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23 /* $XConsortium: jidctfst.c /main/2 1996/05/09 03:51:13 drk $ */
27 * Copyright (C) 1994-1996, Thomas G. Lane.
28 * This file is part of the Independent JPEG Group's software.
29 * For conditions of distribution and use, see the accompanying README file.
31 * This file contains a fast, not so accurate integer implementation of the
32 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
33 * must also perform dequantization of the input coefficients.
35 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
36 * on each row (or vice versa, but it's more convenient to emit a row at
37 * a time). Direct algorithms are also available, but they are much more
38 * complex and seem not to be any faster when reduced to code.
40 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
41 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
42 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
43 * JPEG textbook (see REFERENCES section in file README). The following code
44 * is based directly on figure 4-8 in P&M.
45 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
46 * possible to arrange the computation so that many of the multiplies are
47 * simple scalings of the final outputs. These multiplies can then be
48 * folded into the multiplications or divisions by the JPEG quantization
49 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
50 * to be done in the DCT itself.
51 * The primary disadvantage of this method is that with fixed-point math,
52 * accuracy is lost due to imprecise representation of the scaled
53 * quantization values. The smaller the quantization table entry, the less
54 * precise the scaled value, so this implementation does worse with high-
55 * quality-setting files than with low-quality ones.
58 #define JPEG_INTERNALS
61 #include "jdct.h" /* Private declarations for DCT subsystem */
63 #ifdef DCT_IFAST_SUPPORTED
67 * This module is specialized to the case DCTSIZE = 8.
71 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
75 /* Scaling decisions are generally the same as in the LL&M algorithm;
76 * see jidctint.c for more details. However, we choose to descale
77 * (right shift) multiplication products as soon as they are formed,
78 * rather than carrying additional fractional bits into subsequent additions.
79 * This compromises accuracy slightly, but it lets us save a few shifts.
80 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
81 * everywhere except in the multiplications proper; this saves a good deal
82 * of work on 16-bit-int machines.
84 * The dequantized coefficients are not integers because the AA&N scaling
85 * factors have been incorporated. We represent them scaled up by PASS1_BITS,
86 * so that the first and second IDCT rounds have the same input scaling.
87 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
88 * avoid a descaling shift; this compromises accuracy rather drastically
89 * for small quantization table entries, but it saves a lot of shifts.
90 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
91 * so we use a much larger scaling factor to preserve accuracy.
93 * A final compromise is to represent the multiplicative constants to only
94 * 8 fractional bits, rather than 13. This saves some shifting work on some
95 * machines, and may also reduce the cost of multiplication (since there
96 * are fewer one-bits in the constants).
99 #if BITS_IN_JSAMPLE == 8
104 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
107 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
108 * causing a lot of useless floating-point operations at run time.
109 * To get around this we use the following pre-calculated constants.
110 * If you change CONST_BITS you may want to add appropriate values.
111 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
115 #define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
116 #define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
117 #define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
118 #define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
120 #define FIX_1_082392200 FIX(1.082392200)
121 #define FIX_1_414213562 FIX(1.414213562)
122 #define FIX_1_847759065 FIX(1.847759065)
123 #define FIX_2_613125930 FIX(2.613125930)
127 /* We can gain a little more speed, with a further compromise in accuracy,
128 * by omitting the addition in a descaling shift. This yields an incorrectly
129 * rounded result half the time...
132 #ifndef USE_ACCURATE_ROUNDING
134 #define DESCALE(x,n) RIGHT_SHIFT(x, n)
138 /* Multiply a DCTELEM variable by an INT32 constant, and immediately
139 * descale to yield a DCTELEM result.
142 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
145 /* Dequantize a coefficient by multiplying it by the multiplier-table
146 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16
147 * multiplication will do. For 12-bit data, the multiplier table is
148 * declared INT32, so a 32-bit multiply will be used.
151 #if BITS_IN_JSAMPLE == 8
152 #define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
154 #define DEQUANTIZE(coef,quantval) \
155 DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS)
159 /* Like DESCALE, but applies to a DCTELEM and produces an int.
160 * We assume that int right shift is unsigned if INT32 right shift is.
163 #ifdef RIGHT_SHIFT_IS_UNSIGNED
164 #define ISHIFT_TEMPS DCTELEM ishift_temp;
165 #if BITS_IN_JSAMPLE == 8
166 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
168 #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
170 #define IRIGHT_SHIFT(x,shft) \
171 ((ishift_temp = (x)) < 0 ? \
172 (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
173 (ishift_temp >> (shft)))
176 #define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
179 #ifdef USE_ACCURATE_ROUNDING
180 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
182 #define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
187 * Perform dequantization and inverse DCT on one block of coefficients.
191 jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr,
193 JSAMPARRAY output_buf, JDIMENSION output_col)
195 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
196 DCTELEM tmp10, tmp11, tmp12, tmp13;
197 DCTELEM z5, z10, z11, z12, z13;
199 IFAST_MULT_TYPE * quantptr;
202 JSAMPLE *range_limit = IDCT_range_limit(cinfo);
204 int workspace[DCTSIZE2]; /* buffers data between passes */
205 SHIFT_TEMPS /* for DESCALE */
206 ISHIFT_TEMPS /* for IDESCALE */
208 /* Pass 1: process columns from input, store into work array. */
211 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
213 for (ctr = DCTSIZE; ctr > 0; ctr--) {
214 /* Due to quantization, we will usually find that many of the input
215 * coefficients are zero, especially the AC terms. We can exploit this
216 * by short-circuiting the IDCT calculation for any column in which all
217 * the AC terms are zero. In that case each output is equal to the
218 * DC coefficient (with scale factor as needed).
219 * With typical images and quantization tables, half or more of the
220 * column DCT calculations can be simplified this way.
223 if ((inptr[DCTSIZE*1] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] |
224 inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] |
225 inptr[DCTSIZE*7]) == 0) {
226 /* AC terms all zero */
227 int dcval = (int) DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
229 wsptr[DCTSIZE*0] = dcval;
230 wsptr[DCTSIZE*1] = dcval;
231 wsptr[DCTSIZE*2] = dcval;
232 wsptr[DCTSIZE*3] = dcval;
233 wsptr[DCTSIZE*4] = dcval;
234 wsptr[DCTSIZE*5] = dcval;
235 wsptr[DCTSIZE*6] = dcval;
236 wsptr[DCTSIZE*7] = dcval;
238 inptr++; /* advance pointers to next column */
246 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
247 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
248 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
249 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
251 tmp10 = tmp0 + tmp2; /* phase 3 */
254 tmp13 = tmp1 + tmp3; /* phases 5-3 */
255 tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */
257 tmp0 = tmp10 + tmp13; /* phase 2 */
258 tmp3 = tmp10 - tmp13;
259 tmp1 = tmp11 + tmp12;
260 tmp2 = tmp11 - tmp12;
264 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
265 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
266 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
267 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
269 z13 = tmp6 + tmp5; /* phase 6 */
274 tmp7 = z11 + z13; /* phase 5 */
275 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
277 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
278 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
279 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
281 tmp6 = tmp12 - tmp7; /* phase 2 */
285 wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7);
286 wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7);
287 wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6);
288 wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6);
289 wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5);
290 wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5);
291 wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4);
292 wsptr[DCTSIZE*3] = (int) (tmp3 - tmp4);
294 inptr++; /* advance pointers to next column */
299 /* Pass 2: process rows from work array, store into output array. */
300 /* Note that we must descale the results by a factor of 8 == 2**3, */
301 /* and also undo the PASS1_BITS scaling. */
304 for (ctr = 0; ctr < DCTSIZE; ctr++) {
305 outptr = output_buf[ctr] + output_col;
306 /* Rows of zeroes can be exploited in the same way as we did with columns.
307 * However, the column calculation has created many nonzero AC terms, so
308 * the simplification applies less often (typically 5% to 10% of the time).
309 * On machines with very fast multiplication, it's possible that the
310 * test takes more time than it's worth. In that case this section
311 * may be commented out.
314 #ifndef NO_ZERO_ROW_TEST
315 if ((wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] |
317 /* AC terms all zero */
318 JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3)
330 wsptr += DCTSIZE; /* advance pointer to next row */
337 tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]);
338 tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]);
340 tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]);
341 tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562)
344 tmp0 = tmp10 + tmp13;
345 tmp3 = tmp10 - tmp13;
346 tmp1 = tmp11 + tmp12;
347 tmp2 = tmp11 - tmp12;
351 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
352 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
353 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
354 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];
356 tmp7 = z11 + z13; /* phase 5 */
357 tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */
359 z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */
360 tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */
361 tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */
363 tmp6 = tmp12 - tmp7; /* phase 2 */
367 /* Final output stage: scale down by a factor of 8 and range-limit */
369 outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3)
371 outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3)
373 outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3)
375 outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3)
377 outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3)
379 outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3)
381 outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3)
383 outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3)
386 wsptr += DCTSIZE; /* advance pointer to next row */
390 #endif /* DCT_IFAST_SUPPORTED */