path: root/src/gen_lib/sail_operators.lem

open import Pervasives_extra
open import Machine_word
open import Sail_values

(*** Bit vector operations *)

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_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_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 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 bitwise_binop_bv : forall 'a. Bitvector 'a =>
  (bool -> bool -> bool) -> 'a -> 'a -> 'a
let bitwise_binop_bv op l r = of_bits (binop_bits op (bits_of l) (bits_of r))

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_bv : forall 'a 'b. Bitvector 'a, Bitvector 'b =>
  (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> 'b
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_int (size * length l) n


let add_bv   = arith_op_bv integerAdd false 1
let sadd_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 smult_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_bv_int : forall 'a 'b. Bitvector 'a, Bitvector 'b =>
  (integer -> integer -> integer) -> bool -> integer -> 'a -> integer -> 'b
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_int (size * length l) n

let add_bv_int = arith_op_bv_int integerAdd false 1
let sadd_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 smult_bv_int = arith_op_bv_int integerMult true 2

val arith_op_int_bv : forall 'a 'b. Bitvector 'a, Bitvector 'b =>
  (integer -> integer -> integer) -> bool -> integer -> integer -> 'a -> 'b
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_int (size * length r) n

let add_int_bv = arith_op_int_bv integerAdd false 1
let sadd_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 smult_int_bv = arith_op_int_bv integerMult true 2

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_int (size * length l) n

let add_bv_bit = arith_op_bv_bit integerAdd false 1
let sadd_bv_bit = arith_op_bv_bit integerAdd true 1
let sub_bv_bit = arith_op_bv_bit integerMinus true 1

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_bv op sign size l r =
  let len = length l in
  let act_size = len * size 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 = 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
  (correct_size,overflow,c_out)

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_bv_bit : forall 'a 'b. Bitvector 'a, Bitvector 'b =>
  (integer -> integer -> integer) -> bool -> integer -> 'a -> bitU -> ('b * bitU * bitU)
let arith_op_overflow_bv_bit op sign size l r_bit =
  let act_size = length l * size 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_bv_bit applied to undefined bit"
    end 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
    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,overflow,most_significant one_larger)

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 | RR_shift_arith | LL_rot | RR_rot

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_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)
let rotl_mword w n = Machine_word.rotateLeft (natFromInteger n) w
let rotr_mword w n = Machine_word.rotateRight (natFromInteger n) w

let rec arith_op_no0 (op : integer -> integer -> integer) l r =
  if r = 0
  then Nothing
  else Just (op l r)

val arith_op_bv_no0 : forall 'a 'b. Bitvector 'a, Bitvector 'b =>
  (integer -> integer -> integer) -> bool -> integer -> 'a -> 'a -> 'b
let arith_op_bv_no0 op sign size l r =
  let act_size = length l * size 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
    | 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 (of_int act_size n') else (of_bits (repeat [BU] act_size))

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

let arith_op_bv_int_no0 op sign size l r =
  arith_op_bv_no0 op sign size l (of_int (length 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

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 eq_bv : forall 'a. Bitvector 'a => 'a -> 'a -> bool
let eq_bv 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_bv : forall 'a. Bitvector 'a => (integer -> integer -> bool) -> 'a -> 'a -> bool
let ucmp_bv cmp l r = cmp (unsigned l) (unsigned 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_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 (>=)