mck 0.7.1

Utility crate for the formal verification tool machine-check
Documentation 
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
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269

use core::panic;

use crate::{
    concr::{PanicResult, Test},
    forward::{Bitwise, Ext, HwArith, HwShift, TypedCmp, TypedEq},
    misc::CBound,
    panic::message::{PANIC_NUM_DIV_BY_ZERO, PANIC_NUM_NO_PANIC, PANIC_NUM_REM_BY_ZERO},
};

use super::CConcreteBitvector;

#[test]
fn support() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);

    let zero = CConcreteBitvector::<16>::new(0, CBound);
    let full = CConcreteBitvector::<16>::new(0xFFFF, CBound);
    let min = CConcreteBitvector::<16>::new(0x8000, CBound);

    assert_eq!(a.to_u64(), 0xCAFE);
    assert_eq!(b.to_u64(), 0x1337);
    assert_eq!(zero.to_u64(), 0);
    assert_eq!(full.to_u64(), 0xFFFF);
    assert_eq!(min.to_u64(), 0x8000);

    assert_eq!(a.to_i64(), -0x3502);
    assert_eq!(b.to_i64(), 0x1337);
    assert_eq!(zero.to_i64(), 0);
    assert_eq!(full.to_i64(), -1);
    assert_eq!(min.to_i64(), -0x8000);

    assert!(a.is_nonzero());
    assert!(b.is_nonzero());
    assert!(!zero.is_nonzero());
    assert!(full.is_nonzero());
    assert!(min.is_nonzero());

    assert!(!a.is_zero());
    assert!(!b.is_zero());
    assert!(zero.is_zero());
    assert!(!full.is_zero());
    assert!(!min.is_zero());

    assert!(a.is_sign_bit_set());
    assert!(!b.is_sign_bit_set());
    assert!(!zero.is_sign_bit_set());
    assert!(full.is_sign_bit_set());
    assert!(min.is_sign_bit_set());

    assert_eq!(min, CConcreteBitvector::sign_bit_mask(CBound));
    assert_eq!(full, CConcreteBitvector::bit_mask(CBound));

    assert_eq!(
        CConcreteBitvector::<8>::all_with_bound_iter(CBound).count(),
        2usize.pow(8)
    );
}

#[test]
fn eq() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);

    assert!(a.eq(a).into_bool());
    assert!(b.eq(b).into_bool());
    assert!(!a.eq(b).into_bool());
    assert!(!b.eq(a).into_bool());
}

#[test]
fn cmp() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);

    // identity
    assert!(!a.ult(a).into_bool());
    assert!(a.ule(a).into_bool());
    assert!(!a.slt(a).into_bool());
    assert!(a.sle(a).into_bool());

    // comparison
    assert!(!a.ult(b).into_bool());
    assert!(!a.ule(b).into_bool());
    assert!(a.slt(b).into_bool());
    assert!(a.sle(b).into_bool());

    // try flipped the other way, they are not equal
    assert!(b.ult(a).into_bool());
    assert!(b.ule(a).into_bool());
    assert!(!b.slt(a).into_bool());
    assert!(!b.sle(a).into_bool());
}

#[test]
fn bitwise() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);

    // compare results to calculated values
    assert_eq!(a.bit_not().to_u64(), 0x3501);
    assert_eq!(b.bit_not().to_u64(), 0xECC8);

    assert_eq!(a.bit_and(b).to_u64(), 0x0236);
    assert_eq!(a.bit_or(b).to_u64(), 0xDBFF);
    assert_eq!(a.bit_xor(b).to_u64(), 0xD9C9);
}

#[test]
fn ext() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);

    // longer uext will preserve unsigned value
    assert_eq!(Ext::<32>::uext(a).to_u64(), 0xCAFE);
    assert_eq!(Ext::<32>::uext(a).to_i64(), 0xCAFE);
    assert_eq!(Ext::<32>::uext(b).to_u64(), 0x1337);
    assert_eq!(Ext::<32>::uext(b).to_i64(), 0x1337);

    // longer sext will preserve signed value
    assert_eq!(Ext::<32>::sext(a).to_u64(), 0xFFFFCAFE);
    assert_eq!(Ext::<32>::sext(a).to_i64(), -0x3502);
    assert_eq!(Ext::<32>::sext(b).to_u64(), 0x1337);
    assert_eq!(Ext::<32>::sext(b).to_i64(), 0x1337);

    // shorter ext will always just cut
    assert_eq!(Ext::<4>::uext(a).to_u64(), 0xE);
    assert_eq!(Ext::<4>::uext(a).to_i64(), -0x2);
    assert_eq!(Ext::<4>::sext(a).to_u64(), 0xE);
    assert_eq!(Ext::<4>::sext(a).to_i64(), -0x2);

    // same ext will preserve value
    assert_eq!(a, Ext::<16>::uext(a));
    assert_eq!(b, Ext::<16>::uext(b));
    assert_eq!(a, Ext::<16>::sext(a));
    assert_eq!(b, Ext::<16>::sext(b));
}

#[test]
fn shift() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);
    let four = CConcreteBitvector::<16>::new(0x4, CBound);
    let sixteen = CConcreteBitvector::<16>::new(0x16, CBound);
    let too_much = CConcreteBitvector::<16>::new(0x42, CBound);

    // shift by a reasonable value
    assert_eq!(a.logic_shl(four).to_u64(), 0xAFE0);
    assert_eq!(b.logic_shl(four).to_u64(), 0x3370);
    assert_eq!(a.logic_shr(four).to_u64(), 0x0CAF);
    assert_eq!(b.logic_shr(four).to_u64(), 0x0133);
    assert_eq!(a.arith_shr(four).to_u64(), 0xFCAF);
    assert_eq!(b.arith_shr(four).to_u64(), 0x0133);

    // shift by exactly all bits
    // should be zero except for arith shift right of negative
    assert_eq!(a.logic_shl(sixteen).to_u64(), 0x0000);
    assert_eq!(b.logic_shl(sixteen).to_u64(), 0x0000);
    assert_eq!(a.logic_shr(sixteen).to_u64(), 0x0000);
    assert_eq!(b.logic_shr(sixteen).to_u64(), 0x0000);
    assert_eq!(a.arith_shr(sixteen).to_u64(), 0xFFFF);
    assert_eq!(b.arith_shr(sixteen).to_u64(), 0x0000);

    // shift by an unreasonable value
    // should give the same results as by all bits
    assert_eq!(a.logic_shl(too_much).to_u64(), 0x0000);
    assert_eq!(b.logic_shl(too_much).to_u64(), 0x0000);
    assert_eq!(a.logic_shr(too_much).to_u64(), 0x0000);
    assert_eq!(b.logic_shr(too_much).to_u64(), 0x0000);
    assert_eq!(a.arith_shr(too_much).to_u64(), 0xFFFF);
    assert_eq!(b.arith_shr(too_much).to_u64(), 0x0000);
}

#[test]
fn arith() {
    let a = CConcreteBitvector::<16>::new(0xCAFE, CBound);
    let b = CConcreteBitvector::<16>::new(0x1337, CBound);
    let c = CConcreteBitvector::<16>::new(0x4000, CBound);
    let d = CConcreteBitvector::<16>::new(0xBADA, CBound);

    let zero = CConcreteBitvector::<16>::new(0, CBound);

    // add, sub, mul do not have corner cases except wrapping
    // compare results to calculated values
    assert_eq!(a.add(b).to_u64(), 0xDE35);
    assert_eq!(a.add(c).to_u64(), 0x0AFE);
    assert_eq!(b.add(c).to_u64(), 0x5337);
    assert_eq!(a.sub(b).to_u64(), 0xB7C7);
    assert_eq!(a.sub(c).to_u64(), 0x8AFE);
    assert_eq!(b.sub(c).to_u64(), 0xD337);
    assert_eq!(a.mul(b).to_u64(), 0x7692);
    assert_eq!(a.mul(c).to_u64(), 0x8000);
    assert_eq!(b.mul(c).to_u64(), 0xC000);

    // unsigned division and remainder have division by zero
    // try out normal first
    assert_eq!(expect_no_panic(a.udiv(b)).to_u64(), 0x000A);
    assert_eq!(expect_no_panic(a.urem(b)).to_u64(), 0x0AD8);
    assert_eq!(expect_no_panic(a.udiv(c)).to_u64(), 0x0003);
    assert_eq!(expect_no_panic(a.urem(c)).to_u64(), 0x0AFE);
    assert_eq!(expect_no_panic(b.udiv(c)).to_u64(), 0x0000);
    assert_eq!(expect_no_panic(b.urem(c)).to_u64(), 0x1337);

    // in case of unsigned division-by-zero
    // division result is all-ones and remainder is the dividend
    assert_eq!(expect_div_panic(a.udiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(a.urem(zero)).to_u64(), 0xCAFE);
    assert_eq!(expect_div_panic(b.udiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(b.urem(zero)).to_u64(), 0x1337);
    assert_eq!(expect_div_panic(c.udiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(c.urem(zero)).to_u64(), 0x4000);

    // signed division and remainder have four-quadrant behaviour,
    // division by zero and overflow
    assert_eq!(expect_no_panic(c.sdiv(b)).to_u64(), 0x0003); // positive / positive
    assert_eq!(expect_no_panic(c.srem(b)).to_u64(), 0x065B);
    assert_eq!(expect_no_panic(a.sdiv(b)).to_u64(), 0xFFFE); // negative / positive
    assert_eq!(expect_no_panic(a.srem(b)).to_u64(), 0xF16C);
    assert_eq!(expect_no_panic(c.sdiv(a)).to_u64(), 0xFFFF); // positive / negative
    assert_eq!(expect_no_panic(c.srem(a)).to_u64(), 0x0AFE);
    assert_eq!(expect_no_panic(d.sdiv(a)).to_u64(), 0x0001); // negative / negative
    assert_eq!(expect_no_panic(d.srem(a)).to_u64(), 0xEFDC);

    // in case of signed division-by-zero
    // division result is all-ones and remainder is the dividend
    // (same as unsigned)
    assert_eq!(expect_div_panic(a.sdiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(a.srem(zero)).to_u64(), 0xCAFE);
    assert_eq!(expect_div_panic(b.sdiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(b.srem(zero)).to_u64(), 0x1337);
    assert_eq!(expect_div_panic(c.sdiv(zero)).to_u64(), 0xFFFF);
    assert_eq!(expect_rem_panic(c.srem(zero)).to_u64(), 0x4000);

    // overflow only happens if the minimum value is divided by minus one
    // because the minimum value is not representable in positive
    // in that case, we expect the minimum value remain in divisor
    // and no remainder
    let min = CConcreteBitvector::<16>::new(0x8000, CBound);
    let minus_one = CConcreteBitvector::<16>::new(0xFFFF, CBound);
    assert_eq!(expect_no_panic(min.sdiv(minus_one)), min);
    assert_eq!(expect_no_panic(min.srem(minus_one)), zero);
}

fn expect_no_panic<const W: u32>(
    panic_result: PanicResult<CConcreteBitvector<W>>,
) -> CConcreteBitvector<W> {
    if panic_result.panic != CConcreteBitvector::new(PANIC_NUM_NO_PANIC, CBound) {
        panic!("Expected no panic")
    }
    panic_result.result
}

fn expect_div_panic<const W: u32>(
    panic_result: PanicResult<CConcreteBitvector<W>>,
) -> CConcreteBitvector<W> {
    if panic_result.panic != CConcreteBitvector::new(PANIC_NUM_DIV_BY_ZERO, CBound) {
        panic!("Expected division panic")
    }
    panic_result.result
}

fn expect_rem_panic<const W: u32>(
    panic_result: PanicResult<CConcreteBitvector<W>>,
) -> CConcreteBitvector<W> {
    if panic_result.panic != CConcreteBitvector::new(PANIC_NUM_REM_BY_ZERO, CBound) {
        panic!("Expected remainder panic")
    }
    panic_result.result
}