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 */
26 /**
27 * @file jfdctint.c
28 * Independent JPEG Group's slow & accurate dct.
29 */
31 #include <stdlib.h>
32 #include <stdio.h>
33 #include "common.h"
34 #include "dsputil.h"
36 #define SHIFT_TEMPS
37 #define DCTSIZE 8
38 #define BITS_IN_JSAMPLE 8
39 #define GLOBAL(x) x
40 #define RIGHT_SHIFT(x, n) ((x) >> (n))
41 #define MULTIPLY16C16(var,const) ((var)*(const))
43 #if 1 //def USE_ACCURATE_ROUNDING
44 #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
45 #else
46 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
47 #endif
50 /*
51 * This module is specialized to the case DCTSIZE = 8.
52 */
54 #if DCTSIZE != 8
55 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
56 #endif
59 /*
60 * The poop on this scaling stuff is as follows:
61 *
62 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
63 * larger than the true DCT outputs. The final outputs are therefore
64 * a factor of N larger than desired; since N=8 this can be cured by
65 * a simple right shift at the end of the algorithm. The advantage of
66 * this arrangement is that we save two multiplications per 1-D DCT,
67 * because the y0 and y4 outputs need not be divided by sqrt(N).
68 * In the IJG code, this factor of 8 is removed by the quantization step
69 * (in jcdctmgr.c), NOT in this module.
70 *
71 * We have to do addition and subtraction of the integer inputs, which
72 * is no problem, and multiplication by fractional constants, which is
73 * a problem to do in integer arithmetic. We multiply all the constants
74 * by CONST_SCALE and convert them to integer constants (thus retaining
75 * CONST_BITS bits of precision in the constants). After doing a
76 * multiplication we have to divide the product by CONST_SCALE, with proper
77 * rounding, to produce the correct output. This division can be done
78 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
79 * as long as possible so that partial sums can be added together with
80 * full fractional precision.
81 *
82 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
83 * they are represented to better-than-integral precision. These outputs
84 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
85 * with the recommended scaling. (For 12-bit sample data, the intermediate
86 * array is int32_t anyway.)
87 *
88 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
89 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
90 * shows that the values given below are the most effective.
91 */
93 #if BITS_IN_JSAMPLE == 8
94 #define CONST_BITS 13
95 #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
96 #else
97 #define CONST_BITS 13
98 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
99 #endif
101 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
102 * causing a lot of useless floating-point operations at run time.
103 * To get around this we use the following pre-calculated constants.
104 * If you change CONST_BITS you may want to add appropriate values.
105 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
106 */
108 #if CONST_BITS == 13
109 #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
110 #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
111 #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
112 #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
113 #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
114 #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
115 #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
116 #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
117 #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
118 #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
119 #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
120 #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
121 #else
122 #define FIX_0_298631336 FIX(0.298631336)
123 #define FIX_0_390180644 FIX(0.390180644)
124 #define FIX_0_541196100 FIX(0.541196100)
125 #define FIX_0_765366865 FIX(0.765366865)
126 #define FIX_0_899976223 FIX(0.899976223)
127 #define FIX_1_175875602 FIX(1.175875602)
128 #define FIX_1_501321110 FIX(1.501321110)
129 #define FIX_1_847759065 FIX(1.847759065)
130 #define FIX_1_961570560 FIX(1.961570560)
131 #define FIX_2_053119869 FIX(2.053119869)
132 #define FIX_2_562915447 FIX(2.562915447)
133 #define FIX_3_072711026 FIX(3.072711026)
134 #endif
137 /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
138 * For 8-bit samples with the recommended scaling, all the variable
139 * and constant values involved are no more than 16 bits wide, so a
140 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
141 * For 12-bit samples, a full 32-bit multiplication will be needed.
142 */
144 #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
145 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
146 #else
147 #define MULTIPLY(var,const) ((var) * (const))
148 #endif
151 /*
152 * Perform the forward DCT on one block of samples.
153 */
155 GLOBAL(void)
156 ff_jpeg_fdct_islow (DCTELEM * data)
157 {
158 int32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
159 int32_t tmp10, tmp11, tmp12, tmp13;
160 int32_t z1, z2, z3, z4, z5;
161 DCTELEM *dataptr;
162 int ctr;
163 SHIFT_TEMPS
165 /* Pass 1: process rows. */
166 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
167 /* furthermore, we scale the results by 2**PASS1_BITS. */
169 dataptr = data;
170 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
171 tmp0 = dataptr + dataptr;
172 tmp7 = dataptr - dataptr;
173 tmp1 = dataptr + dataptr;
174 tmp6 = dataptr - dataptr;
175 tmp2 = dataptr + dataptr;
176 tmp5 = dataptr - dataptr;
177 tmp3 = dataptr + dataptr;
178 tmp4 = dataptr - dataptr;
180 /* Even part per LL&M figure 1 --- note that published figure is faulty;
181 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
182 */
184 tmp10 = tmp0 + tmp3;
185 tmp13 = tmp0 - tmp3;
186 tmp11 = tmp1 + tmp2;
187 tmp12 = tmp1 - tmp2;
189 dataptr = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
190 dataptr = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
192 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
193 dataptr = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
194 CONST_BITS-PASS1_BITS);
195 dataptr = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
196 CONST_BITS-PASS1_BITS);
198 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
199 * cK represents cos(K*pi/16).
200 * i0..i3 in the paper are tmp4..tmp7 here.
201 */
203 z1 = tmp4 + tmp7;
204 z2 = tmp5 + tmp6;
205 z3 = tmp4 + tmp6;
206 z4 = tmp5 + tmp7;
207 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
209 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
210 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
211 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
212 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
213 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
214 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
215 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
216 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
218 z3 += z5;
219 z4 += z5;
221 dataptr = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
222 dataptr = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
223 dataptr = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
224 dataptr = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
226 dataptr += DCTSIZE; /* advance pointer to next row */
227 }
229 /* Pass 2: process columns.
230 * We remove the PASS1_BITS scaling, but leave the results scaled up
231 * by an overall factor of 8.
232 */
234 dataptr = data;
235 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
236 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
237 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
238 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
239 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
240 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
241 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
242 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
243 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
245 /* Even part per LL&M figure 1 --- note that published figure is faulty;
246 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
247 */
249 tmp10 = tmp0 + tmp3;
250 tmp13 = tmp0 - tmp3;
251 tmp11 = tmp1 + tmp2;
252 tmp12 = tmp1 - tmp2;
254 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
255 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
257 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
258 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
259 CONST_BITS+PASS1_BITS);
260 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
261 CONST_BITS+PASS1_BITS);
263 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
264 * cK represents cos(K*pi/16).
265 * i0..i3 in the paper are tmp4..tmp7 here.
266 */
268 z1 = tmp4 + tmp7;
269 z2 = tmp5 + tmp6;
270 z3 = tmp4 + tmp6;
271 z4 = tmp5 + tmp7;
272 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
274 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
275 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
276 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
277 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
278 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
279 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
280 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
281 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
283 z3 += z5;
284 z4 += z5;
286 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
287 CONST_BITS+PASS1_BITS);
288 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
289 CONST_BITS+PASS1_BITS);
290 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
291 CONST_BITS+PASS1_BITS);
292 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
293 CONST_BITS+PASS1_BITS);
295 dataptr++; /* advance pointer to next column */
296 }
297 }