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$ifndef _VECTOR_DEC
$define _VECTOR_DEC
$include <flow.sail>
type bits ('n : Int) = bitvector('n, dec)
val eq_bits = {
ocaml: "eq_list",
interpreter: "eq_list",
lem: "eq_vec",
c: "eq_bits",
coq: "eq_vec"
} : forall 'n. (bits('n), bits('n)) -> bool
overload operator == = {eq_bit, eq_bits}
val neq_bits = {
lem: "neq_vec",
c: "neq_bits",
coq: "neq_vec"
} : forall 'n. (bits('n), bits('n)) -> bool
function neq_bits(x, y) = not_bool(eq_bits(x, y))
overload operator != = {neq_bits}
val bitvector_length = {coq: "length_mword", _:"length"} : forall 'n. bits('n) -> int('n)
val vector_length = {
ocaml: "length",
interpreter: "length",
lem: "length_list",
c: "length",
coq: "vec_length"
} : forall 'n ('a : Type). vector('n, dec, 'a) -> int('n)
overload length = {bitvector_length, vector_length}
val count_leading_zeros = "count_leading_zeros" : forall 'N , 'N >= 1. bits('N) -> {'n, 0 <= 'n <= 'N . atom('n)}
/*
function count_leading_zeros x = {
foreach (i from ('N - 1) to 0 by 1 in dec)
if [x[i]] == [bitone] then return 'N - i - 1;
return 'N;
}
*/
val "print_bits" : forall 'n. (string, bits('n)) -> unit
val "prerr_bits" : forall 'n. (string, bits('n)) -> unit
val sail_sign_extend = "sign_extend" : forall 'n 'm, 'm >= 'n. (bits('n), int('m)) -> bits('m)
val sail_zero_extend = "zero_extend" : forall 'n 'm, 'm >= 'n. (bits('n), int('m)) -> bits('m)
/*!
THIS`(v, n)` truncates `v`, keeping only the _least_ significant `n` bits.
*/
val truncate = {
ocaml: "vector_truncate",
interpreter: "vector_truncate",
lem: "vector_truncate",
coq: "vector_truncate",
c: "sail_truncate"
} : forall 'm 'n, 'm >= 0 & 'm <= 'n. (bits('n), int('m)) -> bits('m)
/*!
THIS`(v, n)` truncates `v`, keeping only the _most_ significant `n` bits.
*/
val truncateLSB = {
ocaml: "vector_truncateLSB",
interpreter: "vector_truncateLSB",
lem: "vector_truncateLSB",
coq: "vector_truncateLSB",
c: "sail_truncateLSB"
} : forall 'm 'n, 'm >= 0 & 'm <= 'n. (bits('n), int('m)) -> bits('m)
val sail_mask : forall 'len 'v, 'len >= 0 & 'v >= 0. (int('len), bits('v)) -> bits('len)
function sail_mask(len, v) = if len <= length(v) then truncate(v, len) else sail_zero_extend(v, len)
overload operator ^ = {sail_mask}
val bitvector_concat = {ocaml: "append", interpreter: "append", lem: "concat_vec", c: "append", coq: "concat_vec"} : forall ('n : Int) ('m : Int).
(bits('n), bits('m)) -> bits('n + 'm)
overload append = {bitvector_concat}
/* Used for creating long bitvector literals in the C backend. */
val "append_64" : forall 'n. (bits('n), bits(64)) -> bits('n + 64)
val bitvector_access = {
ocaml: "access",
interpreter: "access",
lem: "access_vec_dec",
coq: "access_vec_dec",
c: "vector_access"
} : forall ('n : Int) ('m : Int), 0 <= 'm < 'n . (bits('n), int('m)) -> bit
val plain_vector_access = {
ocaml: "access",
interpreter: "access",
lem: "access_list_dec",
coq: "vec_access_dec",
c: "vector_access"
} : forall ('n : Int) ('m : Int) ('a : Type), 0 <= 'm < 'n. (vector('n, dec, 'a), int('m)) -> 'a
overload vector_access = {bitvector_access, plain_vector_access}
val bitvector_update = {
ocaml: "update",
interpreter: "update",
lem: "update_vec_dec",
coq: "update_vec_dec",
c: "vector_update"
} : forall 'n 'm, 0 <= 'm < 'n. (bits('n), int('m), bit) -> bits('n)
val plain_vector_update = {
ocaml: "update",
interpreter: "update",
lem: "update_list_dec",
coq: "vec_update_dec",
c: "vector_update"
} : forall 'n 'm ('a : Type), 0 <= 'm < 'n. (vector('n, dec, 'a), int('m), 'a) -> vector('n, dec, 'a)
overload vector_update = {bitvector_update, plain_vector_update}
val add_bits = {
ocaml: "add_vec",
interpreter: "add_vec",
lem: "add_vec",
c: "add_bits",
coq: "add_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)
val add_bits_int = {
ocaml: "add_vec_int",
interpreter: "add_vec_int",
lem: "add_vec_int",
c: "add_bits_int",
coq: "add_vec_int"
} : forall 'n. (bits('n), int) -> bits('n)
overload operator + = {add_bits, add_bits_int}
val sub_bits = {
ocaml: "sub_vec",
interpreter: "sub_vec",
lem: "sub_vec",
c: "sub_bits",
coq: "sub_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)
val not_vec = {c: "not_bits", _: "not_vec"} : forall 'n. bits('n) -> bits('n)
val and_vec = {
lem: "and_vec",
c: "and_bits",
coq: "and_vec",
ocaml: "and_vec",
interpreter: "and_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)
overload operator & = {and_vec}
val or_vec = {
lem: "or_vec",
c: "or_bits",
coq: "or_vec",
ocaml: "or_vec",
interpreter: "or_vec"
} : forall 'n. (bits('n), bits('n)) -> bits('n)
overload operator | = {or_vec}
val subrange_bits = {
ocaml: "subrange",
interpreter: "subrange",
lem: "subrange_vec_dec",
c: "vector_subrange",
coq: "subrange_vec_dec"
} : forall ('n : Int) ('m : Int) ('o : Int), 0 <= 'o <= 'm < 'n.
(bits('n), int('m), int('o)) -> bits('m - 'o + 1)
overload vector_subrange = {subrange_bits}
val update_subrange_bits = {
ocaml: "update_subrange",
interpreter: "update_subrange",
lem: "update_subrange_vec_dec",
c: "vector_update_subrange",
coq: "update_subrange_vec_dec"
} : forall 'n 'm 'o, 0 <= 'o <= 'm < 'n. (bits('n), int('m), int('o), bits('m - ('o - 1))) -> bits('n)
overload vector_update_subrange = {update_subrange_bits}
val sail_shiftleft = "shiftl" : forall 'n ('ord : Order).
(bitvector('n, 'ord), int) -> bitvector('n, 'ord) effect pure
val sail_shiftright = "shiftr" : forall 'n ('ord : Order).
(bitvector('n, 'ord), int) -> bitvector('n, 'ord) effect pure
val sail_arith_shiftright = "arith_shiftr" : forall 'n ('ord : Order).
(bitvector('n, 'ord), int) -> bitvector('n, 'ord) effect pure
val sail_zeros = "zeros" : forall 'n, 'n >= 0. int('n) -> bits('n)
val sail_ones : forall 'n, 'n >= 0. int('n) -> bits('n)
function sail_ones(n) = not_vec(sail_zeros(n))
// Some ARM specific builtins
val slice = "slice" : forall 'n 'm 'o, 0 <= 'm & 0 <= 'n.
(bits('m), int('o), int('n)) -> bits('n)
val replicate_bits = "replicate_bits" : forall 'n 'm. (bits('n), int('m)) -> bits('n * 'm)
val slice_mask : forall 'n, 'n >= 0. (implicit('n), int, int) -> bits('n) effect pure
function slice_mask(n,i,l) =
if l >= n then {
sail_shiftleft(sail_ones(n), i)
} else {
let one : bits('n) = sail_mask(n, [bitone] : bits(1)) in
sail_shiftleft(sub_bits(sail_shiftleft(one, l), one), i)
}
val get_slice_int = "get_slice_int" : forall 'w. (int('w), int, int) -> bits('w)
val set_slice_int = "set_slice_int" : forall 'w. (int('w), int, int, bits('w)) -> int
val set_slice_bits = "set_slice" : forall 'n 'm.
(implicit('n), int('m), bits('n), int, bits('m)) -> bits('n)
/*!
converts a bit vector of length $n$ to an integer in the range $0$ to $2^n - 1$.
*/
val unsigned = {
ocaml: "uint",
lem: "uint",
interpreter: "uint",
c: "sail_unsigned",
coq: "uint"
} : forall 'n. bits('n) -> range(0, 2 ^ 'n - 1)
/* We need a non-empty vector so that the range makes sense */
/*!
converts a bit vector of length $n$ to an integer in the range $-2^{n-1}$ to $2^{n-1} - 1$ using twos-complement.
*/
val signed = {
c: "sail_signed",
_: "sint"
} : forall 'n, 'n > 0. bits('n) -> range(- (2 ^ ('n - 1)), 2 ^ ('n - 1) - 1)
overload __size = {__id, bitvector_length}
$endif
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