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
11 * This file contains a fast, not so accurate integer implementation of the
12 * forward DCT (Discrete Cosine Transform).
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.
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.
36 #define JPEG_INTERNALS
39 #include "jdct.h" /* Private declarations for DCT subsystem */
41 #ifdef DCT_IFAST_SUPPORTED
45 * This module is specialized to the case DCTSIZE = 8.
49 Sorry
, this code only copes with
8x8 DCTs
. /* deliberate syntax err */
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.
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.
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).
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...)
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) */
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)
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...
99 #ifndef USE_ACCURATE_ROUNDING
101 #define DESCALE(x, n) RIGHT_SHIFT(x, n)
105 /* Multiply a DCTELEM variable by an JLONG constant, and immediately
106 * descale to yield a DCTELEM result.
109 #define MULTIPLY(var, const) ((DCTELEM)DESCALE((var) * (const), CONST_BITS))
113 * Perform the forward DCT on one block of samples.
117 jpeg_fdct_ifast(DCTELEM
*data
)
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
;
126 /* Pass 1: process rows. */
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];
141 tmp10
= tmp0
+ tmp3
; /* phase 2 */
146 dataptr
[0] = tmp10
+ tmp11
; /* phase 3 */
147 dataptr
[4] = tmp10
- tmp11
;
149 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_707106781
); /* c4 */
150 dataptr
[2] = tmp13
+ z1
; /* phase 5 */
151 dataptr
[6] = tmp13
- z1
;
155 tmp10
= tmp4
+ tmp5
; /* phase 2 */
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 */
165 z11
= tmp7
+ z3
; /* phase 5 */
168 dataptr
[5] = z13
+ z2
; /* phase 6 */
169 dataptr
[3] = z13
- z2
;
170 dataptr
[1] = z11
+ z4
;
171 dataptr
[7] = z11
- z4
;
173 dataptr
+= DCTSIZE
; /* advance pointer to next row */
176 /* Pass 2: process columns. */
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];
191 tmp10
= tmp0
+ tmp3
; /* phase 2 */
196 dataptr
[DCTSIZE
* 0] = tmp10
+ tmp11
; /* phase 3 */
197 dataptr
[DCTSIZE
* 4] = tmp10
- tmp11
;
199 z1
= MULTIPLY(tmp12
+ tmp13
, FIX_0_707106781
); /* c4 */
200 dataptr
[DCTSIZE
* 2] = tmp13
+ z1
; /* phase 5 */
201 dataptr
[DCTSIZE
* 6] = tmp13
- z1
;
205 tmp10
= tmp4
+ tmp5
; /* phase 2 */
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 */
215 z11
= tmp7
+ z3
; /* phase 5 */
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
;
223 dataptr
++; /* advance pointer to next column */
227 #endif /* DCT_IFAST_SUPPORTED */