1 /*
2  * jidctflt.c
3  *
4  * Copyright (C) 1994-1998, Thomas G. Lane.
5  * Modified 2010 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 DCTs. /* 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 
68 GLOBAL(void)
69 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
70 		 JCOEFPTR coef_block,
71 		 JSAMPARRAY output_buf, JDIMENSION output_col)
72 {
73   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
74   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
75   FAST_FLOAT z5, z10, z11, z12, z13;
76   JCOEFPTR inptr;
77   FLOAT_MULT_TYPE * quantptr;
78   FAST_FLOAT * wsptr;
79   JSAMPROW outptr;
80   JSAMPLE *range_limit = cinfo->sample_range_limit;
81   int ctr;
82   FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
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 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
156     tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 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*3] = tmp3 + tmp4;
169     wsptr[DCTSIZE*4] = 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 
178   wsptr = workspace;
179   for (ctr = 0; ctr < DCTSIZE; ctr++) {
180     outptr = output_buf[ctr] + output_col;
181     /* Rows of zeroes can be exploited in the same way as we did with columns.
182      * However, the column calculation has created many nonzero AC terms, so
183      * the simplification applies less often (typically 5% to 10% of the time).
184      * And testing floats for zero is relatively expensive, so we don't bother.
185      */
186 
187     /* Even part */
188 
189     /* Apply signed->unsigned and prepare float->int conversion */
190     z5 = wsptr[0] + ((FAST_FLOAT) CENTERJSAMPLE + (FAST_FLOAT) 0.5);
191     tmp10 = z5 + wsptr[4];
192     tmp11 = z5 - wsptr[4];
193 
194     tmp13 = wsptr[2] + wsptr[6];
195     tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
196 
197     tmp0 = tmp10 + tmp13;
198     tmp3 = tmp10 - tmp13;
199     tmp1 = tmp11 + tmp12;
200     tmp2 = tmp11 - tmp12;
201 
202     /* Odd part */
203 
204     z13 = wsptr[5] + wsptr[3];
205     z10 = wsptr[5] - wsptr[3];
206     z11 = wsptr[1] + wsptr[7];
207     z12 = wsptr[1] - wsptr[7];
208 
209     tmp7 = z11 + z13;
210     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
211 
212     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
213     tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
214     tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */
215 
216     tmp6 = tmp12 - tmp7;
217     tmp5 = tmp11 - tmp6;
218     tmp4 = tmp10 - tmp5;
219 
220     /* Final output stage: float->int conversion and range-limit */
221 
222     outptr[0] = range_limit[((int) (tmp0 + tmp7)) & RANGE_MASK];
223     outptr[7] = range_limit[((int) (tmp0 - tmp7)) & RANGE_MASK];
224     outptr[1] = range_limit[((int) (tmp1 + tmp6)) & RANGE_MASK];
225     outptr[6] = range_limit[((int) (tmp1 - tmp6)) & RANGE_MASK];
226     outptr[2] = range_limit[((int) (tmp2 + tmp5)) & RANGE_MASK];
227     outptr[5] = range_limit[((int) (tmp2 - tmp5)) & RANGE_MASK];
228     outptr[3] = range_limit[((int) (tmp3 + tmp4)) & RANGE_MASK];
229     outptr[4] = range_limit[((int) (tmp3 - tmp4)) & RANGE_MASK];
230 
231     wsptr += DCTSIZE;		/* advance pointer to next row */
232   }
233 }
234 
235 #endif /* DCT_FLOAT_SUPPORTED */
236