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 floating-point 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
* This implementation should be more accurate than either of the integer
13
* IDCT implementations. However, it may not give the same results on all
14
* machines because of differences in roundoff behavior. Speed will depend
15
* on the hardware's floating point capacity.
17
* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
18
* on each row (or vice versa, but it's more convenient to emit a row at
19
* a time). Direct algorithms are also available, but they are much more
20
* complex and seem not to be any faster when reduced to code.
22
* This implementation is based on Arai, Agui, and Nakajima's algorithm for
23
* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
24
* Japanese, but the algorithm is described in the Pennebaker & Mitchell
25
* JPEG textbook (see REFERENCES section in file README). The following code
26
* is based directly on figure 4-8 in P&M.
27
* While an 8-point DCT cannot be done in less than 11 multiplies, it is
28
* possible to arrange the computation so that many of the multiplies are
29
* simple scalings of the final outputs. These multiplies can then be
30
* folded into the multiplications or divisions by the JPEG quantization
31
* table entries. The AA&N method leaves only 5 multiplies and 29 adds
32
* to be done in the DCT itself.
33
* The primary disadvantage of this method is that with a fixed-point
34
* implementation, accuracy is lost due to imprecise representation of the
35
* scaled quantization values. However, that problem does not arise if
36
* we use floating point arithmetic.
39
#define JPEG_INTERNALS
42
#include "jdct.h" /* Private declarations for DCT subsystem */
44
#ifdef DCT_FLOAT_SUPPORTED
48
* This module is specialized to the case DCTSIZE = 8.
52
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
56
/* Dequantize a coefficient by multiplying it by the multiplier-table
57
* entry; produce a float result.
60
#define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
64
* Perform dequantization and inverse DCT on one block of coefficients.
68
jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
70
JSAMPARRAY output_buf, JDIMENSION output_col)
72
FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
73
FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
74
FAST_FLOAT z5, z10, z11, z12, z13;
76
FLOAT_MULT_TYPE * quantptr;
79
JSAMPLE *range_limit = IDCT_range_limit(cinfo);
81
FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
84
/* Pass 1: process columns from input, store into work array. */
87
quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
89
for (ctr = DCTSIZE; ctr > 0; ctr--) {
90
/* Due to quantization, we will usually find that many of the input
91
* coefficients are zero, especially the AC terms. We can exploit this
92
* by short-circuiting the IDCT calculation for any column in which all
93
* the AC terms are zero. In that case each output is equal to the
94
* DC coefficient (with scale factor as needed).
95
* With typical images and quantization tables, half or more of the
96
* column DCT calculations can be simplified this way.
99
if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
100
inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
101
inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
102
inptr[DCTSIZE*7] == 0) {
103
/* AC terms all zero */
104
FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
106
wsptr[DCTSIZE*0] = dcval;
107
wsptr[DCTSIZE*1] = dcval;
108
wsptr[DCTSIZE*2] = dcval;
109
wsptr[DCTSIZE*3] = dcval;
110
wsptr[DCTSIZE*4] = dcval;
111
wsptr[DCTSIZE*5] = dcval;
112
wsptr[DCTSIZE*6] = dcval;
113
wsptr[DCTSIZE*7] = dcval;
115
inptr++; /* advance pointers to next column */
123
tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
124
tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
125
tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
126
tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
128
tmp10 = tmp0 + tmp2; /* phase 3 */
131
tmp13 = tmp1 + tmp3; /* phases 5-3 */
132
tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
134
tmp0 = tmp10 + tmp13; /* phase 2 */
135
tmp3 = tmp10 - tmp13;
136
tmp1 = tmp11 + tmp12;
137
tmp2 = tmp11 - tmp12;
141
tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
142
tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
143
tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
144
tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
146
z13 = tmp6 + tmp5; /* phase 6 */
151
tmp7 = z11 + z13; /* phase 5 */
152
tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
154
z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
155
tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
156
tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
158
tmp6 = tmp12 - tmp7; /* phase 2 */
162
wsptr[DCTSIZE*0] = tmp0 + tmp7;
163
wsptr[DCTSIZE*7] = tmp0 - tmp7;
164
wsptr[DCTSIZE*1] = tmp1 + tmp6;
165
wsptr[DCTSIZE*6] = tmp1 - tmp6;
166
wsptr[DCTSIZE*2] = tmp2 + tmp5;
167
wsptr[DCTSIZE*5] = tmp2 - tmp5;
168
wsptr[DCTSIZE*4] = tmp3 + tmp4;
169
wsptr[DCTSIZE*3] = tmp3 - tmp4;
171
inptr++; /* advance pointers to next column */
176
/* Pass 2: process rows from work array, store into output array. */
177
/* Note that we must descale the results by a factor of 8 == 2**3. */
180
for (ctr = 0; ctr < DCTSIZE; ctr++) {
181
outptr = output_buf[ctr] + output_col;
182
/* Rows of zeroes can be exploited in the same way as we did with columns.
183
* However, the column calculation has created many nonzero AC terms, so
184
* the simplification applies less often (typically 5% to 10% of the time).
185
* And testing floats for zero is relatively expensive, so we don't bother.
190
tmp10 = wsptr[0] + wsptr[4];
191
tmp11 = wsptr[0] - wsptr[4];
193
tmp13 = wsptr[2] + wsptr[6];
194
tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
196
tmp0 = tmp10 + tmp13;
197
tmp3 = tmp10 - tmp13;
198
tmp1 = tmp11 + tmp12;
199
tmp2 = tmp11 - tmp12;
203
z13 = wsptr[5] + wsptr[3];
204
z10 = wsptr[5] - wsptr[3];
205
z11 = wsptr[1] + wsptr[7];
206
z12 = wsptr[1] - wsptr[7];
209
tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
211
z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
212
tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
213
tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
219
/* Final output stage: scale down by a factor of 8 and range-limit */
221
outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
223
outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
225
outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
227
outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
229
outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
231
outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
233
outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
235
outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
238
wsptr += DCTSIZE; /* advance pointer to next row */
242
#endif /* DCT_FLOAT_SUPPORTED */