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