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$ifndef _MONO_REWRITES
$define _MONO_REWRITES
/* Definitions for use with the -mono_rewrites option */
$include <arith.sail>
$include <vector_dec.sail>
/* External definitions not in the usual asl prelude */
val extzv = "extz_vec" : forall 'n 'm. (implicit('m), vector('n, dec, bit)) -> vector('m, dec, bit) effect pure
val extsv = "exts_vec" : forall 'n 'm. (implicit('m), vector('n, dec, bit)) -> vector('m, dec, bit) effect pure
/* This is generated internally to deal with case splits which reveal the size
of a bitvector */
val bitvector_cast_in = "zeroExtend" : forall 'n. bits('n) -> bits('n) effect pure
val bitvector_cast_out = "zeroExtend" : forall 'n. bits('n) -> bits('n) effect pure
/* Definitions for the rewrites */
val is_zero_subrange : forall 'n, 'n >= 0.
(bits('n), int, int) -> bool effect pure
function is_zero_subrange (xs, i, j) = {
(xs & slice_mask(j, i-j+1)) == extzv([bitzero] : bits(1))
}
val is_zeros_slice : forall 'n, 'n >= 0.
(bits('n), int, int) -> bool effect pure
function is_zeros_slice (xs, i, l) = {
(xs & slice_mask(i, l)) == extzv([bitzero] : bits(1))
}
val is_ones_subrange : forall 'n, 'n >= 0.
(bits('n), int, int) -> bool effect pure
function is_ones_subrange (xs, i, j) = {
let m : bits('n) = slice_mask(j,j-i+1) in
(xs & m) == m
}
val is_ones_slice : forall 'n, 'n >= 0.
(bits('n), int, int) -> bool effect pure
function is_ones_slice (xs, i, j) = {
let m : bits('n) = slice_mask(i,j) in
(xs & m) == m
}
val slice_slice_concat : forall 'n 'm 'r, 'n >= 0 & 'm >= 0 & 'r >= 0.
(implicit('r), bits('n), int, int, bits('m), int, int) -> bits('r) effect pure
function slice_slice_concat (r, xs, i, l, ys, i', l') = {
let xs = sail_shiftright(xs & slice_mask(i,l), i) in
let ys = sail_shiftright(ys & slice_mask(i',l'), i') in
sail_shiftleft(extzv(r, xs), l') | extzv(r, ys)
}
val slice_zeros_concat : forall 'n 'p 'q, 'n >= 0 & 'p + 'q >= 0.
(bits('n), int, atom('p), atom('q)) -> bits('p + 'q) effect pure
function slice_zeros_concat (xs, i, l, l') = {
let xs = sail_shiftright(xs & slice_mask(i,l), i) in
sail_shiftleft(extzv(l + l', xs), l')
}
/* Assumes initial vectors are of equal size */
val subrange_subrange_eq : forall 'n, 'n >= 0.
(bits('n), int, int, bits('n), int, int) -> bool effect pure
function subrange_subrange_eq (xs, i, j, ys, i', j') = {
let xs = sail_shiftright(xs & slice_mask(j,i-j+1), j) in
let ys = sail_shiftright(ys & slice_mask(j',i'-j'+1), j') in
xs == ys
}
val subrange_subrange_concat : forall 'n 'o 'p 'm 'q 'r 's, 's >= 0 & 'n >= 0 & 'm >= 0.
(implicit('s), bits('n), atom('o), atom('p), bits('m), atom('q), atom('r)) -> bits('s) effect pure
function subrange_subrange_concat (s, xs, i, j, ys, i', j') = {
let xs = sail_shiftright(xs & slice_mask(j,i-j+1), j) in
let ys = sail_shiftright(ys & slice_mask(j',i'-j'+1), j) in
sail_shiftleft(extzv(s, xs), i' - j' + 1) | extzv(s, ys)
}
val place_subrange : forall 'n 'm, 'n >= 0 & 'm >= 0.
(implicit('m), bits('n), int, int, int) -> bits('m) effect pure
function place_subrange(m,xs,i,j,shift) = {
let xs = sail_shiftright(xs & slice_mask(j,i-j+1), j) in
sail_shiftleft(extzv(m, xs), shift)
}
val place_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(implicit('m), bits('n), int, int, int) -> bits('m) effect pure
function place_slice(m,xs,i,l,shift) = {
let xs = sail_shiftright(xs & slice_mask(i,l), i) in
sail_shiftleft(extzv(m, xs), shift)
}
val set_slice_zeros : forall 'n, 'n >= 0.
(atom('n), bits('n), int, int) -> bits('n) effect pure
function set_slice_zeros(n, xs, i, l) = {
let ys : bits('n) = slice_mask(n, i, l) in
xs & not_vec(ys)
}
val zext_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(implicit('m), bits('n), int, int) -> bits('m) effect pure
function zext_slice(m,xs,i,l) = {
let xs = sail_shiftright(xs & slice_mask(i,l), i) in
extzv(m, xs)
}
val sext_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(implicit('m), bits('n), int, int) -> bits('m) effect pure
function sext_slice(m,xs,i,l) = {
let xs = sail_arith_shiftright(sail_shiftleft((xs & slice_mask(i,l)), ('n - i - l)), 'n - l) in
extsv(m, xs)
}
val place_slice_signed : forall 'n 'm, 'n >= 0 & 'm >= 0.
(implicit('m), bits('n), int, int, int) -> bits('m) effect pure
function place_slice_signed(m,xs,i,l,shift) = {
sail_shiftleft(sext_slice(m, xs, i, l), shift)
}
/* This has different names in the aarch64 prelude (UInt) and the other
preludes (unsigned). To avoid variable name clashes, we redeclare it
here with a suitably awkward name. */
val _builtin_unsigned = {
ocaml: "uint",
lem: "uint",
interpreter: "uint",
c: "sail_uint"
} : forall 'n. bits('n) -> {'m, 0 <= 'm < 2 ^ 'n. int('m)}
/* There are different implementation choices for division and remainder, but
they agree on positive values. We use this here to give more precise return
types for unsigned_slice and unsigned_subrange. */
val _builtin_mod_nat = {
smt: "mod",
ocaml: "modulus",
lem: "integerMod",
c: "tmod_int",
coq: "Z.rem"
} : forall 'n 'm, 'n >= 0 & 'm >= 0. (int('n), int('m)) -> {'r, 0 <= 'r < 'm. int('r)}
/* Below we need the fact that 2 ^ 'n >= 0, so we axiomatise it in the return
type of pow2, as SMT solvers tend to have problems with exponentiation. */
val _builtin_pow2 = "pow2" : forall 'n, 'n >= 0. int('n) -> {'m, 'm == 2 ^ 'n & 'm >= 0. int('m)}
val unsigned_slice : forall 'n 'l, 'n >= 0 & 'l >= 0.
(bits('n), int, int('l)) -> {'m, 0 <= 'm < 2 ^ 'l. int('m)} effect pure
function unsigned_slice(xs,i,l) = {
let xs = sail_shiftright(xs & slice_mask(i,l), i) in
_builtin_mod_nat(_builtin_unsigned(xs), _builtin_pow2(l))
}
val unsigned_subrange : forall 'n 'i 'j, 'n >= 0 & ('i - 'j) >= 0.
(bits('n), int('i), int('j)) -> {'m, 0 <= 'm < 2 ^ ('i - 'j + 1). int('m)} effect pure
function unsigned_subrange(xs,i,j) = {
let xs = sail_shiftright(xs & slice_mask(j,i-j+1), i) in
_builtin_mod_nat(_builtin_unsigned(xs), _builtin_pow2(i - j + 1))
}
val zext_ones : forall 'n, 'n >= 0. (implicit('n), int) -> bits('n) effect pure
function zext_ones(n, m) = {
let v : bits('n) = extsv([bitone] : bits(1)) in
sail_shiftright(v, n - m)
}
$endif
|
