1/*
2 * reserved comment block
3 * DO NOT REMOVE OR ALTER!
4 */
5/*
6 * jidctflt.c
7 *
8 * Copyright (C) 1994-1998, Thomas G. Lane.
9 * This file is part of the Independent JPEG Group's software.
10 * For conditions of distribution and use, see the accompanying README file.
11 *
12 * This file contains a floating-point implementation of the
13 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
14 * must also perform dequantization of the input coefficients.
15 *
16 * This implementation should be more accurate than either of the integer
17 * IDCT implementations. However, it may not give the same results on all
18 * machines because of differences in roundoff behavior. Speed will depend
19 * on the hardware's floating point capacity.
20 *
21 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
22 * on each row (or vice versa, but it's more convenient to emit a row at
23 * a time). Direct algorithms are also available, but they are much more
24 * complex and seem not to be any faster when reduced to code.
25 *
26 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
27 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
28 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
29 * JPEG textbook (see REFERENCES section in file README). The following code
30 * is based directly on figure 4-8 in P&M.
31 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
32 * possible to arrange the computation so that many of the multiplies are
33 * simple scalings of the final outputs. These multiplies can then be
34 * folded into the multiplications or divisions by the JPEG quantization
35 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
36 * to be done in the DCT itself.
37 * The primary disadvantage of this method is that with a fixed-point
38 * implementation, accuracy is lost due to imprecise representation of the
39 * scaled quantization values. However, that problem does not arise if
40 * we use floating point arithmetic.
41 */
42
43#define JPEG_INTERNALS
44#include "jinclude.h"
45#include "jpeglib.h"
46#include "jdct.h" /* Private declarations for DCT subsystem */
47
48#ifdef DCT_FLOAT_SUPPORTED
49
50
51/*
52 * This module is specialized to the case DCTSIZE = 8.
53 */
54
55#if DCTSIZE != 8
56 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
57#endif
58
59
60/* Dequantize a coefficient by multiplying it by the multiplier-table
61 * entry; produce a float result.
62 */
63
64#define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
65
66
67/*
68 * Perform dequantization and inverse DCT on one block of coefficients.
69 */
70
71GLOBAL(void)
72jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
73 JCOEFPTR coef_block,
74 JSAMPARRAY output_buf, JDIMENSION output_col)
75{
76 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
77 FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
78 FAST_FLOAT z5, z10, z11, z12, z13;
79 JCOEFPTR inptr;
80 FLOAT_MULT_TYPE * quantptr;
81 FAST_FLOAT * wsptr;
82 JSAMPROW outptr;
83 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
84 int ctr;
85 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
86 SHIFT_TEMPS
87
88 /* Pass 1: process columns from input, store into work array. */
89
90 inptr = coef_block;
91 quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
92 wsptr = workspace;
93 for (ctr = DCTSIZE; ctr > 0; ctr--) {
94 /* Due to quantization, we will usually find that many of the input
95 * coefficients are zero, especially the AC terms. We can exploit this
96 * by short-circuiting the IDCT calculation for any column in which all
97 * the AC terms are zero. In that case each output is equal to the
98 * DC coefficient (with scale factor as needed).
99 * With typical images and quantization tables, half or more of the
100 * column DCT calculations can be simplified this way.
101 */
102
103 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
104 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
105 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
106 inptr[DCTSIZE*7] == 0) {
107 /* AC terms all zero */
108 FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
109
110 wsptr[DCTSIZE*0] = dcval;
111 wsptr[DCTSIZE*1] = dcval;
112 wsptr[DCTSIZE*2] = dcval;
113 wsptr[DCTSIZE*3] = dcval;
114 wsptr[DCTSIZE*4] = dcval;
115 wsptr[DCTSIZE*5] = dcval;
116 wsptr[DCTSIZE*6] = dcval;
117 wsptr[DCTSIZE*7] = dcval;
118
119 inptr++; /* advance pointers to next column */
120 quantptr++;
121 wsptr++;
122 continue;
123 }
124
125 /* Even part */
126
127 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
128 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
129 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
130 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
131
132 tmp10 = tmp0 + tmp2; /* phase 3 */
133 tmp11 = tmp0 - tmp2;
134
135 tmp13 = tmp1 + tmp3; /* phases 5-3 */
136 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
137
138 tmp0 = tmp10 + tmp13; /* phase 2 */
139 tmp3 = tmp10 - tmp13;
140 tmp1 = tmp11 + tmp12;
141 tmp2 = tmp11 - tmp12;
142
143 /* Odd part */
144
145 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
146 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
147 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
148 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
149
150 z13 = tmp6 + tmp5; /* phase 6 */
151 z10 = tmp6 - tmp5;
152 z11 = tmp4 + tmp7;
153 z12 = tmp4 - tmp7;
154
155 tmp7 = z11 + z13; /* phase 5 */
156 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
157
158 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
159 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
160 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
161
162 tmp6 = tmp12 - tmp7; /* phase 2 */
163 tmp5 = tmp11 - tmp6;
164 tmp4 = tmp10 + tmp5;
165
166 wsptr[DCTSIZE*0] = tmp0 + tmp7;
167 wsptr[DCTSIZE*7] = tmp0 - tmp7;
168 wsptr[DCTSIZE*1] = tmp1 + tmp6;
169 wsptr[DCTSIZE*6] = tmp1 - tmp6;
170 wsptr[DCTSIZE*2] = tmp2 + tmp5;
171 wsptr[DCTSIZE*5] = tmp2 - tmp5;
172 wsptr[DCTSIZE*4] = tmp3 + tmp4;
173 wsptr[DCTSIZE*3] = tmp3 - tmp4;
174
175 inptr++; /* advance pointers to next column */
176 quantptr++;
177 wsptr++;
178 }
179
180 /* Pass 2: process rows from work array, store into output array. */
181 /* Note that we must descale the results by a factor of 8 == 2**3. */
182
183 wsptr = workspace;
184 for (ctr = 0; ctr < DCTSIZE; ctr++) {
185 outptr = output_buf[ctr] + output_col;
186 /* Rows of zeroes can be exploited in the same way as we did with columns.
187 * However, the column calculation has created many nonzero AC terms, so
188 * the simplification applies less often (typically 5% to 10% of the time).
189 * And testing floats for zero is relatively expensive, so we don't bother.
190 */
191
192 /* Even part */
193
194 tmp10 = wsptr[0] + wsptr[4];
195 tmp11 = wsptr[0] - wsptr[4];
196
197 tmp13 = wsptr[2] + wsptr[6];
198 tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
199
200 tmp0 = tmp10 + tmp13;
201 tmp3 = tmp10 - tmp13;
202 tmp1 = tmp11 + tmp12;
203 tmp2 = tmp11 - tmp12;
204
205 /* Odd part */
206
207 z13 = wsptr[5] + wsptr[3];
208 z10 = wsptr[5] - wsptr[3];
209 z11 = wsptr[1] + wsptr[7];
210 z12 = wsptr[1] - wsptr[7];
211
212 tmp7 = z11 + z13;
213 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
214
215 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
216 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
217 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
218
219 tmp6 = tmp12 - tmp7;
220 tmp5 = tmp11 - tmp6;
221 tmp4 = tmp10 + tmp5;
222
223 /* Final output stage: scale down by a factor of 8 and range-limit */
224
225 outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
226 & RANGE_MASK];
227 outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
228 & RANGE_MASK];
229 outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
230 & RANGE_MASK];
231 outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
232 & RANGE_MASK];
233 outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
234 & RANGE_MASK];
235 outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
236 & RANGE_MASK];
237 outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
238 & RANGE_MASK];
239 outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
240 & RANGE_MASK];
241
242 wsptr += DCTSIZE; /* advance pointer to next row */
243 }
244}
245
246#endif /* DCT_FLOAT_SUPPORTED */
247