{-# LANGUAGE CPP #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
module Grisette.Core.Data.Class.SafeArith
(
ArithException (..),
SafeDivision (..),
SafeLinearArith (..),
SymIntegerOp,
)
where
import Control.Exception (ArithException (DivideByZero, Overflow, Underflow))
import Control.Monad.Except (MonadError (throwError))
import Data.Int (Int16, Int32, Int64, Int8)
import Data.Typeable (Proxy (Proxy), type (:~:) (Refl))
import Data.Word (Word16, Word32, Word64, Word8)
import GHC.TypeNats (KnownNat, sameNat, type (<=))
import Grisette.Core.Control.Monad.Union (MonadUnion)
import Grisette.Core.Data.BV
( BitwidthMismatch (BitwidthMismatch),
IntN,
SomeIntN (SomeIntN),
SomeWordN (SomeWordN),
WordN,
)
import Grisette.Core.Data.Class.Bool
( LogicalOp ((&&~), (||~)),
SEq ((==~)),
)
import Grisette.Core.Data.Class.Mergeable (Mergeable)
import Grisette.Core.Data.Class.SOrd
( SOrd ((<=~), (<~), (>=~), (>~)),
)
import Grisette.Core.Data.Class.SimpleMergeable
( merge,
mrgIf,
mrgSingle,
)
import Grisette.Core.Data.Class.Solvable (Solvable (con))
class (SOrd a, Num a, Mergeable a, Mergeable e) => SafeDivision e a | a -> e where
safeDiv :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeDiv a
l a
r = do
(a
d, a
_) <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf (a, a)
safeDivMod a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
d
safeMod :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeMod a
l a
r = do
(a
_, a
m) <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf (a, a)
safeDivMod a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
m
safeDivMod :: (MonadError e uf, MonadUnion uf) => a -> a -> uf (a, a)
safeDivMod a
l a
r = do
a
d <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf a
safeDiv a
l a
r
a
m <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf a
safeMod a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d, a
m)
safeQuot :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeQuot a
l a
r = do
(a
d, a
m) <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf (a, a)
safeDivMod a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
d)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle forall a b. (a -> b) -> a -> b
$ a
d forall a. Num a => a -> a -> a
+ a
1)
safeRem :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeRem a
l a
r = do
(a
_, a
m) <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf (a, a)
safeDivMod a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
m)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle forall a b. (a -> b) -> a -> b
$ a
m forall a. Num a => a -> a -> a
- a
r)
safeQuotRem :: (MonadError e uf, MonadUnion uf) => a -> a -> uf (a, a)
safeQuotRem a
l a
r = do
(a
d, a
m) <- forall e a (uf :: * -> *).
(SafeDivision e a, MonadError e uf, MonadUnion uf) =>
a -> a -> uf (a, a)
safeDivMod a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d, a
m))
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d forall a. Num a => a -> a -> a
+ a
1, a
m forall a. Num a => a -> a -> a
- a
r))
safeDiv' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
safeDiv' e -> e'
t a
l a
r = do
(a
d, a
_) <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
d
safeMod' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
safeMod' e -> e'
t a
l a
r = do
(a
_, a
m) <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
m
safeDivMod' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r = do
a
d <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf a
safeDiv' e -> e'
t a
l a
r
a
m <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf a
safeMod' e -> e'
t a
l a
r
forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d, a
m)
safeQuot' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
safeQuot' e -> e'
t a
l a
r = do
(a
d, a
m) <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
d)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle forall a b. (a -> b) -> a -> b
$ a
d forall a. Num a => a -> a -> a
+ a
1)
safeRem' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
safeRem' e -> e'
t a
l a
r = do
(a
_, a
m) <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle a
m)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle forall a b. (a -> b) -> a -> b
$ a
m forall a. Num a => a -> a -> a
- a
r)
safeQuotRem' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf (a, a)
safeQuotRem' e -> e'
t a
l a
r = do
(a
d, a
m) <- forall e a e' (uf :: * -> *).
(SafeDivision e a, MonadError e' uf, MonadUnion uf,
Mergeable e') =>
(e -> e') -> a -> a -> uf (a, a)
safeDivMod' e -> e'
t a
l a
r
forall (u :: * -> *) a.
(UnionLike u, Mergeable a) =>
SymBool -> u a -> u a -> u a
mrgIf
((a
l forall a. SOrd a => a -> a -> SymBool
>=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
>~ a
0) forall b. LogicalOp b => b -> b -> b
||~ (a
l forall a. SOrd a => a -> a -> SymBool
<=~ a
0 forall b. LogicalOp b => b -> b -> b
&&~ a
r forall a. SOrd a => a -> a -> SymBool
<~ a
0) forall b. LogicalOp b => b -> b -> b
||~ a
m forall a. SEq a => a -> a -> SymBool
==~ a
0)
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d, a
m))
(forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (a
d forall a. Num a => a -> a -> a
+ a
1, a
m forall a. Num a => a -> a -> a
- a
r))
{-# MINIMAL (safeDivMod | (safeDiv, safeMod)), (safeDivMod' | (safeDiv', safeMod')) #-}
#define QUOTE() '
#define QID(a) a
#define QRIGHT(a) QID(a)'
#define QRIGHTT(a) QID(a)' t'
#define QRIGHTU(a) QID(a)' _'
#define SAFE_DIVISION_FUNC(name, op) \
name _ r | r == 0 = merge $ throwError DivideByZero; \
name l r = mrgSingle $ l `op` r; \
QRIGHTT(name) _ r | r == 0 = let _ = t' in merge $ throwError (t' DivideByZero); \
QRIGHTU(name) l r = mrgSingle $ l `op` r
#define SAFE_DIVISION_CONCRETE(type) \
instance SafeDivision ArithException type where \
SAFE_DIVISION_FUNC(safeDiv, div); \
SAFE_DIVISION_FUNC(safeMod, mod); \
SAFE_DIVISION_FUNC(safeDivMod, divMod); \
SAFE_DIVISION_FUNC(safeQuot, quot); \
SAFE_DIVISION_FUNC(safeRem, rem); \
SAFE_DIVISION_FUNC(safeQuotRem, quotRem)
#define SAFE_DIVISION_CONCRETE_BV(type) \
instance (KnownNat n, 1 <= n) => SafeDivision ArithException (type n) where \
SAFE_DIVISION_FUNC(safeDiv, div); \
SAFE_DIVISION_FUNC(safeMod, mod); \
SAFE_DIVISION_FUNC(safeDivMod, divMod); \
SAFE_DIVISION_FUNC(safeQuot, quot); \
SAFE_DIVISION_FUNC(safeRem, rem); \
SAFE_DIVISION_FUNC(safeQuotRem, quotRem)
#if 1
SAFE_DIVISION_CONCRETE(Integer)
SAFE_DIVISION_CONCRETE(Int8)
SAFE_DIVISION_CONCRETE(Int16)
SAFE_DIVISION_CONCRETE(Int32)
SAFE_DIVISION_CONCRETE(Int64)
SAFE_DIVISION_CONCRETE(Int)
SAFE_DIVISION_CONCRETE(Word8)
SAFE_DIVISION_CONCRETE(Word16)
SAFE_DIVISION_CONCRETE(Word32)
SAFE_DIVISION_CONCRETE(Word64)
SAFE_DIVISION_CONCRETE(Word)
#endif
#define SAFE_DIVISION_FUNC_SOME(stype, type, name, op) \
name (stype (l :: type l)) (stype (r :: type r)) = \
(case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> \
if r == 0 \
then merge $ throwError $ Right DivideByZero \
else mrgSingle $ stype $ l `op` r; \
Nothing -> merge $ throwError $ Left BitwidthMismatch); \
QRIGHT(name) t (stype (l :: type l)) (stype (r :: type r)) = \
(case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> \
if r == 0 \
then merge $ throwError $ t (Right DivideByZero) \
else mrgSingle $ stype $ l `op` r; \
Nothing -> merge $ throwError $ t (Left BitwidthMismatch))
#define SAFE_DIVISION_FUNC_SOME_DIVMOD(stype, type, name, op) \
name (stype (l :: type l)) (stype (r :: type r)) = \
(case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> \
if r == 0 \
then merge $ throwError $ Right DivideByZero \
else (case l `op` r of (d, m) -> mrgSingle (stype d, stype m)); \
Nothing -> merge $ throwError $ Left BitwidthMismatch); \
QRIGHT(name) t (stype (l :: type l)) (stype (r :: type r)) = \
(case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> \
if r == 0 \
then merge $ throwError $ t (Right DivideByZero) \
else (case l `op` r of (d, m) -> mrgSingle (stype d, stype m)); \
Nothing -> merge $ throwError $ t (Left BitwidthMismatch))
#if 1
SAFE_DIVISION_CONCRETE_BV(IntN)
SAFE_DIVISION_CONCRETE_BV(WordN)
instance SafeDivision (Either BitwidthMismatch ArithException) SomeIntN where
SAFE_DIVISION_FUNC_SOME(SomeIntN, IntN, safeDiv, div)
SAFE_DIVISION_FUNC_SOME(SomeIntN, IntN, safeMod, mod)
SAFE_DIVISION_FUNC_SOME_DIVMOD(SomeIntN, IntN, safeDivMod, divMod)
SAFE_DIVISION_FUNC_SOME(SomeIntN, IntN, safeQuot, quot)
SAFE_DIVISION_FUNC_SOME(SomeIntN, IntN, safeRem, rem)
SAFE_DIVISION_FUNC_SOME_DIVMOD(SomeIntN, IntN, safeQuotRem, quotRem)
instance SafeDivision (Either BitwidthMismatch ArithException) SomeWordN where
SAFE_DIVISION_FUNC_SOME(SomeWordN, WordN, safeDiv, div)
SAFE_DIVISION_FUNC_SOME(SomeWordN, WordN, safeMod, mod)
SAFE_DIVISION_FUNC_SOME_DIVMOD(SomeWordN, WordN, safeDivMod, divMod)
SAFE_DIVISION_FUNC_SOME(SomeWordN, WordN, safeQuot, quot)
SAFE_DIVISION_FUNC_SOME(SomeWordN, WordN, safeRem, rem)
SAFE_DIVISION_FUNC_SOME_DIVMOD(SomeWordN, WordN, safeQuotRem, quotRem)
#endif
class (SOrd a, Num a, Mergeable a, Mergeable e) => SafeLinearArith e a | a -> e where
safeAdd :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeNeg :: (MonadError e uf, MonadUnion uf) => a -> uf a
safeMinus :: (MonadError e uf, MonadUnion uf) => a -> a -> uf a
safeAdd' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
safeNeg' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> uf a
safeMinus' :: (MonadError e' uf, MonadUnion uf, Mergeable e') => (e -> e') -> a -> a -> uf a
instance SafeLinearArith ArithException Integer where
safeAdd :: forall (uf :: * -> *).
(MonadError ArithException uf, MonadUnion uf) =>
Integer -> Integer -> uf Integer
safeAdd Integer
l Integer
r = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (Integer
l forall a. Num a => a -> a -> a
+ Integer
r)
safeNeg :: forall (uf :: * -> *).
(MonadError ArithException uf, MonadUnion uf) =>
Integer -> uf Integer
safeNeg Integer
l = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (-Integer
l)
safeMinus :: forall (uf :: * -> *).
(MonadError ArithException uf, MonadUnion uf) =>
Integer -> Integer -> uf Integer
safeMinus Integer
l Integer
r = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (Integer
l forall a. Num a => a -> a -> a
- Integer
r)
safeAdd' :: forall e' (uf :: * -> *).
(MonadError e' uf, MonadUnion uf, Mergeable e') =>
(ArithException -> e') -> Integer -> Integer -> uf Integer
safeAdd' ArithException -> e'
_ Integer
l Integer
r = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (Integer
l forall a. Num a => a -> a -> a
+ Integer
r)
safeNeg' :: forall e' (uf :: * -> *).
(MonadError e' uf, MonadUnion uf, Mergeable e') =>
(ArithException -> e') -> Integer -> uf Integer
safeNeg' ArithException -> e'
_ Integer
l = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (-Integer
l)
safeMinus' :: forall e' (uf :: * -> *).
(MonadError e' uf, MonadUnion uf, Mergeable e') =>
(ArithException -> e') -> Integer -> Integer -> uf Integer
safeMinus' ArithException -> e'
_ Integer
l Integer
r = forall (u :: * -> *) a. (UnionLike u, Mergeable a) => a -> u a
mrgSingle (Integer
l forall a. Num a => a -> a -> a
- Integer
r)
#define SAFE_LINARITH_SIGNED_CONCRETE_BODY \
safeAdd l r = let res = l + r in \
mrgIf (con $ l > 0 && r > 0 && res < 0) \
(throwError Overflow) \
(mrgIf (con $ l < 0 && r < 0 && res >= 0) \
(throwError Underflow) \
(return res));\
safeAdd' t' l r = let res = l + r in \
mrgIf (con $ l > 0 && r > 0 && res < 0) \
(throwError (t' Overflow)) \
(mrgIf (con $ l < 0 && r < 0 && res >= 0) \
(throwError (t' Underflow)) \
(return res)); \
safeMinus l r = let res = l - r in \
mrgIf (con $ l >= 0 && r < 0 && res < 0) \
(throwError Overflow) \
(mrgIf (con $ l < 0 && r > 0 && res > 0) \
(throwError Underflow) \
(return res));\
safeMinus' t' l r = let res = l - r in \
mrgIf (con $ l >= 0 && r < 0 && res < 0) \
(throwError (t' Overflow)) \
(mrgIf (con $ l < 0 && r > 0 && res > 0) \
(throwError (t' Underflow)) \
(return res)); \
safeNeg v = mrgIf (con $ v == minBound) (throwError Overflow) (return $ -v);\
safeNeg' t' v = mrgIf (con $ v == minBound) (throwError (t' Overflow)) (return $ -v)
#define SAFE_LINARITH_SIGNED_CONCRETE(type) \
instance SafeLinearArith ArithException type where \
SAFE_LINARITH_SIGNED_CONCRETE_BODY
#define SAFE_LINARITH_SIGNED_BV_CONCRETE(type) \
instance (KnownNat n, 1 <= n) => SafeLinearArith ArithException (type n) where \
SAFE_LINARITH_SIGNED_CONCRETE_BODY
#define SAFE_LINARITH_UNSIGNED_CONCRETE_BODY \
safeAdd l r = let res = l + r in \
mrgIf (con $ l > res || r > res) \
(throwError Overflow) \
(return res);\
safeAdd' t' l r = let res = l + r in \
mrgIf (con $ l > res || r > res) \
(throwError (t' Overflow)) \
(return res); \
safeMinus l r = \
mrgIf (con $ r > l) \
(throwError Underflow) \
(return $ l - r);\
safeMinus' t' l r = \
mrgIf (con $ r > l) \
(throwError $ t' Underflow) \
(return $ l - r);\
safeNeg v = mrgIf (con $ v /= 0) (throwError Underflow) (return $ -v);\
safeNeg' t' v = mrgIf (con $ v /= 0) (throwError (t' Underflow)) (return $ -v)
#define SAFE_LINARITH_UNSIGNED_CONCRETE(type) \
instance SafeLinearArith ArithException type where \
SAFE_LINARITH_UNSIGNED_CONCRETE_BODY
#define SAFE_LINARITH_UNSIGNED_BV_CONCRETE(type) \
instance (KnownNat n, 1 <= n) => SafeLinearArith ArithException (type n) where \
SAFE_LINARITH_UNSIGNED_CONCRETE_BODY
#define SAFE_LINARITH_SOME_CONCRETE(type, ctype) \
instance SafeLinearArith (Either BitwidthMismatch ArithException) type where \
safeAdd (type (l :: ctype l)) (type (r :: ctype r)) = merge (\
case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> type <$> safeAdd' Right l r; \
_ -> throwError $ Left BitwidthMismatch); \
safeAdd' t (type (l :: ctype l)) (type (r :: ctype r)) = merge (\
case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> type <$> safeAdd' (t . Right) l r; \
_ -> let t' = t; _ = t' in throwError $ t' $ Left BitwidthMismatch); \
safeMinus (type (l :: ctype l)) (type (r :: ctype r)) = merge (\
case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> type <$> safeMinus' Right l r; \
_ -> throwError $ Left BitwidthMismatch); \
safeMinus' t (type (l :: ctype l)) (type (r :: ctype r)) = merge (\
case sameNat (Proxy @l) (Proxy @r) of \
Just Refl -> type <$> safeMinus' (t . Right) l r; \
_ -> let t' = t; _ = t' in throwError $ t' $ Left BitwidthMismatch); \
safeNeg (type l) = merge $ type <$> safeNeg' Right l; \
safeNeg' t (type l) = merge $ type <$> safeNeg' (t . Right) l
#if 1
SAFE_LINARITH_SIGNED_CONCRETE(Int8)
SAFE_LINARITH_SIGNED_CONCRETE(Int16)
SAFE_LINARITH_SIGNED_CONCRETE(Int32)
SAFE_LINARITH_SIGNED_CONCRETE(Int64)
SAFE_LINARITH_SIGNED_CONCRETE(Int)
SAFE_LINARITH_SIGNED_BV_CONCRETE(IntN)
SAFE_LINARITH_SOME_CONCRETE(SomeIntN, IntN)
SAFE_LINARITH_UNSIGNED_CONCRETE(Word8)
SAFE_LINARITH_UNSIGNED_CONCRETE(Word16)
SAFE_LINARITH_UNSIGNED_CONCRETE(Word32)
SAFE_LINARITH_UNSIGNED_CONCRETE(Word64)
SAFE_LINARITH_UNSIGNED_CONCRETE(Word)
SAFE_LINARITH_UNSIGNED_BV_CONCRETE(WordN)
SAFE_LINARITH_SOME_CONCRETE(SomeWordN, WordN)
#endif
class (Num a, SEq a, SOrd a, Solvable Integer a) => SymIntegerOp a