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21 KiB
21 KiB
Util
Utility functions.
External C functions
erf_float |
Error function erf from libm |
erfc_float |
Complementary error function erfc from libm |
gamma_float |
Gamma function gamma from libm |
popcnt |
popcnt instruction |
trailz |
ctz instruction |
leadz |
bsf instruction |
Erf
external erf_float : float -> float = "erf_float_bytecode" "erf_float" [@@unboxed] [@@noalloc]
Erfc
external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float" [@@unboxed] [@@noalloc]
Gamma
external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float" [@@unboxed] [@@noalloc]
Popcnt
val popcnt : int64 -> int
Trailz
val trailz : int64 -> int
Leadz
val leadz : int64 -> int
Test
General functions
val fact : int -> float
(* @raise Invalid_argument for negative arguments or arguments >100. *)
val binom : int -> int -> int
val binom_float : int -> int -> float
val chop : float -> (unit -> float) -> float
val pow : float -> int -> float
val float_of_int_fast : int -> float
val not_implemented : unit -> 'a
val of_some : 'a option -> 'a
fact |
Factorial function. |
binom |
Binomial coefficient. binom n k = $C_n^k$ |
binom_float |
float variant of binom |
pow |
Fast implementation of the power function for small integer powers |
chop |
In chop a f , evaluate f only if the absolute value of a is larger than Constants.epsilon , and return a *. f () . |
float_of_int_fast |
Faster implementation of float_of_int for small positive ints |
not_implemented |
Fails with error message if some functionality is not implemented |
of_some |
Extracts the value of an option |
Functions related to the Boys function
val incomplete_gamma : alpha:float -> float -> float
(* @raise Failure when the calculation doesn't converge. *)
The lower Incomplete Gamma function is implemented : \[ \gamma(\alpha,x) = \int_0^x e^{-t} t^{\alpha-1} dt \]
p: $\frac{1}{\Gamma(\alpha)} \int_0^x e^{-t} t^{\alpha-1} dt$
q: $\frac{1}{\Gamma(\alpha)} \int_x^\infty e^{-t} t^{\alpha-1} dt$
Reference : Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten (New Algorithm handbook in C language) (Gijyutsu hyouron sha, Tokyo, 1991) p.227 [in Japanese]
val boys_function : maxm:int -> float -> float array
The Generalized Boys function is implemented,
maxm
is the maximum total angular momentum.
\[ F_m(x) = \frac{\gamma(m+1/2,x)}{2x^{m+1/2}} \] where $\gamma$ is the incomplete gamma function.
- $F_0(0.) = 1$
- $F_0(t) = \frac{\sqrt{\pi}}{2\sqrt{t}} \text{erf} ( \sqrt{t} )$
- $F_m(0.) = \frac{1}{2m+1}$
- $F_m(t) = \frac{\gamma{m+1/2,t}}{2t^{m+1/2}}$
- $F_m(t) = \frac{ 2t\, F_{m+1}(t) + e^{-t} }{2m+1}$
List functions
val list_some : 'a option list -> 'a list
val list_range : int -> int -> int list
val list_pack : int -> 'a list -> 'a list list
list_some |
Filters out all None elements of the list, and returns the elements without the Some |
list_range |
Creates a list of consecutive integers |
list_pack |
list_pack n l Creates a list of n -elements lists |
Array functions
val array_range : int -> int -> int array
val array_sum : float array -> float
val array_product : float array -> float
array_range |
Creates an array of consecutive integers |
array_sum |
Returns the sum of all the elements of the array |
array_product |
Returns the product of all the elements of the array |
Stream functions
val stream_range : int -> int -> int Stream.t
val stream_to_list : 'a Stream.t -> 'a list
val stream_fold : ('a -> 'b -> 'a) -> 'a -> 'b Stream.t -> 'a
stream_range |
Creates a stream returning consecutive integers |
stream_to_list |
Read a stream and put items in a list |
stream_fold |
Apply a fold to the elements of the stream |
Printers
val pp_float_array_size : Format.formatter -> float array -> unit
val pp_float_array : Format.formatter -> float array -> unit
val pp_float_2darray_size : Format.formatter -> float array array -> unit
val pp_float_2darray : Format.formatter -> float array array -> unit
val pp_bitstring : int -> Format.formatter -> Z.t -> unit
pp_float_array |
Printer for float arrays |
pp_float_array_size |
Printer for float arrays with size |
pp_float_2darray |
Printer for matrices |
pp_float_2darray_size |
Printer for matrices with size |
pp_bitstring |
Printer for bit strings (used by Bitstring module) |
pp_float_array_size: [ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] pp_float_array: [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] pp_float_2darray_size [ 2:[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] [ 4: 1.000000 2.000000 3.000000 4.000000 ] ] pp_float_2darray: [ [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] [ 1.000000 2.000000 3.000000 4.000000 ] ] pp_bitstring 14: +++++------+--