diff options
Diffstat (limited to 'src/gen_lib/sail_operators.lem')
| -rw-r--r-- | src/gen_lib/sail_operators.lem | 284 |
1 files changed, 109 insertions, 175 deletions
diff --git a/src/gen_lib/sail_operators.lem b/src/gen_lib/sail_operators.lem index 230ab84e..ada91bd0 100644 --- a/src/gen_lib/sail_operators.lem +++ b/src/gen_lib/sail_operators.lem @@ -5,53 +5,22 @@ open import Sail_values (*** Bit vector operations *) -val concat_vec : forall 'a 'b 'c. Bitvector 'a, Bitvector 'b, Bitvector 'c => 'a -> 'b -> 'c -let concat_vec l r = of_bits (bits_of l ++ bits_of r) +val concat_bv : forall 'a 'b 'c. Bitvector 'a, Bitvector 'b, Bitvector 'c => 'a -> 'b -> 'c +let concat_bv l r = of_bits (bits_of l ++ bits_of r) -val cons_vec : forall 'a 'b 'c. Bitvector 'a, Bitvector 'b => bitU -> 'a -> 'b -let cons_vec b v = of_bits (b :: bits_of v) +val cons_bv : forall 'a 'b 'c. Bitvector 'a, Bitvector 'b => bitU -> 'a -> 'b +let cons_bv b v = of_bits (b :: bits_of v) -let bool_of_vec v = extract_only_element (bits_of v) -let vec_of_bit len b = of_bits (extz_bits len [b]) -let cast_unit_vec b = of_bits [b] +let bool_of_bv v = extract_only_element (bits_of v) +let cast_unit_bv b = of_bits [b] +let bv_of_bit len b = of_bits (extz_bits len [b]) +let int_of_bv sign = if sign then signed else unsigned let most_significant v = match bits_of v with | b :: _ -> b | _ -> failwith "most_significant applied to empty vector" end -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 int_of_vec sign = if sign then signed else unsigned -let vec_of_int len n = of_bits (bits_of_int len n) - -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 @@ -68,106 +37,106 @@ let get_min_representable_in _ (n : integer) : integer = else if n = 5 then min_5 else 0 - (integerPow 2 (natFromInteger n)) -val bitwise_binop_vec : forall 'a. Bitvector 'a => +val bitwise_binop_bv : forall 'a. Bitvector 'a => (bool -> bool -> bool) -> 'a -> 'a -> 'a -let bitwise_binop_vec op l r = of_bits (binop_bits op (bits_of l) (bits_of r)) +let bitwise_binop_bv op l r = of_bits (binop_bits op (bits_of l) (bits_of r)) -let and_vec = bitwise_binop_vec (&&) -let or_vec = bitwise_binop_vec (||) -let xor_vec = bitwise_binop_vec xor -let not_vec v = of_bits (not_bits (bits_of v)) +let and_bv = bitwise_binop_bv (&&) +let or_bv = bitwise_binop_bv (||) +let xor_bv = bitwise_binop_bv xor +let not_bv v = of_bits (not_bits (bits_of v)) -val arith_op_vec : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_bv : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> 'b -let arith_op_vec op sign size l r = - let (l',r') = (int_of_vec sign l, int_of_vec sign r) in +let arith_op_bv op sign size l r = + let (l',r') = (int_of_bv sign l, int_of_bv sign r) in let n = op l' r' in - of_bits (bits_of_int (size * length l) n) + of_int (size * length l) n -let add_vec = arith_op_vec integerAdd false 1 -let addS_vec = arith_op_vec integerAdd true 1 -let sub_vec = arith_op_vec integerMinus false 1 -let mult_vec = arith_op_vec integerMult false 2 -let multS_vec = arith_op_vec integerMult true 2 +let add_bv = arith_op_bv integerAdd false 1 +let addS_bv = arith_op_bv integerAdd true 1 +let sub_bv = arith_op_bv integerMinus false 1 +let mult_bv = arith_op_bv integerMult false 2 +let multS_bv = arith_op_bv integerMult true 2 let inline add_mword = Machine_word.plus let inline sub_mword = Machine_word.minus val mult_mword : forall 'a 'b. Size 'b => mword 'a -> mword 'a -> mword 'b let mult_mword l r = times (zeroExtend l) (zeroExtend r) -val arith_op_vec_int : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_bv_int : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> 'a -> integer -> 'b -let arith_op_vec_int op sign size l r = - let l' = int_of_vec sign l in +let arith_op_bv_int op sign size l r = + let l' = int_of_bv sign l in let n = op l' r in - of_bits (bits_of_int (size * length l) n) + of_int (size * length l) n -let add_vec_int = arith_op_vec_int integerAdd false 1 -let addS_vec_int = arith_op_vec_int integerAdd true 1 -let sub_vec_int = arith_op_vec_int integerMinus false 1 -let mult_vec_int = arith_op_vec_int integerMult false 2 -let multS_vec_int = arith_op_vec_int integerMult true 2 +let add_bv_int = arith_op_bv_int integerAdd false 1 +let addS_bv_int = arith_op_bv_int integerAdd true 1 +let sub_bv_int = arith_op_bv_int integerMinus false 1 +let mult_bv_int = arith_op_bv_int integerMult false 2 +let multS_bv_int = arith_op_bv_int integerMult true 2 -val arith_op_int_vec : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_int_bv : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> integer -> 'a -> 'b -let arith_op_int_vec op sign size l r = - let r' = int_of_vec sign r in +let arith_op_int_bv op sign size l r = + let r' = int_of_bv sign r in let n = op l r' in - of_bits (bits_of_int (size * length r) n) + of_int (size * length r) n -let add_int_vec = arith_op_int_vec integerAdd false 1 -let addS_int_vec = arith_op_int_vec integerAdd true 1 -let sub_int_vec = arith_op_int_vec integerMinus false 1 -let mult_int_vec = arith_op_int_vec integerMult false 2 -let multS_int_vec = arith_op_int_vec integerMult true 2 +let add_int_bv = arith_op_int_bv integerAdd false 1 +let addS_int_bv = arith_op_int_bv integerAdd true 1 +let sub_int_bv = arith_op_int_bv integerMinus false 1 +let mult_int_bv = arith_op_int_bv integerMult false 2 +let multS_int_bv = arith_op_int_bv integerMult true 2 -let arith_op_vec_bit op sign (size : integer) l r = - let l' = int_of_vec sign l in +let arith_op_bv_bit op sign (size : integer) l r = + let l' = int_of_bv sign l in let n = op l' (match r with | B1 -> (1 : integer) | _ -> 0 end) in - of_bits (bits_of_int (size * length l) n) + of_int (size * length l) n -let add_vec_bit = arith_op_vec_bit integerAdd false 1 -let addS_vec_bit = arith_op_vec_bit integerAdd true 1 -let sub_vec_bit = arith_op_vec_bit integerMinus true 1 +let add_bv_bit = arith_op_bv_bit integerAdd false 1 +let addS_bv_bit = arith_op_bv_bit integerAdd true 1 +let sub_bv_bit = arith_op_bv_bit integerMinus true 1 -val arith_op_overflow_vec : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_overflow_bv : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> ('b * bitU * bitU) -let arith_op_overflow_vec op sign size l r = +let arith_op_overflow_bv op sign size l r = let len = length l in let act_size = len * size in - let (l_sign,r_sign) = (int_of_vec sign l,int_of_vec sign r) in - let (l_unsign,r_unsign) = (int_of_vec false l,int_of_vec false r) in + let (l_sign,r_sign) = (int_of_bv sign l,int_of_bv sign r) in + let (l_unsign,r_unsign) = (int_of_bv false l,int_of_bv false r) in let n = op l_sign r_sign in let n_unsign = op l_unsign r_unsign in - let correct_size = bits_of_int act_size n in + let correct_size = of_int act_size n in let one_more_size_u = bits_of_int (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 - (of_bits correct_size,overflow,c_out) + (correct_size,overflow,c_out) -let add_overflow_vec = arith_op_overflow_vec integerAdd false 1 -let add_overflow_vec_signed = arith_op_overflow_vec integerAdd true 1 -let sub_overflow_vec = arith_op_overflow_vec integerMinus false 1 -let sub_overflow_vec_signed = arith_op_overflow_vec integerMinus true 1 -let mult_overflow_vec = arith_op_overflow_vec integerMult false 2 -let mult_overflow_vec_signed = arith_op_overflow_vec integerMult true 2 +let add_overflow_bv = arith_op_overflow_bv integerAdd false 1 +let add_overflow_bv_signed = arith_op_overflow_bv integerAdd true 1 +let sub_overflow_bv = arith_op_overflow_bv integerMinus false 1 +let sub_overflow_bv_signed = arith_op_overflow_bv integerMinus true 1 +let mult_overflow_bv = arith_op_overflow_bv integerMult false 2 +let mult_overflow_bv_signed = arith_op_overflow_bv integerMult true 2 -val arith_op_overflow_vec_bit : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_overflow_bv_bit : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> 'a -> bitU -> ('b * bitU * bitU) -let arith_op_overflow_vec_bit op sign size l r_bit = +let arith_op_overflow_bv_bit op sign size l r_bit = let act_size = length l * size in - let l' = int_of_vec sign l in - let l_u = int_of_vec false l in + let l' = int_of_bv sign l in + let l_u = int_of_bv 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" + | BU -> failwith "arith_op_overflow_bv_bit applied to undefined bit" end in - let correct_size = bits_of_int act_size n in + let correct_size = of_int act_size n in let one_larger = bits_of_int (act_size + 1) nu in let overflow = if changed @@ -175,32 +144,35 @@ let arith_op_overflow_vec_bit op sign size l r_bit = if n <= get_max_representable_in sign act_size && n >= get_min_representable_in sign act_size then B0 else B1 else B0 in - (of_bits correct_size,overflow,most_significant one_larger) + (correct_size,overflow,most_significant one_larger) -let add_overflow_vec_bit = arith_op_overflow_vec_bit integerAdd false 1 -let add_overflow_vec_bit_signed = arith_op_overflow_vec_bit integerAdd true 1 -let sub_overflow_vec_bit = arith_op_overflow_vec_bit integerMinus false 1 -let sub_overflow_vec_bit_signed = arith_op_overflow_vec_bit integerMinus true 1 +let add_overflow_bv_bit = arith_op_overflow_bv_bit integerAdd false 1 +let add_overflow_bv_bit_signed = arith_op_overflow_bv_bit integerAdd true 1 +let sub_overflow_bv_bit = arith_op_overflow_bv_bit integerMinus false 1 +let sub_overflow_bv_bit_signed = arith_op_overflow_bv_bit integerMinus true 1 -type shift = LL_shift | RR_shift | LL_rot | RR_rot +type shift = LL_shift | RR_shift | RR_shift_arith | LL_rot | RR_rot -val shift_op_vec : forall 'a. Bitvector 'a => shift -> 'a -> integer -> 'a -let shift_op_vec op v n = +val shift_op_bv : forall 'a. Bitvector 'a => shift -> 'a -> integer -> 'a +let shift_op_bv op v n = match op with | LL_shift -> of_bits (get_bits true v n (length v - 1) ++ repeat [B0] n) | RR_shift -> of_bits (repeat [B0] n ++ get_bits true v 0 (length v - n - 1)) + | RR_shift_arith -> + of_bits (repeat [most_significant v] n ++ get_bits true v 0 (length v - n - 1)) | LL_rot -> of_bits (get_bits true v n (length v - 1) ++ get_bits true v 0 (n - 1)) | RR_rot -> of_bits (get_bits false v 0 (n - 1) ++ get_bits false v n (length v - 1)) end -let shiftl = shift_op_vec LL_shift (*"<<"*) -let shiftr = shift_op_vec RR_shift (*">>"*) -let rotl = shift_op_vec LL_rot (*"<<<"*) -let rotr = shift_op_vec LL_rot (*">>>"*) +let shiftl_bv = shift_op_bv LL_shift (*"<<"*) +let shiftr_bv = shift_op_bv RR_shift (*">>"*) +let arith_shiftr_bv = shift_op_bv RR_shift_arith +let rotl_bv = shift_op_bv LL_rot (*"<<<"*) +let rotr_bv = shift_op_bv LL_rot (*">>>"*) let shiftl_mword w n = Machine_word.shiftLeft w (natFromInteger n) let shiftr_mword w n = Machine_word.shiftRight w (natFromInteger n) @@ -212,11 +184,11 @@ let rec arith_op_no0 (op : integer -> integer -> integer) l r = then Nothing else Just (op l r) -val arith_op_vec_no0 : forall 'a 'b. Bitvector 'a, Bitvector 'b => +val arith_op_bv_no0 : forall 'a 'b. Bitvector 'a, Bitvector 'b => (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> 'b -let arith_op_vec_no0 op sign size l r = +let arith_op_bv_no0 op sign size l r = let act_size = length l * size in - let (l',r') = (int_of_vec sign l,int_of_vec sign r) in + let (l',r') = (int_of_bv sign l,int_of_bv sign r) in let n = arith_op_no0 op l' r' in let (representable,n') = match n with @@ -225,80 +197,42 @@ let arith_op_vec_no0 op sign size l r = n' >= get_min_representable_in sign act_size, n') | _ -> (false,0) end in - of_bits (if representable then bits_of_int act_size n' else repeat [BU] act_size) + if representable then (of_int act_size n') else (of_bits (repeat [BU] act_size)) -let mod_vec = arith_op_vec_no0 hardware_mod false 1 -let quot_vec = arith_op_vec_no0 hardware_quot false 1 -let quot_vec_signed = arith_op_vec_no0 hardware_quot true 1 +let mod_bv = arith_op_bv_no0 hardware_mod false 1 +let quot_bv = arith_op_bv_no0 hardware_quot false 1 +let quot_bv_signed = arith_op_bv_no0 hardware_quot true 1 let mod_mword = Machine_word.modulo let quot_mword = Machine_word.unsignedDivide let quot_mword_signed = Machine_word.signedDivide -val arith_op_overflow_vec_no0 : forall 'a 'b. Bitvector 'a, Bitvector 'b => - (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> ('b * bitU * bitU) -let arith_op_overflow_vec_no0 op sign size l r = - let rep_size = length r * size in - let act_size = length l * size in - let (l',r') = (int_of_vec sign l,int_of_vec sign r) in - let (l_u,r_u) = (int_of_vec false l,int_of_vec 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,one_more) = - if representable then - (bits_of_int act_size n', bits_of_int (act_size + 1) n_u') - else - (repeat [BU] act_size, repeat [BU] (act_size + 1)) in - let overflow = if representable then B0 else B1 in - (of_bits correct_size,overflow,most_significant one_more) - -let quot_overflow_vec = arith_op_overflow_vec_no0 hardware_quot false 1 -let quot_overflow_vec_signed = arith_op_overflow_vec_no0 hardware_quot true 1 - -let arith_op_vec_int_no0 op sign size l r = - arith_op_vec_no0 op sign size l (of_bits (bits_of_int (length l) r)) - -let quot_vec_int = arith_op_vec_int_no0 hardware_quot false 1 -let mod_vec_int = arith_op_vec_int_no0 hardware_mod false 1 - -let replicate_bits v count = of_bits (repeat v count) -let duplicate bit len = replicate_bits [bit] len - -let lt = (<) -let gt = (>) -let lteq = (<=) -let gteq = (>=) +let arith_op_bv_int_no0 op sign size l r = + arith_op_bv_no0 op sign size l (of_int (length l) r) -val eq : forall 'a. Eq 'a => 'a -> 'a -> bool -let eq l r = (l = r) +let quot_bv_int = arith_op_bv_int_no0 hardware_quot false 1 +let mod_bv_int = arith_op_bv_int_no0 hardware_mod false 1 -val eq_vec : forall 'a. Bitvector 'a => 'a -> 'a -> bool -let eq_vec l r = (unsigned l = unsigned r) +let replicate_bits_bv v count = of_bits (repeat (bits_of v) count) +let duplicate_bit_bv bit len = replicate_bits_bv [bit] len -val neq : forall 'a. Eq 'a => 'a -> 'a -> bool -let neq l r = (l <> r) +val eq_bv : forall 'a. Bitvector 'a => 'a -> 'a -> bool +let eq_bv l r = (unsigned l = unsigned r) -val neq_vec : forall 'a. Bitvector 'a => 'a -> 'a -> bool -let neq_vec l r = (unsigned l <> unsigned r) +val neq_bv : forall 'a. Bitvector 'a => 'a -> 'a -> bool +let neq_bv l r = (unsigned l <> unsigned r) -val ucmp_vec : forall 'a. Bitvector 'a => (integer -> integer -> bool) -> 'a -> 'a -> bool -let ucmp_vec cmp l r = cmp (unsigned l) (unsigned r) +val ucmp_bv : forall 'a. Bitvector 'a => (integer -> integer -> bool) -> 'a -> 'a -> bool +let ucmp_bv cmp l r = cmp (unsigned l) (unsigned r) -val scmp_vec : forall 'a. Bitvector 'a => (integer -> integer -> bool) -> 'a -> 'a -> bool -let scmp_vec cmp l r = cmp (signed l) (signed r) +val scmp_bv : forall 'a. Bitvector 'a => (integer -> integer -> bool) -> 'a -> 'a -> bool +let scmp_bv cmp l r = cmp (signed l) (signed r) -let ult_vec = ucmp_vec (<) -let slt_vec = scmp_vec (<) -let ugt_vec = ucmp_vec (>) -let sgt_vec = scmp_vec (>) -let ulteq_vec = ucmp_vec (<=) -let slteq_vec = scmp_vec (<=) -let ugteq_vec = ucmp_vec (>=) -let sgteq_vec = scmp_vec (>=) +let ult_bv = ucmp_bv (<) +let slt_bv = scmp_bv (<) +let ugt_bv = ucmp_bv (>) +let sgt_bv = scmp_bv (>) +let ulteq_bv = ucmp_bv (<=) +let slteq_bv = scmp_bv (<=) +let ugteq_bv = ucmp_bv (>=) +let sgteq_bv = scmp_bv (>=) |
