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1  /*
2   * jidctfst.c
3   *
4   * Copyright (C) 1994-1998, Thomas G. Lane.
5   * This file is part of the Independent JPEG Group's software.
6   * For conditions of distribution and use, see the accompanying README file.
7   *
8   * This file contains a fast, not so accurate integer implementation of the
9   * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
10   * must also perform dequantization of the input coefficients.
11   *
12   * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
13   * on each row (or vice versa, but it's more convenient to emit a row at
14   * a time).  Direct algorithms are also available, but they are much more
15   * complex and seem not to be any faster when reduced to code.
16   *
17   * This implementation is based on Arai, Agui, and Nakajima's algorithm for
18   * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
19   * Japanese, but the algorithm is described in the Pennebaker & Mitchell
20   * JPEG textbook (see REFERENCES section in file README).  The following code
21   * is based directly on figure 4-8 in P&M.
22   * While an 8-point DCT cannot be done in less than 11 multiplies, it is
23   * possible to arrange the computation so that many of the multiplies are
24   * simple scalings of the final outputs.  These multiplies can then be
25   * folded into the multiplications or divisions by the JPEG quantization
26   * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
27   * to be done in the DCT itself.
28   * The primary disadvantage of this method is that with fixed-point math,
29   * accuracy is lost due to imprecise representation of the scaled
30   * quantization values.  The smaller the quantization table entry, the less
31   * precise the scaled value, so this implementation does worse with high-
32   * quality-setting files than with low-quality ones.
33   */
34  
35  #define JPEG_INTERNALS
36  #include "jinclude.h"
37  #include "jpeglib.h"
38  #include "jdct.h"		/* Private declarations for DCT subsystem */
39  
40  #ifdef DCT_IFAST_SUPPORTED
41  
42  
43  /*
44   * This module is specialized to the case DCTSIZE = 8.
45   */
46  
47  #if DCTSIZE != 8
48    Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
49  #endif
50  
51  
52  /* Scaling decisions are generally the same as in the LL&M algorithm;
53   * see jidctint.c for more details.  However, we choose to descale
54   * (right shift) multiplication products as soon as they are formed,
55   * rather than carrying additional fractional bits into subsequent additions.
56   * This compromises accuracy slightly, but it lets us save a few shifts.
57   * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
58   * everywhere except in the multiplications proper; this saves a good deal
59   * of work on 16-bit-int machines.
60   *
61   * The dequantized coefficients are not integers because the AA&N scaling
62   * factors have been incorporated.  We represent them scaled up by PASS1_BITS,
63   * so that the first and second IDCT rounds have the same input scaling.
64   * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
65   * avoid a descaling shift; this compromises accuracy rather drastically
66   * for small quantization table entries, but it saves a lot of shifts.
67   * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
68   * so we use a much larger scaling factor to preserve accuracy.
69   *
70   * A final compromise is to represent the multiplicative constants to only
71   * 8 fractional bits, rather than 13.  This saves some shifting work on some
72   * machines, and may also reduce the cost of multiplication (since there
73   * are fewer one-bits in the constants).
74   */
75  
76  #if BITS_IN_JSAMPLE == 8
77  #define CONST_BITS  8
78  #define PASS1_BITS  2
79  #else
80  #define CONST_BITS  8
81  #define PASS1_BITS  1		/* lose a little precision to avoid overflow */
82  #endif
83  
84  /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
85   * causing a lot of useless floating-point operations at run time.
86   * To get around this we use the following pre-calculated constants.
87   * If you change CONST_BITS you may want to add appropriate values.
88   * (With a reasonable C compiler, you can just rely on the FIX() macro...)
89   */
90  
91  #if CONST_BITS == 8
92  #define FIX_1_082392200  ((INT32)  277)		/* FIX(1.082392200) */
93  #define FIX_1_414213562  ((INT32)  362)		/* FIX(1.414213562) */
94  #define FIX_1_847759065  ((INT32)  473)		/* FIX(1.847759065) */
95  #define FIX_2_613125930  ((INT32)  669)		/* FIX(2.613125930) */
96  #else
97  #define FIX_1_082392200  FIX(1.082392200)
98  #define FIX_1_414213562  FIX(1.414213562)
99  #define FIX_1_847759065  FIX(1.847759065)
100  #define FIX_2_613125930  FIX(2.613125930)
101  #endif
102  
103  
104  /* We can gain a little more speed, with a further compromise in accuracy,
105   * by omitting the addition in a descaling shift.  This yields an incorrectly
106   * rounded result half the time...
107   */
108  
109  #ifndef USE_ACCURATE_ROUNDING
110  #undef DESCALE
111  #define DESCALE(x,n)  RIGHT_SHIFT(x, n)
112  #endif
113  
114  
115  /* Multiply a DCTELEM variable by an INT32 constant, and immediately
116   * descale to yield a DCTELEM result.
117   */
118  
119  #define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
120  
121  
122  /* Dequantize a coefficient by multiplying it by the multiplier-table
123   * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16
124   * multiplication will do.  For 12-bit data, the multiplier table is
125   * declared INT32, so a 32-bit multiply will be used.
126   */
127  
128  #if BITS_IN_JSAMPLE == 8
129  #define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval))
130  #else
131  #define DEQUANTIZE(coef,quantval)  \
132  	DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
133  #endif
134  
135  
136  /* Like DESCALE, but applies to a DCTELEM and produces an int.
137   * We assume that int right shift is unsigned if INT32 right shift is.
138   */
139  
140  #ifdef RIGHT_SHIFT_IS_UNSIGNED
141  #define ISHIFT_TEMPS	DCTELEM ishift_temp;
142  #if BITS_IN_JSAMPLE == 8
143  #define DCTELEMBITS  16		/* DCTELEM may be 16 or 32 bits */
144  #else
145  #define DCTELEMBITS  32		/* DCTELEM must be 32 bits */
146  #endif
147  #define IRIGHT_SHIFT(x,shft)  \
148      ((ishift_temp = (x)) < 0 ? \
149       (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
150       (ishift_temp >> (shft)))
151  #else
152  #define ISHIFT_TEMPS
153  #define IRIGHT_SHIFT(x,shft)	((x) >> (shft))
154  #endif
155  
156  #ifdef USE_ACCURATE_ROUNDING
157  #define IDESCALE(x,n)  ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
158  #else
159  #define IDESCALE(x,n)  ((int) IRIGHT_SHIFT(x, n))
160  #endif
161  
162  
163  /*
164   * Perform dequantization and inverse DCT on one block of coefficients.
165   */
166  
167  GLOBAL(void)
168  jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
169  		 JCOEFPTR coef_block,
170  		 JSAMPARRAY output_buf, JDIMENSION output_col)
171  {
172    DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
173    DCTELEM tmp10, tmp11, tmp12, tmp13;
174    DCTELEM z5, z10, z11, z12, z13;
175    JCOEFPTR inptr;
176    IFAST_MULT_TYPE * quantptr;
177    int * wsptr;
178    JSAMPROW outptr;
179    JSAMPLE *range_limit = IDCT_range_limit(cinfo);
180    int ctr;
181    int workspace[DCTSIZE2];	/* buffers data between passes */
182    SHIFT_TEMPS			/* for DESCALE */
183    ISHIFT_TEMPS			/* for IDESCALE */
184  
185    /* Pass 1: process columns from input, store into work array. */
186  
187    inptr = coef_block;
188    quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
189    wsptr = workspace;
190    for (ctr = DCTSIZE; ctr > 0; ctr--) {
191      /* Due to quantization, we will usually find that many of the input
192       * coefficients are zero, especially the AC terms.  We can exploit this
193       * by short-circuiting the IDCT calculation for any column in which all
194       * the AC terms are zero.  In that case each output is equal to the
195       * DC coefficient (with scale factor as needed).
196       * With typical images and quantization tables, half or more of the
197       * column DCT calculations can be simplified this way.
198       */
199  
200      if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
201  	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
202  	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
203  	inptr[DCTSIZE*7] == 0) {
204        /* AC terms all zero */
205        int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
206  
207        wsptr[DCTSIZE*0] = dcval;
208        wsptr[DCTSIZE*1] = dcval;
209        wsptr[DCTSIZE*2] = dcval;
210        wsptr[DCTSIZE*3] = dcval;
211        wsptr[DCTSIZE*4] = dcval;
212        wsptr[DCTSIZE*5] = dcval;
213        wsptr[DCTSIZE*6] = dcval;
214        wsptr[DCTSIZE*7] = dcval;
215  
216        inptr++;			/* advance pointers to next column */
217        quantptr++;
218        wsptr++;
219        continue;
220      }
221  
222      /* Even part */
223  
224      tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
225      tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
226      tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
227      tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
228  
229      tmp10 = tmp0 + tmp2;	/* phase 3 */
230      tmp11 = tmp0 - tmp2;
231  
232      tmp13 = tmp1 + tmp3;	/* phases 5-3 */
233      tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
234  
235      tmp0 = tmp10 + tmp13;	/* phase 2 */
236      tmp3 = tmp10 - tmp13;
237      tmp1 = tmp11 + tmp12;
238      tmp2 = tmp11 - tmp12;
239  
240      /* Odd part */
241  
242      tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
243      tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
244      tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
245      tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
246  
247      z13 = tmp6 + tmp5;		/* phase 6 */
248      z10 = tmp6 - tmp5;
249      z11 = tmp4 + tmp7;
250      z12 = tmp4 - tmp7;
251  
252      tmp7 = z11 + z13;		/* phase 5 */
253      tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
254  
255      z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
256      tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
257      tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
258  
259      tmp6 = tmp12 - tmp7;	/* phase 2 */
260      tmp5 = tmp11 - tmp6;
261      tmp4 = tmp10 + tmp5;
262  
263      wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
264      wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
265      wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
266      wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
267      wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
268      wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
269      wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
270      wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
271  
272      inptr++;			/* advance pointers to next column */
273      quantptr++;
274      wsptr++;
275    }
276  
277    /* Pass 2: process rows from work array, store into output array. */
278    /* Note that we must descale the results by a factor of 8 == 2**3, */
279    /* and also undo the PASS1_BITS scaling. */
280  
281    wsptr = workspace;
282    for (ctr = 0; ctr < DCTSIZE; ctr++) {
283      outptr = output_buf[ctr] + output_col;
284      /* Rows of zeroes can be exploited in the same way as we did with columns.
285       * However, the column calculation has created many nonzero AC terms, so
286       * the simplification applies less often (typically 5% to 10% of the time).
287       * On machines with very fast multiplication, it's possible that the
288       * test takes more time than it's worth.  In that case this section
289       * may be commented out.
290       */
291  
292  #ifndef NO_ZERO_ROW_TEST
293      if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
294  	wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
295        /* AC terms all zero */
296        JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
297  				  & RANGE_MASK];
298  
299        outptr[0] = dcval;
300        outptr[1] = dcval;
301        outptr[2] = dcval;
302        outptr[3] = dcval;
303        outptr[4] = dcval;
304        outptr[5] = dcval;
305        outptr[6] = dcval;
306        outptr[7] = dcval;
307  
308        wsptr += DCTSIZE;		/* advance pointer to next row */
309        continue;
310      }
311  #endif
312  
313      /* Even part */
314  
315      tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
316      tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
317  
318      tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
319      tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
320  	    - tmp13;
321  
322      tmp0 = tmp10 + tmp13;
323      tmp3 = tmp10 - tmp13;
324      tmp1 = tmp11 + tmp12;
325      tmp2 = tmp11 - tmp12;
326  
327      /* Odd part */
328  
329      z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
330      z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
331      z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
332      z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
333  
334      tmp7 = z11 + z13;		/* phase 5 */
335      tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
336  
337      z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
338      tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
339      tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
340  
341      tmp6 = tmp12 - tmp7;	/* phase 2 */
342      tmp5 = tmp11 - tmp6;
343      tmp4 = tmp10 + tmp5;
344  
345      /* Final output stage: scale down by a factor of 8 and range-limit */
346  
347      outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
348  			    & RANGE_MASK];
349      outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
350  			    & RANGE_MASK];
351      outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
352  			    & RANGE_MASK];
353      outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
354  			    & RANGE_MASK];
355      outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
356  			    & RANGE_MASK];
357      outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
358  			    & RANGE_MASK];
359      outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
360  			    & RANGE_MASK];
361      outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
362  			    & RANGE_MASK];
363  
364      wsptr += DCTSIZE;		/* advance pointer to next row */
365    }
366  }
367  
368  #endif /* DCT_IFAST_SUPPORTED */
369