diff options
Diffstat (limited to '')
| -rw-r--r-- | backends/coq/Primitives.v | 76 | ||||
| -rw-r--r-- | backends/fstar/Primitives.fst | 167 | ||||
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 42 |
3 files changed, 275 insertions, 10 deletions
diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v index 83f860b6..99ffe070 100644 --- a/backends/coq/Primitives.v +++ b/backends/coq/Primitives.v @@ -255,6 +255,12 @@ Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)). +Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) +Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) +Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) +Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *) +Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *) + (** Cast an integer from a [src_ty] to a [tgt_ty] *) (* TODO: check the semantics of casts in Rust *) Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) := @@ -372,6 +378,76 @@ Definition u32_mul := @scalar_mul U32. Definition u64_mul := @scalar_mul U64. Definition u128_mul := @scalar_mul U128. +(** Xor *) +Definition u8_xor := @scalar_xor U8. +Definition u16_xor := @scalar_xor U16. +Definition u32_xor := @scalar_xor U32. +Definition u64_xor := @scalar_xor U64. +Definition u128_xor := @scalar_xor U128. +Definition usize_xor := @scalar_xor Usize. +Definition i8_xor := @scalar_xor I8. +Definition i16_xor := @scalar_xor I16. +Definition i32_xor := @scalar_xor I32. +Definition i64_xor := @scalar_xor I64. +Definition i128_xor := @scalar_xor I128. +Definition isize_xor := @scalar_xor Isize. + +(** Or *) +Definition u8_or := @scalar_or U8. +Definition u16_or := @scalar_or U16. +Definition u32_or := @scalar_or U32. +Definition u64_or := @scalar_or U64. +Definition u128_or := @scalar_or U128. +Definition usize_or := @scalar_or Usize. +Definition i8_or := @scalar_or I8. +Definition i16_or := @scalar_or I16. +Definition i32_or := @scalar_or I32. +Definition i64_or := @scalar_or I64. +Definition i128_or := @scalar_or I128. +Definition isize_or := @scalar_or Isize. + +(** And *) +Definition u8_and := @scalar_and U8. +Definition u16_and := @scalar_and U16. +Definition u32_and := @scalar_and U32. +Definition u64_and := @scalar_and U64. +Definition u128_and := @scalar_and U128. +Definition usize_and := @scalar_and Usize. +Definition i8_and := @scalar_and I8. +Definition i16_and := @scalar_and I16. +Definition i32_and := @scalar_and I32. +Definition i64_and := @scalar_and I64. +Definition i128_and := @scalar_and I128. +Definition isize_and := @scalar_and Isize. + +(** Shift left *) +Definition u8_shl {ty} := @scalar_shl U8 ty. +Definition u16_shl {ty} := @scalar_shl U16 ty. +Definition u32_shl {ty} := @scalar_shl U32 ty. +Definition u64_shl {ty} := @scalar_shl U64 ty. +Definition u128_shl {ty} := @scalar_shl U128 ty. +Definition usize_shl {ty} := @scalar_shl Usize ty. +Definition i8_shl {ty} := @scalar_shl I8 ty. +Definition i16_shl {ty} := @scalar_shl I16 ty. +Definition i32_shl {ty} := @scalar_shl I32 ty. +Definition i64_shl {ty} := @scalar_shl I64 ty. +Definition i128_shl {ty} := @scalar_shl I128 ty. +Definition isize_shl {ty} := @scalar_shl Isize ty. + +(** Shift right *) +Definition u8_shr {ty} := @scalar_shr U8 ty. +Definition u16_shr {ty} := @scalar_shr U16 ty. +Definition u32_shr {ty} := @scalar_shr U32 ty. +Definition u64_shr {ty} := @scalar_shr U64 ty. +Definition u128_shr {ty} := @scalar_shr U128 ty. +Definition usize_shr {ty} := @scalar_shr Usize ty. +Definition i8_shr {ty} := @scalar_shr I8 ty. +Definition i16_shr {ty} := @scalar_shr I16 ty. +Definition i32_shr {ty} := @scalar_shr I32 ty. +Definition i64_shr {ty} := @scalar_shr I64 ty. +Definition i128_shr {ty} := @scalar_shr I128 ty. +Definition isize_shr {ty} := @scalar_shr Isize ty. + (** Small utility *) Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x). diff --git a/backends/fstar/Primitives.fst b/backends/fstar/Primitives.fst index 94322ead..dd340c00 100644 --- a/backends/fstar/Primitives.fst +++ b/backends/fstar/Primitives.fst @@ -65,6 +65,10 @@ type const_raw_ptr (t : Type0) = { v : t } (*** Scalars *) /// Rem.: most of the following code was partially generated +assume val size_numbits : pos + +// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t + let isize_min : int = -9223372036854775808 // TODO: should be opaque let isize_max : int = 9223372036854775807 // TODO: should be opaque let i8_min : int = -128 @@ -108,7 +112,6 @@ let is_unsigned = function | Isize | I8 | I16 | I32 | I64 | I128 -> false | Usize | U8 | U16 | U32 | U64 | U128 -> true - let scalar_min (ty : scalar_ty) : int = match ty with | Isize -> isize_min @@ -171,7 +174,7 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = mk_scalar ty (x * y) -let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize }) +let scalar_xor (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : scalar ty = match ty with | U8 -> FStar.UInt.logxor #8 x y @@ -179,6 +182,91 @@ let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize }) | U32 -> FStar.UInt.logxor #32 x y | U64 -> FStar.UInt.logxor #64 x y | U128 -> FStar.UInt.logxor #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logxor #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logxor #16 x y + | I32 -> FStar.Int.logxor #32 x y + | I64 -> FStar.Int.logxor #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logxor #128 x y + | Isize -> admit() // TODO + +let scalar_or (#ty : scalar_ty) + (x : scalar ty) (y : scalar ty) : scalar ty = + match ty with + | U8 -> FStar.UInt.logor #8 x y + | U16 -> FStar.UInt.logor #16 x y + | U32 -> FStar.UInt.logor #32 x y + | U64 -> FStar.UInt.logor #64 x y + | U128 -> FStar.UInt.logor #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logor #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logor #16 x y + | I32 -> FStar.Int.logor #32 x y + | I64 -> FStar.Int.logor #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logor #128 x y + | Isize -> admit() // TODO + +let scalar_and (#ty : scalar_ty) + (x : scalar ty) (y : scalar ty) : scalar ty = + match ty with + | U8 -> FStar.UInt.logand #8 x y + | U16 -> FStar.UInt.logand #16 x y + | U32 -> FStar.UInt.logand #32 x y + | U64 -> FStar.UInt.logand #64 x y + | U128 -> FStar.UInt.logand #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logand #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logand #16 x y + | I32 -> FStar.Int.logand #32 x y + | I64 -> FStar.Int.logand #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logand #128 x y + | Isize -> admit() // TODO + +// Shift left +let scalar_shl (#ty0 #ty1 : scalar_ty) + (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = + admit() + +// Shift right +let scalar_shr (#ty0 #ty1 : scalar_ty) + (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = + admit() (** Cast an integer from a [src_ty] to a [tgt_ty] *) // TODO: check the semantics of casts in Rust @@ -304,12 +392,75 @@ let u32_mul = scalar_mul #U32 let u64_mul = scalar_mul #U64 let u128_mul = scalar_mul #U128 -/// Logical operators, defined for unsigned types only, so far -let u8_xor = scalar_lxor #U8 -let u16_xor = scalar_lxor #U16 -let u32_xor = scalar_lxor #U32 -let u64_xor = scalar_lxor #U64 -let u128_xor = scalar_lxor #U128 +/// Xor +let u8_xor = scalar_xor #U8 +let u16_xor = scalar_xor #U16 +let u32_xor = scalar_xor #U32 +let u64_xor = scalar_xor #U64 +let u128_xor = scalar_xor #U128 +let usize_xor = scalar_xor #Usize +let i8_xor = scalar_xor #I8 +let i16_xor = scalar_xor #I16 +let i32_xor = scalar_xor #I32 +let i64_xor = scalar_xor #I64 +let i128_xor = scalar_xor #I128 +let isize_xor = scalar_xor #Isize + +/// Or +let u8_or = scalar_or #U8 +let u16_or = scalar_or #U16 +let u32_or = scalar_or #U32 +let u64_or = scalar_or #U64 +let u128_or = scalar_or #U128 +let usize_or = scalar_or #Usize +let i8_or = scalar_or #I8 +let i16_or = scalar_or #I16 +let i32_or = scalar_or #I32 +let i64_or = scalar_or #I64 +let i128_or = scalar_or #I128 +let isize_or = scalar_or #Isize + +/// And +let u8_and = scalar_and #U8 +let u16_and = scalar_and #U16 +let u32_and = scalar_and #U32 +let u64_and = scalar_and #U64 +let u128_and = scalar_and #U128 +let usize_and = scalar_and #Usize +let i8_and = scalar_and #I8 +let i16_and = scalar_and #I16 +let i32_and = scalar_and #I32 +let i64_and = scalar_and #I64 +let i128_and = scalar_and #I128 +let isize_and = scalar_and #Isize + +/// Shift left +let u8_shl #ty = scalar_shl #U8 #ty +let u16_shl #ty = scalar_shl #U16 #ty +let u32_shl #ty = scalar_shl #U32 #ty +let u64_shl #ty = scalar_shl #U64 #ty +let u128_shl #ty = scalar_shl #U128 #ty +let usize_shl #ty = scalar_shl #Usize #ty +let i8_shl #ty = scalar_shl #I8 #ty +let i16_shl #ty = scalar_shl #I16 #ty +let i32_shl #ty = scalar_shl #I32 #ty +let i64_shl #ty = scalar_shl #I64 #ty +let i128_shl #ty = scalar_shl #I128 #ty +let isize_shl #ty = scalar_shl #Isize #ty + +/// Shift right +let u8_shr #ty = scalar_shr #U8 #ty +let u16_shr #ty = scalar_shr #U16 #ty +let u32_shr #ty = scalar_shr #U32 #ty +let u64_shr #ty = scalar_shr #U64 #ty +let u128_shr #ty = scalar_shr #U128 #ty +let usize_shr #ty = scalar_shr #Usize #ty +let i8_shr #ty = scalar_shr #I8 #ty +let i16_shr #ty = scalar_shr #I16 #ty +let i32_shr #ty = scalar_shr #I32 #ty +let i64_shr #ty = scalar_shr #I64 #ty +let i128_shr #ty = scalar_shr #I128 #ty +let isize_shr #ty = scalar_shr #Isize #ty (*** core::ops *) diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index ec9665a5..cdd6d6f9 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -386,10 +386,28 @@ def Scalar.sub {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar def Scalar.mul {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (x.val * y.val) --- TODO: instances of +, -, * etc. for scalars +-- TODO: shift left +def Scalar.shiftl {ty0 ty1 : ScalarTy} (x : Scalar ty0) (y : Scalar ty1) : Result (Scalar ty0) := + sorry + +-- TODO: shift right +def Scalar.shiftr {ty0 ty1 : ScalarTy} (x : Scalar ty0) (y : Scalar ty1) : Result (Scalar ty0) := + sorry + +-- TODO: xor +def Scalar.xor {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry + +-- TODO: and +def Scalar.and {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry + +-- TODO: or +def Scalar.or {ty : ScalarTy} (x : Scalar ty) (y : Scalar ty) : Scalar ty := + sorry -- Cast an integer from a [src_ty] to a [tgt_ty] --- TODO: check the semantics of casts in Rust +-- TODO: double-check the semantics of casts in Rust def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Result (Scalar tgt_ty) := Scalar.tryMk tgt_ty x.val @@ -486,6 +504,26 @@ instance {ty} : HDiv (Scalar ty) (Scalar ty) (Result (Scalar ty)) where instance {ty} : HMod (Scalar ty) (Scalar ty) (Result (Scalar ty)) where hMod x y := Scalar.rem x y +-- Shift left +instance {ty0 ty1} : HShiftLeft (Scalar ty0) (Scalar ty1) (Result (Scalar ty0)) where + hShiftLeft x y := Scalar.shiftl x y + +-- Shift right +instance {ty0 ty1} : HShiftRight (Scalar ty0) (Scalar ty1) (Result (Scalar ty0)) where + hShiftRight x y := Scalar.shiftr x y + +-- Xor +instance {ty} : HXor (Scalar ty) (Scalar ty) (Scalar ty) where + hXor x y := Scalar.xor x y + +-- Or +instance {ty} : HOr (Scalar ty) (Scalar ty) (Scalar ty) where + hOr x y := Scalar.or x y + +-- And +instance {ty} : HAnd (Scalar ty) (Scalar ty) (Scalar ty) where + hAnd x y := Scalar.and x y + -- Generic theorem - shouldn't be used much @[cpspec] theorem Scalar.add_spec {ty} {x y : Scalar ty} |