QCaml/common/lib/util.ml

(** 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[@inline] popcnt i = Int32.to_int (popcnt i)

external trailz : int64 -> int32 = "trailz_bytecode" "trailz" "int"
[@@unboxed] [@@noalloc]

let[@inline] trailz i = Int32.to_int (trailz i)

external leadz : int64 -> int32 = "leadz_bytecode" "leadz" "int"
[@@unboxed] [@@noalloc]

let[@inline] leadz i = Int32.to_int (leadz i)




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@]"