source: Daodan/MSYS2/mingw32/include/c++/11.2.0/tr1/cmath@ 1177

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[1166]1// TR1 cmath -*- C++ -*-
2
3// Copyright (C) 2006-2021 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file tr1/cmath
26 * This is a TR1 C++ Library header.
27 */
28
29#ifndef _GLIBCXX_TR1_CMATH
30#define _GLIBCXX_TR1_CMATH 1
31
32#pragma GCC system_header
33
34#include <cmath>
35
36#ifdef _GLIBCXX_USE_C99_MATH_TR1
37
38#undef acosh
39#undef acoshf
40#undef acoshl
41#undef asinh
42#undef asinhf
43#undef asinhl
44#undef atanh
45#undef atanhf
46#undef atanhl
47#undef cbrt
48#undef cbrtf
49#undef cbrtl
50#undef copysign
51#undef copysignf
52#undef copysignl
53#undef erf
54#undef erff
55#undef erfl
56#undef erfc
57#undef erfcf
58#undef erfcl
59#undef exp2
60#undef exp2f
61#undef exp2l
62#undef expm1
63#undef expm1f
64#undef expm1l
65#undef fdim
66#undef fdimf
67#undef fdiml
68#undef fma
69#undef fmaf
70#undef fmal
71#undef fmax
72#undef fmaxf
73#undef fmaxl
74#undef fmin
75#undef fminf
76#undef fminl
77#undef hypot
78#undef hypotf
79#undef hypotl
80#undef ilogb
81#undef ilogbf
82#undef ilogbl
83#undef lgamma
84#undef lgammaf
85#undef lgammal
86#undef llrint
87#undef llrintf
88#undef llrintl
89#undef llround
90#undef llroundf
91#undef llroundl
92#undef log1p
93#undef log1pf
94#undef log1pl
95#undef log2
96#undef log2f
97#undef log2l
98#undef logb
99#undef logbf
100#undef logbl
101#undef lrint
102#undef lrintf
103#undef lrintl
104#undef lround
105#undef lroundf
106#undef lroundl
107#undef nan
108#undef nanf
109#undef nanl
110#undef nearbyint
111#undef nearbyintf
112#undef nearbyintl
113#undef nextafter
114#undef nextafterf
115#undef nextafterl
116#undef nexttoward
117#undef nexttowardf
118#undef nexttowardl
119#undef remainder
120#undef remainderf
121#undef remainderl
122#undef remquo
123#undef remquof
124#undef remquol
125#undef rint
126#undef rintf
127#undef rintl
128#undef round
129#undef roundf
130#undef roundl
131#undef scalbln
132#undef scalblnf
133#undef scalblnl
134#undef scalbn
135#undef scalbnf
136#undef scalbnl
137#undef tgamma
138#undef tgammaf
139#undef tgammal
140#undef trunc
141#undef truncf
142#undef truncl
143
144#endif
145
146namespace std _GLIBCXX_VISIBILITY(default)
147{
148_GLIBCXX_BEGIN_NAMESPACE_VERSION
149
150namespace tr1
151{
152#if _GLIBCXX_USE_C99_MATH_TR1
153
154 // Using declarations to bring names from libc's <math.h> into std::tr1.
155
156 // types
157 using ::double_t;
158 using ::float_t;
159
160 // functions
161 using ::acosh;
162 using ::acoshf;
163 using ::acoshl;
164
165 using ::asinh;
166 using ::asinhf;
167 using ::asinhl;
168
169 using ::atanh;
170 using ::atanhf;
171 using ::atanhl;
172
173 using ::cbrt;
174 using ::cbrtf;
175 using ::cbrtl;
176
177 using ::copysign;
178 using ::copysignf;
179 using ::copysignl;
180
181 using ::erf;
182 using ::erff;
183 using ::erfl;
184
185 using ::erfc;
186 using ::erfcf;
187 using ::erfcl;
188
189 using ::exp2;
190 using ::exp2f;
191 using ::exp2l;
192
193 using ::expm1;
194 using ::expm1f;
195 using ::expm1l;
196
197 using ::fdim;
198 using ::fdimf;
199 using ::fdiml;
200
201 using ::fma;
202 using ::fmaf;
203 using ::fmal;
204
205 using ::fmax;
206 using ::fmaxf;
207 using ::fmaxl;
208
209 using ::fmin;
210 using ::fminf;
211 using ::fminl;
212
213 using ::hypot;
214 using ::hypotf;
215 using ::hypotl;
216
217 using ::ilogb;
218 using ::ilogbf;
219 using ::ilogbl;
220
221 using ::lgamma;
222 using ::lgammaf;
223 using ::lgammal;
224
225 using ::llrint;
226 using ::llrintf;
227 using ::llrintl;
228
229 using ::llround;
230 using ::llroundf;
231 using ::llroundl;
232
233 using ::log1p;
234 using ::log1pf;
235 using ::log1pl;
236
237 using ::log2;
238 using ::log2f;
239 using ::log2l;
240
241 using ::logb;
242 using ::logbf;
243 using ::logbl;
244
245 using ::lrint;
246 using ::lrintf;
247 using ::lrintl;
248
249 using ::lround;
250 using ::lroundf;
251 using ::lroundl;
252
253 using ::nan;
254 using ::nanf;
255 using ::nanl;
256
257 using ::nearbyint;
258 using ::nearbyintf;
259 using ::nearbyintl;
260
261 using ::nextafter;
262 using ::nextafterf;
263 using ::nextafterl;
264
265 using ::nexttoward;
266 using ::nexttowardf;
267 using ::nexttowardl;
268
269 using ::remainder;
270 using ::remainderf;
271 using ::remainderl;
272
273 using ::remquo;
274 using ::remquof;
275 using ::remquol;
276
277 using ::rint;
278 using ::rintf;
279 using ::rintl;
280
281 using ::round;
282 using ::roundf;
283 using ::roundl;
284
285 using ::scalbln;
286 using ::scalblnf;
287 using ::scalblnl;
288
289 using ::scalbn;
290 using ::scalbnf;
291 using ::scalbnl;
292
293 using ::tgamma;
294 using ::tgammaf;
295 using ::tgammal;
296
297 using ::trunc;
298 using ::truncf;
299 using ::truncl;
300
301#endif
302
303#if _GLIBCXX_USE_C99_MATH
304#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
305
306 /// Function template definitions [8.16.3].
307 template<typename _Tp>
308 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
309 int>::__type
310 fpclassify(_Tp __f)
311 {
312 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
313 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
314 FP_SUBNORMAL, FP_ZERO, __type(__f));
315 }
316
317 template<typename _Tp>
318 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
319 int>::__type
320 isfinite(_Tp __f)
321 {
322 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
323 return __builtin_isfinite(__type(__f));
324 }
325
326 template<typename _Tp>
327 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
328 int>::__type
329 isinf(_Tp __f)
330 {
331 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
332 return __builtin_isinf(__type(__f));
333 }
334
335 template<typename _Tp>
336 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
337 int>::__type
338 isnan(_Tp __f)
339 {
340 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
341 return __builtin_isnan(__type(__f));
342 }
343
344 template<typename _Tp>
345 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
346 int>::__type
347 isnormal(_Tp __f)
348 {
349 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
350 return __builtin_isnormal(__type(__f));
351 }
352
353 template<typename _Tp>
354 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
355 int>::__type
356 signbit(_Tp __f)
357 {
358 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
359 return __builtin_signbit(__type(__f));
360 }
361
362 template<typename _Tp>
363 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
364 int>::__type
365 isgreater(_Tp __f1, _Tp __f2)
366 {
367 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
368 return __builtin_isgreater(__type(__f1), __type(__f2));
369 }
370
371 template<typename _Tp>
372 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
373 int>::__type
374 isgreaterequal(_Tp __f1, _Tp __f2)
375 {
376 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
377 return __builtin_isgreaterequal(__type(__f1), __type(__f2));
378 }
379
380 template<typename _Tp>
381 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
382 int>::__type
383 isless(_Tp __f1, _Tp __f2)
384 {
385 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
386 return __builtin_isless(__type(__f1), __type(__f2));
387 }
388
389 template<typename _Tp>
390 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
391 int>::__type
392 islessequal(_Tp __f1, _Tp __f2)
393 {
394 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
395 return __builtin_islessequal(__type(__f1), __type(__f2));
396 }
397
398 template<typename _Tp>
399 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
400 int>::__type
401 islessgreater(_Tp __f1, _Tp __f2)
402 {
403 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
404 return __builtin_islessgreater(__type(__f1), __type(__f2));
405 }
406
407 template<typename _Tp>
408 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
409 int>::__type
410 isunordered(_Tp __f1, _Tp __f2)
411 {
412 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
413 return __builtin_isunordered(__type(__f1), __type(__f2));
414 }
415
416#endif
417#endif
418
419#if _GLIBCXX_USE_C99_MATH_TR1
420
421 /** Additional overloads [8.16.4].
422 * @{
423 */
424
425 // For functions defined in C++03 the additional overloads are already
426 // declared in <cmath> so we can just re-declare them in std::tr1.
427
428 using std::acos;
429 using std::asin;
430 using std::atan;
431 using std::atan2;
432 using std::ceil;
433 using std::cos;
434 using std::cosh;
435 using std::exp;
436 using std::floor;
437 using std::fmod;
438 using std::frexp;
439 using std::ldexp;
440 using std::log;
441 using std::log10;
442 using std::sin;
443 using std::sinh;
444 using std::sqrt;
445 using std::tan;
446 using std::tanh;
447
448#if __cplusplus >= 201103L
449
450 // Since C++11, <cmath> defines additional overloads for these functions
451 // in namespace std.
452
453 using std::acosh;
454 using std::asinh;
455 using std::atanh;
456 using std::cbrt;
457 using std::copysign;
458 using std::erf;
459 using std::erfc;
460 using std::exp2;
461 using std::expm1;
462 using std::fdim;
463 using std::fma;
464 using std::fmax;
465 using std::fmin;
466 using std::hypot;
467 using std::ilogb;
468 using std::lgamma;
469 using std::llrint;
470 using std::llround;
471 using std::log1p;
472 using std::log2;
473 using std::logb;
474 using std::lrint;
475 using std::lround;
476 using std::nan;
477 using std::nearbyint;
478 using std::nextafter;
479 using std::nexttoward;
480 using std::remainder;
481 using std::remquo;
482 using std::rint;
483 using std::round;
484 using std::scalbln;
485 using std::scalbn;
486 using std::tgamma;
487 using std::trunc;
488
489#else // __cplusplus < 201103L
490
491 // In C++03 we need to provide the additional overloads.
492
493#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
494 inline float
495 acosh(float __x)
496 { return __builtin_acoshf(__x); }
497
498 inline long double
499 acosh(long double __x)
500 { return __builtin_acoshl(__x); }
501#endif
502
503 template<typename _Tp>
504 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
505 double>::__type
506 acosh(_Tp __x)
507 { return __builtin_acosh(__x); }
508
509#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
510 inline float
511 asinh(float __x)
512 { return __builtin_asinhf(__x); }
513
514 inline long double
515 asinh(long double __x)
516 { return __builtin_asinhl(__x); }
517#endif
518
519 template<typename _Tp>
520 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
521 double>::__type
522 asinh(_Tp __x)
523 { return __builtin_asinh(__x); }
524
525#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
526 inline float
527 atanh(float __x)
528 { return __builtin_atanhf(__x); }
529
530 inline long double
531 atanh(long double __x)
532 { return __builtin_atanhl(__x); }
533#endif
534
535 template<typename _Tp>
536 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
537 double>::__type
538 atanh(_Tp __x)
539 { return __builtin_atanh(__x); }
540
541#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
542 inline float
543 cbrt(float __x)
544 { return __builtin_cbrtf(__x); }
545
546 inline long double
547 cbrt(long double __x)
548 { return __builtin_cbrtl(__x); }
549#endif
550
551 template<typename _Tp>
552 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
553 double>::__type
554 cbrt(_Tp __x)
555 { return __builtin_cbrt(__x); }
556
557#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
558 inline float
559 copysign(float __x, float __y)
560 { return __builtin_copysignf(__x, __y); }
561
562 inline long double
563 copysign(long double __x, long double __y)
564 { return __builtin_copysignl(__x, __y); }
565#endif
566
567 template<typename _Tp, typename _Up>
568 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
569 copysign(_Tp __x, _Up __y)
570 {
571 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
572 return copysign(__type(__x), __type(__y));
573 }
574
575#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
576 inline float
577 erf(float __x)
578 { return __builtin_erff(__x); }
579
580 inline long double
581 erf(long double __x)
582 { return __builtin_erfl(__x); }
583#endif
584
585 template<typename _Tp>
586 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
587 double>::__type
588 erf(_Tp __x)
589 { return __builtin_erf(__x); }
590
591#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
592 inline float
593 erfc(float __x)
594 { return __builtin_erfcf(__x); }
595
596 inline long double
597 erfc(long double __x)
598 { return __builtin_erfcl(__x); }
599#endif
600
601 template<typename _Tp>
602 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
603 double>::__type
604 erfc(_Tp __x)
605 { return __builtin_erfc(__x); }
606
607#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
608 inline float
609 exp2(float __x)
610 { return __builtin_exp2f(__x); }
611
612 inline long double
613 exp2(long double __x)
614 { return __builtin_exp2l(__x); }
615#endif
616
617 template<typename _Tp>
618 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
619 double>::__type
620 exp2(_Tp __x)
621 { return __builtin_exp2(__x); }
622
623#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
624 inline float
625 expm1(float __x)
626 { return __builtin_expm1f(__x); }
627
628 inline long double
629 expm1(long double __x)
630 { return __builtin_expm1l(__x); }
631#endif
632
633 template<typename _Tp>
634 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
635 double>::__type
636 expm1(_Tp __x)
637 { return __builtin_expm1(__x); }
638
639#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
640 inline float
641 fdim(float __x, float __y)
642 { return __builtin_fdimf(__x, __y); }
643
644 inline long double
645 fdim(long double __x, long double __y)
646 { return __builtin_fdiml(__x, __y); }
647#endif
648
649 template<typename _Tp, typename _Up>
650 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
651 fdim(_Tp __x, _Up __y)
652 {
653 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
654 return fdim(__type(__x), __type(__y));
655 }
656
657#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
658 inline float
659 fma(float __x, float __y, float __z)
660 { return __builtin_fmaf(__x, __y, __z); }
661
662 inline long double
663 fma(long double __x, long double __y, long double __z)
664 { return __builtin_fmal(__x, __y, __z); }
665#endif
666
667 template<typename _Tp, typename _Up, typename _Vp>
668 inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
669 fma(_Tp __x, _Up __y, _Vp __z)
670 {
671 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
672 return fma(__type(__x), __type(__y), __type(__z));
673 }
674
675#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
676 inline float
677 fmax(float __x, float __y)
678 { return __builtin_fmaxf(__x, __y); }
679
680 inline long double
681 fmax(long double __x, long double __y)
682 { return __builtin_fmaxl(__x, __y); }
683#endif
684
685 template<typename _Tp, typename _Up>
686 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
687 fmax(_Tp __x, _Up __y)
688 {
689 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
690 return fmax(__type(__x), __type(__y));
691 }
692
693#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
694 inline float
695 fmin(float __x, float __y)
696 { return __builtin_fminf(__x, __y); }
697
698 inline long double
699 fmin(long double __x, long double __y)
700 { return __builtin_fminl(__x, __y); }
701#endif
702
703 template<typename _Tp, typename _Up>
704 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
705 fmin(_Tp __x, _Up __y)
706 {
707 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
708 return fmin(__type(__x), __type(__y));
709 }
710
711#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
712 inline float
713 hypot(float __x, float __y)
714 { return __builtin_hypotf(__x, __y); }
715
716 inline long double
717 hypot(long double __x, long double __y)
718 { return __builtin_hypotl(__x, __y); }
719#endif
720
721 template<typename _Tp, typename _Up>
722 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
723 hypot(_Tp __y, _Up __x)
724 {
725 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
726 return hypot(__type(__y), __type(__x));
727 }
728
729#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
730 inline int
731 ilogb(float __x)
732 { return __builtin_ilogbf(__x); }
733
734 inline int
735 ilogb(long double __x)
736 { return __builtin_ilogbl(__x); }
737#endif
738
739 template<typename _Tp>
740 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
741 int>::__type
742 ilogb(_Tp __x)
743 { return __builtin_ilogb(__x); }
744
745#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
746 inline float
747 lgamma(float __x)
748 { return __builtin_lgammaf(__x); }
749
750 inline long double
751 lgamma(long double __x)
752 { return __builtin_lgammal(__x); }
753#endif
754
755 template<typename _Tp>
756 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
757 double>::__type
758 lgamma(_Tp __x)
759 { return __builtin_lgamma(__x); }
760
761#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
762 inline long long
763 llrint(float __x)
764 { return __builtin_llrintf(__x); }
765
766 inline long long
767 llrint(long double __x)
768 { return __builtin_llrintl(__x); }
769#endif
770
771 template<typename _Tp>
772 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
773 long long>::__type
774 llrint(_Tp __x)
775 { return __builtin_llrint(__x); }
776
777#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
778 inline long long
779 llround(float __x)
780 { return __builtin_llroundf(__x); }
781
782 inline long long
783 llround(long double __x)
784 { return __builtin_llroundl(__x); }
785#endif
786
787 template<typename _Tp>
788 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
789 long long>::__type
790 llround(_Tp __x)
791 { return __builtin_llround(__x); }
792
793#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
794 inline float
795 log1p(float __x)
796 { return __builtin_log1pf(__x); }
797
798 inline long double
799 log1p(long double __x)
800 { return __builtin_log1pl(__x); }
801#endif
802
803 template<typename _Tp>
804 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
805 double>::__type
806 log1p(_Tp __x)
807 { return __builtin_log1p(__x); }
808
809 // DR 568.
810#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
811 inline float
812 log2(float __x)
813 { return __builtin_log2f(__x); }
814
815 inline long double
816 log2(long double __x)
817 { return __builtin_log2l(__x); }
818#endif
819
820 template<typename _Tp>
821 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
822 double>::__type
823 log2(_Tp __x)
824 { return __builtin_log2(__x); }
825
826#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
827 inline float
828 logb(float __x)
829 { return __builtin_logbf(__x); }
830
831 inline long double
832 logb(long double __x)
833 { return __builtin_logbl(__x); }
834#endif
835
836 template<typename _Tp>
837 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
838 double>::__type
839 logb(_Tp __x)
840 {
841 return __builtin_logb(__x);
842 }
843
844#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
845 inline long
846 lrint(float __x)
847 { return __builtin_lrintf(__x); }
848
849 inline long
850 lrint(long double __x)
851 { return __builtin_lrintl(__x); }
852#endif
853
854 template<typename _Tp>
855 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
856 long>::__type
857 lrint(_Tp __x)
858 { return __builtin_lrint(__x); }
859
860#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
861 inline long
862 lround(float __x)
863 { return __builtin_lroundf(__x); }
864
865 inline long
866 lround(long double __x)
867 { return __builtin_lroundl(__x); }
868#endif
869
870 template<typename _Tp>
871 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
872 long>::__type
873 lround(_Tp __x)
874 { return __builtin_lround(__x); }
875
876#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
877 inline float
878 nearbyint(float __x)
879 { return __builtin_nearbyintf(__x); }
880
881 inline long double
882 nearbyint(long double __x)
883 { return __builtin_nearbyintl(__x); }
884#endif
885
886 template<typename _Tp>
887 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
888 double>::__type
889 nearbyint(_Tp __x)
890 { return __builtin_nearbyint(__x); }
891
892#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
893 inline float
894 nextafter(float __x, float __y)
895 { return __builtin_nextafterf(__x, __y); }
896
897 inline long double
898 nextafter(long double __x, long double __y)
899 { return __builtin_nextafterl(__x, __y); }
900#endif
901
902 template<typename _Tp, typename _Up>
903 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
904 nextafter(_Tp __x, _Up __y)
905 {
906 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
907 return nextafter(__type(__x), __type(__y));
908 }
909
910#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
911 inline float
912 nexttoward(float __x, long double __y)
913 { return __builtin_nexttowardf(__x, __y); }
914
915 inline long double
916 nexttoward(long double __x, long double __y)
917 { return __builtin_nexttowardl(__x, __y); }
918#endif
919
920 template<typename _Tp>
921 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
922 double>::__type
923 nexttoward(_Tp __x, long double __y)
924 { return __builtin_nexttoward(__x, __y); }
925
926#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
927 inline float
928 remainder(float __x, float __y)
929 { return __builtin_remainderf(__x, __y); }
930
931 inline long double
932 remainder(long double __x, long double __y)
933 { return __builtin_remainderl(__x, __y); }
934#endif
935
936 template<typename _Tp, typename _Up>
937 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
938 remainder(_Tp __x, _Up __y)
939 {
940 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
941 return remainder(__type(__x), __type(__y));
942 }
943
944#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
945 inline float
946 remquo(float __x, float __y, int* __pquo)
947 { return __builtin_remquof(__x, __y, __pquo); }
948
949 inline long double
950 remquo(long double __x, long double __y, int* __pquo)
951 { return __builtin_remquol(__x, __y, __pquo); }
952#endif
953
954 template<typename _Tp, typename _Up>
955 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
956 remquo(_Tp __x, _Up __y, int* __pquo)
957 {
958 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
959 return remquo(__type(__x), __type(__y), __pquo);
960 }
961
962#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
963 inline float
964 rint(float __x)
965 { return __builtin_rintf(__x); }
966
967 inline long double
968 rint(long double __x)
969 { return __builtin_rintl(__x); }
970#endif
971
972 template<typename _Tp>
973 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
974 double>::__type
975 rint(_Tp __x)
976 { return __builtin_rint(__x); }
977
978#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
979 inline float
980 round(float __x)
981 { return __builtin_roundf(__x); }
982
983 inline long double
984 round(long double __x)
985 { return __builtin_roundl(__x); }
986#endif
987
988 template<typename _Tp>
989 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
990 double>::__type
991 round(_Tp __x)
992 { return __builtin_round(__x); }
993
994#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
995 inline float
996 scalbln(float __x, long __ex)
997 { return __builtin_scalblnf(__x, __ex); }
998
999 inline long double
1000 scalbln(long double __x, long __ex)
1001 { return __builtin_scalblnl(__x, __ex); }
1002#endif
1003
1004 template<typename _Tp>
1005 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1006 double>::__type
1007 scalbln(_Tp __x, long __ex)
1008 { return __builtin_scalbln(__x, __ex); }
1009
1010#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1011 inline float
1012 scalbn(float __x, int __ex)
1013 { return __builtin_scalbnf(__x, __ex); }
1014
1015 inline long double
1016 scalbn(long double __x, int __ex)
1017 { return __builtin_scalbnl(__x, __ex); }
1018#endif
1019
1020 template<typename _Tp>
1021 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1022 double>::__type
1023 scalbn(_Tp __x, int __ex)
1024 { return __builtin_scalbn(__x, __ex); }
1025
1026#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1027 inline float
1028 tgamma(float __x)
1029 { return __builtin_tgammaf(__x); }
1030
1031 inline long double
1032 tgamma(long double __x)
1033 { return __builtin_tgammal(__x); }
1034#endif
1035
1036 template<typename _Tp>
1037 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1038 double>::__type
1039 tgamma(_Tp __x)
1040 { return __builtin_tgamma(__x); }
1041
1042#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1043 inline float
1044 trunc(float __x)
1045 { return __builtin_truncf(__x); }
1046
1047 inline long double
1048 trunc(long double __x)
1049 { return __builtin_truncl(__x); }
1050#endif
1051
1052 template<typename _Tp>
1053 inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1054 double>::__type
1055 trunc(_Tp __x)
1056 { return __builtin_trunc(__x); }
1057
1058#endif // __cplusplus < 201103L
1059
1060 /// @}
1061
1062#endif /* _GLIBCXX_USE_C99_MATH_TR1 */
1063
1064 // DR 550. What should the return type of pow(float,int) be?
1065 // NB: C++11 and TR1 != C++03.
1066
1067 // We cannot do "using std::pow;" because that would bring in unwanted
1068 // pow(*, int) overloads in C++03, with the wrong return type. Instead we
1069 // define all the necessary overloads, but the std::tr1::pow(double, double)
1070 // overload cannot be provided here, because <tr1/math.h> would add it to
1071 // the global namespace where it would clash with ::pow(double,double) from
1072 // libc (revealed by the fix of PR c++/54537).
1073 // The solution is to forward std::tr1::pow(double,double) to
1074 // std::pow(double,double) via the function template below. See
1075 // the discussion about this issue here:
1076 // http://gcc.gnu.org/ml/gcc-patches/2012-09/msg01278.html
1077
1078#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1079 inline float
1080 pow(float __x, float __y)
1081 { return std::pow(__x, __y); }
1082
1083 inline long double
1084 pow(long double __x, long double __y)
1085 { return std::pow(__x, __y); }
1086#endif
1087
1088 template<typename _Tp, typename _Up>
1089 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1090 pow(_Tp __x, _Up __y)
1091 {
1092 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1093 return std::pow(__type(__x), __type(__y));
1094 }
1095
1096#if __cplusplus >= 201103L
1097 // We also deal with fabs in a special way, because "using std::fabs;"
1098 // could bring in C++11's std::fabs<T>(const std::complex<T>&) with a
1099 // different return type from std::tr1::fabs<T>(const std::complex<T>&).
1100 // We define the necessary overloads, except std::tr1::fabs(double) which
1101 // could clash with ::fabs(double) from libc.
1102 // The function template handles double as well as integers, forwarding
1103 // to std::fabs.
1104
1105#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
1106#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1107 inline float
1108 fabs(float __x)
1109 { return __builtin_fabsf(__x); }
1110
1111 inline long double
1112 fabs(long double __x)
1113 { return __builtin_fabsl(__x); }
1114#endif
1115#endif
1116
1117 template<typename _Tp>
1118 inline typename __gnu_cxx::__promote<_Tp>::__type
1119 fabs(_Tp __x)
1120 { return std::fabs(__x); }
1121
1122#else // ! C++11
1123
1124 // For C++03 just use std::fabs as there is no overload for std::complex<>.
1125 using std::fabs;
1126
1127#endif // C++11
1128
1129} // namespace tr1
1130_GLIBCXX_END_NAMESPACE_VERSION
1131} // namespace std
1132
1133/**
1134 * @defgroup tr1_math_spec_func TR1 Mathematical Special Functions
1135 * @ingroup numerics
1136 *
1137 * A collection of advanced mathematical special functions.
1138 */
1139
1140#if _GLIBCXX_USE_STD_SPEC_FUNCS
1141
1142namespace std _GLIBCXX_VISIBILITY(default)
1143{
1144_GLIBCXX_BEGIN_NAMESPACE_VERSION
1145
1146namespace tr1
1147{
1148 using std::assoc_laguerref;
1149 using std::assoc_laguerrel;
1150 using std::assoc_laguerre;
1151
1152 using std::assoc_legendref;
1153 using std::assoc_legendrel;
1154 using std::assoc_legendre;
1155
1156 using std::betaf;
1157 using std::betal;
1158 using std::beta;
1159
1160 using std::comp_ellint_1f;
1161 using std::comp_ellint_1l;
1162 using std::comp_ellint_1;
1163
1164 using std::comp_ellint_2f;
1165 using std::comp_ellint_2l;
1166 using std::comp_ellint_2;
1167
1168 using std::comp_ellint_3f;
1169 using std::comp_ellint_3l;
1170 using std::comp_ellint_3;
1171
1172 using std::cyl_bessel_if;
1173 using std::cyl_bessel_il;
1174 using std::cyl_bessel_i;
1175
1176 using std::cyl_bessel_jf;
1177 using std::cyl_bessel_jl;
1178 using std::cyl_bessel_j;
1179
1180 using std::cyl_bessel_kf;
1181 using std::cyl_bessel_kl;
1182 using std::cyl_bessel_k;
1183
1184 using std::cyl_neumannf;
1185 using std::cyl_neumannl;
1186 using std::cyl_neumann;
1187
1188 using std::ellint_1f;
1189 using std::ellint_1l;
1190 using std::ellint_1;
1191
1192 using std::ellint_2f;
1193 using std::ellint_2l;
1194 using std::ellint_2;
1195
1196 using std::ellint_3f;
1197 using std::ellint_3l;
1198 using std::ellint_3;
1199
1200 using std::expintf;
1201 using std::expintl;
1202 using std::expint;
1203
1204 using std::hermitef;
1205 using std::hermitel;
1206 using std::hermite;
1207
1208 using std::laguerref;
1209 using std::laguerrel;
1210 using std::laguerre;
1211
1212 using std::legendref;
1213 using std::legendrel;
1214 using std::legendre;
1215
1216 using std::riemann_zetaf;
1217 using std::riemann_zetal;
1218 using std::riemann_zeta;
1219
1220 using std::sph_besself;
1221 using std::sph_bessell;
1222 using std::sph_bessel;
1223
1224 using std::sph_legendref;
1225 using std::sph_legendrel;
1226 using std::sph_legendre;
1227
1228 using std::sph_neumannf;
1229 using std::sph_neumannl;
1230 using std::sph_neumann;
1231
1232} // namespace tr1
1233_GLIBCXX_END_NAMESPACE_VERSION
1234} // namespace std
1235
1236#else // ! _GLIBCXX_USE_STD_SPEC_FUNCS
1237
1238#include <bits/stl_algobase.h>
1239#include <limits>
1240#include <tr1/type_traits>
1241
1242#include <tr1/gamma.tcc>
1243#include <tr1/bessel_function.tcc>
1244#include <tr1/beta_function.tcc>
1245#include <tr1/ell_integral.tcc>
1246#include <tr1/exp_integral.tcc>
1247#include <tr1/legendre_function.tcc>
1248#include <tr1/modified_bessel_func.tcc>
1249#include <tr1/poly_hermite.tcc>
1250#include <tr1/poly_laguerre.tcc>
1251#include <tr1/riemann_zeta.tcc>
1252
1253namespace std _GLIBCXX_VISIBILITY(default)
1254{
1255_GLIBCXX_BEGIN_NAMESPACE_VERSION
1256namespace tr1
1257 {
1258 /** @addtogroup tr1_math_spec_func
1259 * @{
1260 */
1261
1262 inline float
1263 assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1264 { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1265
1266 inline long double
1267 assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1268 {
1269 return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1270 }
1271
1272 /// 5.2.1.1 Associated Laguerre polynomials.
1273 template<typename _Tp>
1274 inline typename __gnu_cxx::__promote<_Tp>::__type
1275 assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1276 {
1277 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1278 return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1279 }
1280
1281 inline float
1282 assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1283 { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1284
1285 inline long double
1286 assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1287 { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1288
1289 /// 5.2.1.2 Associated Legendre functions.
1290 template<typename _Tp>
1291 inline typename __gnu_cxx::__promote<_Tp>::__type
1292 assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1293 {
1294 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1295 return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1296 }
1297
1298 inline float
1299 betaf(float __x, float __y)
1300 { return __detail::__beta<float>(__x, __y); }
1301
1302 inline long double
1303 betal(long double __x, long double __y)
1304 { return __detail::__beta<long double>(__x, __y); }
1305
1306 /// 5.2.1.3 Beta functions.
1307 template<typename _Tpx, typename _Tpy>
1308 inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1309 beta(_Tpx __x, _Tpy __y)
1310 {
1311 typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1312 return __detail::__beta<__type>(__x, __y);
1313 }
1314
1315 inline float
1316 comp_ellint_1f(float __k)
1317 { return __detail::__comp_ellint_1<float>(__k); }
1318
1319 inline long double
1320 comp_ellint_1l(long double __k)
1321 { return __detail::__comp_ellint_1<long double>(__k); }
1322
1323 /// 5.2.1.4 Complete elliptic integrals of the first kind.
1324 template<typename _Tp>
1325 inline typename __gnu_cxx::__promote<_Tp>::__type
1326 comp_ellint_1(_Tp __k)
1327 {
1328 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1329 return __detail::__comp_ellint_1<__type>(__k);
1330 }
1331
1332 inline float
1333 comp_ellint_2f(float __k)
1334 { return __detail::__comp_ellint_2<float>(__k); }
1335
1336 inline long double
1337 comp_ellint_2l(long double __k)
1338 { return __detail::__comp_ellint_2<long double>(__k); }
1339
1340 /// 5.2.1.5 Complete elliptic integrals of the second kind.
1341 template<typename _Tp>
1342 inline typename __gnu_cxx::__promote<_Tp>::__type
1343 comp_ellint_2(_Tp __k)
1344 {
1345 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1346 return __detail::__comp_ellint_2<__type>(__k);
1347 }
1348
1349 inline float
1350 comp_ellint_3f(float __k, float __nu)
1351 { return __detail::__comp_ellint_3<float>(__k, __nu); }
1352
1353 inline long double
1354 comp_ellint_3l(long double __k, long double __nu)
1355 { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1356
1357 /// 5.2.1.6 Complete elliptic integrals of the third kind.
1358 template<typename _Tp, typename _Tpn>
1359 inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1360 comp_ellint_3(_Tp __k, _Tpn __nu)
1361 {
1362 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1363 return __detail::__comp_ellint_3<__type>(__k, __nu);
1364 }
1365
1366 inline float
1367 cyl_bessel_if(float __nu, float __x)
1368 { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1369
1370 inline long double
1371 cyl_bessel_il(long double __nu, long double __x)
1372 { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1373
1374 /// 5.2.1.8 Regular modified cylindrical Bessel functions.
1375 template<typename _Tpnu, typename _Tp>
1376 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1377 cyl_bessel_i(_Tpnu __nu, _Tp __x)
1378 {
1379 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1380 return __detail::__cyl_bessel_i<__type>(__nu, __x);
1381 }
1382
1383 inline float
1384 cyl_bessel_jf(float __nu, float __x)
1385 { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1386
1387 inline long double
1388 cyl_bessel_jl(long double __nu, long double __x)
1389 { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1390
1391 /// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
1392 template<typename _Tpnu, typename _Tp>
1393 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1394 cyl_bessel_j(_Tpnu __nu, _Tp __x)
1395 {
1396 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1397 return __detail::__cyl_bessel_j<__type>(__nu, __x);
1398 }
1399
1400 inline float
1401 cyl_bessel_kf(float __nu, float __x)
1402 { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1403
1404 inline long double
1405 cyl_bessel_kl(long double __nu, long double __x)
1406 { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1407
1408 /// 5.2.1.10 Irregular modified cylindrical Bessel functions.
1409 template<typename _Tpnu, typename _Tp>
1410 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1411 cyl_bessel_k(_Tpnu __nu, _Tp __x)
1412 {
1413 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1414 return __detail::__cyl_bessel_k<__type>(__nu, __x);
1415 }
1416
1417 inline float
1418 cyl_neumannf(float __nu, float __x)
1419 { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1420
1421 inline long double
1422 cyl_neumannl(long double __nu, long double __x)
1423 { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1424
1425 /// 5.2.1.11 Cylindrical Neumann functions.
1426 template<typename _Tpnu, typename _Tp>
1427 inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1428 cyl_neumann(_Tpnu __nu, _Tp __x)
1429 {
1430 typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1431 return __detail::__cyl_neumann_n<__type>(__nu, __x);
1432 }
1433
1434 inline float
1435 ellint_1f(float __k, float __phi)
1436 { return __detail::__ellint_1<float>(__k, __phi); }
1437
1438 inline long double
1439 ellint_1l(long double __k, long double __phi)
1440 { return __detail::__ellint_1<long double>(__k, __phi); }
1441
1442 /// 5.2.1.12 Incomplete elliptic integrals of the first kind.
1443 template<typename _Tp, typename _Tpp>
1444 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1445 ellint_1(_Tp __k, _Tpp __phi)
1446 {
1447 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1448 return __detail::__ellint_1<__type>(__k, __phi);
1449 }
1450
1451 inline float
1452 ellint_2f(float __k, float __phi)
1453 { return __detail::__ellint_2<float>(__k, __phi); }
1454
1455 inline long double
1456 ellint_2l(long double __k, long double __phi)
1457 { return __detail::__ellint_2<long double>(__k, __phi); }
1458
1459 /// 5.2.1.13 Incomplete elliptic integrals of the second kind.
1460 template<typename _Tp, typename _Tpp>
1461 inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1462 ellint_2(_Tp __k, _Tpp __phi)
1463 {
1464 typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1465 return __detail::__ellint_2<__type>(__k, __phi);
1466 }
1467
1468 inline float
1469 ellint_3f(float __k, float __nu, float __phi)
1470 { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1471
1472 inline long double
1473 ellint_3l(long double __k, long double __nu, long double __phi)
1474 { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1475
1476 /// 5.2.1.14 Incomplete elliptic integrals of the third kind.
1477 template<typename _Tp, typename _Tpn, typename _Tpp>
1478 inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1479 ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1480 {
1481 typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1482 return __detail::__ellint_3<__type>(__k, __nu, __phi);
1483 }
1484
1485 inline float
1486 expintf(float __x)
1487 { return __detail::__expint<float>(__x); }
1488
1489 inline long double
1490 expintl(long double __x)
1491 { return __detail::__expint<long double>(__x); }
1492
1493 /// 5.2.1.15 Exponential integrals.
1494 template<typename _Tp>
1495 inline typename __gnu_cxx::__promote<_Tp>::__type
1496 expint(_Tp __x)
1497 {
1498 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1499 return __detail::__expint<__type>(__x);
1500 }
1501
1502 inline float
1503 hermitef(unsigned int __n, float __x)
1504 { return __detail::__poly_hermite<float>(__n, __x); }
1505
1506 inline long double
1507 hermitel(unsigned int __n, long double __x)
1508 { return __detail::__poly_hermite<long double>(__n, __x); }
1509
1510 /// 5.2.1.16 Hermite polynomials.
1511 template<typename _Tp>
1512 inline typename __gnu_cxx::__promote<_Tp>::__type
1513 hermite(unsigned int __n, _Tp __x)
1514 {
1515 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1516 return __detail::__poly_hermite<__type>(__n, __x);
1517 }
1518
1519 inline float
1520 laguerref(unsigned int __n, float __x)
1521 { return __detail::__laguerre<float>(__n, __x); }
1522
1523 inline long double
1524 laguerrel(unsigned int __n, long double __x)
1525 { return __detail::__laguerre<long double>(__n, __x); }
1526
1527 /// 5.2.1.18 Laguerre polynomials.
1528 template<typename _Tp>
1529 inline typename __gnu_cxx::__promote<_Tp>::__type
1530 laguerre(unsigned int __n, _Tp __x)
1531 {
1532 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1533 return __detail::__laguerre<__type>(__n, __x);
1534 }
1535
1536 inline float
1537 legendref(unsigned int __n, float __x)
1538 { return __detail::__poly_legendre_p<float>(__n, __x); }
1539
1540 inline long double
1541 legendrel(unsigned int __n, long double __x)
1542 { return __detail::__poly_legendre_p<long double>(__n, __x); }
1543
1544 /// 5.2.1.19 Legendre polynomials.
1545 template<typename _Tp>
1546 inline typename __gnu_cxx::__promote<_Tp>::__type
1547 legendre(unsigned int __n, _Tp __x)
1548 {
1549 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1550 return __detail::__poly_legendre_p<__type>(__n, __x);
1551 }
1552
1553 inline float
1554 riemann_zetaf(float __x)
1555 { return __detail::__riemann_zeta<float>(__x); }
1556
1557 inline long double
1558 riemann_zetal(long double __x)
1559 { return __detail::__riemann_zeta<long double>(__x); }
1560
1561 /// 5.2.1.20 Riemann zeta function.
1562 template<typename _Tp>
1563 inline typename __gnu_cxx::__promote<_Tp>::__type
1564 riemann_zeta(_Tp __x)
1565 {
1566 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1567 return __detail::__riemann_zeta<__type>(__x);
1568 }
1569
1570 inline float
1571 sph_besself(unsigned int __n, float __x)
1572 { return __detail::__sph_bessel<float>(__n, __x); }
1573
1574 inline long double
1575 sph_bessell(unsigned int __n, long double __x)
1576 { return __detail::__sph_bessel<long double>(__n, __x); }
1577
1578 /// 5.2.1.21 Spherical Bessel functions.
1579 template<typename _Tp>
1580 inline typename __gnu_cxx::__promote<_Tp>::__type
1581 sph_bessel(unsigned int __n, _Tp __x)
1582 {
1583 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1584 return __detail::__sph_bessel<__type>(__n, __x);
1585 }
1586
1587 inline float
1588 sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1589 { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1590
1591 inline long double
1592 sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1593 { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1594
1595 /// 5.2.1.22 Spherical associated Legendre functions.
1596 template<typename _Tp>
1597 inline typename __gnu_cxx::__promote<_Tp>::__type
1598 sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1599 {
1600 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1601 return __detail::__sph_legendre<__type>(__l, __m, __theta);
1602 }
1603
1604 inline float
1605 sph_neumannf(unsigned int __n, float __x)
1606 { return __detail::__sph_neumann<float>(__n, __x); }
1607
1608 inline long double
1609 sph_neumannl(unsigned int __n, long double __x)
1610 { return __detail::__sph_neumann<long double>(__n, __x); }
1611
1612 /// 5.2.1.23 Spherical Neumann functions.
1613 template<typename _Tp>
1614 inline typename __gnu_cxx::__promote<_Tp>::__type
1615 sph_neumann(unsigned int __n, _Tp __x)
1616 {
1617 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1618 return __detail::__sph_neumann<__type>(__n, __x);
1619 }
1620
1621 /// @} tr1_math_spec_func
1622
1623} // namespace tr1
1624
1625_GLIBCXX_END_NAMESPACE_VERSION
1626} // namespace std
1627
1628#endif // _GLIBCXX_USE_STD_SPEC_FUNCS
1629
1630#if _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1631namespace std _GLIBCXX_VISIBILITY(default)
1632{
1633_GLIBCXX_BEGIN_NAMESPACE_VERSION
1634
1635namespace tr1
1636{
1637 using __gnu_cxx::conf_hypergf;
1638 using __gnu_cxx::conf_hypergl;
1639 using __gnu_cxx::conf_hyperg;
1640
1641 using __gnu_cxx::hypergf;
1642 using __gnu_cxx::hypergl;
1643 using __gnu_cxx::hyperg;
1644} // namespace tr1
1645
1646_GLIBCXX_END_NAMESPACE_VERSION
1647} // namespace std
1648
1649#else // ! (_GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__))
1650
1651#include <bits/stl_algobase.h>
1652#include <limits>
1653#include <tr1/type_traits>
1654
1655#include <tr1/hypergeometric.tcc>
1656
1657namespace std _GLIBCXX_VISIBILITY(default)
1658{
1659_GLIBCXX_BEGIN_NAMESPACE_VERSION
1660
1661namespace tr1
1662{
1663 /** @addtogroup tr1_math_spec_func
1664 * @{
1665 */
1666
1667 inline float
1668 conf_hypergf(float __a, float __c, float __x)
1669 { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1670
1671 inline long double
1672 conf_hypergl(long double __a, long double __c, long double __x)
1673 { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1674
1675 /// 5.2.1.7 Confluent hypergeometric functions.
1676 template<typename _Tpa, typename _Tpc, typename _Tp>
1677 inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1678 conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1679 {
1680 typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1681 return __detail::__conf_hyperg<__type>(__a, __c, __x);
1682 }
1683
1684 inline float
1685 hypergf(float __a, float __b, float __c, float __x)
1686 { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1687
1688 inline long double
1689 hypergl(long double __a, long double __b, long double __c, long double __x)
1690 { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1691
1692 /// 5.2.1.17 Hypergeometric functions.
1693 template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1694 inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1695 hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1696 {
1697 typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1698 return __detail::__hyperg<__type>(__a, __b, __c, __x);
1699 }
1700
1701 /// @} tr1_math_spec_func
1702
1703} // namespace tr1
1704
1705_GLIBCXX_END_NAMESPACE_VERSION
1706} // namespace std
1707#endif // _GLIBCXX_USE_STD_SPEC_FUNCS && !defined(__STRICT_ANSI__)
1708
1709#endif // _GLIBCXX_TR1_CMATH
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