or divisions by the JPEG quantization
30 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
31 * to be done in the DCT itself.
32 * The primary disadvantage of this method is that with fixed-point math,
33 * accuracy is lost due to imprecise representation of the scaled
34 * quantization values. The smaller the quantization table entry, the less
35 * precise the scaled value, so this implementation does worse with high-
36 * quality-setting files than with low-quality ones.
37 */
38
39#define JPEG_INTERNALS
40#include "jinclude.h"
41#include "jpeglib.h"
42#include "jdct.h" /* Private declarations for DCT subsystem */
43
44#ifdef DCT_IFAST_SUPPORTED
45
46
47/*
48 * This module is specialized to the case DCTSIZE = 8.
49 */
50
51#if DCTSIZE != 8
52 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
53#endif
54
55
56/* Scaling decisions are generally the same as in the LL&M algorithm;
57 * see jidctint.c for more details. However, we choose to descale
58 * (right shift) multiplication products as soon as they are formed,
59 * rather than carrying additional fractional bits into subsequent additions.
60 * This compromises accuracy slightly, but it lets us save a few shifts.
61 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
62 * everywhere except in the multiplications proper; this saves a good deal
63 * of work on 16-bit-int machines.
64 *
65 * The dequantized coefficients are not integers because the AA&N scaling
66 * factors have been incorporated. We represent them scaled up by PASS1_BITS,
67 * so that the first and second IDCT rounds have the same input scaling.
68 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
69 * avoid a descaling shift; this compromises accuracy rather drastically
70 * for small quantization table entries, but it saves a lot of shifts.
71 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
72 * so we use a much larger scaling factor to preserve accuracy.
73 *
74 * A final compromise is to represent the multiplicative constants to only
75 * 8 fractional bits, rather than 13. This saves some shifting work on some
76 * machines, and may also reduce the cost of multiplication (since there
77 * are fewer one-bits in the constants).
78 */
79
80#if BITS_IN_JSAMPLE == 8
81#define CONST_BITS 8
82#define PASS1_BITS 2
83#else
84#define CONST_BITS 8
85#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
86#endif
87
88/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
89 * causing a lot of useless floating-point operations at run time.
90 * To get around this we use the following pre-calculated constants.
91 * If you change CONST_BITS you may want to add appropriate values.
92 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
93 */
94
95#if CONST_BITS == 8
96#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
97#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
98#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
99#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
100#else
101#define FIX_1_082392200 FIX(1.082392200)
102#define FIX_1_414213562 FIX(1.414213562)
103#define FIX_1_847759065 FIX(1.847759065)
104#define FIX_2_613125930 FIX(2.613125930)
105#endif
106
107
108/* We can gain a little more speed, with a further compromise in accuracy,
109 * by omitting the addition in a descaling shift. This yields an incorrectly
110 * rounded result half the time...
111 */
112
113#ifndef USE_ACCURATE_ROUNDING
114#undef DESCALE
115#define DESCALE(x,n) RIGHT_SHIFT(x, n)
116#endif
117
118
119/* Multiply a DCTELEM variable by an INT32 constant, and immediately
120 * descale to yield a DCTELEM result.
121 */
122
123#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
124
125
126/* Dequantize a coefficient by multiplying it by the multiplier-table
127 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
128 * multiplication will do. For 12-bit data, the multiplier table is
129 * declared INT32, so a 32-bit multiply will be used.
130 */
131
132#if BITS_IN_JSAMPLE == 8
133#define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
134#else
135#define DEQUANTIZE(coef,quantval) \
136 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
137#endif
138
139
140/* Like DESCALE, but applies to a DCTELEM and produces an int.
141 * We assume that int right shift is unsigned if INT32 right shift is.
142 */
143
144#ifdef RIGHT_SHIFT_IS_UNSIGNED
145#define ISHIFT_TEMPS DCTELEM ishift_temp;
146#if BITS_IN_JSAMPLE == 8
147#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
148#else
149#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
150#endif
151#define IRIGHT_SHIFT(x,shft) \
152 ((ishift_temp = (x)) < 0 ? \
153 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
154 (ishift_temp >> (shft)))
155#else
156#define ISHIFT_TEMPS
157#define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
158#endif
159
160#ifdef USE_ACCURATE_ROUNDING
161#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
162#else
163#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
164#endif
165
166
167/*
168 * Perform dequantization and inverse DCT on one block of coefficients.
169 */
170
171GLOBAL(void)
172jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
173 JCOEFPTR coef_block,
174 JSAMPARRAY output_buf, JDIMENSION output_col)
175{
176 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
177 DCTELEM tmp10, tmp11, tmp12, tmp13;
178 DCTELEM z5, z10, z11, z12, z13;
179 JCOEFPTR inptr;
180 IFAST_MULT_TYPE * quantptr;
181 int * wsptr;
182 JSAMPROW outptr;
183 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
184 int ctr;
185 int workspace[DCTSIZE2]; /* buffers data between passes */
186 SHIFT_TEMPS /* for DESCALE */
187 ISHIFT_TEMPS /* for IDESCALE */
188
189 /* Pass 1: process columns from input, store into work array. */
190
191 inptr = coef_block;
192 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
193 wsptr = workspace;
194 for (ctr = DCTSIZE; ctr > 0; ctr--) {
195 /* Due to quantization, we will usually find that many of the input
196 * coefficients are zero, especially the AC terms. We can exploit this
197 * by short-circuiting the IDCT calculation for any column in which all
198 * the AC terms are zero. In that case each output is equal to the
199 * DC coefficient (with scale factor as needed).
200 * With typical images and quantization tables, half or more of the
201 * column DCT calculations can be simplified this way.
202 */
203
204 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
205 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
206 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
207 inptr[DCTSIZE*7] == 0) {
208 /* AC terms all zero */
209 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
210
211 wsptr[DCTSIZE*0] = dcval;
212 wsptr[DCTSIZE*1] = dcval;
213 wsptr[DCTSIZE*2] = dcval;
214 wsptr[DCTSIZE*3] = dcval;
215 wsptr[DCTSIZE*4] = dcval;
216 wsptr[DCTSIZE*5] = dcval;
217 wsptr[DCTSIZE*6] = dcval;
218 wsptr[DCTSIZE*7] = dcval;
219
220 inptr++; /* advance pointers to next column */
221 quantptr++;
222 wsptr++;
223 continue;
224 }
225
226 /* Even part */
227
228 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
229 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
230 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
231 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
232
233 tmp10 = tmp0 + tmp2; /* phase 3 */
234 tmp11 = tmp0 - tmp2;
235
236 tmp13 = tmp1 + tmp3; /* phases 5-3 */
237 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
238
239 tmp0 = tmp10 + tmp13; /* phase 2 */
240 tmp3 = tmp10 - tmp13;
241 tmp1 = tmp11 + tmp12;
242 tmp2 = tmp11 - tmp12;
243
244 /* Odd part */
245
246 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
247 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
248 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
249 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
250
251 z13 = tmp6 + tmp5; /* phase 6 */
252 z10 = tmp6 - tmp5;
253 z11 = tmp4 + tmp7;
254 z12 = tmp4 - tmp7;
255
256 tmp7 = z11 + z13; /* phase 5 */
257 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
258
259 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
260 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
261 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
262
263 tmp6 = tmp12 - tmp7; /* phase 2 */
264 tmp5 = tmp11 - tmp6;
265 tmp4 = tmp10 + tmp5;
266
267 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
268 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
269 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
270 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
271 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
272 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
273 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
274 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
275
276 inptr++; /* advance pointers to next column */
277 quantptr++;
278 wsptr++;
279 }
280
281 /* Pass 2: process rows from work array, store into output array. */
282 /* Note that we must descale the results by a factor of 8 == 2**3, */
283 /* and also undo the PASS1_BITS scaling. */
284
285 wsptr = workspace;
286 for (ctr = 0; ctr < DCTSIZE; ctr++) {
287 outptr = output_buf[ctr] + output_col;
288 /* Rows of zeroes can be exploited in the same way as we did with columns.
289 * However, the column calculation has created many nonzero AC terms, so
290 * the simplification applies less often (typically 5% to 10% of the time).
291 * On machines with very fast multiplication, it's possible that the
292 * test takes more time than it's worth. In that case this section
293 * may be commented out.
294 */
295
296#ifndef NO_ZERO_ROW_TEST
297 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
298 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
299 /* AC terms all zero */
300 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
301 & RANGE_MASK];
302
303 outptr[0] = dcval;
304 outptr[1] = dcval;
305 outptr[2] = dcval;
306 outptr[3] = dcval;
307 outptr[4] = dcval;
308 outptr[5] = dcval;
309 outptr[6] = dcval;
310 outptr[7] = dcval;
311
312 wsptr += DCTSIZE; /* advance pointer to next row */
313 continue;
314 }
315#endif
316
317 /* Even part */
318
319 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
320 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
321
322 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
323 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
324 - tmp13;
325
326 tmp0 = tmp10 + tmp13;
327 tmp3 = tmp10 - tmp13;
328 tmp1 = tmp11 + tmp12;
329 tmp2 = tmp11 - tmp12;
330
331 /* Odd part */
332
333 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
334 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
335 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
336 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
337
338 tmp7 = z11 + z13; /* phase 5 */
339 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
340
341 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
342 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
343 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
344
345 tmp6 = tmp12 - tmp7; /* phase 2 */
346 tmp5 = tmp11 - tmp6;
347 tmp4 = tmp10 + tmp5;
348
349 /* Final output stage: scale down by a factor of 8 and range-limit */
350
351 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
352 & RANGE_MASK];
353 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
354 & RANGE_MASK];
355 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
356 & RANGE_MASK];
357 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
358 & RANGE_MASK];
359 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
360 & RANGE_MASK];
361 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
362 & RANGE_MASK];
363 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
364 & RANGE_MASK];
365 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
366 & RANGE_MASK];
367
368 wsptr += DCTSIZE; /* advance pointer to next row */
369 }
370}
371
372#endif /* DCT_IFAST_SUPPORTED */
373