1/*
2 * jidctflt.c
3 *
4 * This file was part of the Independent JPEG Group's software:
5 * Copyright (C) 1994-1998, Thomas G. Lane.
6 * Modified 2010 by Guido Vollbeding.
7 * libjpeg-turbo Modifications:
8 * Copyright (C) 2014, D. R. Commander.
9 * For conditions of distribution and use, see the accompanying README.ijg
10 * 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.ijg). The following
30 * code 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, JSAMPARRAY output_buf,
74 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 = cinfo->sample_range_limit;
84 int ctr;
85 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
86#define _0_125 ((FLOAT_MULT_TYPE)0.125)
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],
109 quantptr[DCTSIZE * 0] * _0_125);
110
111 wsptr[DCTSIZE * 0] = dcval;
112 wsptr[DCTSIZE * 1] = dcval;
113 wsptr[DCTSIZE * 2] = dcval;
114 wsptr[DCTSIZE * 3] = dcval;
115 wsptr[DCTSIZE * 4] = dcval;
116 wsptr[DCTSIZE * 5] = dcval;
117 wsptr[DCTSIZE * 6] = dcval;
118 wsptr[DCTSIZE * 7] = dcval;
119
120 inptr++; /* advance pointers to next column */
121 quantptr++;
122 wsptr++;
123 continue;
124 }
125
126 /* Even part */
127
128 tmp0 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] * _0_125);
129 tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] * _0_125);
130 tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] * _0_125);
131 tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] * _0_125);
132
133 tmp10 = tmp0 + tmp2; /* phase 3 */
134 tmp11 = tmp0 - tmp2;
135
136 tmp13 = tmp1 + tmp3; /* phases 5-3 */
137 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT)1.414213562) - tmp13; /* 2*c4 */
138
139 tmp0 = tmp10 + tmp13; /* phase 2 */
140 tmp3 = tmp10 - tmp13;
141 tmp1 = tmp11 + tmp12;
142 tmp2 = tmp11 - tmp12;
143
144 /* Odd part */
145
146 tmp4 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] * _0_125);
147 tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] * _0_125);
148 tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] * _0_125);
149 tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] * _0_125);
150
151 z13 = tmp6 + tmp5; /* phase 6 */
152 z10 = tmp6 - tmp5;
153 z11 = tmp4 + tmp7;
154 z12 = tmp4 - tmp7;
155
156 tmp7 = z11 + z13; /* phase 5 */
157 tmp11 = (z11 - z13) * ((FAST_FLOAT)1.414213562); /* 2*c4 */
158
159 z5 = (z10 + z12) * ((FAST_FLOAT)1.847759065); /* 2*c2 */
160 tmp10 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */
161 tmp12 = z5 - z10 * ((FAST_FLOAT)2.613125930); /* 2*(c2+c6) */
162
163 tmp6 = tmp12 - tmp7; /* phase 2 */
164 tmp5 = tmp11 - tmp6;
165 tmp4 = tmp10 - tmp5;
166
167 wsptr[DCTSIZE * 0] = tmp0 + tmp7;
168 wsptr[DCTSIZE * 7] = tmp0 - tmp7;
169 wsptr[DCTSIZE * 1] = tmp1 + tmp6;
170 wsptr[DCTSIZE * 6] = tmp1 - tmp6;
171 wsptr[DCTSIZE * 2] = tmp2 + tmp5;
172 wsptr[DCTSIZE * 5] = tmp2 - tmp5;
173 wsptr[DCTSIZE * 3] = tmp3 + tmp4;
174 wsptr[DCTSIZE * 4] = tmp3 - tmp4;
175
176 inptr++; /* advance pointers to next column */
177 quantptr++;
178 wsptr++;
179 }
180
181 /* Pass 2: process rows from work array, store into output array. */
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 /* Apply signed->unsigned and prepare float->int conversion */
195 z5 = wsptr[0] + ((FAST_FLOAT)CENTERJSAMPLE + (FAST_FLOAT)0.5);
196 tmp10 = z5 + wsptr[4];
197 tmp11 = z5 - wsptr[4];
198
199 tmp13 = wsptr[2] + wsptr[6];
200 tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT)1.414213562) - tmp13;
201
202 tmp0 = tmp10 + tmp13;
203 tmp3 = tmp10 - tmp13;
204 tmp1 = tmp11 + tmp12;
205 tmp2 = tmp11 - tmp12;
206
207 /* Odd part */
208
209 z13 = wsptr[5] + wsptr[3];
210 z10 = wsptr[5] - wsptr[3];
211 z11 = wsptr[1] + wsptr[7];
212 z12 = wsptr[1] - wsptr[7];
213
214 tmp7 = z11 + z13;
215 tmp11 = (z11 - z13) * ((FAST_FLOAT)1.414213562);
216
217 z5 = (z10 + z12) * ((FAST_FLOAT)1.847759065); /* 2*c2 */
218 tmp10 = z5 - z12 * ((FAST_FLOAT)1.082392200); /* 2*(c2-c6) */
219 tmp12 = z5 - z10 * ((FAST_FLOAT)2.613125930); /* 2*(c2+c6) */
220
221 tmp6 = tmp12 - tmp7;
222 tmp5 = tmp11 - tmp6;
223 tmp4 = tmp10 - tmp5;
224
225 /* Final output stage: float->int conversion and range-limit */
226
227 outptr[0] = range_limit[((int)(tmp0 + tmp7)) & RANGE_MASK];
228 outptr[7] = range_limit[((int)(tmp0 - tmp7)) & RANGE_MASK];
229 outptr[1] = range_limit[((int)(tmp1 + tmp6)) & RANGE_MASK];
230 outptr[6] = range_limit[((int)(tmp1 - tmp6)) & RANGE_MASK];
231 outptr[2] = range_limit[((int)(tmp2 + tmp5)) & RANGE_MASK];
232 outptr[5] = range_limit[((int)(tmp2 - tmp5)) & RANGE_MASK];
233 outptr[3] = range_limit[((int)(tmp3 + tmp4)) & RANGE_MASK];
234 outptr[4] = range_limit[((int)(tmp3 - tmp4)) & RANGE_MASK];
235
236 wsptr += DCTSIZE; /* advance pointer to next row */
237 }
238}
239
240#endif /* DCT_FLOAT_SUPPORTED */
241