Line data Source code
1 : /*
2 : * jfdctint.c
3 : *
4 : * This file was part of the Independent JPEG Group's software.
5 : * Copyright (C) 1991-1996, Thomas G. Lane.
6 : * libjpeg-turbo Modifications:
7 : * Copyright (C) 2015, D. R. Commander.
8 : * For conditions of distribution and use, see the accompanying README.ijg
9 : * file.
10 : *
11 : * This file contains a slow-but-accurate integer implementation of the
12 : * forward DCT (Discrete Cosine Transform).
13 : *
14 : * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
15 : * on each column. Direct algorithms are also available, but they are
16 : * much more complex and seem not to be any faster when reduced to code.
17 : *
18 : * This implementation is based on an algorithm described in
19 : * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
20 : * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
21 : * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
22 : * The primary algorithm described there uses 11 multiplies and 29 adds.
23 : * We use their alternate method with 12 multiplies and 32 adds.
24 : * The advantage of this method is that no data path contains more than one
25 : * multiplication; this allows a very simple and accurate implementation in
26 : * scaled fixed-point arithmetic, with a minimal number of shifts.
27 : */
28 :
29 : #define JPEG_INTERNALS
30 : #include "jinclude.h"
31 : #include "jpeglib.h"
32 : #include "jdct.h" /* Private declarations for DCT subsystem */
33 :
34 : #ifdef DCT_ISLOW_SUPPORTED
35 :
36 :
37 : /*
38 : * This module is specialized to the case DCTSIZE = 8.
39 : */
40 :
41 : #if DCTSIZE != 8
42 : Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
43 : #endif
44 :
45 :
46 : /*
47 : * The poop on this scaling stuff is as follows:
48 : *
49 : * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
50 : * larger than the true DCT outputs. The final outputs are therefore
51 : * a factor of N larger than desired; since N=8 this can be cured by
52 : * a simple right shift at the end of the algorithm. The advantage of
53 : * this arrangement is that we save two multiplications per 1-D DCT,
54 : * because the y0 and y4 outputs need not be divided by sqrt(N).
55 : * In the IJG code, this factor of 8 is removed by the quantization step
56 : * (in jcdctmgr.c), NOT in this module.
57 : *
58 : * We have to do addition and subtraction of the integer inputs, which
59 : * is no problem, and multiplication by fractional constants, which is
60 : * a problem to do in integer arithmetic. We multiply all the constants
61 : * by CONST_SCALE and convert them to integer constants (thus retaining
62 : * CONST_BITS bits of precision in the constants). After doing a
63 : * multiplication we have to divide the product by CONST_SCALE, with proper
64 : * rounding, to produce the correct output. This division can be done
65 : * cheaply as a right shift of CONST_BITS bits. We postpone shifting
66 : * as long as possible so that partial sums can be added together with
67 : * full fractional precision.
68 : *
69 : * The outputs of the first pass are scaled up by PASS1_BITS bits so that
70 : * they are represented to better-than-integral precision. These outputs
71 : * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
72 : * with the recommended scaling. (For 12-bit sample data, the intermediate
73 : * array is JLONG anyway.)
74 : *
75 : * To avoid overflow of the 32-bit intermediate results in pass 2, we must
76 : * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
77 : * shows that the values given below are the most effective.
78 : */
79 :
80 : #if BITS_IN_JSAMPLE == 8
81 : #define CONST_BITS 13
82 : #define PASS1_BITS 2
83 : #else
84 : #define CONST_BITS 13
85 : #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
86 : #endif
87 :
88 : /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
89 : * causing a lot of useless floating-point operations at run time.
90 : * To get around this we use the following pre-calculated constants.
91 : * If you change CONST_BITS you may want to add appropriate values.
92 : * (With a reasonable C compiler, you can just rely on the FIX() macro...)
93 : */
94 :
95 : #if CONST_BITS == 13
96 : #define FIX_0_298631336 ((JLONG) 2446) /* FIX(0.298631336) */
97 : #define FIX_0_390180644 ((JLONG) 3196) /* FIX(0.390180644) */
98 : #define FIX_0_541196100 ((JLONG) 4433) /* FIX(0.541196100) */
99 : #define FIX_0_765366865 ((JLONG) 6270) /* FIX(0.765366865) */
100 : #define FIX_0_899976223 ((JLONG) 7373) /* FIX(0.899976223) */
101 : #define FIX_1_175875602 ((JLONG) 9633) /* FIX(1.175875602) */
102 : #define FIX_1_501321110 ((JLONG) 12299) /* FIX(1.501321110) */
103 : #define FIX_1_847759065 ((JLONG) 15137) /* FIX(1.847759065) */
104 : #define FIX_1_961570560 ((JLONG) 16069) /* FIX(1.961570560) */
105 : #define FIX_2_053119869 ((JLONG) 16819) /* FIX(2.053119869) */
106 : #define FIX_2_562915447 ((JLONG) 20995) /* FIX(2.562915447) */
107 : #define FIX_3_072711026 ((JLONG) 25172) /* FIX(3.072711026) */
108 : #else
109 : #define FIX_0_298631336 FIX(0.298631336)
110 : #define FIX_0_390180644 FIX(0.390180644)
111 : #define FIX_0_541196100 FIX(0.541196100)
112 : #define FIX_0_765366865 FIX(0.765366865)
113 : #define FIX_0_899976223 FIX(0.899976223)
114 : #define FIX_1_175875602 FIX(1.175875602)
115 : #define FIX_1_501321110 FIX(1.501321110)
116 : #define FIX_1_847759065 FIX(1.847759065)
117 : #define FIX_1_961570560 FIX(1.961570560)
118 : #define FIX_2_053119869 FIX(2.053119869)
119 : #define FIX_2_562915447 FIX(2.562915447)
120 : #define FIX_3_072711026 FIX(3.072711026)
121 : #endif
122 :
123 :
124 : /* Multiply an JLONG variable by an JLONG constant to yield an JLONG result.
125 : * For 8-bit samples with the recommended scaling, all the variable
126 : * and constant values involved are no more than 16 bits wide, so a
127 : * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
128 : * For 12-bit samples, a full 32-bit multiplication will be needed.
129 : */
130 :
131 : #if BITS_IN_JSAMPLE == 8
132 : #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
133 : #else
134 : #define MULTIPLY(var,const) ((var) * (const))
135 : #endif
136 :
137 :
138 : /*
139 : * Perform the forward DCT on one block of samples.
140 : */
141 :
142 : GLOBAL(void)
143 0 : jpeg_fdct_islow (DCTELEM *data)
144 : {
145 : JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
146 : JLONG tmp10, tmp11, tmp12, tmp13;
147 : JLONG z1, z2, z3, z4, z5;
148 : DCTELEM *dataptr;
149 : int ctr;
150 : SHIFT_TEMPS
151 :
152 : /* Pass 1: process rows. */
153 : /* Note results are scaled up by sqrt(8) compared to a true DCT; */
154 : /* furthermore, we scale the results by 2**PASS1_BITS. */
155 :
156 0 : dataptr = data;
157 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
158 0 : tmp0 = dataptr[0] + dataptr[7];
159 0 : tmp7 = dataptr[0] - dataptr[7];
160 0 : tmp1 = dataptr[1] + dataptr[6];
161 0 : tmp6 = dataptr[1] - dataptr[6];
162 0 : tmp2 = dataptr[2] + dataptr[5];
163 0 : tmp5 = dataptr[2] - dataptr[5];
164 0 : tmp3 = dataptr[3] + dataptr[4];
165 0 : tmp4 = dataptr[3] - dataptr[4];
166 :
167 : /* Even part per LL&M figure 1 --- note that published figure is faulty;
168 : * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
169 : */
170 :
171 0 : tmp10 = tmp0 + tmp3;
172 0 : tmp13 = tmp0 - tmp3;
173 0 : tmp11 = tmp1 + tmp2;
174 0 : tmp12 = tmp1 - tmp2;
175 :
176 0 : dataptr[0] = (DCTELEM) LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS);
177 0 : dataptr[4] = (DCTELEM) LEFT_SHIFT(tmp10 - tmp11, PASS1_BITS);
178 :
179 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
180 0 : dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
181 : CONST_BITS-PASS1_BITS);
182 0 : dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
183 : CONST_BITS-PASS1_BITS);
184 :
185 : /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
186 : * cK represents cos(K*pi/16).
187 : * i0..i3 in the paper are tmp4..tmp7 here.
188 : */
189 :
190 0 : z1 = tmp4 + tmp7;
191 0 : z2 = tmp5 + tmp6;
192 0 : z3 = tmp4 + tmp6;
193 0 : z4 = tmp5 + tmp7;
194 0 : z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
195 :
196 0 : tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
197 0 : tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
198 0 : tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
199 0 : tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
200 0 : z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
201 0 : z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
202 0 : z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
203 0 : z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
204 :
205 0 : z3 += z5;
206 0 : z4 += z5;
207 :
208 0 : dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
209 0 : dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
210 0 : dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
211 0 : dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
212 :
213 0 : dataptr += DCTSIZE; /* advance pointer to next row */
214 : }
215 :
216 : /* Pass 2: process columns.
217 : * We remove the PASS1_BITS scaling, but leave the results scaled up
218 : * by an overall factor of 8.
219 : */
220 :
221 0 : dataptr = data;
222 0 : for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
223 0 : tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
224 0 : tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
225 0 : tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
226 0 : tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
227 0 : tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
228 0 : tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
229 0 : tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
230 0 : tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
231 :
232 : /* Even part per LL&M figure 1 --- note that published figure is faulty;
233 : * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
234 : */
235 :
236 0 : tmp10 = tmp0 + tmp3;
237 0 : tmp13 = tmp0 - tmp3;
238 0 : tmp11 = tmp1 + tmp2;
239 0 : tmp12 = tmp1 - tmp2;
240 :
241 0 : dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
242 0 : dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
243 :
244 0 : z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
245 0 : dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
246 : CONST_BITS+PASS1_BITS);
247 0 : dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
248 : CONST_BITS+PASS1_BITS);
249 :
250 : /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
251 : * cK represents cos(K*pi/16).
252 : * i0..i3 in the paper are tmp4..tmp7 here.
253 : */
254 :
255 0 : z1 = tmp4 + tmp7;
256 0 : z2 = tmp5 + tmp6;
257 0 : z3 = tmp4 + tmp6;
258 0 : z4 = tmp5 + tmp7;
259 0 : z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
260 :
261 0 : tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
262 0 : tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
263 0 : tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
264 0 : tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
265 0 : z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
266 0 : z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
267 0 : z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
268 0 : z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
269 :
270 0 : z3 += z5;
271 0 : z4 += z5;
272 :
273 0 : dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
274 : CONST_BITS+PASS1_BITS);
275 0 : dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
276 : CONST_BITS+PASS1_BITS);
277 0 : dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
278 : CONST_BITS+PASS1_BITS);
279 0 : dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
280 : CONST_BITS+PASS1_BITS);
281 :
282 0 : dataptr++; /* advance pointer to next column */
283 : }
284 0 : }
285 :
286 : #endif /* DCT_ISLOW_SUPPORTED */
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