jfdctint.c
Go to the documentation of this file.
1 /*
2  * jfdctint.c
3  *
4  * Copyright (C) 1991-1996, 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  * forward DCT (Discrete Cosine Transform).
10  *
11  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
12  * on each column. Direct algorithms are also available, but they are
13  * much more complex and seem not to be any faster when reduced to code.
14  *
15  * This implementation is based on an algorithm described in
16  * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
17  * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
18  * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
19  * The primary algorithm described there uses 11 multiplies and 29 adds.
20  * We use their alternate method with 12 multiplies and 32 adds.
21  * The advantage of this method is that no data path contains more than one
22  * multiplication; this allows a very simple and accurate implementation in
23  * scaled fixed-point arithmetic, with a minimal number of shifts.
24  */
25 
26 #define JPEG_INTERNALS
27 #include "jinclude.h"
28 #include "jpeglib.h"
29 #include "jdct.h" /* Private declarations for DCT subsystem */
30 
31 #ifdef DCT_ISLOW_SUPPORTED
32 
33 
34 /*
35  * This module is specialized to the case DCTSIZE = 8.
36  */
37 
38 #if DCTSIZE != 8
39  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
40 #endif
41 
42 
43 /*
44  * The poop on this scaling stuff is as follows:
45  *
46  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
47  * larger than the true DCT outputs. The final outputs are therefore
48  * a factor of N larger than desired; since N=8 this can be cured by
49  * a simple right shift at the end of the algorithm. The advantage of
50  * this arrangement is that we save two multiplications per 1-D DCT,
51  * because the y0 and y4 outputs need not be divided by sqrt(N).
52  * In the IJG code, this factor of 8 is removed by the quantization step
53  * (in jcdctmgr.c), NOT in this module.
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. (For 12-bit sample data, the intermediate
70  * array is INT32 anyway.)
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 /*
136  * Perform the forward DCT on one block of samples.
137  */
138 
139 GLOBAL(void)
141 {
142  INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
143  INT32 tmp10, tmp11, tmp12, tmp13;
144  INT32 z1, z2, z3, z4, z5;
145  DCTELEM *dataptr;
146  int ctr;
148 
149  /* Pass 1: process rows. */
150  /* Note results are scaled up by sqrt(8) compared to a true DCT; */
151  /* furthermore, we scale the results by 2**PASS1_BITS. */
152 
153  dataptr = data;
154  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
155  tmp0 = dataptr[0] + dataptr[7];
156  tmp7 = dataptr[0] - dataptr[7];
157  tmp1 = dataptr[1] + dataptr[6];
158  tmp6 = dataptr[1] - dataptr[6];
159  tmp2 = dataptr[2] + dataptr[5];
160  tmp5 = dataptr[2] - dataptr[5];
161  tmp3 = dataptr[3] + dataptr[4];
162  tmp4 = dataptr[3] - dataptr[4];
163 
164  /* Even part per LL&M figure 1 --- note that published figure is faulty;
165  * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
166  */
167 
168  tmp10 = tmp0 + tmp3;
169  tmp13 = tmp0 - tmp3;
170  tmp11 = tmp1 + tmp2;
171  tmp12 = tmp1 - tmp2;
172 
173  dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
174  dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
175 
176  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
177  dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
179  dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
181 
182  /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
183  * cK represents cos(K*pi/16).
184  * i0..i3 in the paper are tmp4..tmp7 here.
185  */
186 
187  z1 = tmp4 + tmp7;
188  z2 = tmp5 + tmp6;
189  z3 = tmp4 + tmp6;
190  z4 = tmp5 + tmp7;
191  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
192 
193  tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
194  tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
195  tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
196  tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
197  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
198  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
199  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
200  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
201 
202  z3 += z5;
203  z4 += z5;
204 
205  dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
206  dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
207  dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
208  dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
209 
210  dataptr += DCTSIZE; /* advance pointer to next row */
211  }
212 
213  /* Pass 2: process columns.
214  * We remove the PASS1_BITS scaling, but leave the results scaled up
215  * by an overall factor of 8.
216  */
217 
218  dataptr = data;
219  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
220  tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
221  tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
222  tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
223  tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
224  tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
225  tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
226  tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
227  tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
228 
229  /* Even part per LL&M figure 1 --- note that published figure is faulty;
230  * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
231  */
232 
233  tmp10 = tmp0 + tmp3;
234  tmp13 = tmp0 - tmp3;
235  tmp11 = tmp1 + tmp2;
236  tmp12 = tmp1 - tmp2;
237 
238  dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
239  dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
240 
241  z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
242  dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
244  dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
246 
247  /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
248  * cK represents cos(K*pi/16).
249  * i0..i3 in the paper are tmp4..tmp7 here.
250  */
251 
252  z1 = tmp4 + tmp7;
253  z2 = tmp5 + tmp6;
254  z3 = tmp4 + tmp6;
255  z4 = tmp5 + tmp7;
256  z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
257 
258  tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
259  tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
260  tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
261  tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
262  z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
263  z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
264  z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
265  z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
266 
267  z3 += z5;
268  z4 += z5;
269 
270  dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
272  dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
274  dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
276  dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
278 
279  dataptr++; /* advance pointer to next column */
280  }
281 }
282 
283 #endif /* DCT_ISLOW_SUPPORTED */
#define DESCALE(x, n)
Definition: jdct.h:146
#define CONST_BITS
Definition: jfdctint.c:78
#define FIX_2_053119869
Definition: jfdctint.c:102
INT32 DCTELEM
Definition: jdct.h:32
long INT32
Definition: jmorecfg.h:161
#define FIX_1_847759065
Definition: jfdctint.c:100
#define SHIFT_TEMPS
Definition: jpegint.h:289
#define FIX_1_961570560
Definition: jfdctint.c:101
#define FIX_0_899976223
Definition: jfdctint.c:97
jpeg_fdct_islow(DCTELEM *data)
Definition: jfdctint.c:140
#define FIX_0_390180644
Definition: jfdctint.c:94
#define MULTIPLY(var, const)
Definition: jfdctint.c:129
#define PASS1_BITS
Definition: jfdctint.c:79
Definition: inftrees.h:24
#define FIX_2_562915447
Definition: jfdctint.c:103
#define GLOBAL(type)
Definition: jmorecfg.h:188
#define FIX_0_298631336
Definition: jfdctint.c:93
#define FIX_3_072711026
Definition: jfdctint.c:104
#define DCTSIZE
Definition: jpeglib.h:41
#define FIX_0_765366865
Definition: jfdctint.c:96
JSAMPIMAGE data
Definition: jpeglib.h:945
int const JOCTET * dataptr
Definition: jpeglib.h:950
#define FIX_0_541196100
Definition: jfdctint.c:95
#define FIX_1_501321110
Definition: jfdctint.c:99
#define FIX_1_175875602
Definition: jfdctint.c:98


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