# 1 "kernel/uint63_31.ml"
(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(* Invariant: the msb should be 0 *)
type t = Int64.t

let _ = assert (Sys.word_size = 32)

let uint_size = 63

let maxuint63 = 0x7FFF_FFFF_FFFF_FFFFL
let maxuint31 = 0x7FFF_FFFFL

let zero = Int64.zero
let one = Int64.one

    (* conversion from an int *)
let mask63 i = Int64.logand i maxuint63
let of_int i = mask63 (Int64.of_int i)
let to_int2 i = (Int64.to_int (Int64.shift_right_logical i 31), Int64.to_int i)
let of_int64 = mask63
let to_int64 i = i

let to_int_min n m =
  if Int64.(compare n (of_int m)) < 0 then Int64.to_int n else m

let of_float f = mask63 (Int64.of_float f)
let to_float = Int64.to_float

let hash i =
  let (h,l) = to_int2 i in
  (*Hashset.combine h l*)
  h * 65599 + l

    (* conversion of an uint63 to a string *)
let to_string i = Int64.to_string i

(* Compiles an unsigned int to OCaml code *)
let compile i = Printf.sprintf "Uint63.of_int64 (%LiL)" i

    (* comparison *)
let lt x y =
  Int64.compare x y < 0

let le x y =
  Int64.compare x y <= 0

    (* signed comparison *)
(* We shift the arguments by 1 to the left so that the top-most bit is interpreted as a sign *)
(* The zero at the end doesn't change the order (it is stable by multiplication by 2) *)
let lts x y =
  Int64.(compare (shift_left x 1) (shift_left y 1)) < 0

let les x y =
  Int64.(compare (shift_left x 1) (shift_left y 1)) <= 0

    (* logical shift *)
let l_sl x y =
  if le 0L y && lt y 63L then mask63 (Int64.shift_left x (Int64.to_int y)) else 0L

let l_sr x y =
  if le 0L y && lt y 63L then Int64.shift_right x (Int64.to_int y) else 0L

    (* arithmetic shift (for sint63) *)
let a_sr x y =
  if les 0L y && lts y 63L then
    mask63 (Int64.shift_right (Int64.shift_left x 1) ((Int64.to_int y) + 1))
  else 0L

let l_and x y = Int64.logand x y
let l_or x y = Int64.logor x y
let l_xor x y = Int64.logxor x y

    (* addition of int63 *)
let add x y = mask63 (Int64.add x y)

let addcarry x y = mask63 Int64.(add (add x y) one)

    (* subtraction *)
let sub x y = mask63 (Int64.sub x y)

let subcarry x y = mask63 Int64.(sub (sub x y) one)

    (* multiplication *)
let mul x y = mask63 (Int64.mul x y)

    (* division *)
let div x y =
  if y = 0L then 0L else Int64.div x y

    (* modulo *)
let rem x y =
  if y = 0L then x else Int64.rem x y

let diveucl x y = (div x y, rem x y)

    (* signed division *)
let divs x y =
  if y = 0L then 0L else mask63 Int64.(div (shift_left x 1) (shift_left y 1))

    (* signed modulo *)
let rems x y =
  if y = 0L then x else
    Int64.shift_right_logical (Int64.(rem (shift_left x 1) (shift_left y 1))) 1

let addmuldiv p x y =
  l_or (l_sl x p) (l_sr y Int64.(sub (of_int uint_size) p))

    (* division of two numbers by one *)
(* precondition: xh < y *)
(* outputs: q, r s.t. x = q * y + r, r < y *)
let div21 xh xl y =
  let nh = ref xh in
  let nl = ref xl in
  let q = ref 0L in
  for _i = 0 to 62 do
    (* invariants: 0 <= nh < y, nl = (xl*2^i) % 2^64,
       (q*y + nh) * 2^(63-i) + (xl % 2^(63-i)) = (xh%y) * 2^63 + xl *)
    nl := Int64.shift_left !nl 1;
    nh := Int64.logor (Int64.shift_left !nh 1) (Int64.shift_right_logical !nl 63);
    q := Int64.shift_left !q 1;
    if Int64.unsigned_compare !nh y >= 0 then
      begin q := Int64.logor !q 1L; nh := Int64.sub !nh y; end
  done;
  !q, !nh

let div21 xh xl y =
  if Int64.compare y xh <= 0 then zero, zero else div21 xh xl y

(* exact multiplication *)
let mulc x y =
  let lx = Int64.logand x maxuint31 in
  let ly = Int64.logand y maxuint31 in
  let hx = Int64.shift_right x 31 in
  let hy = Int64.shift_right y 31 in
  (* compute the median products *)
  let s = Int64.add (Int64.mul lx hy) (Int64.mul hx ly) in
  (* s fits on 64 bits, split it into a 33-bit high part and a 31-bit low part *)
  let lr = Int64.shift_left (Int64.logand s maxuint31) 31 in
  let hr = Int64.shift_right_logical s 31 in
  (* add the outer products *)
  let lr = Int64.add (Int64.mul lx ly) lr in
  let hr = Int64.add (Int64.mul hx hy) hr in
  (* hr fits on 64 bits, since the final result fits on 126 bits *)
  (* now x * y = hr * 2^62 + lr and lr < 2^63 *)
  let lr = Int64.add lr (Int64.shift_left (Int64.logand hr 1L) 62) in
  let hr = Int64.shift_right_logical hr 1 in
  (* now x * y = hr * 2^63 + lr, but lr might be too large *)
  if Int64.logand lr Int64.min_int <> 0L
  then Int64.add hr 1L, mask63 lr
  else hr, lr

let equal (x : t) y = x = y

let compare x y = Int64.compare x y

let compares x y = Int64.(compare (shift_left x 1) (shift_left y 1))

(* Number of leading zeroes *)
let head0 x =
  let r = ref 0 in
  let x = ref x in
  if Int64.logand !x 0x7FFFFFFF00000000L = 0L then r := !r + 31
  else x := Int64.shift_right !x 31;
  if Int64.logand !x 0xFFFF0000L = 0L then (x := Int64.shift_left !x 16; r := !r + 16);
  if Int64.logand !x 0xFF000000L = 0L then (x := Int64.shift_left !x 8; r := !r + 8);
  if Int64.logand !x 0xF0000000L = 0L then (x := Int64.shift_left !x 4; r := !r + 4);
  if Int64.logand !x 0xC0000000L = 0L then (x := Int64.shift_left !x 2; r := !r + 2);
  if Int64.logand !x 0x80000000L = 0L then (x := Int64.shift_left !x 1; r := !r + 1);
  if Int64.logand !x 0x80000000L = 0L then (r := !r + 1);
  Int64.of_int !r

(* Number of trailing zeroes *)
let tail0 x =
  let r = ref 0 in
  let x = ref x in
  if Int64.logand !x 0xFFFFFFFFL = 0L then (x := Int64.shift_right !x 32; r := !r + 32);
  if Int64.logand !x 0xFFFFL = 0L then (x := Int64.shift_right !x 16; r := !r + 16);
  if Int64.logand !x 0xFFL = 0L then (x := Int64.shift_right !x 8; r := !r + 8);
  if Int64.logand !x 0xFL = 0L then (x := Int64.shift_right !x 4; r := !r + 4);
  if Int64.logand !x 0x3L = 0L then (x := Int64.shift_right !x 2; r := !r + 2);
  if Int64.logand !x 0x1L = 0L then (r := !r + 1);
  Int64.of_int !r

(* May an object be safely cast into an Uint63.t ? *)
let is_uint63 t =
  Obj.is_block t && Int.equal (Obj.tag t) Obj.custom_tag
  && le (Obj.magic t) maxuint63

(* Arithmetic with explicit carries *)

(* Analog of Numbers.Abstract.Cyclic.carry *)
type 'a carry = C0 of 'a | C1 of 'a

let addc x y =
  let r = add x y in
  if lt r x then C1 r else C0 r

let addcarryc x y =
  let r = addcarry x y in
  if le r x then C1 r else C0 r

let subc x y =
  let r = sub x y in
  if le y x then C0 r else C1 r

let subcarryc x y =
  let r = subcarry x y in
  if lt y x then C0 r else C1 r

(* Register all exported functions so that they can be called from C code *)

let () =
  Callback.register "uint63 add" add;
  Callback.register "uint63 addcarry" addcarry;
  Callback.register "uint63 addmuldiv" addmuldiv;
  Callback.register "uint63 div" div;
  Callback.register "uint63 divs" divs;
  Callback.register "uint63 div21_ml" div21;
  Callback.register "uint63 eq" equal;
  Callback.register "uint63 eq0" (equal Int64.zero);
  Callback.register "uint63 eqm1" (equal (sub zero one));
  Callback.register "uint63 head0" head0;
  Callback.register "uint63 land" l_and;
  Callback.register "uint63 leq" le;
  Callback.register "uint63 les" les;
  Callback.register "uint63 lor" l_or;
  Callback.register "uint63 lsl" l_sl;
  Callback.register "uint63 lsr" l_sr;
  Callback.register "uint63 asr" a_sr;
  Callback.register "uint63 lt" lt;
  Callback.register "uint63 lts" lts;
  Callback.register "uint63 lxor" l_xor;
  Callback.register "uint63 mod" rem;
  Callback.register "uint63 mods" rems;
  Callback.register "uint63 mul" mul;
  Callback.register "uint63 mulc_ml" mulc;
  Callback.register "uint63 zero" zero;
  Callback.register "uint63 one" one;
  Callback.register "uint63 sub" sub;
  Callback.register "uint63 neg" (sub zero);
  Callback.register "uint63 subcarry" subcarry;
  Callback.register "uint63 tail0" tail0;
  Callback.register "uint63 of_float" of_float;
  Callback.register "uint63 to_float" to_float;
  Callback.register "uint63 of_int" of_int;
  Callback.register "uint63 to_int_min" to_int_min
