#include "physconst.h"

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Classes
class	UltraGen

struct	trieNode

Functions
bool	linfit (long n, const double x[], const double y[], double &a, double &siga, double &b, double &sigb)

double	factorial (long n)

double	lfactorial (long n)

complex< double >	cdgamma (complex< double > x)

double	bessel_j0 (double x)

double	bessel_y0 (double x)

double	bessel_j1 (double x)

double	bessel_y1 (double x)

double	bessel_jn (int n, double x)

double	bessel_yn (int n, double x)

double	ellpk (double x)

double	expn (int n, double x)

double	erfce (double)

double	igam (double a, double x)

double	igamc (double a, double x)

double	igamc_scaled (double a, double x)

double	bessel_k0 (double x)

double	bessel_k0_scaled (double x)

double	bessel_k1 (double x)

double	bessel_k1_scaled (double x)

void	bessel_k0_k1 (double x, double k0val, double k1val)

void	bessel_k0_k1_scaled (double x, double k0val, double k1val)

double	bessel_i0 (double x)

double	bessel_i0_scaled (double x)

double	bessel_i1 (double x)

double	bessel_i1_scaled (double x)

void	bessel_i0_i1 (double x, double k0val, double k1val)

void	bessel_i0_i1_scaled (double x, double k0val, double k1val)

void	sincos (double x, double s, double c)

double	e1 (double x)

double	e1_scaled (double x)

double	e2 (double t)

void	xoroshiro128plus (uint64 *pool, size_t size, uint64 state[], size_t ns)

void	xoroshiro128plus_jump (uint64 &state0, uint64 &state1)

void	xoshiro256starstar (uint64 *pool, size_t size, uint64 state[], size_t ns)

void	xoshiro256starstar_jump (uint64 &state0, uint64 &state1, uint64 &state2, uint64 &state3)

uint64	splitmix64 (uint64 &state)

void	spline_cubic_set (long n, const double t[], const double y[], double ypp[], int ibcbeg, double ybcbeg, int ibcend, double ybcend)

void	spline_cubic_val (long n, const double t[], double tval, const double y[], const double ypp[], double yval, double ypval, double *yppval)

void	spline (const double x[], const double y[], long int n, double yp1, double ypn, double y2a[])

void	splint (const double xa[], const double ya[], const double y2a[], long int n, double x, double *y)

void	spldrv (const double xa[], const double ya[], const double y2a[], long int n, double x, double *y)

void	splint_safe (const double xa[], const double ya[], const double y2a[], long int n, double x, double y, bool lgOutOfBounds)

void	spldrv_safe (const double xa[], const double ya[], const double y2a[], long int n, double x, double y, bool lgOutOfBounds)

double	lagrange (const double x[], const double y[], long n, double xval)

template<class T >
long	hunt_bisect (const T x[], long n, T xval)

template<class T >
long	hunt_bisect (const vector< T > &x, T xval)

template<class T >
long	hunt_bisect (const vector< T > &x, size_t n, T xval)

template<class T >
long	hunt_bisect_reverse (const T x[], long n, T xval)

template<class T >
long	hunt_bisect_reverse (const vector< T > &x, T xval)

template<class T >
long	hunt_bisect_reverse (const vector< T > &x, size_t n, T xval)

template<class T >
T	linint (const T x[], const T y[], long n, T xval)

void	getrf_wrapper (long M, long N, double A, long lda, int32 ipiv, int32 *info)

void	getrs_wrapper (char trans, long N, long nrhs, double A, long lda, int32 ipiv, double B, long ldb, int32 info)

double	dawson (double x)

void	humlik (int n, const realnum x[], realnum y, realnum k[])

realnum	FastVoigtH (realnum a, realnum v)

void	FastVoigtH (realnum a, const realnum v[], realnum y[], size_t n)

void	VoigtH (realnum a, const realnum v[], realnum y[], int n)

void	VoigtU (realnum a, const realnum v[], realnum y[], int n)

double	VoigtH0 (double a)

double	VoigtU0 (double a)

string	MD5file (const char *fnam, access_scheme scheme=AS_DEFAULT)

string	MD5datafile (const char *fnam, access_scheme scheme=AS_DEFAULT)

string	MD5datastream (fstream &ioFile)

string	MD5string (const string &str)

void	MD5string (const string &str, uint64 md5sum[2])

void	test_expn ()

void	chbfit (double a, double b, vector< double > &c, double(*func)(double))

void	svd (const int nm, const int m, const int n, double a, double w, bool matu, double u, bool matv, double v, int ierr, double rv1)

double	gegenbauer (long n, double al, double x)

bool	Triangle2 (long J1, long J2, long J3)

double	sjs (long j1, long j2, long j3, long l1, long l2, long l3)

double	SixJFull (long j1, long j2, long j3, long j4, long j5, long j6)

void	rec6j (double sixcof, double l2, double l3, double l4, double l5, double l6, double l1min, double l1max, double lmatch, long ndim, long *ier)

void	insertToken (trieNode *root, const string &token)

size_t	findUniqueLen (trieNode *root, const string &token)

size_t	LevenshteinDistance (const string &s, const string &t)

Variables
static const int	NPRE_FACTORIAL = 171

static const int	MXDSF = 340

static const unsigned int	NMD5 = 32

static const size_t	TRIESZ = 128

Function Documentation

double bessel_i0 ( double x )

References BESSEL_I0_P1, BESSEL_I0_P2, BESSEL_I0_Q1, BESSEL_I0_Q2, DEBUG_ENTRY, ratevl_15_6(), and ratevl_7_8().

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void bessel_i0_i1	(	double	x,
		double *	k0val,
		double *	k1val
	)

References BESSEL_I0_P1, BESSEL_I0_P2, BESSEL_I0_Q1, BESSEL_I0_Q2, BESSEL_I1_P1, BESSEL_I1_P2, BESSEL_I1_Q1, BESSEL_I1_Q2, DEBUG_ENTRY, ratevl_15_6(), ratevl_7_8(), and ratevl_8_7().

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void bessel_i0_i1_scaled	(	double	x,
		double *	k0val,
		double *	k1val
	)

References BESSEL_I0_P1, BESSEL_I0_P2, BESSEL_I0_Q1, BESSEL_I0_Q2, BESSEL_I1_P1, BESSEL_I1_P2, BESSEL_I1_Q1, BESSEL_I1_Q2, DEBUG_ENTRY, ratevl_15_6(), ratevl_7_8(), and ratevl_8_7().

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double bessel_i0_scaled ( double x )

References BESSEL_I0_P1, BESSEL_I0_P2, BESSEL_I0_Q1, BESSEL_I0_Q2, DEBUG_ENTRY, ratevl_15_6(), and ratevl_7_8().

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double bessel_i1 ( double x )

References BESSEL_I1_P1, BESSEL_I1_P2, BESSEL_I1_Q1, BESSEL_I1_Q2, DEBUG_ENTRY, ratevl_15_6(), and ratevl_8_7().

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double bessel_i1_scaled ( double x )

References BESSEL_I1_P1, BESSEL_I1_P2, BESSEL_I1_Q1, BESSEL_I1_Q2, DEBUG_ENTRY, ratevl_15_6(), and ratevl_8_7().

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double bessel_j0 ( double x )

References b0_PP, b0_PQ, b0_QP, b0_QQ, b0_RP, b0_RQ, DEBUG_ENTRY, DR1, DR2, p1evl(), PIO4, polevl(), and SQ2OPI.

Referenced by bessel_jn(), and bessel_y0().

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double bessel_j1 ( double x )

References b1_PP, b1_PQ, b1_QP, b1_QQ, b1_RP, b1_RQ, DEBUG_ENTRY, p1evl(), polevl(), SQ2OPI, THPIO4, Z1, and Z2.

Referenced by bessel_jn(), and bessel_y1().

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double bessel_jn	(	int	n,
		double	x
	)

References bessel_j0(), bessel_j1(), DEBUG_ENTRY, factorial(), powi(), and sign().

Referenced by AngerJ().

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double bessel_k0 ( double x )

References BESSEL_K0_P1, BESSEL_K0_P2, BESSEL_K0_P3, BESSEL_K0_Q1, BESSEL_K0_Q2, BESSEL_K0_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_10_11(), ratevl_5_4(), and ratevl_6_3().

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void bessel_k0_k1	(	double	x,
		double *	k0val,
		double *	k1val
	)

References BESSEL_K0_P1, BESSEL_K0_P2, BESSEL_K0_P3, BESSEL_K0_Q1, BESSEL_K0_Q2, BESSEL_K0_Q3, BESSEL_K1_P1, BESSEL_K1_P2, BESSEL_K1_P3, BESSEL_K1_Q1, BESSEL_K1_Q2, BESSEL_K1_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_10_11(), ratevl_11_10(), ratevl_5_4(), ratevl_6_3(), and ratevl_6_4().

Referenced by my_Integrand_S62::operator()().

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void bessel_k0_k1_scaled	(	double	x,
		double *	k0val,
		double *	k1val
	)

References BESSEL_K0_P1, BESSEL_K0_P2, BESSEL_K0_P3, BESSEL_K0_Q1, BESSEL_K0_Q2, BESSEL_K0_Q3, BESSEL_K1_P1, BESSEL_K1_P2, BESSEL_K1_P3, BESSEL_K1_Q1, BESSEL_K1_Q2, BESSEL_K1_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_10_11(), ratevl_11_10(), ratevl_5_4(), ratevl_6_3(), and ratevl_6_4().

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double bessel_k0_scaled ( double x )

References BESSEL_K0_P1, BESSEL_K0_P2, BESSEL_K0_P3, BESSEL_K0_Q1, BESSEL_K0_Q2, BESSEL_K0_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_10_11(), ratevl_5_4(), and ratevl_6_3().

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double bessel_k1 ( double x )

References BESSEL_K1_P1, BESSEL_K1_P2, BESSEL_K1_P3, BESSEL_K1_Q1, BESSEL_K1_Q2, BESSEL_K1_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_11_10(), and ratevl_6_4().

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double bessel_k1_scaled ( double x )

References BESSEL_K1_P1, BESSEL_K1_P2, BESSEL_K1_P3, BESSEL_K1_Q1, BESSEL_K1_Q2, BESSEL_K1_Q3, DEBUG_ENTRY, DOMAIN_ERROR(), ratevl_11_10(), and ratevl_6_4().

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double bessel_y0 ( double x )

References b0_PP, b0_PQ, b0_QP, b0_QQ, b0_YP, b0_YQ, bessel_j0(), cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), ioQQQ, p1evl(), PIO4, polevl(), SQ2OPI, and TWOOPI.

Referenced by bessel_yn().

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double bessel_y1 ( double x )

References b1_PP, b1_PQ, b1_QP, b1_QQ, b1_YP, b1_YQ, bessel_j1(), cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), ioQQQ, p1evl(), polevl(), SQ2OPI, THPIO4, and TWOOPI.

Referenced by bessel_yn().

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double bessel_yn	(	int	n,
		double	x
	)

References bessel_y0(), bessel_y1(), cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), ioQQQ, and sign().

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complex<double> cdgamma ( complex< double > x )

References DEBUG_ENTRY.

void chbfit	(	double	a,
		double	b,
		vector< double > &	c,
		double(*)(double)	func
	)

References frac().

Referenced by test_expn().

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double dawson ( double x )

References dawson(), and dawson10().

Referenced by dawson().

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double e1 ( double x )

e1 first exponential integral

Parameters

x	optical depth argument

References cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), and ioQQQ.

Referenced by ColStrGBar(), CS_l_mixing_PS64_expI(), dqelg_(), e1_scaled(), expe1(), H21_cm_pops(), Hion_coll_ioniz_ratecoef(), Hydcs123(), hydro_vanRegemorter_deexcit(), mie_step(), newton_step(), qelg_(), SanityCheckBegin(), and Energy::set().

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double e1_scaled ( double x )

e1_scaled is exp(x)*e1(x)

References cdEXIT, DEBUG_ENTRY, e1(), EXIT_FAILURE, fprintf(), and ioQQQ.

Referenced by eeBremsSpectrum(), and Recomb_Seaton59().

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double e2 ( double t )

e2 second exponential integral

Parameters

t	optical depth argument

References cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), and ioQQQ.

Referenced by dqelg_(), H21_cm_pops(), Hion_coll_ioniz_ratecoef(), humlik(), IterRestart(), IterStart(), mie_step(), newton_step(), t_ran::normal(), qelg_(), RT_continuum(), RT_tau_reset(), and SanityCheckBegin().

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double ellpk ( double x )

References C1, cdEXIT, DEBUG_ENTRY, elk_P, elk_Q, EXIT_FAILURE, fprintf(), ioQQQ, and polevl().

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double erfce ( double )

erfce(a) returns erfc(a)*exp(a^2)

References DEBUG_ENTRY, erf_P, erf_Q, erf_R, erf_S, p1evl(), and polevl().

Referenced by VoigtH0(), and VoigtU0().

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double expn	(	int	n,
		double	x
	)

expn, returns exponential integral,

Parameters

n	is order, 1 for first integral integral
x	is argument, must be positive

References BIG, cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, factorial(), fprintf(), ioQQQ, is_odd(), MAXLOG, and powi().

Referenced by expn2_scaled(), Hion_coll_ioniz_ratecoef(), and SanityCheckBegin().

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double factorial ( long n )

factorial: compute n! by lookup in table of predefined factorials

References cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), ioQQQ, NPRE_FACTORIAL, and pre_factorial.

Referenced by bessel_jn(), expn(), and fc2().

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realnum FastVoigtH	(	realnum	a,
		realnum	v
	)

References ASSERT, dawson10(), DEBUG_ENTRY, dsexp(), order(), and pow2().

Referenced by VoigtH().

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void FastVoigtH	(	realnum	a,
		const realnum	v[],
		realnum	y[],
		size_t	n
	)

References ASSERT, dawson10(), DEBUG_ENTRY, order(), pow2(), avx_ptr< T, lgBC >::ptr0(), and vexp().

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size_t findUniqueLen	(	trieNode *	root,
		const string &	token
	)

References ASSERT, trieNode::child, DEBUG_ENTRY, trieNode::freq, and TRIESZ.

Referenced by Parser::init().

double gegenbauer	(	long	n,
		double	al,
		double	x
	)

References DEBUG_ENTRY.

void getrf_wrapper	(	long	M,
		long	N,
		double *	A,
		long	lda,
		int32 *	ipiv,
		int32 *	info
	)

getrf_wrapper return value is zero for success, non-zero is error condition

Parameters

M
N
*A
lda
*ipiv
*info

References ASSERT, DGETRF(), and INT32_MAX.

Referenced by find_solution(), iso_level(), SanityCheckBegin(), and solve_system().

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void getrs_wrapper	(	char	trans,
		long	N,
		long	nrhs,
		double *	A,
		long	lda,
		int32 *	ipiv,
		double *	B,
		long	ldb,
		int32 *	info
	)

getrs_wrapper return value is zero for success, non-zero is error condition

Parameters

trans
N
nrhs
*A
lda
*ipiv
*B
ldb
*info

References ASSERT, DGETRS(), and INT32_MAX.

Referenced by find_solution(), iso_level(), SanityCheckBegin(), and solve_system().

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void humlik	(	int	n,
		const realnum	x[],
		realnum	y,
		realnum	k[]
	)

References a0, DEBUG_ENTRY, e2(), and h2.

Referenced by VoigtH().

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template<class T >

long hunt_bisect	(	const T	x[],
		long	n,
		T	xval
	)

inline

find index ilo such that x[ilo] <= xval < x[ilo+1] using bisection this version implicitly assumes that x is monotonically increasing

Referenced by t_hydro_tbl::cs(), hunt_bisect(), t_mesh::ipointC(), iso_dielec_recomb_rate(), t_mesh::ithreshC(), linint(), mc_escape(), RebinFind(), spline_cubic_val(), TempInterp(), and TempInterp2().

template<class T >

long hunt_bisect	(	const vector< T > &	x,
		T	xval
	)

inline

vector<> versions of the above

References get_ptr(), and hunt_bisect().

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template<class T >

long hunt_bisect	(	const vector< T > &	x,
		size_t	n,
		T	xval
	)

inline

References ASSERT, get_ptr(), and hunt_bisect().

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template<class T >

long hunt_bisect_reverse	(	const T	x[],
		long	n,
		T	xval
	)

inline

find index ilo such that x[ilo] >= xval > x[ilo+1] using bisection this version implicitly assumes that x is monotonically decreasing

Referenced by hunt_bisect_reverse().

template<class T >

long hunt_bisect_reverse	(	const vector< T > &	x,
		T	xval
	)

inline

vector<> versions of the above

References get_ptr(), and hunt_bisect_reverse().

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template<class T >

long hunt_bisect_reverse	(	const vector< T > &	x,
		size_t	n,
		T	xval
	)

inline

References ASSERT, get_ptr(), and hunt_bisect_reverse().

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double igam	(	double	a,
		double	x
	)

References ASSERT, DEBUG_ENTRY, igamc(), and MAXLOG.

Referenced by igamc(), and igamc_scaled().

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double igamc	(	double	a,
		double	x
	)

References ASSERT, DEBUG_ENTRY, igam(), igamc_fraction(), and MAXLOG.

Referenced by CS_l_mixing_PS64_expI(), and igam().

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double igamc_scaled	(	double	a,
		double	x
	)

References ASSERT, DEBUG_ENTRY, igam(), igamc_fraction(), and MAXLOG.

Referenced by Recomb_Seaton59().

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void insertToken	(	trieNode *	root,
		const string &	token
	)

References ASSERT, trieNode::child, DEBUG_ENTRY, trieNode::freq, NULL, and TRIESZ.

Referenced by Parser::init().

double lagrange	(	const double	x[],
		const double	y[],
		long	n,
		double	xval
	)

lagrange: do lagrange interpolation of order n on x[], y[]

use with caution, especialy for high order n! using spline interpolation above is preferred

Parameters

x[]
y[]
n
xval	do lagrange interpolation of order n on x[], y[]

References DEBUG_ENTRY.

Referenced by t_hydro_tbl::cs(), dawson10(), t_gaunt::gauntff(), TempInterp(), and TempInterp2().

size_t LevenshteinDistance	(	const string &	s,
		const string &	t
	)

References MIN3.

Referenced by Parser::ClosestMatch().

double lfactorial ( long n )

lfactorial: compute log10(n!), this sroutine cahes its results for efficiency

References cdEXIT, DEBUG_ENTRY, EXIT_FAILURE, fprintf(), t_lfact::get_lfact(), Singleton< t_lfact >::Inst(), and ioQQQ.

Referenced by bhg_log(), bhG_mx(), fsff_log10(), and hrii_log().

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bool linfit	(	long	n,
		const double	x[],
		const double	y[],
		double &	a,
		double &	siga,
		double &	b,
		double &	sigb
	)

References ASSERT, DEBUG_ENTRY, and pow2().

Referenced by iter_track::deriv(), and iter_track::zero_fit().

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template<class T >

T linint	(	const T	x[],
		const T	y[],
		long	n,
		T	xval
	)

do linear interpolation on x[], y[];

it is assumed that x[] is strictly monotonically increasing

Parameters

x[]
y[]
n
xval

References ASSERT, and hunt_bisect().

Referenced by CHIANTI_Upsilon(), cross_section(), DynaIterStart(), GetHS98CrossSection(), HCSAR_interp(), HeCSTableInterp(), hydro_vanRegemorter_deexcit(), InterpCollRate(), lines_helium(), MolDissocCrossSection(), StoutCollRate(), and DepthTable::tabval().

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string MD5datafile	(	const char *	fnam,
		access_scheme	scheme = `AS_DEFAULT`
	)

non-standard MD5 algorithm that skips eol characters and comments lines

References DEBUG_ENTRY, MD5datastream(), mode_r, and open_data().

Referenced by t_mesh::InitMesh().

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string MD5datastream ( fstream & ioFile )

same as MD5datafile(), but operates on an already open fstream

References DEBUG_ENTRY, and MD5string().

Referenced by MD5datafile().

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string MD5file	(	const char *	fnam,
		access_scheme	scheme = `AS_DEFAULT`
	)

calculate the MD5 sum of a file

References DEBUG_ENTRY, MD5string(), mode_r, and open_data().

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string MD5string ( const string & str )

calculate the MD5 sum of a string

References DEBUG_ENTRY, MD5string_core(), and MD5swap().

Referenced by MD5datastream(), MD5file(), and t_ran::p_generate_random_seed().

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void MD5string	(	const string &	str,
		uint64	md5sum[2]
	)

References DEBUG_ENTRY, MD5string_core(), and MD5swap().

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void rec6j	(	double *	sixcof,
		double	l2,
		double	l3,
		double	l4,
		double	l5,
		double	l6,
		double *	l1min,
		double *	l1max,
		double *	lmatch,
		long	ndim,
		long *	ier
	)

References a1, a2, DEBUG_ENTRY, fprintf(), frac(), ioQQQ, max(), min(), x1, and x2.

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void sincos	(	double	x,
		double *	s,
		double *	c
	)

inline

Referenced by sinpar().

double SixJFull	(	long	j1,
		long	j2,
		long	j3,
		long	j4,
		long	j5,
		long	j6
	)

References DEBUG_ENTRY, Delta(), fc2(), max(), min(), sg(), and Triangle2().

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double sjs	(	long	j1,
		long	j2,
		long	j3,
		long	l1,
		long	l2,
		long	l3
	)

References DEBUG_ENTRY, fc2_scl(), max(), min(), sg(), and Triangle2().

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void spldrv	(	const double	xa[],
		const double	ya[],
		const double	y2a[],
		long int	n,
		double	x,
		double *	y
	)

inline

References NULL, and spline_cubic_val().

Referenced by spldrv_safe().

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void spldrv_safe	(	const double	xa[],
		const double	ya[],
		const double	y2a[],
		long int	n,
		double	x,
		double *	y,
		bool *	lgOutOfBounds
	)

inline

References DEBUG_ENTRY, MAX2, MIN2, SAFETY, and spldrv().

Referenced by GetProbDistr_LowLimit(), and qheat().

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void spline	(	const double	x[],
		const double	y[],
		long int	n,
		double	yp1,
		double	ypn,
		double	y2a[]
	)

inline

spline: set of routines to do spline interpolation

call spline first to set coefficients up, then call splint to interpolate spldrv gives dy/dx(x) rather than y(x) splint_safe and spldrv_safe check whether x is within bounds

Parameters

x[]	- array of x values given
y[]	- array of y values given
n	- number of points in these arrays
yp1	some sort of boundary condition, set to 2e31
yp2	some sort of boundary condition, set to 2e31
y2a[]	- array n long to save coefficients

References spline_cubic_set().

Referenced by atmdat_2phot_setSplineCoefs(), atmdat_CHIANTI_readin(), hmiopc(), HyperfineCreate(), InitEmissivities(), and InitEnthalpy().

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void spline_cubic_set	(	long	n,
		const double	t[],
		const double	y[],
		double	ypp[],
		int	ibcbeg,
		double	ybcbeg,
		int	ibcend,
		double	ybcend
	)

References ASSERT, cdEXIT, d3_np_fs(), DEBUG_ENTRY, EXIT_FAILURE, fprintf(), ioQQQ, and NULL.

Referenced by spline().

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void spline_cubic_val	(	long	n,
		const double	t[],
		double	tval,
		const double	y[],
		const double	ypp[],
		double *	yval,
		double *	ypval,
		double *	yppval
	)

References DEBUG_ENTRY, hunt_bisect(), and NULL.

Referenced by spldrv(), and splint().

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void splint	(	const double	xa[],
		const double	ya[],
		const double	y2a[],
		long int	n,
		double	x,
		double *	y
	)

inline

splint: do spline interpolation

Parameters

x[]	- array of x values given
y[]	- array of y valus
y2a[]	- array of save values found above
n	- number of points in these arrays
x	value where x is desired
y2a[]	- array n long to save coefficients