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