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
use std::collections::HashMap;
use triton_vm::prelude::*;
use crate::prelude::*;
use crate::traits::basic_snippet::Reviewer;
use crate::traits::basic_snippet::SignOffFingerprint;
/// [Shift right][shr] for unsigned 64-bit integers.
///
/// # Behavior
///
/// ```text
/// BEFORE: _ [arg: u64] shift_amount
/// AFTER: _ [result: u64]
/// ```
///
/// # Preconditions
///
/// - input argument `arg` is properly [`BFieldCodec`] encoded
/// - input argument `shift_amount` is in `0..64`
///
/// # Postconditions
///
/// - the output is the input argument `arg` bit-shifted to the right by
/// input argument `shift_amount`
/// - the output is properly [`BFieldCodec`] encoded
///
/// [shr]: core::ops::Shr
#[derive(Debug, Copy, Clone, Eq, PartialEq, Hash)]
pub struct ShiftRight;
impl ShiftRight {
pub const SHIFT_AMOUNT_TOO_BIG_ERROR_ID: i128 = 330;
}
impl BasicSnippet for ShiftRight {
fn parameters(&self) -> Vec<(DataType, String)> {
let arg = (DataType::U64, "arg".to_string());
let shift_amount = (DataType::U32, "shift_amount".to_string());
vec![arg, shift_amount]
}
fn return_values(&self) -> Vec<(DataType, String)> {
vec![(DataType::U64, "shifted_arg".to_string())]
}
fn entrypoint(&self) -> String {
"tasmlib_arithmetic_u64_shift_right".to_string()
}
fn code(&self, _: &mut Library) -> Vec<LabelledInstruction> {
let entrypoint = self.entrypoint();
let shift_amount_gt_32 = format!("{entrypoint}_shift_amount_gt_32");
triton_asm!(
// BEFORE: _ arg_hi arg_lo shift
// AFTER: _ (arg >> shift)_hi (arg >> shift)_lo
{entrypoint}:
/* bounds check */
push 64
dup 1
lt
assert error_id {Self::SHIFT_AMOUNT_TOO_BIG_ERROR_ID}
// _ arg_hi arg_lo shift
/* special case if shift amount is greater than 32 */
dup 0
push 32
lt
// _ arg_hi arg_lo shift (32 < shift)
skiz
call {shift_amount_gt_32}
// _ arg_hi arg_lo shift
/* Over a finite field, both right shift and integer division are difficult.
* However, integer multiplication and therefore left shift are easy, provided
* the field elements are within the right ranges.
* General strategy: multiply by the correct power of 2 to shift left by
* (32 - shift_amount), then `split` and throw away the low limb. For example,
* 0b10_0001 >> 5 gives 0b1, as does a left shift by 27 after throwing away the
* low limb:
*
* 0b10_0001 << 27 = 0b1_0000_1000_0000_0000_0000_0000_0000_0000
* ╰─────────────╴ low limb ╶────────────╯
*/
push -1
mul
addi 32
// _ arg_hi arg_lo (32 - shift)
push 2
pow
// _ arg_hi arg_lo (2^(32 - shift))
pick 2
dup 1
mul
// _ arg_lo (2^(32 - shift)) (arg_hi << (32 - shift))
split
// _ arg_lo (2^(32 - shift)) (arg_hi >> shift) carry
// _ arg_lo (2^(32 - shift)) (arg >> shift)_hi carry
place 3
place 3
// _ (arg >> shift)_hi carry arg_lo (2^(32 - shift))
mul
split
pop 1
// _ (arg >> shift)_hi carry (arg_lo >> shift)
add
// _ (arg >> shift)_hi (arg >> shift)_lo
return
// BEFORE: _ arg_hi arg_lo shift
// AFTER: _ 0 arg_hi (shift - 32)
{shift_amount_gt_32}:
addi -32
// _ arg_hi arg_lo (shift - 32)
pick 1
pop 1
// _ arg_hi (shift - 32)
push 0
place 2
// _ 0 arg_hi (shift - 32)
return
)
}
fn sign_offs(&self) -> HashMap<Reviewer, SignOffFingerprint> {
let mut sign_offs = HashMap::new();
sign_offs.insert(Reviewer("ferdinand"), 0xa7cfa746b15b2d76.into());
sign_offs
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::test_prelude::*;
impl ShiftRight {
pub fn assert_expected_shift_right_behavior(&self, shift_amount: u32, arg: u64) {
let initial_stack = self.set_up_test_stack((arg, shift_amount));
let mut expected_stack = initial_stack.clone();
self.rust_shadow(&mut expected_stack);
test_rust_equivalence_given_complete_state(
&ShadowedClosure::new(Self),
&initial_stack,
&[],
&NonDeterminism::default(),
&None,
Some(&expected_stack),
);
}
}
impl Closure for ShiftRight {
type Args = (u64, u32);
fn rust_shadow(&self, stack: &mut Vec<BFieldElement>) {
let (arg, shift_amount) = pop_encodable::<Self::Args>(stack);
assert!(shift_amount < 64);
push_encodable(stack, &(arg >> shift_amount));
}
fn pseudorandom_args(
&self,
seed: [u8; 32],
bench_case: Option<BenchmarkCase>,
) -> Self::Args {
let mut rng = StdRng::from_seed(seed);
match bench_case {
Some(BenchmarkCase::CommonCase) => (0x642, 15),
Some(BenchmarkCase::WorstCase) => (0x123, 33),
None => (rng.random(), rng.random_range(0..64)),
}
}
fn corner_case_args(&self) -> Vec<Self::Args> {
(0..64).map(|i| (1 << i, i)).collect()
}
}
#[test]
fn rust_shadow() {
ShadowedClosure::new(ShiftRight).test()
}
#[test]
fn unit_test() {
ShiftRight.assert_expected_shift_right_behavior(2, 8);
}
#[proptest]
fn property_test(arg: u64, #[strategy(0_u32..64)] shift_amount: u32) {
ShiftRight.assert_expected_shift_right_behavior(shift_amount, arg);
}
#[proptest]
fn negative_property_test(arg: u64, #[strategy(64_u32..)] shift_amount: u32) {
test_assertion_failure(
&ShadowedClosure::new(ShiftRight),
InitVmState::with_stack(ShiftRight.set_up_test_stack((arg, shift_amount))),
&[ShiftRight::SHIFT_AMOUNT_TOO_BIG_ERROR_ID],
);
}
}
#[cfg(test)]
mod benches {
use super::*;
use crate::test_prelude::*;
#[test]
fn benchmark() {
ShadowedClosure::new(ShiftRight).bench();
}
}