aboutsummaryrefslogtreecommitdiff
path: root/soft-fp/op-2.h
blob: b9f86e6b9e1e8e242f9896218f7311580db1b077 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
/* Software floating-point emulation.
   Basic two-word fraction declaration and manipulation.
   Copyright (C) 1997-2021 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   In addition to the permissions in the GNU Lesser General Public
   License, the Free Software Foundation gives you unlimited
   permission to link the compiled version of this file into
   combinations with other programs, and to distribute those
   combinations without any restriction coming from the use of this
   file.  (The Lesser General Public License restrictions do apply in
   other respects; for example, they cover modification of the file,
   and distribution when not linked into a combine executable.)

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <https://www.gnu.org/licenses/>.  */

#ifndef SOFT_FP_OP_2_H
#define SOFT_FP_OP_2_H	1

#define _FP_FRAC_DECL_2(X)				\
  _FP_W_TYPE X##_f0 _FP_ZERO_INIT, X##_f1 _FP_ZERO_INIT
#define _FP_FRAC_COPY_2(D, S)	(D##_f0 = S##_f0, D##_f1 = S##_f1)
#define _FP_FRAC_SET_2(X, I)	__FP_FRAC_SET_2 (X, I)
#define _FP_FRAC_HIGH_2(X)	(X##_f1)
#define _FP_FRAC_LOW_2(X)	(X##_f0)
#define _FP_FRAC_WORD_2(X, w)	(X##_f##w)

#define _FP_FRAC_SLL_2(X, N)						\
  (void) (((N) < _FP_W_TYPE_SIZE)					\
	  ? ({								\
	      if (__builtin_constant_p (N) && (N) == 1)			\
		{							\
		  X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE) (X##_f0)) < 0); \
		  X##_f0 += X##_f0;					\
		}							\
	      else							\
		{							\
		  X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
		  X##_f0 <<= (N);					\
		}							\
	      0;							\
	    })								\
	  : ({								\
	      X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE);		\
	      X##_f0 = 0;						\
	    }))


#define _FP_FRAC_SRL_2(X, N)						\
  (void) (((N) < _FP_W_TYPE_SIZE)					\
	  ? ({								\
	      X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
	      X##_f1 >>= (N);						\
	    })								\
	  : ({								\
	      X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE);		\
	      X##_f1 = 0;						\
	    }))

/* Right shift with sticky-lsb.  */
#define _FP_FRAC_SRST_2(X, S, N, sz)					\
  (void) (((N) < _FP_W_TYPE_SIZE)					\
	  ? ({								\
	      S = (__builtin_constant_p (N) && (N) == 1			\
		   ? X##_f0 & 1						\
		   : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0);		\
	      X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \
	      X##_f1 >>= (N);						\
	    })								\
	  : ({								\
	      S = ((((N) == _FP_W_TYPE_SIZE				\
		     ? 0						\
		     : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N))))		\
		    | X##_f0) != 0);					\
	      X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE));		\
	      X##_f1 = 0;						\
	    }))

#define _FP_FRAC_SRS_2(X, N, sz)					\
  (void) (((N) < _FP_W_TYPE_SIZE)					\
	  ? ({								\
	      X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \
			| (__builtin_constant_p (N) && (N) == 1		\
			   ? X##_f0 & 1					\
			   : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
	      X##_f1 >>= (N);						\
	    })								\
	  : ({								\
	      X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)		\
			| ((((N) == _FP_W_TYPE_SIZE			\
			     ? 0					\
			     : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N))))	\
			    | X##_f0) != 0));				\
	      X##_f1 = 0;						\
	    }))

#define _FP_FRAC_ADDI_2(X, I)	\
  __FP_FRAC_ADDI_2 (X##_f1, X##_f0, I)

#define _FP_FRAC_ADD_2(R, X, Y)	\
  __FP_FRAC_ADD_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_SUB_2(R, X, Y)	\
  __FP_FRAC_SUB_2 (R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_DEC_2(X, Y)	\
  __FP_FRAC_DEC_2 (X##_f1, X##_f0, Y##_f1, Y##_f0)

#define _FP_FRAC_CLZ_2(R, X)			\
  do						\
    {						\
      if (X##_f1)				\
	__FP_CLZ ((R), X##_f1);			\
      else					\
	{					\
	  __FP_CLZ ((R), X##_f0);		\
	  (R) += _FP_W_TYPE_SIZE;		\
	}					\
    }						\
  while (0)

/* Predicates.  */
#define _FP_FRAC_NEGP_2(X)	((_FP_WS_TYPE) X##_f1 < 0)
#define _FP_FRAC_ZEROP_2(X)	((X##_f1 | X##_f0) == 0)
#define _FP_FRAC_OVERP_2(fs, X)	(_FP_FRAC_HIGH_##fs (X) & _FP_OVERFLOW_##fs)
#define _FP_FRAC_CLEAR_OVERP_2(fs, X)	(_FP_FRAC_HIGH_##fs (X) &= ~_FP_OVERFLOW_##fs)
#define _FP_FRAC_HIGHBIT_DW_2(fs, X)	\
  (_FP_FRAC_HIGH_DW_##fs (X) & _FP_HIGHBIT_DW_##fs)
#define _FP_FRAC_EQ_2(X, Y)	(X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
#define _FP_FRAC_GT_2(X, Y)	\
  (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
#define _FP_FRAC_GE_2(X, Y)	\
  (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))

#define _FP_ZEROFRAC_2		0, 0
#define _FP_MINFRAC_2		0, 1
#define _FP_MAXFRAC_2		(~(_FP_WS_TYPE) 0), (~(_FP_WS_TYPE) 0)

/* Internals.  */

#define __FP_FRAC_SET_2(X, I1, I0)	(X##_f0 = I0, X##_f1 = I1)

#define __FP_CLZ_2(R, xh, xl)			\
  do						\
    {						\
      if (xh)					\
	__FP_CLZ ((R), xh);			\
      else					\
	{					\
	  __FP_CLZ ((R), xl);			\
	  (R) += _FP_W_TYPE_SIZE;		\
	}					\
    }						\
  while (0)

#if 0

# ifndef __FP_FRAC_ADDI_2
#  define __FP_FRAC_ADDI_2(xh, xl, i)	\
  (xh += ((xl += i) < i))
# endif
# ifndef __FP_FRAC_ADD_2
#  define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl)	\
  (rh = xh + yh + ((rl = xl + yl) < xl))
# endif
# ifndef __FP_FRAC_SUB_2
#  define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl)	\
  (rh = xh - yh - ((rl = xl - yl) > xl))
# endif
# ifndef __FP_FRAC_DEC_2
#  define __FP_FRAC_DEC_2(xh, xl, yh, yl)		\
  do							\
    {							\
      UWtype __FP_FRAC_DEC_2_t = xl;			\
      xh -= yh + ((xl -= yl) > __FP_FRAC_DEC_2_t);	\
    }							\
  while (0)
# endif

#else

# undef __FP_FRAC_ADDI_2
# define __FP_FRAC_ADDI_2(xh, xl, i)	add_ssaaaa (xh, xl, xh, xl, 0, i)
# undef __FP_FRAC_ADD_2
# define __FP_FRAC_ADD_2		add_ssaaaa
# undef __FP_FRAC_SUB_2
# define __FP_FRAC_SUB_2		sub_ddmmss
# undef __FP_FRAC_DEC_2
# define __FP_FRAC_DEC_2(xh, xl, yh, yl)	\
  sub_ddmmss (xh, xl, xh, xl, yh, yl)

#endif

/* Unpack the raw bits of a native fp value.  Do not classify or
   normalize the data.  */

#define _FP_UNPACK_RAW_2(fs, X, val)			\
  do							\
    {							\
      union _FP_UNION_##fs _FP_UNPACK_RAW_2_flo;	\
      _FP_UNPACK_RAW_2_flo.flt = (val);			\
							\
      X##_f0 = _FP_UNPACK_RAW_2_flo.bits.frac0;		\
      X##_f1 = _FP_UNPACK_RAW_2_flo.bits.frac1;		\
      X##_e  = _FP_UNPACK_RAW_2_flo.bits.exp;		\
      X##_s  = _FP_UNPACK_RAW_2_flo.bits.sign;		\
    }							\
  while (0)

#define _FP_UNPACK_RAW_2_P(fs, X, val)			\
  do							\
    {							\
      union _FP_UNION_##fs *_FP_UNPACK_RAW_2_P_flo	\
	= (union _FP_UNION_##fs *) (val);		\
							\
      X##_f0 = _FP_UNPACK_RAW_2_P_flo->bits.frac0;	\
      X##_f1 = _FP_UNPACK_RAW_2_P_flo->bits.frac1;	\
      X##_e  = _FP_UNPACK_RAW_2_P_flo->bits.exp;	\
      X##_s  = _FP_UNPACK_RAW_2_P_flo->bits.sign;	\
    }							\
  while (0)


/* Repack the raw bits of a native fp value.  */

#define _FP_PACK_RAW_2(fs, val, X)		\
  do						\
    {						\
      union _FP_UNION_##fs _FP_PACK_RAW_2_flo;	\
						\
      _FP_PACK_RAW_2_flo.bits.frac0 = X##_f0;	\
      _FP_PACK_RAW_2_flo.bits.frac1 = X##_f1;	\
      _FP_PACK_RAW_2_flo.bits.exp   = X##_e;	\
      _FP_PACK_RAW_2_flo.bits.sign  = X##_s;	\
						\
      (val) = _FP_PACK_RAW_2_flo.flt;		\
    }						\
  while (0)

#define _FP_PACK_RAW_2_P(fs, val, X)			\
  do							\
    {							\
      union _FP_UNION_##fs *_FP_PACK_RAW_2_P_flo	\
	= (union _FP_UNION_##fs *) (val);		\
							\
      _FP_PACK_RAW_2_P_flo->bits.frac0 = X##_f0;	\
      _FP_PACK_RAW_2_P_flo->bits.frac1 = X##_f1;	\
      _FP_PACK_RAW_2_P_flo->bits.exp   = X##_e;		\
      _FP_PACK_RAW_2_P_flo->bits.sign  = X##_s;		\
    }							\
  while (0)


/* Multiplication algorithms: */

/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */

#define _FP_MUL_MEAT_DW_2_wide(wfracbits, R, X, Y, doit)		\
  do									\
    {									\
      _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_b);			\
      _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_c);			\
									\
      doit (_FP_FRAC_WORD_4 (R, 1), _FP_FRAC_WORD_4 (R, 0),		\
	    X##_f0, Y##_f0);						\
      doit (_FP_MUL_MEAT_DW_2_wide_b_f1, _FP_MUL_MEAT_DW_2_wide_b_f0,	\
	    X##_f0, Y##_f1);						\
      doit (_FP_MUL_MEAT_DW_2_wide_c_f1, _FP_MUL_MEAT_DW_2_wide_c_f0,	\
	    X##_f1, Y##_f0);						\
      doit (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),		\
	    X##_f1, Y##_f1);						\
									\
      __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1), 0,			\
		       _FP_MUL_MEAT_DW_2_wide_b_f1,			\
		       _FP_MUL_MEAT_DW_2_wide_b_f0,			\
		       _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1));				\
      __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1), 0,			\
		       _FP_MUL_MEAT_DW_2_wide_c_f1,			\
		       _FP_MUL_MEAT_DW_2_wide_c_f0,			\
		       _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1));				\
    }									\
  while (0)

#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit)			\
  do									\
    {									\
      _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_z);				\
									\
      _FP_MUL_MEAT_DW_2_wide ((wfracbits), _FP_MUL_MEAT_2_wide_z,	\
			      X, Y, doit);				\
									\
      /* Normalize since we know where the msb of the multiplicands	\
	 were (bit B), we know that the msb of the of the product is	\
	 at either 2B or 2B-1.  */					\
      _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_z, (wfracbits)-1,		\
		      2*(wfracbits));					\
      R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 0);		\
      R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_z, 1);		\
    }									\
  while (0)

/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
   Do only 3 multiplications instead of four. This one is for machines
   where multiplication is much more expensive than subtraction.  */

#define _FP_MUL_MEAT_DW_2_wide_3mul(wfracbits, R, X, Y, doit)		\
  do									\
    {									\
      _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_b);			\
      _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_2_wide_3mul_c);			\
      _FP_W_TYPE _FP_MUL_MEAT_DW_2_wide_3mul_d;				\
      int _FP_MUL_MEAT_DW_2_wide_3mul_c1;				\
      int _FP_MUL_MEAT_DW_2_wide_3mul_c2;				\
									\
      _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 = X##_f0 + X##_f1;		\
      _FP_MUL_MEAT_DW_2_wide_3mul_c1					\
	= _FP_MUL_MEAT_DW_2_wide_3mul_b_f0 < X##_f0;			\
      _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 = Y##_f0 + Y##_f1;		\
      _FP_MUL_MEAT_DW_2_wide_3mul_c2					\
	= _FP_MUL_MEAT_DW_2_wide_3mul_b_f1 < Y##_f0;			\
      doit (_FP_MUL_MEAT_DW_2_wide_3mul_d, _FP_FRAC_WORD_4 (R, 0),	\
	    X##_f0, Y##_f0);						\
      doit (_FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1),		\
	    _FP_MUL_MEAT_DW_2_wide_3mul_b_f0,				\
	    _FP_MUL_MEAT_DW_2_wide_3mul_b_f1);				\
      doit (_FP_MUL_MEAT_DW_2_wide_3mul_c_f1,				\
	    _FP_MUL_MEAT_DW_2_wide_3mul_c_f0, X##_f1, Y##_f1);		\
									\
      _FP_MUL_MEAT_DW_2_wide_3mul_b_f0					\
	&= -_FP_MUL_MEAT_DW_2_wide_3mul_c2;				\
      _FP_MUL_MEAT_DW_2_wide_3mul_b_f1					\
	&= -_FP_MUL_MEAT_DW_2_wide_3mul_c1;				\
      __FP_FRAC_ADD_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1),				\
		       (_FP_MUL_MEAT_DW_2_wide_3mul_c1			\
			& _FP_MUL_MEAT_DW_2_wide_3mul_c2), 0,		\
		       _FP_MUL_MEAT_DW_2_wide_3mul_d,			\
		       0, _FP_FRAC_WORD_4 (R, 2), _FP_FRAC_WORD_4 (R, 1)); \
      __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
			_FP_MUL_MEAT_DW_2_wide_3mul_b_f0);		\
      __FP_FRAC_ADDI_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
			_FP_MUL_MEAT_DW_2_wide_3mul_b_f1);		\
      __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1),				\
		       0, _FP_MUL_MEAT_DW_2_wide_3mul_d,		\
		       _FP_FRAC_WORD_4 (R, 0));				\
      __FP_FRAC_DEC_3 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_FRAC_WORD_4 (R, 1), 0,			\
		       _FP_MUL_MEAT_DW_2_wide_3mul_c_f1,		\
		       _FP_MUL_MEAT_DW_2_wide_3mul_c_f0);		\
      __FP_FRAC_ADD_2 (_FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2),	\
		       _FP_MUL_MEAT_DW_2_wide_3mul_c_f1,		\
		       _FP_MUL_MEAT_DW_2_wide_3mul_c_f0,		\
		       _FP_FRAC_WORD_4 (R, 3), _FP_FRAC_WORD_4 (R, 2));	\
    }									\
  while (0)

#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit)		\
  do									\
    {									\
      _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_wide_3mul_z);			\
									\
      _FP_MUL_MEAT_DW_2_wide_3mul ((wfracbits),				\
				   _FP_MUL_MEAT_2_wide_3mul_z,		\
				   X, Y, doit);				\
									\
      /* Normalize since we know where the msb of the multiplicands	\
	 were (bit B), we know that the msb of the of the product is	\
	 at either 2B or 2B-1.  */					\
      _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_wide_3mul_z,			\
		      (wfracbits)-1, 2*(wfracbits));			\
      R##_f0 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 0);		\
      R##_f1 = _FP_FRAC_WORD_4 (_FP_MUL_MEAT_2_wide_3mul_z, 1);		\
    }									\
  while (0)

#define _FP_MUL_MEAT_DW_2_gmp(wfracbits, R, X, Y)	\
  do							\
    {							\
      _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_x[2];		\
      _FP_W_TYPE _FP_MUL_MEAT_DW_2_gmp_y[2];		\
      _FP_MUL_MEAT_DW_2_gmp_x[0] = X##_f0;		\
      _FP_MUL_MEAT_DW_2_gmp_x[1] = X##_f1;		\
      _FP_MUL_MEAT_DW_2_gmp_y[0] = Y##_f0;		\
      _FP_MUL_MEAT_DW_2_gmp_y[1] = Y##_f1;		\
							\
      mpn_mul_n (R##_f, _FP_MUL_MEAT_DW_2_gmp_x,	\
		 _FP_MUL_MEAT_DW_2_gmp_y, 2);		\
    }							\
  while (0)

#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y)				\
  do									\
    {									\
      _FP_FRAC_DECL_4 (_FP_MUL_MEAT_2_gmp_z);				\
									\
      _FP_MUL_MEAT_DW_2_gmp ((wfracbits), _FP_MUL_MEAT_2_gmp_z, X, Y);	\
									\
      /* Normalize since we know where the msb of the multiplicands	\
	 were (bit B), we know that the msb of the of the product is	\
	 at either 2B or 2B-1.  */					\
      _FP_FRAC_SRS_4 (_FP_MUL_MEAT_2_gmp_z, (wfracbits)-1,		\
		      2*(wfracbits));					\
      R##_f0 = _FP_MUL_MEAT_2_gmp_z_f[0];				\
      R##_f1 = _FP_MUL_MEAT_2_gmp_z_f[1];				\
    }									\
  while (0)

/* Do at most 120x120=240 bits multiplication using double floating
   point multiplication.  This is useful if floating point
   multiplication has much bigger throughput than integer multiply.
   It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
   between 106 and 120 only.
   Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
   SETFETZ is a macro which will disable all FPU exceptions and set rounding
   towards zero,  RESETFE should optionally reset it back.  */

#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \
  do									\
    {									\
      static const double _const[] =					\
	{								\
	  /* 2^-24 */ 5.9604644775390625e-08,				\
	  /* 2^-48 */ 3.5527136788005009e-15,				\
	  /* 2^-72 */ 2.1175823681357508e-22,				\
	  /* 2^-96 */ 1.2621774483536189e-29,				\
	  /* 2^28 */ 2.68435456e+08,					\
	  /* 2^4 */ 1.600000e+01,					\
	  /* 2^-20 */ 9.5367431640625e-07,				\
	  /* 2^-44 */ 5.6843418860808015e-14,				\
	  /* 2^-68 */ 3.3881317890172014e-21,				\
	  /* 2^-92 */ 2.0194839173657902e-28,				\
	  /* 2^-116 */ 1.2037062152420224e-35				\
	};								\
      double _a240, _b240, _c240, _d240, _e240, _f240,			\
	_g240, _h240, _i240, _j240, _k240;				\
      union { double d; UDItype i; } _l240, _m240, _n240, _o240,	\
				       _p240, _q240, _r240, _s240;	\
      UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0;		\
									\
      _FP_STATIC_ASSERT ((wfracbits) >= 106 && (wfracbits) <= 120,	\
			 "wfracbits out of range");			\
									\
      setfetz;								\
									\
      _e240 = (double) (long) (X##_f0 & 0xffffff);			\
      _j240 = (double) (long) (Y##_f0 & 0xffffff);			\
      _d240 = (double) (long) ((X##_f0 >> 24) & 0xffffff);		\
      _i240 = (double) (long) ((Y##_f0 >> 24) & 0xffffff);		\
      _c240 = (double) (long) (((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \
      _h240 = (double) (long) (((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \
      _b240 = (double) (long) ((X##_f1 >> 8) & 0xffffff);		\
      _g240 = (double) (long) ((Y##_f1 >> 8) & 0xffffff);		\
      _a240 = (double) (long) (X##_f1 >> 32);				\
      _f240 = (double) (long) (Y##_f1 >> 32);				\
      _e240 *= _const[3];						\
      _j240 *= _const[3];						\
      _d240 *= _const[2];						\
      _i240 *= _const[2];						\
      _c240 *= _const[1];						\
      _h240 *= _const[1];						\
      _b240 *= _const[0];						\
      _g240 *= _const[0];						\
      _s240.d =							      _e240*_j240; \
      _r240.d =						_d240*_j240 + _e240*_i240; \
      _q240.d =				  _c240*_j240 + _d240*_i240 + _e240*_h240; \
      _p240.d =		    _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240; \
      _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240; \
      _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240;	\
      _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240;		\
      _l240.d = _a240*_g240 + _b240*_f240;				\
      _k240 =   _a240*_f240;						\
      _r240.d += _s240.d;						\
      _q240.d += _r240.d;						\
      _p240.d += _q240.d;						\
      _o240.d += _p240.d;						\
      _n240.d += _o240.d;						\
      _m240.d += _n240.d;						\
      _l240.d += _m240.d;						\
      _k240 += _l240.d;							\
      _s240.d -= ((_const[10]+_s240.d)-_const[10]);			\
      _r240.d -= ((_const[9]+_r240.d)-_const[9]);			\
      _q240.d -= ((_const[8]+_q240.d)-_const[8]);			\
      _p240.d -= ((_const[7]+_p240.d)-_const[7]);			\
      _o240.d += _const[7];						\
      _n240.d += _const[6];						\
      _m240.d += _const[5];						\
      _l240.d += _const[4];						\
      if (_s240.d != 0.0)						\
	_y240 = 1;							\
      if (_r240.d != 0.0)						\
	_y240 = 1;							\
      if (_q240.d != 0.0)						\
	_y240 = 1;							\
      if (_p240.d != 0.0)						\
	_y240 = 1;							\
      _t240 = (DItype) _k240;						\
      _u240 = _l240.i;							\
      _v240 = _m240.i;							\
      _w240 = _n240.i;							\
      _x240 = _o240.i;							\
      R##_f1 = ((_t240 << (128 - (wfracbits - 1)))			\
		| ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)));	\
      R##_f0 = (((_u240 & 0xffffff) << (168 - (wfracbits - 1)))		\
		| ((_v240 & 0xffffff) << (144 - (wfracbits - 1)))	\
		| ((_w240 & 0xffffff) << (120 - (wfracbits - 1)))	\
		| ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96))	\
		| _y240);						\
      resetfe;								\
    }									\
  while (0)

/* Division algorithms: */

#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y)				\
  do									\
    {									\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f2;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f1;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_n_f0;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f1;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_r_f0;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f1;				\
      _FP_W_TYPE _FP_DIV_MEAT_2_udiv_m_f0;				\
      if (_FP_FRAC_GE_2 (X, Y))						\
	{								\
	  _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1 >> 1;			\
	  _FP_DIV_MEAT_2_udiv_n_f1					\
	    = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1;		\
	  _FP_DIV_MEAT_2_udiv_n_f0					\
	    = X##_f0 << (_FP_W_TYPE_SIZE - 1);				\
	}								\
      else								\
	{								\
	  R##_e--;							\
	  _FP_DIV_MEAT_2_udiv_n_f2 = X##_f1;				\
	  _FP_DIV_MEAT_2_udiv_n_f1 = X##_f0;				\
	  _FP_DIV_MEAT_2_udiv_n_f0 = 0;					\
	}								\
									\
      /* Normalize, i.e. make the most significant bit of the		\
	 denominator set.  */						\
      _FP_FRAC_SLL_2 (Y, _FP_WFRACXBITS_##fs);				\
									\
      udiv_qrnnd (R##_f1, _FP_DIV_MEAT_2_udiv_r_f1,			\
		  _FP_DIV_MEAT_2_udiv_n_f2, _FP_DIV_MEAT_2_udiv_n_f1,	\
		  Y##_f1);						\
      umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1, _FP_DIV_MEAT_2_udiv_m_f0,	\
		 R##_f1, Y##_f0);					\
      _FP_DIV_MEAT_2_udiv_r_f0 = _FP_DIV_MEAT_2_udiv_n_f0;		\
      if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m, _FP_DIV_MEAT_2_udiv_r))	\
	{								\
	  R##_f1--;							\
	  _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y,			\
			  _FP_DIV_MEAT_2_udiv_r);			\
	  if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y)			\
	      && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m,			\
				_FP_DIV_MEAT_2_udiv_r))			\
	    {								\
	      R##_f1--;							\
	      _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y,			\
			      _FP_DIV_MEAT_2_udiv_r);			\
	    }								\
	}								\
      _FP_FRAC_DEC_2 (_FP_DIV_MEAT_2_udiv_r, _FP_DIV_MEAT_2_udiv_m);	\
									\
      if (_FP_DIV_MEAT_2_udiv_r_f1 == Y##_f1)				\
	{								\
	  /* This is a special case, not an optimization		\
	     (_FP_DIV_MEAT_2_udiv_r/Y##_f1 would not fit into UWtype).	\
	     As _FP_DIV_MEAT_2_udiv_r is guaranteed to be < Y,		\
	     R##_f0 can be either (UWtype)-1 or (UWtype)-2.  But as we	\
	     know what kind of bits it is (sticky, guard, round),	\
	     we don't care.  We also don't care what the reminder is,	\
	     because the guard bit will be set anyway.  -jj */		\
	  R##_f0 = -1;							\
	}								\
      else								\
	{								\
	  udiv_qrnnd (R##_f0, _FP_DIV_MEAT_2_udiv_r_f1,			\
		      _FP_DIV_MEAT_2_udiv_r_f1,				\
		      _FP_DIV_MEAT_2_udiv_r_f0, Y##_f1);		\
	  umul_ppmm (_FP_DIV_MEAT_2_udiv_m_f1,				\
		     _FP_DIV_MEAT_2_udiv_m_f0, R##_f0, Y##_f0);		\
	  _FP_DIV_MEAT_2_udiv_r_f0 = 0;					\
	  if (_FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m,			\
			     _FP_DIV_MEAT_2_udiv_r))			\
	    {								\
	      R##_f0--;							\
	      _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y,			\
			      _FP_DIV_MEAT_2_udiv_r);			\
	      if (_FP_FRAC_GE_2 (_FP_DIV_MEAT_2_udiv_r, Y)		\
		  && _FP_FRAC_GT_2 (_FP_DIV_MEAT_2_udiv_m,		\
				    _FP_DIV_MEAT_2_udiv_r))		\
		{							\
		  R##_f0--;						\
		  _FP_FRAC_ADD_2 (_FP_DIV_MEAT_2_udiv_r, Y,		\
				  _FP_DIV_MEAT_2_udiv_r);		\
		}							\
	    }								\
	  if (!_FP_FRAC_EQ_2 (_FP_DIV_MEAT_2_udiv_r,			\
			      _FP_DIV_MEAT_2_udiv_m))			\
	    R##_f0 |= _FP_WORK_STICKY;					\
	}								\
    }									\
  while (0)


/* Square root algorithms:
   We have just one right now, maybe Newton approximation
   should be added for those machines where division is fast.  */

#define _FP_SQRT_MEAT_2(R, S, T, X, q)				\
  do								\
    {								\
      while (q)							\
	{							\
	  T##_f1 = S##_f1 + (q);				\
	  if (T##_f1 <= X##_f1)					\
	    {							\
	      S##_f1 = T##_f1 + (q);				\
	      X##_f1 -= T##_f1;					\
	      R##_f1 += (q);					\
	    }							\
	  _FP_FRAC_SLL_2 (X, 1);				\
	  (q) >>= 1;						\
	}							\
      (q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1);		\
      while ((q) != _FP_WORK_ROUND)				\
	{							\
	  T##_f0 = S##_f0 + (q);				\
	  T##_f1 = S##_f1;					\
	  if (T##_f1 < X##_f1					\
	      || (T##_f1 == X##_f1 && T##_f0 <= X##_f0))	\
	    {							\
	      S##_f0 = T##_f0 + (q);				\
	      S##_f1 += (T##_f0 > S##_f0);			\
	      _FP_FRAC_DEC_2 (X, T);				\
	      R##_f0 += (q);					\
	    }							\
	  _FP_FRAC_SLL_2 (X, 1);				\
	  (q) >>= 1;						\
	}							\
      if (X##_f0 | X##_f1)					\
	{							\
	  if (S##_f1 < X##_f1					\
	      || (S##_f1 == X##_f1 && S##_f0 < X##_f0))		\
	    R##_f0 |= _FP_WORK_ROUND;				\
	  R##_f0 |= _FP_WORK_STICKY;				\
	}							\
    }								\
  while (0)


/* Assembly/disassembly for converting to/from integral types.
   No shifting or overflow handled here.  */

#define _FP_FRAC_ASSEMBLE_2(r, X, rsize)	\
  (void) (((rsize) <= _FP_W_TYPE_SIZE)		\
	  ? ({ (r) = X##_f0; })			\
	  : ({					\
	      (r) = X##_f1;			\
	      (r) <<= _FP_W_TYPE_SIZE;		\
	      (r) += X##_f0;			\
	    }))

#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize)	\
  do						\
    {						\
      X##_f0 = (r);				\
      X##_f1 = ((rsize) <= _FP_W_TYPE_SIZE	\
		? 0				\
		: (r) >> _FP_W_TYPE_SIZE);	\
    }						\
  while (0)

/* Convert FP values between word sizes.  */

#define _FP_FRAC_COPY_1_2(D, S)		(D##_f = S##_f0)

#define _FP_FRAC_COPY_2_1(D, S)		((D##_f0 = S##_f), (D##_f1 = 0))

#define _FP_FRAC_COPY_2_2(D, S)		_FP_FRAC_COPY_2 (D, S)

#endif /* !SOFT_FP_OP_2_H */