|
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 */ |