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