1 /*
2 * jfdctfst.c
3 *
4 * Copyright (C) 1994-1996, Thomas G. Lane.
5 * Modified 2003-2017 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 DCT blocks. /* 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 * cK represents cos(K*pi/16).
114 */
115
116 GLOBAL(void)
117 jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col)
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 JSAMPROW elemptr;
124 int ctr;
125 SHIFT_TEMPS
126
127 /* Pass 1: process rows. */
128
129 dataptr = data;
130 for (ctr = 0; ctr < DCTSIZE; ctr++) {
131 elemptr = sample_data[ctr] + start_col;
132
133 /* Load data into workspace */
134 tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]);
135 tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]);
136 tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]);
137 tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]);
138 tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]);
139 tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]);
140 tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]);
141 tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]);
142
143 /* Even part */
144
145 tmp10 = tmp0 + tmp3; /* phase 2 */
146 tmp13 = tmp0 - tmp3;
147 tmp11 = tmp1 + tmp2;
148 tmp12 = tmp1 - tmp2;
149
150 /* Apply unsigned->signed conversion. */
151 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */
152 dataptr[4] = tmp10 - tmp11;
153
154 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
155 dataptr[2] = tmp13 + z1; /* phase 5 */
156 dataptr[6] = tmp13 - z1;
157
158 /* Odd part */
159
160 tmp10 = tmp4 + tmp5; /* phase 2 */
161 tmp11 = tmp5 + tmp6;
162 tmp12 = tmp6 + tmp7;
163
164 /* The rotator is modified from fig 4-8 to avoid extra negations. */
165 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
166 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
167 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
168 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
169
170 z11 = tmp7 + z3; /* phase 5 */
171 z13 = tmp7 - z3;
172
173 dataptr[5] = z13 + z2; /* phase 6 */
174 dataptr[3] = z13 - z2;
175 dataptr[1] = z11 + z4;
176 dataptr[7] = z11 - z4;
177
178 dataptr += DCTSIZE; /* advance pointer to next row */
179 }
180
181 /* Pass 2: process columns. */
182
183 dataptr = data;
184 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
185 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
186 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
187 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
188 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
189 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
190 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
191 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
192 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
193
194 /* Even part */
195
196 tmp10 = tmp0 + tmp3; /* phase 2 */
197 tmp13 = tmp0 - tmp3;
198 tmp11 = tmp1 + tmp2;
199 tmp12 = tmp1 - tmp2;
200
201 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
202 dataptr[DCTSIZE*4] = tmp10 - tmp11;
203
204 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
205 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
206 dataptr[DCTSIZE*6] = tmp13 - z1;
207
208 /* Odd part */
209
210 tmp10 = tmp4 + tmp5; /* phase 2 */
211 tmp11 = tmp5 + tmp6;
212 tmp12 = tmp6 + tmp7;
213
214 /* The rotator is modified from fig 4-8 to avoid extra negations. */
215 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
216 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
217 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
218 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
219
220 z11 = tmp7 + z3; /* phase 5 */
221 z13 = tmp7 - z3;
222
223 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
224 dataptr[DCTSIZE*3] = z13 - z2;
225 dataptr[DCTSIZE*1] = z11 + z4;
226 dataptr[DCTSIZE*7] = z11 - z4;
227
228 dataptr++; /* advance pointer to next column */
229 }
230 }
231
232 #endif /* DCT_IFAST_SUPPORTED */