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open Farith
let ops_rm =
Value.ops
~compare:Mode.compare
~print:Mode.pp
()
let ops =
Value.ops
~compare:(fun b b' -> F.compare b b')
~print:(fun fmt b -> Format.fprintf fmt "%a" F.pp b)
()
exception Min_Max_with_different_zeros
exception FP_to_BV_undefined
module E = Dolmen.Std.Expr
module B = Dolmen.Std.Builtin
let mk f = Value.mk ~ops f
let mode v = (Value.extract_exn ~ops:ops_rm v)
let fp v = (Value.extract_exn ~ops v)
let test ~cst p = Some (Fun.fun_1 ~cst (fun x -> Bool.mk @@ p (fp x)))
let cmp ~cst p = Some (Fun.fun_2 ~cst (fun x y -> Bool.mk @@ p (fp x) (fp y)))
let op2_mode ~cst f =
Some (Fun.fun_3 ~cst (fun m x y -> mk @@ f (mode m) (fp x) (fp y)))
let op1_mode ~cst f =
Some (Fun.fun_2 ~cst (fun m x -> mk @@ f (mode m) (fp x)))
let op1 ~cst f = Some (Fun.fun_1 ~cst(fun x -> mk @@ f (fp x)))
let min_max ~cmp ~cst =
Some (Fun.fun_2 ~cst (fun x y ->
let x = fp x in
let y = fp y in
match F.classify x, F.classify y with
| NaN, _ -> mk y
| _, NaN -> mk x
| PZero, NZero | NZero, PZero -> raise Min_Max_with_different_zeros
| _ -> if cmp x y then mk x else mk y
))
let round_q ~neg ~mw ~ew mode r =
if Q.equal Q.zero r then F.zero ~mw ~ew neg else F.of_q ~mw ~ew mode r
let nearest_no_tie x =
assert (not (Z.equal x.Q.den (Z.of_int 2)));
Int.ceil (Q.sub x (Q.make Z.one (Z.of_int 2)))
let toIntegral mode q =
match mode with
| Mode.NE ->
if Z.equal (Z.of_int 2) q.Q.den then
let r = Int.floor q in
(if Z.is_even r then r else Z.succ r)
else
(nearest_no_tie q)
| Mode.NA ->
if Z.equal (Z.of_int 2) q.Q.den then
let r = if Z.sign q.Q.num < 0 then Int.floor q else Int.ceil q in
r
else
(nearest_no_tie q)
| Mode.ZR -> (Int.truncate q)
| Mode.DN -> (Int.floor q)
| Mode.UP -> (Int.ceil q)
let builtins _ (cst : Dolmen.Std.Expr.Term.Const.t) =
match cst.builtin with
| B.RoundNearestTiesToEven -> Some (Value.mk ~ops:ops_rm Mode.NE)
| B.RoundNearestTiesToAway -> Some (Value.mk ~ops:ops_rm Mode.NA)
| B.RoundTowardPositive -> Some (Value.mk ~ops:ops_rm Mode.UP)
| B.RoundTowardNegative -> Some (Value.mk ~ops:ops_rm Mode.DN)
| B.RoundTowardZero -> Some (Value.mk ~ops:ops_rm Mode.ZR)
| B.Real_to_fp (ew, prec) ->
Some (Fun.fun_2 ~cst (fun m r ->
mk (F.of_q ~ew ~mw:(prec - 1) (mode m) (Real.get r))))
| B.Fp_to_fp (_ew1, _prec1, ew2, prec2) ->
Some (Fun.fun_2 ~cst
(fun m f1 -> mk @@ F.round ~ew:ew2 ~mw:(prec2 - 1) (mode m) (fp f1)))
| B.Sbv_to_fp (n, ew, prec) ->
Some (Fun.fun_2 ~cst (fun m bv ->
mk @@ F.of_q ~ew ~mw:(prec - 1) (mode m) (Q.of_bigint (Bitv.sbitv n bv))))
| B.Ubv_to_fp (n, ew, prec) ->
Some (Fun.fun_2 ~cst (fun m bv ->
mk @@ F.of_q ~ew ~mw:(prec - 1) (mode m) (Q.of_bigint (Bitv.ubitv n bv))))
| B.Fp (ew, prec) ->
Some (Fun.fun_3 ~cst (fun bvs bve bvm ->
mk @@
F.of_bits ~ew ~mw:(prec - 1)
(Z.logor
(Z.logor
(Z.shift_left
(Bitv.ubitv 1 bvs)
(ew + prec - 1))
(Z.shift_left
(Bitv.ubitv ew bve)
(prec - 1)))
(Bitv.ubitv (prec - 1) bvm))))
| B.Ieee_format_to_fp (ew, prec) ->
Some (Fun.fun_1 ~cst (fun bv ->
mk @@
F.of_bits ~ew ~mw:(prec - 1) (Bitv.ubitv (ew + prec) bv)))
| B.To_real (_ew, _prec) ->
Some (Fun.fun_1 ~cst (fun f -> Real.mk @@ (F.to_q (fp f))))
| B.Plus_infinity (ew, prec) ->
Some (mk @@ F.inf ~ew ~mw:(prec - 1) false)
| B.Minus_infinity (ew, prec) ->
Some (mk @@ F.inf ~ew ~mw:(prec - 1) true)
| B.NaN (ew, prec) ->
Some (mk @@ F.nan ~ew ~mw:(prec - 1))
| B.Plus_zero (ew, prec) ->
Some (mk @@ F.zero ~ew ~mw:(prec - 1) false)
| B.Minus_zero (ew, prec) ->
Some (mk @@ F.zero ~ew ~mw:(prec - 1) true)
| B.Fp_add (_ew, _prec) ->
op2_mode ~cst F.add
| B.Fp_sub (_ew, _prec) ->
op2_mode ~cst F.sub
| B.Fp_mul (_ew, _prec) ->
op2_mode ~cst F.mul
| B.Fp_abs (_ew, _prec) ->
op1 ~cst F.abs
| B.Fp_neg (_ew, _prec) ->
op1 ~cst F.neg
| B.Fp_sqrt (_ew, _prec) ->
op1_mode ~cst F.sqrt
| B.Fp_div (_ew, _prec) ->
op2_mode ~cst F.div
| B.Fp_fma (_ew, _prec) ->
Some (Fun.fun_4 ~cst (fun m x y z -> mk @@ F.fma (mode m) (fp x) (fp y) (fp z)))
| B.Fp_eq (_ew, _prec) ->
cmp ~cst F.eq
| B.Fp_leq (_ew, _prec) ->
cmp ~cst F.le
| B.Fp_lt (_ew, _prec) ->
cmp ~cst F.lt
| B.Fp_geq (_ew, _prec) ->
cmp ~cst F.ge
| B.Fp_gt (_ew, _prec) ->
cmp ~cst F.gt
| B.Fp_isInfinite (_ew, _prec) ->
test ~cst F.is_infinite
| B.Fp_isZero (_ew, _prec) ->
test ~cst F.is_zero
| B.Fp_isNaN (_ew, _prec) ->
test ~cst F.is_nan
| B.Fp_isNegative (_ew, _prec) ->
test ~cst F.is_negative
| B.Fp_isPositive (_ew, _prec) ->
test ~cst F.is_positive
| B.Fp_isNormal (_ew, _prec) ->
test ~cst F.is_normal
| B.Fp_isSubnormal (_ew, _prec) ->
test ~cst F.is_subnormal
| B.Fp_rem (ew,prec) ->
Some (Fun.fun_2 ~cst (fun f g ->
let f = fp f in
let g = fp g in
let mode = Farith.Mode.NE in
let mw = prec - 1 in
match F.classify f, F.classify g with
| (NaN | PInf | NInf), _ -> mk (F.nan ~ew ~mw)
| _, (NaN | PZero | NZero) -> mk (F.nan ~ew ~mw)
| _, (PInf | NInf) -> mk f
| (PZero | NZero | PNormal | NNormal | PSubn | NSubn) ,
(PNormal | NNormal | PSubn | NSubn) ->
let qf = F.to_q f and qg = F.to_q g in
let y = toIntegral mode (Q.div qf qg) in
let x = Q.sub qf (Q.mul qg (Q.of_bigint y)) in
mk (round_q ~neg:(F.is_negative f) mode ~ew ~mw x)
))
| B.Fp_roundToIntegral (ew,prec) ->
Some (Fun.fun_2 ~cst (fun m f ->
let f = fp f in
let mode = mode m in
let mw = prec - 1 in
match F.classify f with
| (NaN | PInf | NInf | PZero | NZero) -> mk f
| (PNormal | NNormal | PSubn | NSubn) ->
let q = F.to_q f in
let n = toIntegral mode q in
mk (round_q ~neg:(F.is_negative f) ~mw ~ew mode (Q.of_bigint n))
))
| B.Fp_min (_ew,_prec) -> min_max ~cmp:F.lt ~cst
| B.Fp_max (_ew,_prec) -> min_max ~cmp:F.gt ~cst
| B.To_ubv (_ew,_prec,size) ->
Some (Fun.fun_2 ~cst (fun m f ->
let f = fp f in
let mode = mode m in
match F.classify f with
| (NaN | PInf | NInf) -> raise FP_to_BV_undefined
| (PNormal | NNormal | PSubn | NSubn | PZero | NZero) ->
let q = F.to_q f in
let n = toIntegral mode q in
if Z.sign n >= 0 && Z.numbits n <= size then
Bitv.mk size n
else raise FP_to_BV_undefined
))
| B.To_sbv (_ew,_prec,size) ->
Some (Fun.fun_2 ~cst (fun m f ->
let f = fp f in
let mode = mode m in
match F.classify f with
| (NaN | PInf | NInf) -> raise FP_to_BV_undefined
| (PNormal | NNormal | PSubn | NSubn | PZero | NZero) ->
let q = F.to_q f in
let n = toIntegral mode q in
let n' = Z.extract n 0 size in
if Z.equal n (Z.signed_extract n' 0 size) then
Bitv.mk size n'
else raise FP_to_BV_undefined
))
| _ -> None