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
67GLOBAL(void)
68jpeg_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 */
243