Source file builtins_math.ml
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let () =
let add op name descr =
let t = Lang.float_t in
ignore
(Lang.add_builtin name ~category:`Math ~descr
[("", t, None, None)]
t
(fun p ->
let a = Lang.to_float (List.assoc "" p) in
Lang.float (op a)))
in
add sqrt "sqrt" "Square root.";
add exp "exp" "Exponential.";
add Stdlib.log "ln" "Natural logarithm.";
add log10 "log10" "Base 10 logarithm.";
add sin "sin" "Sine. Argument is in radians.";
add cos "cos" "Cosine. Argument is in radians.";
add tan "tan" "Tangent. Argument is in radians.";
add acos "acos"
"Arc cosine. The argument must fall within the range [-1.0, 1.0]. Result \
is in radians and is between 0.0 and pi.";
add asin "asin"
"Arc sine. The argument must fall within the range [-1.0, 1.0]. Result is \
in radians and is between -pi/2 and pi/2.";
add atan "atan"
"Arc tangent. Result is in radians and is between -pi/2 and pi/2.";
add cosh "cosh" "Hyperbolic cosine. Argument is in radians.";
add sinh "sinh" "Hyperbolic sine. Argument is in radians.";
add tanh "tanh" "Hyperbolic tangent. Argument is in radians."
let _ =
let t = Lang.univ_t ~constraints:[Type.num_constr] () in
Lang.add_builtin "~-" ~category:`Math
~descr:"Returns the opposite of its argument."
[("", t, None, None)]
t
(fun p ->
match Lang.to_num (List.assoc "" p) with
| `Int i -> Lang.int ~-i
| `Float i -> Lang.float ~-.i)
let _ =
let t = Lang.univ_t ~constraints:[Type.num_constr] () in
Lang.add_builtin "abs" ~category:`Math ~descr:"Absolute value."
[("", t, None, None)]
t
(fun p ->
match Lang.to_num (List.assoc "" p) with
| `Int i -> Lang.int (abs i)
| `Float i -> Lang.float (abs_float i))
let () =
let register_op doc name op_int op_float =
let t = Lang.univ_t ~constraints:[Type.num_constr] () in
ignore
(Lang.add_builtin name ~category:`Math
~descr:(Printf.sprintf "%s of numbers." doc)
[("", t, None, None); ("", t, None, None)]
t
(fun p ->
let a = Lang.to_num (Lang.assoc "" 1 p) in
let b = Lang.to_num (Lang.assoc "" 2 p) in
match (a, b) with
| `Int a, `Int b -> Lang.int (op_int a b)
| `Float a, `Float b -> Lang.float (op_float a b)
| _ -> assert false))
in
register_op "Multiplication" "*" ( * ) ( *. );
register_op "Division" "/" ( / ) ( /. );
register_op "Addition" "+" ( + ) ( +. );
register_op "Subtraction " "-" ( - ) ( -. );
register_op "Exponentiation" "pow"
(fun a b -> int_of_float (float_of_int a ** float_of_int b))
( ** );
register_op "Remainder of division" "mod" ( mod ) mod_float
let _ =
let t = Lang.univ_t ~constraints:[Type.num_constr] () in
Lang.add_builtin "float" ~category:`Math ~descr:"Convert a number to a float."
[("", t, None, None)]
Lang.float_t
(fun p ->
let x = List.assoc "" p |> Lang.to_num in
let x = match x with `Int x -> float x | `Float x -> x in
Lang.float x)
let _ =
let t = Lang.univ_t ~constraints:[Type.num_constr] () in
Lang.add_builtin "int" ~category:`Math
~descr:"Convert a number to an integer."
[("", t, None, None)]
Lang.int_t
(fun p ->
let x = List.assoc "" p |> Lang.to_num in
let x = match x with `Int x -> x | `Float x -> int_of_float x in
Lang.int x)
let _ =
Lang.add_builtin ~base:Modules.random "float" ~category:`Math
~descr:
"Generate a random value between `min` (included) and `max` (excluded)."
[
("min", Lang.float_t, Some (Lang.float 0.), None);
("max", Lang.float_t, Some (Lang.float 1.), None);
]
Lang.float_t
(fun p ->
let min = Lang.to_float (List.assoc "min" p) in
let max = Lang.to_float (List.assoc "max" p) in
Lang.float (Random.float (max -. min) +. min))
let _ =
Lang.add_builtin ~base:Modules.random "int" ~category:`Math
~descr:
"Generate a random value between `min` (included) and `max` (excluded)."
[
("min", Lang.int_t, Some (Lang.int (1 - (1 lsl 29))), None);
("max", Lang.int_t, Some (Lang.int (1 lsl 29)), None);
]
Lang.int_t
(fun p ->
let min = Lang.to_int (List.assoc "min" p) in
let max = Lang.to_int (List.assoc "max" p) in
Lang.int (Random.int (max - min) + min))
let _ =
Lang.add_builtin ~base:Modules.random "bool" ~category:`Bool
~descr:"Generate a random boolean." [] Lang.bool_t (fun _ ->
Lang.bool (Random.bool ()))
let _ =
Lang.add_builtin_base ~category:`Math ~descr:"Maximal representable integer."
"max_int"
Lang.(Ground (Ground.Int max_int))
Lang.int_t
let _ =
Lang.add_builtin_base ~category:`Math ~descr:"Minimal representable integer."
"min_int"
Lang.(Ground (Ground.Int min_int))
Lang.int_t
let _ =
Lang.add_builtin_base ~category:`Math
~descr:"Float representation of infinity." "infinity"
Lang.(Ground (Ground.Float infinity))
Lang.float_t
let _ =
Lang.add_builtin_base ~category:`Math
~descr:
"A special floating-point value denoting the result of an undefined \
operation such as 0.0 /. 0.0. Stands for 'not a number'. Any \
floating-point operation with nan as argument returns nan as result. As \
for floating-point comparisons, `==`, `<`, `<=`, `>` and `>=` return \
`false` and `!=` returns `true` if one or both of their arguments is \
`nan`."
"nan"
Lang.(Ground (Ground.Float nan))
Lang.float_t
let _ =
Lang.add_builtin "lsl" ~category:`Math ~descr:"Logical shift left."
[
("", Lang.int_t, None, Some "Number to shift.");
("", Lang.int_t, None, Some "Number of bits to shift.");
]
Lang.int_t
(fun p ->
let n = Lang.to_int (Lang.assoc "" 1 p) in
let b = Lang.to_int (Lang.assoc "" 2 p) in
Lang.int (n lsl b))
let _ =
Lang.add_builtin "lsr" ~category:`Math ~descr:"Logical shift right."
[
("", Lang.int_t, None, Some "Number to shift.");
("", Lang.int_t, None, Some "Number of bits to shift.");
]
Lang.int_t
(fun p ->
let n = Lang.to_int (Lang.assoc "" 1 p) in
let b = Lang.to_int (Lang.assoc "" 2 p) in
Lang.int (n lsr b))