Header Factorial.h

Detailed Description

Static tables of the factorial and double-factorial functions, and derived quantities.

Author

Karl Wette

Description

The following tables of the factorial function are provided:

• UINT8 LAL_FACT[ \(i\)] = \(i!\)
• REAL8 LAL_FACT_INV[ \(i\)] = \(1/i!\)
• REAL8 LAL_FACT_LOG[ \(i\)] = \(\log i!\)

The maximum allowable index \(i\) of these tables is LAL_FACT_MAX. This value is determines by the maximum value of \(i!\) that can be stored in an UINT8.

The following tables of the double-factorial function are provided:

• UINT8 LAL_FACT2[ \(i\)] = \(i!!\)
• REAL8 LAL_FACT2_INV[ \(i\)] = \(1/i!!\)
• REAL8 LAL_FACT2_LOG[ \(i\)] = \(\log i!!\)

The maximum allowable index \(i\) of these tables is LAL_FACT2_MAX. This value is determines by the maximum value of \(i!!\) that can be stored in an UINT8.

All values were computed to 35 significant figures with Mathematica v8.0.1.0 on 64-bit Linux.

Macros
#define	LAL_FACT_MAX   20
#define	LAL_FACT2_MAX   33

Variables
static const UINT8	LAL_FACT []
static const REAL8	LAL_FACT_INV []
static const REAL8	LAL_FACT_LOG []
static const UINT8	LAL_FACT2 []
static const REAL8	LAL_FACT2_INV []
static const REAL8	LAL_FACT2_LOG []

Macro Definition Documentation

LAL_FACT_MAX

#define LAL_FACT_MAX   20

Definition at line 57 of file Factorial.h.

LAL_FACT2_MAX

#define LAL_FACT2_MAX   33

Definition at line 131 of file Factorial.h.

Variable Documentation

LAL_FACT

const UINT8 LAL_FACT[]

static

Initial value:

= { 
  1, 
  1, 
  2, 
  6, 
  24, 
  120, 
  720, 
  5040, 
  40320, 
  362880, 
  3628800, 
  39916800, 
  479001600, 
  6227020800, 
  87178291200, 
  1307674368000, 
  20922789888000, 
  355687428096000, 
  6402373705728000, 
  121645100408832000, 
  2432902008176640000 
}

Definition at line 59 of file Factorial.h.

LAL_FACT_INV

const REAL8 LAL_FACT_INV[]

static

Initial value:

= { 
  1., 
  1., 
  0.5, 
  0.16666666666666666666666666666666667, 
  0.041666666666666666666666666666666667, 
  0.0083333333333333333333333333333333333, 
  0.0013888888888888888888888888888888889, 
  0.00019841269841269841269841269841269841, 
  0.000024801587301587301587301587301587302, 
  2.7557319223985890652557319223985891e-6, 
  2.7557319223985890652557319223985891e-7, 
  2.5052108385441718775052108385441719e-8, 
  2.0876756987868098979210090321201432e-9, 
  1.6059043836821614599392377170154948e-10, 
  1.1470745597729724713851697978682106e-11, 
  7.6471637318198164759011319857880704e-13, 
  4.779477332387385297438207491117544e-14, 
  2.81145725434552076319894558301032e-15, 
  1.5619206968586226462216364350057333e-16, 
  8.2206352466243297169559812368722807e-18, 
  4.1103176233121648584779906184361404e-19 
}

Definition at line 83 of file Factorial.h.

LAL_FACT_LOG

const REAL8 LAL_FACT_LOG[]

static

Initial value:

= { 
  0., 
  0., 
  0.6931471805599453094172321214581766, 
  1.7917594692280550008124773583807023, 
  3.1780538303479456196469416012970554, 
  4.787491742782045994247700934523243, 
  6.5792512120101009950601782929039453, 
  8.5251613610654143001655310363471251, 
  10.6046029027452502284172274007216548, 
  12.8018274800814696112077178745667062, 
  15.1044125730755152952257093292510704, 
  17.5023078458738858392876529072161997, 
  19.9872144956618861495173623870550785, 
  22.5521638531234228855708498286203971, 
  25.1912211827386815000934346935217534, 
  27.8992713838408915660894392636704668, 
  30.671860106080672803758367749503173, 
  33.5050734501368888840079023673762996, 
  36.3954452080330535762156249626795275, 
  39.3398841871994940362246523945673811, 
  42.3356164607534850296598759707099219 
}

Definition at line 107 of file Factorial.h.

LAL_FACT2

const UINT8 LAL_FACT2[]

static

Definition at line 133 of file Factorial.h.

LAL_FACT2_INV

const REAL8 LAL_FACT2_INV[]

static

Definition at line 170 of file Factorial.h.

LAL_FACT2_LOG

const REAL8 LAL_FACT2_LOG[]

static

Definition at line 207 of file Factorial.h.