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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