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|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \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 = Int64.of_string "0x7FFFFFFFFFFFFFFF"
let maxuint31 = Int64.of_string "0x7FFFFFFF"
let zero = Int64.zero
let one = Int64.one
(* conversion from an int *)
let mask63 i = Int64.logand i maxuint63
let of_int i = Int64.of_int i
let to_int2 i = (Int64.to_int (Int64.shift_right_logical i 31), Int64.to_int i)
let of_int64 i = i
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
let of_string s =
let i64 = Int64.of_string s in
if Int64.compare Int64.zero i64 <= 0
&& Int64.compare i64 maxuint63 <= 0
then i64
else raise (Failure "Int63.of_string")
(* 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
(* 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
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 = add (add x y) Int64.one
(* subtraction *)
let sub x y = mask63 (Int64.sub x y)
let subcarry x y = sub (sub x y) Int64.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 0L else Int64.rem x y
let addmuldiv p x y =
l_or (l_sl x p) (l_sr y Int64.(sub (of_int uint_size) p))
(* A few helper functions on 128 bits *)
let lt128 xh xl yh yl =
lt xh yh || (xh = yh && lt xl yl)
let le128 xh xl yh yl =
lt xh yh || (xh = yh && le xl yl)
(* division of two numbers by one *)
(* precondition: y <> 0 *)
(* outputs: q % 2^63, r s.t. x = q * y + r, r < y *)
let div21 xh xl y =
let maskh = ref zero in
let maskl = ref one in
let dh = ref zero in
let dl = ref y in
let cmp = ref true in
(* n = ref 0 *)
(* loop invariant: mask = 2^n, d = mask * y, (2 * d <= x -> cmp), n >= 0 *)
while Int64.equal (l_sr !dh (of_int (uint_size - 1))) zero && !cmp do
(* We don't use addmuldiv below to avoid checks on 1 *)
dh := l_or (l_sl !dh one) (l_sr !dl (of_int (uint_size - 1)));
dl := l_sl !dl one;
maskh := l_or (l_sl !maskh one) (l_sr !maskl (of_int (uint_size - 1)));
maskl := l_sl !maskl one;
(* incr n *)
cmp := lt128 !dh !dl xh xl;
done; (* mask = 2^n, d = 2^n * d, 2 * d > x *)
let remh = ref xh in
let reml = ref xl in
(* quotienth = ref 0 *)
let quotientl = ref zero in
(* loop invariant: x = quotient * y + rem, y * 2^(n+1) > r,
mask = floor(2^n), d = mask * y, n >= -1 *)
while not (Int64.equal (l_or !maskh !maskl) zero) do
if le128 !dh !dl !remh !reml then begin (* if rem >= d, add one bit and subtract d *)
(* quotienth := !quotienth lor !maskh *)
quotientl := l_or !quotientl !maskl;
remh := if lt !reml !dl then sub (sub !remh !dh) one else sub !remh !dh;
reml := sub !reml !dl
end;
maskl := l_or (l_sr !maskl one) (l_sl !maskh (of_int (uint_size - 1)));
maskh := l_sr !maskh one;
dl := l_or (l_sr !dl one) (l_sl !dh (of_int (uint_size - 1)));
dh := l_sr !dh one
(* decr n *)
done;
!quotientl, !reml
let div21 xh xl y = if Int64.equal y zero then zero, zero else div21 xh xl y
(* exact multiplication *)
let mulc x y =
let lx = ref (Int64.logand x maxuint31) in
let ly = ref (Int64.logand y maxuint31) in
let hx = Int64.shift_right x 31 in
let hy = Int64.shift_right y 31 in
let hr = ref (Int64.mul hx hy) in
let lr = ref (Int64.logor (Int64.mul !lx !ly) (Int64.shift_left !hr 62)) in
hr := (Int64.shift_right_logical !hr 1);
lx := Int64.mul !lx hy;
ly := Int64.mul hx !ly;
hr := Int64.logor !hr (Int64.add (Int64.shift_right !lx 32) (Int64.shift_right !ly 32));
lr := Int64.add !lr (Int64.shift_left !lx 31);
hr := Int64.add !hr (Int64.shift_right_logical !lr 63);
lr := Int64.add (Int64.shift_left !ly 31) (mask63 !lr);
hr := Int64.add !hr (Int64.shift_right_logical !lr 63);
if Int64.logand !lr Int64.min_int <> 0L
then Int64.(sub !hr one, mask63 !lr)
else (!hr, !lr)
let equal x y = mask63 x = mask63 y
let compare x y = Int64.compare x y
(* 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
(* 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 div21_ml" div21;
Callback.register "uint63 eq" equal;
Callback.register "uint63 eq0" (equal Int64.zero);
Callback.register "uint63 head0" head0;
Callback.register "uint63 land" l_and;
Callback.register "uint63 leq" le;
Callback.register "uint63 lor" l_or;
Callback.register "uint63 lsl" l_sl;
Callback.register "uint63 lsl1" (fun x -> l_sl x Int64.one);
Callback.register "uint63 lsr" l_sr;
Callback.register "uint63 lsr1" (fun x -> l_sr x Int64.one);
Callback.register "uint63 lt" lt;
Callback.register "uint63 lxor" l_xor;
Callback.register "uint63 mod" rem;
Callback.register "uint63 mul" mul;
Callback.register "uint63 mulc_ml" mulc;
Callback.register "uint63 one" one;
Callback.register "uint63 sub" sub;
Callback.register "uint63 subcarry" subcarry;
Callback.register "uint63 tail0" tail0
|
