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e1929140 RR |
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 | |
39c2d6bd VZ |
92 | #define FIX_1_082392200 ((JPEG_INT32) 277) /* FIX(1.082392200) */ |
93 | #define FIX_1_414213562 ((JPEG_INT32) 362) /* FIX(1.414213562) */ | |
94 | #define FIX_1_847759065 ((JPEG_INT32) 473) /* FIX(1.847759065) */ | |
95 | #define FIX_2_613125930 ((JPEG_INT32) 669) /* FIX(2.613125930) */ | |
e1929140 RR |
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 */ |