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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 | 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 | 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 | inptr = coef_block; | |
87 | quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table; | |
88 | wsptr = workspace; | |
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. | |
97 | */ | |
98 | ||
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]); | |
105 | ||
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; | |
114 | ||
115 | inptr++; /* advance pointers to next column */ | |
116 | quantptr++; | |
117 | wsptr++; | |
118 | continue; | |
119 | } | |
120 | ||
121 | /* Even part */ | |
122 | ||
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]); | |
127 | ||
128 | tmp10 = tmp0 + tmp2; /* phase 3 */ | |
129 | tmp11 = tmp0 - tmp2; | |
130 | ||
131 | tmp13 = tmp1 + tmp3; /* phases 5-3 */ | |
132 | tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ | |
133 | ||
134 | tmp0 = tmp10 + tmp13; /* phase 2 */ | |
135 | tmp3 = tmp10 - tmp13; | |
136 | tmp1 = tmp11 + tmp12; | |
137 | tmp2 = tmp11 - tmp12; | |
138 | ||
139 | /* Odd part */ | |
140 | ||
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]); | |
145 | ||
146 | z13 = tmp6 + tmp5; /* phase 6 */ | |
147 | z10 = tmp6 - tmp5; | |
148 | z11 = tmp4 + tmp7; | |
149 | z12 = tmp4 - tmp7; | |
150 | ||
151 | tmp7 = z11 + z13; /* phase 5 */ | |
152 | tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ | |
153 | ||
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) */ | |
157 | ||
158 | tmp6 = tmp12 - tmp7; /* phase 2 */ | |
159 | tmp5 = tmp11 - tmp6; | |
160 | tmp4 = tmp10 + tmp5; | |
161 | ||
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; | |
170 | ||
171 | inptr++; /* advance pointers to next column */ | |
172 | quantptr++; | |
173 | 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 | wsptr = workspace; | |
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. | |
186 | */ | |
187 | ||
188 | /* Even part */ | |
189 | ||
190 | tmp10 = wsptr[0] + wsptr[4]; | |
191 | tmp11 = wsptr[0] - wsptr[4]; | |
192 | ||
193 | tmp13 = wsptr[2] + wsptr[6]; | |
194 | tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; | |
195 | ||
196 | tmp0 = tmp10 + tmp13; | |
197 | tmp3 = tmp10 - tmp13; | |
198 | tmp1 = tmp11 + tmp12; | |
199 | tmp2 = tmp11 - tmp12; | |
200 | ||
201 | /* Odd part */ | |
202 | ||
203 | z13 = wsptr[5] + wsptr[3]; | |
204 | z10 = wsptr[5] - wsptr[3]; | |
205 | z11 = wsptr[1] + wsptr[7]; | |
206 | z12 = wsptr[1] - wsptr[7]; | |
207 | ||
208 | tmp7 = z11 + z13; | |
209 | tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); | |
210 | ||
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) */ | |
214 | ||
215 | tmp6 = tmp12 - tmp7; | |
216 | tmp5 = tmp11 - tmp6; | |
217 | tmp4 = tmp10 + tmp5; | |
218 | ||
219 | /* Final output stage: scale down by a factor of 8 and range-limit */ | |
220 | ||
221 | outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) | |
222 | & RANGE_MASK]; | |
223 | outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) | |
224 | & RANGE_MASK]; | |
225 | outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) | |
226 | & RANGE_MASK]; | |
227 | outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) | |
228 | & RANGE_MASK]; | |
229 | outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) | |
230 | & RANGE_MASK]; | |
231 | outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) | |
232 | & RANGE_MASK]; | |
233 | outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) | |
234 | & RANGE_MASK]; | |
235 | outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) | |
236 | & RANGE_MASK]; | |
237 | ||
238 | wsptr += DCTSIZE; /* advance pointer to next row */ | |
239 | } | |
240 | } | |
241 | ||
242 | #endif /* DCT_FLOAT_SUPPORTED */ |