jidctint.c
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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 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  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  inptr = coef_block;
169  quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
170  wsptr = workspace;
171  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  if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
182  inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
183  inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
184  inptr[DCTSIZE*7] == 0) {
185  /* AC terms all zero */
186  int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
187 
188  wsptr[DCTSIZE*0] = dcval;
189  wsptr[DCTSIZE*1] = dcval;
190  wsptr[DCTSIZE*2] = dcval;
191  wsptr[DCTSIZE*3] = dcval;
192  wsptr[DCTSIZE*4] = dcval;
193  wsptr[DCTSIZE*5] = dcval;
194  wsptr[DCTSIZE*6] = dcval;
195  wsptr[DCTSIZE*7] = dcval;
196 
197  inptr++; /* advance pointers to next column */
198  quantptr++;
199  wsptr++;
200  continue;
201  }
202 
203  /* Even part: reverse the even part of the forward DCT. */
204  /* The rotator is sqrt(2)*c(-6). */
205 
206  z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
207  z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
208 
209  z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
210  tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
211  tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
212 
213  z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
214  z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
215 
216  tmp0 = (z2 + z3) << CONST_BITS;
217  tmp1 = (z2 - z3) << CONST_BITS;
218 
219  tmp10 = tmp0 + tmp3;
220  tmp13 = tmp0 - tmp3;
221  tmp11 = tmp1 + tmp2;
222  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  tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
229  tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
230  tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
231  tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
232 
233  z1 = tmp0 + tmp3;
234  z2 = tmp1 + tmp2;
235  z3 = tmp0 + tmp2;
236  z4 = tmp1 + tmp3;
237  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
238 
239  tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
240  tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
241  tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
242  tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
243  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
244  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
245  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
246  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
247 
248  z3 += z5;
249  z4 += z5;
250 
251  tmp0 += z1 + z3;
252  tmp1 += z2 + z4;
253  tmp2 += z2 + z3;
254  tmp3 += z1 + z4;
255 
256  /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
257 
258  wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
259  wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
260  wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
261  wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
262  wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
263  wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
264  wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
265  wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
266 
267  inptr++; /* advance pointers to next column */
268  quantptr++;
269  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  wsptr = workspace;
277  for (ctr = 0; ctr < DCTSIZE; ctr++) {
278  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  if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
289  wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
290  /* AC terms all zero */
291  JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
292  & RANGE_MASK];
293 
294  outptr[0] = dcval;
295  outptr[1] = dcval;
296  outptr[2] = dcval;
297  outptr[3] = dcval;
298  outptr[4] = dcval;
299  outptr[5] = dcval;
300  outptr[6] = dcval;
301  outptr[7] = dcval;
302 
303  wsptr += DCTSIZE; /* advance pointer to next row */
304  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  z2 = (INT32) wsptr[2];
312  z3 = (INT32) wsptr[6];
313 
314  z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
315  tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
316  tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
317 
318  tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
319  tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
320 
321  tmp10 = tmp0 + tmp3;
322  tmp13 = tmp0 - tmp3;
323  tmp11 = tmp1 + tmp2;
324  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  tmp0 = (INT32) wsptr[7];
331  tmp1 = (INT32) wsptr[5];
332  tmp2 = (INT32) wsptr[3];
333  tmp3 = (INT32) wsptr[1];
334 
335  z1 = tmp0 + tmp3;
336  z2 = tmp1 + tmp2;
337  z3 = tmp0 + tmp2;
338  z4 = tmp1 + tmp3;
339  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
340 
341  tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
342  tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
343  tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
344  tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
345  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
346  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
347  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
348  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
349 
350  z3 += z5;
351  z4 += z5;
352 
353  tmp0 += z1 + z3;
354  tmp1 += z2 + z4;
355  tmp2 += z2 + z3;
356  tmp3 += z1 + z4;
357 
358  /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
359 
360  outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
361  CONST_BITS+PASS1_BITS+3)
362  & RANGE_MASK];
363  outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
364  CONST_BITS+PASS1_BITS+3)
365  & RANGE_MASK];
366  outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
367  CONST_BITS+PASS1_BITS+3)
368  & RANGE_MASK];
369  outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
370  CONST_BITS+PASS1_BITS+3)
371  & RANGE_MASK];
372  outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
373  CONST_BITS+PASS1_BITS+3)
374  & RANGE_MASK];
375  outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
376  CONST_BITS+PASS1_BITS+3)
377  & RANGE_MASK];
378  outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
379  CONST_BITS+PASS1_BITS+3)
380  & RANGE_MASK];
381  outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
382  CONST_BITS+PASS1_BITS+3)
383  & RANGE_MASK];
384 
385  wsptr += DCTSIZE; /* advance pointer to next row */
386  }
387 }
388 
389 #endif /* DCT_ISLOW_SUPPORTED */
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openhrp3
Author(s): AIST, General Robotix Inc., Nakamura Lab of Dept. of Mechano Informatics at University of Tokyo
autogenerated on Thu Sep 8 2022 02:24:04