47 #ifndef _GLIBCXX_TR1_BESSEL_FUNCTION_TCC
48 #define _GLIBCXX_TR1_BESSEL_FUNCTION_TCC 1
88 template <
typename _Tp>
91 _Tp & __gam1, _Tp & __gam2, _Tp & __gampl, _Tp & __gammi)
93 #if _GLIBCXX_USE_C99_MATH_TR1
94 __gampl = _Tp(1) / std::tr1::tgamma(_Tp(1) + __mu);
95 __gammi = _Tp(1) / std::tr1::tgamma(_Tp(1) - __mu);
97 __gampl = _Tp(1) /
__gamma(_Tp(1) + __mu);
98 __gammi = _Tp(1) /
__gamma(_Tp(1) - __mu);
104 __gam1 = (__gammi - __gampl) / (_Tp(2) * __mu);
106 __gam2 = (__gammi + __gampl) / (_Tp(2));
126 template <
typename _Tp>
129 _Tp & __Jnu, _Tp & __Nnu, _Tp & __Jpnu, _Tp & __Npnu)
138 else if (__nu == _Tp(1))
159 const int __max_iter = 15000;
160 const _Tp __x_min = _Tp(2);
162 const int __nl = (__x < __x_min
163 ?
static_cast<int>(__nu + _Tp(0.5L))
164 :
std::max(0, static_cast<int>(__nu - __x + _Tp(1.5L))));
166 const _Tp __mu = __nu - __nl;
167 const _Tp __mu2 = __mu * __mu;
168 const _Tp __xi = _Tp(1) / __x;
169 const _Tp __xi2 = _Tp(2) * __xi;
172 _Tp __h = __nu * __xi;
175 _Tp __b = __xi2 * __nu;
179 for (__i = 1; __i <= __max_iter; ++__i)
185 __c = __b - _Tp(1) / __c;
189 const _Tp __del = __c * __d;
193 if (
std::abs(__del - _Tp(1)) < __eps)
196 if (__i > __max_iter)
197 std::__throw_runtime_error(__N(
"Argument x too large in __bessel_jn; "
198 "try asymptotic expansion."));
199 _Tp __Jnul = __isign * __fp_min;
200 _Tp __Jpnul = __h * __Jnul;
201 _Tp __Jnul1 = __Jnul;
202 _Tp __Jpnu1 = __Jpnul;
203 _Tp __fact = __nu * __xi;
204 for (
int __l = __nl; __l >= 1; --__l )
206 const _Tp __Jnutemp = __fact * __Jnul + __Jpnul;
208 __Jpnul = __fact * __Jnutemp - __Jnul;
211 if (__Jnul == _Tp(0))
213 _Tp __f= __Jpnul / __Jnul;
214 _Tp __Nmu, __Nnu1, __Npmu, __Jmu;
217 const _Tp __x2 = __x / _Tp(2);
219 _Tp __fact = (
std::abs(__pimu) < __eps
220 ? _Tp(1) : __pimu /
std::sin(__pimu));
222 _Tp __e = __mu * __d;
223 _Tp __fact2 = (
std::abs(__e) < __eps
225 _Tp __gam1, __gam2, __gampl, __gammi;
228 * __fact * (__gam1 *
std::cosh(__e) + __gam2 * __fact2 * __d);
232 const _Tp __pimu2 = __pimu / _Tp(2);
233 _Tp __fact3 = (
std::abs(__pimu2) < __eps
234 ? _Tp(1) :
std::sin(__pimu2) / __pimu2 );
238 _Tp __sum = __ff + __r * __q;
240 for (__i = 1; __i <= __max_iter; ++__i)
242 __ff = (__i * __ff + __p + __q) / (__i * __i - __mu2);
243 __c *= __d / _Tp(__i);
244 __p /= _Tp(__i) - __mu;
245 __q /= _Tp(__i) + __mu;
246 const _Tp __del = __c * (__ff + __r * __q);
248 const _Tp __del1 = __c * __p - __i * __del;
253 if ( __i > __max_iter )
254 std::__throw_runtime_error(__N(
"Bessel y series failed to converge "
257 __Nnu1 = -__sum1 * __xi2;
258 __Npmu = __mu * __xi * __Nmu - __Nnu1;
259 __Jmu = __w / (__Npmu - __f * __Nmu);
263 _Tp __a = _Tp(0.25L) - __mu2;
265 _Tp __p = -__xi / _Tp(2);
266 _Tp __br = _Tp(2) * __x;
268 _Tp __fact = __a * __xi / (__p * __p + __q * __q);
269 _Tp __cr = __br + __q * __fact;
270 _Tp __ci = __bi + __p * __fact;
271 _Tp __den = __br * __br + __bi * __bi;
272 _Tp __dr = __br / __den;
273 _Tp __di = -__bi / __den;
274 _Tp __dlr = __cr * __dr - __ci * __di;
275 _Tp __dli = __cr * __di + __ci * __dr;
276 _Tp __temp = __p * __dlr - __q * __dli;
277 __q = __p * __dli + __q * __dlr;
280 for (__i = 2; __i <= __max_iter; ++__i)
282 __a += _Tp(2 * (__i - 1));
284 __dr = __a * __dr + __br;
285 __di = __a * __di + __bi;
288 __fact = __a / (__cr * __cr + __ci * __ci);
289 __cr = __br + __cr * __fact;
290 __ci = __bi - __ci * __fact;
293 __den = __dr * __dr + __di * __di;
296 __dlr = __cr * __dr - __ci * __di;
297 __dli = __cr * __di + __ci * __dr;
298 __temp = __p * __dlr - __q * __dli;
299 __q = __p * __dli + __q * __dlr;
304 if (__i > __max_iter)
305 std::__throw_runtime_error(__N(
"Lentz's method failed "
307 const _Tp __gam = (__p - __f) / __q;
308 __Jmu =
std::sqrt(__w / ((__p - __f) * __gam + __q));
309 #if _GLIBCXX_USE_C99_MATH_TR1
310 __Jmu = std::tr1::copysign(__Jmu, __Jnul);
312 if (__Jmu * __Jnul < _Tp(0))
315 __Nmu = __gam * __Jmu;
316 __Npmu = (__p + __q / __gam) * __Nmu;
317 __Nnu1 = __mu * __xi * __Nmu - __Npmu;
319 __fact = __Jmu / __Jnul;
320 __Jnu = __fact * __Jnul1;
321 __Jpnu = __fact * __Jpnu1;
322 for (__i = 1; __i <= __nl; ++__i)
324 const _Tp __Nnutemp = (__mu + __i) * __xi2 * __Nnu1 - __Nmu;
329 __Npnu = __nu * __xi * __Nmu - __Nnu1;
351 template <
typename _Tp>
354 _Tp & __Jnu, _Tp & __Nnu)
358 const _Tp __mu = _Tp(4) * __nu * __nu;
359 const _Tp __mum1 = __mu - _Tp(1);
360 const _Tp __mum9 = __mu - _Tp(9);
361 const _Tp __mum25 = __mu - _Tp(25);
362 const _Tp __mum49 = __mu - _Tp(49);
363 const _Tp __xx = _Tp(64) * __x * __x;
364 const _Tp __P = _Tp(1) - __mum1 * __mum9 / (_Tp(2) * __xx)
365 * (_Tp(1) - __mum25 * __mum49 / (_Tp(12) * __xx));
366 const _Tp __Q = __mum1 / (_Tp(8) * __x)
367 * (_Tp(1) - __mum9 * __mum25 / (_Tp(6) * __xx));
369 const _Tp __chi = __x - (__nu + _Tp(0.5L))
374 __Jnu = __coef * (__c * __P - __s * __Q);
375 __Nnu = __coef * (__s * __P + __c * __Q);
408 template <
typename _Tp>
411 const unsigned int __max_iter)
414 const _Tp __x2 = __x / _Tp(2);
416 #if _GLIBCXX_USE_C99_MATH_TR1
417 __fact -= std::tr1::lgamma(__nu + _Tp(1));
422 const _Tp __xx4 = __sgn * __x2 * __x2;
426 for (
unsigned int __i = 1; __i < __max_iter; ++__i)
428 __term *= __xx4 / (_Tp(__i) * (__nu + _Tp(__i)));
434 return __fact * __Jn;
452 template<
typename _Tp>
456 if (__nu < _Tp(0) || __x < _Tp(0))
457 std::__throw_domain_error(__N(
"Bad argument "
458 "in __cyl_bessel_j."));
459 else if (__isnan(__nu) || __isnan(__x))
461 else if (__x * __x < _Tp(10) * (__nu + _Tp(1)))
463 else if (__x > _Tp(1000))
471 _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
472 __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
494 template<
typename _Tp>
498 if (__nu < _Tp(0) || __x < _Tp(0))
499 std::__throw_domain_error(__N(
"Bad argument "
500 "in __cyl_neumann_n."));
501 else if (__isnan(__nu) || __isnan(__x))
503 else if (__x > _Tp(1000))
511 _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
512 __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
531 template <
typename _Tp>
534 _Tp & __j_n, _Tp & __n_n, _Tp & __jp_n, _Tp & __np_n)
536 const _Tp __nu = _Tp(__n) + _Tp(0.5L);
538 _Tp __J_nu, __N_nu, __Jp_nu, __Np_nu;
539 __bessel_jn(__nu, __x, __J_nu, __N_nu, __Jp_nu, __Np_nu);
544 __j_n = __factor * __J_nu;
545 __n_n = __factor * __N_nu;
546 __jp_n = __factor * __Jp_nu - __j_n / (_Tp(2) * __x);
547 __np_n = __factor * __Np_nu - __n_n / (_Tp(2) * __x);
566 template <
typename _Tp>
571 std::__throw_domain_error(__N(
"Bad argument "
572 "in __sph_bessel."));
573 else if (__isnan(__x))
575 else if (__x == _Tp(0))
584 _Tp __j_n, __n_n, __jp_n, __np_n;
604 template <
typename _Tp>
609 std::__throw_domain_error(__N(
"Bad argument "
610 "in __sph_neumann."));
611 else if (__isnan(__x))
613 else if (__x == _Tp(0))
617 _Tp __j_n, __n_n, __jp_n, __np_n;
627 #endif // _GLIBCXX_TR1_BESSEL_FUNCTION_TCC