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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 | 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 | 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), | |
178 | CONST_BITS-PASS1_BITS); | |
179 | 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 | 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), | |
243 | CONST_BITS+PASS1_BITS); | |
244 | 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 | 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, | |
271 | CONST_BITS+PASS1_BITS); | |
272 | dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, | |
273 | CONST_BITS+PASS1_BITS); | |
274 | dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, | |
275 | CONST_BITS+PASS1_BITS); | |
276 | dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, | |
277 | CONST_BITS+PASS1_BITS); | |
278 | ||
279 | dataptr++; /* advance pointer to next column */ | |
280 | } | |
281 | } | |
282 | ||
283 | #endif /* DCT_ISLOW_SUPPORTED */ |