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)
140 0 : jpeg_fdct_islow (DCTELEM * data)
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;
147 : SHIFT_TEMPS
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 0 : dataptr = data;
154 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
155 0 : tmp0 = dataptr[0] + dataptr[7];
156 0 : tmp7 = dataptr[0] - dataptr[7];
157 0 : tmp1 = dataptr[1] + dataptr[6];
158 0 : tmp6 = dataptr[1] - dataptr[6];
159 0 : tmp2 = dataptr[2] + dataptr[5];
160 0 : tmp5 = dataptr[2] - dataptr[5];
161 0 : tmp3 = dataptr[3] + dataptr[4];
162 0 : 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 0 : tmp10 = tmp0 + tmp3;
169 0 : tmp13 = tmp0 - tmp3;
170 0 : tmp11 = tmp1 + tmp2;
171 0 : tmp12 = tmp1 - tmp2;
172 :
173 0 : dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
174 0 : dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
175 :
176 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
177 0 : dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
178 : CONST_BITS-PASS1_BITS);
179 0 : dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
180 : CONST_BITS-PASS1_BITS);
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 0 : z1 = tmp4 + tmp7;
188 0 : z2 = tmp5 + tmp6;
189 0 : z3 = tmp4 + tmp6;
190 0 : z4 = tmp5 + tmp7;
191 0 : z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
192 :
193 0 : tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
194 0 : tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
195 0 : tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
196 0 : tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
197 0 : z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
198 0 : z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
199 0 : z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
200 0 : z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
201 :
202 0 : z3 += z5;
203 0 : z4 += z5;
204 :
205 0 : dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
206 0 : dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
207 0 : dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
208 0 : dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
209 :
210 0 : 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 0 : dataptr = data;
219 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
220 0 : tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
221 0 : tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
222 0 : tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
223 0 : tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
224 0 : tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
225 0 : tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
226 0 : tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
227 0 : 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 0 : tmp10 = tmp0 + tmp3;
234 0 : tmp13 = tmp0 - tmp3;
235 0 : tmp11 = tmp1 + tmp2;
236 0 : tmp12 = tmp1 - tmp2;
237 :
238 0 : dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
239 0 : dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
240 :
241 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
242 0 : dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
243 : CONST_BITS+PASS1_BITS);
244 0 : dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
245 : CONST_BITS+PASS1_BITS);
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 0 : z1 = tmp4 + tmp7;
253 0 : z2 = tmp5 + tmp6;
254 0 : z3 = tmp4 + tmp6;
255 0 : z4 = tmp5 + tmp7;
256 0 : z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
257 :
258 0 : tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
259 0 : tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
260 0 : tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
261 0 : tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
262 0 : z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
263 0 : z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
264 0 : z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
265 0 : z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
266 :
267 0 : z3 += z5;
268 0 : z4 += z5;
269 :
270 0 : dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
271 : CONST_BITS+PASS1_BITS);
272 0 : dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
273 : CONST_BITS+PASS1_BITS);
274 0 : dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
275 : CONST_BITS+PASS1_BITS);
276 0 : dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
277 : CONST_BITS+PASS1_BITS);
278 :
279 0 : dataptr++; /* advance pointer to next column */
280 : }
281 0 : }
282 :
283 : #endif /* DCT_ISLOW_SUPPORTED */
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