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,
74                 JSAMPARRAY output_buf, 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