1 : /*
2 : * jidctflt.c
3 : *
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.
7 : *
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.
11 : *
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.
16 : *
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.
21 : *
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.
37 : */
38 :
39 : #define JPEG_INTERNALS
40 : #include "jinclude.h"
41 : #include "jpeglib.h"
42 : #include "jdct.h" /* Private declarations for DCT subsystem */
43 :
44 : #ifdef DCT_FLOAT_SUPPORTED
45 :
46 :
47 : /*
48 : * This module is specialized to the case DCTSIZE = 8.
49 : */
50 :
51 : #if DCTSIZE != 8
52 : Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
53 : #endif
54 :
55 :
56 : /* Dequantize a coefficient by multiplying it by the multiplier-table
57 : * entry; produce a float result.
58 : */
59 :
60 : #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
61 :
62 :
63 : /*
64 : * Perform dequantization and inverse DCT on one block of coefficients.
65 : */
66 :
67 : GLOBAL(void)
68 0 : jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
69 : JCOEFPTR coef_block,
70 : JSAMPARRAY output_buf, JDIMENSION output_col)
71 : {
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;
75 : JCOEFPTR inptr;
76 : FLOAT_MULT_TYPE * quantptr;
77 : FAST_FLOAT * wsptr;
78 : JSAMPROW outptr;
79 0 : JSAMPLE *range_limit = IDCT_range_limit(cinfo);
80 : int ctr;
81 : FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
82 : SHIFT_TEMPS
83 :
84 : /* Pass 1: process columns from input, store into work array. */
85 :
86 0 : inptr = coef_block;
87 0 : quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
88 0 : wsptr = workspace;
89 0 : 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.
97 : */
98 :
99 0 : if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
100 0 : inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
101 0 : inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
102 0 : inptr[DCTSIZE*7] == 0) {
103 : /* AC terms all zero */
104 0 : FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
105 :
106 0 : wsptr[DCTSIZE*0] = dcval;
107 0 : wsptr[DCTSIZE*1] = dcval;
108 0 : wsptr[DCTSIZE*2] = dcval;
109 0 : wsptr[DCTSIZE*3] = dcval;
110 0 : wsptr[DCTSIZE*4] = dcval;
111 0 : wsptr[DCTSIZE*5] = dcval;
112 0 : wsptr[DCTSIZE*6] = dcval;
113 0 : wsptr[DCTSIZE*7] = dcval;
114 :
115 0 : inptr++; /* advance pointers to next column */
116 0 : quantptr++;
117 0 : wsptr++;
118 0 : continue;
119 : }
120 :
121 : /* Even part */
122 :
123 0 : tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
124 0 : tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
125 0 : tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
126 0 : tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
127 :
128 0 : tmp10 = tmp0 + tmp2; /* phase 3 */
129 0 : tmp11 = tmp0 - tmp2;
130 :
131 0 : tmp13 = tmp1 + tmp3; /* phases 5-3 */
132 0 : tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
133 :
134 0 : tmp0 = tmp10 + tmp13; /* phase 2 */
135 0 : tmp3 = tmp10 - tmp13;
136 0 : tmp1 = tmp11 + tmp12;
137 0 : tmp2 = tmp11 - tmp12;
138 :
139 : /* Odd part */
140 :
141 0 : tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
142 0 : tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
143 0 : tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
144 0 : tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
145 :
146 0 : z13 = tmp6 + tmp5; /* phase 6 */
147 0 : z10 = tmp6 - tmp5;
148 0 : z11 = tmp4 + tmp7;
149 0 : z12 = tmp4 - tmp7;
150 :
151 0 : tmp7 = z11 + z13; /* phase 5 */
152 0 : tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
153 :
154 0 : z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
155 0 : tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
156 0 : tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
157 :
158 0 : tmp6 = tmp12 - tmp7; /* phase 2 */
159 0 : tmp5 = tmp11 - tmp6;
160 0 : tmp4 = tmp10 + tmp5;
161 :
162 0 : wsptr[DCTSIZE*0] = tmp0 + tmp7;
163 0 : wsptr[DCTSIZE*7] = tmp0 - tmp7;
164 0 : wsptr[DCTSIZE*1] = tmp1 + tmp6;
165 0 : wsptr[DCTSIZE*6] = tmp1 - tmp6;
166 0 : wsptr[DCTSIZE*2] = tmp2 + tmp5;
167 0 : wsptr[DCTSIZE*5] = tmp2 - tmp5;
168 0 : wsptr[DCTSIZE*4] = tmp3 + tmp4;
169 0 : wsptr[DCTSIZE*3] = tmp3 - tmp4;
170 :
171 0 : inptr++; /* advance pointers to next column */
172 0 : quantptr++;
173 0 : wsptr++;
174 : }
175 :
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. */
178 :
179 0 : wsptr = workspace;
180 0 : for (ctr = 0; ctr < DCTSIZE; ctr++) {
181 0 : 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.
186 : */
187 :
188 : /* Even part */
189 :
190 0 : tmp10 = wsptr[0] + wsptr[4];
191 0 : tmp11 = wsptr[0] - wsptr[4];
192 :
193 0 : tmp13 = wsptr[2] + wsptr[6];
194 0 : tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
195 :
196 0 : tmp0 = tmp10 + tmp13;
197 0 : tmp3 = tmp10 - tmp13;
198 0 : tmp1 = tmp11 + tmp12;
199 0 : tmp2 = tmp11 - tmp12;
200 :
201 : /* Odd part */
202 :
203 0 : z13 = wsptr[5] + wsptr[3];
204 0 : z10 = wsptr[5] - wsptr[3];
205 0 : z11 = wsptr[1] + wsptr[7];
206 0 : z12 = wsptr[1] - wsptr[7];
207 :
208 0 : tmp7 = z11 + z13;
209 0 : tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
210 :
211 0 : z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
212 0 : tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
213 0 : tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
214 :
215 0 : tmp6 = tmp12 - tmp7;
216 0 : tmp5 = tmp11 - tmp6;
217 0 : tmp4 = tmp10 + tmp5;
218 :
219 : /* Final output stage: scale down by a factor of 8 and range-limit */
220 :
221 0 : outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
222 : & RANGE_MASK];
223 0 : outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
224 : & RANGE_MASK];
225 0 : outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
226 : & RANGE_MASK];
227 0 : outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
228 : & RANGE_MASK];
229 0 : outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
230 : & RANGE_MASK];
231 0 : outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
232 : & RANGE_MASK];
233 0 : outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
234 : & RANGE_MASK];
235 0 : outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
236 : & RANGE_MASK];
237 :
238 0 : wsptr += DCTSIZE; /* advance pointer to next row */
239 : }
240 0 : }
241 :
242 : #endif /* DCT_FLOAT_SUPPORTED */
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