diff options
| author | Alasdair Armstrong | 2017-07-26 14:12:09 +0100 |
|---|---|---|
| committer | Alasdair Armstrong | 2017-07-26 14:12:09 +0100 |
| commit | 678ab0e23ba4a8d95010df2bd2467dae7d544e29 (patch) | |
| tree | 0b2e02773327b9483f24b2e1ad46b7235ec9633e /src/gen_lib | |
| parent | 26e59493cde0ffbf1868426fe3bec158f2dbaad0 (diff) | |
| parent | 18cf235fad35a0e06e26ea91ee0e1c673febddb8 (diff) | |
Merge remote-tracking branch 'origin/master' into sail_new_tc
Diffstat (limited to 'src/gen_lib')
| -rw-r--r-- | src/gen_lib/sail_values.lem | 14 | ||||
| -rw-r--r-- | src/gen_lib/sail_values.ml | 63 | ||||
| -rw-r--r-- | src/gen_lib/sail_values_word.lem | 1030 |
3 files changed, 1080 insertions, 27 deletions
diff --git a/src/gen_lib/sail_values.lem b/src/gen_lib/sail_values.lem index d7318567..5dbdb157 100644 --- a/src/gen_lib/sail_values.lem +++ b/src/gen_lib/sail_values.lem @@ -343,12 +343,16 @@ let hardware_mod (a: integer) (b:integer) : integer = then (a mod b) - b else a mod b +(* There are different possible answers for integer divide regarding +rounding behaviour on negative operands. Positive operands always +round down so derive the one we want (trucation towards zero) from +that *) let hardware_quot (a:integer) (b:integer) : integer = - if a < 0 && b < 0 - then (abs a) / (abs b) - else if (a < 0 && b > 0) - then (a/b) + 1 - else a/b + let q = (abs a) / (abs b) in + if ((a<0) = (b<0)) then + q (* same sign -- result positive *) + else + ~q (* different sign -- result negative *) let quot_signed = hardware_quot diff --git a/src/gen_lib/sail_values.ml b/src/gen_lib/sail_values.ml index e2ddd3e9..d160e84a 100644 --- a/src/gen_lib/sail_values.ml +++ b/src/gen_lib/sail_values.ml @@ -24,6 +24,8 @@ type value = exception Sail_exit exception Sail_return +let _print s = print_string s + let string_of_bit = function | Vone -> "1" | Vzero -> "0" @@ -331,6 +333,8 @@ let most_significant = function | Vregister(array,_,_,_,_) -> !array.(0) | _ -> assert false +let _most_significant = most_significant + let bitwise_not_bit = function | Vone -> Vzero | Vzero -> Vone @@ -466,22 +470,25 @@ let min_32 = big_int_of_int (-2147483648) let max_8 = big_int_of_int 127 let min_8 = big_int_of_int (-128) let max_5 = big_int_of_int 31 -let min_5 = big_int_of_int (-32) let get_max_representable_in sign n = - if (n = 64) then match sign with | true -> max_64 | false -> max_64u - else if (n=32) then match sign with | true -> max_32 | false -> max_32u - else if (n=8) then max_8 - else if (n=5) then max_5 - else match sign with | true -> power_big two_big_int (pred_big_int (big_int_of_int n)) - | false -> power_big two_big_int (big_int_of_int n) - -let get_min_representable_in _ n = - if (n = 64) then min_64 - else if (n=32) then min_32 - else if (n=8) then min_8 - else if (n=5) then min_5 - else minus_big_int (power_big two_big_int (big_int_of_int n)) + match (sign, n) with + | (true, 64) -> max_64 + | (false, 64) -> max_64u + | (true, 32) -> max_32 + | (false, 32) -> max_32u + | (true, 8) -> max_8 + | (false, 5) -> max_5 + | (true, _) -> pred_big_int (power_big two_big_int (big_int_of_int (n-1))) + | (false, _) -> pred_big_int (power_big two_big_int (big_int_of_int n)) + +let get_min_representable_in sign n = + match (sign, n) with + | (false, _) -> zero_big_int + | (true, 64) -> min_64 + | (true, 32) -> min_32 + | (true, 8) -> min_8 + | (true, _) -> minus_big_int (power_big two_big_int (big_int_of_int (n-1))) let to_vec_int ord len n = let array = Array.make len Vzero in @@ -603,6 +610,9 @@ let min_int = min (* the built-in version *) let min = min_big (* is overwritten here *) let max_int = max (* likewise *) let max = max_big +let abs_int = abs +let abs_big = abs_big_int +let abs = abs_big let arith_op_vec_big op sign size (l,r) = let ord = get_ord l in @@ -910,8 +920,8 @@ let rec arith_op_no0_big op (l,r) = then None else Some (op l r) -let modulo_no0_big = arith_op_no0_big mod_big_int -let quot_no0_big = arith_op_no0_big div_big_int +let modulo_no0_big = arith_op_no0_big (Z.rem) +let quot_no0_big = arith_op_no0_big (Z.div) let rec arith_op_no0_int op (l,r) = if r = 0 @@ -960,9 +970,9 @@ let rec arith_op_vec_no0_big op sign size (l,r) = Vvector((Array.make act_size Vundef), start, ord) | _ -> assert false -let mod_vec_big = arith_op_vec_no0_big mod_big_int false unit_big_int -let quot_vec_big = arith_op_vec_no0_big div_big_int false unit_big_int -let quot_vec_signed_big = arith_op_vec_no0_big div_big_int true unit_big_int +let mod_vec_big = arith_op_vec_no0_big (Z.rem) false unit_big_int +let quot_vec_big = arith_op_vec_no0_big (Z.div) false unit_big_int +let quot_vec_signed_big = arith_op_vec_no0_big (Z.div) true unit_big_int let mod_vec = mod_vec_big let quot_vec = quot_vec_big @@ -1021,8 +1031,8 @@ let arith_op_overflow_no0_vec_big op sign size (l,r) = let overflow = if representable then Vzero else Vone in (correct_size_num,overflow,most_significant one_more) -let quot_overflow_vec_big = arith_op_overflow_no0_vec_big div_big_int false unit_big_int -let quot_overflow_vec_signed_big = arith_op_overflow_no0_vec_big div_big_int true unit_big_int +let quot_overflow_vec_big = arith_op_overflow_no0_vec_big (Z.div) false unit_big_int +let quot_overflow_vec_signed_big = arith_op_overflow_no0_vec_big (Z.div) true unit_big_int let quot_overflow_vec = quot_overflow_vec_big let quot_overflow_vec_signed = quot_overflow_vec_signed_big @@ -1038,7 +1048,7 @@ let arith_op_vec_range_no0_big op sign size (l,r) = let ord = get_ord l in arith_op_vec_no0_big op sign size (l,(to_vec_big ord (length_big l) r)) -let mod_vec_range_big = arith_op_vec_range_no0_big mod_big_int false unit_big_int +let mod_vec_range_big = arith_op_vec_range_no0_big (Z.rem) false unit_big_int let mod_vec_range = mod_vec_range_big @@ -1051,6 +1061,15 @@ let duplicate_big (bit,length) = let duplicate = duplicate_big +let duplicate_bits_big (bits, x) = + let len = (length_int bits) * (int_of_big_int x) in + let is_inc = get_ord bits in + let bits_arr = get_barray bits in + let arr = Array.concat (Array.to_list(Array.make (int_of_big_int x) bits_arr)) in + Vvector(arr, (if is_inc then 0 else (len - 1)), is_inc) + +let duplicate_bits = duplicate_bits_big + let compare_op op (l,r) = if (op l r) then Vone diff --git a/src/gen_lib/sail_values_word.lem b/src/gen_lib/sail_values_word.lem new file mode 100644 index 00000000..048bf30a --- /dev/null +++ b/src/gen_lib/sail_values_word.lem @@ -0,0 +1,1030 @@ +(* Version of sail_values.lem that uses Lem's machine words library *) + +open import Pervasives_extra +open import Machine_word +open import Sail_impl_base + + +type ii = integer +type nn = natural + +val pow : integer -> integer -> integer +let pow m n = m ** (natFromInteger n) + +let rec replace bs ((n : integer),b') = match bs with + | [] -> [] + | b :: bs -> + if n = 0 then b' :: bs + else b :: replace bs (n - 1,b') + end + + +(*** Bits *) +type bitU = B0 | B1 | BU + +let showBitU = function + | B0 -> "O" + | B1 -> "I" + | BU -> "U" +end + +instance (Show bitU) + let show = showBitU +end + + +let bitU_to_bool = function + | B0 -> false + | B1 -> true + | BU -> failwith "to_bool applied to BU" + end + +let bit_lifted_of_bitU = function + | B0 -> Bitl_zero + | B1 -> Bitl_one + | BU -> Bitl_undef + end + +let bitU_of_bit = function + | Bitc_zero -> B0 + | Bitc_one -> B1 + end + +let bit_of_bitU = function + | B0 -> Bitc_zero + | B1 -> Bitc_one + | BU -> failwith "bit_of_bitU: BU" + end + +let bitU_of_bit_lifted = function + | Bitl_zero -> B0 + | Bitl_one -> B1 + | Bitl_undef -> BU + | Bitl_unknown -> failwith "bitU_of_bit_lifted Bitl_unknown" + end + +let bitwise_not_bit = function + | B1 -> B0 + | B0 -> B1 + | BU -> BU + end + +let inline (~) = bitwise_not_bit + +val is_one : integer -> bitU +let is_one i = + if i = 1 then B1 else B0 + +let bool_to_bitU b = if b then B1 else B0 + +let bitwise_binop_bit op = function + | (BU,_) -> BU (*Do we want to do this or to respect | of I and & of B0 rules?*) + | (_,BU) -> BU (*Do we want to do this or to respect | of I and & of B0 rules?*) + | (x,y) -> bool_to_bitU (op (bitU_to_bool x) (bitU_to_bool y)) + end + +val bitwise_and_bit : bitU * bitU -> bitU +let bitwise_and_bit = bitwise_binop_bit (&&) + +val bitwise_or_bit : bitU * bitU -> bitU +let bitwise_or_bit = bitwise_binop_bit (||) + +val bitwise_xor_bit : bitU * bitU -> bitU +let bitwise_xor_bit = bitwise_binop_bit xor + +val (&.) : bitU -> bitU -> bitU +let inline (&.) x y = bitwise_and_bit (x,y) + +val (|.) : bitU -> bitU -> bitU +let inline (|.) x y = bitwise_or_bit (x,y) + +val (+.) : bitU -> bitU -> bitU +let inline (+.) x y = bitwise_xor_bit (x,y) + + + +(*** Vectors *) + +(* element list * start * has increasing direction *) +type vector 'a = Vector of list 'a * integer * bool + +let showVector (Vector elems start inc) = + "Vector " ^ show elems ^ " " ^ show start ^ " " ^ show inc + +let get_dir (Vector _ _ ord) = ord +let get_start (Vector _ s _) = s +let get_elems (Vector elems _ _) = elems +let length (Vector bs _ _) = integerFromNat (length bs) + +instance forall 'a. Show 'a => (Show (vector 'a)) + let show = showVector +end + +let dir is_inc = if is_inc then D_increasing else D_decreasing +let bool_of_dir = function + | D_increasing -> true + | D_decreasing -> false + end + +(*** Vector operations *) + +val set_vector_start : forall 'a. integer -> vector 'a -> vector 'a +let set_vector_start new_start (Vector bs _ is_inc) = + Vector bs new_start is_inc + +let reset_vector_start v = + set_vector_start (if (get_dir v) then 0 else (length v - 1)) v + +let set_vector_start_to_length v = + set_vector_start (length v - 1) v + +let vector_concat (Vector bs start is_inc) (Vector bs' _ _) = + Vector (bs ++ bs') start is_inc + +let inline (^^) = vector_concat + +val sublist : forall 'a. list 'a -> (nat * nat) -> list 'a +let sublist xs (i,j) = + let (toJ,_suffix) = List.splitAt (j+1) xs in + let (_prefix,fromItoJ) = List.splitAt i toJ in + fromItoJ + +val update_sublist : forall 'a. list 'a -> (nat * nat) -> list 'a -> list 'a +let update_sublist xs (i,j) xs' = + let (toJ,suffix) = List.splitAt (j+1) xs in + let (prefix,_fromItoJ) = List.splitAt i toJ in + prefix ++ xs' ++ suffix + +val slice : forall 'a. vector 'a -> integer -> integer -> vector 'a +let slice (Vector bs start is_inc) i j = + let iN = natFromInteger i in + let jN = natFromInteger j in + let startN = natFromInteger start in + let subvector_bits = + sublist bs (if is_inc then (iN-startN,jN-startN) else (startN-iN,startN-jN)) in + Vector subvector_bits i is_inc + +(* this is for the vector slicing introduced in vector-concat patterns: i and j +index into the "raw data", the list of bits. Therefore getting the bit list is +easy, but the start index has to be transformed to match the old vector start +and the direction. *) +val slice_raw : forall 'a. vector 'a -> integer -> integer -> vector 'a +let slice_raw (Vector bs start is_inc) i j = + let iN = natFromInteger i in + let jN = natFromInteger j in + let bits = sublist bs (iN,jN) in + let len = integerFromNat (List.length bits) in + Vector bits (if is_inc then 0 else len - 1) is_inc + + +val update_aux : forall 'a. vector 'a -> integer -> integer -> list 'a -> vector 'a +let update_aux (Vector bs start is_inc) i j bs' = + let iN = natFromInteger i in + let jN = natFromInteger j in + let startN = natFromInteger start in + let bits = + (update_sublist bs) + (if is_inc then (iN-startN,jN-startN) else (startN-iN,startN-jN)) bs' in + Vector bits start is_inc + +val update : forall 'a. vector 'a -> integer -> integer -> vector 'a -> vector 'a +let update v i j (Vector bs' _ _) = + update_aux v i j bs' + +val access : forall 'a. vector 'a -> integer -> 'a +let access (Vector bs start is_inc) n = + if is_inc then List_extra.nth bs (natFromInteger (n - start)) + else List_extra.nth bs (natFromInteger (start - n)) + +val update_pos : forall 'a. vector 'a -> integer -> 'a -> vector 'a +let update_pos v n b = + update_aux v n n [b] + +(*** Bitvectors *) + +(* element list * start * has increasing direction *) +type bitvector 'a = Bitvector of mword 'a * integer * bool + +let showBitvector (Bitvector elems start inc) = + "Bitvector " ^ show elems ^ " " ^ show start ^ " " ^ show inc + +let bvget_dir (Bitvector _ _ ord) = ord +let bvget_start (Bitvector _ s _) = s +let bvget_elems (Bitvector elems _ _) = elems +let bvlength (Bitvector bs _ _) = integerFromNat (word_length bs) + +instance forall 'a. Show 'a => (Show (bitvector 'a)) + let show = showBitvector +end + +(*** Vector operations *) + +val set_bitvector_start : forall 'a. integer -> bitvector 'a -> bitvector 'a +let set_bitvector_start new_start (Bitvector bs _ is_inc) = + Bitvector bs new_start is_inc + +let reset_bitvector_start v = + set_bitvector_start (if (bvget_dir v) then 0 else (bvlength v - 1)) v + +let set_bitvector_start_to_length v = + set_bitvector_start (bvlength v - 1) v + +let bitvector_concat (Bitvector bs start is_inc) (Bitvector bs' _ _) = + Bitvector (word_concat bs bs') start is_inc + +let inline (^^^) = bitvector_concat + +val bvslice : forall 'a 'b. bitvector 'a -> integer -> integer -> bitvector 'b +let bvslice (Bitvector bs start is_inc) i j = + let iN = natFromInteger i in + let jN = natFromInteger j in + let startN = natFromInteger start in + let (lo,hi) = if is_inc then (iN-startN,jN-startN) else (startN-iN,startN-jN) in + let subvector_bits = word_extract lo hi bs in + Bitvector subvector_bits i is_inc + +(* this is for the vector slicing introduced in vector-concat patterns: i and j +index into the "raw data", the list of bits. Therefore getting the bit list is +easy, but the start index has to be transformed to match the old vector start +and the direction. *) +val bvslice_raw : forall 'a 'b. Size 'b => bitvector 'a -> integer -> integer -> bitvector 'b +let bvslice_raw (Bitvector bs start is_inc) i j = + let iN = natFromInteger i in + let jN = natFromInteger j in + let bits = word_extract iN jN bs in + let len = integerFromNat (word_length bits) in + Bitvector bits (if is_inc then 0 else len - 1) is_inc + +val bvupdate_aux : forall 'a 'b. bitvector 'a -> integer -> integer -> mword 'b -> bitvector 'a +let bvupdate_aux (Bitvector bs start is_inc) i j bs' = + let iN = natFromInteger i in + let jN = natFromInteger j in + let startN = natFromInteger start in + let (lo,hi) = if is_inc then (iN-startN,jN-startN) else (startN-iN,startN-jN) in + let bits = word_update bs lo hi bs' in + Bitvector bits start is_inc + +val bvupdate : forall 'a. bitvector 'a -> integer -> integer -> bitvector 'a -> bitvector 'a +let bvupdate v i j (Bitvector bs' _ _) = + bvupdate_aux v i j bs' + +(* TODO: decide between nat/natural, change either here or in machine_word *) +val getBit' : forall 'a. mword 'a -> nat -> bool +let getBit' w n = getBit w (naturalFromNat n) + +val bvaccess : forall 'a. bitvector 'a -> integer -> bool +let bvaccess (Bitvector bs start is_inc) n = + if is_inc then getBit' bs (natFromInteger (n - start)) + else getBit' bs (natFromInteger (start - n)) + +val bvupdate_pos : forall 'a. Size 'a => bitvector 'a -> integer -> bool -> bitvector 'a +let bvupdate_pos v n b = + bvupdate_aux v n n (wordFromNatural (if b then 1 else 0)) + +(*** Bit vector operations *) + +let extract_only_bit (Bitvector elems _ _) = + let l = word_length elems in + if l = 1 then + msb elems + else if l = 0 then + failwith "extract_single_bit called for empty vector" + else + failwith "extract_single_bit called for vector with more bits" + +let pp_bitu_vector (Vector elems start inc) = + let elems_pp = List.foldl (fun acc elem -> acc ^ showBitU elem) "" elems in + "Vector [" ^ elems_pp ^ "] " ^ show start ^ " " ^ show inc + + +let most_significant (Bitvector v _ _) = + if word_length v = 0 then + failwith "most_significant applied to empty vector" + else + msb v + +let bitwise_not_bitlist = List.map bitwise_not_bit + +let bitwise_not (Bitvector bs start is_inc) = + Bitvector (lNot bs) start is_inc + +let bitwise_binop op (Bitvector bsl start is_inc, Bitvector bsr _ _) = + Bitvector (op bsl bsr) start is_inc + +let bitwise_and = bitwise_binop lAnd +let bitwise_or = bitwise_binop lOr +let bitwise_xor = bitwise_binop lXor + +let unsigned (Bitvector bs _ _) : integer = unsignedIntegerFromWord bs +let unsigned_big = unsigned + +let signed (Bitvector v _ _) : integer = signedIntegerFromWord v + +let hardware_mod (a: integer) (b:integer) : integer = + if a < 0 && b < 0 + then (abs a) mod (abs b) + else if (a < 0 && b >= 0) + then (a mod b) - b + else a mod b + +(* There are different possible answers for integer divide regarding +rounding behaviour on negative operands. Positive operands always +round down so derive the one we want (trucation towards zero) from +that *) +let hardware_quot (a:integer) (b:integer) : integer = + let q = (abs a) / (abs b) in + if ((a<0) = (b<0)) then + q (* same sign -- result positive *) + else + ~q (* different sign -- result negative *) + +let quot_signed = hardware_quot + + +let signed_big = signed + +let to_num sign = if sign then signed else unsigned + +let max_64u = (integerPow 2 64) - 1 +let max_64 = (integerPow 2 63) - 1 +let min_64 = 0 - (integerPow 2 63) +let max_32u = (4294967295 : integer) +let max_32 = (2147483647 : integer) +let min_32 = (0 - 2147483648 : integer) +let max_8 = (127 : integer) +let min_8 = (0 - 128 : integer) +let max_5 = (31 : integer) +let min_5 = (0 - 32 : integer) + +let get_max_representable_in sign (n : integer) : integer = + if (n = 64) then match sign with | true -> max_64 | false -> max_64u end + else if (n=32) then match sign with | true -> max_32 | false -> max_32u end + else if (n=8) then max_8 + else if (n=5) then max_5 + else match sign with | true -> integerPow 2 ((natFromInteger n) -1) + | false -> integerPow 2 (natFromInteger n) + end + +let get_min_representable_in _ (n : integer) : integer = + if n = 64 then min_64 + else if n = 32 then min_32 + else if n = 8 then min_8 + else if n = 5 then min_5 + else 0 - (integerPow 2 (natFromInteger n)) + +val to_bin_aux : natural -> list bitU +let rec to_bin_aux x = + if x = 0 then [] + else (if x mod 2 = 1 then B1 else B0) :: to_bin_aux (x / 2) +let to_bin n = List.reverse (to_bin_aux n) + +val pad_zero : list bitU -> integer -> list bitU +let rec pad_zero bits n = + if n = 0 then bits else pad_zero (B0 :: bits) (n -1) + + +let rec add_one_bit_ignore_overflow_aux bits = match bits with + | [] -> [] + | B0 :: bits -> B1 :: bits + | B1 :: bits -> B0 :: add_one_bit_ignore_overflow_aux bits + | BU :: _ -> failwith "add_one_bit_ignore_overflow: undefined bit" +end + +let add_one_bit_ignore_overflow bits = + List.reverse (add_one_bit_ignore_overflow_aux (List.reverse bits)) + +let to_vec is_inc ((len : integer),(n : integer)) = + let start = if is_inc then 0 else len - 1 in + let bits = wordFromInteger n in + if integerFromNat (word_length bits) = len then + Bitvector bits start is_inc + else + failwith "Vector length mismatch in to_vec" + +let to_vec_big = to_vec + +let to_vec_inc = to_vec true +let to_vec_dec = to_vec false +(* TODO?? +let to_vec_undef is_inc (len : integer) = + Vector (replicate (natFromInteger len) BU) (if is_inc then 0 else len-1) is_inc + +let to_vec_inc_undef = to_vec_undef true +let to_vec_dec_undef = to_vec_undef false +*) +let exts (len, vec) = to_vec (bvget_dir vec) (len,signed vec) +let extz (len, vec) = to_vec (bvget_dir vec) (len,unsigned vec) + +let exts_big (len, vec) = to_vec_big (bvget_dir vec) (len, signed_big vec) +let extz_big (len, vec) = to_vec_big (bvget_dir vec) (len, unsigned_big vec) + +let add = integerAdd +let add_signed = integerAdd +let minus = integerMinus +let multiply = integerMult +let modulo = hardware_mod +let quot = hardware_quot +let power = integerPow + +(* TODO: this, and the definitions that use it, currently requires Size for + to_vec, which I'd rather avoid *) +let arith_op_vec op sign (size : integer) (Bitvector _ _ is_inc as l) r = + let (l',r') = (to_num sign l, to_num sign r) in + let n = op l' r' in + to_vec is_inc (size * (bvlength l),n) + + +(* add_vec + * add_vec_signed + * minus_vec + * multiply_vec + * multiply_vec_signed + *) +let add_VVV = arith_op_vec integerAdd false 1 +let addS_VVV = arith_op_vec integerAdd true 1 +let minus_VVV = arith_op_vec integerMinus false 1 +let mult_VVV = arith_op_vec integerMult false 2 +let multS_VVV = arith_op_vec integerMult true 2 + +val arith_op_vec_range : forall 'a. Size 'a => (integer -> integer -> integer) -> bool -> integer -> bitvector 'a -> integer -> bitvector 'a +let arith_op_vec_range op sign size (Bitvector _ _ is_inc as l) r = + arith_op_vec op sign size l (to_vec is_inc (bvlength l,r)) + +(* add_vec_range + * add_vec_range_signed + * minus_vec_range + * mult_vec_range + * mult_vec_range_signed + *) +let add_VIV = arith_op_vec_range integerAdd false 1 +let addS_VIV = arith_op_vec_range integerAdd true 1 +let minus_VIV = arith_op_vec_range integerMinus false 1 +let mult_VIV = arith_op_vec_range integerMult false 2 +let multS_VIV = arith_op_vec_range integerMult true 2 + +val arith_op_range_vec : forall 'a. Size 'a => (integer -> integer -> integer) -> bool -> integer -> integer -> bitvector 'a -> bitvector 'a +let arith_op_range_vec op sign size l (Bitvector _ _ is_inc as r) = + arith_op_vec op sign size (to_vec is_inc (bvlength r, l)) r + +(* add_range_vec + * add_range_vec_signed + * minus_range_vec + * mult_range_vec + * mult_range_vec_signed + *) +let add_IVV = arith_op_range_vec integerAdd false 1 +let addS_IVV = arith_op_range_vec integerAdd true 1 +let minus_IVV = arith_op_range_vec integerMinus false 1 +let mult_IVV = arith_op_range_vec integerMult false 2 +let multS_IVV = arith_op_range_vec integerMult true 2 + +let arith_op_range_vec_range op sign l r = op l (to_num sign r) + +(* add_range_vec_range + * add_range_vec_range_signed + * minus_range_vec_range + *) +let add_IVI = arith_op_range_vec_range integerAdd false +let addS_IVI = arith_op_range_vec_range integerAdd true +let minus_IVI = arith_op_range_vec_range integerMinus false + +let arith_op_vec_range_range op sign l r = op (to_num sign l) r + +(* add_vec_range_range + * add_vec_range_range_signed + * minus_vec_range_range + *) +let add_VII = arith_op_vec_range_range integerAdd false +let addS_VII = arith_op_vec_range_range integerAdd true +let minus_VII = arith_op_vec_range_range integerMinus false + + + +let arith_op_vec_vec_range op sign l r = + let (l',r') = (to_num sign l,to_num sign r) in + op l' r' + +(* add_vec_vec_range + * add_vec_vec_range_signed + *) +let add_VVI = arith_op_vec_vec_range integerAdd false +let addS_VVI = arith_op_vec_vec_range integerAdd true + +let arith_op_vec_bit op sign (size : integer) (Bitvector _ _ is_inc as l)r = + let l' = to_num sign l in + let n = op l' (match r with | B1 -> (1 : integer) | _ -> 0 end) in + to_vec is_inc (bvlength l * size,n) + +(* add_vec_bit + * add_vec_bit_signed + * minus_vec_bit_signed + *) +let add_VBV = arith_op_vec_bit integerAdd false 1 +let addS_VBV = arith_op_vec_bit integerAdd true 1 +let minus_VBV = arith_op_vec_bit integerMinus true 1 + +val arith_op_overflow_vec : forall 'a. Size 'a => (integer -> integer -> integer) -> bool -> integer -> bitvector 'a -> bitvector 'a -> bitvector 'a * bitU * bool +let rec arith_op_overflow_vec op sign size (Bitvector _ _ is_inc as l) r = + let len = bvlength l in + let act_size = len * size in + let (l_sign,r_sign) = (to_num sign l,to_num sign r) in + let (l_unsign,r_unsign) = (to_num false l,to_num false r) in + let n = op l_sign r_sign in + let n_unsign = op l_unsign r_unsign in + let correct_size_num = to_vec is_inc (act_size,n) in + let one_more_size_u = to_vec is_inc (act_size + 1,n_unsign) in + let overflow = + if n <= get_max_representable_in sign len && + n >= get_min_representable_in sign len + then B0 else B1 in + let c_out = most_significant one_more_size_u in + (correct_size_num,overflow,c_out) + +(* add_overflow_vec + * add_overflow_vec_signed + * minus_overflow_vec + * minus_overflow_vec_signed + * mult_overflow_vec + * mult_overflow_vec_signed + *) +let addO_VVV = arith_op_overflow_vec integerAdd false 1 +let addSO_VVV = arith_op_overflow_vec integerAdd true 1 +let minusO_VVV = arith_op_overflow_vec integerMinus false 1 +let minusSO_VVV = arith_op_overflow_vec integerMinus true 1 +let multO_VVV = arith_op_overflow_vec integerMult false 2 +let multSO_VVV = arith_op_overflow_vec integerMult true 2 + +val arith_op_overflow_vec_bit : forall 'a. Size 'a => (integer -> integer -> integer) -> bool -> integer -> + bitvector 'a -> bitU -> bitvector 'a * bitU * bool +let rec arith_op_overflow_vec_bit (op : integer -> integer -> integer) sign (size : integer) + (Bitvector _ _ is_inc as l) r_bit = + let act_size = bvlength l * size in + let l' = to_num sign l in + let l_u = to_num false l in + let (n,nu,changed) = match r_bit with + | B1 -> (op l' 1, op l_u 1, true) + | B0 -> (l',l_u,false) + | BU -> failwith "arith_op_overflow_vec_bit applied to undefined bit" + end in +(* | _ -> assert false *) + let correct_size_num = to_vec is_inc (act_size,n) in + let one_larger = to_vec is_inc (act_size + 1,nu) in + let overflow = + if changed + then + if n <= get_max_representable_in sign act_size && n >= get_min_representable_in sign act_size + then B0 else B1 + else B0 in + (correct_size_num,overflow,most_significant one_larger) + +(* add_overflow_vec_bit_signed + * minus_overflow_vec_bit + * minus_overflow_vec_bit_signed + *) +let addSO_VBV = arith_op_overflow_vec_bit integerAdd true 1 +let minusO_VBV = arith_op_overflow_vec_bit integerMinus false 1 +let minusSO_VBV = arith_op_overflow_vec_bit integerMinus true 1 + +type shift = LL_shift | RR_shift | LLL_shift + +let shift_op_vec op (Bitvector bs start is_inc,(n : integer)) = + let n = natFromInteger n in + match op with + | LL_shift (*"<<"*) -> + Bitvector (shiftLeft bs (naturalFromNat n)) start is_inc + | RR_shift (*">>"*) -> + Bitvector (shiftRight bs (naturalFromNat n)) start is_inc + | LLL_shift (*"<<<"*) -> + Bitvector (rotateLeft (naturalFromNat n) bs) start is_inc + end + +let bitwise_leftshift = shift_op_vec LL_shift (*"<<"*) +let bitwise_rightshift = shift_op_vec RR_shift (*">>"*) +let bitwise_rotate = shift_op_vec LLL_shift (*"<<<"*) + +let rec arith_op_no0 (op : integer -> integer -> integer) l r = + if r = 0 + then Nothing + else Just (op l r) +(* TODO +let rec arith_op_vec_no0 (op : integer -> integer -> integer) sign size ((Bitvector _ start is_inc) as l) r = + let act_size = bvlength l * size in + let (l',r') = (to_num sign l,to_num sign r) in + let n = arith_op_no0 op l' r' in + let (representable,n') = + match n with + | Just n' -> + (n' <= get_max_representable_in sign act_size && + n' >= get_min_representable_in sign act_size, n') + | _ -> (false,0) + end in + if representable + then to_vec is_inc (act_size,n') + else Vector (List.replicate (natFromInteger act_size) BU) start is_inc + +let mod_VVV = arith_op_vec_no0 hardware_mod false 1 +let quot_VVV = arith_op_vec_no0 hardware_quot false 1 +let quotS_VVV = arith_op_vec_no0 hardware_quot true 1 + +let arith_op_overflow_no0_vec op sign size ((Vector _ start is_inc) as l) r = + let rep_size = length r * size in + let act_size = length l * size in + let (l',r') = (to_num sign l,to_num sign r) in + let (l_u,r_u) = (to_num false l,to_num false r) in + let n = arith_op_no0 op l' r' in + let n_u = arith_op_no0 op l_u r_u in + let (representable,n',n_u') = + match (n, n_u) with + | (Just n',Just n_u') -> + ((n' <= get_max_representable_in sign rep_size && + n' >= (get_min_representable_in sign rep_size)), n', n_u') + | _ -> (true,0,0) + end in + let (correct_size_num,one_more) = + if representable then + (to_vec is_inc (act_size,n'),to_vec is_inc (act_size + 1,n_u')) + else + (Vector (List.replicate (natFromInteger act_size) BU) start is_inc, + Vector (List.replicate (natFromInteger (act_size + 1)) BU) start is_inc) in + let overflow = if representable then B0 else B1 in + (correct_size_num,overflow,most_significant one_more) + +let quotO_VVV = arith_op_overflow_no0_vec hardware_quot false 1 +let quotSO_VVV = arith_op_overflow_no0_vec hardware_quot true 1 + +let arith_op_vec_range_no0 op sign size (Vector _ _ is_inc as l) r = + arith_op_vec_no0 op sign size l (to_vec is_inc (length l,r)) + +let mod_VIV = arith_op_vec_range_no0 hardware_mod false 1 +*) +val repeat : forall 'a. list 'a -> integer -> list 'a +let rec repeat xs n = + if n = 0 then [] + else xs ++ repeat xs (n-1) + +(* +let duplicate bit length = + Vector (repeat [bit] length) (if dir then 0 else length - 1) dir + *) + +let compare_op op (l,r) = bool_to_bitU (op l r) + +let lt = compare_op (<) +let gt = compare_op (>) +let lteq = compare_op (<=) +let gteq = compare_op (>=) + + +let compare_op_vec op sign (l,r) = + let (l',r') = (to_num sign l, to_num sign r) in + compare_op op (l',r') + +let lt_vec = compare_op_vec (<) true +let gt_vec = compare_op_vec (>) true +let lteq_vec = compare_op_vec (<=) true +let gteq_vec = compare_op_vec (>=) true + +let lt_vec_signed = compare_op_vec (<) true +let gt_vec_signed = compare_op_vec (>) true +let lteq_vec_signed = compare_op_vec (<=) true +let gteq_vec_signed = compare_op_vec (>=) true +let lt_vec_unsigned = compare_op_vec (<) false +let gt_vec_unsigned = compare_op_vec (>) false +let lteq_vec_unsigned = compare_op_vec (<=) false +let gteq_vec_unsigned = compare_op_vec (>=) false + +let compare_op_vec_range op sign (l,r) = + compare_op op ((to_num sign l),r) + +let lt_vec_range = compare_op_vec_range (<) true +let gt_vec_range = compare_op_vec_range (>) true +let lteq_vec_range = compare_op_vec_range (<=) true +let gteq_vec_range = compare_op_vec_range (>=) true + +let compare_op_range_vec op sign (l,r) = + compare_op op (l, (to_num sign r)) + +let lt_range_vec = compare_op_range_vec (<) true +let gt_range_vec = compare_op_range_vec (>) true +let lteq_range_vec = compare_op_range_vec (<=) true +let gteq_range_vec = compare_op_range_vec (>=) true + +let eq (l,r) = bool_to_bitU (l = r) +let eq_range (l,r) = bool_to_bitU (l = r) +let eq_vec (l,r) = bool_to_bitU (l = r) +let eq_bit (l,r) = bool_to_bitU (l = r) +let eq_vec_range (l,r) = eq (to_num false l,r) +let eq_range_vec (l,r) = eq (l, to_num false r) +let eq_vec_vec (l,r) = eq (to_num true l, to_num true r) + +let neq (l,r) = bitwise_not_bit (eq (l,r)) +let neq_bit (l,r) = bitwise_not_bit (eq_bit (l,r)) +let neq_range (l,r) = bitwise_not_bit (eq_range (l,r)) +let neq_vec (l,r) = bitwise_not_bit (eq_vec_vec (l,r)) +let neq_vec_range (l,r) = bitwise_not_bit (eq_vec_range (l,r)) +let neq_range_vec (l,r) = bitwise_not_bit (eq_range_vec (l,r)) + + +val make_indexed_vector : forall 'a. list (integer * 'a) -> 'a -> integer -> integer -> bool -> vector 'a +let make_indexed_vector entries default start length dir = + let length = natFromInteger length in + Vector (List.foldl replace (replicate length default) entries) start dir + +(* +val make_bit_vector_undef : integer -> vector bitU +let make_bitvector_undef length = + Vector (replicate (natFromInteger length) BU) 0 true + *) + +(* let bitwise_not_range_bit n = bitwise_not (to_vec defaultDir n) *) + +let mask (n,Vector bits start dir) = + let current_size = List.length bits in + Vector (drop (current_size - (natFromInteger n)) bits) (if dir then 0 else (n-1)) dir + + +val byte_chunks : forall 'a. nat -> list 'a -> list (list 'a) +let rec byte_chunks n list = match (n,list) with + | (0,_) -> [] + | (n+1, a::b::c::d::e::f::g::h::rest) -> [a;b;c;d;e;f;g;h] :: byte_chunks n rest + | _ -> failwith "byte_chunks not given enough bits" +end + +val bitv_of_byte_lifteds : bool -> list Sail_impl_base.byte_lifted -> vector bitU +let bitv_of_byte_lifteds dir v = + let bits = foldl (fun x (Byte_lifted y) -> x ++ (List.map bitU_of_bit_lifted y)) [] v in + let len = integerFromNat (List.length bits) in + Vector bits (if dir then 0 else len - 1) dir + +val bitv_of_bytes : bool -> list Sail_impl_base.byte -> vector bitU +let bitv_of_bytes dir v = + let bits = foldl (fun x (Byte y) -> x ++ (List.map bitU_of_bit y)) [] v in + let len = integerFromNat (List.length bits) in + Vector bits (if dir then 0 else len - 1) dir + + +val byte_lifteds_of_bitv : vector bitU -> list byte_lifted +let byte_lifteds_of_bitv (Vector bits length is_inc) = + let bits = List.map bit_lifted_of_bitU bits in + byte_lifteds_of_bit_lifteds bits + +val bytes_of_bitv : vector bitU -> list byte +let bytes_of_bitv (Vector bits length is_inc) = + let bits = List.map bit_of_bitU bits in + bytes_of_bits bits + +val bit_lifteds_of_bitUs : list bitU -> list bit_lifted +let bit_lifteds_of_bitUs bits = List.map bit_lifted_of_bitU bits + +val bit_lifteds_of_bitv : vector bitU -> list bit_lifted +let bit_lifteds_of_bitv v = bit_lifteds_of_bitUs (get_elems v) + + +val address_lifted_of_bitv : vector bitU -> address_lifted +let address_lifted_of_bitv v = + let byte_lifteds = byte_lifteds_of_bitv v in + let maybe_address_integer = + match (maybe_all (List.map byte_of_byte_lifted byte_lifteds)) with + | Just bs -> Just (integer_of_byte_list bs) + | _ -> Nothing + end in + Address_lifted byte_lifteds maybe_address_integer + +val address_of_bitv : vector bitU -> address +let address_of_bitv v = + let bytes = bytes_of_bitv v in + address_of_byte_list bytes + + + +(*** Registers *) + +type register_field = string +type register_field_index = string * (integer * integer) (* name, start and end *) + +type register = + | Register of string * (* name *) + integer * (* length *) + integer * (* start index *) + bool * (* is increasing *) + list register_field_index + | UndefinedRegister of integer (* length *) + | RegisterPair of register * register + +let name_of_reg = function + | Register name _ _ _ _ -> name + | UndefinedRegister _ -> failwith "name_of_reg UndefinedRegister" + | RegisterPair _ _ -> failwith "name_of_reg RegisterPair" +end + +let size_of_reg = function + | Register _ size _ _ _ -> size + | UndefinedRegister size -> size + | RegisterPair _ _ -> failwith "size_of_reg RegisterPair" +end + +let start_of_reg = function + | Register _ _ start _ _ -> start + | UndefinedRegister _ -> failwith "start_of_reg UndefinedRegister" + | RegisterPair _ _ -> failwith "start_of_reg RegisterPair" +end + +let is_inc_of_reg = function + | Register _ _ _ is_inc _ -> is_inc + | UndefinedRegister _ -> failwith "is_inc_of_reg UndefinedRegister" + | RegisterPair _ _ -> failwith "in_inc_of_reg RegisterPair" +end + +let dir_of_reg = function + | Register _ _ _ is_inc _ -> dir is_inc + | UndefinedRegister _ -> failwith "dir_of_reg UndefinedRegister" + | RegisterPair _ _ -> failwith "dir_of_reg RegisterPair" +end + +let size_of_reg_nat reg = natFromInteger (size_of_reg reg) +let start_of_reg_nat reg = natFromInteger (start_of_reg reg) + +val register_field_indices_aux : register -> register_field -> maybe (integer * integer) +let rec register_field_indices_aux register rfield = + match register with + | Register _ _ _ _ rfields -> List.lookup rfield rfields + | RegisterPair r1 r2 -> + let m_indices = register_field_indices_aux r1 rfield in + if isJust m_indices then m_indices else register_field_indices_aux r2 rfield + | UndefinedRegister _ -> Nothing + end + +val register_field_indices : register -> register_field -> integer * integer +let register_field_indices register rfield = + match register_field_indices_aux register rfield with + | Just indices -> indices + | Nothing -> failwith "Invalid register/register-field combination" + end + +let register_field_indices_nat reg regfield= + let (i,j) = register_field_indices reg regfield in + (natFromInteger i,natFromInteger j) + +let rec external_reg_value reg_name v = + let (internal_start, external_start, direction) = + match reg_name with + | Reg _ start size dir -> + (start, (if dir = D_increasing then start else (start - (size +1))), dir) + | Reg_slice _ reg_start dir (slice_start, slice_end) -> + ((if dir = D_increasing then slice_start else (reg_start - slice_start)), + slice_start, dir) + | Reg_field _ reg_start dir _ (slice_start, slice_end) -> + ((if dir = D_increasing then slice_start else (reg_start - slice_start)), + slice_start, dir) + | Reg_f_slice _ reg_start dir _ _ (slice_start, slice_end) -> + ((if dir = D_increasing then slice_start else (reg_start - slice_start)), + slice_start, dir) + end in + let bits = bit_lifteds_of_bitv v in + <| rv_bits = bits; + rv_dir = direction; + rv_start = external_start; + rv_start_internal = internal_start |> + +val internal_reg_value : register_value -> vector bitU +let internal_reg_value v = + Vector (List.map bitU_of_bit_lifted v.rv_bits) + (integerFromNat v.rv_start_internal) + (v.rv_dir = D_increasing) + + +let external_slice (d:direction) (start:nat) ((i,j):(nat*nat)) = + match d with + (*This is the case the thread/concurrecny model expects, so no change needed*) + | D_increasing -> (i,j) + | D_decreasing -> let slice_i = start - i in + let slice_j = (i - j) + slice_i in + (slice_i,slice_j) + end + +let external_reg_whole reg = + Reg (name_of_reg reg) (start_of_reg_nat reg) (size_of_reg_nat reg) (dir_of_reg reg) + +let external_reg_slice reg (i,j) = + let start = start_of_reg_nat reg in + let dir = dir_of_reg reg in + Reg_slice (name_of_reg reg) start dir (external_slice dir start (i,j)) + +let external_reg_field_whole reg rfield = + let (m,n) = register_field_indices_nat reg rfield in + let start = start_of_reg_nat reg in + let dir = dir_of_reg reg in + Reg_field (name_of_reg reg) start dir rfield (external_slice dir start (m,n)) + +let external_reg_field_slice reg rfield (i,j) = + let (m,n) = register_field_indices_nat reg rfield in + let start = start_of_reg_nat reg in + let dir = dir_of_reg reg in + Reg_f_slice (name_of_reg reg) start dir rfield + (external_slice dir start (m,n)) + (external_slice dir start (i,j)) + +let external_mem_value v = + byte_lifteds_of_bitv v $> List.reverse + +let internal_mem_value direction bytes = + List.reverse bytes $> bitv_of_byte_lifteds direction + + + + + +val foreach_inc : forall 'vars. (integer * integer * integer) -> 'vars -> + (integer -> 'vars -> 'vars) -> 'vars +let rec foreach_inc (i,stop,by) vars body = + if i <= stop + then let vars = body i vars in + foreach_inc (i + by,stop,by) vars body + else vars + +val foreach_dec : forall 'vars. (integer * integer * integer) -> 'vars -> + (integer -> 'vars -> 'vars) -> 'vars +let rec foreach_dec (i,stop,by) vars body = + if i >= stop + then let vars = body i vars in + foreach_dec (i - by,stop,by) vars body + else vars + +let assert' b msg_opt = + let msg = match msg_opt with + | Just msg -> msg + | Nothing -> "unspecified error" + end in + if bitU_to_bool b then () else failwith msg + +(* convert numbers unsafely to naturals *) + +class (ToNatural 'a) val toNatural : 'a -> natural end +(* eta-expanded for Isabelle output, otherwise it breaks *) +instance (ToNatural integer) let toNatural = (fun n -> naturalFromInteger n) end +instance (ToNatural int) let toNatural = (fun n -> naturalFromInt n) end +instance (ToNatural nat) let toNatural = (fun n -> naturalFromNat n) end +instance (ToNatural natural) let toNatural = (fun n -> n) end + +let toNaturalFiveTup (n1,n2,n3,n4,n5) = + (toNatural n1, + toNatural n2, + toNatural n3, + toNatural n4, + toNatural n5) + + +type regfp = + | RFull of (string) + | RSlice of (string * integer * integer) + | RSliceBit of (string * integer) + | RField of (string * string) + +type niafp = + | NIAFP_successor + | NIAFP_concrete_address of vector bitU + | NIAFP_LR + | NIAFP_CTR + | NIAFP_register of regfp + +(* only for MIPS *) +type diafp = + | DIAFP_none + | DIAFP_concrete of vector bitU + | DIAFP_reg of regfp + +let regfp_to_reg (reg_info : string -> maybe string -> (nat * nat * direction * (nat * nat))) = function + | RFull name -> + let (start,length,direction,_) = reg_info name Nothing in + Reg name start length direction + | RSlice (name,i,j) -> + let i = natFromInteger i in + let j = natFromInteger j in + let (start,length,direction,_) = reg_info name Nothing in + let slice = external_slice direction start (i,j) in + Reg_slice name start direction slice + | RSliceBit (name,i) -> + let i = natFromInteger i in + let (start,length,direction,_) = reg_info name Nothing in + let slice = external_slice direction start (i,i) in + Reg_slice name start direction slice + | RField (name,field_name) -> + let (start,length,direction,span) = reg_info name (Just field_name) in + let slice = external_slice direction start span in + Reg_field name start direction field_name slice +end + +let niafp_to_nia reginfo = function + | NIAFP_successor -> NIA_successor + | NIAFP_concrete_address v -> NIA_concrete_address (address_of_bitv v) + | NIAFP_LR -> NIA_LR + | NIAFP_CTR -> NIA_CTR + | NIAFP_register r -> NIA_register (regfp_to_reg reginfo r) +end + +let diafp_to_dia reginfo = function + | DIAFP_none -> DIA_none + | DIAFP_concrete v -> DIA_concrete_address (address_of_bitv v) + | DIAFP_reg r -> DIA_register (regfp_to_reg reginfo r) +end + |
