1 /*
2 * jfdctfst.c
3 *
4 * Copyright (C) 1994-1996, Thomas G. Lane.
5 * Modified 2003-2009 by Guido Vollbeding.
6 * This file is part of the Independent JPEG Group's software.
7 * For conditions of distribution and use, see the accompanying README file.
8 *
9 * This file contains a fast, not so accurate integer implementation of the
10 * forward DCT (Discrete Cosine Transform).
11 *
12 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
13 * on each column. Direct algorithms are also available, but they are
14 * much more complex and seem not to be any faster when reduced to code.
15 *
16 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
17 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
18 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
19 * JPEG textbook (see REFERENCES section in file README). The following code
20 * is based directly on figure 4-8 in P&M.
21 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
22 * possible to arrange the computation so that many of the multiplies are
23 * simple scalings of the final outputs. These multiplies can then be
24 * folded into the multiplications or divisions by the JPEG quantization
25 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
26 * to be done in the DCT itself.
27 * The primary disadvantage of this method is that with fixed-point math,
28 * accuracy is lost due to imprecise representation of the scaled
29 * quantization values. The smaller the quantization table entry, the less
30 * precise the scaled value, so this implementation does worse with high-
31 * quality-setting files than with low-quality ones.
32 */
33
34 #define JPEG_INTERNALS
35 #include "jinclude.h"
36 #include "jpeglib.h"
37 #include "jdct.h" /* Private declarations for DCT subsystem */
38
39 #ifdef DCT_IFAST_SUPPORTED
40
41
42 /*
43 * This module is specialized to the case DCTSIZE = 8.
44 */
45
46 #if DCTSIZE != 8
47 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
48 #endif
49
50
51 /* Scaling decisions are generally the same as in the LL&M algorithm;
52 * see jfdctint.c for more details. However, we choose to descale
53 * (right shift) multiplication products as soon as they are formed,
54 * rather than carrying additional fractional bits into subsequent additions.
55 * This compromises accuracy slightly, but it lets us save a few shifts.
56 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
57 * everywhere except in the multiplications proper; this saves a good deal
58 * of work on 16-bit-int machines.
59 *
60 * Again to save a few shifts, the intermediate results between pass 1 and
61 * pass 2 are not upscaled, but are represented only to integral precision.
62 *
63 * A final compromise is to represent the multiplicative constants to only
64 * 8 fractional bits, rather than 13. This saves some shifting work on some
65 * machines, and may also reduce the cost of multiplication (since there
66 * are fewer one-bits in the constants).
67 */
68
69 #define CONST_BITS 8
70
71
72 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
73 * causing a lot of useless floating-point operations at run time.
74 * To get around this we use the following pre-calculated constants.
75 * If you change CONST_BITS you may want to add appropriate values.
76 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
77 */
78
79 #if CONST_BITS == 8
80 #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */
81 #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */
82 #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */
83 #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */
84 #else
85 #define FIX_0_382683433 FIX(0.382683433)
86 #define FIX_0_541196100 FIX(0.541196100)
87 #define FIX_0_707106781 FIX(0.707106781)
88 #define FIX_1_306562965 FIX(1.306562965)
89 #endif
90
91
92 /* We can gain a little more speed, with a further compromise in accuracy,
93 * by omitting the addition in a descaling shift. This yields an incorrectly
94 * rounded result half the time...
95 */
96
97 #ifndef USE_ACCURATE_ROUNDING
98 #undef DESCALE
99 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
100 #endif
101
102
103 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
104 * descale to yield a DCTELEM result.
105 */
106
107 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
108
109
110 /*
111 * Perform the forward DCT on one block of samples.
112 */
113
114 GLOBAL(void)
115 jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
116 {
117 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
118 DCTELEM tmp10, tmp11, tmp12, tmp13;
119 DCTELEM z1, z2, z3, z4, z5, z11, z13;
120 DCTELEM *dataptr;
121 JSAMPROW elemptr;
122 int ctr;
123 SHIFT_TEMPS
124
125 /* Pass 1: process rows. */
126
127 dataptr = data;
128 for (ctr = 0; ctr < DCTSIZE; ctr++) {
129 elemptr = sample_data[ctr] + start_col;
130
131 /* Load data into workspace */
132 tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);
133 tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);
134 tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);
135 tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);
136 tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);
137 tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);
138 tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);
139 tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);
140
141 /* Even part */
142
143 tmp10 = tmp0 + tmp3; /* phase 2 */
144 tmp13 = tmp0 - tmp3;
145 tmp11 = tmp1 + tmp2;
146 tmp12 = tmp1 - tmp2;
147
148 /* Apply unsigned->signed conversion */
149 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */
150 dataptr[4] = tmp10 - tmp11;
151
152 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
153 dataptr[2] = tmp13 + z1; /* phase 5 */
154 dataptr[6] = tmp13 - z1;
155
156 /* Odd part */
157
158 tmp10 = tmp4 + tmp5; /* phase 2 */
159 tmp11 = tmp5 + tmp6;
160 tmp12 = tmp6 + tmp7;
161
162 /* The rotator is modified from fig 4-8 to avoid extra negations. */
163 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
164 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
165 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
166 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
167
168 z11 = tmp7 + z3; /* phase 5 */
169 z13 = tmp7 - z3;
170
171 dataptr[5] = z13 + z2; /* phase 6 */
172 dataptr[3] = z13 - z2;
173 dataptr[1] = z11 + z4;
174 dataptr[7] = z11 - z4;
175
176 dataptr += DCTSIZE; /* advance pointer to next row */
177 }
178
179 /* Pass 2: process columns. */
180
181 dataptr = data;
182 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
183 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
184 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
185 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
186 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
187 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
188 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
189 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
190 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
191
192 /* Even part */
193
194 tmp10 = tmp0 + tmp3; /* phase 2 */
195 tmp13 = tmp0 - tmp3;
196 tmp11 = tmp1 + tmp2;
197 tmp12 = tmp1 - tmp2;
198
199 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
200 dataptr[DCTSIZE*4] = tmp10 - tmp11;
201
202 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
203 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
204 dataptr[DCTSIZE*6] = tmp13 - z1;
205
206 /* Odd part */
207
208 tmp10 = tmp4 + tmp5; /* phase 2 */
209 tmp11 = tmp5 + tmp6;
210 tmp12 = tmp6 + tmp7;
211
212 /* The rotator is modified from fig 4-8 to avoid extra negations. */
213 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
214 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
215 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
216 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
217
218 z11 = tmp7 + z3; /* phase 5 */
219 z13 = tmp7 - z3;
220
221 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
222 dataptr[DCTSIZE*3] = z13 - z2;
223 dataptr[DCTSIZE*1] = z11 + z4;
224 dataptr[DCTSIZE*7] = z11 - z4;
225
226 dataptr++; /* advance pointer to next column */
227 }
228 }
229
230 #endif /* DCT_IFAST_SUPPORTED */