1 /*
2 * jidctflt.c
3 *
4 * Copyright (C) 1994-1998, Thomas G. Lane.
5 * Modified 2010-2017 by Guido Vollbeding.
6 * This file is part of the Independent JPEG Group's software.
7 * For conditions of distribution and use, see the accompanying README file.
8 *
9 * This file contains a floating-point implementation of the
10 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
11 * must also perform dequantization of the input coefficients.
12 *
13 * This implementation should be more accurate than either of the integer
14 * IDCT implementations. However, it may not give the same results on all
15 * machines because of differences in roundoff behavior. Speed will depend
16 * on the hardware's floating point capacity.
17 *
18 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
19 * on each row (or vice versa, but it's more convenient to emit a row at
20 * a time). Direct algorithms are also available, but they are much more
21 * complex and seem not to be any faster when reduced to code.
22 *
23 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
24 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
25 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
26 * JPEG textbook (see REFERENCES section in file README). The following code
27 * is based directly on figure 4-8 in P&M.
28 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
29 * possible to arrange the computation so that many of the multiplies are
30 * simple scalings of the final outputs. These multiplies can then be
31 * folded into the multiplications or divisions by the JPEG quantization
32 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
33 * to be done in the DCT itself.
34 * The primary disadvantage of this method is that with a fixed-point
35 * implementation, accuracy is lost due to imprecise representation of the
36 * scaled quantization values. However, that problem does not arise if
37 * we use floating point arithmetic.
38 */
39
40 #define JPEG_INTERNALS
41 #include "jinclude.h"
42 #include "jpeglib.h"
43 #include "jdct.h" /* Private declarations for DCT subsystem */
44
45 #ifdef DCT_FLOAT_SUPPORTED
46
47
48 /*
49 * This module is specialized to the case DCTSIZE = 8.
50 */
51
52 #if DCTSIZE != 8
53 Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */
54 #endif
55
56
57 /* Dequantize a coefficient by multiplying it by the multiplier-table
58 * entry; produce a float result.
59 */
60
61 #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
62
63
64 /*
65 * Perform dequantization and inverse DCT on one block of coefficients.
66 *
67 * cK represents cos(K*pi/16).
68 */
69
70 GLOBAL(void)
71 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
72 JCOEFPTR coef_block,
73 JSAMPARRAY output_buf, JDIMENSION output_col)
74 {
75 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
76 FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
77 FAST_FLOAT z5, z10, z11, z12, z13;
78 JCOEFPTR inptr;
79 FLOAT_MULT_TYPE * quantptr;
80 FAST_FLOAT * wsptr;
81 JSAMPROW outptr;
82 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
83 int ctr;
84 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
85
86 /* Pass 1: process columns from input, store into work array. */
87
88 inptr = coef_block;
89 quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
90 wsptr = workspace;
91 for (ctr = DCTSIZE; ctr > 0; ctr--) {
92 /* Due to quantization, we will usually find that many of the input
93 * coefficients are zero, especially the AC terms. We can exploit this
94 * by short-circuiting the IDCT calculation for any column in which all
95 * the AC terms are zero. In that case each output is equal to the
96 * DC coefficient (with scale factor as needed).
97 * With typical images and quantization tables, half or more of the
98 * column DCT calculations can be simplified this way.
99 */
100
101 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
102 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
103 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
104 inptr[DCTSIZE*7] == 0) {
105 /* AC terms all zero */
106 FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
107
108 wsptr[DCTSIZE*0] = dcval;
109 wsptr[DCTSIZE*1] = dcval;
110 wsptr[DCTSIZE*2] = dcval;
111 wsptr[DCTSIZE*3] = dcval;
112 wsptr[DCTSIZE*4] = dcval;
113 wsptr[DCTSIZE*5] = dcval;
114 wsptr[DCTSIZE*6] = dcval;
115 wsptr[DCTSIZE*7] = dcval;
116
117 inptr++; /* advance pointers to next column */
118 quantptr++;
119 wsptr++;
120 continue;
121 }
122
123 /* Even part */
124
125 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
126 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
127 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
128 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
129
130 tmp10 = tmp0 + tmp2; /* phase 3 */
131 tmp11 = tmp0 - tmp2;
132
133 tmp13 = tmp1 + tmp3; /* phases 5-3 */
134 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
135
136 tmp0 = tmp10 + tmp13; /* phase 2 */
137 tmp3 = tmp10 - tmp13;
138 tmp1 = tmp11 + tmp12;
139 tmp2 = tmp11 - tmp12;
140
141 /* Odd part */
142
143 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
144 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
145 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
146 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
147
148 z13 = tmp6 + tmp5; /* phase 6 */
149 z10 = tmp6 - tmp5;
150 z11 = tmp4 + tmp7;
151 z12 = tmp4 - tmp7;
152
153 tmp7 = z11 + z13; /* phase 5 */
154 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
155
156 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
157 tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
158 tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */
159
160 tmp6 = tmp12 - tmp7; /* phase 2 */
161 tmp5 = tmp11 - tmp6;
162 tmp4 = tmp10 - tmp5;
163
164 wsptr[DCTSIZE*0] = tmp0 + tmp7;
165 wsptr[DCTSIZE*7] = tmp0 - tmp7;
166 wsptr[DCTSIZE*1] = tmp1 + tmp6;
167 wsptr[DCTSIZE*6] = tmp1 - tmp6;
168 wsptr[DCTSIZE*2] = tmp2 + tmp5;
169 wsptr[DCTSIZE*5] = tmp2 - tmp5;
170 wsptr[DCTSIZE*3] = tmp3 + tmp4;
171 wsptr[DCTSIZE*4] = tmp3 - tmp4;
172
173 inptr++; /* advance pointers to next column */
174 quantptr++;
175 wsptr++;
176 }
177
178 /* Pass 2: process rows from work array, store into output array. */
179
180 wsptr = workspace;
181 for (ctr = 0; ctr < DCTSIZE; ctr++) {
182 outptr = output_buf[ctr] + output_col;
183 /* Rows of zeroes can be exploited in the same way as we did with columns.
184 * However, the column calculation has created many nonzero AC terms, so
185 * the simplification applies less often (typically 5% to 10% of the time).
186 * And testing floats for zero is relatively expensive, so we don't bother.
187 */
188
189 /* Even part */
190
191 /* Prepare range-limit and float->int conversion */
192 z5 = wsptr[0] + (((FAST_FLOAT) RANGE_CENTER) + ((FAST_FLOAT) 0.5));
193 tmp10 = z5 + wsptr[4];
194 tmp11 = z5 - wsptr[4];
195
196 tmp13 = wsptr[2] + wsptr[6];
197 tmp12 = (wsptr[2] - wsptr[6]) *
198 ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
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; /* phase 5 */
213 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
214
215 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
216 tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
217 tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */
218
219 tmp6 = tmp12 - tmp7; /* phase 2 */
220 tmp5 = tmp11 - tmp6;
221 tmp4 = tmp10 - tmp5;
222
223 /* Final output stage: float->int conversion and range-limit */
224
225 outptr[0] = range_limit[(int) (tmp0 + tmp7) & RANGE_MASK];
226 outptr[7] = range_limit[(int) (tmp0 - tmp7) & RANGE_MASK];
227 outptr[1] = range_limit[(int) (tmp1 + tmp6) & RANGE_MASK];
228 outptr[6] = range_limit[(int) (tmp1 - tmp6) & RANGE_MASK];
229 outptr[2] = range_limit[(int) (tmp2 + tmp5) & RANGE_MASK];
230 outptr[5] = range_limit[(int) (tmp2 - tmp5) & RANGE_MASK];
231 outptr[3] = range_limit[(int) (tmp3 + tmp4) & RANGE_MASK];
232 outptr[4] = range_limit[(int) (tmp3 - tmp4) & RANGE_MASK];
233
234 wsptr += DCTSIZE; /* advance pointer to next row */
235 }
236 }
237
238 #endif /* DCT_FLOAT_SUPPORTED */