1/*
2 * reserved comment block
3 * DO NOT REMOVE OR ALTER!
4 */
5/*
6 * jfdctint.c
7 *
8 * Copyright (C) 1991-1996, Thomas G. Lane.
9 * This file is part of the Independent JPEG Group's software.
10 * For conditions of distribution and use, see the accompanying README file.
11 *
12 * This file contains a slow-but-accurate integer implementation of the
13 * forward DCT (Discrete Cosine Transform).
14 *
15 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
16 * on each column. Direct algorithms are also available, but they are
17 * much more complex and seem not to be any faster when reduced to code.
18 *
19 * This implementation is based on an algorithm described in
20 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
21 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
22 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
23 * The primary algorithm described there uses 11 multiplies and 29 adds.
24 * We use their alternate method with 12 multiplies and 32 adds.
25 * The advantage of this method is that no data path contains more than one
26 * multiplication; this allows a very simple and accurate implementation in
27 * scaled fixed-point arithmetic, with a minimal number of shifts.
28 */
29
30#define JPEG_INTERNALS
31#include "jinclude.h"
32#include "jpeglib.h"
33#include "jdct.h" /* Private declarations for DCT subsystem */
34
35#ifdef DCT_ISLOW_SUPPORTED
36
37
38/*
39 * This module is specialized to the case DCTSIZE = 8.
40 */
41
42#if DCTSIZE != 8
43 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
44#endif
45
46
47/*
48 * The poop on this scaling stuff is as follows:
49 *
50 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
51 * larger than the true DCT outputs. The final outputs are therefore
52 * a factor of N larger than desired; since N=8 this can be cured by
53 * a simple right shift at the end of the algorithm. The advantage of
54 * this arrangement is that we save two multiplications per 1-D DCT,
55 * because the y0 and y4 outputs need not be divided by sqrt(N).
56 * In the IJG code, this factor of 8 is removed by the quantization step
57 * (in jcdctmgr.c), NOT in this module.
58 *
59 * We have to do addition and subtraction of the integer inputs, which
60 * is no problem, and multiplication by fractional constants, which is
61 * a problem to do in integer arithmetic. We multiply all the constants
62 * by CONST_SCALE and convert them to integer constants (thus retaining
63 * CONST_BITS bits of precision in the constants). After doing a
64 * multiplication we have to divide the product by CONST_SCALE, with proper
65 * rounding, to produce the correct output. This division can be done
66 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
67 * as long as possible so that partial sums can be added together with
68 * full fractional precision.
69 *
70 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
71 * they are represented to better-than-integral precision. These outputs
72 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
73 * with the recommended scaling. (For 12-bit sample data, the intermediate
74 * array is INT32 anyway.)
75 *
76 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
77 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
78 * shows that the values given below are the most effective.
79 */
80
81#if BITS_IN_JSAMPLE == 8
82#define CONST_BITS 13
83#define PASS1_BITS 2
84#else
85#define CONST_BITS 13
86#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
87#endif
88
89/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
90 * causing a lot of useless floating-point operations at run time.
91 * To get around this we use the following pre-calculated constants.
92 * If you change CONST_BITS you may want to add appropriate values.
93 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
94 */
95
96#if CONST_BITS == 13
97#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
98#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
99#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
100#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
101#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
102#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
103#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
104#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
105#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
106#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
107#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
108#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
109#else
110#define FIX_0_298631336 FIX(0.298631336)
111#define FIX_0_390180644 FIX(0.390180644)
112#define FIX_0_541196100 FIX(0.541196100)
113#define FIX_0_765366865 FIX(0.765366865)
114#define FIX_0_899976223 FIX(0.899976223)
115#define FIX_1_175875602 FIX(1.175875602)
116#define FIX_1_501321110 FIX(1.501321110)
117#define FIX_1_847759065 FIX(1.847759065)
118#define FIX_1_961570560 FIX(1.961570560)
119#define FIX_2_053119869 FIX(2.053119869)
120#define FIX_2_562915447 FIX(2.562915447)
121#define FIX_3_072711026 FIX(3.072711026)
122#endif
123
124
125/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
126 * For 8-bit samples with the recommended scaling, all the variable
127 * and constant values involved are no more than 16 bits wide, so a
128 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
129 * For 12-bit samples, a full 32-bit multiplication will be needed.
130 */
131
132#if BITS_IN_JSAMPLE == 8
133#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
134#else
135#define MULTIPLY(var,const) ((var) * (const))
136#endif
137
138
139/*
140 * Perform the forward DCT on one block of samples.
141 */
142
143GLOBAL(void)
144jpeg_fdct_islow (DCTELEM * data)
145{
146 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
147 INT32 tmp10, tmp11, tmp12, tmp13;
148 INT32 z1, z2, z3, z4, z5;
149 DCTELEM *dataptr;
150 int ctr;
151 SHIFT_TEMPS
152
153 /* Pass 1: process rows. */
154 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
155 /* furthermore, we scale the results by 2**PASS1_BITS. */
156
157 dataptr = data;
158 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
159 tmp0 = dataptr[0] + dataptr[7];
160 tmp7 = dataptr[0] - dataptr[7];
161 tmp1 = dataptr[1] + dataptr[6];
162 tmp6 = dataptr[1] - dataptr[6];
163 tmp2 = dataptr[2] + dataptr[5];
164 tmp5 = dataptr[2] - dataptr[5];
165 tmp3 = dataptr[3] + dataptr[4];
166 tmp4 = dataptr[3] - dataptr[4];
167
168 /* Even part per LL&M figure 1 --- note that published figure is faulty;
169 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
170 */
171
172 tmp10 = tmp0 + tmp3;
173 tmp13 = tmp0 - tmp3;
174 tmp11 = tmp1 + tmp2;
175 tmp12 = tmp1 - tmp2;
176
177 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
178 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
179
180 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
181 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
182 CONST_BITS-PASS1_BITS);
183 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
184 CONST_BITS-PASS1_BITS);
185
186 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
187 * cK represents cos(K*pi/16).
188 * i0..i3 in the paper are tmp4..tmp7 here.
189 */
190
191 z1 = tmp4 + tmp7;
192 z2 = tmp5 + tmp6;
193 z3 = tmp4 + tmp6;
194 z4 = tmp5 + tmp7;
195 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
196
197 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
198 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
199 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
200 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
201 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
202 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
203 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
204 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
205
206 z3 += z5;
207 z4 += z5;
208
209 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
210 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
211 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
212 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
213
214 dataptr += DCTSIZE; /* advance pointer to next row */
215 }
216
217 /* Pass 2: process columns.
218 * We remove the PASS1_BITS scaling, but leave the results scaled up
219 * by an overall factor of 8.
220 */
221
222 dataptr = data;
223 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
224 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
225 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
226 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
227 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
228 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
229 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
230 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
231 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
232
233 /* Even part per LL&M figure 1 --- note that published figure is faulty;
234 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
235 */
236
237 tmp10 = tmp0 + tmp3;
238 tmp13 = tmp0 - tmp3;
239 tmp11 = tmp1 + tmp2;
240 tmp12 = tmp1 - tmp2;
241
242 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
243 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
244
245 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
246 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
247 CONST_BITS+PASS1_BITS);
248 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
249 CONST_BITS+PASS1_BITS);
250
251 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
252 * cK represents cos(K*pi/16).
253 * i0..i3 in the paper are tmp4..tmp7 here.
254 */
255
256 z1 = tmp4 + tmp7;
257 z2 = tmp5 + tmp6;
258 z3 = tmp4 + tmp6;
259 z4 = tmp5 + tmp7;
260 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
261
262 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
263 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
264 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
265 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
266 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
267 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
268 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
269 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
270
271 z3 += z5;
272 z4 += z5;
273
274 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
275 CONST_BITS+PASS1_BITS);
276 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
277 CONST_BITS+PASS1_BITS);
278 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
279 CONST_BITS+PASS1_BITS);
280 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
281 CONST_BITS+PASS1_BITS);
282
283 dataptr++; /* advance pointer to next column */
284 }
285}
286
287#endif /* DCT_ISLOW_SUPPORTED */
288