4 * Copyright (C) 1994-1998, Thomas G. Lane.
5 * This file is part of the Independent JPEG Group's software.
7 * The authors make NO WARRANTY or representation, either express or implied,
8 * with respect to this software, its quality, accuracy, merchantability, or
9 * fitness for a particular purpose. This software is provided "AS IS", and you,
10 * its user, assume the entire risk as to its quality and accuracy.
12 * This software is copyright (C) 1991-1998, Thomas G. Lane.
13 * All Rights Reserved except as specified below.
15 * Permission is hereby granted to use, copy, modify, and distribute this
16 * software (or portions thereof) for any purpose, without fee, subject to these
18 * (1) If any part of the source code for this software is distributed, then this
19 * README file must be included, with this copyright and no-warranty notice
20 * unaltered; and any additions, deletions, or changes to the original files
21 * must be clearly indicated in accompanying documentation.
22 * (2) If only executable code is distributed, then the accompanying
23 * documentation must state that "this software is based in part on the work of
24 * the Independent JPEG Group".
25 * (3) Permission for use of this software is granted only if the user accepts
26 * full responsibility for any undesirable consequences; the authors accept
27 * NO LIABILITY for damages of any kind.
29 * These conditions apply to any software derived from or based on the IJG code,
30 * not just to the unmodified library. If you use our work, you ought to
33 * Permission is NOT granted for the use of any IJG author's name or company name
34 * in advertising or publicity relating to this software or products derived from
35 * it. This software may be referred to only as "the Independent JPEG Group's
38 * We specifically permit and encourage the use of this software as the basis of
39 * commercial products, provided that all warranty or liability claims are
40 * assumed by the product vendor.
43 * This file contains a floating-point implementation of the
44 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
45 * must also perform dequantization of the input coefficients.
47 * This implementation should be more accurate than either of the integer
48 * IDCT implementations. However, it may not give the same results on all
49 * machines because of differences in roundoff behavior. Speed will depend
50 * on the hardware's floating point capacity.
52 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
53 * on each row (or vice versa, but it's more convenient to emit a row at
54 * a time). Direct algorithms are also available, but they are much more
55 * complex and seem not to be any faster when reduced to code.
57 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
58 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
59 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
60 * JPEG textbook (see REFERENCES section in file README). The following code
61 * is based directly on figure 4-8 in P&M.
62 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
63 * possible to arrange the computation so that many of the multiplies are
64 * simple scalings of the final outputs. These multiplies can then be
65 * folded into the multiplications or divisions by the JPEG quantization
66 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
67 * to be done in the DCT itself.
68 * The primary disadvantage of this method is that with a fixed-point
69 * implementation, accuracy is lost due to imprecise representation of the
70 * scaled quantization values. However, that problem does not arise if
71 * we use floating point arithmetic.
75 #include "tinyjpeg-internal.h"
77 #define FAST_FLOAT float
79 #define DCTSIZE2 (DCTSIZE*DCTSIZE)
81 #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
83 #if defined(__GNUC__) && defined(__i686__) || defined(__x86_64__)
85 static inline unsigned char descale_and_clamp(int x
, int shift
)
91 "\tcmovl %5,%1\n" /* Use the sub to compare to 0 */
95 : "0"(x
), "i"(shift
), "i"(1UL<<(shift
-1)), "r" (0xff), "r" (0)
101 static inline unsigned char descale_and_clamp(int x
, int shift
)
103 x
+= (1UL<<(shift
-1));
105 x
= (x
>> shift
) | ((~(0UL)) << (32-(shift
)));
119 * Perform dequantization and inverse DCT on one block of coefficients.
123 jpeg_idct_float (struct component
*compptr
, uint8_t *output_buf
, int stride
)
125 FAST_FLOAT tmp0
, tmp1
, tmp2
, tmp3
, tmp4
, tmp5
, tmp6
, tmp7
;
126 FAST_FLOAT tmp10
, tmp11
, tmp12
, tmp13
;
127 FAST_FLOAT z5
, z10
, z11
, z12
, z13
;
129 FAST_FLOAT
*quantptr
;
133 FAST_FLOAT workspace
[DCTSIZE2
]; /* buffers data between passes */
135 /* Pass 1: process columns from input, store into work array. */
137 inptr
= compptr
->DCT
;
138 quantptr
= compptr
->Q_table
;
140 for (ctr
= DCTSIZE
; ctr
> 0; ctr
--) {
141 /* Due to quantization, we will usually find that many of the input
142 * coefficients are zero, especially the AC terms. We can exploit this
143 * by short-circuiting the IDCT calculation for any column in which all
144 * the AC terms are zero. In that case each output is equal to the
145 * DC coefficient (with scale factor as needed).
146 * With typical images and quantization tables, half or more of the
147 * column DCT calculations can be simplified this way.
150 if (inptr
[DCTSIZE
*1] == 0 && inptr
[DCTSIZE
*2] == 0 &&
151 inptr
[DCTSIZE
*3] == 0 && inptr
[DCTSIZE
*4] == 0 &&
152 inptr
[DCTSIZE
*5] == 0 && inptr
[DCTSIZE
*6] == 0 &&
153 inptr
[DCTSIZE
*7] == 0) {
154 /* AC terms all zero */
155 FAST_FLOAT dcval
= DEQUANTIZE(inptr
[DCTSIZE
*0], quantptr
[DCTSIZE
*0]);
157 wsptr
[DCTSIZE
*0] = dcval
;
158 wsptr
[DCTSIZE
*1] = dcval
;
159 wsptr
[DCTSIZE
*2] = dcval
;
160 wsptr
[DCTSIZE
*3] = dcval
;
161 wsptr
[DCTSIZE
*4] = dcval
;
162 wsptr
[DCTSIZE
*5] = dcval
;
163 wsptr
[DCTSIZE
*6] = dcval
;
164 wsptr
[DCTSIZE
*7] = dcval
;
166 inptr
++; /* advance pointers to next column */
174 tmp0
= DEQUANTIZE(inptr
[DCTSIZE
*0], quantptr
[DCTSIZE
*0]);
175 tmp1
= DEQUANTIZE(inptr
[DCTSIZE
*2], quantptr
[DCTSIZE
*2]);
176 tmp2
= DEQUANTIZE(inptr
[DCTSIZE
*4], quantptr
[DCTSIZE
*4]);
177 tmp3
= DEQUANTIZE(inptr
[DCTSIZE
*6], quantptr
[DCTSIZE
*6]);
179 tmp10
= tmp0
+ tmp2
; /* phase 3 */
182 tmp13
= tmp1
+ tmp3
; /* phases 5-3 */
183 tmp12
= (tmp1
- tmp3
) * ((FAST_FLOAT
) 1.414213562) - tmp13
; /* 2*c4 */
185 tmp0
= tmp10
+ tmp13
; /* phase 2 */
186 tmp3
= tmp10
- tmp13
;
187 tmp1
= tmp11
+ tmp12
;
188 tmp2
= tmp11
- tmp12
;
192 tmp4
= DEQUANTIZE(inptr
[DCTSIZE
*1], quantptr
[DCTSIZE
*1]);
193 tmp5
= DEQUANTIZE(inptr
[DCTSIZE
*3], quantptr
[DCTSIZE
*3]);
194 tmp6
= DEQUANTIZE(inptr
[DCTSIZE
*5], quantptr
[DCTSIZE
*5]);
195 tmp7
= DEQUANTIZE(inptr
[DCTSIZE
*7], quantptr
[DCTSIZE
*7]);
197 z13
= tmp6
+ tmp5
; /* phase 6 */
202 tmp7
= z11
+ z13
; /* phase 5 */
203 tmp11
= (z11
- z13
) * ((FAST_FLOAT
) 1.414213562); /* 2*c4 */
205 z5
= (z10
+ z12
) * ((FAST_FLOAT
) 1.847759065); /* 2*c2 */
206 tmp10
= ((FAST_FLOAT
) 1.082392200) * z12
- z5
; /* 2*(c2-c6) */
207 tmp12
= ((FAST_FLOAT
) -2.613125930) * z10
+ z5
; /* -2*(c2+c6) */
209 tmp6
= tmp12
- tmp7
; /* phase 2 */
213 wsptr
[DCTSIZE
*0] = tmp0
+ tmp7
;
214 wsptr
[DCTSIZE
*7] = tmp0
- tmp7
;
215 wsptr
[DCTSIZE
*1] = tmp1
+ tmp6
;
216 wsptr
[DCTSIZE
*6] = tmp1
- tmp6
;
217 wsptr
[DCTSIZE
*2] = tmp2
+ tmp5
;
218 wsptr
[DCTSIZE
*5] = tmp2
- tmp5
;
219 wsptr
[DCTSIZE
*4] = tmp3
+ tmp4
;
220 wsptr
[DCTSIZE
*3] = tmp3
- tmp4
;
222 inptr
++; /* advance pointers to next column */
227 /* Pass 2: process rows from work array, store into output array. */
228 /* Note that we must descale the results by a factor of 8 == 2**3. */
232 for (ctr
= 0; ctr
< DCTSIZE
; ctr
++) {
233 /* Rows of zeroes can be exploited in the same way as we did with columns.
234 * However, the column calculation has created many nonzero AC terms, so
235 * the simplification applies less often (typically 5% to 10% of the time).
236 * And testing floats for zero is relatively expensive, so we don't bother.
241 tmp10
= wsptr
[0] + wsptr
[4];
242 tmp11
= wsptr
[0] - wsptr
[4];
244 tmp13
= wsptr
[2] + wsptr
[6];
245 tmp12
= (wsptr
[2] - wsptr
[6]) * ((FAST_FLOAT
) 1.414213562) - tmp13
;
247 tmp0
= tmp10
+ tmp13
;
248 tmp3
= tmp10
- tmp13
;
249 tmp1
= tmp11
+ tmp12
;
250 tmp2
= tmp11
- tmp12
;
254 z13
= wsptr
[5] + wsptr
[3];
255 z10
= wsptr
[5] - wsptr
[3];
256 z11
= wsptr
[1] + wsptr
[7];
257 z12
= wsptr
[1] - wsptr
[7];
260 tmp11
= (z11
- z13
) * ((FAST_FLOAT
) 1.414213562);
262 z5
= (z10
+ z12
) * ((FAST_FLOAT
) 1.847759065); /* 2*c2 */
263 tmp10
= ((FAST_FLOAT
) 1.082392200) * z12
- z5
; /* 2*(c2-c6) */
264 tmp12
= ((FAST_FLOAT
) -2.613125930) * z10
+ z5
; /* -2*(c2+c6) */
270 /* Final output stage: scale down by a factor of 8 and range-limit */
272 outptr
[0] = descale_and_clamp(tmp0
+ tmp7
, 3);
273 outptr
[7] = descale_and_clamp(tmp0
- tmp7
, 3);
274 outptr
[1] = descale_and_clamp(tmp1
+ tmp6
, 3);
275 outptr
[6] = descale_and_clamp(tmp1
- tmp6
, 3);
276 outptr
[2] = descale_and_clamp(tmp2
+ tmp5
, 3);
277 outptr
[5] = descale_and_clamp(tmp2
- tmp5
, 3);
278 outptr
[4] = descale_and_clamp(tmp3
+ tmp4
, 3);
279 outptr
[3] = descale_and_clamp(tmp3
- tmp4
, 3);
282 wsptr
+= DCTSIZE
; /* advance pointer to next row */