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
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
|
(*
* How to evaluate constants for various widths.
*
* Internally, we represent machine_int as a signed integer.
* So when we do bit or unsigned operations we have to convert to
* the unsigned representation first.
*
* Note: this implementation requires andb, orb, xorb etc in IntInf.
* You have to upgrade to the latest version of smlnj-lib if this
* fails to compile.
*)
local
val maxSz = 65
in
structure MachineInt : MACHINE_INT =
struct
structure I = IntInf
structure S = String
type machine_int = I.int
type sz = int
datatype div_rounding_mode = DIV_TO_ZERO | DIV_TO_NEGINF
val itow = Word.fromInt
(* Parse hex or binary, but not octal, that's for wussies *)
val hexToInt = StringCvt.scanString (I.scan StringCvt.HEX)
val binToInt = StringCvt.scanString (I.scan StringCvt.BIN)
(* Precompute some tables for faster arithmetic *)
local
val pow2table = Array.tabulate(maxSz,fn n => I.<<(1,itow n)) (* 2^n *)
val masktable = Array.tabulate(maxSz,
fn n => I.-(I.<<(1,itow n),1)) (* 2^n-1 *)
val maxtable = Array.tabulate(maxSz+1,
fn 0 => 0
| n => I.-(I.<<(1,itow(n-1)),1)) (* 2^{n-1}-1 *)
val mintable = Array.tabulate(maxSz+1,
fn 0 => 0
| n => I.~(I.<<(1,itow(n-1)))) (* -2^{n-1} *)
in
fun pow2 i = if i < maxSz then Array.sub(pow2table, i)
else I.<<(1,itow i)
fun maskOf sz = if sz < maxSz then Array.sub(masktable, sz)
else I.-(I.<<(1,itow sz),1)
fun maxOfSize sz = if sz < maxSz then Array.sub(maxtable, sz)
else I.-(I.<<(1,itow(sz-1)),1)
fun minOfSize sz = if sz < maxSz then Array.sub(mintable, sz)
else I.~(I.<<(1,itow(sz-1)))
end
(* queries *)
fun isNeg(i) = I.sign i < 0
fun isPos(i) = I.sign i > 0
fun isZero(i) = I.sign i = 0
fun isNonNeg(i) = I.sign i >= 0
fun isNonPos(i) = I.sign i <= 0
fun isEven(i) = isZero(I.rem(i,2))
fun isOdd(i) = not(isEven(i))
(* to unsigned representation *)
fun unsigned(sz, i) = if isNeg i then I.+(i, pow2 sz) else i
(* to signed representation *)
fun signed(sz, i) = if I.>(i, maxOfSize sz) then I.-(i, pow2 sz) else i
(* Narrow to the representation of a given type *)
fun narrow(sz, i) = signed(sz, I.andb(i, maskOf sz))
(* Recognize 0x and 0b prefix and do the right thing *)
fun fromString(sz, s) =
let val n = S.size s
fun conv(i,negate) =
if n >= 2+i andalso S.sub(s, i) = #"0" then
(case S.sub(s, i+1) of
#"x" => (hexToInt (S.substring(s,2+i,n-2-i)), negate)
| #"b" => (binToInt (S.substring(s,2+i,n-2-i)), negate)
| _ => (I.fromString s, false)
)
else (I.fromString s, false)
val (result, negate) =
if s = "" then (NONE, false)
else if S.sub(s, 0) = #"~" then conv(1, true)
else conv(0, false)
in case (result, negate) of
(SOME n, true) => SOME(narrow(sz, I.~ n))
| (SOME n, false) => SOME(narrow(sz, n))
| (NONE, _) => NONE
end
(* Convert types into IntInf without losing precision. *)
structure Cvt =
struct
structure W = Word
structure W32 = Word32
val wtoi = W.toIntX
val w32toi = W32.toIntX
val fromInt = I.fromInt
val fromInt32 = Int32.toLarge
val fromInt64 = Int64.toLarge
fun fromWord w = I.fromLarge(Word.toLargeInt w)
(*
fun fromWord32 w = I.+(I.<<(I.fromInt(w32toi(W32.>>(w,0w16))),0w16),
I.fromInt(w32toi(W32.andb(w,0wxffff))))
*)
fun fromWord32 w = I.fromLarge(Word32.toLargeInt w)
fun fromWord64 w = I.fromLarge(Word64.toLargeInt w)
end
(* machine_int <-> other types *)
fun fromInt(sz,i) = narrow(sz,Cvt.fromInt i)
fun fromInt32(sz,i) = narrow(sz,Cvt.fromInt32 i)
fun fromInt64(sz,i) = narrow(sz,Cvt.fromInt64 i)
fun fromWord(sz,w) = narrow(sz,Cvt.fromWord w)
fun fromWord32(sz,w) = narrow(sz,Cvt.fromWord32 w)
fun fromWord64(sz,w) = narrow(sz,Cvt.fromWord64 w)
fun toString(sz,i) = I.toString i
val toHex = I.fmt StringCvt.HEX
val toBin = I.fmt StringCvt.BIN
fun toHexString(sz, i) = "0x"^toHex(unsigned(sz, i))
fun toBinString(sz, i) = "0b"^toBin(unsigned(sz, i))
fun toInt(sz, i) = I.toInt(narrow(sz, i))
fun toInt32(sz, i) = Int32.fromLarge(narrow(sz, i))
fun toInt64(sz, i) = Int64.fromLarge(narrow(sz, i))
fun toWord(sz, i) = Word.fromLargeInt(I.toLarge(unsigned(sz, i)))
fun toWord32(sz, i) = Word32.fromLargeInt(I.toLarge(unsigned(sz, i)))
(*
let val i = unsigned(sz, i)
val lo = I.andb(i,0xffff)
val hi = I.~>>(i,0w16)
fun tow32 i = Word32.fromLargeInt(I.toLarge i)
in tow32 lo + Word32.<<(tow32 hi, 0w16) end
*)
fun toWord64(sz, i) = Word64.fromLargeInt(I.toLarge(unsigned(sz, i)))
fun hash i = Word.fromInt(I.toInt(I.andb(i,0x1fffffff)))
fun isInRange(sz, i) = I.<=(minOfSize sz,i) andalso I.<=(i,maxOfSize sz)
fun signedBinOp f (sz,i,j) = narrow(sz, f(i, j))
fun signedUnaryOp f (sz,i) = narrow(sz, f i)
fun unsignedBinOp f (sz,i,j) = narrow(sz, f(unsigned(sz,i), unsigned(sz,j)))
fun trappingUnaryOp f (sz,i) =
let val x = f i
in if isInRange(sz, x) then x else raise Overflow
end
fun trappingBinOp f (sz,i,j) =
let val x = f(i,j)
in if isInRange(sz, x) then x else raise Overflow
end
(* two's complement operators *)
val NEG = signedUnaryOp I.~
val ABS = signedUnaryOp I.abs
val ADD = signedBinOp I.+
val SUB = signedBinOp I.-
val MULS = signedBinOp I.*
fun DIVS (DIV_TO_ZERO, ty, x, y) = signedBinOp I.quot (ty, x, y)
| DIVS (DIV_TO_NEGINF, ty, x, y) = signedBinOp I.div (ty, x, y)
fun REMS (DIV_TO_ZERO, ty, x, y) = signedBinOp I.rem (ty, x, y)
| REMS (DIV_TO_NEGINF, ty, x, y) = signedBinOp I.mod (ty, x, y)
val MULU = unsignedBinOp I.*
val DIVU = unsignedBinOp I.div
(*
val QUOTU = unsignedBinOp I.quot
*)
val REMU = unsignedBinOp I.rem
val NEGT = trappingUnaryOp I.~
val ABST = trappingUnaryOp I.abs
val ADDT = trappingBinOp I.+
val SUBT = trappingBinOp I.-
val MULT = trappingBinOp I.*
fun DIVT (DIV_TO_ZERO, ty, x, y) = trappingBinOp I.quot (ty, x, y)
| DIVT (DIV_TO_NEGINF, ty, x, y) = trappingBinOp I.div (ty, x, y)
fun NOTB(sz,x) = narrow(sz,I.notb x)
fun ANDB(sz,x,y) = narrow(sz,I.andb(x,y))
fun ORB(sz,x,y) = narrow(sz,I.orb(x,y))
fun XORB(sz,x,y) = narrow(sz,I.xorb(x,y))
fun EQVB(sz,x,y) = narrow(sz,I.xorb(I.notb x,y))
fun Sll(sz,x,y) = narrow(sz,I.<<(x, y))
fun Srl(sz,x,y) = narrow(sz,I.~>>(unsigned(sz, x), y))
fun Sra(sz,x,y) = narrow(sz,I.~>>(x, y))
fun SLL(sz,x,y) = Sll(sz,x,toWord(sz, y))
fun SRL(sz,x,y) = Srl(sz,x,toWord(sz, y))
fun SRA(sz,x,y) = Sra(sz,x,toWord(sz, y))
fun BITSLICE(sz,sl,x) =
let fun slice([],n) = n
| slice((from,to)::sl,n) =
slice(sl, ORB(sz, narrow(to-from+1,
Srl(sz, x, Word.fromInt from)), n))
in slice(sl, 0)
end
fun bitOf(sz, i, b) =
toWord(1, narrow(1, Srl(sz, i, Word.fromInt b)))
fun byteOf(sz, i, b) =
toWord(8, narrow(8, Srl(sz, i, Word.fromInt(b*8))))
fun halfOf(sz, i, h) =
toWord(16, narrow(16, Srl(sz, i, Word.fromInt(h*16))))
fun wordOf(sz, i, w) =
toWord32(32, narrow(32, Srl(sz, i, Word.fromInt(w*32))))
(* type promotion *)
fun SX(toSz,fromSz,i) = narrow(toSz, narrow(fromSz, i))
fun ZX(toSz,fromSz,i) = narrow(toSz, unsigned(fromSz, narrow(fromSz, i)))
(* comparisions *)
fun EQ(sz,i:I.int,j) = i = j
fun NE(sz,i:I.int,j) = i <> j
fun GT(sz,i:I.int,j) = i > j
fun GE(sz,i:I.int,j) = i >= j
fun LT(sz,i:I.int,j) = i < j
fun LE(sz,i:I.int,j) = i <= j
fun LTU(sz,i,j) = unsigned(sz, i) < unsigned(sz, j)
fun GTU(sz,i,j) = unsigned(sz, i) > unsigned(sz, j)
fun LEU(sz,i,j) = unsigned(sz, i) <= unsigned(sz, j)
fun GEU(sz,i,j) = unsigned(sz, i) >= unsigned(sz, j)
(*
* Split an integer "i" of size "sz" into words of size "wordSize"
*)
fun split{sz, wordSize, i} =
let fun loop(sz, i, ws) =
if sz <= 0 then rev ws
else
let val w = narrow(wordSize, i)
val i = IntInf.~>>(i, Word.fromInt wordSize)
in loop(sz - wordSize, i, w::ws)
end
in loop(sz, unsigned(sz, i), [])
end
end
end
|
