libstdc++
tr1/cmath
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1 // TR1 cmath -*- C++ -*-
2 
3 // Copyright (C) 2006, 2007, 2008, 2009, 2010, 2011
4 // Free Software Foundation, Inc.
5 //
6 // This file is part of the GNU ISO C++ Library. This library is free
7 // software; you can redistribute it and/or modify it under the
8 // terms of the GNU General Public License as published by the
9 // Free Software Foundation; either version 3, or (at your option)
10 // any later version.
11 
12 // This library is distributed in the hope that it will be useful,
13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 // GNU General Public License for more details.
16 
17 // Under Section 7 of GPL version 3, you are granted additional
18 // permissions described in the GCC Runtime Library Exception, version
19 // 3.1, as published by the Free Software Foundation.
20 
21 // You should have received a copy of the GNU General Public License and
22 // a copy of the GCC Runtime Library Exception along with this program;
23 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
24 // <http://www.gnu.org/licenses/>.
25 
26 /** @file tr1/cmath
27  * This is a TR1 C++ Library header.
28  */
29 
30 #ifndef _GLIBCXX_TR1_CMATH
31 #define _GLIBCXX_TR1_CMATH 1
32 
33 #pragma GCC system_header
34 
35 #include <cmath>
36 
37 #ifdef _GLIBCXX_USE_C99_MATH_TR1
38 
39 #undef acosh
40 #undef acoshf
41 #undef acoshl
42 #undef asinh
43 #undef asinhf
44 #undef asinhl
45 #undef atanh
46 #undef atanhf
47 #undef atanhl
48 #undef cbrt
49 #undef cbrtf
50 #undef cbrtl
51 #undef copysign
52 #undef copysignf
53 #undef copysignl
54 #undef erf
55 #undef erff
56 #undef erfl
57 #undef erfc
58 #undef erfcf
59 #undef erfcl
60 #undef exp2
61 #undef exp2f
62 #undef exp2l
63 #undef expm1
64 #undef expm1f
65 #undef expm1l
66 #undef fdim
67 #undef fdimf
68 #undef fdiml
69 #undef fma
70 #undef fmaf
71 #undef fmal
72 #undef fmax
73 #undef fmaxf
74 #undef fmaxl
75 #undef fmin
76 #undef fminf
77 #undef fminl
78 #undef hypot
79 #undef hypotf
80 #undef hypotl
81 #undef ilogb
82 #undef ilogbf
83 #undef ilogbl
84 #undef lgamma
85 #undef lgammaf
86 #undef lgammal
87 #undef llrint
88 #undef llrintf
89 #undef llrintl
90 #undef llround
91 #undef llroundf
92 #undef llroundl
93 #undef log1p
94 #undef log1pf
95 #undef log1pl
96 #undef log2
97 #undef log2f
98 #undef log2l
99 #undef logb
100 #undef logbf
101 #undef logbl
102 #undef lrint
103 #undef lrintf
104 #undef lrintl
105 #undef lround
106 #undef lroundf
107 #undef lroundl
108 #undef nan
109 #undef nanf
110 #undef nanl
111 #undef nearbyint
112 #undef nearbyintf
113 #undef nearbyintl
114 #undef nextafter
115 #undef nextafterf
116 #undef nextafterl
117 #undef nexttoward
118 #undef nexttowardf
119 #undef nexttowardl
120 #undef remainder
121 #undef remainderf
122 #undef remainderl
123 #undef remquo
124 #undef remquof
125 #undef remquol
126 #undef rint
127 #undef rintf
128 #undef rintl
129 #undef round
130 #undef roundf
131 #undef roundl
132 #undef scalbln
133 #undef scalblnf
134 #undef scalblnl
135 #undef scalbn
136 #undef scalbnf
137 #undef scalbnl
138 #undef tgamma
139 #undef tgammaf
140 #undef tgammal
141 #undef trunc
142 #undef truncf
143 #undef truncl
144 
145 #endif
146 
147 namespace std _GLIBCXX_VISIBILITY(default)
148 {
149 namespace tr1
150 {
151 _GLIBCXX_BEGIN_NAMESPACE_VERSION
152 
153 #if _GLIBCXX_USE_C99_MATH_TR1
154 
155  // types
156  using ::double_t;
157  using ::float_t;
158 
159  // functions
161  using ::acoshf;
162  using ::acoshl;
163 
165  using ::asinhf;
166  using ::asinhl;
167 
169  using ::atanhf;
170  using ::atanhl;
171 
172  using ::cbrt;
173  using ::cbrtf;
174  using ::cbrtl;
175 
176  using ::copysign;
177  using ::copysignf;
178  using ::copysignl;
179 
180  using ::erf;
181  using ::erff;
182  using ::erfl;
183 
184  using ::erfc;
185  using ::erfcf;
186  using ::erfcl;
187 
188  using ::exp2;
189  using ::exp2f;
190  using ::exp2l;
191 
192  using ::expm1;
193  using ::expm1f;
194  using ::expm1l;
195 
196  using ::fdim;
197  using ::fdimf;
198  using ::fdiml;
199 
200  using ::fma;
201  using ::fmaf;
202  using ::fmal;
203 
204  using ::fmax;
205  using ::fmaxf;
206  using ::fmaxl;
207 
208  using ::fmin;
209  using ::fminf;
210  using ::fminl;
211 
212  using ::hypot;
213  using ::hypotf;
214  using ::hypotl;
215 
216  using ::ilogb;
217  using ::ilogbf;
218  using ::ilogbl;
219 
220  using ::lgamma;
221  using ::lgammaf;
222  using ::lgammal;
223 
224  using ::llrint;
225  using ::llrintf;
226  using ::llrintl;
227 
228  using ::llround;
229  using ::llroundf;
230  using ::llroundl;
231 
232  using ::log1p;
233  using ::log1pf;
234  using ::log1pl;
235 
236  using ::log2;
237  using ::log2f;
238  using ::log2l;
239 
240  using ::logb;
241  using ::logbf;
242  using ::logbl;
243 
244  using ::lrint;
245  using ::lrintf;
246  using ::lrintl;
247 
248  using ::lround;
249  using ::lroundf;
250  using ::lroundl;
251 
252  using ::nan;
253  using ::nanf;
254  using ::nanl;
255 
256  using ::nearbyint;
257  using ::nearbyintf;
258  using ::nearbyintl;
259 
260  using ::nextafter;
261  using ::nextafterf;
262  using ::nextafterl;
263 
264  using ::nexttoward;
265  using ::nexttowardf;
266  using ::nexttowardl;
267 
268  using ::remainder;
269  using ::remainderf;
270  using ::remainderl;
271 
272  using ::remquo;
273  using ::remquof;
274  using ::remquol;
275 
276  using ::rint;
277  using ::rintf;
278  using ::rintl;
279 
280  using ::round;
281  using ::roundf;
282  using ::roundl;
283 
284  using ::scalbln;
285  using ::scalblnf;
286  using ::scalblnl;
287 
288  using ::scalbn;
289  using ::scalbnf;
290  using ::scalbnl;
291 
292  using ::tgamma;
293  using ::tgammaf;
294  using ::tgammal;
295 
296  using ::trunc;
297  using ::truncf;
298  using ::truncl;
299 
300 #endif
301 
302 #if _GLIBCXX_USE_C99_MATH
303 #if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
304 
305  /// Function template definitions [8.16.3].
306  template<typename _Tp>
307  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
308  int>::__type
309  fpclassify(_Tp __f)
310  {
311  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
312  return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
313  FP_SUBNORMAL, FP_ZERO, __type(__f));
314  }
315 
316  template<typename _Tp>
317  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
318  int>::__type
319  isfinite(_Tp __f)
320  {
321  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
322  return __builtin_isfinite(__type(__f));
323  }
324 
325  template<typename _Tp>
326  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
327  int>::__type
328  isinf(_Tp __f)
329  {
330  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
331  return __builtin_isinf(__type(__f));
332  }
333 
334  template<typename _Tp>
335  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
336  int>::__type
337  isnan(_Tp __f)
338  {
339  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
340  return __builtin_isnan(__type(__f));
341  }
342 
343  template<typename _Tp>
344  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
345  int>::__type
346  isnormal(_Tp __f)
347  {
348  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
349  return __builtin_isnormal(__type(__f));
350  }
351 
352  template<typename _Tp>
353  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
354  int>::__type
355  signbit(_Tp __f)
356  {
357  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
358  return __builtin_signbit(__type(__f));
359  }
360 
361  template<typename _Tp>
362  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
363  int>::__type
364  isgreater(_Tp __f1, _Tp __f2)
365  {
366  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
367  return __builtin_isgreater(__type(__f1), __type(__f2));
368  }
369 
370  template<typename _Tp>
371  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
372  int>::__type
373  isgreaterequal(_Tp __f1, _Tp __f2)
374  {
375  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
376  return __builtin_isgreaterequal(__type(__f1), __type(__f2));
377  }
378 
379  template<typename _Tp>
380  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
381  int>::__type
382  isless(_Tp __f1, _Tp __f2)
383  {
384  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
385  return __builtin_isless(__type(__f1), __type(__f2));
386  }
387 
388  template<typename _Tp>
389  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
390  int>::__type
391  islessequal(_Tp __f1, _Tp __f2)
392  {
393  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
394  return __builtin_islessequal(__type(__f1), __type(__f2));
395  }
396 
397  template<typename _Tp>
398  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
399  int>::__type
400  islessgreater(_Tp __f1, _Tp __f2)
401  {
402  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
403  return __builtin_islessgreater(__type(__f1), __type(__f2));
404  }
405 
406  template<typename _Tp>
407  inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
408  int>::__type
409  isunordered(_Tp __f1, _Tp __f2)
410  {
411  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
412  return __builtin_isunordered(__type(__f1), __type(__f2));
413  }
414 
415 #endif
416 #endif
417 
418 #if _GLIBCXX_USE_C99_MATH_TR1
419 
420  /// Additional overloads [8.16.4].
421  using std::acos;
422 
423  inline float
424  acosh(float __x)
425  { return __builtin_acoshf(__x); }
426 
427  inline long double
428  acosh(long double __x)
429  { return __builtin_acoshl(__x); }
430 
431  template<typename _Tp>
432  inline typename __gnu_cxx::__promote<_Tp>::__type
433  acosh(_Tp __x)
434  {
435  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
436  return acosh(__type(__x));
437  }
438 
439  using std::asin;
440 
441  inline float
442  asinh(float __x)
443  { return __builtin_asinhf(__x); }
444 
445  inline long double
446  asinh(long double __x)
447  { return __builtin_asinhl(__x); }
448 
449  template<typename _Tp>
450  inline typename __gnu_cxx::__promote<_Tp>::__type
451  asinh(_Tp __x)
452  {
453  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
454  return asinh(__type(__x));
455  }
456 
457  using std::atan;
458  using std::atan2;
459 
460  inline float
461  atanh(float __x)
462  { return __builtin_atanhf(__x); }
463 
464  inline long double
465  atanh(long double __x)
466  { return __builtin_atanhl(__x); }
467 
468  template<typename _Tp>
469  inline typename __gnu_cxx::__promote<_Tp>::__type
470  atanh(_Tp __x)
471  {
472  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
473  return atanh(__type(__x));
474  }
475 
476  inline float
477  cbrt(float __x)
478  { return __builtin_cbrtf(__x); }
479 
480  inline long double
481  cbrt(long double __x)
482  { return __builtin_cbrtl(__x); }
483 
484  template<typename _Tp>
485  inline typename __gnu_cxx::__promote<_Tp>::__type
486  cbrt(_Tp __x)
487  {
488  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
489  return cbrt(__type(__x));
490  }
491 
492  using std::ceil;
493 
494  inline float
495  copysign(float __x, float __y)
496  { return __builtin_copysignf(__x, __y); }
497 
498  inline long double
499  copysign(long double __x, long double __y)
500  { return __builtin_copysignl(__x, __y); }
501 
502  template<typename _Tp, typename _Up>
503  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
504  copysign(_Tp __x, _Up __y)
505  {
506  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
507  return copysign(__type(__x), __type(__y));
508  }
509 
510  using std::cos;
511  using std::cosh;
512 
513  inline float
514  erf(float __x)
515  { return __builtin_erff(__x); }
516 
517  inline long double
518  erf(long double __x)
519  { return __builtin_erfl(__x); }
520 
521  template<typename _Tp>
522  inline typename __gnu_cxx::__promote<_Tp>::__type
523  erf(_Tp __x)
524  {
525  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
526  return erf(__type(__x));
527  }
528 
529  inline float
530  erfc(float __x)
531  { return __builtin_erfcf(__x); }
532 
533  inline long double
534  erfc(long double __x)
535  { return __builtin_erfcl(__x); }
536 
537  template<typename _Tp>
538  inline typename __gnu_cxx::__promote<_Tp>::__type
539  erfc(_Tp __x)
540  {
541  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
542  return erfc(__type(__x));
543  }
544 
545  using std::exp;
546 
547  inline float
548  exp2(float __x)
549  { return __builtin_exp2f(__x); }
550 
551  inline long double
552  exp2(long double __x)
553  { return __builtin_exp2l(__x); }
554 
555  template<typename _Tp>
556  inline typename __gnu_cxx::__promote<_Tp>::__type
557  exp2(_Tp __x)
558  {
559  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
560  return exp2(__type(__x));
561  }
562 
563  inline float
564  expm1(float __x)
565  { return __builtin_expm1f(__x); }
566 
567  inline long double
568  expm1(long double __x)
569  { return __builtin_expm1l(__x); }
570 
571  template<typename _Tp>
572  inline typename __gnu_cxx::__promote<_Tp>::__type
573  expm1(_Tp __x)
574  {
575  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
576  return expm1(__type(__x));
577  }
578 
579  // Note: we deal with fabs in a special way, because an using std::fabs
580  // would bring in also the overloads for complex types, which in C++0x
581  // mode have a different return type.
582  using ::fabs;
583 
584  inline float
585  fabs(float __x)
586  { return __builtin_fabsf(__x); }
587 
588  inline long double
589  fabs(long double __x)
590  { return __builtin_fabsl(__x); }
591 
592  template<typename _Tp>
593  inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
594  double>::__type
595  fabs(_Tp __x)
596  { return __builtin_fabs(__x); }
597 
598  inline float
599  fdim(float __x, float __y)
600  { return __builtin_fdimf(__x, __y); }
601 
602  inline long double
603  fdim(long double __x, long double __y)
604  { return __builtin_fdiml(__x, __y); }
605 
606  template<typename _Tp, typename _Up>
607  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
608  fdim(_Tp __x, _Up __y)
609  {
610  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
611  return fdim(__type(__x), __type(__y));
612  }
613 
614  using std::floor;
615 
616  inline float
617  fma(float __x, float __y, float __z)
618  { return __builtin_fmaf(__x, __y, __z); }
619 
620  inline long double
621  fma(long double __x, long double __y, long double __z)
622  { return __builtin_fmal(__x, __y, __z); }
623 
624  template<typename _Tp, typename _Up, typename _Vp>
625  inline typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
626  fma(_Tp __x, _Up __y, _Vp __z)
627  {
628  typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
629  return fma(__type(__x), __type(__y), __type(__z));
630  }
631 
632  inline float
633  fmax(float __x, float __y)
634  { return __builtin_fmaxf(__x, __y); }
635 
636  inline long double
637  fmax(long double __x, long double __y)
638  { return __builtin_fmaxl(__x, __y); }
639 
640  template<typename _Tp, typename _Up>
641  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
642  fmax(_Tp __x, _Up __y)
643  {
644  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
645  return fmax(__type(__x), __type(__y));
646  }
647 
648  inline float
649  fmin(float __x, float __y)
650  { return __builtin_fminf(__x, __y); }
651 
652  inline long double
653  fmin(long double __x, long double __y)
654  { return __builtin_fminl(__x, __y); }
655 
656  template<typename _Tp, typename _Up>
657  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
658  fmin(_Tp __x, _Up __y)
659  {
660  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
661  return fmin(__type(__x), __type(__y));
662  }
663 
664  using std::fmod;
665  using std::frexp;
666 
667  inline float
668  hypot(float __x, float __y)
669  { return __builtin_hypotf(__x, __y); }
670 
671  inline long double
672  hypot(long double __x, long double __y)
673  { return __builtin_hypotl(__x, __y); }
674 
675  template<typename _Tp, typename _Up>
676  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
677  hypot(_Tp __x, _Up __y)
678  {
679  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
680  return hypot(__type(__x), __type(__y));
681  }
682 
683  inline int
684  ilogb(float __x)
685  { return __builtin_ilogbf(__x); }
686 
687  inline int
688  ilogb(long double __x)
689  { return __builtin_ilogbl(__x); }
690 
691  template<typename _Tp>
692  inline int
693  ilogb(_Tp __x)
694  {
695  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
696  return ilogb(__type(__x));
697  }
698 
699  using std::ldexp;
700 
701  inline float
702  lgamma(float __x)
703  { return __builtin_lgammaf(__x); }
704 
705  inline long double
706  lgamma(long double __x)
707  { return __builtin_lgammal(__x); }
708 
709  template<typename _Tp>
710  inline typename __gnu_cxx::__promote<_Tp>::__type
711  lgamma(_Tp __x)
712  {
713  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
714  return lgamma(__type(__x));
715  }
716 
717  inline long long
718  llrint(float __x)
719  { return __builtin_llrintf(__x); }
720 
721  inline long long
722  llrint(long double __x)
723  { return __builtin_llrintl(__x); }
724 
725  template<typename _Tp>
726  inline long long
727  llrint(_Tp __x)
728  {
729  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
730  return llrint(__type(__x));
731  }
732 
733  inline long long
734  llround(float __x)
735  { return __builtin_llroundf(__x); }
736 
737  inline long long
738  llround(long double __x)
739  { return __builtin_llroundl(__x); }
740 
741  template<typename _Tp>
742  inline long long
743  llround(_Tp __x)
744  {
745  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
746  return llround(__type(__x));
747  }
748 
749  using std::log;
750  using std::log10;
751 
752  inline float
753  log1p(float __x)
754  { return __builtin_log1pf(__x); }
755 
756  inline long double
757  log1p(long double __x)
758  { return __builtin_log1pl(__x); }
759 
760  template<typename _Tp>
761  inline typename __gnu_cxx::__promote<_Tp>::__type
762  log1p(_Tp __x)
763  {
764  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
765  return log1p(__type(__x));
766  }
767 
768  // DR 568.
769  inline float
770  log2(float __x)
771  { return __builtin_log2f(__x); }
772 
773  inline long double
774  log2(long double __x)
775  { return __builtin_log2l(__x); }
776 
777  template<typename _Tp>
778  inline typename __gnu_cxx::__promote<_Tp>::__type
779  log2(_Tp __x)
780  {
781  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
782  return log2(__type(__x));
783  }
784 
785  inline float
786  logb(float __x)
787  { return __builtin_logbf(__x); }
788 
789  inline long double
790  logb(long double __x)
791  { return __builtin_logbl(__x); }
792 
793  template<typename _Tp>
794  inline typename __gnu_cxx::__promote<_Tp>::__type
795  logb(_Tp __x)
796  {
797  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
798  return logb(__type(__x));
799  }
800 
801  inline long
802  lrint(float __x)
803  { return __builtin_lrintf(__x); }
804 
805  inline long
806  lrint(long double __x)
807  { return __builtin_lrintl(__x); }
808 
809  template<typename _Tp>
810  inline long
811  lrint(_Tp __x)
812  {
813  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
814  return lrint(__type(__x));
815  }
816 
817  inline long
818  lround(float __x)
819  { return __builtin_lroundf(__x); }
820 
821  inline long
822  lround(long double __x)
823  { return __builtin_lroundl(__x); }
824 
825  template<typename _Tp>
826  inline long
827  lround(_Tp __x)
828  {
829  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
830  return lround(__type(__x));
831  }
832 
833  inline float
834  nearbyint(float __x)
835  { return __builtin_nearbyintf(__x); }
836 
837  inline long double
838  nearbyint(long double __x)
839  { return __builtin_nearbyintl(__x); }
840 
841  template<typename _Tp>
842  inline typename __gnu_cxx::__promote<_Tp>::__type
843  nearbyint(_Tp __x)
844  {
845  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
846  return nearbyint(__type(__x));
847  }
848 
849  inline float
850  nextafter(float __x, float __y)
851  { return __builtin_nextafterf(__x, __y); }
852 
853  inline long double
854  nextafter(long double __x, long double __y)
855  { return __builtin_nextafterl(__x, __y); }
856 
857  template<typename _Tp, typename _Up>
858  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
859  nextafter(_Tp __x, _Up __y)
860  {
861  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
862  return nextafter(__type(__x), __type(__y));
863  }
864 
865  inline float
866  nexttoward(float __x, long double __y)
867  { return __builtin_nexttowardf(__x, __y); }
868 
869  inline long double
870  nexttoward(long double __x, long double __y)
871  { return __builtin_nexttowardl(__x, __y); }
872 
873  template<typename _Tp>
874  inline typename __gnu_cxx::__promote<_Tp>::__type
875  nexttoward(_Tp __x, long double __y)
876  {
877  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
878  return nexttoward(__type(__x), __y);
879  }
880 
881  // DR 550. What should the return type of pow(float,int) be?
882  // NB: C++0x and TR1 != C++03.
883  // using std::pow;
884 
885  inline float
886  remainder(float __x, float __y)
887  { return __builtin_remainderf(__x, __y); }
888 
889  inline long double
890  remainder(long double __x, long double __y)
891  { return __builtin_remainderl(__x, __y); }
892 
893  template<typename _Tp, typename _Up>
894  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
895  remainder(_Tp __x, _Up __y)
896  {
897  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
898  return remainder(__type(__x), __type(__y));
899  }
900 
901  inline float
902  remquo(float __x, float __y, int* __pquo)
903  { return __builtin_remquof(__x, __y, __pquo); }
904 
905  inline long double
906  remquo(long double __x, long double __y, int* __pquo)
907  { return __builtin_remquol(__x, __y, __pquo); }
908 
909  template<typename _Tp, typename _Up>
910  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
911  remquo(_Tp __x, _Up __y, int* __pquo)
912  {
913  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
914  return remquo(__type(__x), __type(__y), __pquo);
915  }
916 
917  inline float
918  rint(float __x)
919  { return __builtin_rintf(__x); }
920 
921  inline long double
922  rint(long double __x)
923  { return __builtin_rintl(__x); }
924 
925  template<typename _Tp>
926  inline typename __gnu_cxx::__promote<_Tp>::__type
927  rint(_Tp __x)
928  {
929  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
930  return rint(__type(__x));
931  }
932 
933  inline float
934  round(float __x)
935  { return __builtin_roundf(__x); }
936 
937  inline long double
938  round(long double __x)
939  { return __builtin_roundl(__x); }
940 
941  template<typename _Tp>
942  inline typename __gnu_cxx::__promote<_Tp>::__type
943  round(_Tp __x)
944  {
945  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
946  return round(__type(__x));
947  }
948 
949  inline float
950  scalbln(float __x, long __ex)
951  { return __builtin_scalblnf(__x, __ex); }
952 
953  inline long double
954  scalbln(long double __x, long __ex)
955  { return __builtin_scalblnl(__x, __ex); }
956 
957  template<typename _Tp>
958  inline typename __gnu_cxx::__promote<_Tp>::__type
959  scalbln(_Tp __x, long __ex)
960  {
961  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
962  return scalbln(__type(__x), __ex);
963  }
964 
965  inline float
966  scalbn(float __x, int __ex)
967  { return __builtin_scalbnf(__x, __ex); }
968 
969  inline long double
970  scalbn(long double __x, int __ex)
971  { return __builtin_scalbnl(__x, __ex); }
972 
973  template<typename _Tp>
974  inline typename __gnu_cxx::__promote<_Tp>::__type
975  scalbn(_Tp __x, int __ex)
976  {
977  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
978  return scalbn(__type(__x), __ex);
979  }
980 
981  using std::sin;
982  using std::sinh;
983  using std::sqrt;
984  using std::tan;
985  using std::tanh;
986 
987  inline float
988  tgamma(float __x)
989  { return __builtin_tgammaf(__x); }
990 
991  inline long double
992  tgamma(long double __x)
993  { return __builtin_tgammal(__x); }
994 
995  template<typename _Tp>
996  inline typename __gnu_cxx::__promote<_Tp>::__type
997  tgamma(_Tp __x)
998  {
999  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1000  return tgamma(__type(__x));
1001  }
1002 
1003  inline float
1004  trunc(float __x)
1005  { return __builtin_truncf(__x); }
1006 
1007  inline long double
1008  trunc(long double __x)
1009  { return __builtin_truncl(__x); }
1010 
1011  template<typename _Tp>
1012  inline typename __gnu_cxx::__promote<_Tp>::__type
1013  trunc(_Tp __x)
1014  {
1015  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1016  return trunc(__type(__x));
1017  }
1018 
1019 #endif
1020 _GLIBCXX_END_NAMESPACE_VERSION
1021 }
1022 }
1023 
1024 namespace std _GLIBCXX_VISIBILITY(default)
1025 {
1026 namespace tr1
1027 {
1028 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1029 
1030  // DR 550. What should the return type of pow(float,int) be?
1031  // NB: C++0x and TR1 != C++03.
1032  inline double
1033  pow(double __x, double __y)
1034  { return std::pow(__x, __y); }
1035 
1036  inline float
1037  pow(float __x, float __y)
1038  { return std::pow(__x, __y); }
1039 
1040  inline long double
1041  pow(long double __x, long double __y)
1042  { return std::pow(__x, __y); }
1043 
1044  template<typename _Tp, typename _Up>
1045  inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1046  pow(_Tp __x, _Up __y)
1047  {
1048  typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1049  return std::pow(__type(__x), __type(__y));
1050  }
1051 
1052 _GLIBCXX_END_NAMESPACE_VERSION
1053 }
1054 }
1055 
1056 #include <bits/stl_algobase.h>
1057 #include <limits>
1058 #include <tr1/type_traits>
1059 
1060 #include <tr1/gamma.tcc>
1061 #include <tr1/bessel_function.tcc>
1062 #include <tr1/beta_function.tcc>
1063 #include <tr1/ell_integral.tcc>
1064 #include <tr1/exp_integral.tcc>
1065 #include <tr1/hypergeometric.tcc>
1066 #include <tr1/legendre_function.tcc>
1067 #include <tr1/modified_bessel_func.tcc>
1068 #include <tr1/poly_hermite.tcc>
1069 #include <tr1/poly_laguerre.tcc>
1070 #include <tr1/riemann_zeta.tcc>
1071 
1072 namespace std _GLIBCXX_VISIBILITY(default)
1073 {
1074 namespace tr1
1075 {
1076 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1077 
1078  /**
1079  * @defgroup tr1_math_spec_func Mathematical Special Functions
1080  * @ingroup numerics
1081  *
1082  * A collection of advanced mathematical special functions.
1083  * @{
1084  */
1085 
1086  inline float
1087  assoc_laguerref(unsigned int __n, unsigned int __m, float __x)
1088  { return __detail::__assoc_laguerre<float>(__n, __m, __x); }
1089 
1090  inline long double
1091  assoc_laguerrel(unsigned int __n, unsigned int __m, long double __x)
1092  {
1093  return __detail::__assoc_laguerre<long double>(__n, __m, __x);
1094  }
1095 
1096  /// 5.2.1.1 Associated Laguerre polynomials.
1097  template<typename _Tp>
1098  inline typename __gnu_cxx::__promote<_Tp>::__type
1099  assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
1100  {
1101  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1102  return __detail::__assoc_laguerre<__type>(__n, __m, __x);
1103  }
1104 
1105  inline float
1106  assoc_legendref(unsigned int __l, unsigned int __m, float __x)
1107  { return __detail::__assoc_legendre_p<float>(__l, __m, __x); }
1108 
1109  inline long double
1110  assoc_legendrel(unsigned int __l, unsigned int __m, long double __x)
1111  { return __detail::__assoc_legendre_p<long double>(__l, __m, __x); }
1112 
1113  /// 5.2.1.2 Associated Legendre functions.
1114  template<typename _Tp>
1115  inline typename __gnu_cxx::__promote<_Tp>::__type
1116  assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
1117  {
1118  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1119  return __detail::__assoc_legendre_p<__type>(__l, __m, __x);
1120  }
1121 
1122  inline float
1123  betaf(float __x, float __y)
1124  { return __detail::__beta<float>(__x, __y); }
1125 
1126  inline long double
1127  betal(long double __x, long double __y)
1128  { return __detail::__beta<long double>(__x, __y); }
1129 
1130  /// 5.2.1.3 Beta functions.
1131  template<typename _Tpx, typename _Tpy>
1132  inline typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type
1133  beta(_Tpx __x, _Tpy __y)
1134  {
1135  typedef typename __gnu_cxx::__promote_2<_Tpx, _Tpy>::__type __type;
1136  return __detail::__beta<__type>(__x, __y);
1137  }
1138 
1139  inline float
1140  comp_ellint_1f(float __k)
1141  { return __detail::__comp_ellint_1<float>(__k); }
1142 
1143  inline long double
1144  comp_ellint_1l(long double __k)
1145  { return __detail::__comp_ellint_1<long double>(__k); }
1146 
1147  /// 5.2.1.4 Complete elliptic integrals of the first kind.
1148  template<typename _Tp>
1149  inline typename __gnu_cxx::__promote<_Tp>::__type
1150  comp_ellint_1(_Tp __k)
1151  {
1152  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1153  return __detail::__comp_ellint_1<__type>(__k);
1154  }
1155 
1156  inline float
1157  comp_ellint_2f(float __k)
1158  { return __detail::__comp_ellint_2<float>(__k); }
1159 
1160  inline long double
1161  comp_ellint_2l(long double __k)
1162  { return __detail::__comp_ellint_2<long double>(__k); }
1163 
1164  /// 5.2.1.5 Complete elliptic integrals of the second kind.
1165  template<typename _Tp>
1166  inline typename __gnu_cxx::__promote<_Tp>::__type
1167  comp_ellint_2(_Tp __k)
1168  {
1169  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1170  return __detail::__comp_ellint_2<__type>(__k);
1171  }
1172 
1173  inline float
1174  comp_ellint_3f(float __k, float __nu)
1175  { return __detail::__comp_ellint_3<float>(__k, __nu); }
1176 
1177  inline long double
1178  comp_ellint_3l(long double __k, long double __nu)
1179  { return __detail::__comp_ellint_3<long double>(__k, __nu); }
1180 
1181  /// 5.2.1.6 Complete elliptic integrals of the third kind.
1182  template<typename _Tp, typename _Tpn>
1183  inline typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type
1184  comp_ellint_3(_Tp __k, _Tpn __nu)
1185  {
1186  typedef typename __gnu_cxx::__promote_2<_Tp, _Tpn>::__type __type;
1187  return __detail::__comp_ellint_3<__type>(__k, __nu);
1188  }
1189 
1190  inline float
1191  conf_hypergf(float __a, float __c, float __x)
1192  { return __detail::__conf_hyperg<float>(__a, __c, __x); }
1193 
1194  inline long double
1195  conf_hypergl(long double __a, long double __c, long double __x)
1196  { return __detail::__conf_hyperg<long double>(__a, __c, __x); }
1197 
1198  /// 5.2.1.7 Confluent hypergeometric functions.
1199  template<typename _Tpa, typename _Tpc, typename _Tp>
1200  inline typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type
1201  conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
1202  {
1203  typedef typename __gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type __type;
1204  return __detail::__conf_hyperg<__type>(__a, __c, __x);
1205  }
1206 
1207  inline float
1208  cyl_bessel_if(float __nu, float __x)
1209  { return __detail::__cyl_bessel_i<float>(__nu, __x); }
1210 
1211  inline long double
1212  cyl_bessel_il(long double __nu, long double __x)
1213  { return __detail::__cyl_bessel_i<long double>(__nu, __x); }
1214 
1215  /// 5.2.1.8 Regular modified cylindrical Bessel functions.
1216  template<typename _Tpnu, typename _Tp>
1217  inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1218  cyl_bessel_i(_Tpnu __nu, _Tp __x)
1219  {
1220  typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1221  return __detail::__cyl_bessel_i<__type>(__nu, __x);
1222  }
1223 
1224  inline float
1225  cyl_bessel_jf(float __nu, float __x)
1226  { return __detail::__cyl_bessel_j<float>(__nu, __x); }
1227 
1228  inline long double
1229  cyl_bessel_jl(long double __nu, long double __x)
1230  { return __detail::__cyl_bessel_j<long double>(__nu, __x); }
1231 
1232  /// 5.2.1.9 Cylindrical Bessel functions (of the first kind).
1233  template<typename _Tpnu, typename _Tp>
1234  inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1235  cyl_bessel_j(_Tpnu __nu, _Tp __x)
1236  {
1237  typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1238  return __detail::__cyl_bessel_j<__type>(__nu, __x);
1239  }
1240 
1241  inline float
1242  cyl_bessel_kf(float __nu, float __x)
1243  { return __detail::__cyl_bessel_k<float>(__nu, __x); }
1244 
1245  inline long double
1246  cyl_bessel_kl(long double __nu, long double __x)
1247  { return __detail::__cyl_bessel_k<long double>(__nu, __x); }
1248 
1249  /// 5.2.1.10 Irregular modified cylindrical Bessel functions.
1250  template<typename _Tpnu, typename _Tp>
1251  inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1252  cyl_bessel_k(_Tpnu __nu, _Tp __x)
1253  {
1254  typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1255  return __detail::__cyl_bessel_k<__type>(__nu, __x);
1256  }
1257 
1258  inline float
1259  cyl_neumannf(float __nu, float __x)
1260  { return __detail::__cyl_neumann_n<float>(__nu, __x); }
1261 
1262  inline long double
1263  cyl_neumannl(long double __nu, long double __x)
1264  { return __detail::__cyl_neumann_n<long double>(__nu, __x); }
1265 
1266  /// 5.2.1.11 Cylindrical Neumann functions.
1267  template<typename _Tpnu, typename _Tp>
1268  inline typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type
1269  cyl_neumann(_Tpnu __nu, _Tp __x)
1270  {
1271  typedef typename __gnu_cxx::__promote_2<_Tpnu, _Tp>::__type __type;
1272  return __detail::__cyl_neumann_n<__type>(__nu, __x);
1273  }
1274 
1275  inline float
1276  ellint_1f(float __k, float __phi)
1277  { return __detail::__ellint_1<float>(__k, __phi); }
1278 
1279  inline long double
1280  ellint_1l(long double __k, long double __phi)
1281  { return __detail::__ellint_1<long double>(__k, __phi); }
1282 
1283  /// 5.2.1.12 Incomplete elliptic integrals of the first kind.
1284  template<typename _Tp, typename _Tpp>
1285  inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1286  ellint_1(_Tp __k, _Tpp __phi)
1287  {
1288  typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1289  return __detail::__ellint_1<__type>(__k, __phi);
1290  }
1291 
1292  inline float
1293  ellint_2f(float __k, float __phi)
1294  { return __detail::__ellint_2<float>(__k, __phi); }
1295 
1296  inline long double
1297  ellint_2l(long double __k, long double __phi)
1298  { return __detail::__ellint_2<long double>(__k, __phi); }
1299 
1300  /// 5.2.1.13 Incomplete elliptic integrals of the second kind.
1301  template<typename _Tp, typename _Tpp>
1302  inline typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type
1303  ellint_2(_Tp __k, _Tpp __phi)
1304  {
1305  typedef typename __gnu_cxx::__promote_2<_Tp, _Tpp>::__type __type;
1306  return __detail::__ellint_2<__type>(__k, __phi);
1307  }
1308 
1309  inline float
1310  ellint_3f(float __k, float __nu, float __phi)
1311  { return __detail::__ellint_3<float>(__k, __nu, __phi); }
1312 
1313  inline long double
1314  ellint_3l(long double __k, long double __nu, long double __phi)
1315  { return __detail::__ellint_3<long double>(__k, __nu, __phi); }
1316 
1317  /// 5.2.1.14 Incomplete elliptic integrals of the third kind.
1318  template<typename _Tp, typename _Tpn, typename _Tpp>
1319  inline typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type
1320  ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
1321  {
1322  typedef typename __gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type __type;
1323  return __detail::__ellint_3<__type>(__k, __nu, __phi);
1324  }
1325 
1326  inline float
1327  expintf(float __x)
1328  { return __detail::__expint<float>(__x); }
1329 
1330  inline long double
1331  expintl(long double __x)
1332  { return __detail::__expint<long double>(__x); }
1333 
1334  /// 5.2.1.15 Exponential integrals.
1335  template<typename _Tp>
1336  inline typename __gnu_cxx::__promote<_Tp>::__type
1337  expint(_Tp __x)
1338  {
1339  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1340  return __detail::__expint<__type>(__x);
1341  }
1342 
1343  inline float
1344  hermitef(unsigned int __n, float __x)
1345  { return __detail::__poly_hermite<float>(__n, __x); }
1346 
1347  inline long double
1348  hermitel(unsigned int __n, long double __x)
1349  { return __detail::__poly_hermite<long double>(__n, __x); }
1350 
1351  /// 5.2.1.16 Hermite polynomials.
1352  template<typename _Tp>
1353  inline typename __gnu_cxx::__promote<_Tp>::__type
1354  hermite(unsigned int __n, _Tp __x)
1355  {
1356  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1357  return __detail::__poly_hermite<__type>(__n, __x);
1358  }
1359 
1360  inline float
1361  hypergf(float __a, float __b, float __c, float __x)
1362  { return __detail::__hyperg<float>(__a, __b, __c, __x); }
1363 
1364  inline long double
1365  hypergl(long double __a, long double __b, long double __c, long double __x)
1366  { return __detail::__hyperg<long double>(__a, __b, __c, __x); }
1367 
1368  /// 5.2.1.17 Hypergeometric functions.
1369  template<typename _Tpa, typename _Tpb, typename _Tpc, typename _Tp>
1370  inline typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type
1371  hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
1372  {
1373  typedef typename __gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type __type;
1374  return __detail::__hyperg<__type>(__a, __b, __c, __x);
1375  }
1376 
1377  inline float
1378  laguerref(unsigned int __n, float __x)
1379  { return __detail::__laguerre<float>(__n, __x); }
1380 
1381  inline long double
1382  laguerrel(unsigned int __n, long double __x)
1383  { return __detail::__laguerre<long double>(__n, __x); }
1384 
1385  /// 5.2.1.18 Laguerre polynomials.
1386  template<typename _Tp>
1387  inline typename __gnu_cxx::__promote<_Tp>::__type
1388  laguerre(unsigned int __n, _Tp __x)
1389  {
1390  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1391  return __detail::__laguerre<__type>(__n, __x);
1392  }
1393 
1394  inline float
1395  legendref(unsigned int __n, float __x)
1396  { return __detail::__poly_legendre_p<float>(__n, __x); }
1397 
1398  inline long double
1399  legendrel(unsigned int __n, long double __x)
1400  { return __detail::__poly_legendre_p<long double>(__n, __x); }
1401 
1402  /// 5.2.1.19 Legendre polynomials.
1403  template<typename _Tp>
1404  inline typename __gnu_cxx::__promote<_Tp>::__type
1405  legendre(unsigned int __n, _Tp __x)
1406  {
1407  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1408  return __detail::__poly_legendre_p<__type>(__n, __x);
1409  }
1410 
1411  inline float
1412  riemann_zetaf(float __x)
1413  { return __detail::__riemann_zeta<float>(__x); }
1414 
1415  inline long double
1416  riemann_zetal(long double __x)
1417  { return __detail::__riemann_zeta<long double>(__x); }
1418 
1419  /// 5.2.1.20 Riemann zeta function.
1420  template<typename _Tp>
1421  inline typename __gnu_cxx::__promote<_Tp>::__type
1422  riemann_zeta(_Tp __x)
1423  {
1424  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1425  return __detail::__riemann_zeta<__type>(__x);
1426  }
1427 
1428  inline float
1429  sph_besself(unsigned int __n, float __x)
1430  { return __detail::__sph_bessel<float>(__n, __x); }
1431 
1432  inline long double
1433  sph_bessell(unsigned int __n, long double __x)
1434  { return __detail::__sph_bessel<long double>(__n, __x); }
1435 
1436  /// 5.2.1.21 Spherical Bessel functions.
1437  template<typename _Tp>
1438  inline typename __gnu_cxx::__promote<_Tp>::__type
1439  sph_bessel(unsigned int __n, _Tp __x)
1440  {
1441  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1442  return __detail::__sph_bessel<__type>(__n, __x);
1443  }
1444 
1445  inline float
1446  sph_legendref(unsigned int __l, unsigned int __m, float __theta)
1447  { return __detail::__sph_legendre<float>(__l, __m, __theta); }
1448 
1449  inline long double
1450  sph_legendrel(unsigned int __l, unsigned int __m, long double __theta)
1451  { return __detail::__sph_legendre<long double>(__l, __m, __theta); }
1452 
1453  /// 5.2.1.22 Spherical associated Legendre functions.
1454  template<typename _Tp>
1455  inline typename __gnu_cxx::__promote<_Tp>::__type
1456  sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
1457  {
1458  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1459  return __detail::__sph_legendre<__type>(__l, __m, __theta);
1460  }
1461 
1462  inline float
1463  sph_neumannf(unsigned int __n, float __x)
1464  { return __detail::__sph_neumann<float>(__n, __x); }
1465 
1466  inline long double
1467  sph_neumannl(unsigned int __n, long double __x)
1468  { return __detail::__sph_neumann<long double>(__n, __x); }
1469 
1470  /// 5.2.1.23 Spherical Neumann functions.
1471  template<typename _Tp>
1472  inline typename __gnu_cxx::__promote<_Tp>::__type
1473  sph_neumann(unsigned int __n, _Tp __x)
1474  {
1475  typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1476  return __detail::__sph_neumann<__type>(__n, __x);
1477  }
1478 
1479  /* @} */ // tr1_math_spec_func
1480 _GLIBCXX_END_NAMESPACE_VERSION
1481 }
1482 }
1483 
1484 #endif // _GLIBCXX_TR1_CMATH
__gnu_cxx::__promote< _Tp >::__type comp_ellint_2(_Tp __k)
5.2.1.5 Complete elliptic integrals of the second kind.
Definition: tr1/cmath:1167
__gnu_cxx::__promote< _Tp >::__type expint(_Tp __x)
5.2.1.15 Exponential integrals.
Definition: tr1/cmath:1337
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
5.2.1.14 Incomplete elliptic integrals of the third kind.
Definition: tr1/cmath:1320
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition: complex:920
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition: complex:819
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
Definition: complex:1726
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition: complex:893
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_neumann(_Tpnu __nu, _Tp __x)
5.2.1.11 Cylindrical Neumann functions.
Definition: tr1/cmath:1269
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition: complex:849
__gnu_cxx::__promote< _Tp >::__type comp_ellint_1(_Tp __k)
5.2.1.4 Complete elliptic integrals of the first kind.
Definition: tr1/cmath:1150
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition: complex:731
std::complex< _Tp > fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition: tr1/complex:308
__gnu_cxx::__promote< _Tp >::__type laguerre(unsigned int __n, _Tp __x)
5.2.1.18 Laguerre polynomials.
Definition: tr1/cmath:1388
complex< _Tp > pow(const complex< _Tp > &, const _Tp &)
Return x to the y'th power.
Definition: complex:986
_Tp fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition: complex:1818
std::complex< _Tp > asin(const std::complex< _Tp > &)
asin(__z) [8.1.3].
Definition: complex:1646
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition: complex:948
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition: complex:701
__gnu_cxx::__promote< _Tp >::__type sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
5.2.1.22 Spherical associated Legendre functions.
Definition: tr1/cmath:1456
std::complex< _Tp > acos(const std::complex< _Tp > &)
acos(__z) [8.1.2].
Definition: complex:1610
__gnu_cxx::__promote_4< _Tpa, _Tpb, _Tpc, _Tp >::__type hyperg(_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
5.2.1.17 Hypergeometric functions.
Definition: tr1/cmath:1371
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_2(_Tp __k, _Tpp __phi)
5.2.1.13 Incomplete elliptic integrals of the second kind.
Definition: tr1/cmath:1303
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
Definition: tr1/complex:255
__gnu_cxx::__promote_3< _Tpa, _Tpc, _Tp >::__type conf_hyperg(_Tpa __a, _Tpc __c, _Tp __x)
5.2.1.7 Confluent hypergeometric functions.
Definition: tr1/cmath:1201
__gnu_cxx::__promote< _Tp >::__type assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
5.2.1.2 Associated Legendre functions.
Definition: tr1/cmath:1116
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_1(_Tp __k, _Tpp __phi)
5.2.1.12 Incomplete elliptic integrals of the first kind.
Definition: tr1/cmath:1286
__gnu_cxx::__promote< _Tp >::__type legendre(unsigned int __n, _Tp __x)
5.2.1.19 Legendre polynomials.
Definition: tr1/cmath:1405
std::complex< _Tp > atan(const std::complex< _Tp > &)
atan(__z) [8.1.4].
Definition: complex:1690
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_k(_Tpnu __nu, _Tp __x)
5.2.1.10 Irregular modified cylindrical Bessel functions.
Definition: tr1/cmath:1252
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition: complex:789
__gnu_cxx::__promote< _Tp >::__type riemann_zeta(_Tp __x)
5.2.1.20 Riemann zeta function.
Definition: tr1/cmath:1422
__gnu_cxx::__promote< _Tp >::__type sph_bessel(unsigned int __n, _Tp __x)
5.2.1.21 Spherical Bessel functions.
Definition: tr1/cmath:1439
__gnu_cxx::__promote< _Tp >::__type sph_neumann(unsigned int __n, _Tp __x)
5.2.1.23 Spherical Neumann functions.
Definition: tr1/cmath:1473
__gnu_cxx::__promote< _Tp >::__type assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
5.2.1.1 Associated Laguerre polynomials.
Definition: tr1/cmath:1099
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
Definition: complex:1765
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type comp_ellint_3(_Tp __k, _Tpn __nu)
5.2.1.6 Complete elliptic integrals of the third kind.
Definition: tr1/cmath:1184
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
Definition: complex:1809
__gnu_cxx::__promote_2< _Tpx, _Tpy >::__type beta(_Tpx __x, _Tpy __y)
5.2.1.3 Beta functions.
Definition: tr1/cmath:1133
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
Definition: tr1/complex:216
__gnu_cxx::__promote< _Tp >::__type hermite(unsigned int __n, _Tp __x)
5.2.1.16 Hermite polynomials.
Definition: tr1/cmath:1354
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition: complex:757
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition: complex:784
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
Definition: tr1/complex:299
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_i(_Tpnu __nu, _Tp __x)
5.2.1.8 Regular modified cylindrical Bessel functions.
Definition: tr1/cmath:1218
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_j(_Tpnu __nu, _Tp __x)
5.2.1.9 Cylindrical Bessel functions (of the first kind).
Definition: tr1/cmath:1235