1/*
2 * jidctfst.c
3 *
4 * This file was part of the Independent JPEG Group's software:
5 * Copyright (C) 1994-1998, Thomas G. Lane.
6 * libjpeg-turbo Modifications:
7 * Copyright (C) 2015, D. R. Commander.
8 * For conditions of distribution and use, see the accompanying README.ijg
9 * file.
10 *
11 * This file contains a fast, not so accurate integer 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 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
16 * on each row (or vice versa, but it's more convenient to emit a row at
17 * a time).  Direct algorithms are also available, but they are much more
18 * complex and seem not to be any faster when reduced to code.
19 *
20 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
21 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
22 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
23 * JPEG textbook (see REFERENCES section in file README.ijg).  The following
24 * code is based directly on figure 4-8 in P&M.
25 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
26 * possible to arrange the computation so that many of the multiplies are
27 * simple scalings of the final outputs.  These multiplies can then be
28 * folded into the multiplications or divisions by the JPEG quantization
29 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
30 * to be done in the DCT itself.
31 * The primary disadvantage of this method is that with fixed-point math,
32 * accuracy is lost due to imprecise representation of the scaled
33 * quantization values.  The smaller the quantization table entry, the less
34 * precise the scaled value, so this implementation does worse with high-
35 * quality-setting files than with low-quality ones.
36 */
37
38#define JPEG_INTERNALS
39#include "jinclude.h"
40#include "jpeglib.h"
41#include "jdct.h"               /* Private declarations for DCT subsystem */
42
43#ifdef DCT_IFAST_SUPPORTED
44
45
46/*
47 * This module is specialized to the case DCTSIZE = 8.
48 */
49
50#if DCTSIZE != 8
51  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
52#endif
53
54
55/* Scaling decisions are generally the same as in the LL&M algorithm;
56 * see jidctint.c for more details.  However, we choose to descale
57 * (right shift) multiplication products as soon as they are formed,
58 * rather than carrying additional fractional bits into subsequent additions.
59 * This compromises accuracy slightly, but it lets us save a few shifts.
60 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
61 * everywhere except in the multiplications proper; this saves a good deal
62 * of work on 16-bit-int machines.
63 *
64 * The dequantized coefficients are not integers because the AA&N scaling
65 * factors have been incorporated.  We represent them scaled up by PASS1_BITS,
66 * so that the first and second IDCT rounds have the same input scaling.
67 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
68 * avoid a descaling shift; this compromises accuracy rather drastically
69 * for small quantization table entries, but it saves a lot of shifts.
70 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
71 * so we use a much larger scaling factor to preserve accuracy.
72 *
73 * A final compromise is to represent the multiplicative constants to only
74 * 8 fractional bits, rather than 13.  This saves some shifting work on some
75 * machines, and may also reduce the cost of multiplication (since there
76 * are fewer one-bits in the constants).
77 */
78
79#if BITS_IN_JSAMPLE == 8
80#define CONST_BITS  8
81#define PASS1_BITS  2
82#else
83#define CONST_BITS  8
84#define PASS1_BITS  1           /* lose a little precision to avoid overflow */
85#endif
86
87/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
88 * causing a lot of useless floating-point operations at run time.
89 * To get around this we use the following pre-calculated constants.
90 * If you change CONST_BITS you may want to add appropriate values.
91 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
92 */
93
94#if CONST_BITS == 8
95#define FIX_1_082392200  ((JLONG)  277)         /* FIX(1.082392200) */
96#define FIX_1_414213562  ((JLONG)  362)         /* FIX(1.414213562) */
97#define FIX_1_847759065  ((JLONG)  473)         /* FIX(1.847759065) */
98#define FIX_2_613125930  ((JLONG)  669)         /* FIX(2.613125930) */
99#else
100#define FIX_1_082392200  FIX(1.082392200)
101#define FIX_1_414213562  FIX(1.414213562)
102#define FIX_1_847759065  FIX(1.847759065)
103#define FIX_2_613125930  FIX(2.613125930)
104#endif
105
106
107/* We can gain a little more speed, with a further compromise in accuracy,
108 * by omitting the addition in a descaling shift.  This yields an incorrectly
109 * rounded result half the time...
110 */
111
112#ifndef USE_ACCURATE_ROUNDING
113#undef DESCALE
114#define DESCALE(x,n)  RIGHT_SHIFT(x, n)
115#endif
116
117
118/* Multiply a DCTELEM variable by an JLONG constant, and immediately
119 * descale to yield a DCTELEM result.
120 */
121
122#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
123
124
125/* Dequantize a coefficient by multiplying it by the multiplier-table
126 * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16
127 * multiplication will do.  For 12-bit data, the multiplier table is
128 * declared JLONG, so a 32-bit multiply will be used.
129 */
130
131#if BITS_IN_JSAMPLE == 8
132#define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval))
133#else
134#define DEQUANTIZE(coef,quantval)  \
135        DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
136#endif
137
138
139/* Like DESCALE, but applies to a DCTELEM and produces an int.
140 * We assume that int right shift is unsigned if JLONG right shift is.
141 */
142
143#ifdef RIGHT_SHIFT_IS_UNSIGNED
144#define ISHIFT_TEMPS    DCTELEM ishift_temp;
145#if BITS_IN_JSAMPLE == 8
146#define DCTELEMBITS  16         /* DCTELEM may be 16 or 32 bits */
147#else
148#define DCTELEMBITS  32         /* DCTELEM must be 32 bits */
149#endif
150#define IRIGHT_SHIFT(x,shft)  \
151    ((ishift_temp = (x)) < 0 ? \
152     (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
153     (ishift_temp >> (shft)))
154#else
155#define ISHIFT_TEMPS
156#define IRIGHT_SHIFT(x,shft)    ((x) >> (shft))
157#endif
158
159#ifdef USE_ACCURATE_ROUNDING
160#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
161#else
162#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT(x, n))
163#endif
164
165
166/*
167 * Perform dequantization and inverse DCT on one block of coefficients.
168 */
169
170GLOBAL(void)
171jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info *compptr,
172                 JCOEFPTR coef_block,
173                 JSAMPARRAY output_buf, JDIMENSION output_col)
174{
175  DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
176  DCTELEM tmp10, tmp11, tmp12, tmp13;
177  DCTELEM z5, z10, z11, z12, z13;
178  JCOEFPTR inptr;
179  IFAST_MULT_TYPE *quantptr;
180  int *wsptr;
181  JSAMPROW outptr;
182  JSAMPLE *range_limit = IDCT_range_limit(cinfo);
183  int ctr;
184  int workspace[DCTSIZE2];      /* buffers data between passes */
185  SHIFT_TEMPS                   /* for DESCALE */
186  ISHIFT_TEMPS                  /* for IDESCALE */
187
188  /* Pass 1: process columns from input, store into work array. */
189
190  inptr = coef_block;
191  quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
192  wsptr = workspace;
193  for (ctr = DCTSIZE; ctr > 0; ctr--) {
194    /* Due to quantization, we will usually find that many of the input
195     * coefficients are zero, especially the AC terms.  We can exploit this
196     * by short-circuiting the IDCT calculation for any column in which all
197     * the AC terms are zero.  In that case each output is equal to the
198     * DC coefficient (with scale factor as needed).
199     * With typical images and quantization tables, half or more of the
200     * column DCT calculations can be simplified this way.
201     */
202
203    if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
204        inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
205        inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
206        inptr[DCTSIZE*7] == 0) {
207      /* AC terms all zero */
208      int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
209
210      wsptr[DCTSIZE*0] = dcval;
211      wsptr[DCTSIZE*1] = dcval;
212      wsptr[DCTSIZE*2] = dcval;
213      wsptr[DCTSIZE*3] = dcval;
214      wsptr[DCTSIZE*4] = dcval;
215      wsptr[DCTSIZE*5] = dcval;
216      wsptr[DCTSIZE*6] = dcval;
217      wsptr[DCTSIZE*7] = dcval;
218
219      inptr++;                  /* advance pointers to next column */
220      quantptr++;
221      wsptr++;
222      continue;
223    }
224
225    /* Even part */
226
227    tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
228    tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
229    tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
230    tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
231
232    tmp10 = tmp0 + tmp2;        /* phase 3 */
233    tmp11 = tmp0 - tmp2;
234
235    tmp13 = tmp1 + tmp3;        /* phases 5-3 */
236    tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
237
238    tmp0 = tmp10 + tmp13;       /* phase 2 */
239    tmp3 = tmp10 - tmp13;
240    tmp1 = tmp11 + tmp12;
241    tmp2 = tmp11 - tmp12;
242
243    /* Odd part */
244
245    tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
246    tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
247    tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
248    tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
249
250    z13 = tmp6 + tmp5;          /* phase 6 */
251    z10 = tmp6 - tmp5;
252    z11 = tmp4 + tmp7;
253    z12 = tmp4 - tmp7;
254
255    tmp7 = z11 + z13;           /* phase 5 */
256    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
257
258    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
259    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
260    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
261
262    tmp6 = tmp12 - tmp7;        /* phase 2 */
263    tmp5 = tmp11 - tmp6;
264    tmp4 = tmp10 + tmp5;
265
266    wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
267    wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
268    wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
269    wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
270    wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
271    wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
272    wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
273    wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
274
275    inptr++;                    /* advance pointers to next column */
276    quantptr++;
277    wsptr++;
278  }
279
280  /* Pass 2: process rows from work array, store into output array. */
281  /* Note that we must descale the results by a factor of 8 == 2**3, */
282  /* and also undo the PASS1_BITS scaling. */
283
284  wsptr = workspace;
285  for (ctr = 0; ctr < DCTSIZE; ctr++) {
286    outptr = output_buf[ctr] + output_col;
287    /* Rows of zeroes can be exploited in the same way as we did with columns.
288     * However, the column calculation has created many nonzero AC terms, so
289     * the simplification applies less often (typically 5% to 10% of the time).
290     * On machines with very fast multiplication, it's possible that the
291     * test takes more time than it's worth.  In that case this section
292     * may be commented out.
293     */
294
295#ifndef NO_ZERO_ROW_TEST
296    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
297        wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
298      /* AC terms all zero */
299      JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
300                                  & RANGE_MASK];
301
302      outptr[0] = dcval;
303      outptr[1] = dcval;
304      outptr[2] = dcval;
305      outptr[3] = dcval;
306      outptr[4] = dcval;
307      outptr[5] = dcval;
308      outptr[6] = dcval;
309      outptr[7] = dcval;
310
311      wsptr += DCTSIZE;         /* advance pointer to next row */
312      continue;
313    }
314#endif
315
316    /* Even part */
317
318    tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
319    tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
320
321    tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
322    tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
323            - tmp13;
324
325    tmp0 = tmp10 + tmp13;
326    tmp3 = tmp10 - tmp13;
327    tmp1 = tmp11 + tmp12;
328    tmp2 = tmp11 - tmp12;
329
330    /* Odd part */
331
332    z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
333    z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
334    z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
335    z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
336
337    tmp7 = z11 + z13;           /* phase 5 */
338    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
339
340    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
341    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
342    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
343
344    tmp6 = tmp12 - tmp7;        /* phase 2 */
345    tmp5 = tmp11 - tmp6;
346    tmp4 = tmp10 + tmp5;
347
348    /* Final output stage: scale down by a factor of 8 and range-limit */
349
350    outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
351                            & RANGE_MASK];
352    outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
353                            & RANGE_MASK];
354    outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
355                            & RANGE_MASK];
356    outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
357                            & RANGE_MASK];
358    outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
359                            & RANGE_MASK];
360    outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
361                            & RANGE_MASK];
362    outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
363                            & RANGE_MASK];
364    outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
365                            & RANGE_MASK];
366
367    wsptr += DCTSIZE;           /* advance pointer to next row */
368  }
369}
370
371#endif /* DCT_IFAST_SUPPORTED */
372