1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
|
/* Definitions for use with the -mono_rewrites option */
/* External definitions not in the usual asl prelude */
infix 6 <<
val "shiftleft" : forall 'n ('ord : Order).
(vector('n, 'ord, bit), int) -> vector('n, 'ord, bit) effect pure
overload operator << = {shiftleft}
infix 6 >>
val "shiftright" : forall 'n ('ord : Order).
(vector('n, 'ord, bit), int) -> vector('n, 'ord, bit) effect pure
overload operator >> = {shiftright}
val "extz" : forall 'n 'm. (atom('m),vector('n, dec, bit)) -> vector('m, dec, bit) effect pure
val extzv : forall 'n 'm. vector('n, dec, bit) -> vector('m, dec, bit) effect pure
function extzv(v) = extz(sizeof('m),v)
val "exts" : forall 'n 'm. (atom('m),vector('n, dec, bit)) -> vector('m, dec, bit) effect pure
val extsv : forall 'n 'm. vector('n, dec, bit) -> vector('m, dec, bit) effect pure
function extsv(v) = exts(sizeof('m),v)
/* Definitions for the rewrites */
val slice_mask : forall 'n, 'n >= 0. (int, int) -> bits('n) effect pure
function slice_mask(i,l) =
let one : bits('n) = extzv(0b1) in
((one << l) - one) << i
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)) == extzv(0b0)
}
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) in
(xs & m) == m
}
val slice_slice_concat : forall 'n 'm 'r, 'n >= 0 & 'm >= 0 & 'r >= 0.
(bits('n), int, int, bits('m), int, int) -> bits('r) effect pure
function slice_slice_concat (xs, i, l, ys, i', l') = {
let xs = (xs & slice_mask(i,l)) >> i in
let ys = (ys & slice_mask(i',l')) >> i' in
extzv(xs) << l' | extzv(ys)
}
val slice_zeros_concat : forall 'n 'p 'q 'r, 'r = 'p + 'q & 'n >= 0 & 'p >= 0 & 'q >= 0 & 'r >= 0.
(bits('n), int, atom('p), atom('q)) -> bits('r) effect pure
function slice_zeros_concat (xs, i, l, l') = {
let xs = (xs & slice_mask(i,l)) >> i in
extzv(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 = (xs & slice_mask(j,i-j)) >> j in
let ys = (ys & slice_mask(j',i'-j')) >> j' in
xs == ys
}
val subrange_subrange_concat : forall 'n 'o 'p 'm 'q 'r 's, 's = 'o - ('p - 1) + 'q - ('r - 1) & 'n >= 0 & 'm >= 0.
(bits('n), atom('o), atom('p), bits('m), atom('q), atom('r)) -> bits('s) effect pure
function subrange_subrange_concat (xs, i, j, ys, i', j') = {
let xs = (xs & slice_mask(j,i-j)) >> j in
let ys = (ys & slice_mask(j',i'-j')) >> j' in
extzv(xs) << i' - (j' - 1) | extzv(ys)
}
val place_subrange : forall 'n 'm, 'n >= 0 & 'm >= 0.
(bits('n), int, int, int) -> bits('m) effect pure
function place_subrange(xs,i,j,shift) = {
let xs = (xs & slice_mask(j,i-j)) >> j in
extzv(xs) << shift
}
val place_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(bits('n), int, int, int) -> bits('m) effect pure
function place_slice(xs,i,l,shift) = {
let xs = (xs & slice_mask(i,l)) >> i in
extzv(xs) << shift
}
val zext_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(bits('n), int, int) -> bits('m) effect pure
function zext_slice(xs,i,l) = {
let xs = (xs & slice_mask(i,l)) >> i in
extzv(xs)
}
val sext_slice : forall 'n 'm, 'n >= 0 & 'm >= 0.
(bits('n), int, int) -> bits('m) effect pure
function sext_slice(xs,i,l) = {
let xs = (xs & slice_mask(i,l)) >> i in
extsv(xs)
}
val UInt_slice : forall 'n, 'n >= 0.
(bits('n), int, int) -> int effect pure
function UInt_slice(xs,i,l) = {
let xs = (xs & slice_mask(i,l)) >> i in
UInt(xs)
}
|