mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-06-29 00:14:45 +02:00
286 lines
6.9 KiB
OCaml
286 lines
6.9 KiB
OCaml
(** Utility functions *)
|
|
|
|
external erf_float : float -> float
|
|
= "erf_float_bytecode" "erf_float" [@@unboxed] [@@noalloc]
|
|
|
|
external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float" [@@unboxed] [@@noalloc]
|
|
|
|
external gamma_float : float -> float
|
|
= "gamma_float_bytecode" "gamma_float" [@@unboxed] [@@noalloc]
|
|
|
|
external popcnt : int64 -> int32 = "popcnt_bytecode" "popcnt"
|
|
[@@unboxed] [@@noalloc]
|
|
|
|
let popcnt i = (popcnt [@inlined] ) i |> Int32.to_int
|
|
|
|
external trailz : int64 -> int32 = "trailz_bytecode" "trailz" "int"
|
|
[@@unboxed] [@@noalloc]
|
|
|
|
let trailz i = trailz i |> Int32.to_int
|
|
|
|
external leadz : int64 -> int32 = "leadz_bytecode" "leadz" "int"
|
|
[@@unboxed] [@@noalloc]
|
|
|
|
let leadz i = leadz i |> Int32.to_int
|
|
|
|
|
|
|
|
|
|
let memo_float_of_int =
|
|
Array.init 64 float_of_int
|
|
|
|
let float_of_int_fast i =
|
|
if Int.logand i 63 = i then
|
|
memo_float_of_int.(i)
|
|
else
|
|
float_of_int i
|
|
|
|
|
|
let factmax = 150
|
|
|
|
let fact_memo =
|
|
let rec aux accu_l accu = function
|
|
| 0 -> (aux [@tailcall]) [1.] 1. 1
|
|
| i when (i = factmax) ->
|
|
let x = (float_of_int factmax) *. accu in
|
|
List.rev (x::accu_l)
|
|
| i -> let x = (float_of_int i) *. accu in
|
|
(aux [@tailcall]) (x::accu_l) x (i+1)
|
|
in
|
|
aux [] 0. 0
|
|
|> Array.of_list
|
|
|
|
let fact = function
|
|
| i when (i < 0) ->
|
|
raise (Invalid_argument "Argument of factorial should be non-negative")
|
|
| i when (i > 150) ->
|
|
raise (Invalid_argument "Result of factorial is infinite")
|
|
| i -> fact_memo.(i)
|
|
|
|
|
|
let binom =
|
|
let memo =
|
|
let m = Array.make_matrix 64 64 0 in
|
|
for n=0 to Array.length m - 1 do
|
|
m.(n).(0) <- 1;
|
|
m.(n).(n) <- 1;
|
|
for k=1 to (n - 1) do
|
|
m.(n).(k) <- m.(n-1).(k-1) + m.(n-1).(k)
|
|
done
|
|
done;
|
|
m
|
|
in
|
|
let rec f n k =
|
|
assert (k >= 0);
|
|
assert (n >= k);
|
|
if k = 0 || k = n then
|
|
1
|
|
else if n < 64 then
|
|
memo.(n).(k)
|
|
else
|
|
f (n-1) (k-1) + f (n-1) k
|
|
in f
|
|
|
|
|
|
let binom_float n k =
|
|
binom n k
|
|
|> float_of_int_fast
|
|
|
|
|
|
let rec pow a = function
|
|
| 0 -> 1.
|
|
| 1 -> a
|
|
| 2 -> a *. a
|
|
| 3 -> a *. a *. a
|
|
| -1 -> 1. /. a
|
|
| n when n > 0 ->
|
|
let b = pow a (n / 2) in
|
|
b *. b *. (if n mod 2 = 0 then 1. else a)
|
|
| n when n < 0 -> (pow [@tailcall]) (1./.a) (-n)
|
|
| _ -> assert false
|
|
|
|
|
|
let chop f g =
|
|
if (abs_float f) < Constants.epsilon then 0.
|
|
else f *. (g ())
|
|
|
|
|
|
exception Not_implemented of string
|
|
let not_implemented string =
|
|
raise (Not_implemented string)
|
|
|
|
|
|
let of_some = function
|
|
| Some a -> a
|
|
| None -> assert false
|
|
|
|
|
|
|
|
|
|
|
|
let incomplete_gamma ~alpha x =
|
|
assert (alpha >= 0.);
|
|
assert (x >= 0.);
|
|
let a = alpha in
|
|
let a_inv = 1./. a in
|
|
let gf = gamma_float alpha in
|
|
let loggamma_a = log gf in
|
|
let rec p_gamma x =
|
|
if x >= 1. +. a then 1. -. q_gamma x
|
|
else if x = 0. then 0.
|
|
else
|
|
let rec pg_loop prev res term k =
|
|
if k > 1000. then failwith "p_gamma did not converge."
|
|
else if prev = res then res
|
|
else
|
|
let term = term *. x /. (a +. k) in
|
|
(pg_loop [@tailcall]) res (res +. term) term (k +. 1.)
|
|
in
|
|
let r0 = exp (a *. log x -. x -. loggamma_a) *. a_inv in
|
|
pg_loop min_float r0 r0 1.
|
|
|
|
and q_gamma x =
|
|
if x < 1. +. a then 1. -. p_gamma x
|
|
else
|
|
let rec qg_loop prev res la lb w k =
|
|
if k > 1000. then failwith "q_gamma did not converge."
|
|
else if prev = res then res
|
|
else
|
|
let k_inv = 1. /. k in
|
|
let kma = (k -. 1. -. a) *. k_inv in
|
|
let la, lb =
|
|
lb, kma *. (lb -. la) +. (k +. x) *. lb *. k_inv
|
|
in
|
|
let w = w *. kma in
|
|
let prev, res = res, res +. w /. (la *. lb) in
|
|
(qg_loop [@tailcall]) prev res la lb w (k +. 1.)
|
|
in
|
|
let w = exp (a *. log x -. x -. loggamma_a) in
|
|
let lb = (1. +. x -. a) in
|
|
qg_loop min_float (w /. lb) 1. lb w 2.0
|
|
in
|
|
gf *. p_gamma x
|
|
|
|
|
|
let boys_function ~maxm t =
|
|
assert (t >= 0.);
|
|
match maxm with
|
|
| 0 ->
|
|
begin
|
|
if t = 0. then [| 1. |] else
|
|
let sq_t = sqrt t in
|
|
[| (Constants.sq_pi_over_two /. sq_t) *. erf_float sq_t |]
|
|
end
|
|
| _ ->
|
|
begin
|
|
assert (maxm > 0);
|
|
let result =
|
|
Array.init (maxm+1) (fun m -> 1. /. float_of_int (2*m+1))
|
|
in
|
|
let power_t_inv = (maxm+maxm+1) in
|
|
try
|
|
let fmax =
|
|
let t_inv = sqrt (1. /. t) in
|
|
let n = float_of_int maxm in
|
|
let dm = 0.5 +. n in
|
|
let f = (pow t_inv power_t_inv ) in
|
|
match classify_float f with
|
|
| FP_normal -> (incomplete_gamma ~alpha:dm t) *. 0.5 *. f
|
|
| FP_zero
|
|
| FP_subnormal -> 0.
|
|
| _ -> raise Exit
|
|
in
|
|
let emt = exp (-. t) in
|
|
result.(maxm) <- fmax;
|
|
for n=maxm-1 downto 0 do
|
|
result.(n) <- ( (t+.t) *. result.(n+1) +. emt) *. result.(n)
|
|
done;
|
|
result
|
|
with Exit -> result
|
|
end
|
|
|
|
|
|
let list_some l =
|
|
List.filter (function None -> false | _ -> true) l
|
|
|> List.rev_map (function Some x -> x | _ -> assert false)
|
|
|> List.rev
|
|
|
|
|
|
let list_range first last =
|
|
if last < first then [] else
|
|
let rec aux accu = function
|
|
| 0 -> first :: accu
|
|
| i -> (aux [@tailcall]) ( (first+i)::accu ) (i-1)
|
|
in
|
|
aux [] (last-first)
|
|
|
|
|
|
let list_pack n l =
|
|
assert (n>=0);
|
|
let rec aux i accu1 accu2 = function
|
|
| [] -> if accu1 = [] then
|
|
List.rev accu2
|
|
else
|
|
List.rev ((List.rev accu1) :: accu2)
|
|
| a :: rest ->
|
|
match i with
|
|
| 0 -> (aux [@tailcall]) (n-1) [] ((List.rev (a::accu1)) :: accu2) rest
|
|
| _ -> (aux [@tailcall]) (i-1) (a::accu1) accu2 rest
|
|
in
|
|
aux (n-1) [] [] l
|
|
|
|
|
|
|
|
let array_range first last =
|
|
if last < first then [| |] else
|
|
Array.init (last-first+1) (fun i -> i+first)
|
|
|
|
|
|
let array_sum a =
|
|
Array.fold_left ( +. ) 0. a
|
|
|
|
|
|
let array_product a =
|
|
Array.fold_left ( *. ) 1. a
|
|
|
|
|
|
let seq_range first last =
|
|
Seq.init (last-first) (fun i -> i+first)
|
|
|
|
let seq_to_list seq =
|
|
let rec aux accu xs =
|
|
match Seq.uncons xs with
|
|
| Some (x, xs) -> aux (x::accu) xs
|
|
| None -> List.rev accu
|
|
in
|
|
aux [] seq
|
|
|
|
|
|
let seq_fold f init seq =
|
|
Seq.fold_left f init seq
|
|
|
|
|
|
let pp_float_array ppf a =
|
|
Format.fprintf ppf "@[<2>[@ ";
|
|
Array.iter (fun f -> Format.fprintf ppf "@[%10f@]@ " f) a;
|
|
Format.fprintf ppf "]@]"
|
|
|
|
let pp_float_array_size ppf a =
|
|
Format.fprintf ppf "@[<2>@[ %d:@[<2>" (Array.length a);
|
|
Array.iter (fun f -> Format.fprintf ppf "@[%10f@]@ " f) a;
|
|
Format.fprintf ppf "]@]@]"
|
|
|
|
let pp_float_2darray ppf a =
|
|
Format.fprintf ppf "@[<2>[@ ";
|
|
Array.iter (fun f -> Format.fprintf ppf "@[%a@]@ " pp_float_array f) a;
|
|
Format.fprintf ppf "]@]"
|
|
|
|
let pp_float_2darray_size ppf a =
|
|
Format.fprintf ppf "@[<2>@[ %d:@[" (Array.length a);
|
|
Array.iter (fun f -> Format.fprintf ppf "@[%a@]@ " pp_float_array_size f) a;
|
|
Format.fprintf ppf "]@]@]"
|
|
|
|
let pp_bitstring n ppf bs =
|
|
String.init n (fun i -> if (Z.testbit bs i) then '+' else '-')
|
|
|> Format.fprintf ppf "@[<h>%s@]"
|