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