1/*
2 * reserved comment block
3 * DO NOT REMOVE OR ALTER!
4 */
5/*
6 * jidctint.c
7 *
8 * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in
22 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
23 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
24 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
25 * The primary algorithm described there uses 11 multiplies and 29 adds.
26 * We use their alternate method with 12 multiplies and 32 adds.
27 * The advantage of this method is that no data path contains more than one
28 * multiplication; this allows a very simple and accurate implementation in
29 * scaled fixed-point arithmetic, with a minimal number of shifts.
30 */
31
32#define JPEG_INTERNALS
33#include "jinclude.h"
34#include "jpeglib.h"
35#include "jdct.h" /* Private declarations for DCT subsystem */
36
37#ifdef DCT_ISLOW_SUPPORTED
38
39
40/*
41 * This module is specialized to the case DCTSIZE = 8.
42 */
43
44#if DCTSIZE != 8
45 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
46#endif
47
48
49/*
50 * The poop on this scaling stuff is as follows:
51 *
52 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
53 * larger than the true IDCT outputs. The final outputs are therefore
54 * a factor of N larger than desired; since N=8 this can be cured by
55 * a simple right shift at the end of the algorithm. The advantage of
56 * this arrangement is that we save two multiplications per 1-D IDCT,
57 * because the y0 and y4 inputs need not be divided by sqrt(N).
58 *
59 * We have to do addition and subtraction of the integer inputs, which
60 * is no problem, and multiplication by fractional constants, which is
61 * a problem to do in integer arithmetic. We multiply all the constants
62 * by CONST_SCALE and convert them to integer constants (thus retaining
63 * CONST_BITS bits of precision in the constants). After doing a
64 * multiplication we have to divide the product by CONST_SCALE, with proper
65 * rounding, to produce the correct output. This division can be done
66 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
67 * as long as possible so that partial sums can be added together with
68 * full fractional precision.
69 *
70 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
71 * they are represented to better-than-integral precision. These outputs
72 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
73 * with the recommended scaling. (To scale up 12-bit sample data further, an
74 * intermediate INT32 array would be needed.)
75 *
76 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
77 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
78 * shows that the values given below are the most effective.
79 */
80
81#if BITS_IN_JSAMPLE == 8
82#define CONST_BITS 13
83#define PASS1_BITS 2
84#else
85#define CONST_BITS 13
86#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
87#endif
88
89/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
90 * causing a lot of useless floating-point operations at run time.
91 * To get around this we use the following pre-calculated constants.
92 * If you change CONST_BITS you may want to add appropriate values.
93 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
94 */
95
96#if CONST_BITS == 13
97#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
98#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
99#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
100#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
101#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
102#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
103#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
104#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
105#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
106#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
107#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
108#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
109#else
110#define FIX_0_298631336 FIX(0.298631336)
111#define FIX_0_390180644 FIX(0.390180644)
112#define FIX_0_541196100 FIX(0.541196100)
113#define FIX_0_765366865 FIX(0.765366865)
114#define FIX_0_899976223 FIX(0.899976223)
115#define FIX_1_175875602 FIX(1.175875602)
116#define FIX_1_501321110 FIX(1.501321110)
117#define FIX_1_847759065 FIX(1.847759065)
118#define FIX_1_961570560 FIX(1.961570560)
119#define FIX_2_053119869 FIX(2.053119869)
120#define FIX_2_562915447 FIX(2.562915447)
121#define FIX_3_072711026 FIX(3.072711026)
122#endif
123
124
125/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
126 * For 8-bit samples with the recommended scaling, all the variable
127 * and constant values involved are no more than 16 bits wide, so a
128 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
129 * For 12-bit samples, a full 32-bit multiplication will be needed.
130 */
131
132#if BITS_IN_JSAMPLE == 8
133#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
134#else
135#define MULTIPLY(var,const) ((var) * (const))
136#endif
137
138
139/* Dequantize a coefficient by multiplying it by the multiplier-table
140 * entry; produce an int result. In this module, both inputs and result
141 * are 16 bits or less, so either int or short multiply will work.
142 */
143
144#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
145
146
147/*
148 * Perform dequantization and inverse DCT on one block of coefficients.
149 */
150
151GLOBAL(void)
152jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
153 JCOEFPTR coef_block,
154 JSAMPARRAY output_buf, JDIMENSION output_col)
155{
156 INT32 tmp0, tmp1, tmp2, tmp3;
157 INT32 tmp10, tmp11, tmp12, tmp13;
158 INT32 z1, z2, z3, z4, z5;
159 JCOEFPTR inptr;
160 ISLOW_MULT_TYPE * quantptr;
161 int * wsptr;
162 JSAMPROW outptr;
163 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
164 int ctr;
165 int workspace[DCTSIZE2]; /* buffers data between passes */
166 SHIFT_TEMPS
167
168 /* Pass 1: process columns from input, store into work array. */
169 /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
170 /* furthermore, we scale the results by 2**PASS1_BITS. */
171
172 inptr = coef_block;
173 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
174 wsptr = workspace;
175 for (ctr = DCTSIZE; ctr > 0; ctr--) {
176 /* Due to quantization, we will usually find that many of the input
177 * coefficients are zero, especially the AC terms. We can exploit this
178 * by short-circuiting the IDCT calculation for any column in which all
179 * the AC terms are zero. In that case each output is equal to the
180 * DC coefficient (with scale factor as needed).
181 * With typical images and quantization tables, half or more of the
182 * column DCT calculations can be simplified this way.
183 */
184
185 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
186 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
187 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
188 inptr[DCTSIZE*7] == 0) {
189 /* AC terms all zero */
190 int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
191
192 wsptr[DCTSIZE*0] = dcval;
193 wsptr[DCTSIZE*1] = dcval;
194 wsptr[DCTSIZE*2] = dcval;
195 wsptr[DCTSIZE*3] = dcval;
196 wsptr[DCTSIZE*4] = dcval;
197 wsptr[DCTSIZE*5] = dcval;
198 wsptr[DCTSIZE*6] = dcval;
199 wsptr[DCTSIZE*7] = dcval;
200
201 inptr++; /* advance pointers to next column */
202 quantptr++;
203 wsptr++;
204 continue;
205 }
206
207 /* Even part: reverse the even part of the forward DCT. */
208 /* The rotator is sqrt(2)*c(-6). */
209
210 z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
211 z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
212
213 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
214 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
215 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
216
217 z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
218 z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
219
220 tmp0 = (z2 + z3) << CONST_BITS;
221 tmp1 = (z2 - z3) << CONST_BITS;
222
223 tmp10 = tmp0 + tmp3;
224 tmp13 = tmp0 - tmp3;
225 tmp11 = tmp1 + tmp2;
226 tmp12 = tmp1 - tmp2;
227
228 /* Odd part per figure 8; the matrix is unitary and hence its
229 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
230 */
231
232 tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
233 tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
234 tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
235 tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
236
237 z1 = tmp0 + tmp3;
238 z2 = tmp1 + tmp2;
239 z3 = tmp0 + tmp2;
240 z4 = tmp1 + tmp3;
241 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
242
243 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
244 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
245 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
246 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
247 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
248 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
249 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
250 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
251
252 z3 += z5;
253 z4 += z5;
254
255 tmp0 += z1 + z3;
256 tmp1 += z2 + z4;
257 tmp2 += z2 + z3;
258 tmp3 += z1 + z4;
259
260 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
261
262 wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
263 wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
264 wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
265 wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
266 wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
267 wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
268 wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
269 wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
270
271 inptr++; /* advance pointers to next column */
272 quantptr++;
273 wsptr++;
274 }
275
276 /* Pass 2: process rows from work array, store into output array. */
277 /* Note that we must descale the results by a factor of 8 == 2**3, */
278 /* and also undo the PASS1_BITS scaling. */
279
280 wsptr = workspace;
281 for (ctr = 0; ctr < DCTSIZE; ctr++) {
282 outptr = output_buf[ctr] + output_col;
283 /* Rows of zeroes can be exploited in the same way as we did with columns.
284 * However, the column calculation has created many nonzero AC terms, so
285 * the simplification applies less often (typically 5% to 10% of the time).
286 * On machines with very fast multiplication, it's possible that the
287 * test takes more time than it's worth. In that case this section
288 * may be commented out.
289 */
290
291#ifndef NO_ZERO_ROW_TEST
292 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
293 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
294 /* AC terms all zero */
295 JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
296 & RANGE_MASK];
297
298 outptr[0] = dcval;
299 outptr[1] = dcval;
300 outptr[2] = dcval;
301 outptr[3] = dcval;
302 outptr[4] = dcval;
303 outptr[5] = dcval;
304 outptr[6] = dcval;
305 outptr[7] = dcval;
306
307 wsptr += DCTSIZE; /* advance pointer to next row */
308 continue;
309 }
310#endif
311
312 /* Even part: reverse the even part of the forward DCT. */
313 /* The rotator is sqrt(2)*c(-6). */
314
315 z2 = (INT32) wsptr[2];
316 z3 = (INT32) wsptr[6];
317
318 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
319 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
320 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
321
322 tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
323 tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
324
325 tmp10 = tmp0 + tmp3;
326 tmp13 = tmp0 - tmp3;
327 tmp11 = tmp1 + tmp2;
328 tmp12 = tmp1 - tmp2;
329
330 /* Odd part per figure 8; the matrix is unitary and hence its
331 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
332 */
333
334 tmp0 = (INT32) wsptr[7];
335 tmp1 = (INT32) wsptr[5];
336 tmp2 = (INT32) wsptr[3];
337 tmp3 = (INT32) wsptr[1];
338
339 z1 = tmp0 + tmp3;
340 z2 = tmp1 + tmp2;
341 z3 = tmp0 + tmp2;
342 z4 = tmp1 + tmp3;
343 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
344
345 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
346 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
347 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
348 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
349 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
350 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
351 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
352 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
353
354 z3 += z5;
355 z4 += z5;
356
357 tmp0 += z1 + z3;
358 tmp1 += z2 + z4;
359 tmp2 += z2 + z3;
360 tmp3 += z1 + z4;
361
362 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
363
364 outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
365 CONST_BITS+PASS1_BITS+3)
366 & RANGE_MASK];
367 outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
368 CONST_BITS+PASS1_BITS+3)
369 & RANGE_MASK];
370 outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
371 CONST_BITS+PASS1_BITS+3)
372 & RANGE_MASK];
373 outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
374 CONST_BITS+PASS1_BITS+3)
375 & RANGE_MASK];
376 outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
377 CONST_BITS+PASS1_BITS+3)
378 & RANGE_MASK];
379 outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
380 CONST_BITS+PASS1_BITS+3)
381 & RANGE_MASK];
382 outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
383 CONST_BITS+PASS1_BITS+3)
384 & RANGE_MASK];
385 outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
386 CONST_BITS+PASS1_BITS+3)
387 & RANGE_MASK];
388
389 wsptr += DCTSIZE; /* advance pointer to next row */
390 }
391}
392
393#endif /* DCT_ISLOW_SUPPORTED */
394