thirdparty.cpp File Reference

#include "cddefines.h"
#include "vectorize.h"
#include "container_classes.h"
#include "thirdparty.h"

Include dependency graph for thirdparty.cpp:

Classes
class	t_lfact

Macros
#define	F1(x, y, z)   (z ^ (x & (y ^ z)))
#define	F2(x, y, z)   F1(z, x, y)
#define	F3(x, y, z)   (x ^ y ^ z)
#define	F4(x, y, z)   (y ^ (x | ~z))
#define	MD5STEP(f, w, x, y, z, data, s)   w = rotlFixed(w + f(x, y, z) + data, s) + x

Functions
double	polevl (double x, const double coef[], int N)
double	p1evl (double x, const double coef[], int N)
double	chbevl (double, const double[], int)
double	dawson10 (double x, int order)
bool	linfit (long n, const double xorg[], const double yorg[], double &a, double &siga, double &b, double &sigb)
double	factorial (long n)
double	fc2_scl (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 x)
STATIC double	igamc_fraction (double a, double x)
double	igamc (double a, double x)
double	igamc_scaled (double a, double x)
double	igam (double a, double x)
double	ratevl_5_4 (double x, const double a[5], const double b[4])
double	ratevl_6_3 (double x, const double a[6], const double b[3])
double	ratevl_6_4 (double x, const double a[6], const double b[4])
double	ratevl_7_8 (double x, const double a[7], const double b[8])
double	ratevl_8_7 (double x, const double a[8], const double b[7])
double	ratevl_10_11 (double x, const double a[10], const double b[11])
double	ratevl_11_10 (double x, const double a[11], const double b[10])
double	ratevl_15_6 (double x, const double a[15], const double b[6])
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 *i0val, double *i1val)
void	bessel_i0_i1_scaled (double x, double *i0val, double *i1val)
double	e1 (double x)
double	e1_scaled (double x)
double	e2 (double x)
double	expn2_scaled (double x)
void	chbfit (double a, double b, vector< double > &c, double(*func)(double))
void	test_expn ()
double	gegenbauer (long n, double al, double x)
double	sg (long S)
double	sjs (long j1, long j2, long j3, long l1, long l2, long l3)
double	fc2 (long n2)
double	Delta (long j1, long j2, long j3)
double	SixJFull (long j1, long j2, long j3, long j4, long j5, long j6)
double	frac (double d)
void	rec6j (double *sixcof, double l2, double l3, double l4, double l5, double l6, double *l1min, double *l1max, double *lmatch, long ndim, long *ier)
uint64	rotl (const uint64 x, int k)
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)
double	dawson (double x)
realnum	FastVoigtH (realnum a, realnum v)
void	FastVoigtH (realnum a, const realnum v[], realnum y[], size_t n)
void	humlik (int n, const realnum x[], realnum y, realnum k[])
STATIC uint32	MD5swap (uint32 word)
STATIC void	MD5_Transform (uint32 *digest, const uint32 *in)
string	MD5file (const char *fnam, access_scheme scheme)
string	MD5datafile (const char *fnam, access_scheme scheme)
string	MD5datastream (fstream &ioFile)
STATIC void	MD5string_core (const string &str, uint32 state[4])
string	MD5string (const string &str)
void	MD5string (const string &str, uint64 md5sum[2])
uint32	rotlFixed (uint32 x, unsigned int y)
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)
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 double	pre_factorial [NPRE_FACTORIAL]
static const double	dsf [MXDSF]
static const double	b0_PP [7]
static const double	b0_PQ [7]
static const double	b0_QP [8]
static const double	b0_QQ [7]
static const double	b0_YP [8]
static const double	b0_YQ [7]
static const double	DR1 = 5.78318596294678452118e0
static const double	DR2 = 3.04712623436620863991e1
static const double	b0_RP [4]
static const double	b0_RQ [8]
static const double	TWOOPI = 2./PI
static const double	SQ2OPI = sqrt(2./PI)
static const double	PIO4 = PI/4.
static const double	b1_RP [4]
static const double	b1_RQ [8]
static const double	b1_PP [7]
static const double	b1_PQ [7]
static const double	b1_QP [8]
static const double	b1_QQ [7]
static const double	b1_YP [6]
static const double	b1_YQ [8]
static const double	Z1 = 1.46819706421238932572E1
static const double	Z2 = 4.92184563216946036703E1
static const double	THPIO4 = 3.*PI/4.
static const double	elk_P []
static const double	elk_Q []
static const double	C1 = 1.3862943611198906188e0
static const double	MAXLOG = log(DBL_MAX)
static const double	BIG = 1.44115188075855872E+17
static const double	erf_P []
static const double	erf_Q []
static const double	erf_R []
static const double	erf_S []
static const double	igam_big = 4.503599627370496e15
static const double	igam_biginv = 2.22044604925031308085e-16
static const double	BESSEL_K0_P1 []
static const double	BESSEL_K0_Q1 []
static const double	BESSEL_K0_P2 []
static const double	BESSEL_K0_Q2 []
static const double	BESSEL_K0_P3 []
static const double	BESSEL_K0_Q3 []
static const double	BESSEL_K1_P1 []
static const double	BESSEL_K1_Q1 []
static const double	BESSEL_K1_P2 []
static const double	BESSEL_K1_Q2 []
static const double	BESSEL_K1_P3 []
static const double	BESSEL_K1_Q3 []
static const double	BESSEL_I0_P1 []
static const double	BESSEL_I0_Q1 []
static const double	BESSEL_I0_P2 []
static const double	BESSEL_I0_Q2 []
static const double	BESSEL_I1_P1 []
static const double	BESSEL_I1_Q1 []
static const double	BESSEL_I1_P2 []
static const double	BESSEL_I1_Q2 []
const int	N_DAWSON = 100
static const double	tbl_dawson [N_DAWSON+1]

Macro Definition Documentation

#define F1	(		x,
			y,
			z
	)		(z ^ (x & (y ^ z)))

Referenced by MD5_Transform(), and phymir_state< X, Y, NP, NSTR >::p_setup_next_hyperblock().

#define F2	(		x,
			y,
			z
	)		F1(z, x, y)

Referenced by MD5_Transform(), and phymir_state< X, Y, NP, NSTR >::p_setup_next_hyperblock().

#define F3	(		x,
			y,
			z
	)		(x ^ y ^ z)

Referenced by MD5_Transform().

#define F4	(		x,
			y,
			z
	)		(y ^ (x | ~z))

Referenced by MD5_Transform().

#define MD5STEP	(		f,
			w,
			x,
			y,
			z,
			data,
			s
	)		w = rotlFixed(w + f(x, y, z) + data, s) + x

Referenced by MD5_Transform().

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 *	i0val,
		double *	i1val
	)

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 *	i0val,
		double *	i1val
	)

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.

double chbevl ( double  x, const double  array[], int  n  )

inline

References b0, b1, and b2.

Referenced by test_expn().

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 dawson10 ( double  x, int  order  )

inline

References get_ptr(), lagrange(), max(), min(), and order().

Referenced by dawson(), and FastVoigtH().

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double Delta ( long  j1, long  j2, long  j3  )

inline

References fc2().

Referenced by SixJFull().

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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 expn2_scaled ( double  x )

inline

References ASSERT, and expn().

Referenced by test_expn().

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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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double fc2 ( long  n2 )

inline

References factorial(), and TotalInsanity().

Referenced by Delta(), InterpolateModel(), and SixJFull().

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double fc2_scl ( long  n )

inline

References cdEXIT, dsf, EXIT_FAILURE, fprintf(), ioQQQ, and MXDSF.

Referenced by sjs().

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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 frac ( double  d )

inline

Referenced by AbundancesTable(), chbfit(), FindHCoStar(), diatomics::H2_PunchDo(), ion_widen(), t_mole_global::make_species(), mc_escape(), mie_calc_ial(), mie_cs(), mie_read_form(), mie_read_mix(), mie_write_opc(), mole_return_cached_species(), newisotope(), OpacityAddTotal(), pah1_fun(), PrintE71(), PrintE82(), PrintE93(), PrtLinePres(), RebinQHeatResults(), rec6j(), RT_line_all_escape(), SetDeuteriumFractionation(), SetIsotopeFractions(), GroupMap::setup(), size_distr(), and tbl_fun().

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

References DEBUG_ENTRY.

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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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 igam().

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STATIC double igamc_fraction	(	double	a,
		double	x
	)

References igam_big, and igam_biginv.

Referenced by igamc(), and igamc_scaled().

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().

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	xorg[],
		const double	yorg[],
		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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STATIC void MD5_Transform	(	uint32 *	digest,
		const uint32 *	in
	)

References DEBUG_ENTRY, F1, F2, F3, F4, and MD5STEP.

Referenced by MD5string_core().

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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STATIC void MD5string_core	(	const string &	str,
		uint32	state[4]
	)

References ASSERT, cpu, DEBUG_ENTRY, t_cpu::i(), t_cpu_i::little_endian(), and MD5_Transform().

Referenced by MD5string().

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STATIC uint32 MD5swap

(

uint32

word

)

References DEBUG_ENTRY.

Referenced by MD5string().

double p1evl ( double  x, const double  coef[], int  N  )

inline

Referenced by bessel_j0(), bessel_j1(), bessel_y0(), bessel_y1(), and erfce().

double polevl ( double  x, const double  coef[], int  N  )

inline

Referenced by bessel_j0(), bessel_j1(), bessel_y0(), bessel_y1(), ellpk(), and erfce().

double ratevl_10_11 ( double  x, const double  a[10], const double  b[11]  )

inline

References x2.

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

double ratevl_11_10 ( double  x, const double  a[11], const double  b[10]  )

inline

References x2.

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

double ratevl_15_6 ( double  x, const double  a[15], const double  b[6]  )

inline

References x2.

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i0_scaled(), bessel_i1(), and bessel_i1_scaled().

double ratevl_5_4 ( double  x, const double  a[5], const double  b[4]  )

inline

References x2.

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

double ratevl_6_3 ( double  x, const double  a[6], const double  b[3]  )

inline

References x2.

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

double ratevl_6_4 ( double  x, const double  a[6], const double  b[4]  )

inline

References x2.

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

double ratevl_7_8 ( double  x, const double  a[7], const double  b[8]  )

inline

References x2.

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), and bessel_i0_scaled().

double ratevl_8_7 ( double  x, const double  a[8], const double  b[7]  )

inline

References x2.

Referenced by bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i1(), and bessel_i1_scaled().

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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uint64 rotl ( const uint64  x, int  k  )

inline

Referenced by xoroshiro128plus(), xoroshiro128plus_jump(), xoshiro256starstar(), and xoshiro256starstar_jump().

uint32 rotlFixed ( uint32  x, unsigned int  y  )

inline

double sg ( long  S )

inline

References TotalInsanity().

Referenced by SixJFull(), and sjs().

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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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uint64 splitmix64

(

uint64 &

state

)

Referenced by init_seed().

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
	)

void test_expn

(

)

References chbevl(), chbfit(), expn2_scaled(), fprintf(), and ioQQQ.

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

References DEBUG_ENTRY, and rotl().

Referenced by t_ran::p_xoroshiro128plus().

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void xoroshiro128plus_jump	(	uint64 &	state0,
		uint64 &	state1
	)

References DEBUG_ENTRY, and rotl().

Referenced by init_seed().

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

References DEBUG_ENTRY, and rotl().

Referenced by t_ran::p_xoshiro256starstar().

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

References DEBUG_ENTRY, and rotl().

Referenced by init_seed().

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Variable Documentation

const double b0_PP[7]

static

Initial value:

= {
        7.96936729297347051624e-4,
        8.28352392107440799803e-2,
        1.23953371646414299388e0,
        5.44725003058768775090e0,
        8.74716500199817011941e0,
        5.30324038235394892183e0,
        9.99999999999999997821e-1,
}

Referenced by bessel_j0(), and bessel_y0().

const double b0_PQ[7]

static

Initial value:

= {
        9.24408810558863637013e-4,
        8.56288474354474431428e-2,
        1.25352743901058953537e0,
        5.47097740330417105182e0,
        8.76190883237069594232e0,
        5.30605288235394617618e0,
        1.00000000000000000218e0,
}

Referenced by bessel_j0(), and bessel_y0().

const double b0_QP[8]

static

Initial value:

= {
        -1.13663838898469149931e-2,
        -1.28252718670509318512e0,
        -1.95539544257735972385e1,
        -9.32060152123768231369e1,
        -1.77681167980488050595e2,
        -1.47077505154951170175e2,
        -5.14105326766599330220e1,
        -6.05014350600728481186e0,
}

Referenced by bessel_j0(), and bessel_y0().

const double b0_QQ[7]

static

Initial value:

= {
        
        6.43178256118178023184e1,
        8.56430025976980587198e2,
        3.88240183605401609683e3,
        7.24046774195652478189e3,
        5.93072701187316984827e3,
        2.06209331660327847417e3,
        2.42005740240291393179e2,
}

Referenced by bessel_j0(), and bessel_y0().

const double b0_RP[4]

static

Initial value:

= {
        -4.79443220978201773821e9,
        1.95617491946556577543e12,
        -2.49248344360967716204e14,
        9.70862251047306323952e15,
}

Referenced by bessel_j0().

const double b0_RQ[8]

static

Initial value:

= {
        
        4.99563147152651017219e2,
        1.73785401676374683123e5,
        4.84409658339962045305e7,
        1.11855537045356834862e10,
        2.11277520115489217587e12,
        3.10518229857422583814e14,
        3.18121955943204943306e16,
        1.71086294081043136091e18,
}

Referenced by bessel_j0().

const double b0_YP[8]

static

Initial value:

= {
        1.55924367855235737965e4,
        -1.46639295903971606143e7,
        5.43526477051876500413e9,
        -9.82136065717911466409e11,
        8.75906394395366999549e13,
        -3.46628303384729719441e15,
        4.42733268572569800351e16,
        -1.84950800436986690637e16,
}

Referenced by bessel_y0().

const double b0_YQ[7]

static

Initial value:

= {
        
        1.04128353664259848412e3,
        6.26107330137134956842e5,
        2.68919633393814121987e8,
        8.64002487103935000337e10,
        2.02979612750105546709e13,
        3.17157752842975028269e15,
        2.50596256172653059228e17,
}

Referenced by bessel_y0().

const double b1_PP[7]

static

Initial value:

= {
        7.62125616208173112003e-4,
        7.31397056940917570436e-2,
        1.12719608129684925192e0,
        5.11207951146807644818e0,
        8.42404590141772420927e0,
        5.21451598682361504063e0,
        1.00000000000000000254e0,
}

Referenced by bessel_j1(), and bessel_y1().

const double b1_PQ[7]

static

Initial value:

= {
        5.71323128072548699714e-4,
        6.88455908754495404082e-2,
        1.10514232634061696926e0,
        5.07386386128601488557e0,
        8.39985554327604159757e0,
        5.20982848682361821619e0,
        9.99999999999999997461e-1,
}

Referenced by bessel_j1(), and bessel_y1().

const double b1_QP[8]

static

Initial value:

= {
        5.10862594750176621635e-2,
        4.98213872951233449420e0,
        7.58238284132545283818e1,
        3.66779609360150777800e2,
        7.10856304998926107277e2,
        5.97489612400613639965e2,
        2.11688757100572135698e2,
        2.52070205858023719784e1,
}

Referenced by bessel_j1(), and bessel_y1().

const double b1_QQ[7]

static

Initial value:

= {
        
        7.42373277035675149943e1,
        1.05644886038262816351e3,
        4.98641058337653607651e3,
        9.56231892404756170795e3,
        7.99704160447350683650e3,
        2.82619278517639096600e3,
        3.36093607810698293419e2,
}

Referenced by bessel_j1(), and bessel_y1().

const double b1_RP[4]

static

Initial value:

= {
        -8.99971225705559398224e8,
        4.52228297998194034323e11,
        -7.27494245221818276015e13,
        3.68295732863852883286e15,
}

Referenced by bessel_j1().

const double b1_RQ[8]

static

Initial value:

= {
        
        6.20836478118054335476e2,
        2.56987256757748830383e5,
        8.35146791431949253037e7,
        2.21511595479792499675e10,
        4.74914122079991414898e12,
        7.84369607876235854894e14,
        8.95222336184627338078e16,
        5.32278620332680085395e18,
}

Referenced by bessel_j1().

const double b1_YP[6]

static

Initial value:

= {
        1.26320474790178026440e9,
        -6.47355876379160291031e11,
        1.14509511541823727583e14,
        -8.12770255501325109621e15,
        2.02439475713594898196e17,
        -7.78877196265950026825e17,
}

Referenced by bessel_y1().

const double b1_YQ[8]

static

Initial value:

= {
        
        5.94301592346128195359E2,
        2.35564092943068577943E5,
        7.34811944459721705660E7,
        1.87601316108706159478E10,
        3.88231277496238566008E12,
        6.20557727146953693363E14,
        6.87141087355300489866E16,
        3.97270608116560655612E18,
}

Referenced by bessel_y1().

const double BESSEL_I0_P1[]

static

Initial value:

= {
        -2.2335582639474375249e+15, -5.5050369673018427753e+14, -3.2940087627407749166e+13,
        -8.4925101247114157499e+11, -1.1912746104985237192e+10, -1.0313066708737980747e+08,
        -5.9545626019847898221e+05, -2.4125195876041896775e+03, -7.0935347449210549190e+00,
        -1.5453977791786851041e-02, -2.5172644670688975051e-05, -3.0517226450451067446e-08,
        -2.6843448573468483278e-11, -1.5982226675653184646e-14, -5.2487866627945699800e-18
}

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), and bessel_i0_scaled().

const double BESSEL_I0_P2[]

static

Initial value:

= {
        -2.2210262233306573296e-04, 1.3067392038106924055e-02, -4.4700805721174453923e-01,
        5.5674518371240761397e+00, -2.3517945679239481621e+01, 3.1611322818701131207e+01,
        -9.6090021968656180000e+00
}

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), and bessel_i0_scaled().

const double BESSEL_I0_Q1[]

static

Initial value:

= {
        -2.2335582639474375245e+15, 7.8858692566751002988e+12, -1.2207067397808979846e+10,
        1.0377081058062166144e+07, -4.8527560179962773045e+03, 1.0
}

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), and bessel_i0_scaled().

const double BESSEL_I0_Q2[]

static

Initial value:

= {
        -5.5194330231005480228e-04, 3.2547697594819615062e-02, -1.1151759188741312645e+00,
        1.3982595353892851542e+01, -6.0228002066743340583e+01, 8.5539563258012929600e+01,
        -3.1446690275135491500e+01, 1.0
}

Referenced by bessel_i0(), bessel_i0_i1(), bessel_i0_i1_scaled(), and bessel_i0_scaled().

const double BESSEL_I1_P1[]

static

Initial value:

= {
        -1.4577180278143463643e+15, -1.7732037840791591320e+14, -6.9876779648010090070e+12,
        -1.3357437682275493024e+11, -1.4828267606612366099e+09, -1.0588550724769347106e+07,
        -5.1894091982308017540e+04, -1.8225946631657315931e+02, -4.7207090827310162436e-01,
        -9.1746443287817501309e-04, -1.3466829827635152875e-06, -1.4831904935994647675e-09,
        -1.1928788903603238754e-12, -6.5245515583151902910e-16, -1.9705291802535139930e-19
}

Referenced by bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i1(), and bessel_i1_scaled().

const double BESSEL_I1_P2[]

static

Initial value:

= {
        1.4582087408985668208e-05, -8.9359825138577646443e-04, 2.9204895411257790122e-02,
        -3.4198728018058047439e-01, 1.3960118277609544334e+00, -1.9746376087200685843e+00,
        8.5591872901933459000e-01, -6.0437159056137599999e-02
}

Referenced by bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i1(), and bessel_i1_scaled().

const double BESSEL_I1_Q1[]

static

Initial value:

= {
        -2.9154360556286927285e+15, 9.7887501377547640438e+12, -1.4386907088588283434e+10,
        1.1594225856856884006e+07, -5.1326864679904189920e+03, 1.0
}

Referenced by bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i1(), and bessel_i1_scaled().

const double BESSEL_I1_Q2[]

static

Initial value:

= {
        3.7510433111922824643e-05, -2.2835624489492512649e-03, 7.4212010813186530069e-02,
        -8.5017476463217924408e-01, 3.2593714889036996297e+00, -3.8806586721556593450e+00, 1.0
}

Referenced by bessel_i0_i1(), bessel_i0_i1_scaled(), bessel_i1(), and bessel_i1_scaled().

const double BESSEL_K0_P1[]

static

Initial value:

= {
        2.4708152720399552679e+03, 5.9169059852270512312e+03, 4.6850901201934832188e+02,
        1.1999463724910714109e+01, 1.3166052564989571850e-01, 5.8599221412826100000e-04
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K0_P2[]

static

Initial value:

= {
        -1.6128136304458193998e+06, -3.7333769444840079748e+05, -1.7984434409411765813e+04,
        -2.9501657892958843865e+02, -1.6414452837299064100e+00
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K0_P3[]

static

Initial value:

= {
        1.1600249425076035558e+02, 2.3444738764199315021e+03, 1.8321525870183537725e+04,
        7.1557062783764037541e+04, 1.5097646353289914539e+05, 1.7398867902565686251e+05,
        1.0577068948034021957e+05, 3.1075408980684392399e+04, 3.6832589957340267940e+03,
        1.1394980557384778174e+02
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K0_Q1[]

static

Initial value:

= {
        2.1312714303849120380e+04, -2.4994418972832303646e+02, 1.0
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K0_Q2[]

static

Initial value:

= {
        -1.6128136304458193998e+06, 2.9865713163054025489e+04, -2.5064972445877992730e+02, 1.0
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K0_Q3[]

static

Initial value:

= {
        9.2556599177304839811e+01, 1.8821890840982713696e+03, 1.4847228371802360957e+04,
        5.8824616785857027752e+04, 1.2689839587977598727e+05, 1.5144644673520157801e+05,
        9.7418829762268075784e+04, 3.1474655750295278825e+04, 4.4329628889746408858e+03,
        2.0013443064949242491e+02, 1.0
}

Referenced by bessel_k0(), bessel_k0_k1(), bessel_k0_k1_scaled(), and bessel_k0_scaled().

const double BESSEL_K1_P1[]

static

Initial value:

= {
        -2.2149374878243304548e+06, 7.1938920065420586101e+05, 1.7733324035147015630e+05,
        7.1885382604084798576e+03, 9.9991373567429309922e+01, 4.8127070456878442310e-01
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BESSEL_K1_P2[]

static

Initial value:

= {
        0.0, -1.3531161492785421328e+06, -1.4758069205414222471e+05,
        -4.5051623763436087023e+03, -5.3103913335180275253e+01, -2.2795590826955002390e-01
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BESSEL_K1_P3[]

static

Initial value:

= {
        2.2196792496874548962e+00, 4.4137176114230414036e+01, 3.4122953486801312910e+02,
        1.3319486433183221990e+03, 2.8590657697910288226e+03, 3.4540675585544584407e+03,
        2.3123742209168871550e+03, 8.1094256146537402173e+02, 1.3182609918569941308e+02,
        7.5584584631176030810e+00, 6.4257745859173138767e-02
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BESSEL_K1_Q1[]

static

Initial value:

= {
        -2.2149374878243304548e+06, 3.7264298672067697862e+04, -2.8143915754538725829e+02, 1.0
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BESSEL_K1_Q2[]

static

Initial value:

= {
        -2.7062322985570842656e+06, 4.3117653211351080007e+04, -3.0507151578787595807e+02, 1.0
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BESSEL_K1_Q3[]

static

Initial value:

= {
        1.7710478032601086579e+00, 3.4552228452758912848e+01, 2.5951223655579051357e+02,
        9.6929165726802648634e+02, 1.9448440788918006154e+03, 2.1181000487171943810e+03,
        1.2082692316002348638e+03, 3.3031020088765390854e+02, 3.6001069306861518855e+01, 1.0
}

Referenced by bessel_k0_k1(), bessel_k0_k1_scaled(), bessel_k1(), and bessel_k1_scaled().

const double BIG = 1.44115188075855872E+17

static

Referenced by expn(), and ffun1().

const double C1 = 1.3862943611198906188e0

static

Referenced by ellpk(), Hydcs123(), and ILAENV().

const double DR1 = 5.78318596294678452118e0

static

Referenced by bessel_j0().

const double DR2 = 3.04712623436620863991e1

static

Referenced by bessel_j0().

const double dsf[MXDSF]

static

Referenced by fc2_scl().

const double elk_P[]

static

Initial value:

=
{
        1.37982864606273237150e-4,
        2.28025724005875567385e-3,
        7.97404013220415179367e-3,
        9.85821379021226008714e-3,
        6.87489687449949877925e-3,
        6.18901033637687613229e-3,
        8.79078273952743772254e-3,
        1.49380448916805252718e-2,
        3.08851465246711995998e-2,
        9.65735902811690126535e-2,
        1.38629436111989062502e0
}

Referenced by ellpk().

const double elk_Q[]

static

Initial value:

=
{
        2.94078955048598507511e-5,
        9.14184723865917226571e-4,
        5.94058303753167793257e-3,
        1.54850516649762399335e-2,
        2.39089602715924892727e-2,
        3.01204715227604046988e-2,
        3.73774314173823228969e-2,
        4.88280347570998239232e-2,
        7.03124996963957469739e-2,
        1.24999999999870820058e-1,
        4.99999999999999999821e-1
}

Referenced by ellpk().

const double erf_P[]

static

Initial value:

= {
 2.46196981473530512524e-10,
 5.64189564831068821977e-1,
 7.46321056442269912687e0,
 4.86371970985681366614e1,
 1.96520832956077098242e2,
 5.26445194995477358631e2,
 9.34528527171957607540e2,
 1.02755188689515710272e3,
 5.57535335369399327526e2
}

Referenced by erfce().

const double erf_Q[]

static

Initial value:

= {

 1.32281951154744992508e1,
 8.67072140885989742329e1,
 3.54937778887819891062e2,
 9.75708501743205489753e2,
 1.82390916687909736289e3,
 2.24633760818710981792e3,
 1.65666309194161350182e3,
 5.57535340817727675546e2
}

Referenced by erfce().

const double erf_R[]

static

Initial value:

= {
 5.64189583547755073984e-1,
 1.27536670759978104416e0,
 5.01905042251180477414e0,
 6.16021097993053585195e0,
 7.40974269950448939160e0,
 2.97886665372100240670e0
}

Referenced by erfce().

const double erf_S[]

static

Initial value:

= {

 2.26052863220117276590e0,
 9.39603524938001434673e0,
 1.20489539808096656605e1,
 1.70814450747565897222e1,
 9.60896809063285878198e0,
 3.36907645100081516050e0
}

Referenced by erfce().

const double igam_big = 4.503599627370496e15

static

Referenced by igamc_fraction().

const double igam_biginv = 2.22044604925031308085e-16

static

Referenced by igamc_fraction().

const double MAXLOG = log(DBL_MAX)

static

Referenced by expn(), igam(), igamc(), and igamc_scaled().

const int N_DAWSON = 100

const double PIO4 = PI/4.

static

Referenced by bessel_j0(), and bessel_y0().

const double pre_factorial[NPRE_FACTORIAL]

static

Referenced by factorial().

const double SQ2OPI = sqrt(2./PI)

static

Referenced by bessel_j0(), bessel_j1(), bessel_y0(), and bessel_y1().

const double tbl_dawson[N_DAWSON+1]

static

const double THPIO4 = 3.*PI/4.

static

Referenced by bessel_j1(), and bessel_y1().

const double TWOOPI = 2./PI

static

Referenced by bessel_y0(), and bessel_y1().

const double Z1 = 1.46819706421238932572E1

static

Referenced by bessel_j1().

const double Z2 = 4.92184563216946036703E1

static

Referenced by bessel_j1().