summary refs log tree commit diff
path: root/math/tgmath.h
blob: d37a1567f8af916a9b6d5664c329d19046752d40 (plain) (blame)
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
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
/* Copyright (C) 1997-2019 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.

   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
   <http://www.gnu.org/licenses/>.  */

/*
 *	ISO C99 Standard: 7.22 Type-generic math	<tgmath.h>
 */

#ifndef _TGMATH_H
#define _TGMATH_H	1

#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
#include <bits/libc-header-start.h>

/* Include the needed headers.  */
#include <bits/floatn.h>
#include <math.h>
#include <complex.h>


/* There are two variant implementations of type-generic macros in
   this file: one for GCC 8 and later, using __builtin_tgmath and
   where each macro expands each of its arguments only once, and one
   for older GCC, using other compiler extensions but with macros
   expanding their arguments many times (so resulting in exponential
   blowup of the size of expansions when calls to such macros are
   nested inside arguments to such macros).  */

#define __HAVE_BUILTIN_TGMATH __GNUC_PREREQ (8, 0)

#if __GNUC_PREREQ (2, 7)

# if __HAVE_BUILTIN_TGMATH

#  if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F16_ARG(X) X ## f16,
#  else
#   define __TG_F16_ARG(X)
#  endif
#  if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F32_ARG(X) X ## f32,
#  else
#   define __TG_F32_ARG(X)
#  endif
#  if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F64_ARG(X) X ## f64,
#  else
#   define __TG_F64_ARG(X)
#  endif
#  if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F128_ARG(X) X ## f128,
#  else
#   define __TG_F128_ARG(X)
#  endif
#  if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F32X_ARG(X) X ## f32x,
#  else
#   define __TG_F32X_ARG(X)
#  endif
#  if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F64X_ARG(X) X ## f64x,
#  else
#   define __TG_F64X_ARG(X)
#  endif
#  if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   define __TG_F128X_ARG(X) X ## f128x,
#  else
#   define __TG_F128X_ARG(X)
#  endif

#  define __TGMATH_FUNCS(X) X ## f, X, X ## l,				\
    __TG_F16_ARG (X) __TG_F32_ARG (X) __TG_F64_ARG (X) __TG_F128_ARG (X) \
    __TG_F32X_ARG (X) __TG_F64X_ARG (X) __TG_F128X_ARG (X)
#  define __TGMATH_RCFUNCS(F, C) __TGMATH_FUNCS (F) __TGMATH_FUNCS (C)
#  define __TGMATH_1(F, X) __builtin_tgmath (__TGMATH_FUNCS (F) (X))
#  define __TGMATH_2(F, X, Y) __builtin_tgmath (__TGMATH_FUNCS (F) (X), (Y))
#  define __TGMATH_2STD(F, X, Y) __builtin_tgmath (F ## f, F, F ## l, (X), (Y))
#  define __TGMATH_3(F, X, Y, Z) __builtin_tgmath (__TGMATH_FUNCS (F)	\
						   (X), (Y), (Z))
#  define __TGMATH_1C(F, C, X) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) (X))
#  define __TGMATH_2C(F, C, X, Y) __builtin_tgmath (__TGMATH_RCFUNCS (F, C) \
						    (X), (Y))

# else /* !__HAVE_BUILTIN_TGMATH.  */

#  ifdef __NO_LONG_DOUBLE_MATH
#   define __tgml(fct) fct
#  else
#   define __tgml(fct) fct ## l
#  endif

/* __floating_type expands to 1 if TYPE is a floating type (including
   complex floating types), 0 if TYPE is an integer type (including
   complex integer types).  __real_integer_type expands to 1 if TYPE
   is a real integer type.  __complex_integer_type expands to 1 if
   TYPE is a complex integer type.  All these macros expand to integer
   constant expressions.  All these macros can assume their argument
   has an arithmetic type (not vector, decimal floating-point or
   fixed-point), valid to pass to tgmath.h macros.  */
#  if __GNUC_PREREQ (3, 1)
/* __builtin_classify_type expands to an integer constant expression
   in GCC 3.1 and later.  Default conversions applied to the argument
   of __builtin_classify_type mean it always returns 1 for real
   integer types rather than ever returning different values for
   character, boolean or enumerated types.  */
#   define __floating_type(type)				\
  (__builtin_classify_type (__real__ ((type) 0)) == 8)
#   define __real_integer_type(type)		\
  (__builtin_classify_type ((type) 0) == 1)
#   define __complex_integer_type(type)				\
  (__builtin_classify_type ((type) 0) == 9			\
   && __builtin_classify_type (__real__ ((type) 0)) == 1)
#  else
/* GCC versions predating __builtin_classify_type are also looser on
   what counts as an integer constant expression.  */
#   define __floating_type(type) (((type) 1.25) != 1)
#   define __real_integer_type(type) (((type) (1.25 + _Complex_I)) == 1)
#   define __complex_integer_type(type)			\
  (((type) (1.25 + _Complex_I)) == (1 + _Complex_I))
#  endif

/* Whether an expression (of arithmetic type) has a real type.  */
#  define __expr_is_real(E) (__builtin_classify_type (E) != 9)

/* The tgmath real type for T, where E is 0 if T is an integer type
   and 1 for a floating type.  If T has a complex type, it is
   unspecified whether the return type is real or complex (but it has
   the correct corresponding real type).  */
#  define __tgmath_real_type_sub(T, E) \
  __typeof__ (*(0 ? (__typeof__ (0 ? (double *) 0 : (void *) (E))) 0	      \
		  : (__typeof__ (0 ? (T *) 0 : (void *) (!(E)))) 0))

/* The tgmath real type of EXPR.  */
#  define __tgmath_real_type(expr) \
  __tgmath_real_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),	      \
			  __floating_type (__typeof__ (+(expr))))

/* The tgmath complex type for T, where E1 is 1 if T has a floating
   type and 0 otherwise, E2 is 1 if T has a real integer type and 0
   otherwise, and E3 is 1 if T has a complex type and 0 otherwise.  */
#  define __tgmath_complex_type_sub(T, E1, E2, E3)			\
  __typeof__ (*(0							\
		? (__typeof__ (0 ? (T *) 0 : (void *) (!(E1)))) 0	\
		: (__typeof__ (0					\
			       ? (__typeof__ (0				\
					      ? (double *) 0		\
					      : (void *) (!(E2)))) 0	\
			       : (__typeof__ (0				\
					      ? (_Complex double *) 0	\
					      : (void *) (!(E3)))) 0)) 0))

/* The tgmath complex type of EXPR.  */
#  define __tgmath_complex_type(expr)					\
  __tgmath_complex_type_sub (__typeof__ ((__typeof__ (+(expr))) 0),	\
			     __floating_type (__typeof__ (+(expr))),	\
			     __real_integer_type (__typeof__ (+(expr))), \
			     __complex_integer_type (__typeof__ (+(expr))))

#  if (__HAVE_DISTINCT_FLOAT16			\
      || __HAVE_DISTINCT_FLOAT32		\
      || __HAVE_DISTINCT_FLOAT64		\
      || __HAVE_DISTINCT_FLOAT32X		\
      || __HAVE_DISTINCT_FLOAT64X		\
      || __HAVE_DISTINCT_FLOAT128X)
#   error "Unsupported _FloatN or _FloatNx types for <tgmath.h>."
#  endif

/* Expand to text that checks if ARG_COMB has type _Float128, and if
   so calls the appropriately suffixed FCT (which may include a cast),
   or FCT and CFCT for complex functions, with arguments ARG_CALL.  */
#  if __HAVE_DISTINCT_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
#   if (!__HAVE_FLOAT64X			\
       || __HAVE_FLOAT64X_LONG_DOUBLE		\
       || !__HAVE_FLOATN_NOT_TYPEDEF)
#    define __TGMATH_F128(arg_comb, fct, arg_call)			\
  __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)	\
  ? fct ## f128 arg_call :
#    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)		\
  __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
  ? (__expr_is_real (arg_comb)						\
     ? fct ## f128 arg_call						\
     : cfct ## f128 arg_call) :
#   else
/* _Float64x is a distinct type at the C language level, which must be
   handled like _Float128.  */
#    define __TGMATH_F128(arg_comb, fct, arg_call)			\
  (__builtin_types_compatible_p (__typeof (+(arg_comb)), _Float128)	\
   || __builtin_types_compatible_p (__typeof (+(arg_comb)), _Float64x)) \
  ? fct ## f128 arg_call :
#    define __TGMATH_CF128(arg_comb, fct, cfct, arg_call)		\
  (__builtin_types_compatible_p (__typeof (+__real__ (arg_comb)), _Float128) \
   || __builtin_types_compatible_p (__typeof (+__real__ (arg_comb)),	\
				    _Float64x))				\
  ? (__expr_is_real (arg_comb)						\
     ? fct ## f128 arg_call						\
     : cfct ## f128 arg_call) :
#   endif
#  else
#   define __TGMATH_F128(arg_comb, fct, arg_call) /* Nothing.  */
#   define __TGMATH_CF128(arg_comb, fct, cfct, arg_call) /* Nothing.  */
#  endif

# endif /* !__HAVE_BUILTIN_TGMATH.  */

/* We have two kinds of generic macros: to support functions which are
   only defined on real valued parameters and those which are defined
   for complex functions as well.  */
# if __HAVE_BUILTIN_TGMATH

#  define __TGMATH_UNARY_REAL_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
#  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) __TGMATH_1 (Fct, (Val))
#  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct)	\
  __TGMATH_2 (Fct, (Val1), (Val2))
#  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct)	\
  __TGMATH_2STD (Fct, (Val1), (Val2))
#  define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct)	\
  __TGMATH_2 (Fct, (Val1), (Val2))
#  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct)	\
  __TGMATH_2STD (Fct, (Val1), (Val2))
#  define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct)	\
  __TGMATH_2 (Fct, (Val1), (Val2))
#  define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
#  define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct)	\
  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
#  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct)	\
  __TGMATH_3 (Fct, (Val1), (Val2), (Val3))
#  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct)	\
  __TGMATH_1C (Fct, Cfct, (Val))
#  define __TGMATH_UNARY_IMAG(Val, Cfct) __TGMATH_1 (Cfct, (Val))
#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct)	\
  __TGMATH_1C (Fct, Cfct, (Val))
#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)	\
  __TGMATH_1 (Cfct, (Val))
#  define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct)	\
  __TGMATH_2C (Fct, Cfct, (Val1), (Val2))

# else /* !__HAVE_BUILTIN_TGMATH.  */

#  define __TGMATH_UNARY_REAL_ONLY(Val, Fct)				\
  (__extension__ ((sizeof (+(Val)) == sizeof (double)			      \
		      || __builtin_classify_type (Val) != 8)		      \
		     ? (__tgmath_real_type (Val)) Fct (Val)		      \
		     : (sizeof (+(Val)) == sizeof (float))		      \
		     ? (__tgmath_real_type (Val)) Fct##f (Val)		      \
		     : __TGMATH_F128 ((Val), (__tgmath_real_type (Val)) Fct,  \
				      (Val))				      \
		     (__tgmath_real_type (Val)) __tgml(Fct) (Val)))

#  define __TGMATH_UNARY_REAL_RET_ONLY(Val, Fct) \
     (__extension__ ((sizeof (+(Val)) == sizeof (double)		      \
		      || __builtin_classify_type (Val) != 8)		      \
		     ? Fct (Val)					      \
		     : (sizeof (+(Val)) == sizeof (float))		      \
		     ? Fct##f (Val)					      \
		     : __TGMATH_F128 ((Val), Fct, (Val))		      \
		     __tgml(Fct) (Val)))

#  define __TGMATH_BINARY_FIRST_REAL_ONLY(Val1, Val2, Fct) \
     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		      \
		      || __builtin_classify_type (Val1) != 8)		      \
		     ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)	      \
		     : (sizeof (+(Val1)) == sizeof (float))		      \
		     ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)	      \
		     : __TGMATH_F128 ((Val1), (__tgmath_real_type (Val1)) Fct, \
				    (Val1, Val2))			      \
		     (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))

#  define __TGMATH_BINARY_FIRST_REAL_STD_ONLY(Val1, Val2, Fct) \
     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		      \
		      || __builtin_classify_type (Val1) != 8)		      \
		     ? (__tgmath_real_type (Val1)) Fct (Val1, Val2)	      \
		     : (sizeof (+(Val1)) == sizeof (float))		      \
		     ? (__tgmath_real_type (Val1)) Fct##f (Val1, Val2)	      \
		     : (__tgmath_real_type (Val1)) __tgml(Fct) (Val1, Val2)))

#  define __TGMATH_BINARY_REAL_ONLY(Val1, Val2, Fct) \
     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
		     ? __TGMATH_F128 ((Val1) + (Val2),			      \
				      (__typeof				      \
				       ((__tgmath_real_type (Val1)) 0	      \
					+ (__tgmath_real_type (Val2)) 0)) Fct, \
				      (Val1, Val2))			      \
		     (__typeof ((__tgmath_real_type (Val1)) 0		      \
				+ (__tgmath_real_type (Val2)) 0))	      \
		     __tgml(Fct) (Val1, Val2)				      \
		     : (sizeof (+(Val1)) == sizeof (double)		      \
			|| sizeof (+(Val2)) == sizeof (double)		      \
			|| __builtin_classify_type (Val1) != 8		      \
			|| __builtin_classify_type (Val2) != 8)		      \
		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct (Val1, Val2)					      \
		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct##f (Val1, Val2)))

#  define __TGMATH_BINARY_REAL_STD_ONLY(Val1, Val2, Fct) \
     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
				  + (__tgmath_real_type (Val2)) 0))	      \
		       __tgml(Fct) (Val1, Val2)				      \
		     : (sizeof (+(Val1)) == sizeof (double)		      \
			|| sizeof (+(Val2)) == sizeof (double)		      \
			|| __builtin_classify_type (Val1) != 8		      \
			|| __builtin_classify_type (Val2) != 8)		      \
		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct (Val1, Val2)					      \
		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct##f (Val1, Val2)))

#  define __TGMATH_BINARY_REAL_RET_ONLY(Val1, Val2, Fct) \
     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
		     ? __TGMATH_F128 ((Val1) + (Val2), Fct, (Val1, Val2))     \
		     __tgml(Fct) (Val1, Val2)				      \
		     : (sizeof (+(Val1)) == sizeof (double)		      \
			|| sizeof (+(Val2)) == sizeof (double)		      \
			|| __builtin_classify_type (Val1) != 8		      \
			|| __builtin_classify_type (Val2) != 8)		      \
		     ? Fct (Val1, Val2)					      \
		     : Fct##f (Val1, Val2)))

#  define __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY(Val1, Val2, Val3, Fct) \
     (__extension__ ((sizeof ((Val1) + (Val2)) > sizeof (double)	      \
		      && __builtin_classify_type ((Val1) + (Val2)) == 8)      \
		     ? __TGMATH_F128 ((Val1) + (Val2),			      \
				      (__typeof				      \
				       ((__tgmath_real_type (Val1)) 0	      \
					+ (__tgmath_real_type (Val2)) 0)) Fct, \
				      (Val1, Val2, Val3))		      \
		     (__typeof ((__tgmath_real_type (Val1)) 0		      \
				+ (__tgmath_real_type (Val2)) 0))	      \
		     __tgml(Fct) (Val1, Val2, Val3)			      \
		     : (sizeof (+(Val1)) == sizeof (double)		      \
			|| sizeof (+(Val2)) == sizeof (double)		      \
			|| __builtin_classify_type (Val1) != 8		      \
			|| __builtin_classify_type (Val2) != 8)		      \
		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct (Val1, Val2, Val3)				      \
		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0))	      \
		       Fct##f (Val1, Val2, Val3)))

#  define __TGMATH_TERNARY_REAL_ONLY(Val1, Val2, Val3, Fct) \
     (__extension__ ((sizeof ((Val1) + (Val2) + (Val3)) > sizeof (double)     \
		      && __builtin_classify_type ((Val1) + (Val2) + (Val3))   \
			 == 8)						      \
		     ? __TGMATH_F128 ((Val1) + (Val2) + (Val3),		      \
				      (__typeof				      \
				       ((__tgmath_real_type (Val1)) 0	      \
					+ (__tgmath_real_type (Val2)) 0	      \
					+ (__tgmath_real_type (Val3)) 0)) Fct, \
				      (Val1, Val2, Val3))		      \
		     (__typeof ((__tgmath_real_type (Val1)) 0		      \
				+ (__tgmath_real_type (Val2)) 0		      \
				+ (__tgmath_real_type (Val3)) 0))	      \
		       __tgml(Fct) (Val1, Val2, Val3)			      \
		     : (sizeof (+(Val1)) == sizeof (double)		      \
			|| sizeof (+(Val2)) == sizeof (double)		      \
			|| sizeof (+(Val3)) == sizeof (double)		      \
			|| __builtin_classify_type (Val1) != 8		      \
			|| __builtin_classify_type (Val2) != 8		      \
			|| __builtin_classify_type (Val3) != 8)		      \
		     ? (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0	      \
				   + (__tgmath_real_type (Val3)) 0))	      \
		       Fct (Val1, Val2, Val3)				      \
		     : (__typeof ((__tgmath_real_type (Val1)) 0		      \
				   + (__tgmath_real_type (Val2)) 0	      \
				   + (__tgmath_real_type (Val3)) 0))	      \
		       Fct##f (Val1, Val2, Val3)))

#  define __TGMATH_TERNARY_FIRST_REAL_RET_ONLY(Val1, Val2, Val3, Fct) \
     (__extension__ ((sizeof (+(Val1)) == sizeof (double)		\
		      || __builtin_classify_type (Val1) != 8)		\
		     ? Fct (Val1, Val2, Val3)				\
		     : (sizeof (+(Val1)) == sizeof (float))		\
		     ? Fct##f (Val1, Val2, Val3)			\
		     : __TGMATH_F128 ((Val1), Fct, (Val1, Val2, Val3))	\
		     __tgml(Fct) (Val1, Val2, Val3)))

/* XXX This definition has to be changed as soon as the compiler understands
   the imaginary keyword.  */
#  define __TGMATH_UNARY_REAL_IMAG(Val, Fct, Cfct) \
     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
		     ? (__expr_is_real (Val)				      \
			? (__tgmath_complex_type (Val)) Fct (Val)	      \
			: (__tgmath_complex_type (Val)) Cfct (Val))	      \
		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
		     ? (__expr_is_real (Val)				      \
			? (__tgmath_complex_type (Val)) Fct##f (Val)	      \
			: (__tgmath_complex_type (Val)) Cfct##f (Val))	      \
		     : __TGMATH_CF128 ((Val),				      \
				       (__tgmath_complex_type (Val)) Fct,     \
				       (__tgmath_complex_type (Val)) Cfct,    \
				       (Val))				      \
		     (__expr_is_real (Val)				      \
		      ? (__tgmath_complex_type (Val)) __tgml(Fct) (Val)	      \
		      : (__tgmath_complex_type (Val)) __tgml(Cfct) (Val))))

#  define __TGMATH_UNARY_IMAG(Val, Cfct) \
     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
				    + _Complex_I)) Cfct (Val)		      \
		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
		     ? (__typeof__ ((__tgmath_real_type (Val)) 0	      \
				    + _Complex_I)) Cfct##f (Val)	      \
		     : __TGMATH_F128 (__real__ (Val),			      \
				      (__typeof__			      \
				       ((__tgmath_real_type (Val)) 0	      \
					+ _Complex_I)) Cfct, (Val))	      \
		     (__typeof__ ((__tgmath_real_type (Val)) 0		      \
				  + _Complex_I)) __tgml(Cfct) (Val)))

/* XXX This definition has to be changed as soon as the compiler understands
   the imaginary keyword.  */
#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL(Val, Fct, Cfct) \
     (__extension__ ((sizeof (+__real__ (Val)) == sizeof (double)	      \
		      || __builtin_classify_type (__real__ (Val)) != 8)	      \
		     ? (__expr_is_real (Val)				      \
			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
			  Fct (Val)					      \
			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
			  Cfct (Val))					      \
		     : (sizeof (+__real__ (Val)) == sizeof (float))	      \
		     ? (__expr_is_real (Val)				      \
			? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
			  Fct##f (Val)					      \
			: (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))\
			  Cfct##f (Val))				      \
		     : __TGMATH_CF128 ((Val), \
				       (__typeof__			      \
					(__real__			      \
					 (__tgmath_real_type (Val)) 0)) Fct,  \
				       (__typeof__			      \
					(__real__			      \
					 (__tgmath_real_type (Val)) 0)) Cfct, \
				       (Val))				      \
		     (__expr_is_real (Val)				      \
		      ? (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
		      __tgml(Fct) (Val)					      \
		      : (__typeof__ (__real__ (__tgmath_real_type (Val)) 0))  \
		      __tgml(Cfct) (Val))))
#  define __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME(Val, Cfct)	\
  __TGMATH_UNARY_REAL_IMAG_RET_REAL ((Val), Cfct, Cfct)

/* XXX This definition has to be changed as soon as the compiler understands
   the imaginary keyword.  */
#  define __TGMATH_BINARY_REAL_IMAG(Val1, Val2, Fct, Cfct) \
     (__extension__ ((sizeof (__real__ (Val1)				      \
			      + __real__ (Val2)) > sizeof (double)	      \
		      && __builtin_classify_type (__real__ (Val1)	      \
						  + __real__ (Val2)) == 8)    \
		     ? __TGMATH_CF128 ((Val1) + (Val2),			      \
				       (__typeof			      \
					((__tgmath_complex_type (Val1)) 0     \
					 + (__tgmath_complex_type (Val2)) 0)) \
				       Fct,				      \
				       (__typeof			      \
					((__tgmath_complex_type (Val1)) 0     \
					 + (__tgmath_complex_type (Val2)) 0)) \
				       Cfct,				      \
				       (Val1, Val2))			      \
		     (__expr_is_real ((Val1) + (Val2))			      \
		      ? (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
		      __tgml(Fct) (Val1, Val2)				      \
		      : (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
		      __tgml(Cfct) (Val1, Val2))			      \
		     : (sizeof (+__real__ (Val1)) == sizeof (double)	      \
			|| sizeof (+__real__ (Val2)) == sizeof (double)	      \
			|| __builtin_classify_type (__real__ (Val1)) != 8     \
			|| __builtin_classify_type (__real__ (Val2)) != 8)    \
		     ? (__expr_is_real ((Val1) + (Val2))		      \
			? (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
			  Fct (Val1, Val2)				      \
			: (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
			  Cfct (Val1, Val2))				      \
		     : (__expr_is_real ((Val1) + (Val2))		      \
			? (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
			  Fct##f (Val1, Val2)				      \
			: (__typeof ((__tgmath_complex_type (Val1)) 0	      \
				   + (__tgmath_complex_type (Val2)) 0))	      \
			  Cfct##f (Val1, Val2))))
# endif /* !__HAVE_BUILTIN_TGMATH.  */
#else
# error "Unsupported compiler; you cannot use <tgmath.h>"
#endif


/* Unary functions defined for real and complex values.  */


/* Trigonometric functions.  */

/* Arc cosine of X.  */
#define acos(Val) __TGMATH_UNARY_REAL_IMAG (Val, acos, cacos)
/* Arc sine of X.  */
#define asin(Val) __TGMATH_UNARY_REAL_IMAG (Val, asin, casin)
/* Arc tangent of X.  */
#define atan(Val) __TGMATH_UNARY_REAL_IMAG (Val, atan, catan)
/* Arc tangent of Y/X.  */
#define atan2(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, atan2)

/* Cosine of X.  */
#define cos(Val) __TGMATH_UNARY_REAL_IMAG (Val, cos, ccos)
/* Sine of X.  */
#define sin(Val) __TGMATH_UNARY_REAL_IMAG (Val, sin, csin)
/* Tangent of X.  */
#define tan(Val) __TGMATH_UNARY_REAL_IMAG (Val, tan, ctan)


/* Hyperbolic functions.  */

/* Hyperbolic arc cosine of X.  */
#define acosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, acosh, cacosh)
/* Hyperbolic arc sine of X.  */
#define asinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, asinh, casinh)
/* Hyperbolic arc tangent of X.  */
#define atanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, atanh, catanh)

/* Hyperbolic cosine of X.  */
#define cosh(Val) __TGMATH_UNARY_REAL_IMAG (Val, cosh, ccosh)
/* Hyperbolic sine of X.  */
#define sinh(Val) __TGMATH_UNARY_REAL_IMAG (Val, sinh, csinh)
/* Hyperbolic tangent of X.  */
#define tanh(Val) __TGMATH_UNARY_REAL_IMAG (Val, tanh, ctanh)


/* Exponential and logarithmic functions.  */

/* Exponential function of X.  */
#define exp(Val) __TGMATH_UNARY_REAL_IMAG (Val, exp, cexp)

/* Break VALUE into a normalized fraction and an integral power of 2.  */
#define frexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, frexp)

/* X times (two to the EXP power).  */
#define ldexp(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, ldexp)

/* Natural logarithm of X.  */
#define log(Val) __TGMATH_UNARY_REAL_IMAG (Val, log, clog)

/* Base-ten logarithm of X.  */
#ifdef __USE_GNU
# define log10(Val) __TGMATH_UNARY_REAL_IMAG (Val, log10, clog10)
#else
# define log10(Val) __TGMATH_UNARY_REAL_ONLY (Val, log10)
#endif

/* Return exp(X) - 1.  */
#define expm1(Val) __TGMATH_UNARY_REAL_ONLY (Val, expm1)

/* Return log(1 + X).  */
#define log1p(Val) __TGMATH_UNARY_REAL_ONLY (Val, log1p)

/* Return the base 2 signed integral exponent of X.  */
#define logb(Val) __TGMATH_UNARY_REAL_ONLY (Val, logb)

/* Compute base-2 exponential of X.  */
#define exp2(Val) __TGMATH_UNARY_REAL_ONLY (Val, exp2)

/* Compute base-2 logarithm of X.  */
#define log2(Val) __TGMATH_UNARY_REAL_ONLY (Val, log2)


/* Power functions.  */

/* Return X to the Y power.  */
#define pow(Val1, Val2) __TGMATH_BINARY_REAL_IMAG (Val1, Val2, pow, cpow)

/* Return the square root of X.  */
#define sqrt(Val) __TGMATH_UNARY_REAL_IMAG (Val, sqrt, csqrt)

/* Return `sqrt(X*X + Y*Y)'.  */
#define hypot(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, hypot)

/* Return the cube root of X.  */
#define cbrt(Val) __TGMATH_UNARY_REAL_ONLY (Val, cbrt)


/* Nearest integer, absolute value, and remainder functions.  */

/* Smallest integral value not less than X.  */
#define ceil(Val) __TGMATH_UNARY_REAL_ONLY (Val, ceil)

/* Absolute value of X.  */
#define fabs(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL (Val, fabs, cabs)

/* Largest integer not greater than X.  */
#define floor(Val) __TGMATH_UNARY_REAL_ONLY (Val, floor)

/* Floating-point modulo remainder of X/Y.  */
#define fmod(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmod)

/* Round X to integral valuein floating-point format using current
   rounding direction, but do not raise inexact exception.  */
#define nearbyint(Val) __TGMATH_UNARY_REAL_ONLY (Val, nearbyint)

/* Round X to nearest integral value, rounding halfway cases away from
   zero.  */
#define round(Val) __TGMATH_UNARY_REAL_ONLY (Val, round)

/* Round X to the integral value in floating-point format nearest but
   not larger in magnitude.  */
#define trunc(Val) __TGMATH_UNARY_REAL_ONLY (Val, trunc)

/* Compute remainder of X and Y and put in *QUO a value with sign of x/y
   and magnitude congruent `mod 2^n' to the magnitude of the integral
   quotient x/y, with n >= 3.  */
#define remquo(Val1, Val2, Val3) \
     __TGMATH_TERNARY_FIRST_SECOND_REAL_ONLY (Val1, Val2, Val3, remquo)

/* Round X to nearest integral value according to current rounding
   direction.  */
#define lrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lrint)
#define llrint(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llrint)

/* Round X to nearest integral value, rounding halfway cases away from
   zero.  */
#define lround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, lround)
#define llround(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llround)


/* Return X with its signed changed to Y's.  */
#define copysign(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, copysign)

/* Error and gamma functions.  */
#define erf(Val) __TGMATH_UNARY_REAL_ONLY (Val, erf)
#define erfc(Val) __TGMATH_UNARY_REAL_ONLY (Val, erfc)
#define tgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, tgamma)
#define lgamma(Val) __TGMATH_UNARY_REAL_ONLY (Val, lgamma)


/* Return the integer nearest X in the direction of the
   prevailing rounding mode.  */
#define rint(Val) __TGMATH_UNARY_REAL_ONLY (Val, rint)

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Return X - epsilon.  */
# define nextdown(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextdown)
/* Return X + epsilon.  */
# define nextup(Val) __TGMATH_UNARY_REAL_ONLY (Val, nextup)
#endif

/* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
#define nextafter(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, nextafter)
#define nexttoward(Val1, Val2) \
     __TGMATH_BINARY_FIRST_REAL_STD_ONLY (Val1, Val2, nexttoward)

/* Return the remainder of integer divison X / Y with infinite precision.  */
#define remainder(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, remainder)

/* Return X times (2 to the Nth power).  */
#ifdef __USE_MISC
# define scalb(Val1, Val2) __TGMATH_BINARY_REAL_STD_ONLY (Val1, Val2, scalb)
#endif

/* Return X times (2 to the Nth power).  */
#define scalbn(Val1, Val2) __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbn)

/* Return X times (2 to the Nth power).  */
#define scalbln(Val1, Val2) \
     __TGMATH_BINARY_FIRST_REAL_ONLY (Val1, Val2, scalbln)

/* Return the binary exponent of X, which must be nonzero.  */
#define ilogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, ilogb)


/* Return positive difference between X and Y.  */
#define fdim(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fdim)

/* Return maximum numeric value from X and Y.  */
#define fmax(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmax)

/* Return minimum numeric value from X and Y.  */
#define fmin(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmin)


/* Multiply-add function computed as a ternary operation.  */
#define fma(Val1, Val2, Val3) \
     __TGMATH_TERNARY_REAL_ONLY (Val1, Val2, Val3, fma)

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Round X to nearest integer value, rounding halfway cases to even.  */
# define roundeven(Val) __TGMATH_UNARY_REAL_ONLY (Val, roundeven)

# define fromfp(Val1, Val2, Val3)					\
  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfp)

# define ufromfp(Val1, Val2, Val3)					\
  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfp)

# define fromfpx(Val1, Val2, Val3)					\
  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, fromfpx)

# define ufromfpx(Val1, Val2, Val3)					\
  __TGMATH_TERNARY_FIRST_REAL_RET_ONLY (Val1, Val2, Val3, ufromfpx)

/* Like ilogb, but returning long int.  */
# define llogb(Val) __TGMATH_UNARY_REAL_RET_ONLY (Val, llogb)

/* Return value with maximum magnitude.  */
# define fmaxmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fmaxmag)

/* Return value with minimum magnitude.  */
# define fminmag(Val1, Val2) __TGMATH_BINARY_REAL_ONLY (Val1, Val2, fminmag)

/* Total order operation.  */
# define totalorder(Val1, Val2)					\
  __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalorder)

/* Total order operation on absolute values.  */
# define totalordermag(Val1, Val2)				\
  __TGMATH_BINARY_REAL_RET_ONLY (Val1, Val2, totalordermag)
#endif


/* Absolute value, conjugates, and projection.  */

/* Argument value of Z.  */
#define carg(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, carg)

/* Complex conjugate of Z.  */
#define conj(Val) __TGMATH_UNARY_IMAG (Val, conj)

/* Projection of Z onto the Riemann sphere.  */
#define cproj(Val) __TGMATH_UNARY_IMAG (Val, cproj)


/* Decomposing complex values.  */

/* Imaginary part of Z.  */
#define cimag(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, cimag)

/* Real part of Z.  */
#define creal(Val) __TGMATH_UNARY_REAL_IMAG_RET_REAL_SAME (Val, creal)

#endif /* tgmath.h */