1 /*
2  * jrevdct.c
3  *
4  * Copyright (C) 1991, 1992, 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 the basic inverse-DCT transformation subroutine.
9  *
10  * This implementation is based on an algorithm described in
11  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
12  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
13  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
14  * The primary algorithm described there uses 11 multiplies and 29 adds.
15  * We use their alternate method with 12 multiplies and 32 adds.
16  * The advantage of this method is that no data path contains more than one
17  * multiplication; this allows a very simple and accurate implementation in
18  * scaled fixed-point arithmetic, with a minimal number of shifts.
19  *
20  * I've made lots of modifications to attempt to take advantage of the
21  * sparse nature of the DCT matrices we're getting.  Although the logic
22  * is cumbersome, it's straightforward and the resulting code is much
23  * faster.
24  *
25  * A better way to do this would be to pass in the DCT block as a sparse
26  * matrix, perhaps with the difference cases encoded.
27  */
28 
29 #define _XOPEN_SOURCE 500  /* get M_PI in math.h */
30 
31 #include <memory.h>
32 #include <math.h>
33 
34 #include "all.h"
35 #include "dct.h"
36 
37 
38 #define CONST_BITS 13
39 
40 /*
41  * This routine is specialized to the case DCTSIZE = 8.
42  */
43 
44 #if DCTSIZE != 8
45   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
46 #endif
47 
48 
49 /*
50  * A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT
51  * on each column.  Direct algorithms are also available, but they are
52  * much more complex and seem not to be any faster when reduced to code.
53  *
54  * The poop on this scaling stuff is as follows:
55  *
56  * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
57  * larger than the true IDCT outputs.  The final outputs are therefore
58  * a factor of N larger than desired; since N=8 this can be cured by
59  * a simple right shift at the end of the algorithm.  The advantage of
60  * this arrangement is that we save two multiplications per 1-D IDCT,
61  * because the y0 and y4 inputs need not be divided by sqrt(N).
62  *
63  * We have to do addition and subtraction of the integer inputs, which
64  * is no problem, and multiplication by fractional constants, which is
65  * a problem to do in integer arithmetic.  We multiply all the constants
66  * by CONST_SCALE and convert them to integer constants (thus retaining
67  * CONST_BITS bits of precision in the constants).  After doing a
68  * multiplication we have to divide the product by CONST_SCALE, with proper
69  * rounding, to produce the correct output.  This division can be done
70  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
71  * as long as possible so that partial sums can be added together with
72  * full fractional precision.
73  *
74  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
75  * they are represented to better-than-integral precision.  These outputs
76  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
77  * with the recommended scaling.  (To scale up 12-bit sample data further, an
78  * intermediate int32 array would be needed.)
79  *
80  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
81  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
82  * shows that the values given below are the most effective.
83  */
84 
85 #ifdef EIGHT_BIT_SAMPLES
86 #define PASS1_BITS  2
87 #else
88 #define PASS1_BITS  1		/* lose a little precision to avoid overflow */
89 #endif
90 
91 #define ONE	((int32) 1)
92 
93 #define CONST_SCALE (ONE << CONST_BITS)
94 
95 /* Convert a positive real constant to an integer scaled by CONST_SCALE.
96  * IMPORTANT: if your compiler doesn't do this arithmetic at compile time,
97  * you will pay a significant penalty in run time.  In that case, figure
98  * the correct integer constant values and insert them by hand.
99  */
100 
101 /* Actually FIX is no longer used, we precomputed them all */
102 #define FIX(x)	((int32) ((x) * CONST_SCALE + 0.5))
103 
104 /* Descale and correctly round an int32 value that's scaled by N bits.
105  * We assume RIGHT_SHIFT rounds towards minus infinity, so adding
106  * the fudge factor is correct for either sign of X.
107  */
108 
109 #define DESCALE(x,n)  RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)
110 
111 /* Multiply an int32 variable by an int32 constant to yield an int32 result.
112  * For 8-bit samples with the recommended scaling, all the variable
113  * and constant values involved are no more than 16 bits wide, so a
114  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply;
115  * this provides a useful speedup on many machines.
116  * There is no way to specify a 16x16->32 multiply in portable C, but
117  * some C compilers will do the right thing if you provide the correct
118  * combination of casts.
119  * NB: for 12-bit samples, a full 32-bit multiplication will be needed.
120  */
121 
122 #ifdef EIGHT_BIT_SAMPLES
123 #ifdef SHORTxSHORT_32		/* may work if 'int' is 32 bits */
124 #define MULTIPLY(var,const)  (((INT16) (var)) * ((INT16) (const)))
125 #endif
126 #ifdef SHORTxLCONST_32		/* known to work with Microsoft C 6.0 */
127 #define MULTIPLY(var,const)  (((INT16) (var)) * ((int32) (const)))
128 #endif
129 #endif
130 
131 #ifndef MULTIPLY		/* default definition */
132 #define MULTIPLY(var,const)  ((var) * (const))
133 #endif
134 
135 
136 /*
137   Unlike our decoder where we approximate the FIXes, we need to use exact
138 ones here or successive P-frames will drift too much with Reference frame coding
139 */
140 #define FIX_0_211164243 1730
141 #define FIX_0_275899380 2260
142 #define FIX_0_298631336 2446
143 #define FIX_0_390180644 3196
144 #define FIX_0_509795579 4176
145 #define FIX_0_541196100 4433
146 #define FIX_0_601344887 4926
147 #define FIX_0_765366865 6270
148 #define FIX_0_785694958 6436
149 #define FIX_0_899976223 7373
150 #define FIX_1_061594337 8697
151 #define FIX_1_111140466 9102
152 #define FIX_1_175875602 9633
153 #define FIX_1_306562965 10703
154 #define FIX_1_387039845 11363
155 #define FIX_1_451774981 11893
156 #define FIX_1_501321110 12299
157 #define FIX_1_662939225 13623
158 #define FIX_1_847759065 15137
159 #define FIX_1_961570560 16069
160 #define FIX_2_053119869 16819
161 #define FIX_2_172734803 17799
162 #define FIX_2_562915447 20995
163 #define FIX_3_072711026 25172
164 
165 /*
166   Switch on reverse_dct choices
167 */
168 void reference_rev_dct (int16 *block);
169 void mpeg_jrevdct_quick (int16 *block);
170 void init_idctref (void);
171 
172 extern boolean pureDCT;
173 
174 void
mpeg_jrevdct(data)175 mpeg_jrevdct(data)
176     DCTBLOCK data;
177 {
178   if (pureDCT) reference_rev_dct(data);
179   else mpeg_jrevdct_quick(data);
180 }
181 
182 /*
183  * Perform the inverse DCT on one block of coefficients.
184  */
185 
186 void
mpeg_jrevdct_quick(data)187 mpeg_jrevdct_quick(data)
188     DCTBLOCK data;
189 {
190   int32 tmp0, tmp1, tmp2, tmp3;
191   int32 tmp10, tmp11, tmp12, tmp13;
192   int32 z1, z2, z3, z4, z5;
193   int32 d0, d1, d2, d3, d4, d5, d6, d7;
194   register DCTELEM *dataptr;
195   int rowctr;
196   SHIFT_TEMPS
197 
198   /* Pass 1: process rows. */
199   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
200   /* furthermore, we scale the results by 2**PASS1_BITS. */
201 
202   dataptr = data;
203 
204   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
205     /* Because of quantization, we will usually find that many of the input
206      * coefficients are zero, especially the AC terms.  We can exploit this
207      * by short-circuiting the IDCT calculation for any row in which all
208      * the AC terms are zero.  In that case each output is equal to the
209      * DC coefficient (with scale factor as needed).
210      * With typical images and quantization tables, half or more of the
211      * row DCT calculations can be simplified this way.
212      */
213 
214     register int *idataptr = (int*)dataptr;
215     d0 = dataptr[0];
216     d1 = dataptr[1];
217     if ((d1 == 0) && (idataptr[1] | idataptr[2] | idataptr[3]) == 0) {
218       /* AC terms all zero */
219       if (d0) {
220 	  /* Compute a 32 bit value to assign. */
221 	  DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);
222 	  register int v = (dcval & 0xffff) | ((dcval << 16) & 0xffff0000);
223 
224 	  idataptr[0] = v;
225 	  idataptr[1] = v;
226 	  idataptr[2] = v;
227 	  idataptr[3] = v;
228       }
229 
230       dataptr += DCTSIZE;	/* advance pointer to next row */
231       continue;
232     }
233     d2 = dataptr[2];
234     d3 = dataptr[3];
235     d4 = dataptr[4];
236     d5 = dataptr[5];
237     d6 = dataptr[6];
238     d7 = dataptr[7];
239 
240     /* Even part: reverse the even part of the forward DCT. */
241     /* The rotator is sqrt(2)*c(-6). */
242 {
243     if (d6) {
244 	if (d4) {
245 	    if (d2) {
246 		if (d0) {
247 		    /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
248 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
249 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
250 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
251 
252 		    tmp0 = (d0 + d4) << CONST_BITS;
253 		    tmp1 = (d0 - d4) << CONST_BITS;
254 
255 		    tmp10 = tmp0 + tmp3;
256 		    tmp13 = tmp0 - tmp3;
257 		    tmp11 = tmp1 + tmp2;
258 		    tmp12 = tmp1 - tmp2;
259 		} else {
260 		    /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
261 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
262 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
263 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
264 
265 		    tmp0 = d4 << CONST_BITS;
266 
267 		    tmp10 = tmp0 + tmp3;
268 		    tmp13 = tmp0 - tmp3;
269 		    tmp11 = tmp2 - tmp0;
270 		    tmp12 = -(tmp0 + tmp2);
271 		}
272 	    } else {
273 		if (d0) {
274 		    /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
275 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
276 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
277 
278 		    tmp0 = (d0 + d4) << CONST_BITS;
279 		    tmp1 = (d0 - d4) << CONST_BITS;
280 
281 		    tmp10 = tmp0 + tmp3;
282 		    tmp13 = tmp0 - tmp3;
283 		    tmp11 = tmp1 + tmp2;
284 		    tmp12 = tmp1 - tmp2;
285 		} else {
286 		    /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
287 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
288 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
289 
290 		    tmp0 = d4 << CONST_BITS;
291 
292 		    tmp10 = tmp0 + tmp3;
293 		    tmp13 = tmp0 - tmp3;
294 		    tmp11 = tmp2 - tmp0;
295 		    tmp12 = -(tmp0 + tmp2);
296 		}
297 	    }
298 	} else {
299 	    if (d2) {
300 		if (d0) {
301 		    /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
302 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
303 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
304 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
305 
306 		    tmp0 = d0 << CONST_BITS;
307 
308 		    tmp10 = tmp0 + tmp3;
309 		    tmp13 = tmp0 - tmp3;
310 		    tmp11 = tmp0 + tmp2;
311 		    tmp12 = tmp0 - tmp2;
312 		} else {
313 		    /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
314 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
315 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
316 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
317 
318 		    tmp10 = tmp3;
319 		    tmp13 = -tmp3;
320 		    tmp11 = tmp2;
321 		    tmp12 = -tmp2;
322 		}
323 	    } else {
324 		if (d0) {
325 		    /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
326 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
327 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
328 
329 		    tmp0 = d0 << CONST_BITS;
330 
331 		    tmp10 = tmp0 + tmp3;
332 		    tmp13 = tmp0 - tmp3;
333 		    tmp11 = tmp0 + tmp2;
334 		    tmp12 = tmp0 - tmp2;
335 		} else {
336 		    /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
337 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
338 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
339 
340 		    tmp10 = tmp3;
341 		    tmp13 = -tmp3;
342 		    tmp11 = tmp2;
343 		    tmp12 = -tmp2;
344 		}
345 	    }
346 	}
347     } else {
348 	if (d4) {
349 	    if (d2) {
350 		if (d0) {
351 		    /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
352 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
353 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
354 
355 		    tmp0 = (d0 + d4) << CONST_BITS;
356 		    tmp1 = (d0 - d4) << CONST_BITS;
357 
358 		    tmp10 = tmp0 + tmp3;
359 		    tmp13 = tmp0 - tmp3;
360 		    tmp11 = tmp1 + tmp2;
361 		    tmp12 = tmp1 - tmp2;
362 		} else {
363 		    /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
364 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
365 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
366 
367 		    tmp0 = d4 << CONST_BITS;
368 
369 		    tmp10 = tmp0 + tmp3;
370 		    tmp13 = tmp0 - tmp3;
371 		    tmp11 = tmp2 - tmp0;
372 		    tmp12 = -(tmp0 + tmp2);
373 		}
374 	    } else {
375 		if (d0) {
376 		    /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
377 		    tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
378 		    tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
379 		} else {
380 		    /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
381 		    tmp10 = tmp13 = d4 << CONST_BITS;
382 		    tmp11 = tmp12 = -tmp10;
383 		}
384 	    }
385 	} else {
386 	    if (d2) {
387 		if (d0) {
388 		    /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
389 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
390 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
391 
392 		    tmp0 = d0 << CONST_BITS;
393 
394 		    tmp10 = tmp0 + tmp3;
395 		    tmp13 = tmp0 - tmp3;
396 		    tmp11 = tmp0 + tmp2;
397 		    tmp12 = tmp0 - tmp2;
398 		} else {
399 		    /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
400 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
401 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
402 
403 		    tmp10 = tmp3;
404 		    tmp13 = -tmp3;
405 		    tmp11 = tmp2;
406 		    tmp12 = -tmp2;
407 		}
408 	    } else {
409 		if (d0) {
410 		    /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
411 		    tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
412 		} else {
413 		    /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
414 		    tmp10 = tmp13 = tmp11 = tmp12 = 0;
415 		}
416 	    }
417 	}
418       }
419 
420     /* Odd part per figure 8; the matrix is unitary and hence its
421      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
422      */
423 
424     if (d7) {
425 	if (d5) {
426 	    if (d3) {
427 		if (d1) {
428 		    /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
429 		    z1 = d7 + d1;
430 		    z2 = d5 + d3;
431 		    z3 = d7 + d3;
432 		    z4 = d5 + d1;
433 		    z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
434 
435 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
436 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
437 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
438 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
439 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
440 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
441 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
442 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
443 
444 		    z3 += z5;
445 		    z4 += z5;
446 
447 		    tmp0 += z1 + z3;
448 		    tmp1 += z2 + z4;
449 		    tmp2 += z2 + z3;
450 		    tmp3 += z1 + z4;
451 		} else {
452 		    /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
453 		    z2 = d5 + d3;
454 		    z3 = d7 + d3;
455 		    z5 = MULTIPLY(z3 + d5, FIX_1_175875602);
456 
457 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
458 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
459 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
460 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
461 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
462 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
463 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
464 
465 		    z3 += z5;
466 		    z4 += z5;
467 
468 		    tmp0 += z1 + z3;
469 		    tmp1 += z2 + z4;
470 		    tmp2 += z2 + z3;
471 		    tmp3 = z1 + z4;
472 		}
473 	    } else {
474 		if (d1) {
475 		    /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
476 		    z1 = d7 + d1;
477 		    z4 = d5 + d1;
478 		    z5 = MULTIPLY(d7 + z4, FIX_1_175875602);
479 
480 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
481 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
482 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
483 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
484 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
485 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
486 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
487 
488 		    z3 += z5;
489 		    z4 += z5;
490 
491 		    tmp0 += z1 + z3;
492 		    tmp1 += z2 + z4;
493 		    tmp2 = z2 + z3;
494 		    tmp3 += z1 + z4;
495 		} else {
496 		    /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
497 		    tmp0 = MULTIPLY(-d7, FIX_0_601344887);
498 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
499 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
500 		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
501 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
502 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
503 		    z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
504 
505 		    z3 += z5;
506 		    z4 += z5;
507 
508 		    tmp0 += z3;
509 		    tmp1 += z4;
510 		    tmp2 = z2 + z3;
511 		    tmp3 = z1 + z4;
512 		}
513 	    }
514 	} else {
515 	    if (d3) {
516 		if (d1) {
517 		    /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
518 		    z1 = d7 + d1;
519 		    z3 = d7 + d3;
520 		    z5 = MULTIPLY(z3 + d1, FIX_1_175875602);
521 
522 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
523 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
524 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
525 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
526 		    z2 = MULTIPLY(-d3, FIX_2_562915447);
527 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
528 		    z4 = MULTIPLY(-d1, FIX_0_390180644);
529 
530 		    z3 += z5;
531 		    z4 += z5;
532 
533 		    tmp0 += z1 + z3;
534 		    tmp1 = z2 + z4;
535 		    tmp2 += z2 + z3;
536 		    tmp3 += z1 + z4;
537 		} else {
538 		    /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
539 		    z3 = d7 + d3;
540 
541 		    tmp0 = MULTIPLY(-d7, FIX_0_601344887);
542 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
543 		    tmp2 = MULTIPLY(d3, FIX_0_509795579);
544 		    z2 = MULTIPLY(-d3, FIX_2_562915447);
545 		    z5 = MULTIPLY(z3, FIX_1_175875602);
546 		    z3 = MULTIPLY(-z3, FIX_0_785694958);
547 
548 		    tmp0 += z3;
549 		    tmp1 = z2 + z5;
550 		    tmp2 += z3;
551 		    tmp3 = z1 + z5;
552 		}
553 	    } else {
554 		if (d1) {
555 		    /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
556 		    z1 = d7 + d1;
557 		    z5 = MULTIPLY(z1, FIX_1_175875602);
558 
559 		    z1 = MULTIPLY(z1, FIX_0_275899380);
560 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
561 		    tmp0 = MULTIPLY(-d7, FIX_1_662939225);
562 		    z4 = MULTIPLY(-d1, FIX_0_390180644);
563 		    tmp3 = MULTIPLY(d1, FIX_1_111140466);
564 
565 		    tmp0 += z1;
566 		    tmp1 = z4 + z5;
567 		    tmp2 = z3 + z5;
568 		    tmp3 += z1;
569 		} else {
570 		    /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
571 		    tmp0 = MULTIPLY(-d7, FIX_1_387039845);
572 		    tmp1 = MULTIPLY(d7, FIX_1_175875602);
573 		    tmp2 = MULTIPLY(-d7, FIX_0_785694958);
574 		    tmp3 = MULTIPLY(d7, FIX_0_275899380);
575 		}
576 	    }
577 	}
578     } else {
579 	if (d5) {
580 	    if (d3) {
581 		if (d1) {
582 		    /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
583 		    z2 = d5 + d3;
584 		    z4 = d5 + d1;
585 		    z5 = MULTIPLY(d3 + z4, FIX_1_175875602);
586 
587 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
588 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
589 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
590 		    z1 = MULTIPLY(-d1, FIX_0_899976223);
591 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
592 		    z3 = MULTIPLY(-d3, FIX_1_961570560);
593 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
594 
595 		    z3 += z5;
596 		    z4 += z5;
597 
598 		    tmp0 = z1 + z3;
599 		    tmp1 += z2 + z4;
600 		    tmp2 += z2 + z3;
601 		    tmp3 += z1 + z4;
602 		} else {
603 		    /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
604 		    z2 = d5 + d3;
605 
606 		    z5 = MULTIPLY(z2, FIX_1_175875602);
607 		    tmp1 = MULTIPLY(d5, FIX_1_662939225);
608 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
609 		    z2 = MULTIPLY(-z2, FIX_1_387039845);
610 		    tmp2 = MULTIPLY(d3, FIX_1_111140466);
611 		    z3 = MULTIPLY(-d3, FIX_1_961570560);
612 
613 		    tmp0 = z3 + z5;
614 		    tmp1 += z2;
615 		    tmp2 += z2;
616 		    tmp3 = z4 + z5;
617 		}
618 	    } else {
619 		if (d1) {
620 		    /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
621 		    z4 = d5 + d1;
622 
623 		    z5 = MULTIPLY(z4, FIX_1_175875602);
624 		    z1 = MULTIPLY(-d1, FIX_0_899976223);
625 		    tmp3 = MULTIPLY(d1, FIX_0_601344887);
626 		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
627 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
628 		    z4 = MULTIPLY(z4, FIX_0_785694958);
629 
630 		    tmp0 = z1 + z5;
631 		    tmp1 += z4;
632 		    tmp2 = z2 + z5;
633 		    tmp3 += z4;
634 		} else {
635 		    /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
636 		    tmp0 = MULTIPLY(d5, FIX_1_175875602);
637 		    tmp1 = MULTIPLY(d5, FIX_0_275899380);
638 		    tmp2 = MULTIPLY(-d5, FIX_1_387039845);
639 		    tmp3 = MULTIPLY(d5, FIX_0_785694958);
640 		}
641 	    }
642 	} else {
643 	    if (d3) {
644 		if (d1) {
645 		    /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
646 		    z5 = d1 + d3;
647 		    tmp3 = MULTIPLY(d1, FIX_0_211164243);
648 		    tmp2 = MULTIPLY(-d3, FIX_1_451774981);
649 		    z1 = MULTIPLY(d1, FIX_1_061594337);
650 		    z2 = MULTIPLY(-d3, FIX_2_172734803);
651 		    z4 = MULTIPLY(z5, FIX_0_785694958);
652 		    z5 = MULTIPLY(z5, FIX_1_175875602);
653 
654 		    tmp0 = z1 - z4;
655 		    tmp1 = z2 + z4;
656 		    tmp2 += z5;
657 		    tmp3 += z5;
658 		} else {
659 		    /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
660 		    tmp0 = MULTIPLY(-d3, FIX_0_785694958);
661 		    tmp1 = MULTIPLY(-d3, FIX_1_387039845);
662 		    tmp2 = MULTIPLY(-d3, FIX_0_275899380);
663 		    tmp3 = MULTIPLY(d3, FIX_1_175875602);
664 		}
665 	    } else {
666 		if (d1) {
667 		    /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
668 		    tmp0 = MULTIPLY(d1, FIX_0_275899380);
669 		    tmp1 = MULTIPLY(d1, FIX_0_785694958);
670 		    tmp2 = MULTIPLY(d1, FIX_1_175875602);
671 		    tmp3 = MULTIPLY(d1, FIX_1_387039845);
672 		} else {
673 		    /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
674 		    tmp0 = tmp1 = tmp2 = tmp3 = 0;
675 		}
676 	    }
677 	}
678     }
679 }
680     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
681 
682     dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
683     dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
684     dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
685     dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
686     dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
687     dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
688     dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
689     dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
690 
691     dataptr += DCTSIZE;		/* advance pointer to next row */
692   }
693 
694   /* Pass 2: process columns. */
695   /* Note that we must descale the results by a factor of 8 == 2**3, */
696   /* and also undo the PASS1_BITS scaling. */
697 
698   dataptr = data;
699   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {
700     /* Columns of zeroes can be exploited in the same way as we did with rows.
701      * However, the row calculation has created many nonzero AC terms, so the
702      * simplification applies less often (typically 5% to 10% of the time).
703      * On machines with very fast multiplication, it's possible that the
704      * test takes more time than it's worth.  In that case this section
705      * may be commented out.
706      */
707 
708     d0 = dataptr[DCTSIZE*0];
709     d1 = dataptr[DCTSIZE*1];
710     d2 = dataptr[DCTSIZE*2];
711     d3 = dataptr[DCTSIZE*3];
712     d4 = dataptr[DCTSIZE*4];
713     d5 = dataptr[DCTSIZE*5];
714     d6 = dataptr[DCTSIZE*6];
715     d7 = dataptr[DCTSIZE*7];
716 
717     /* Even part: reverse the even part of the forward DCT. */
718     /* The rotator is sqrt(2)*c(-6). */
719     if (d6) {
720 	if (d4) {
721 	    if (d2) {
722 		if (d0) {
723 		    /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */
724 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
725 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
726 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
727 
728 		    tmp0 = (d0 + d4) << CONST_BITS;
729 		    tmp1 = (d0 - d4) << CONST_BITS;
730 
731 		    tmp10 = tmp0 + tmp3;
732 		    tmp13 = tmp0 - tmp3;
733 		    tmp11 = tmp1 + tmp2;
734 		    tmp12 = tmp1 - tmp2;
735 		} else {
736 		    /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */
737 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
738 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
739 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
740 
741 		    tmp0 = d4 << CONST_BITS;
742 
743 		    tmp10 = tmp0 + tmp3;
744 		    tmp13 = tmp0 - tmp3;
745 		    tmp11 = tmp2 - tmp0;
746 		    tmp12 = -(tmp0 + tmp2);
747 		}
748 	    } else {
749 		if (d0) {
750 		    /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */
751 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
752 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
753 
754 		    tmp0 = (d0 + d4) << CONST_BITS;
755 		    tmp1 = (d0 - d4) << CONST_BITS;
756 
757 		    tmp10 = tmp0 + tmp3;
758 		    tmp13 = tmp0 - tmp3;
759 		    tmp11 = tmp1 + tmp2;
760 		    tmp12 = tmp1 - tmp2;
761 		} else {
762 		    /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */
763 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
764 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
765 
766 		    tmp0 = d4 << CONST_BITS;
767 
768 		    tmp10 = tmp0 + tmp3;
769 		    tmp13 = tmp0 - tmp3;
770 		    tmp11 = tmp2 - tmp0;
771 		    tmp12 = -(tmp0 + tmp2);
772 		}
773 	    }
774 	} else {
775 	    if (d2) {
776 		if (d0) {
777 		    /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */
778 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
779 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
780 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
781 
782 		    tmp0 = d0 << CONST_BITS;
783 
784 		    tmp10 = tmp0 + tmp3;
785 		    tmp13 = tmp0 - tmp3;
786 		    tmp11 = tmp0 + tmp2;
787 		    tmp12 = tmp0 - tmp2;
788 		} else {
789 		    /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */
790 		    z1 = MULTIPLY(d2 + d6, FIX_0_541196100);
791 		    tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);
792 		    tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);
793 
794 		    tmp10 = tmp3;
795 		    tmp13 = -tmp3;
796 		    tmp11 = tmp2;
797 		    tmp12 = -tmp2;
798 		}
799 	    } else {
800 		if (d0) {
801 		    /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */
802 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
803 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
804 
805 		    tmp0 = d0 << CONST_BITS;
806 
807 		    tmp10 = tmp0 + tmp3;
808 		    tmp13 = tmp0 - tmp3;
809 		    tmp11 = tmp0 + tmp2;
810 		    tmp12 = tmp0 - tmp2;
811 		} else {
812 		    /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */
813 		    tmp2 = MULTIPLY(-d6, FIX_1_306562965);
814 		    tmp3 = MULTIPLY(d6, FIX_0_541196100);
815 
816 		    tmp10 = tmp3;
817 		    tmp13 = -tmp3;
818 		    tmp11 = tmp2;
819 		    tmp12 = -tmp2;
820 		}
821 	    }
822 	}
823     } else {
824 	if (d4) {
825 	    if (d2) {
826 		if (d0) {
827 		    /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */
828 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
829 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
830 
831 		    tmp0 = (d0 + d4) << CONST_BITS;
832 		    tmp1 = (d0 - d4) << CONST_BITS;
833 
834 		    tmp10 = tmp0 + tmp3;
835 		    tmp13 = tmp0 - tmp3;
836 		    tmp11 = tmp1 + tmp2;
837 		    tmp12 = tmp1 - tmp2;
838 		} else {
839 		    /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */
840 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
841 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
842 
843 		    tmp0 = d4 << CONST_BITS;
844 
845 		    tmp10 = tmp0 + tmp3;
846 		    tmp13 = tmp0 - tmp3;
847 		    tmp11 = tmp2 - tmp0;
848 		    tmp12 = -(tmp0 + tmp2);
849 		}
850 	    } else {
851 		if (d0) {
852 		    /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */
853 		    tmp10 = tmp13 = (d0 + d4) << CONST_BITS;
854 		    tmp11 = tmp12 = (d0 - d4) << CONST_BITS;
855 		} else {
856 		    /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */
857 		    tmp10 = tmp13 = d4 << CONST_BITS;
858 		    tmp11 = tmp12 = -tmp10;
859 		}
860 	    }
861 	} else {
862 	    if (d2) {
863 		if (d0) {
864 		    /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */
865 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
866 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
867 
868 		    tmp0 = d0 << CONST_BITS;
869 
870 		    tmp10 = tmp0 + tmp3;
871 		    tmp13 = tmp0 - tmp3;
872 		    tmp11 = tmp0 + tmp2;
873 		    tmp12 = tmp0 - tmp2;
874 		} else {
875 		    /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */
876 		    tmp2 = MULTIPLY(d2, FIX_0_541196100);
877 		    tmp3 = MULTIPLY(d2, FIX_1_306562965);
878 
879 		    tmp10 = tmp3;
880 		    tmp13 = -tmp3;
881 		    tmp11 = tmp2;
882 		    tmp12 = -tmp2;
883 		}
884 	    } else {
885 		if (d0) {
886 		    /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */
887 		    tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS;
888 		} else {
889 		    /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */
890 		    tmp10 = tmp13 = tmp11 = tmp12 = 0;
891 		}
892 	    }
893 	}
894     }
895 
896     /* Odd part per figure 8; the matrix is unitary and hence its
897      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
898      */
899     if (d7) {
900 	if (d5) {
901 	    if (d3) {
902 		if (d1) {
903 		    /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */
904 		    z1 = d7 + d1;
905 		    z2 = d5 + d3;
906 		    z3 = d7 + d3;
907 		    z4 = d5 + d1;
908 		    z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
909 
910 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
911 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
912 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
913 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
914 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
915 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
916 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
917 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
918 
919 		    z3 += z5;
920 		    z4 += z5;
921 
922 		    tmp0 += z1 + z3;
923 		    tmp1 += z2 + z4;
924 		    tmp2 += z2 + z3;
925 		    tmp3 += z1 + z4;
926 		} else {
927 		    /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */
928 		    z1 = d7;
929 		    z2 = d5 + d3;
930 		    z3 = d7 + d3;
931 		    z5 = MULTIPLY(z3 + d5, FIX_1_175875602);
932 
933 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
934 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
935 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
936 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
937 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
938 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
939 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
940 
941 		    z3 += z5;
942 		    z4 += z5;
943 
944 		    tmp0 += z1 + z3;
945 		    tmp1 += z2 + z4;
946 		    tmp2 += z2 + z3;
947 		    tmp3 = z1 + z4;
948 		}
949 	    } else {
950 		if (d1) {
951 		    /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */
952 		    z1 = d7 + d1;
953 		    z2 = d5;
954 		    z3 = d7;
955 		    z4 = d5 + d1;
956 		    z5 = MULTIPLY(z3 + z4, FIX_1_175875602);
957 
958 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
959 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
960 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
961 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
962 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
963 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
964 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
965 
966 		    z3 += z5;
967 		    z4 += z5;
968 
969 		    tmp0 += z1 + z3;
970 		    tmp1 += z2 + z4;
971 		    tmp2 = z2 + z3;
972 		    tmp3 += z1 + z4;
973 		} else {
974 		    /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */
975 		    tmp0 = MULTIPLY(-d7, FIX_0_601344887);
976 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
977 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
978 		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
979 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
980 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
981 		    z5 = MULTIPLY(d5 + d7, FIX_1_175875602);
982 
983 		    z3 += z5;
984 		    z4 += z5;
985 
986 		    tmp0 += z3;
987 		    tmp1 += z4;
988 		    tmp2 = z2 + z3;
989 		    tmp3 = z1 + z4;
990 		}
991 	    }
992 	} else {
993 	    if (d3) {
994 		if (d1) {
995 		    /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */
996 		    z1 = d7 + d1;
997 		    z3 = d7 + d3;
998 		    z5 = MULTIPLY(z3 + d1, FIX_1_175875602);
999 
1000 		    tmp0 = MULTIPLY(d7, FIX_0_298631336);
1001 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
1002 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
1003 		    z1 = MULTIPLY(-z1, FIX_0_899976223);
1004 		    z2 = MULTIPLY(-d3, FIX_2_562915447);
1005 		    z3 = MULTIPLY(-z3, FIX_1_961570560);
1006 		    z4 = MULTIPLY(-d1, FIX_0_390180644);
1007 
1008 		    z3 += z5;
1009 		    z4 += z5;
1010 
1011 		    tmp0 += z1 + z3;
1012 		    tmp1 = z2 + z4;
1013 		    tmp2 += z2 + z3;
1014 		    tmp3 += z1 + z4;
1015 		} else {
1016 		    /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */
1017 		    z3 = d7 + d3;
1018 
1019 		    tmp0 = MULTIPLY(-d7, FIX_0_601344887);
1020 		    z1 = MULTIPLY(-d7, FIX_0_899976223);
1021 		    tmp2 = MULTIPLY(d3, FIX_0_509795579);
1022 		    z2 = MULTIPLY(-d3, FIX_2_562915447);
1023 		    z5 = MULTIPLY(z3, FIX_1_175875602);
1024 		    z3 = MULTIPLY(-z3, FIX_0_785694958);
1025 
1026 		    tmp0 += z3;
1027 		    tmp1 = z2 + z5;
1028 		    tmp2 += z3;
1029 		    tmp3 = z1 + z5;
1030 		}
1031 	    } else {
1032 		if (d1) {
1033 		    /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */
1034 		    z1 = d7 + d1;
1035 		    z5 = MULTIPLY(z1, FIX_1_175875602);
1036 
1037 		    z1 = MULTIPLY(z1, FIX_0_275899380);
1038 		    z3 = MULTIPLY(-d7, FIX_1_961570560);
1039 		    tmp0 = MULTIPLY(-d7, FIX_1_662939225);
1040 		    z4 = MULTIPLY(-d1, FIX_0_390180644);
1041 		    tmp3 = MULTIPLY(d1, FIX_1_111140466);
1042 
1043 		    tmp0 += z1;
1044 		    tmp1 = z4 + z5;
1045 		    tmp2 = z3 + z5;
1046 		    tmp3 += z1;
1047 		} else {
1048 		    /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */
1049 		    tmp0 = MULTIPLY(-d7, FIX_1_387039845);
1050 		    tmp1 = MULTIPLY(d7, FIX_1_175875602);
1051 		    tmp2 = MULTIPLY(-d7, FIX_0_785694958);
1052 		    tmp3 = MULTIPLY(d7, FIX_0_275899380);
1053 		}
1054 	    }
1055 	}
1056     } else {
1057 	if (d5) {
1058 	    if (d3) {
1059 		if (d1) {
1060 		    /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */
1061 		    z2 = d5 + d3;
1062 		    z4 = d5 + d1;
1063 		    z5 = MULTIPLY(d3 + z4, FIX_1_175875602);
1064 
1065 		    tmp1 = MULTIPLY(d5, FIX_2_053119869);
1066 		    tmp2 = MULTIPLY(d3, FIX_3_072711026);
1067 		    tmp3 = MULTIPLY(d1, FIX_1_501321110);
1068 		    z1 = MULTIPLY(-d1, FIX_0_899976223);
1069 		    z2 = MULTIPLY(-z2, FIX_2_562915447);
1070 		    z3 = MULTIPLY(-d3, FIX_1_961570560);
1071 		    z4 = MULTIPLY(-z4, FIX_0_390180644);
1072 
1073 		    z3 += z5;
1074 		    z4 += z5;
1075 
1076 		    tmp0 = z1 + z3;
1077 		    tmp1 += z2 + z4;
1078 		    tmp2 += z2 + z3;
1079 		    tmp3 += z1 + z4;
1080 		} else {
1081 		    /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */
1082 		    z2 = d5 + d3;
1083 
1084 		    z5 = MULTIPLY(z2, FIX_1_175875602);
1085 		    tmp1 = MULTIPLY(d5, FIX_1_662939225);
1086 		    z4 = MULTIPLY(-d5, FIX_0_390180644);
1087 		    z2 = MULTIPLY(-z2, FIX_1_387039845);
1088 		    tmp2 = MULTIPLY(d3, FIX_1_111140466);
1089 		    z3 = MULTIPLY(-d3, FIX_1_961570560);
1090 
1091 		    tmp0 = z3 + z5;
1092 		    tmp1 += z2;
1093 		    tmp2 += z2;
1094 		    tmp3 = z4 + z5;
1095 		}
1096 	    } else {
1097 		if (d1) {
1098 		    /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */
1099 		    z4 = d5 + d1;
1100 
1101 		    z5 = MULTIPLY(z4, FIX_1_175875602);
1102 		    z1 = MULTIPLY(-d1, FIX_0_899976223);
1103 		    tmp3 = MULTIPLY(d1, FIX_0_601344887);
1104 		    tmp1 = MULTIPLY(-d5, FIX_0_509795579);
1105 		    z2 = MULTIPLY(-d5, FIX_2_562915447);
1106 		    z4 = MULTIPLY(z4, FIX_0_785694958);
1107 
1108 		    tmp0 = z1 + z5;
1109 		    tmp1 += z4;
1110 		    tmp2 = z2 + z5;
1111 		    tmp3 += z4;
1112 		} else {
1113 		    /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */
1114 		    tmp0 = MULTIPLY(d5, FIX_1_175875602);
1115 		    tmp1 = MULTIPLY(d5, FIX_0_275899380);
1116 		    tmp2 = MULTIPLY(-d5, FIX_1_387039845);
1117 		    tmp3 = MULTIPLY(d5, FIX_0_785694958);
1118 		}
1119 	    }
1120 	} else {
1121 	    if (d3) {
1122 		if (d1) {
1123 		    /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */
1124 		    z5 = d1 + d3;
1125 		    tmp3 = MULTIPLY(d1, FIX_0_211164243);
1126 		    tmp2 = MULTIPLY(-d3, FIX_1_451774981);
1127 		    z1 = MULTIPLY(d1, FIX_1_061594337);
1128 		    z2 = MULTIPLY(-d3, FIX_2_172734803);
1129 		    z4 = MULTIPLY(z5, FIX_0_785694958);
1130 		    z5 = MULTIPLY(z5, FIX_1_175875602);
1131 
1132 		    tmp0 = z1 - z4;
1133 		    tmp1 = z2 + z4;
1134 		    tmp2 += z5;
1135 		    tmp3 += z5;
1136 		} else {
1137 		    /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */
1138 		    tmp0 = MULTIPLY(-d3, FIX_0_785694958);
1139 		    tmp1 = MULTIPLY(-d3, FIX_1_387039845);
1140 		    tmp2 = MULTIPLY(-d3, FIX_0_275899380);
1141 		    tmp3 = MULTIPLY(d3, FIX_1_175875602);
1142 		}
1143 	    } else {
1144 		if (d1) {
1145 		    /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */
1146 		    tmp0 = MULTIPLY(d1, FIX_0_275899380);
1147 		    tmp1 = MULTIPLY(d1, FIX_0_785694958);
1148 		    tmp2 = MULTIPLY(d1, FIX_1_175875602);
1149 		    tmp3 = MULTIPLY(d1, FIX_1_387039845);
1150 		} else {
1151 		    /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */
1152 		    tmp0 = tmp1 = tmp2 = tmp3 = 0;
1153 		}
1154 	    }
1155 	}
1156     }
1157 
1158     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
1159 
1160     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,
1161 					   CONST_BITS+PASS1_BITS+3);
1162     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,
1163 					   CONST_BITS+PASS1_BITS+3);
1164     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,
1165 					   CONST_BITS+PASS1_BITS+3);
1166     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,
1167 					   CONST_BITS+PASS1_BITS+3);
1168     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,
1169 					   CONST_BITS+PASS1_BITS+3);
1170     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,
1171 					   CONST_BITS+PASS1_BITS+3);
1172     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,
1173 					   CONST_BITS+PASS1_BITS+3);
1174     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,
1175 					   CONST_BITS+PASS1_BITS+3);
1176 
1177     dataptr++;			/* advance pointer to next column */
1178   }
1179 }
1180 
1181 
1182 /* here is the reference one, in case of problems with the normal one */
1183 
1184 /* idctref.c, Inverse Discrete Fourier Transform, double precision          */
1185 
1186 /* Copyright (C) 1994, MPEG Software Simulation Group. All Rights Reserved. */
1187 
1188 /*
1189  * Disclaimer of Warranty
1190  *
1191  * These software programs are available to the user without any license fee or
1192  * royalty on an "as is" basis.  The MPEG Software Simulation Group disclaims
1193  * any and all warranties, whether express, implied, or statuary, including any
1194  * implied warranties or merchantability or of fitness for a particular
1195  * purpose.  In no event shall the copyright-holder be liable for any
1196  * incidental, punitive, or consequential damages of any kind whatsoever
1197  * arising from the use of these programs.
1198  *
1199  * This disclaimer of warranty extends to the user of these programs and user's
1200  * customers, employees, agents, transferees, successors, and assigns.
1201  *
1202  * The MPEG Software Simulation Group does not represent or warrant that the
1203  * programs furnished hereunder are free of infringement of any third-party
1204  * patents.
1205  *
1206  * Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
1207  * are subject to royalty fees to patent holders.  Many of these patents are
1208  * general enough such that they are unavoidable regardless of implementation
1209  * design.
1210  *
1211  */
1212 
1213 /*  Perform IEEE 1180 reference (64-bit floating point, separable 8x1
1214  *  direct matrix multiply) Inverse Discrete Cosine Transform
1215 */
1216 
1217 
1218 /* cosine transform matrix for 8x1 IDCT */
1219 static double itrans_coef[8][8];
1220 
1221 
1222 
init_idctref()1223 void init_idctref() {
1224 /*----------------------------------------------------------------------------
1225    initialize DCT coefficient matrix
1226 -----------------------------------------------------------------------------*/
1227     unsigned int freq;
1228 
1229     for (freq=0; freq < 8; ++freq) {
1230         double const scale = (freq == 0) ? sqrt(0.125) : 0.5;
1231 
1232         unsigned int time;
1233 
1234         for (time = 0; time < 8; ++time)
1235             itrans_coef[freq][time] = scale*cos((M_PI/8.0)*freq*(time + 0.5));
1236     }
1237 }
1238 
1239 
1240 
1241 /* perform IDCT matrix multiply for 8x8 coefficient block */
1242 
reference_rev_dct(block)1243 void reference_rev_dct(block)
1244 int16 *block;
1245 {
1246   int i, j, k, v;
1247   double partial_product;
1248   double tmp[64];
1249 
1250   for (i=0; i<8; i++)
1251     for (j=0; j<8; j++)
1252     {
1253       partial_product = 0.0;
1254 
1255       for (k=0; k<8; k++)
1256         partial_product+= itrans_coef[k][j]*block[8*i+k];
1257 
1258       tmp[8*i+j] = partial_product;
1259     }
1260 
1261   /* Transpose operation is integrated into address mapping by switching
1262      loop order of i and j */
1263 
1264   for (j=0; j<8; j++)
1265     for (i=0; i<8; i++)
1266     {
1267       partial_product = 0.0;
1268 
1269       for (k=0; k<8; k++)
1270         partial_product+= itrans_coef[k][i]*tmp[8*k+j];
1271 
1272       v = floor(partial_product+0.5);
1273       block[8*i+j] = (v<-256) ? -256 : ((v>255) ? 255 : v);
1274     }
1275 }
1276