4 * Copyright (C) 1994-1998, 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.
8 * This file contains a fast, not so accurate integer implementation of the
9 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
10 * must also perform dequantization of the input coefficients.
12 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
13 * on each row (or vice versa, but it's more convenient to emit a row at
14 * a time). Direct algorithms are also available, but they are much more
15 * complex and seem not to be any faster when reduced to code.
17 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
18 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
19 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
20 * JPEG textbook (see REFERENCES section in file README). The following code
21 * is based directly on figure 4-8 in P&M.
22 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
23 * possible to arrange the computation so that many of the multiplies are
24 * simple scalings of the final outputs. These multiplies can then be
25 * folded into the multiplications or divisions by the JPEG quantization
26 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
27 * to be done in the DCT itself.
28 * The primary disadvantage of this method is that with fixed-point math,
29 * accuracy is lost due to imprecise representation of the scaled
30 * quantization values. The smaller the quantization table entry, the less
31 * precise the scaled value, so this implementation does worse with high-
32 * quality-setting files than with low-quality ones.
35 #define JPEG_INTERNALS
38 #include "jdct.h" /* Private declarations for DCT subsystem */
40 #ifdef DCT_IFAST_SUPPORTED
44 * This module is specialized to the case DCTSIZE = 8.
48 Sorry
, this code only copes with
8x8 DCTs
. /* deliberate syntax err */
52 /* Scaling decisions are generally the same as in the LL&M algorithm;
53 * see jidctint.c for more details. However, we choose to descale
54 * (right shift) multiplication products as soon as they are formed,
55 * rather than carrying additional fractional bits into subsequent additions.
56 * This compromises accuracy slightly, but it lets us save a few shifts.
57 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
58 * everywhere except in the multiplications proper; this saves a good deal
59 * of work on 16-bit-int machines.
61 * The dequantized coefficients are not integers because the AA&N scaling
62 * factors have been incorporated. We represent them scaled up by PASS1_BITS,
63 * so that the first and second IDCT rounds have the same input scaling.
64 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
65 * avoid a descaling shift; this compromises accuracy rather drastically
66 * for small quantization table entries, but it saves a lot of shifts.
67 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
68 * so we use a much larger scaling factor to preserve accuracy.
70 * A final compromise is to represent the multiplicative constants to only
71 * 8 fractional bits, rather than 13. This saves some shifting work on some
72 * machines, and may also reduce the cost of multiplication (since there
73 * are fewer one-bits in the constants).
76 #if BITS_IN_JSAMPLE == 8
81 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
84 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
85 * causing a lot of useless floating-point operations at run time.
86 * To get around this we use the following pre-calculated constants.
87 * If you change CONST_BITS you may want to add appropriate values.
88 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
92 #define FIX_1_082392200 ((JPEG_INT32) 277) /* FIX(1.082392200) */
93 #define FIX_1_414213562 ((JPEG_INT32) 362) /* FIX(1.414213562) */
94 #define FIX_1_847759065 ((JPEG_INT32) 473) /* FIX(1.847759065) */
95 #define FIX_2_613125930 ((JPEG_INT32) 669) /* FIX(2.613125930) */
97 #define FIX_1_082392200 FIX(1.082392200)
98 #define FIX_1_414213562 FIX(1.414213562)
99 #define FIX_1_847759065 FIX(1.847759065)
100 #define FIX_2_613125930 FIX(2.613125930)
104 /* We can gain a little more speed, with a further compromise in accuracy,
105 * by omitting the addition in a descaling shift. This yields an incorrectly
106 * rounded result half the time...
109 #ifndef USE_ACCURATE_ROUNDING
111 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
115 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
116 * descale to yield a DCTELEM result.
119 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
122 /* Dequantize a coefficient by multiplying it by the multiplier-table
123 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
124 * multiplication will do. For 12-bit data, the multiplier table is
125 * declared INT32, so a 32-bit multiply will be used.
128 #if BITS_IN_JSAMPLE == 8
129 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
131 #define DEQUANTIZE(coef,quantval) \
132 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
136 /* Like DESCALE, but applies to a DCTELEM and produces an int.
137 * We assume that int right shift is unsigned if INT32 right shift is.
140 #ifdef RIGHT_SHIFT_IS_UNSIGNED
141 #define ISHIFT_TEMPS DCTELEM ishift_temp;
142 #if BITS_IN_JSAMPLE == 8
143 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
145 #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
147 #define IRIGHT_SHIFT(x,shft) \
148 ((ishift_temp = (x)) < 0 ? \
149 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
150 (ishift_temp >> (shft)))
153 #define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
156 #ifdef USE_ACCURATE_ROUNDING
157 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
159 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
164 * Perform dequantization and inverse DCT on one block of coefficients.
168 jpeg_idct_ifast (j_decompress_ptr cinfo
, jpeg_component_info
* compptr
,
170 JSAMPARRAY output_buf
, JDIMENSION output_col
)
172 DCTELEM tmp0
, tmp1
, tmp2
, tmp3
, tmp4
, tmp5
, tmp6
, tmp7
;
173 DCTELEM tmp10
, tmp11
, tmp12
, tmp13
;
174 DCTELEM z5
, z10
, z11
, z12
, z13
;
176 IFAST_MULT_TYPE
* quantptr
;
179 JSAMPLE
*range_limit
= IDCT_range_limit(cinfo
);
181 int workspace
[DCTSIZE2
]; /* buffers data between passes */
182 SHIFT_TEMPS
/* for DESCALE */
183 ISHIFT_TEMPS
/* for IDESCALE */
185 /* Pass 1: process columns from input, store into work array. */
188 quantptr
= (IFAST_MULT_TYPE
*) compptr
->dct_table
;
190 for (ctr
= DCTSIZE
; ctr
> 0; ctr
--) {
191 /* Due to quantization, we will usually find that many of the input
192 * coefficients are zero, especially the AC terms. We can exploit this
193 * by short-circuiting the IDCT calculation for any column in which all
194 * the AC terms are zero. In that case each output is equal to the
195 * DC coefficient (with scale factor as needed).
196 * With typical images and quantization tables, half or more of the
197 * column DCT calculations can be simplified this way.
200 if (inptr
[DCTSIZE
*1] == 0 && inptr
[DCTSIZE
*2] == 0 &&
201 inptr
[DCTSIZE
*3] == 0 && inptr
[DCTSIZE
*4] == 0 &&
202 inptr
[DCTSIZE
*5] == 0 && inptr
[DCTSIZE
*6] == 0 &&
203 inptr
[DCTSIZE
*7] == 0) {
204 /* AC terms all zero */
205 int dcval
= (int) DEQUANTIZE(inptr
[DCTSIZE
*0], quantptr
[DCTSIZE
*0]);
207 wsptr
[DCTSIZE
*0] = dcval
;
208 wsptr
[DCTSIZE
*1] = dcval
;
209 wsptr
[DCTSIZE
*2] = dcval
;
210 wsptr
[DCTSIZE
*3] = dcval
;
211 wsptr
[DCTSIZE
*4] = dcval
;
212 wsptr
[DCTSIZE
*5] = dcval
;
213 wsptr
[DCTSIZE
*6] = dcval
;
214 wsptr
[DCTSIZE
*7] = dcval
;
216 inptr
++; /* advance pointers to next column */
224 tmp0
= DEQUANTIZE(inptr
[DCTSIZE
*0], quantptr
[DCTSIZE
*0]);
225 tmp1
= DEQUANTIZE(inptr
[DCTSIZE
*2], quantptr
[DCTSIZE
*2]);
226 tmp2
= DEQUANTIZE(inptr
[DCTSIZE
*4], quantptr
[DCTSIZE
*4]);
227 tmp3
= DEQUANTIZE(inptr
[DCTSIZE
*6], quantptr
[DCTSIZE
*6]);
229 tmp10
= tmp0
+ tmp2
; /* phase 3 */
232 tmp13
= tmp1
+ tmp3
; /* phases 5-3 */
233 tmp12
= MULTIPLY(tmp1
- tmp3
, FIX_1_414213562
) - tmp13
; /* 2*c4 */
235 tmp0
= tmp10
+ tmp13
; /* phase 2 */
236 tmp3
= tmp10
- tmp13
;
237 tmp1
= tmp11
+ tmp12
;
238 tmp2
= tmp11
- tmp12
;
242 tmp4
= DEQUANTIZE(inptr
[DCTSIZE
*1], quantptr
[DCTSIZE
*1]);
243 tmp5
= DEQUANTIZE(inptr
[DCTSIZE
*3], quantptr
[DCTSIZE
*3]);
244 tmp6
= DEQUANTIZE(inptr
[DCTSIZE
*5], quantptr
[DCTSIZE
*5]);
245 tmp7
= DEQUANTIZE(inptr
[DCTSIZE
*7], quantptr
[DCTSIZE
*7]);
247 z13
= tmp6
+ tmp5
; /* phase 6 */
252 tmp7
= z11
+ z13
; /* phase 5 */
253 tmp11
= MULTIPLY(z11
- z13
, FIX_1_414213562
); /* 2*c4 */
255 z5
= MULTIPLY(z10
+ z12
, FIX_1_847759065
); /* 2*c2 */
256 tmp10
= MULTIPLY(z12
, FIX_1_082392200
) - z5
; /* 2*(c2-c6) */
257 tmp12
= MULTIPLY(z10
, - FIX_2_613125930
) + z5
; /* -2*(c2+c6) */
259 tmp6
= tmp12
- tmp7
; /* phase 2 */
263 wsptr
[DCTSIZE
*0] = (int) (tmp0
+ tmp7
);
264 wsptr
[DCTSIZE
*7] = (int) (tmp0
- tmp7
);
265 wsptr
[DCTSIZE
*1] = (int) (tmp1
+ tmp6
);
266 wsptr
[DCTSIZE
*6] = (int) (tmp1
- tmp6
);
267 wsptr
[DCTSIZE
*2] = (int) (tmp2
+ tmp5
);
268 wsptr
[DCTSIZE
*5] = (int) (tmp2
- tmp5
);
269 wsptr
[DCTSIZE
*4] = (int) (tmp3
+ tmp4
);
270 wsptr
[DCTSIZE
*3] = (int) (tmp3
- tmp4
);
272 inptr
++; /* advance pointers to next column */
277 /* Pass 2: process rows from work array, store into output array. */
278 /* Note that we must descale the results by a factor of 8 == 2**3, */
279 /* and also undo the PASS1_BITS scaling. */
282 for (ctr
= 0; ctr
< DCTSIZE
; ctr
++) {
283 outptr
= output_buf
[ctr
] + output_col
;
284 /* Rows of zeroes can be exploited in the same way as we did with columns.
285 * However, the column calculation has created many nonzero AC terms, so
286 * the simplification applies less often (typically 5% to 10% of the time).
287 * On machines with very fast multiplication, it's possible that the
288 * test takes more time than it's worth. In that case this section
289 * may be commented out.
292 #ifndef NO_ZERO_ROW_TEST
293 if (wsptr
[1] == 0 && wsptr
[2] == 0 && wsptr
[3] == 0 && wsptr
[4] == 0 &&
294 wsptr
[5] == 0 && wsptr
[6] == 0 && wsptr
[7] == 0) {
295 /* AC terms all zero */
296 JSAMPLE dcval
= range_limit
[IDESCALE(wsptr
[0], PASS1_BITS
+3)
308 wsptr
+= DCTSIZE
; /* advance pointer to next row */
315 tmp10
= ((DCTELEM
) wsptr
[0] + (DCTELEM
) wsptr
[4]);
316 tmp11
= ((DCTELEM
) wsptr
[0] - (DCTELEM
) wsptr
[4]);
318 tmp13
= ((DCTELEM
) wsptr
[2] + (DCTELEM
) wsptr
[6]);
319 tmp12
= MULTIPLY((DCTELEM
) wsptr
[2] - (DCTELEM
) wsptr
[6], FIX_1_414213562
)
322 tmp0
= tmp10
+ tmp13
;
323 tmp3
= tmp10
- tmp13
;
324 tmp1
= tmp11
+ tmp12
;
325 tmp2
= tmp11
- tmp12
;
329 z13
= (DCTELEM
) wsptr
[5] + (DCTELEM
) wsptr
[3];
330 z10
= (DCTELEM
) wsptr
[5] - (DCTELEM
) wsptr
[3];
331 z11
= (DCTELEM
) wsptr
[1] + (DCTELEM
) wsptr
[7];
332 z12
= (DCTELEM
) wsptr
[1] - (DCTELEM
) wsptr
[7];
334 tmp7
= z11
+ z13
; /* phase 5 */
335 tmp11
= MULTIPLY(z11
- z13
, FIX_1_414213562
); /* 2*c4 */
337 z5
= MULTIPLY(z10
+ z12
, FIX_1_847759065
); /* 2*c2 */
338 tmp10
= MULTIPLY(z12
, FIX_1_082392200
) - z5
; /* 2*(c2-c6) */
339 tmp12
= MULTIPLY(z10
, - FIX_2_613125930
) + z5
; /* -2*(c2+c6) */
341 tmp6
= tmp12
- tmp7
; /* phase 2 */
345 /* Final output stage: scale down by a factor of 8 and range-limit */
347 outptr
[0] = range_limit
[IDESCALE(tmp0
+ tmp7
, PASS1_BITS
+3)
349 outptr
[7] = range_limit
[IDESCALE(tmp0
- tmp7
, PASS1_BITS
+3)
351 outptr
[1] = range_limit
[IDESCALE(tmp1
+ tmp6
, PASS1_BITS
+3)
353 outptr
[6] = range_limit
[IDESCALE(tmp1
- tmp6
, PASS1_BITS
+3)
355 outptr
[2] = range_limit
[IDESCALE(tmp2
+ tmp5
, PASS1_BITS
+3)
357 outptr
[5] = range_limit
[IDESCALE(tmp2
- tmp5
, PASS1_BITS
+3)
359 outptr
[4] = range_limit
[IDESCALE(tmp3
+ tmp4
, PASS1_BITS
+3)
361 outptr
[3] = range_limit
[IDESCALE(tmp3
- tmp4
, PASS1_BITS
+3)
364 wsptr
+= DCTSIZE
; /* advance pointer to next row */
368 #endif /* DCT_IFAST_SUPPORTED */