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 file.
10  *
11  * This file contains a floating-point implementation of the
12  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
13  * must also perform dequantization of the input coefficients.
14  *
15  * This implementation should be more accurate than either of the integer
16  * IDCT implementations.  However, it may not give the same results on all
17  * machines because of differences in roundoff behavior.  Speed will depend
18  * on the hardware's floating point capacity.
19  *
20  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
21  * on each row (or vice versa, but it's more convenient to emit a row at
22  * a time).  Direct algorithms are also available, but they are much more
23  * complex and seem not to be any faster when reduced to code.
24  *
25  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
26  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
27  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
28  * JPEG textbook (see REFERENCES section in file README).  The following code
29  * is based directly on figure 4-8 in P&M.
30  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
31  * possible to arrange the computation so that many of the multiplies are
32  * simple scalings of the final outputs.  These multiplies can then be
33  * folded into the multiplications or divisions by the JPEG quantization
34  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
35  * to be done in the DCT itself.
36  * The primary disadvantage of this method is that with a fixed-point
37  * implementation, accuracy is lost due to imprecise representation of the
38  * scaled quantization values.  However, that problem does not arise if
39  * we use floating point arithmetic.
40  */
41 
42 #define JPEG_INTERNALS
43 #include "jinclude.h"
44 #include "jpeglib.h"
45 #include "jdct.h"               /* Private declarations for DCT subsystem */
46 
47 #ifdef DCT_FLOAT_SUPPORTED
48 
49 
50 /*
51  * This module is specialized to the case DCTSIZE = 8.
52  */
53 
54 #if DCTSIZE != 8
55   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
56 #endif
57 
58 
59 /* Dequantize a coefficient by multiplying it by the multiplier-table
60  * entry; produce a float result.
61  */
62 
63 #define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval))
64 
65 
66 /*
67  * Perform dequantization and inverse DCT on one block of coefficients.
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 = cinfo->sample_range_limit;
83   int ctr;
84   FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
85   #define _0_125 ((FLOAT_MULT_TYPE)0.125)
86 
87   /* Pass 1: process columns from input, store into work array. */
88 
89   inptr = coef_block;
90   quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
91   wsptr = workspace;
92   for (ctr = DCTSIZE; ctr > 0; ctr--) {
93     /* Due to quantization, we will usually find that many of the input
94      * coefficients are zero, especially the AC terms.  We can exploit this
95      * by short-circuiting the IDCT calculation for any column in which all
96      * the AC terms are zero.  In that case each output is equal to the
97      * DC coefficient (with scale factor as needed).
98      * With typical images and quantization tables, half or more of the
99      * column DCT calculations can be simplified this way.
100      */
101 
102     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
103         inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
104         inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
105         inptr[DCTSIZE*7] == 0) {
106       /* AC terms all zero */
107       FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0],
108                                     quantptr[DCTSIZE*0] * _0_125);
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] * _0_125);
128     tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2] * _0_125);
129     tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4] * _0_125);
130     tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6] * _0_125);
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] * _0_125);
146     tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3] * _0_125);
147     tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5] * _0_125);
148     tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7] * _0_125);
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 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
160     tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 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*3] = tmp3 + tmp4;
173     wsptr[DCTSIZE*4] = 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 
182   wsptr = workspace;
183   for (ctr = 0; ctr < DCTSIZE; ctr++) {
184     outptr = output_buf[ctr] + output_col;
185     /* Rows of zeroes can be exploited in the same way as we did with columns.
186      * However, the column calculation has created many nonzero AC terms, so
187      * the simplification applies less often (typically 5% to 10% of the time).
188      * And testing floats for zero is relatively expensive, so we don't bother.
189      */
190 
191     /* Even part */
192 
193     /* Apply signed->unsigned and prepare float->int conversion */
194     z5 = wsptr[0] + ((FAST_FLOAT) CENTERJSAMPLE + (FAST_FLOAT) 0.5);
195     tmp10 = z5 + wsptr[4];
196     tmp11 = z5 - wsptr[4];
197 
198     tmp13 = wsptr[2] + wsptr[6];
199     tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
200 
201     tmp0 = tmp10 + tmp13;
202     tmp3 = tmp10 - tmp13;
203     tmp1 = tmp11 + tmp12;
204     tmp2 = tmp11 - tmp12;
205 
206     /* Odd part */
207 
208     z13 = wsptr[5] + wsptr[3];
209     z10 = wsptr[5] - wsptr[3];
210     z11 = wsptr[1] + wsptr[7];
211     z12 = wsptr[1] - wsptr[7];
212 
213     tmp7 = z11 + z13;
214     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
215 
216     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
217     tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */
218     tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */
219 
220     tmp6 = tmp12 - tmp7;
221     tmp5 = tmp11 - tmp6;
222     tmp4 = tmp10 - tmp5;
223 
224     /* Final output stage: float->int conversion and range-limit */
225 
226     outptr[0] = range_limit[((int) (tmp0 + tmp7)) & RANGE_MASK];
227     outptr[7] = range_limit[((int) (tmp0 - tmp7)) & RANGE_MASK];
228     outptr[1] = range_limit[((int) (tmp1 + tmp6)) & RANGE_MASK];
229     outptr[6] = range_limit[((int) (tmp1 - tmp6)) & RANGE_MASK];
230     outptr[2] = range_limit[((int) (tmp2 + tmp5)) & RANGE_MASK];
231     outptr[5] = range_limit[((int) (tmp2 - tmp5)) & RANGE_MASK];
232     outptr[3] = range_limit[((int) (tmp3 + tmp4)) & RANGE_MASK];
233     outptr[4] = range_limit[((int) (tmp3 - tmp4)) & RANGE_MASK];
234 
235     wsptr += DCTSIZE;           /* advance pointer to next row */
236   }
237 }
238 
239 #endif /* DCT_FLOAT_SUPPORTED */
240