(************************************************************************) (* * The Rocq Prover / The Rocq 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) *) (************************************************************************)
type t = int
let _ = assert (Sys.word_size = 64)
let uint_size = 63
let maxuint63 = Int64.of_string "0x7FFFFFFFFFFFFFFF" let maxuint31 = 0x7FFFFFFF
(* conversion from an int *) let to_uint64 i = Int64.logand (Int64.of_int i) maxuint63
let of_int i = i
[@@ocaml.inline always]
let to_int2 i = (0,i)
let of_int64 = Int64.to_int let to_int64 = to_uint64
let of_float = int_of_float
external to_float : int -> (float [@unboxed])
= "rocq_uint63_to_float_byte""rocq_uint63_to_float"
[@@noalloc]
let hash i = i
[@@ocaml.inline always]
(* conversion of an uint63 to a string *) let to_string i = Int64.to_string (to_uint64 i)
(* Compiles an unsigned int to OCaml code *) let compile i = Printf.sprintf "Uint63.of_int (%i)" i
let zero = 0 let one = 1
(* logical shift *) let l_sl x y = if 0 <= y && y < 63 then x lsl y else 0
let l_sr x y = if 0 <= y && y < 63 then x lsr y else 0
(* arithmetic shift (for sint63) *) let a_sr x y = if 0 <= y && y < 63 then x asr y else 0
let l_and x y = x land y
[@@ocaml.inline always]
let l_or x y = x lor y
[@@ocaml.inline always]
let l_xor x y = x lxor y
[@@ocaml.inline always]
(* addition of int63 *) let add x y = x + y
[@@ocaml.inline always]
(* subtraction *) letsub x y = x - y
[@@ocaml.inline always]
(* multiplication *) let mul x y = x * y
[@@ocaml.inline always]
(* division *) let div (x : int) (y : int) = if y = 0 then 0 else Int64.to_int (Int64.div (to_uint64 x) (to_uint64 y))
(* modulo *) let rem (x : int) (y : int) = if y = 0 then x else Int64.to_int (Int64.rem (to_uint64 x) (to_uint64 y))
let diveucl x y = (div x y, rem x y)
(* signed division *) let divs (x : int) (y : int) = if y = 0 then 0 else x / y
(* modulo *) let rems (x : int) (y : int) = if y = 0 then x else x mod y
let addmuldiv p x y =
l_or (l_sl x p) (l_sr y (uint_size - p))
let le (x : int) (y : int) =
(x lxor 0x4000000000000000) <= (y lxor 0x4000000000000000)
[@@ocaml.inline always]
(* signed comparison *) let lts (x : int) (y : int) =
x < y
[@@ocaml.inline always]
let les (x : int) (y : int) =
x <= y
[@@ocaml.inline always]
let to_int_min n m = if lt n m then n else m
[@@ocaml.inline always]
(* 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 = (* nh might temporarily grow as large as 2*y - 1 in the loop body,
so we store it as a 64-bit unsigned integer *) let nh = ref xh in let nl = ref xl in let q = ref 0 in
for _i = 0 to 62 do (* invariants: 0 <= nh < y, nl = (xl*2^i) % 2^63,
(q*y + nh) * 2^(63-i) + (xl % 2^(63-i)) = (xh%y) * 2^63 + xl *)
nh := Int64.logor (Int64.shift_left !nh 1) (Int64.of_int (!nl lsr 62));
nl := !nl lsl 1;
q := !q lsl 1; if Int64.unsigned_compare !nh y >= 0 then begin q := !q lor 1; nh := Int64.sub !nh y; end
done;
!q, Int64.to_int !nh
let div21 xh xl y = let xh = to_uint64 xh in let y = to_uint64 y in if Int64.compare y xh <= 0 then 0, 0 else div21 xh xl y
(* exact multiplication *) (* TODO: check that none of these additions could be a logical or *)
(* precondition : (x lsr 62 = 0 || y lsr 62 = 0) *) let mulc_aux x y = let lx = x land maxuint31 in let ly = y land maxuint31 in let hx = x lsr 31 in let hy = y lsr 31 in (* hx and hy are 32 bits value but at most one is 32 *) let hxy = hx * hy in(* 63 bits *) let hxly = hx * ly in(* 63 bits *) let lxhy = lx * hy in(* 63 bits *) let lxy = lx * ly in(* 62 bits *) let l = lxy lor (hxy lsl 62) (* 63 bits *) in let h = hxy lsr 1 in(* 62 bits *) let hl = hxly + lxhy in(* We can have a carry *) let h = if lt hl hxly then h + (1 lsl 31) else h in let hl'= hl lsl 31 in let l = l + hl' in let h = if lt l hl' then h + 1 else h in let h = h + (hl lsr 32) in
(h,l)
let mulc x y = if (x lsr 62 = 0 || y lsr 62 = 0) then mulc_aux x y else let yl = y lxor (1 lsl 62) in let (h,l) = mulc_aux x yl in (* h << 63 + l = x * yl x * y = x * (1 << 62 + yl) =
x << 62 + x*yl = x << 62 + h << 63 + l *) let l' = l + (x lsl 62) in let h = if lt l' l then h + 1 else h in
(h + (x lsr 1), l')
let equal (x : int) (y : int) = x = y
[@@ocaml.inline always]
let compare (x:int) (y:int) = let x = x lxor 0x4000000000000000 in let y = y lxor 0x4000000000000000 in
Int.compare x y
let compares (x : int) (y : int) =
Int.compare x y
(* head tail *)
let head0 x = let r = ref 0 in let x = ref x in if !x land 0x7FFFFFFF00000000 = 0 then r := !r + 31 else x := !x lsr 31; if !x land 0xFFFF0000 = 0 then (x := !x lsl 16; r := !r + 16); if !x land 0xFF000000 = 0 then (x := !x lsl 8; r := !r + 8); if !x land 0xF0000000 = 0 then (x := !x lsl 4; r := !r + 4); if !x land 0xC0000000 = 0 then (x := !x lsl 2; r := !r + 2); if !x land 0x80000000 = 0 then (x := !x lsl 1; r := !r + 1); if !x land 0x80000000 = 0 then ( r := !r + 1);
!r;;
let tail0 x = let r = ref 0 in let x = ref x in if !x land 0xFFFFFFFF = 0 then (x := !x lsr 32; r := !r + 32); if !x land 0xFFFF = 0 then (x := !x lsr 16; r := !r + 16); if !x land 0xFF = 0 then (x := !x lsr 8; r := !r + 8); if !x land 0xF = 0 then (x := !x lsr 4; r := !r + 4); if !x land 0x3 = 0 then (x := !x lsr 2; r := !r + 2); if !x land 0x1 = 0 then ( r := !r + 1);
!r
let is_uint63 t =
Obj.is_int t
[@@ocaml.inline always]
(* 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 = x + y in if lt r x then C1 r else C0 r
let addcarryc x y = let r = x + y + 1 in if le r x then C1 r else C0 r
let subc x y = let r = x - y in if le y x then C0 r else C1 r
let subcarryc x y = let r = x - y - 1 in if lt y x then C0 r else C1 r
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