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Line No. Rev Author Line
1 32 kaklik /*
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 #include "GenericTypeDefs.h"
29  
30  
31 /*
32 * This module is specialized to the case DCTSIZE = 8.
33 */
34  
35 /*
36 * The poop on this scaling stuff is as follows:
37 *
38 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
39 * larger than the true IDCT outputs. The final outputs are therefore
40 * a factor of N larger than desired; since N=8 this can be cured by
41 * a simple right shift at the end of the algorithm. The advantage of
42 * this arrangement is that we save two multiplications per 1-D IDCT,
43 * because the y0 and y4 inputs need not be divided by sqrt(N).
44 *
45 * We have to do addition and subtraction of the integer inputs, which
46 * is no problem, and multiplication by fractional constants, which is
47 * a problem to do in integer arithmetic. We multiply all the constants
48 * by CONST_SCALE and convert them to integer constants (thus retaining
49 * CONST_BITS bits of precision in the constants). After doing a
50 * multiplication we have to divide the product by CONST_SCALE, with proper
51 * rounding, to produce the correct output. This division can be done
52 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
53 * as long as possible so that partial sums can be added together with
54 * full fractional precision.
55 *
56 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
57 * they are represented to better-than-integral precision. These outputs
58 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
59 * with the recommended scaling. (To scale up 12-bit sample data further, an
60 * intermediate INT32 array would be needed.)
61 *
62 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
63 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
64 * shows that the values given below are the most effective.
65 */
66 #define DCTSIZE 8 /* The basic DCT block is 8x8 samples */
67 #define DCTSIZE2 64 /* DCTSIZE squared; # of elements in a block */
68 #define BITS_IN_JSAMPLE 8
69 #define NO_ZERO_ROW_TEST
70 #define DCTELEM LONG
71  
72 #define CONST_BITS 13
73 #define PASS1_BITS 2
74  
75 #define INT32 LONG
76  
77 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
78 * causing a lot of useless floating-point operations at run time.
79 * To get around this we use the following pre-calculated constants.
80 * If you change CONST_BITS you may want to add appropriate values.
81 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
82 */
83  
84 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
85 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
86 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
87 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
88 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
89 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
90 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
91 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
92 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
93 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
94 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
95 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
96  
97  
98 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
99 * For 8-bit samples with the recommended scaling, all the variable
100 * and constant values involved are no more than 16 bits wide, so a
101 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
102 * For 12-bit samples, a full 32-bit multiplication will be needed.
103 */
104  
105 #define DESCALE(x,n) ((x) + ((LONG)0x01 << ((n)-1)))>>(n)
106 #define MULTIPLY(var,constant) ((LONG)(var) * (constant));
107 #define range_limit(x) ((x)<-128)?-128:((x)>127)?127:(x)
108  
109 /* Dequantize a coefficient by multiplying it by the multiplier-table
110 * entry; produce an int result. In this module, both inputs and result
111 * are 16 bits or less, so either int or short multiply will work.
112 */
113  
114 #define DEQUANTIZE(coef,quantval) ((LONG)(coef) * (quantval))
115  
116  
117 /*
118 * Perform dequantization and inverse DCT on one block of coefficients.
119 */
120  
121 void jpeg_idct_islow (SHORT *inbuf, WORD *quantptr)
122 {
123 LONG tmp0, tmp1, tmp2, tmp3;
124 LONG tmp10, tmp11, tmp12, tmp13;
125 LONG z1, z2, z3, z4, z5;
126  
127 BYTE ctr;
128 SHORT *inptr = inbuf, *outptr;
129 DCTELEM *wsptr;
130 DCTELEM workspace[DCTSIZE2]; /* buffers data between passes */
131  
132 wsptr = workspace;
133  
134 /* Pass 1: process columns from input, store into work array. */
135 /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
136 /* furthermore, we scale the results by 2**PASS1_BITS. */
137  
138 for (ctr = DCTSIZE; ctr > 0; ctr--) {
139 /* Due to quantization, we will usually find that many of the input
140 * coefficients are zero, especially the AC terms. We can exploit this
141 * by short-circuiting the IDCT calculation for any column in which all
142 * the AC terms are zero. In that case each output is equal to the
143 * DC coefficient (with scale factor as needed).
144 * With typical images and quantization tables, half or more of the
145 * column DCT calculations can be simplified this way.
146 */
147  
148 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
149 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
150 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
151 inptr[DCTSIZE*7] == 0) {
152 /* AC terms all zero */
153 LONG dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
154  
155 wsptr[DCTSIZE*0] = dcval;
156 wsptr[DCTSIZE*1] = dcval;
157 wsptr[DCTSIZE*2] = dcval;
158 wsptr[DCTSIZE*3] = dcval;
159 wsptr[DCTSIZE*4] = dcval;
160 wsptr[DCTSIZE*5] = dcval;
161 wsptr[DCTSIZE*6] = dcval;
162 wsptr[DCTSIZE*7] = dcval;
163  
164 inptr++; /* advance pointers to next column */
165 quantptr++;
166 wsptr++;
167 continue;
168 }
169  
170 /* Even part: reverse the even part of the forward DCT. */
171 /* The rotator is sqrt(2)*c(-6). */
172  
173 z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
174 z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
175  
176 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
177 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
178 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
179  
180 z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
181 z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
182  
183 tmp0 = (z2 + z3) << CONST_BITS;
184 tmp1 = (z2 - z3) << CONST_BITS;
185  
186 tmp10 = tmp0 + tmp3;
187 tmp13 = tmp0 - tmp3;
188 tmp11 = tmp1 + tmp2;
189 tmp12 = tmp1 - tmp2;
190  
191 /* Odd part per figure 8; the matrix is unitary and hence its
192 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
193 */
194  
195 tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
196 tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
197 tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
198 tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
199  
200 z1 = tmp0 + tmp3;
201 z2 = tmp1 + tmp2;
202 z3 = tmp0 + tmp2;
203 z4 = tmp1 + tmp3;
204 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
205  
206 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
207 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
208 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
209 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
210 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
211 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
212 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
213 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
214  
215 z3 += z5;
216 z4 += z5;
217  
218 tmp0 += z1 + z3;
219 tmp1 += z2 + z4;
220 tmp2 += z2 + z3;
221 tmp3 += z1 + z4;
222  
223 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
224  
225 wsptr[DCTSIZE*0] = (LONG) DESCALE((tmp10 + tmp3), (CONST_BITS-PASS1_BITS));
226 wsptr[DCTSIZE*7] = (LONG) DESCALE((tmp10 - tmp3), (CONST_BITS-PASS1_BITS));
227 wsptr[DCTSIZE*1] = (LONG) DESCALE((tmp11 + tmp2), (CONST_BITS-PASS1_BITS));
228 wsptr[DCTSIZE*6] = (LONG) DESCALE((tmp11 - tmp2), (CONST_BITS-PASS1_BITS));
229 wsptr[DCTSIZE*2] = (LONG) DESCALE((tmp12 + tmp1), (CONST_BITS-PASS1_BITS));
230 wsptr[DCTSIZE*5] = (LONG) DESCALE((tmp12 - tmp1), (CONST_BITS-PASS1_BITS));
231 wsptr[DCTSIZE*3] = (LONG) DESCALE((tmp13 + tmp0), (CONST_BITS-PASS1_BITS));
232 wsptr[DCTSIZE*4] = (LONG) DESCALE((tmp13 - tmp0), (CONST_BITS-PASS1_BITS));
233  
234 inptr++; /* advance pointers to next column */
235 quantptr++;
236 wsptr++;
237 }
238  
239 /* Pass 2: process rows from work array, store into output array. */
240 /* Note that we must descale the results by a factor of 8 == 2**3, */
241 /* and also undo the PASS1_BITS scaling. */
242  
243 wsptr = workspace;
244 outptr = &inbuf[0];
245 for (ctr = 0; ctr < DCTSIZE; ctr++) {
246 /* Rows of zeroes can be exploited in the same way as we did with columns.
247 * However, the column calculation has created many nonzero AC terms, so
248 * the simplification applies less often (typically 5% to 10% of the time).
249 * On machines with very fast multiplication, it's possible that the
250 * test takes more time than it's worth. In that case this section
251 * may be commented out.
252 */
253  
254 #ifndef NO_ZERO_ROW_TEST
255 if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
256 wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
257 /* AC terms all zero */
258 JSAMPLE dcval = range_limit[(LONG) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
259 & RANGE_MASK];
260  
261 outptr[0] = dcval;
262 outptr[1] = dcval;
263 outptr[2] = dcval;
264 outptr[3] = dcval;
265 outptr[4] = dcval;
266 outptr[5] = dcval;
267 outptr[6] = dcval;
268 outptr[7] = dcval;
269  
270 wsptr += DCTSIZE; /* advance pointer to next row */
271 continue;
272 }
273 #endif
274  
275 /* Even part: reverse the even part of the forward DCT. */
276 /* The rotator is sqrt(2)*c(-6). */
277  
278 z2 = (INT32) wsptr[2];
279 z3 = (INT32) wsptr[6];
280  
281 z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
282 tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
283 tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
284  
285 tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
286 tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
287  
288 tmp10 = tmp0 + tmp3;
289 tmp13 = tmp0 - tmp3;
290 tmp11 = tmp1 + tmp2;
291 tmp12 = tmp1 - tmp2;
292  
293 /* Odd part per figure 8; the matrix is unitary and hence its
294 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
295 */
296  
297 tmp0 = (INT32) wsptr[7];
298 tmp1 = (INT32) wsptr[5];
299 tmp2 = (INT32) wsptr[3];
300 tmp3 = (INT32) wsptr[1];
301  
302 z1 = tmp0 + tmp3;
303 z2 = tmp1 + tmp2;
304 z3 = tmp0 + tmp2;
305 z4 = tmp1 + tmp3;
306 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
307  
308 tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
309 tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
310 tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
311 tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
312 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
313 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
314 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
315 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
316  
317 z3 += z5;
318 z4 += z5;
319  
320 tmp0 += z1 + z3;
321 tmp1 += z2 + z4;
322 tmp2 += z2 + z3;
323 tmp3 += z1 + z4;
324  
325 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
326  
327 outptr[0] = (SHORT)range_limit((LONG) DESCALE(tmp10 + tmp3, CONST_BITS+PASS1_BITS+3));
328 outptr[7] = (SHORT)range_limit((LONG) DESCALE(tmp10 - tmp3, CONST_BITS+PASS1_BITS+3));
329 outptr[1] = (SHORT)range_limit((LONG) DESCALE(tmp11 + tmp2, CONST_BITS+PASS1_BITS+3));
330 outptr[6] = (SHORT)range_limit((LONG) DESCALE(tmp11 - tmp2, CONST_BITS+PASS1_BITS+3));
331 outptr[2] = (SHORT)range_limit((LONG) DESCALE(tmp12 + tmp1, CONST_BITS+PASS1_BITS+3));
332 outptr[5] = (SHORT)range_limit((LONG) DESCALE(tmp12 - tmp1, CONST_BITS+PASS1_BITS+3));
333 outptr[3] = (SHORT)range_limit((LONG) DESCALE(tmp13 + tmp0, CONST_BITS+PASS1_BITS+3));
334 outptr[4] = (SHORT)range_limit((LONG) DESCALE(tmp13 - tmp0, CONST_BITS+PASS1_BITS+3));
335  
336 outptr += DCTSIZE; /* advance pointer to next row */
337 wsptr += DCTSIZE; /* advance pointer to next row */
338 }
339 }
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