1/*
2 * jfdctfst.c
3 *
4 * This file was part of the Independent JPEG Group's software:
5 * Copyright (C) 1994-1996, Thomas G. Lane.
6 * libjpeg-turbo Modifications:
7 * Copyright (C) 2015, D. R. Commander.
8 * For conditions of distribution and use, see the accompanying README.ijg
9 * file.
10 *
11 * This file contains a fast, not so accurate integer implementation of the
12 * forward DCT (Discrete Cosine Transform).
13 *
14 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
15 * on each column. Direct algorithms are also available, but they are
16 * much more complex and seem not to be any faster when reduced to code.
17 *
18 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
19 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
20 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
21 * JPEG textbook (see REFERENCES section in file README.ijg). The following
22 * code is based directly on figure 4-8 in P&M.
23 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
24 * possible to arrange the computation so that many of the multiplies are
25 * simple scalings of the final outputs. These multiplies can then be
26 * folded into the multiplications or divisions by the JPEG quantization
27 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
28 * to be done in the DCT itself.
29 * The primary disadvantage of this method is that with fixed-point math,
30 * accuracy is lost due to imprecise representation of the scaled
31 * quantization values. The smaller the quantization table entry, the less
32 * precise the scaled value, so this implementation does worse with high-
33 * quality-setting files than with low-quality ones.
34 */
35
36#define JPEG_INTERNALS
37#include "jinclude.h"
38#include "jpeglib.h"
39#include "jdct.h" /* Private declarations for DCT subsystem */
40
41#ifdef DCT_IFAST_SUPPORTED
42
43
44/*
45 * This module is specialized to the case DCTSIZE = 8.
46 */
47
48#if DCTSIZE != 8
49 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
50#endif
51
52
53/* Scaling decisions are generally the same as in the LL&M algorithm;
54 * see jfdctint.c for more details. However, we choose to descale
55 * (right shift) multiplication products as soon as they are formed,
56 * rather than carrying additional fractional bits into subsequent additions.
57 * This compromises accuracy slightly, but it lets us save a few shifts.
58 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
59 * everywhere except in the multiplications proper; this saves a good deal
60 * of work on 16-bit-int machines.
61 *
62 * Again to save a few shifts, the intermediate results between pass 1 and
63 * pass 2 are not upscaled, but are represented only to integral precision.
64 *
65 * A final compromise is to represent the multiplicative constants to only
66 * 8 fractional bits, rather than 13. This saves some shifting work on some
67 * machines, and may also reduce the cost of multiplication (since there
68 * are fewer one-bits in the constants).
69 */
70
71#define CONST_BITS 8
72
73
74/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
75 * causing a lot of useless floating-point operations at run time.
76 * To get around this we use the following pre-calculated constants.
77 * If you change CONST_BITS you may want to add appropriate values.
78 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
79 */
80
81#if CONST_BITS == 8
82#define FIX_0_382683433 ((JLONG)98) /* FIX(0.382683433) */
83#define FIX_0_541196100 ((JLONG)139) /* FIX(0.541196100) */
84#define FIX_0_707106781 ((JLONG)181) /* FIX(0.707106781) */
85#define FIX_1_306562965 ((JLONG)334) /* FIX(1.306562965) */
86#else
87#define FIX_0_382683433 FIX(0.382683433)
88#define FIX_0_541196100 FIX(0.541196100)
89#define FIX_0_707106781 FIX(0.707106781)
90#define FIX_1_306562965 FIX(1.306562965)
91#endif
92
93
94/* We can gain a little more speed, with a further compromise in accuracy,
95 * by omitting the addition in a descaling shift. This yields an incorrectly
96 * rounded result half the time...
97 */
98
99#ifndef USE_ACCURATE_ROUNDING
100#undef DESCALE
101#define DESCALE(x, n) RIGHT_SHIFT(x, n)
102#endif
103
104
105/* Multiply a DCTELEM variable by an JLONG constant, and immediately
106 * descale to yield a DCTELEM result.
107 */
108
109#define MULTIPLY(var, const) ((DCTELEM)DESCALE((var) * (const), CONST_BITS))
110
111
112/*
113 * Perform the forward DCT on one block of samples.
114 */
115
116GLOBAL(void)
117jpeg_fdct_ifast(DCTELEM *data)
118{
119 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
120 DCTELEM tmp10, tmp11, tmp12, tmp13;
121 DCTELEM z1, z2, z3, z4, z5, z11, z13;
122 DCTELEM *dataptr;
123 int ctr;
124 SHIFT_TEMPS
125
126 /* Pass 1: process rows. */
127
128 dataptr = data;
129 for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
130 tmp0 = dataptr[0] + dataptr[7];
131 tmp7 = dataptr[0] - dataptr[7];
132 tmp1 = dataptr[1] + dataptr[6];
133 tmp6 = dataptr[1] - dataptr[6];
134 tmp2 = dataptr[2] + dataptr[5];
135 tmp5 = dataptr[2] - dataptr[5];
136 tmp3 = dataptr[3] + dataptr[4];
137 tmp4 = dataptr[3] - dataptr[4];
138
139 /* Even part */
140
141 tmp10 = tmp0 + tmp3; /* phase 2 */
142 tmp13 = tmp0 - tmp3;
143 tmp11 = tmp1 + tmp2;
144 tmp12 = tmp1 - tmp2;
145
146 dataptr[0] = tmp10 + tmp11; /* phase 3 */
147 dataptr[4] = tmp10 - tmp11;
148
149 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
150 dataptr[2] = tmp13 + z1; /* phase 5 */
151 dataptr[6] = tmp13 - z1;
152
153 /* Odd part */
154
155 tmp10 = tmp4 + tmp5; /* phase 2 */
156 tmp11 = tmp5 + tmp6;
157 tmp12 = tmp6 + tmp7;
158
159 /* The rotator is modified from fig 4-8 to avoid extra negations. */
160 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
161 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
162 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
163 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
164
165 z11 = tmp7 + z3; /* phase 5 */
166 z13 = tmp7 - z3;
167
168 dataptr[5] = z13 + z2; /* phase 6 */
169 dataptr[3] = z13 - z2;
170 dataptr[1] = z11 + z4;
171 dataptr[7] = z11 - z4;
172
173 dataptr += DCTSIZE; /* advance pointer to next row */
174 }
175
176 /* Pass 2: process columns. */
177
178 dataptr = data;
179 for (ctr = DCTSIZE - 1; ctr >= 0; ctr--) {
180 tmp0 = dataptr[DCTSIZE * 0] + dataptr[DCTSIZE * 7];
181 tmp7 = dataptr[DCTSIZE * 0] - dataptr[DCTSIZE * 7];
182 tmp1 = dataptr[DCTSIZE * 1] + dataptr[DCTSIZE * 6];
183 tmp6 = dataptr[DCTSIZE * 1] - dataptr[DCTSIZE * 6];
184 tmp2 = dataptr[DCTSIZE * 2] + dataptr[DCTSIZE * 5];
185 tmp5 = dataptr[DCTSIZE * 2] - dataptr[DCTSIZE * 5];
186 tmp3 = dataptr[DCTSIZE * 3] + dataptr[DCTSIZE * 4];
187 tmp4 = dataptr[DCTSIZE * 3] - dataptr[DCTSIZE * 4];
188
189 /* Even part */
190
191 tmp10 = tmp0 + tmp3; /* phase 2 */
192 tmp13 = tmp0 - tmp3;
193 tmp11 = tmp1 + tmp2;
194 tmp12 = tmp1 - tmp2;
195
196 dataptr[DCTSIZE * 0] = tmp10 + tmp11; /* phase 3 */
197 dataptr[DCTSIZE * 4] = tmp10 - tmp11;
198
199 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
200 dataptr[DCTSIZE * 2] = tmp13 + z1; /* phase 5 */
201 dataptr[DCTSIZE * 6] = tmp13 - z1;
202
203 /* Odd part */
204
205 tmp10 = tmp4 + tmp5; /* phase 2 */
206 tmp11 = tmp5 + tmp6;
207 tmp12 = tmp6 + tmp7;
208
209 /* The rotator is modified from fig 4-8 to avoid extra negations. */
210 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
211 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
212 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
213 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
214
215 z11 = tmp7 + z3; /* phase 5 */
216 z13 = tmp7 - z3;
217
218 dataptr[DCTSIZE * 5] = z13 + z2; /* phase 6 */
219 dataptr[DCTSIZE * 3] = z13 - z2;
220 dataptr[DCTSIZE * 1] = z11 + z4;
221 dataptr[DCTSIZE * 7] = z11 - z4;
222
223 dataptr++; /* advance pointer to next column */
224 }
225}
226
227#endif /* DCT_IFAST_SUPPORTED */
228