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Shorter documentation
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@ -48,18 +48,37 @@ open Powers
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** Conversions
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*** ~of_char~
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#+begin_src ocaml :tangle (eval mli)
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val of_char : char -> t
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val to_char : t -> char
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val to_int : t -> int
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val of_int : int -> t
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val to_string : t -> string
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#+end_src
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Returns an ~Angular_momentum.t~ when a shell is given as a character
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(case insensitive):
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| ~of_char~ | Returns an ~Angular_momentum.t~ when a shell is given as a character (case insensitive) |
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| ~to_char~ | Converts the angular momentum into a char |
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| ~of_int~ | Returns a shell given an $l$ value. |
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| ~to_int~ | Returns the $l_{max}$ value of the shell |
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| ~to_string~ | Converts the angular momentum into a string |
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#+begin_example
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Angular_momentum.of_char 'p' -> Angular_momentum.P
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Angular_momentum.of_char 'p';;
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- : Angular_momentum.t = Qcaml.Common.Angular_momentum.P
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Angular_momentum.(to_char P);;
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- : char = 'P'
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Angular_momentum.of_int 2;;
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- : Angular_momentum.t = Qcaml.Common.Angular_momentum.D
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Angular_momentum.(to_int D);;
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- : int = 2
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Angular_momentum.(to_string D);;
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- : string = "D"
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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@ -72,21 +91,7 @@ let of_char = function
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| 'm' | 'M' -> M | 'n' | 'N' -> N
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| 'o' | 'O' -> O
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| c -> raise (Angular_momentum_error (String.make 1 c))
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#+end_src
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*** ~to_string~
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#+begin_src ocaml :tangle (eval mli)
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val to_string : t -> string
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#+end_src
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Converts the angular momentum into a string:
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#+begin_example
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Angular_momentum.(to_string D) -> "D"
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let to_string = function
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| S -> "S" | P -> "P"
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| D -> "D" | F -> "F"
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@ -95,21 +100,8 @@ let to_string = function
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| K -> "K" | L -> "L"
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| M -> "M" | N -> "N"
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| O -> "O" | Int i -> string_of_int i
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#+end_src
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*** ~to_char~
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#+begin_src ocaml :tangle (eval mli)
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val to_char : t -> char
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#+end_src
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Converts the angular momentum into a char:
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#+begin_example
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Angular_momentum.(to_char D) -> 'D'
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let to_char = function
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| S -> 'S' | P -> 'P'
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| D -> 'D' | F -> 'F'
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@ -118,21 +110,8 @@ let to_char = function
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| K -> 'K' | L -> 'L'
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| M -> 'M' | N -> 'N'
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| O -> 'O' | Int _ -> '_'
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#+end_src
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*** ~to_int~
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#+begin_src ocaml :tangle (eval mli)
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val to_int : t -> int
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#+end_src
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Returns the $l_{max}$ value of the shell:
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#+begin_example
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Angular_momentum.(to_char D) -> 2
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let to_int = function
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| S -> 0 | P -> 1
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| D -> 2 | F -> 3
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@ -141,21 +120,8 @@ let to_int = function
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| K -> 8 | L -> 9
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| M -> 10 | N -> 11
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| O -> 12 | Int i -> i
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#+end_src
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*** ~of_int~
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#+begin_src ocaml :tangle (eval mli)
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val of_int : int -> t
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#+end_src
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Returns a shell given an $l$ value.
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#+begin_example
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Angular_momentum.of_int 3 -> Angular_momentum.F
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let of_int = function
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| 0 -> S | 1 -> P
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| 2 -> D | 3 -> F
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@ -168,17 +134,24 @@ let of_int = function
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** Shell functions
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*** ~n_functions~
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#+begin_src ocaml :tangle (eval mli)
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val n_functions : t -> int
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val zkey_array : kind -> Zkey.t array
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#+end_src
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Returns the number of cartesian functions in a shell.
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| ~n_functions~ | Returns the number of cartesian functions in a shell. |
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| ~zkey_array~ | Array of ~Zkey.t~, where each element is a a key associated with the the powers of $x,y,z$. |
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#+begin_example
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Angular_momentum.n_functions D -> 6
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Angular_momentum.(n_functions D) ;;
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- : int = 6
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Angular_momentum.( zkey_array (Doublet (P,S)) );;
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- : Zkey.t array =
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[| {Zkey.left = 0; right = 1125899906842624} ;
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{Zkey.left = 0; right = 1099511627776} ;
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{Zkey.left = 0; right = 1073741824} |]
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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@ -187,36 +160,8 @@ let n_functions a =
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to_int a
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in
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(a*a + 3*a + 2)/2
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#+end_src
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*** ~zkey_array~
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#+begin_src ocaml :tangle (eval mli)
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val zkey_array : kind -> Zkey.t array
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#+end_src
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Array of ~Zkey.t~, where each element is a a key associated with the
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the powers of $x,y,z$.
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#+begin_example
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Angular_momentum.( zkey_array Doublet (P,S) ) ->
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[| {Zkey.left = 0; right = 1125899906842624} ;
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{Zkey.left = 0; right = 1099511627776} ;
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{Zkey.left = 0; right = 1073741824} |]
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=
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let s,x,y,z =
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Powers.( of_int_tuple (0,0,0),
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of_int_tuple (1,0,0),
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of_int_tuple (0,1,0),
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of_int_tuple (0,0,1) )
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in
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Array.map (fun (a,b) -> {!Zkey.of_powers_six} a b)
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[| (x,s) ; (y,s) ; (z,s) |]
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let zkey_array_memo : (kind, Zkey.t array) Hashtbl.t =
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Hashtbl.create 13
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@ -301,6 +246,14 @@ val ( + ) : t -> t -> t
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val ( - ) : t -> t -> t
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#+end_src
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#+begin_example
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Angular_momentum.(D + P);;
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- : Angular_momentum.t = Qcaml.Common.Angular_momentum.F
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Angular_momentum.(F - P);;
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- : Angular_momentum.t = Qcaml.Common.Angular_momentum.D
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let ( + ) a b =
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of_int ( (to_int a) + (to_int b) )
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@ -311,9 +264,10 @@ let ( - ) a b =
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** Printers
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Printers can print as a string (~pp_string~) or as an integer (~pp_int~).
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Printers can print as a string (default) or as an integer.
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#+begin_src ocaml :tangle (eval mli)
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val pp : Format.formatter -> t -> unit
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val pp_string : Format.formatter -> t -> unit
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val pp_int : Format.formatter -> t -> unit
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#+end_src
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@ -324,7 +278,8 @@ let pp_string ppf x =
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let pp_int ppf x =
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Format.fprintf ppf "@[%d@]" (to_int x)
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let pp = pp_string
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#+end_src
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** TODO Tests
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@ -14,11 +14,11 @@
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:header-args: :noweb yes :comments both
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:END:
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We define here a data type to handle bit strings efficiently.
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When the bit string contains less than 64 bits, it is stored
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internally in a 63-bit integer and uses bitwise instructions.
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When more than 63 bits are required, the =zarith= library is used to
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consider the bit string as a multi-precision integer.
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We define here a data type to handle bit strings efficiently. When
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the bit string contains less than 64 bits, it is stored internally
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in a 63-bit integer and uses bitwise instructions. When more than
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63 bits are required, the =zarith= library is used to consider the
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bit string as a multi-precision integer.
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** Single-integer implementation :noexport:
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@ -110,7 +110,8 @@ type t =
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#+begin_src ocaml :tangle (eval test-ml)
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open Common.Bitstring
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let check msg x = Alcotest.(check bool) msg true x
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let check_bool = Alcotest.(check bool)
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let check msg x = check_bool msg true x
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let test_all () =
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let x = 8745687 in
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let one_x = of_int x in
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@ -120,13 +121,57 @@ let test_all () =
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** General implementation
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*** ~of_int~
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#+begin_src ocaml :tangle (eval mli)
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val of_int : int -> t
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val of_z : Z.t -> t
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val zero : int -> t
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val is_zero : t -> bool
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val numbits : t -> int
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val testbit : t -> int -> bool
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val neg : t -> t
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val shift_left : t -> int -> t
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val shift_right : t -> int -> t
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val shift_left_one : int -> int -> t
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val logor : t -> t -> t
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val logxor : t -> t -> t
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val logand : t -> t -> t
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val lognot : t -> t
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val plus_one : t -> t
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val minus_one : t -> t
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val hamdist : t -> t -> int
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val trailing_zeros : t -> int
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val popcount : t -> int
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val to_list : ?accu:(int list) -> t -> int list
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val permutations : int -> int -> t list
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#+end_src
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Creates a bit string from an ~int~.
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| ~of_int~ | Creates a bit string from an ~int~ |
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| ~of_z~ | Creates a bit string from an ~Z.t~ multi-precision integer |
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| ~zero~ | ~zero n~ creates a zero bit string with ~n~ bits |
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| ~is_zero~ | True if all the bits of the bit string are zero. |
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| ~numbits~ | Returns the number of bits used to represent the bit string |
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| ~testbit~ | ~testbit t n~ is true if the ~n~-th bit of the bit string ~t~ is set to ~1~ |
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| ~neg~ | Returns the negative of the integer interpretation of the bit string |
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| ~shift_left~ | ~shift_left t n~ returns a new bit strings with all the bits shifted ~n~ positions to the left |
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| ~shift_right~ | ~shift_right t n~ returns a new bit strings with all the bits shifted ~n~ positions to the right |
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| ~shift_left_one~ | ~shift_left_one size n~ returns a new bit strings with the ~n~-th bit set to one. It is equivalent as shifting ~1~ by ~n~ bits to the left, ~size~ is the total number of bits of the bit string |
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| ~logor~ | Bitwise logical or |
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| ~logxor~ | Bitwise logical exclusive or |
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| ~logand~ | Bitwise logical and |
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| ~lognot~ | Bitwise logical negation |
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| ~plus_one~ | Takes the integer representation of the bit string and adds one |
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| ~minus_one~ | Takes the integer representation of the bit string and removes one |
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| ~hamdist~ | Returns the Hamming distance, i.e. the number of bits differing between two bit strings |
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| ~trailing_zeros~ | Returns the number of trailing zeros in the bit string |
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| ~permutations~ | ~permutations m n~ generates the list of all possible ~n~-bit strings with ~m~ bits set to ~1~. Algorithm adapted from [[https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation][Bit twiddling hacks]] |
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| ~popcount~ | Returns the number of bits set to one in the bit string |
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| ~to_list~ | Converts a bit string into a list of integers indicating the positions where the bits are set to ~1~. The first value for the position is not ~0~ but ~1~ |
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#+begin_src ocaml :tangle (eval ml) :exports none
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let of_int x =
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@ -134,16 +179,9 @@ let of_int x =
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#+end_src
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#+begin_src ocaml :tangle (eval test-ml) :exports none
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Alcotest.(check bool) "of_x" true (one_x = (of_int x));
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check_bool "of_x" true (one_x = (of_int x));
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#+end_src
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*** ~of_z~
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#+begin_src ocaml :tangle (eval mli)
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val of_z : Z.t -> t
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#+end_src
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Creates a bit string from an ~Z.t~ multi-precision integer.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let of_z x =
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@ -151,16 +189,9 @@ let of_z x =
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#+end_src
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#+begin_src ocaml :tangle (eval test-ml) :exports none
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Alcotest.(check bool) "of_z" true (one_x = (of_z (Z.of_int x)));
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check_bool "of_z" true (one_x = (of_z (Z.of_int x)));
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#+end_src
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*** ~zero~
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#+begin_src ocaml :tangle (eval mli)
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val zero : int -> t
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#+end_src
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~zero n~ creates a zero bit string with ~n~ bits.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let zero = function
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@ -168,13 +199,6 @@ let zero = function
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| _ -> Many (Many.zero)
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#+end_src
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*** ~numbits~
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#+begin_src ocaml :tangle (eval mli)
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val numbits : t -> int
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#+end_src
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Returns the number of bits used to represent the bit string.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let numbits = function
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@ -182,13 +206,6 @@ let numbits = function
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| Many x -> Many.numbits x
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#+end_src
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*** ~is_zero~
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#+begin_src ocaml :tangle (eval mli)
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val is_zero : t -> bool
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#+end_src
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True if all the bits of the bit string are zero.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let is_zero = function
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@ -196,17 +213,6 @@ let is_zero = function
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| Many x -> Many.is_zero x
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#+end_src
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*** ~neg~
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#+begin_src ocaml :tangle (eval mli)
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val neg : t -> t
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#+end_src
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Returns the negative of the integer interpretation of the bit string.
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#+begin_example
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neg (of_int x) = neg (of_int (-x))
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let neg = function
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@ -214,14 +220,6 @@ let neg = function
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| Many x -> Many (Many.neg x)
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#+end_src
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*** ~shift_left~
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#+begin_src ocaml :tangle (eval mli)
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val shift_left : t -> int -> t
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#+end_src
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~shift_left t n~ returns a new bit strings with all the bits
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shifted ~n~ positions to the left.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let shift_left x i = match x with
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@ -230,20 +228,11 @@ let shift_left x i = match x with
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#+end_src
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#+begin_src ocaml :tangle (eval test-ml) :exports none
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Alcotest.(check bool) "shift_left1" true (of_int (x lsl 3) = shift_left one_x 3);
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Alcotest.(check bool) "shift_left2" true (of_z (Z.shift_left z 3) = shift_left many_x 3);
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Alcotest.(check bool) "shift_left3" true (of_z (Z.shift_left z 100) = shift_left many_x 100);
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check_bool "shift_left1" true (of_int (x lsl 3) = shift_left one_x 3);
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check_bool "shift_left2" true (of_z (Z.shift_left z 3) = shift_left many_x 3);
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check_bool "shift_left3" true (of_z (Z.shift_left z 100) = shift_left many_x 100);
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#+end_src
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*** ~shift_right~
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#+begin_src ocaml :tangle (eval mli)
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val shift_right : t -> int -> t
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#+end_src
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~shift_right t n~ returns a new bit strings with all the bits
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shifted ~n~ positions to the right.
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#+begin_src ocaml :tangle (eval ml) :exports none
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let shift_right x i = match x with
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| One x -> One (One.shift_right x i)
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@ -251,20 +240,10 @@ let shift_right x i = match x with
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#+end_src
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#+begin_src ocaml :tangle (eval test-ml) :exports none
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Alcotest.(check bool) "shift_right1" true (of_int (x lsr 3) = shift_right one_x 3);
|
||||
Alcotest.(check bool) "shift_right2" true (of_z (Z.shift_right z 3) = shift_right many_x 3);
|
||||
check_bool "shift_right1" true (of_int (x lsr 3) = shift_right one_x 3);
|
||||
check_bool "shift_right2" true (of_z (Z.shift_right z 3) = shift_right many_x 3);
|
||||
#+end_src
|
||||
|
||||
*** ~shift_left_one~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val shift_left_one : int -> int -> t
|
||||
#+end_src
|
||||
|
||||
~shift_left_one size n~ returns a new bit strings with the ~n~-th
|
||||
bit set to one.
|
||||
It is equivalent as shifting ~1~ by ~n~ bits to the left.
|
||||
~size~ is the total number of bits of the bit string.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let shift_left_one = function
|
||||
@ -274,18 +253,10 @@ let shift_left_one = function
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "shift_left_one1" true (of_int (1 lsl 3) = shift_left_one 4 3);
|
||||
Alcotest.(check bool) "shift_left_one2" true (of_z (Z.shift_left Z.one 200) = shift_left_one 300 200);
|
||||
check_bool "shift_left_one1" true (of_int (1 lsl 3) = shift_left_one 4 3);
|
||||
check_bool "shift_left_one2" true (of_z (Z.shift_left Z.one 200) = shift_left_one 300 200);
|
||||
#+end_src
|
||||
|
||||
*** ~testbit~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val testbit : t -> int -> bool
|
||||
#+end_src
|
||||
|
||||
~testbit t n~ is true if the ~n~-th bit of the bit string ~t~ is
|
||||
set to ~1~.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let testbit = function
|
||||
@ -294,21 +265,14 @@ let testbit = function
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "testbit1" true (testbit (of_int 8) 3);
|
||||
Alcotest.(check bool) "testbit2" false (testbit (of_int 8) 2);
|
||||
Alcotest.(check bool) "testbit3" false (testbit (of_int 8) 4);
|
||||
Alcotest.(check bool) "testbit4" true (testbit (of_z (Z.of_int 8)) 3);
|
||||
Alcotest.(check bool) "testbit5" false (testbit (of_z (Z.of_int 8)) 2);
|
||||
Alcotest.(check bool) "testbit6" false (testbit (of_z (Z.of_int 8)) 4);
|
||||
check_bool "testbit1" true (testbit (of_int 8) 3);
|
||||
check_bool "testbit2" false (testbit (of_int 8) 2);
|
||||
check_bool "testbit3" false (testbit (of_int 8) 4);
|
||||
check_bool "testbit4" true (testbit (of_z (Z.of_int 8)) 3);
|
||||
check_bool "testbit5" false (testbit (of_z (Z.of_int 8)) 2);
|
||||
check_bool "testbit6" false (testbit (of_z (Z.of_int 8)) 4);
|
||||
#+end_src
|
||||
|
||||
*** ~logor~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val logor : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
Bitwise logical or.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let logor a b =
|
||||
@ -319,17 +283,10 @@ let logor a b =
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "logor1" true (of_int (1 lor 2) = logor (of_int 1) (of_int 2));
|
||||
Alcotest.(check bool) "logor2" true (of_z (Z.of_int (1 lor 2)) = logor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
check_bool "logor1" true (of_int (1 lor 2) = logor (of_int 1) (of_int 2));
|
||||
check_bool "logor2" true (of_z (Z.of_int (1 lor 2)) = logor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
#+end_src
|
||||
|
||||
*** ~logxor~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val logxor : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
Bitwise logical exclusive or.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let logxor a b =
|
||||
@ -340,17 +297,10 @@ let logxor a b =
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "logxor1" true (of_int (1 lxor 2) = logxor (of_int 1) (of_int 2));
|
||||
Alcotest.(check bool) "logxor2" true (of_z (Z.of_int (1 lxor 2)) = logxor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
check_bool "logxor1" true (of_int (1 lxor 2) = logxor (of_int 1) (of_int 2));
|
||||
check_bool "logxor2" true (of_z (Z.of_int (1 lxor 2)) = logxor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
#+end_src
|
||||
|
||||
*** ~logand~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val logand : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
Bitwise logical and.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let logand a b =
|
||||
@ -362,17 +312,10 @@ let logand a b =
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "logand1" true (of_int (1 land 3) = logand (of_int 1) (of_int 3));
|
||||
Alcotest.(check bool) "logand2" true (of_z (Z.of_int (1 land 3)) = logand (of_z Z.one) (of_z (Z.of_int 3)));
|
||||
check_bool "logand1" true (of_int (1 land 3) = logand (of_int 1) (of_int 3));
|
||||
check_bool "logand2" true (of_z (Z.of_int (1 land 3)) = logand (of_z Z.one) (of_z (Z.of_int 3)));
|
||||
#+end_src
|
||||
|
||||
*** ~lognot~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val lognot : t -> t
|
||||
#+end_src
|
||||
|
||||
Bitwise logical negation.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let lognot = function
|
||||
@ -380,13 +323,6 @@ let lognot = function
|
||||
| Many x -> Many (Many.lognot x)
|
||||
#+end_src
|
||||
|
||||
*** ~minus_one~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val minus_one : t -> t
|
||||
#+end_src
|
||||
|
||||
Takes the integer representation of the bit string and removes one.
|
||||
|
||||
#+begin_example
|
||||
minus_one (of_int 10) = of_int 9
|
||||
@ -398,14 +334,6 @@ let minus_one = function
|
||||
| Many x -> Many (Many.minus_one x)
|
||||
#+end_src
|
||||
|
||||
*** ~plus_one~
|
||||
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val plus_one : t -> t
|
||||
#+end_src
|
||||
|
||||
Takes the integer representation of the bit string and adds one.
|
||||
|
||||
#+begin_example
|
||||
plus_one (of_int 10) = of_int 11
|
||||
@ -416,13 +344,6 @@ let plus_one = function
|
||||
| Many x -> Many (Many.plus_one x)
|
||||
#+end_src
|
||||
|
||||
*** ~trailing_zeros~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val trailing_zeros : t -> int
|
||||
#+end_src
|
||||
|
||||
Returns the number of trailing zeros in the bit string.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let trailing_zeros = function
|
||||
@ -430,14 +351,6 @@ let trailing_zeros = function
|
||||
| Many x -> Many.trailing_zeros x
|
||||
#+end_src
|
||||
|
||||
*** ~hamdist~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val hamdist : t -> t -> int
|
||||
#+end_src
|
||||
|
||||
Returns the Hamming distance, i.e. the number of bits differing
|
||||
between two bit strings.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let hamdist a b = match a, b with
|
||||
@ -446,13 +359,6 @@ let hamdist a b = match a, b with
|
||||
| _ -> invalid_arg "Bitstring.hamdist"
|
||||
#+end_src
|
||||
|
||||
*** ~popcount~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val popcount : t -> int
|
||||
#+end_src
|
||||
|
||||
Returns the number of bits set to one in the bit string.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let popcount = function
|
||||
@ -460,15 +366,6 @@ let popcount = function
|
||||
| Many x -> Many.popcount x
|
||||
#+end_src
|
||||
|
||||
*** ~to_list~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val to_list : ?accu:(int list) -> t -> int list
|
||||
#+end_src
|
||||
|
||||
Converts a bit string into a list of integers indicating the
|
||||
positions where the bits are set to ~1~. The first value for the
|
||||
position is not ~0~ but ~1~.
|
||||
|
||||
#+begin_example
|
||||
Bitstring.to_list (of_int 5);;
|
||||
@ -486,19 +383,9 @@ let rec to_list ?(accu=[]) = function
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval test-ml) :exports none
|
||||
Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (of_int 45)));
|
||||
check_bool "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (of_int 45)));
|
||||
#+end_src
|
||||
|
||||
*** ~permutations~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val permutations : int -> int -> t list
|
||||
#+end_src
|
||||
|
||||
~permutations m n~ generates the list of all possible ~n~-bit
|
||||
strings with ~m~ bits set to ~1~.
|
||||
Algorithm adapted from [[https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation][Bit twiddling hacks]].
|
||||
|
||||
#+begin_example
|
||||
Bitstring.permutations 2 4
|
||||
|> List.map (fun x -> Format.asprintf "%a" Bitstring.pp x) ;;
|
||||
|
@ -29,38 +29,24 @@ type t = float
|
||||
|
||||
** Conversions
|
||||
|
||||
*** ~of_float~ / ~to_float~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val of_float : float -> t
|
||||
val to_float : t -> float
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
external of_float : float -> t = "%identity"
|
||||
external to_float : t -> float = "%identity"
|
||||
#+end_src
|
||||
|
||||
*** ~of_int~ / ~to_int~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val of_int : int -> t
|
||||
val to_int : t -> int
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let of_int = float_of_int
|
||||
let to_int = int_of_float
|
||||
#+end_src
|
||||
|
||||
*** ~of_string~ / ~to_string~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val of_string: string -> t
|
||||
val to_string: t -> string
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
external of_float : float -> t = "%identity"
|
||||
external to_float : t -> float = "%identity"
|
||||
|
||||
let of_int = float_of_int
|
||||
let to_int = int_of_float
|
||||
|
||||
let of_string = float_of_string
|
||||
|
||||
let to_string x =
|
||||
|
@ -214,23 +214,20 @@ let output_long max_width x =
|
||||
|
||||
** Query functions
|
||||
|
||||
*** ~anon_args~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val get : long_opt -> string option
|
||||
val get_bool : long_opt -> bool
|
||||
val anon_args : unit -> string list
|
||||
#+end_src
|
||||
|
||||
Returns the list of anonymous arguments
|
||||
| ~get~ | Returns the argument associated with a long option |
|
||||
| ~get_bool~ | True if the ~Optional~ argument is present in the command-line |
|
||||
| ~anon_args~ | Returns the list of anonymous arguments |
|
||||
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let anon_args () = !anon_args_ref
|
||||
#+end_src
|
||||
|
||||
*** ~help~ :noexport:
|
||||
|
||||
Prints the documentation of the program.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let help () =
|
||||
|
||||
(* Print the header *)
|
||||
@ -296,31 +293,13 @@ let help () =
|
||||
(* Print footer *)
|
||||
output_text !footer_doc;
|
||||
Format.printf "@."
|
||||
#+end_src
|
||||
|
||||
*** ~get~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val get : long_opt -> string option
|
||||
#+end_src
|
||||
|
||||
Returns the argument associated with a long option.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let get x =
|
||||
try Some (Hashtbl.find dict x)
|
||||
with Not_found -> None
|
||||
#+end_src
|
||||
|
||||
*** ~get_bool~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val get_bool : long_opt -> bool
|
||||
#+end_src
|
||||
|
||||
True if the ~Optional~ argument is present in the command-line
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let get_bool x = Hashtbl.mem dict x
|
||||
#+end_src
|
||||
|
||||
|
@ -18,41 +18,21 @@
|
||||
|
||||
** Thresholds
|
||||
|
||||
*** ~epsilon~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val epsilon : float
|
||||
#+end_src
|
||||
|
||||
Value below which a float is considered null. Default is
|
||||
\epsilon = 2.10^{-15}.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let epsilon = 2.e-15
|
||||
#+end_src
|
||||
|
||||
*** ~integrals_cutoff~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val integrals_cutoff : float
|
||||
#+end_src
|
||||
|
||||
Cutoff value for integrals. Default is \epsilon .
|
||||
| ~epsilon~ | Value below which a float is considered null. Default is \epsilon = 2.10^{-15} |
|
||||
| ~integrals_cutoff~ | Cutoff value for integrals. Default is \epsilon |
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let epsilon = 2.e-15
|
||||
let integrals_cutoff = epsilon
|
||||
#+end_src
|
||||
|
||||
|
||||
** Mathematical constants
|
||||
|
||||
| ~pi~ | $\pi = 3.141~592~653~589~793~12$ |
|
||||
| ~two_pi~ | $2 \pi$ |
|
||||
| ~sq_pi~ | $\sqrt{\pi}$ |
|
||||
| ~sq_pi_over_two~ | $\sqrt{\pi} / 2$ |
|
||||
| ~pi_inv~ | $1 / \pi$ |
|
||||
| ~two_over_sq_pi~ | $2 / \sqrt{\pi}$ |
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val pi : float
|
||||
val two_pi : float
|
||||
@ -62,6 +42,13 @@ val pi_inv : float
|
||||
val two_over_sq_pi : float
|
||||
#+end_src
|
||||
|
||||
| ~pi~ | $\pi = 3.141~592~653~589~793~12$ |
|
||||
| ~two_pi~ | $2 \pi$ |
|
||||
| ~sq_pi~ | $\sqrt{\pi}$ |
|
||||
| ~sq_pi_over_two~ | $\sqrt{\pi} / 2$ |
|
||||
| ~pi_inv~ | $1 / \pi$ |
|
||||
| ~two_over_sq_pi~ | $2 / \sqrt{\pi}$ |
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let pi = acos (-1.)
|
||||
let two_pi = 2. *. pi
|
||||
@ -71,14 +58,8 @@ let pi_inv = 1. /. pi
|
||||
let two_over_sq_pi = 2. /. sq_pi
|
||||
#+end_src
|
||||
|
||||
|
||||
** Physical constants
|
||||
|
||||
| ~a0~ | Bohr's radius : $a_0 = 0.529~177~210~67(23)$ angstrom |
|
||||
| ~a0_inv~ | $1 / a_0$ |
|
||||
| ~ha_to_ev~ | Hartree to eV conversion factor : $27.211~386~02(17)$ |
|
||||
| ~ev_to_ha~ | eV to Hartree conversion factor : 1 / ~ha_to_ev~ |
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val a0 : float
|
||||
val a0_inv : float
|
||||
@ -86,6 +67,11 @@ val ha_to_ev : float
|
||||
val ev_to_ha : float
|
||||
#+end_src
|
||||
|
||||
| ~a0~ | Bohr's radius : $a_0 = 0.529~177~210~67(23)$ angstrom |
|
||||
| ~a0_inv~ | $1 / a_0$ |
|
||||
| ~ha_to_ev~ | Hartree to eV conversion factor : $27.211~386~02(17)$ |
|
||||
| ~ev_to_ha~ | eV to Hartree conversion factor : 1 / ~ha_to_ev~ |
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let a0 = 0.529_177_210_67
|
||||
let a0_inv = 1. /. a0
|
||||
|
@ -44,210 +44,140 @@ type axis = X | Y | Z
|
||||
<<types>>
|
||||
#+end_src
|
||||
|
||||
** Creation / conversion
|
||||
|
||||
*** ~make~
|
||||
** Creation
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val make : 'a point -> t
|
||||
val make_angstrom : 'a point -> angstrom point
|
||||
val zero : bohr point
|
||||
#+end_src
|
||||
|
||||
Creates a point in atomic units.
|
||||
| ~make~ | Creates a point in atomic units |
|
||||
| ~make_angstrom~ | Creates a point in angstrom |
|
||||
| ~zero~ | $(0., 0., 0.)$ |
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
external make : 'a point -> t = "%identity"
|
||||
#+end_src
|
||||
|
||||
*** ~make_angstrom~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val make_angstrom : 'a point -> angstrom point
|
||||
#+end_src
|
||||
|
||||
Creates a point in angstrom.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
external make_angstrom : 'a point -> angstrom point = "%identity"
|
||||
|
||||
let zero =
|
||||
make { x = 0. ; y = 0. ; z = 0. }
|
||||
#+end_src
|
||||
|
||||
*** ~bohr_to_angstrom~
|
||||
** Conversion
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val bohr_to_angstrom : bohr point -> angstrom point
|
||||
val angstrom_to_bohr : angstrom point -> bohr point
|
||||
#+end_src
|
||||
|
||||
Converts a point in bohr to angstrom.
|
||||
| ~bohr_to_angstrom~ | Converts a point in bohr to angstrom |
|
||||
| ~angstrom_to_bohr~ | Converts a point in angstrom to bohr |
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let b_to_a b = Constants.a0 *. b
|
||||
|
||||
let bohr_to_angstrom { x ; y ; z } =
|
||||
make { x = b_to_a x ;
|
||||
y = b_to_a y ;
|
||||
z = b_to_a z ; }
|
||||
#+end_src
|
||||
|
||||
*** ~angstrom_to_bohr~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val angstrom_to_bohr : angstrom point -> bohr point
|
||||
#+end_src
|
||||
|
||||
Converts a point in angstrom to bohr.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let a_to_b a = Constants.a0_inv *. a
|
||||
|
||||
let angstrom_to_bohr { x ; y ; z } =
|
||||
make { x = a_to_b x ;
|
||||
y = a_to_b y ;
|
||||
z = a_to_b z ; }
|
||||
#+end_src
|
||||
|
||||
*** ~zero~
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val zero : bohr point
|
||||
#+end_src
|
||||
|
||||
~zero~ = (0., 0., 0.)
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let zero =
|
||||
make { x = 0. ; y = 0. ; z = 0. }
|
||||
#+end_src
|
||||
|
||||
*** ~get~
|
||||
** Vector operations
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val neg : t -> t
|
||||
val get : axis -> bohr point -> float
|
||||
val dot : t -> t -> float
|
||||
val norm : t -> float
|
||||
val ( |. ) : float -> t -> t
|
||||
val ( |+ ) : t -> t -> t
|
||||
val ( |- ) : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
Extracts the projection of the coordinate on an axis.
|
||||
| ~neg~ | Negative of a point |
|
||||
| ~get~ | Extracts the projection of the coordinate on an axis |
|
||||
| ~dot~ | Dot product |
|
||||
| ~norm~ | $\ell{^2}$ norm of the vector |
|
||||
| ~¦.~ | Scales the vector by a constant |
|
||||
| ~¦+~ | Adds two vectors |
|
||||
| ~¦-~ | Subtracts two vectors |
|
||||
|
||||
#+begin_example
|
||||
Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -2.; z = -3.}
|
||||
|
||||
Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
|
||||
- : float = 2.
|
||||
|
||||
Coordinate.(
|
||||
2. |. { x=1. ; y=2. ; z=3. }
|
||||
) ;;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = 2.; y = 4.; z = 6.}
|
||||
|
||||
Coordinate.(
|
||||
{ x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. }
|
||||
);;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = 3.; y = 5.; z = 4.}
|
||||
|
||||
Coordinate.(
|
||||
{ x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. }
|
||||
);;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -1.; z = 2.}
|
||||
#+end_example
|
||||
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let get axis { x ; y ; z } =
|
||||
match axis with
|
||||
| X -> x
|
||||
| Y -> y
|
||||
| Z -> z
|
||||
#+end_src
|
||||
|
||||
** Vector operations
|
||||
|
||||
*** Scale
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val ( |. ) : float -> t -> t
|
||||
#+end_src
|
||||
|
||||
#+begin_example
|
||||
Coordinate.(
|
||||
2. |. { x=1. ; y=2. ; z=3. }
|
||||
) ;;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = 2.; y = 4.; z = 6.}
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let ( |. ) s { x ; y ; z } =
|
||||
make { x = s *. x ;
|
||||
y = s *. y ;
|
||||
z = s *. z ; }
|
||||
#+end_src
|
||||
|
||||
*** Add
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val ( |+ ) : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
#+begin_example
|
||||
Coordinate.(
|
||||
{ x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. }
|
||||
);;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = 3.; y = 5.; z = 4.}
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let ( |+ )
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
make { x = x1 +. x2 ;
|
||||
y = y1 +. y2 ;
|
||||
z = z1 +. z2 ; }
|
||||
#+end_src
|
||||
|
||||
*** Subtract
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val ( |- ) : t -> t -> t
|
||||
#+end_src
|
||||
|
||||
#+begin_example
|
||||
Coordinate.(
|
||||
{ x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. }
|
||||
);;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -1.; z = 2.}
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let ( |- )
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
make { x = x1 -. x2 ;
|
||||
y = y1 -. y2 ;
|
||||
z = z1 -. z2 ; }
|
||||
#+end_src
|
||||
|
||||
*** Negative
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val neg : t -> t
|
||||
#+end_src
|
||||
|
||||
#+begin_example
|
||||
Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
|
||||
- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -2.; z = -3.}
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let neg a = -1. |. a
|
||||
#+end_src
|
||||
|
||||
*** Dot product
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val dot : t -> t -> float
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let dot
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
x1 *. x2 +.
|
||||
y1 *. y2 +.
|
||||
z1 *. z2
|
||||
#+end_src
|
||||
|
||||
*** Norm
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val norm : t -> float
|
||||
#+end_src
|
||||
|
||||
$\ell{^2}$ norm of the vector.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let norm u =
|
||||
sqrt ( dot u u )
|
||||
#+end_src
|
||||
|
||||
|
||||
** Printers
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
|
@ -25,15 +25,31 @@ open Powers
|
||||
|
||||
|
||||
|
||||
(* Returns an ~Angular_momentum.t~ when a shell is given as a character
|
||||
* (case insensitive):
|
||||
(* | ~of_char~ | Returns an ~Angular_momentum.t~ when a shell is given as a character (case insensitive) |
|
||||
* | ~to_char~ | Converts the angular momentum into a char |
|
||||
* | ~of_int~ | Returns a shell given an $l$ value. |
|
||||
* | ~to_int~ | Returns the $l_{max}$ value of the shell |
|
||||
* | ~to_string~ | Converts the angular momentum into a string |
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.of_char 'p' -> Angular_momentum.P
|
||||
* Angular_momentum.of_char 'p';;
|
||||
* - : Angular_momentum.t = Qcaml.Common.Angular_momentum.P
|
||||
*
|
||||
* Angular_momentum.(to_char P);;
|
||||
* - : char = 'P'
|
||||
*
|
||||
* Angular_momentum.of_int 2;;
|
||||
* - : Angular_momentum.t = Qcaml.Common.Angular_momentum.D
|
||||
*
|
||||
* Angular_momentum.(to_int D);;
|
||||
* - : int = 2
|
||||
*
|
||||
* Angular_momentum.(to_string D);;
|
||||
* - : string = "D"
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~of_char~][~of_char~:2]] *)
|
||||
(* [[file:../angular_momentum.org::*Conversions][Conversions:2]] *)
|
||||
let of_char = function
|
||||
| 's' | 'S' -> S | 'p' | 'P' -> P
|
||||
| 'd' | 'D' -> D | 'f' | 'F' -> F
|
||||
@ -43,18 +59,7 @@ let of_char = function
|
||||
| 'm' | 'M' -> M | 'n' | 'N' -> N
|
||||
| 'o' | 'O' -> O
|
||||
| c -> raise (Angular_momentum_error (String.make 1 c))
|
||||
(* ~of_char~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Converts the angular momentum into a string:
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.(to_string D) -> "D"
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_string~][~to_string~:2]] *)
|
||||
let to_string = function
|
||||
| S -> "S" | P -> "P"
|
||||
| D -> "D" | F -> "F"
|
||||
@ -63,18 +68,8 @@ let to_string = function
|
||||
| K -> "K" | L -> "L"
|
||||
| M -> "M" | N -> "N"
|
||||
| O -> "O" | Int i -> string_of_int i
|
||||
(* ~to_string~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Converts the angular momentum into a char:
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.(to_char D) -> 'D'
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_char~][~to_char~:2]] *)
|
||||
let to_char = function
|
||||
| S -> 'S' | P -> 'P'
|
||||
| D -> 'D' | F -> 'F'
|
||||
@ -83,18 +78,8 @@ let to_char = function
|
||||
| K -> 'K' | L -> 'L'
|
||||
| M -> 'M' | N -> 'N'
|
||||
| O -> 'O' | Int _ -> '_'
|
||||
(* ~to_char~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the $l_{max}$ value of the shell:
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.(to_char D) -> 2
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_int~][~to_int~:2]] *)
|
||||
let to_int = function
|
||||
| S -> 0 | P -> 1
|
||||
| D -> 2 | F -> 3
|
||||
@ -103,18 +88,8 @@ let to_int = function
|
||||
| K -> 8 | L -> 9
|
||||
| M -> 10 | N -> 11
|
||||
| O -> 12 | Int i -> i
|
||||
(* ~to_int~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns a shell given an $l$ value.
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.of_int 3 -> Angular_momentum.F
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~of_int~][~of_int~:2]] *)
|
||||
let of_int = function
|
||||
| 0 -> S | 1 -> P
|
||||
| 2 -> D | 3 -> F
|
||||
@ -123,49 +98,34 @@ let of_int = function
|
||||
| 8 -> K | 9 -> L
|
||||
| 10 -> M | 11 -> N
|
||||
| 12 -> O | i -> Int i
|
||||
(* ~of_int~:2 ends here *)
|
||||
(* Conversions:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the number of cartesian functions in a shell.
|
||||
(* | ~n_functions~ | Returns the number of cartesian functions in a shell. |
|
||||
* | ~zkey_array~ | Array of ~Zkey.t~, where each element is a a key associated with the the powers of $x,y,z$. |
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.n_functions D -> 6
|
||||
* Angular_momentum.(n_functions D) ;;
|
||||
* - : int = 6
|
||||
*
|
||||
* Angular_momentum.( zkey_array (Doublet (P,S)) );;
|
||||
* - : Zkey.t array =
|
||||
* [| {Zkey.left = 0; right = 1125899906842624} ;
|
||||
* {Zkey.left = 0; right = 1099511627776} ;
|
||||
* {Zkey.left = 0; right = 1073741824} |]
|
||||
*
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~n_functions~][~n_functions~:2]] *)
|
||||
(* [[file:../angular_momentum.org::*Shell functions][Shell functions:2]] *)
|
||||
let n_functions a =
|
||||
let a =
|
||||
to_int a
|
||||
in
|
||||
(a*a + 3*a + 2)/2
|
||||
(* ~n_functions~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Array of ~Zkey.t~, where each element is a a key associated with the
|
||||
* the powers of $x,y,z$.
|
||||
*
|
||||
* #+begin_example
|
||||
* Angular_momentum.( zkey_array Doublet (P,S) ) ->
|
||||
* [| {Zkey.left = 0; right = 1125899906842624} ;
|
||||
* {Zkey.left = 0; right = 1099511627776} ;
|
||||
* {Zkey.left = 0; right = 1073741824} |]
|
||||
* =
|
||||
*
|
||||
* let s,x,y,z =
|
||||
* Powers.( of_int_tuple (0,0,0),
|
||||
* of_int_tuple (1,0,0),
|
||||
* of_int_tuple (0,1,0),
|
||||
* of_int_tuple (0,0,1) )
|
||||
* in
|
||||
* Array.map (fun (a,b) -> {!Zkey.of_powers_six} a b)
|
||||
* [| (x,s) ; (y,s) ; (z,s) |]
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~zkey_array~][~zkey_array~:2]] *)
|
||||
let zkey_array_memo : (kind, Zkey.t array) Hashtbl.t =
|
||||
Hashtbl.create 13
|
||||
|
||||
@ -241,7 +201,18 @@ let zkey_array a =
|
||||
in
|
||||
Hashtbl.add zkey_array_memo a result;
|
||||
result
|
||||
(* ~zkey_array~:2 ends here *)
|
||||
(* Shell functions:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* #+begin_example
|
||||
* Angular_momentum.(D + P);;
|
||||
* - : Angular_momentum.t = Qcaml.Common.Angular_momentum.F
|
||||
*
|
||||
* Angular_momentum.(F - P);;
|
||||
* - : Angular_momentum.t = Qcaml.Common.Angular_momentum.D
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*Arithmetic][Arithmetic:2]] *)
|
||||
let ( + ) a b =
|
||||
@ -257,4 +228,6 @@ let pp_string ppf x =
|
||||
|
||||
let pp_int ppf x =
|
||||
Format.fprintf ppf "@[%d@]" (to_int x)
|
||||
|
||||
let pp = pp_string
|
||||
(* Printers:2 ends here *)
|
||||
|
@ -16,54 +16,26 @@ type kind =
|
||||
| Quartet of (t * t * t * t)
|
||||
(* types ends here *)
|
||||
|
||||
(* ~of_char~ *)
|
||||
(* Conversions *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~of_char~][~of_char~:1]] *)
|
||||
(* [[file:../angular_momentum.org::*Conversions][Conversions:1]] *)
|
||||
val of_char : char -> t
|
||||
(* ~of_char~:1 ends here *)
|
||||
|
||||
(* ~to_string~ *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_string~][~to_string~:1]] *)
|
||||
val to_string : t -> string
|
||||
(* ~to_string~:1 ends here *)
|
||||
|
||||
(* ~to_char~ *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_char~][~to_char~:1]] *)
|
||||
val to_char : t -> char
|
||||
(* ~to_char~:1 ends here *)
|
||||
|
||||
(* ~to_int~ *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~to_int~][~to_int~:1]] *)
|
||||
val to_int : t -> int
|
||||
(* ~to_int~:1 ends here *)
|
||||
|
||||
(* ~of_int~ *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~of_int~][~of_int~:1]] *)
|
||||
val of_int : int -> t
|
||||
(* ~of_int~:1 ends here *)
|
||||
|
||||
(* ~n_functions~ *)
|
||||
val to_string : t -> string
|
||||
(* Conversions:1 ends here *)
|
||||
|
||||
(* Shell functions *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~n_functions~][~n_functions~:1]] *)
|
||||
(* [[file:../angular_momentum.org::*Shell functions][Shell functions:1]] *)
|
||||
val n_functions : t -> int
|
||||
(* ~n_functions~:1 ends here *)
|
||||
|
||||
(* ~zkey_array~ *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*~zkey_array~][~zkey_array~:1]] *)
|
||||
val zkey_array : kind -> Zkey.t array
|
||||
(* ~zkey_array~:1 ends here *)
|
||||
(* Shell functions:1 ends here *)
|
||||
|
||||
(* Arithmetic *)
|
||||
|
||||
@ -75,10 +47,11 @@ val ( - ) : t -> t -> t
|
||||
|
||||
(* Printers
|
||||
*
|
||||
* Printers can print as a string (~pp_string~) or as an integer (~pp_int~). *)
|
||||
* Printers can print as a string (default) or as an integer. *)
|
||||
|
||||
|
||||
(* [[file:../angular_momentum.org::*Printers][Printers:1]] *)
|
||||
val pp : Format.formatter -> t -> unit
|
||||
val pp_string : Format.formatter -> t -> unit
|
||||
val pp_int : Format.formatter -> t -> unit
|
||||
(* Printers:1 ends here *)
|
||||
|
@ -81,249 +81,173 @@ type t =
|
||||
|
||||
|
||||
|
||||
(* Creates a bit string from an ~int~. *)
|
||||
(* | ~of_int~ | Creates a bit string from an ~int~ |
|
||||
* | ~of_z~ | Creates a bit string from an ~Z.t~ multi-precision integer |
|
||||
* | ~zero~ | ~zero n~ creates a zero bit string with ~n~ bits |
|
||||
* | ~is_zero~ | True if all the bits of the bit string are zero. |
|
||||
* | ~numbits~ | Returns the number of bits used to represent the bit string |
|
||||
* | ~testbit~ | ~testbit t n~ is true if the ~n~-th bit of the bit string ~t~ is set to ~1~ |
|
||||
* | ~neg~ | Returns the negative of the integer interpretation of the bit string |
|
||||
* | ~shift_left~ | ~shift_left t n~ returns a new bit strings with all the bits shifted ~n~ positions to the left |
|
||||
* | ~shift_right~ | ~shift_right t n~ returns a new bit strings with all the bits shifted ~n~ positions to the right |
|
||||
* | ~shift_left_one~ | ~shift_left_one size n~ returns a new bit strings with the ~n~-th bit set to one. It is equivalent as shifting ~1~ by ~n~ bits to the left, ~size~ is the total number of bits of the bit string |
|
||||
* | ~logor~ | Bitwise logical or |
|
||||
* | ~logxor~ | Bitwise logical exclusive or |
|
||||
* | ~logand~ | Bitwise logical and |
|
||||
* | ~lognot~ | Bitwise logical negation |
|
||||
* | ~plus_one~ | Takes the integer representation of the bit string and adds one |
|
||||
* | ~minus_one~ | Takes the integer representation of the bit string and removes one |
|
||||
* | ~hamdist~ | Returns the Hamming distance, i.e. the number of bits differing between two bit strings |
|
||||
* | ~trailing_zeros~ | Returns the number of trailing zeros in the bit string |
|
||||
* | ~permutations~ | ~permutations m n~ generates the list of all possible ~n~-bit strings with ~m~ bits set to ~1~. Algorithm adapted from [[https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation][Bit twiddling hacks]] |
|
||||
* | ~popcount~ | Returns the number of bits set to one in the bit string |
|
||||
* | ~to_list~ | Converts a bit string into a list of integers indicating the positions where the bits are set to ~1~. The first value for the position is not ~0~ but ~1~ | *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~of_int~][~of_int~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:2]] *)
|
||||
let of_int x =
|
||||
One (One.of_int x)
|
||||
(* ~of_int~:2 ends here *)
|
||||
(* General implementation:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Creates a bit string from an ~Z.t~ multi-precision integer. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~of_z~][~of_z~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:4]] *)
|
||||
let of_z x =
|
||||
if Z.numbits x < 64 then One (Z.to_int x) else Many (Many.of_z x)
|
||||
(* ~of_z~:2 ends here *)
|
||||
(* General implementation:4 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~zero n~ creates a zero bit string with ~n~ bits. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~zero~][~zero~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:6]] *)
|
||||
let zero = function
|
||||
| n when n < 64 -> One (One.zero)
|
||||
| _ -> Many (Many.zero)
|
||||
(* ~zero~:2 ends here *)
|
||||
(* General implementation:6 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the number of bits used to represent the bit string. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~numbits~][~numbits~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:7]] *)
|
||||
let numbits = function
|
||||
| One x -> One.numbits x
|
||||
| Many x -> Many.numbits x
|
||||
(* ~numbits~:2 ends here *)
|
||||
(* General implementation:7 ends here *)
|
||||
|
||||
|
||||
|
||||
(* True if all the bits of the bit string are zero. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~is_zero~][~is_zero~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:8]] *)
|
||||
let is_zero = function
|
||||
| One x -> One.is_zero x
|
||||
| Many x -> Many.is_zero x
|
||||
(* ~is_zero~:2 ends here *)
|
||||
(* General implementation:8 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the negative of the integer interpretation of the bit string.
|
||||
*
|
||||
* #+begin_example
|
||||
* neg (of_int x) = neg (of_int (-x))
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~neg~][~neg~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:9]] *)
|
||||
let neg = function
|
||||
| One x -> One (One.neg x)
|
||||
| Many x -> Many (Many.neg x)
|
||||
(* ~neg~:2 ends here *)
|
||||
(* General implementation:9 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~shift_left t n~ returns a new bit strings with all the bits
|
||||
* shifted ~n~ positions to the left. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left~][~shift_left~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:10]] *)
|
||||
let shift_left x i = match x with
|
||||
| One x -> One (One.shift_left x i)
|
||||
| Many x -> Many (Many.shift_left x i)
|
||||
(* ~shift_left~:2 ends here *)
|
||||
(* General implementation:10 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~shift_right t n~ returns a new bit strings with all the bits
|
||||
* shifted ~n~ positions to the right. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_right~][~shift_right~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:12]] *)
|
||||
let shift_right x i = match x with
|
||||
| One x -> One (One.shift_right x i)
|
||||
| Many x -> Many (Many.shift_right x i)
|
||||
(* ~shift_right~:2 ends here *)
|
||||
(* General implementation:12 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~shift_left_one size n~ returns a new bit strings with the ~n~-th
|
||||
* bit set to one.
|
||||
* It is equivalent as shifting ~1~ by ~n~ bits to the left.
|
||||
* ~size~ is the total number of bits of the bit string. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left_one~][~shift_left_one~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:14]] *)
|
||||
let shift_left_one = function
|
||||
| n when n < 64 -> fun i -> One (One.shift_left_one i)
|
||||
| _ -> fun i -> Many (Many.shift_left_one i)
|
||||
(* ~shift_left_one~:2 ends here *)
|
||||
(* General implementation:14 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~testbit t n~ is true if the ~n~-th bit of the bit string ~t~ is
|
||||
* set to ~1~. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~testbit~][~testbit~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:16]] *)
|
||||
let testbit = function
|
||||
| One x -> One.testbit x
|
||||
| Many x -> Many.testbit x
|
||||
(* ~testbit~:2 ends here *)
|
||||
(* General implementation:16 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Bitwise logical or. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logor~][~logor~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:18]] *)
|
||||
let logor a b =
|
||||
match a,b with
|
||||
| One a, One b -> One (One.logor a b)
|
||||
| Many a, Many b -> Many (Many.logor a b)
|
||||
| _ -> invalid_arg "Bitstring.logor"
|
||||
(* ~logor~:2 ends here *)
|
||||
(* General implementation:18 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Bitwise logical exclusive or. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logxor~][~logxor~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:20]] *)
|
||||
let logxor a b =
|
||||
match a,b with
|
||||
| One a, One b -> One (One.logxor a b)
|
||||
| Many a, Many b -> Many (Many.logxor a b)
|
||||
| _ -> invalid_arg "Bitstring.logxor"
|
||||
(* ~logxor~:2 ends here *)
|
||||
(* General implementation:20 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Bitwise logical and. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logand~][~logand~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:22]] *)
|
||||
let logand a b =
|
||||
match a,b with
|
||||
| One a, One b -> One (One.logand a b)
|
||||
| Many a, Many b -> Many (Many.logand a b)
|
||||
| _ -> invalid_arg "Bitstring.logand"
|
||||
(* ~logand~:2 ends here *)
|
||||
(* General implementation:22 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Bitwise logical negation. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~lognot~][~lognot~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:24]] *)
|
||||
let lognot = function
|
||||
| One x -> One (One.lognot x)
|
||||
| Many x -> Many (Many.lognot x)
|
||||
(* ~lognot~:2 ends here *)
|
||||
(* General implementation:24 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Takes the integer representation of the bit string and removes one.
|
||||
*
|
||||
* #+begin_example
|
||||
|
||||
(* #+begin_example
|
||||
* minus_one (of_int 10) = of_int 9
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~minus_one~][~minus_one~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:25]] *)
|
||||
let minus_one = function
|
||||
| One x -> One (One.minus_one x)
|
||||
| Many x -> Many (Many.minus_one x)
|
||||
(* ~minus_one~:2 ends here *)
|
||||
(* General implementation:25 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Takes the integer representation of the bit string and adds one.
|
||||
*
|
||||
* #+begin_example
|
||||
|
||||
(* #+begin_example
|
||||
* plus_one (of_int 10) = of_int 11
|
||||
* #+end_example *)
|
||||
|
||||
(* [[file:../bitstring.org::*~plus_one~][~plus_one~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:26]] *)
|
||||
let plus_one = function
|
||||
| One x -> One (One.plus_one x)
|
||||
| Many x -> Many (Many.plus_one x)
|
||||
(* ~plus_one~:2 ends here *)
|
||||
(* General implementation:26 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the number of trailing zeros in the bit string. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~trailing_zeros~][~trailing_zeros~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:27]] *)
|
||||
let trailing_zeros = function
|
||||
| One x -> One.trailing_zeros x
|
||||
| Many x -> Many.trailing_zeros x
|
||||
(* ~trailing_zeros~:2 ends here *)
|
||||
(* General implementation:27 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the Hamming distance, i.e. the number of bits differing
|
||||
* between two bit strings. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~hamdist~][~hamdist~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:28]] *)
|
||||
let hamdist a b = match a, b with
|
||||
| One a, One b -> One.hamdist a b
|
||||
| Many a, Many b -> Many.hamdist a b
|
||||
| _ -> invalid_arg "Bitstring.hamdist"
|
||||
(* ~hamdist~:2 ends here *)
|
||||
(* General implementation:28 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the number of bits set to one in the bit string. *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~popcount~][~popcount~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:29]] *)
|
||||
let popcount = function
|
||||
| One x -> One.popcount x
|
||||
| Many x -> Many.popcount x
|
||||
(* ~popcount~:2 ends here *)
|
||||
(* General implementation:29 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Converts a bit string into a list of integers indicating the
|
||||
* positions where the bits are set to ~1~. The first value for the
|
||||
* position is not ~0~ but ~1~.
|
||||
*
|
||||
* #+begin_example
|
||||
|
||||
(* #+begin_example
|
||||
* Bitstring.to_list (of_int 5);;
|
||||
* - : int list = [1; 3]
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~to_list~][~to_list~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:30]] *)
|
||||
let rec to_list ?(accu=[]) = function
|
||||
| t when (is_zero t) -> List.rev accu
|
||||
| t -> let newlist =
|
||||
@ -331,15 +255,11 @@ let rec to_list ?(accu=[]) = function
|
||||
in
|
||||
logand t @@ minus_one t
|
||||
|> (to_list [@tailcall]) ~accu:newlist
|
||||
(* ~to_list~:2 ends here *)
|
||||
(* General implementation:30 ends here *)
|
||||
|
||||
|
||||
|
||||
(* ~permutations m n~ generates the list of all possible ~n~-bit
|
||||
* strings with ~m~ bits set to ~1~.
|
||||
* Algorithm adapted from [[https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation][Bit twiddling hacks]].
|
||||
*
|
||||
* #+begin_example
|
||||
(* #+begin_example
|
||||
* Bitstring.permutations 2 4
|
||||
* |> List.map (fun x -> Format.asprintf "%a" Bitstring.pp x) ;;
|
||||
* - : string list =
|
||||
@ -352,7 +272,7 @@ let rec to_list ?(accu=[]) = function
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~permutations~][~permutations~:2]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:32]] *)
|
||||
let permutations m n =
|
||||
|
||||
let rec aux k u rest =
|
||||
@ -370,7 +290,7 @@ let permutations m n =
|
||||
(aux [@tailcall]) (k-1) (logor t' t'') (u :: rest)
|
||||
in
|
||||
aux (Util.binom n m) (minus_one (shift_left_one n m)) []
|
||||
(* ~permutations~:2 ends here *)
|
||||
(* General implementation:32 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*Printers][Printers:2]] *)
|
||||
let pp ppf = function
|
||||
|
@ -5,153 +5,38 @@
|
||||
type t
|
||||
(* Type:1 ends here *)
|
||||
|
||||
(* ~of_int~ *)
|
||||
(* General implementation *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~of_int~][~of_int~:1]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:1]] *)
|
||||
val of_int : int -> t
|
||||
(* ~of_int~:1 ends here *)
|
||||
|
||||
(* ~of_z~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~of_z~][~of_z~:1]] *)
|
||||
val of_z : Z.t -> t
|
||||
(* ~of_z~:1 ends here *)
|
||||
|
||||
(* ~zero~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~zero~][~zero~:1]] *)
|
||||
val zero : int -> t
|
||||
(* ~zero~:1 ends here *)
|
||||
|
||||
(* ~numbits~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~numbits~][~numbits~:1]] *)
|
||||
val numbits : t -> int
|
||||
(* ~numbits~:1 ends here *)
|
||||
|
||||
(* ~is_zero~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~is_zero~][~is_zero~:1]] *)
|
||||
val is_zero : t -> bool
|
||||
(* ~is_zero~:1 ends here *)
|
||||
|
||||
(* ~neg~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~neg~][~neg~:1]] *)
|
||||
val neg : t -> t
|
||||
(* ~neg~:1 ends here *)
|
||||
|
||||
(* ~shift_left~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left~][~shift_left~:1]] *)
|
||||
val shift_left : t -> int -> t
|
||||
(* ~shift_left~:1 ends here *)
|
||||
|
||||
(* ~shift_right~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_right~][~shift_right~:1]] *)
|
||||
val shift_right : t -> int -> t
|
||||
(* ~shift_right~:1 ends here *)
|
||||
|
||||
(* ~shift_left_one~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left_one~][~shift_left_one~:1]] *)
|
||||
val shift_left_one : int -> int -> t
|
||||
(* ~shift_left_one~:1 ends here *)
|
||||
|
||||
(* ~testbit~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~testbit~][~testbit~:1]] *)
|
||||
val numbits : t -> int
|
||||
val testbit : t -> int -> bool
|
||||
(* ~testbit~:1 ends here *)
|
||||
|
||||
(* ~logor~ *)
|
||||
val neg : t -> t
|
||||
val shift_left : t -> int -> t
|
||||
val shift_right : t -> int -> t
|
||||
val shift_left_one : int -> int -> t
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logor~][~logor~:1]] *)
|
||||
val logor : t -> t -> t
|
||||
(* ~logor~:1 ends here *)
|
||||
|
||||
(* ~logxor~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logxor~][~logxor~:1]] *)
|
||||
val logxor : t -> t -> t
|
||||
(* ~logxor~:1 ends here *)
|
||||
|
||||
(* ~logand~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~logand~][~logand~:1]] *)
|
||||
val logand : t -> t -> t
|
||||
(* ~logand~:1 ends here *)
|
||||
|
||||
(* ~lognot~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~lognot~][~lognot~:1]] *)
|
||||
val lognot : t -> t
|
||||
(* ~lognot~:1 ends here *)
|
||||
|
||||
(* ~minus_one~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~minus_one~][~minus_one~:1]] *)
|
||||
val minus_one : t -> t
|
||||
(* ~minus_one~:1 ends here *)
|
||||
|
||||
(* ~plus_one~ *)
|
||||
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~plus_one~][~plus_one~:1]] *)
|
||||
val plus_one : t -> t
|
||||
(* ~plus_one~:1 ends here *)
|
||||
val minus_one : t -> t
|
||||
|
||||
(* ~trailing_zeros~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~trailing_zeros~][~trailing_zeros~:1]] *)
|
||||
val trailing_zeros : t -> int
|
||||
(* ~trailing_zeros~:1 ends here *)
|
||||
|
||||
(* ~hamdist~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~hamdist~][~hamdist~:1]] *)
|
||||
val hamdist : t -> t -> int
|
||||
(* ~hamdist~:1 ends here *)
|
||||
|
||||
(* ~popcount~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~popcount~][~popcount~:1]] *)
|
||||
val trailing_zeros : t -> int
|
||||
val popcount : t -> int
|
||||
(* ~popcount~:1 ends here *)
|
||||
|
||||
(* ~to_list~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~to_list~][~to_list~:1]] *)
|
||||
val to_list : ?accu:(int list) -> t -> int list
|
||||
(* ~to_list~:1 ends here *)
|
||||
|
||||
(* ~permutations~ *)
|
||||
|
||||
|
||||
(* [[file:../bitstring.org::*~permutations~][~permutations~:1]] *)
|
||||
val permutations : int -> int -> t list
|
||||
(* ~permutations~:1 ends here *)
|
||||
(* General implementation:1 ends here *)
|
||||
|
||||
(* Printers *)
|
||||
|
||||
|
@ -1,18 +1,19 @@
|
||||
|
||||
|
||||
(* This type should be used for all charges in the program (electrons, nuclei,...). *)
|
||||
|
||||
|
||||
(* [[file:../charge.org::*Type][Type:2]] *)
|
||||
type t = float
|
||||
(* Type:2 ends here *)
|
||||
|
||||
(* [[file:../charge.org::*~of_float~ / ~to_float~][~of_float~ / ~to_float~:2]] *)
|
||||
(* [[file:../charge.org::*Conversions][Conversions:2]] *)
|
||||
external of_float : float -> t = "%identity"
|
||||
external to_float : t -> float = "%identity"
|
||||
(* ~of_float~ / ~to_float~:2 ends here *)
|
||||
|
||||
(* [[file:../charge.org::*~of_int~ / ~to_int~][~of_int~ / ~to_int~:2]] *)
|
||||
let of_int = float_of_int
|
||||
let to_int = int_of_float
|
||||
(* ~of_int~ / ~to_int~:2 ends here *)
|
||||
|
||||
(* [[file:../charge.org::*~of_string~ / ~to_string~][~of_string~ / ~to_string~:2]] *)
|
||||
let of_string = float_of_string
|
||||
|
||||
let to_string x =
|
||||
@ -22,7 +23,7 @@ let to_string x =
|
||||
Printf.sprintf "%f" x
|
||||
else
|
||||
"0.0"
|
||||
(* ~of_string~ / ~to_string~:2 ends here *)
|
||||
(* Conversions:2 ends here *)
|
||||
|
||||
(* [[file:../charge.org::*Simple operations][Simple operations:2]] *)
|
||||
let gen_op op =
|
||||
|
@ -1,35 +1,23 @@
|
||||
(* Type
|
||||
*
|
||||
* This type should be used for all charges in the program (electrons, nuclei,...). *)
|
||||
(* Type *)
|
||||
|
||||
|
||||
(* [[file:../charge.org::*Type][Type:1]] *)
|
||||
type t
|
||||
(* Type:1 ends here *)
|
||||
|
||||
(* ~of_float~ / ~to_float~ *)
|
||||
(* Conversions *)
|
||||
|
||||
|
||||
(* [[file:../charge.org::*~of_float~ / ~to_float~][~of_float~ / ~to_float~:1]] *)
|
||||
(* [[file:../charge.org::*Conversions][Conversions:1]] *)
|
||||
val of_float : float -> t
|
||||
val to_float : t -> float
|
||||
(* ~of_float~ / ~to_float~:1 ends here *)
|
||||
|
||||
(* ~of_int~ / ~to_int~ *)
|
||||
|
||||
|
||||
(* [[file:../charge.org::*~of_int~ / ~to_int~][~of_int~ / ~to_int~:1]] *)
|
||||
val of_int : int -> t
|
||||
val to_int : t -> int
|
||||
(* ~of_int~ / ~to_int~:1 ends here *)
|
||||
|
||||
(* ~of_string~ / ~to_string~ *)
|
||||
|
||||
|
||||
(* [[file:../charge.org::*~of_string~ / ~to_string~][~of_string~ / ~to_string~:1]] *)
|
||||
val of_string: string -> t
|
||||
val to_string: t -> string
|
||||
(* ~of_string~ / ~to_string~:1 ends here *)
|
||||
(* Conversions:1 ends here *)
|
||||
|
||||
(* Simple operations *)
|
||||
|
||||
|
@ -151,19 +151,15 @@ let output_long max_width x =
|
||||
|
||||
|
||||
|
||||
(* Returns the list of anonymous arguments *)
|
||||
(* | ~get~ | Returns the argument associated with a long option |
|
||||
* | ~get_bool~ | True if the ~Optional~ argument is present in the command-line |
|
||||
* | ~anon_args~ | Returns the list of anonymous arguments | *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~anon_args~][~anon_args~:2]] *)
|
||||
|
||||
(* [[file:../command_line.org::*Query functions][Query functions:2]] *)
|
||||
let anon_args () = !anon_args_ref
|
||||
(* ~anon_args~:2 ends here *)
|
||||
|
||||
(* ~help~ :noexport:
|
||||
*
|
||||
* Prints the documentation of the program. *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~help~][~help~:1]] *)
|
||||
let help () =
|
||||
|
||||
(* Print the header *)
|
||||
@ -229,27 +225,15 @@ let help () =
|
||||
(* Print footer *)
|
||||
output_text !footer_doc;
|
||||
Format.printf "@."
|
||||
(* ~help~:1 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Returns the argument associated with a long option. *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~get~][~get~:2]] *)
|
||||
let get x =
|
||||
try Some (Hashtbl.find dict x)
|
||||
with Not_found -> None
|
||||
(* ~get~:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* True if the ~Optional~ argument is present in the command-line *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~get_bool~][~get_bool~:2]] *)
|
||||
let get_bool x = Hashtbl.mem dict x
|
||||
(* ~get_bool~:2 ends here *)
|
||||
(* Query functions:2 ends here *)
|
||||
|
||||
|
||||
|
||||
|
@ -28,26 +28,14 @@ val set_footer_doc : string -> unit
|
||||
val anonymous : long_opt -> optional -> documentation -> description
|
||||
(* Mutable attributes:4 ends here *)
|
||||
|
||||
(* ~anon_args~ *)
|
||||
(* Query functions *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~anon_args~][~anon_args~:1]] *)
|
||||
val anon_args : unit -> string list
|
||||
(* ~anon_args~:1 ends here *)
|
||||
|
||||
(* ~get~ *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~get~][~get~:1]] *)
|
||||
(* [[file:../command_line.org::*Query functions][Query functions:1]] *)
|
||||
val get : long_opt -> string option
|
||||
(* ~get~:1 ends here *)
|
||||
|
||||
(* ~get_bool~ *)
|
||||
|
||||
|
||||
(* [[file:../command_line.org::*~get_bool~][~get_bool~:1]] *)
|
||||
val get_bool : long_opt -> bool
|
||||
(* ~get_bool~:1 ends here *)
|
||||
val anon_args : unit -> string list
|
||||
(* Query functions:1 ends here *)
|
||||
|
||||
(* Specification *)
|
||||
|
||||
|
@ -15,84 +15,69 @@ type t = bohr point
|
||||
type axis = X | Y | Z
|
||||
(* Type:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~make~][~make~:2]] *)
|
||||
|
||||
|
||||
(* | ~make~ | Creates a point in atomic units |
|
||||
* | ~make_angstrom~ | Creates a point in angstrom |
|
||||
* | ~zero~ | $(0., 0., 0.)$ | *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Creation][Creation:2]] *)
|
||||
external make : 'a point -> t = "%identity"
|
||||
(* ~make~:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~make_angstrom~][~make_angstrom~:2]] *)
|
||||
external make_angstrom : 'a point -> angstrom point = "%identity"
|
||||
(* ~make_angstrom~:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~bohr_to_angstrom~][~bohr_to_angstrom~:2]] *)
|
||||
let zero =
|
||||
make { x = 0. ; y = 0. ; z = 0. }
|
||||
(* Creation:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* | ~bohr_to_angstrom~ | Converts a point in bohr to angstrom |
|
||||
* | ~angstrom_to_bohr~ | Converts a point in angstrom to bohr | *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Conversion][Conversion:2]] *)
|
||||
let b_to_a b = Constants.a0 *. b
|
||||
|
||||
let bohr_to_angstrom { x ; y ; z } =
|
||||
make { x = b_to_a x ;
|
||||
y = b_to_a y ;
|
||||
z = b_to_a z ; }
|
||||
(* ~bohr_to_angstrom~:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~angstrom_to_bohr~][~angstrom_to_bohr~:2]] *)
|
||||
|
||||
let a_to_b a = Constants.a0_inv *. a
|
||||
|
||||
let angstrom_to_bohr { x ; y ; z } =
|
||||
make { x = a_to_b x ;
|
||||
y = a_to_b y ;
|
||||
z = a_to_b z ; }
|
||||
(* ~angstrom_to_bohr~:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~zero~][~zero~:2]] *)
|
||||
let zero =
|
||||
make { x = 0. ; y = 0. ; z = 0. }
|
||||
(* ~zero~:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*~get~][~get~:2]] *)
|
||||
let get axis { x ; y ; z } =
|
||||
match axis with
|
||||
| X -> x
|
||||
| Y -> y
|
||||
| Z -> z
|
||||
(* ~get~:2 ends here *)
|
||||
(* Conversion:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* #+begin_example
|
||||
(* | ~neg~ | Negative of a point |
|
||||
* | ~get~ | Extracts the projection of the coordinate on an axis |
|
||||
* | ~dot~ | Dot product |
|
||||
* | ~norm~ | $\ell{^2}$ norm of the vector |
|
||||
* | ~¦.~ | Scales the vector by a constant |
|
||||
* | ~¦+~ | Adds two vectors |
|
||||
* | ~¦-~ | Subtracts two vectors |
|
||||
*
|
||||
* #+begin_example
|
||||
* Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
|
||||
* - : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -2.; z = -3.}
|
||||
*
|
||||
* Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
|
||||
* - : float = 2.
|
||||
*
|
||||
* Coordinate.(
|
||||
* 2. |. { x=1. ; y=2. ; z=3. }
|
||||
* ) ;;
|
||||
* - : Coordinate.t = {Qcaml.Common.Coordinate.x = 2.; y = 4.; z = 6.}
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Scale][Scale:2]] *)
|
||||
let ( |. ) s { x ; y ; z } =
|
||||
make { x = s *. x ;
|
||||
y = s *. y ;
|
||||
z = s *. z ; }
|
||||
(* Scale:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* #+begin_example
|
||||
*
|
||||
* Coordinate.(
|
||||
* { x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. }
|
||||
* );;
|
||||
* - : Coordinate.t = {Qcaml.Common.Coordinate.x = 3.; y = 5.; z = 4.}
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Add][Add:2]] *)
|
||||
let ( |+ )
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
make { x = x1 +. x2 ;
|
||||
y = y1 +. y2 ;
|
||||
z = z1 +. z2 ; }
|
||||
(* Add:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* #+begin_example
|
||||
*
|
||||
* Coordinate.(
|
||||
* { x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. }
|
||||
* );;
|
||||
@ -100,45 +85,56 @@ let ( |+ )
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Subtract][Subtract:2]] *)
|
||||
|
||||
(* [[file:../coordinate.org::*Vector operations][Vector operations:2]] *)
|
||||
let get axis { x ; y ; z } =
|
||||
match axis with
|
||||
| X -> x
|
||||
| Y -> y
|
||||
| Z -> z
|
||||
|
||||
|
||||
let ( |. ) s { x ; y ; z } =
|
||||
make { x = s *. x ;
|
||||
y = s *. y ;
|
||||
z = s *. z ; }
|
||||
|
||||
|
||||
let ( |+ )
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
make { x = x1 +. x2 ;
|
||||
y = y1 +. y2 ;
|
||||
z = z1 +. z2 ; }
|
||||
|
||||
|
||||
let ( |- )
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
make { x = x1 -. x2 ;
|
||||
y = y1 -. y2 ;
|
||||
z = z1 -. z2 ; }
|
||||
(* Subtract:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* #+begin_example
|
||||
* Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
|
||||
* - : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -2.; z = -3.}
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Negative][Negative:2]] *)
|
||||
let neg a = -1. |. a
|
||||
(* Negative:2 ends here *)
|
||||
|
||||
(* [[file:../coordinate.org::*Dot product][Dot product:2]] *)
|
||||
|
||||
let dot
|
||||
{ x = x1 ; y = y1 ; z = z1 }
|
||||
{ x = x2 ; y = y2 ; z = z2 } =
|
||||
x1 *. x2 +.
|
||||
y1 *. y2 +.
|
||||
z1 *. z2
|
||||
(* Dot product:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* $\ell{^2}$ norm of the vector. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Norm][Norm:2]] *)
|
||||
let norm u =
|
||||
sqrt ( dot u u )
|
||||
(* Norm:2 ends here *)
|
||||
(* Vector operations:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* Coordinates can be printed in bohr or angstrom. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Printers][Printers:2]] *)
|
||||
open Format
|
||||
|
@ -19,110 +19,37 @@ type t = bohr point
|
||||
type axis = X | Y | Z
|
||||
(* types ends here *)
|
||||
|
||||
(* ~make~
|
||||
*
|
||||
* Creates a point in atomic units. *)
|
||||
(* Creation *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~make~][~make~:1]] *)
|
||||
(* [[file:../coordinate.org::*Creation][Creation:1]] *)
|
||||
val make : 'a point -> t
|
||||
(* ~make~:1 ends here *)
|
||||
|
||||
(* ~make_angstrom~
|
||||
*
|
||||
* Creates a point in angstrom. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~make_angstrom~][~make_angstrom~:1]] *)
|
||||
val make_angstrom : 'a point -> angstrom point
|
||||
(* ~make_angstrom~:1 ends here *)
|
||||
|
||||
(* ~bohr_to_angstrom~
|
||||
*
|
||||
* Converts a point in bohr to angstrom. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~bohr_to_angstrom~][~bohr_to_angstrom~:1]] *)
|
||||
val bohr_to_angstrom : bohr point -> angstrom point
|
||||
(* ~bohr_to_angstrom~:1 ends here *)
|
||||
|
||||
(* ~angstrom_to_bohr~
|
||||
*
|
||||
* Converts a point in angstrom to bohr. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~angstrom_to_bohr~][~angstrom_to_bohr~:1]] *)
|
||||
val angstrom_to_bohr : angstrom point -> bohr point
|
||||
(* ~angstrom_to_bohr~:1 ends here *)
|
||||
|
||||
(* ~zero~
|
||||
*
|
||||
* ~zero~ = (0., 0., 0.) *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~zero~][~zero~:1]] *)
|
||||
val zero : bohr point
|
||||
(* ~zero~:1 ends here *)
|
||||
(* Creation:1 ends here *)
|
||||
|
||||
(* ~get~
|
||||
*
|
||||
* Extracts the projection of the coordinate on an axis.
|
||||
*
|
||||
* #+begin_example
|
||||
* Coordinate.(get Y { x=1. ; y=2. ; z=3. })
|
||||
* - float: 2.
|
||||
* #+end_example *)
|
||||
(* Conversion *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~get~][~get~:1]] *)
|
||||
val get : axis -> bohr point -> float
|
||||
(* ~get~:1 ends here *)
|
||||
(* [[file:../coordinate.org::*Conversion][Conversion:1]] *)
|
||||
val bohr_to_angstrom : bohr point -> angstrom point
|
||||
val angstrom_to_bohr : angstrom point -> bohr point
|
||||
(* Conversion:1 ends here *)
|
||||
|
||||
(* Scale *)
|
||||
(* Vector operations *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Scale][Scale:1]] *)
|
||||
val ( |. ) : float -> t -> t
|
||||
(* Scale:1 ends here *)
|
||||
|
||||
(* Add *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Add][Add:1]] *)
|
||||
val ( |+ ) : t -> t -> t
|
||||
(* Add:1 ends here *)
|
||||
|
||||
(* Subtract *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Subtract][Subtract:1]] *)
|
||||
val ( |- ) : t -> t -> t
|
||||
(* Subtract:1 ends here *)
|
||||
|
||||
(* Negative *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Negative][Negative:1]] *)
|
||||
(* [[file:../coordinate.org::*Vector operations][Vector operations:1]] *)
|
||||
val neg : t -> t
|
||||
(* Negative:1 ends here *)
|
||||
|
||||
(* Dot product *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Dot product][Dot product:1]] *)
|
||||
val get : axis -> bohr point -> float
|
||||
val dot : t -> t -> float
|
||||
(* Dot product:1 ends here *)
|
||||
|
||||
(* Norm *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Norm][Norm:1]] *)
|
||||
val norm : t -> float
|
||||
(* Norm:1 ends here *)
|
||||
val ( |. ) : float -> t -> t
|
||||
val ( |+ ) : t -> t -> t
|
||||
val ( |- ) : t -> t -> t
|
||||
(* Vector operations:1 ends here *)
|
||||
|
||||
(* Printers
|
||||
*
|
||||
* Coordinates can be printed in bohr or angstrom. *)
|
||||
(* Printers *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Printers][Printers:1]] *)
|
||||
|
@ -1,5 +1,14 @@
|
||||
(* [[file:../non_negative_float.org::*Type][Type:2]] *)
|
||||
type t = float
|
||||
(* Type:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* The ~of_float~ function checks that the float is non-negative.
|
||||
* The unsafe variant doesn't do this check. *)
|
||||
|
||||
|
||||
(* [[file:../non_negative_float.org::*Conversions][Conversions:2]] *)
|
||||
let of_float x =
|
||||
if x < 0. then invalid_arg (__FILE__^": of_float");
|
||||
x
|
||||
@ -12,4 +21,4 @@ let to_string x =
|
||||
|
||||
let of_string x =
|
||||
let f = float_of_string x in of_float f
|
||||
|
||||
(* Conversions:2 ends here *)
|
||||
|
@ -1,7 +1,18 @@
|
||||
(** Floats >= 0. *)
|
||||
(* Type *)
|
||||
|
||||
|
||||
(* [[file:../non_negative_float.org::*Type][Type:1]] *)
|
||||
type t = private float
|
||||
(* Type:1 ends here *)
|
||||
|
||||
(* Conversions *)
|
||||
|
||||
|
||||
(* [[file:../non_negative_float.org::*Conversions][Conversions:1]] *)
|
||||
val of_float : float -> t
|
||||
val unsafe_of_float : float -> t
|
||||
val to_float : t -> float
|
||||
val to_string : t -> string
|
||||
|
||||
val of_string : string -> t
|
||||
val to_string : t -> string
|
||||
(* Conversions:1 ends here *)
|
||||
|
54
common/non_negative_float.org
Normal file
54
common/non_negative_float.org
Normal file
@ -0,0 +1,54 @@
|
||||
#+begin_src elisp tangle: no :results none :exports none
|
||||
(setq pwd (file-name-directory buffer-file-name))
|
||||
(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
|
||||
(setq lib (concat pwd "lib/"))
|
||||
(setq testdir (concat pwd "test/"))
|
||||
(setq mli (concat lib name ".mli"))
|
||||
(setq ml (concat lib name ".ml"))
|
||||
(setq test-ml (concat testdir name ".ml"))
|
||||
(org-babel-tangle)
|
||||
#+end_src
|
||||
|
||||
* Non-negative float
|
||||
:PROPERTIES:
|
||||
:header-args: :noweb yes :comments both
|
||||
:END:
|
||||
|
||||
** Type
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
type t = private float
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
type t = float
|
||||
#+end_src
|
||||
|
||||
** Conversions
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val of_float : float -> t
|
||||
val unsafe_of_float : float -> t
|
||||
val to_float : t -> float
|
||||
|
||||
val of_string : string -> t
|
||||
val to_string : t -> string
|
||||
#+end_src
|
||||
|
||||
The ~of_float~ function checks that the float is non-negative.
|
||||
The unsafe variant doesn't do this check.
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let of_float x =
|
||||
if x < 0. then invalid_arg (__FILE__^": of_float");
|
||||
x
|
||||
|
||||
external to_float : t -> float = "%identity"
|
||||
external unsafe_of_float : float -> t = "%identity"
|
||||
|
||||
let to_string x =
|
||||
let f = to_float x in string_of_float f
|
||||
|
||||
let of_string x =
|
||||
let f = float_of_string x in of_float f
|
||||
#+end_src
|
@ -3,7 +3,8 @@
|
||||
|
||||
(* [[file:../bitstring.org::*Tests header][Tests header:1]] *)
|
||||
open Common.Bitstring
|
||||
let check msg x = Alcotest.(check bool) msg true x
|
||||
let check_bool = Alcotest.(check bool)
|
||||
let check msg x = check_bool msg true x
|
||||
let test_all () =
|
||||
let x = 8745687 in
|
||||
let one_x = of_int x in
|
||||
@ -11,63 +12,63 @@ let test_all () =
|
||||
let many_x = of_z z in
|
||||
(* Tests header:1 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~of_int~][~of_int~:3]] *)
|
||||
Alcotest.(check bool) "of_x" true (one_x = (of_int x));
|
||||
(* ~of_int~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:3]] *)
|
||||
check_bool "of_x" true (one_x = (of_int x));
|
||||
(* General implementation:3 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~of_z~][~of_z~:3]] *)
|
||||
Alcotest.(check bool) "of_z" true (one_x = (of_z (Z.of_int x)));
|
||||
(* ~of_z~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:5]] *)
|
||||
check_bool "of_z" true (one_x = (of_z (Z.of_int x)));
|
||||
(* General implementation:5 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left~][~shift_left~:3]] *)
|
||||
Alcotest.(check bool) "shift_left1" true (of_int (x lsl 3) = shift_left one_x 3);
|
||||
Alcotest.(check bool) "shift_left2" true (of_z (Z.shift_left z 3) = shift_left many_x 3);
|
||||
Alcotest.(check bool) "shift_left3" true (of_z (Z.shift_left z 100) = shift_left many_x 100);
|
||||
(* ~shift_left~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:11]] *)
|
||||
check_bool "shift_left1" true (of_int (x lsl 3) = shift_left one_x 3);
|
||||
check_bool "shift_left2" true (of_z (Z.shift_left z 3) = shift_left many_x 3);
|
||||
check_bool "shift_left3" true (of_z (Z.shift_left z 100) = shift_left many_x 100);
|
||||
(* General implementation:11 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_right~][~shift_right~:3]] *)
|
||||
Alcotest.(check bool) "shift_right1" true (of_int (x lsr 3) = shift_right one_x 3);
|
||||
Alcotest.(check bool) "shift_right2" true (of_z (Z.shift_right z 3) = shift_right many_x 3);
|
||||
(* ~shift_right~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:13]] *)
|
||||
check_bool "shift_right1" true (of_int (x lsr 3) = shift_right one_x 3);
|
||||
check_bool "shift_right2" true (of_z (Z.shift_right z 3) = shift_right many_x 3);
|
||||
(* General implementation:13 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~shift_left_one~][~shift_left_one~:3]] *)
|
||||
Alcotest.(check bool) "shift_left_one1" true (of_int (1 lsl 3) = shift_left_one 4 3);
|
||||
Alcotest.(check bool) "shift_left_one2" true (of_z (Z.shift_left Z.one 200) = shift_left_one 300 200);
|
||||
(* ~shift_left_one~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:15]] *)
|
||||
check_bool "shift_left_one1" true (of_int (1 lsl 3) = shift_left_one 4 3);
|
||||
check_bool "shift_left_one2" true (of_z (Z.shift_left Z.one 200) = shift_left_one 300 200);
|
||||
(* General implementation:15 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~testbit~][~testbit~:3]] *)
|
||||
Alcotest.(check bool) "testbit1" true (testbit (of_int 8) 3);
|
||||
Alcotest.(check bool) "testbit2" false (testbit (of_int 8) 2);
|
||||
Alcotest.(check bool) "testbit3" false (testbit (of_int 8) 4);
|
||||
Alcotest.(check bool) "testbit4" true (testbit (of_z (Z.of_int 8)) 3);
|
||||
Alcotest.(check bool) "testbit5" false (testbit (of_z (Z.of_int 8)) 2);
|
||||
Alcotest.(check bool) "testbit6" false (testbit (of_z (Z.of_int 8)) 4);
|
||||
(* ~testbit~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:17]] *)
|
||||
check_bool "testbit1" true (testbit (of_int 8) 3);
|
||||
check_bool "testbit2" false (testbit (of_int 8) 2);
|
||||
check_bool "testbit3" false (testbit (of_int 8) 4);
|
||||
check_bool "testbit4" true (testbit (of_z (Z.of_int 8)) 3);
|
||||
check_bool "testbit5" false (testbit (of_z (Z.of_int 8)) 2);
|
||||
check_bool "testbit6" false (testbit (of_z (Z.of_int 8)) 4);
|
||||
(* General implementation:17 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~logor~][~logor~:3]] *)
|
||||
Alcotest.(check bool) "logor1" true (of_int (1 lor 2) = logor (of_int 1) (of_int 2));
|
||||
Alcotest.(check bool) "logor2" true (of_z (Z.of_int (1 lor 2)) = logor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
(* ~logor~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:19]] *)
|
||||
check_bool "logor1" true (of_int (1 lor 2) = logor (of_int 1) (of_int 2));
|
||||
check_bool "logor2" true (of_z (Z.of_int (1 lor 2)) = logor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
(* General implementation:19 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~logxor~][~logxor~:3]] *)
|
||||
Alcotest.(check bool) "logxor1" true (of_int (1 lxor 2) = logxor (of_int 1) (of_int 2));
|
||||
Alcotest.(check bool) "logxor2" true (of_z (Z.of_int (1 lxor 2)) = logxor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
(* ~logxor~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:21]] *)
|
||||
check_bool "logxor1" true (of_int (1 lxor 2) = logxor (of_int 1) (of_int 2));
|
||||
check_bool "logxor2" true (of_z (Z.of_int (1 lxor 2)) = logxor (of_z Z.one) (of_z (Z.of_int 2)));
|
||||
(* General implementation:21 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~logand~][~logand~:3]] *)
|
||||
Alcotest.(check bool) "logand1" true (of_int (1 land 3) = logand (of_int 1) (of_int 3));
|
||||
Alcotest.(check bool) "logand2" true (of_z (Z.of_int (1 land 3)) = logand (of_z Z.one) (of_z (Z.of_int 3)));
|
||||
(* ~logand~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:23]] *)
|
||||
check_bool "logand1" true (of_int (1 land 3) = logand (of_int 1) (of_int 3));
|
||||
check_bool "logand2" true (of_z (Z.of_int (1 land 3)) = logand (of_z Z.one) (of_z (Z.of_int 3)));
|
||||
(* General implementation:23 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~to_list~][~to_list~:3]] *)
|
||||
Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (of_int 45)));
|
||||
(* ~to_list~:3 ends here *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:31]] *)
|
||||
check_bool "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (of_int 45)));
|
||||
(* General implementation:31 ends here *)
|
||||
|
||||
(* [[file:../bitstring.org::*~permutations~][~permutations~:3]] *)
|
||||
(* [[file:../bitstring.org::*General implementation][General implementation:33]] *)
|
||||
check "permutations"
|
||||
(permutations 2 4 = List.map of_int
|
||||
[ 3 ; 5 ; 6 ; 9 ; 10 ; 12 ]);
|
||||
(* ~permutations~:3 ends here *)
|
||||
(* General implementation:33 ends here *)
|
||||
|
||||
(* Tests :noexport: *)
|
||||
|
||||
|
@ -69,6 +69,9 @@ with class 'color and highest min-color value."
|
||||
|
||||
(advice-add 'face-attribute :override #'my-face-attribute)
|
||||
|
||||
(setq org-html-htmlize-output-type 'css) ; default: 'inline-css
|
||||
(setq org-html-htmlize-font-prefix "org-") ; default: "org-"
|
||||
|
||||
(setq ml "ml")
|
||||
(setq mli "mli")
|
||||
(setq test-ml "test-ml")
|
||||
|
Loading…
Reference in New Issue
Block a user