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Author SHA1 Message Date
Miguel M f420690041 pure python for comparison 2023-02-28 21:20:06 +00:00
Miguel M 39cfb20f13 touchups 2023-02-28 21:19:50 +00:00
Miguel M e85346e916 could have used a map instead of running twice, preparing to make that 
change
 2023-02-26 18:07:25 +00:00
Miguel M b899ddd63a Final commit, in principle. 
Got things running at about ~1ns per iteration, seems good enough.
Adopted a linear strategy to evaluating the bytecode, rather than a
recursive or even imperative evaluation strategy; this also lets me
elide the offsets and store the bytecode in half the size. Looking
forward to finding out that formulas are evaluated wrongly, but couldn't
find a counterexample. Also restructured things a bit to avoid multiple
alocations when evaluating by this strategy.
 2023-02-24 19:41:51 +00:00
Miguel M 3a6c511ed5 optimized bottlenecks based on benchmarks. fast now 2023-02-24 18:23:37 +00:00
19 changed files with 3132 additions and 302 deletions
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1
Cargo.lock generated
View File

@ -6,6 +6,7 @@ version = 3
name = "adversary"
version = "0.1.0"
dependencies = [
"bitflags",
"criterion",
"pest",
"pest_derive",

11
Cargo.toml
View File

@ -9,6 +9,7 @@ name = "adversary"
crate-type = ["cdylib", "rlib"]
[dependencies]
bitflags = "1.3.2"
pest = "2.5.5"
pest_derive = "2.5.5"
pyo3 = { version = "0.18.0", features = ["extension-module"] }
@ -16,6 +17,14 @@ pyo3 = { version = "0.18.0", features = ["extension-module"] }
[dev-dependencies]
criterion = "0.4.0"
[[bench]]
name = "search_big"
harness = false
[[bench]]
name = "search"
harness = false
harness = false
[[bench]]
name = "vm"
harness = false

13
Makefile
View File

@ -7,5 +7,16 @@ flamegraph:
flamegraph-debug:
cargo flamegraph --dev -o debug_flamegraph.svg --bench search -- --bench
asm:
cargo clean
cargo rustc --release --lib -- --emit asm=.vscode/asm_mangled
pwsh -Command 'Get-Content .vscode/asm_mangled | c++filt > .\src\lib.S'
pwsh -Command 'Remove-Item .vscode/asm_mangled'
maturin:
pwsh -Command 'venv/Scripts/activate; maturin develop --release'
.PHONY: criterion flamegraph flamegraph-debug
hyperfine:
hyperfine --show-output --parameter-scan n 5 20 -S 'pwsh' -s 'venv/scripts/activate' --export-json hyperfine.json --export-csv hyperfine.csv 'python ./pytest/timing.py {n}'
.PHONY: criterion flamegraph flamegraph-debug asm hyperfine maturin

8
benches/search.rs
View File

@ -4,7 +4,7 @@ extern crate adversary;
use criterion::{criterion_group, criterion_main, Criterion};
pub fn criterion_benchmark(c: &mut Criterion) {
fn bench_search(c: &mut Criterion) {
pyo3::prepare_freethreaded_python();
pyo3::Python::with_gil(|_py| {
let obj = adversary::Prover::py_new(
@ -13,11 +13,11 @@ pub fn criterion_benchmark(c: &mut Criterion) {
"<= ham (^ x y) p".to_string(),
)
.unwrap();
c.bench_function("find_bounds", |b| {
c.bench_function("search", |b| {
b.iter(|| criterion::black_box(obj.find_bounds(10, 5, 3)));
});
})
}
criterion_group!(benches, criterion_benchmark);
criterion_main!(benches);
criterion_group!(search, bench_search);
criterion_main!(search);

23
benches/search_big.rs Normal file
View File

@ -0,0 +1,23 @@
#[macro_use]
extern crate criterion;
extern crate adversary;
use criterion::{criterion_group, criterion_main, Criterion};
fn bench_search_big(c: &mut Criterion) {
pyo3::prepare_freethreaded_python();
pyo3::Python::with_gil(|_py| {
let obj = adversary::Prover::py_new(
"= (ham x) k".to_string(),
"= (ham y) (+ k 1)".to_string(),
"<= ham (^ x y) p".to_string(),
)
.unwrap();
c.bench_function("search_big", |b| {
b.iter(|| criterion::black_box(obj.find_bounds(12, 5, 8)));
});
})
}
criterion_group!(search_big, bench_search_big);
criterion_main!(search_big);

35
benches/vm.rs Normal file
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@ -0,0 +1,35 @@
#[macro_use]
extern crate criterion;
extern crate adversary;
use criterion::{criterion_group, criterion_main, Criterion};
fn bench_vm(c: &mut Criterion) {
let expression =
adversary::vm::parsing::parse_relation("and (= (ham (^ x y)) (ham (+ 3 x))) (> (* x y) 5)");
if let Err(e) = expression {
println!("{}", e);
panic!();
}
let code = adversary::vm::compile_boolean(expression.unwrap());
let mut stack = adversary::vm::VmStack::from_code(&code);
c.bench_function("vm", |b| {
b.iter(|| {
for x in 0..(1 << 6) {
for y in 0..(1 << 6) {
criterion::black_box(
adversary::vm::Vm::load(
&code,
adversary::vm::Registers::load(x, y, 6, 0, 0),
&mut stack,
)
.run(),
);
}
}
})
});
}
criterion_group!(vm, bench_vm);
criterion_main!(vm);

17
hyperfine.csv Normal file
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@ -0,0 +1,17 @@
#command,mean,stddev,median,user,system,min,max,parameter_n
"python ./pytest/timing.py 5",0.04581394800000006,0.00816270671734837,0.04668517800000005,0.026718750000000003,0.019218749999999996,0.032075278000000096,0.05514677800000001,5
"python ./pytest/timing.py 6",0.042371348000000066,0.007327761603207661,0.04315997800000004,0.009812500000000002,0.010281249999999997,0.03199467800000011,0.05567727800000011,6
"python ./pytest/timing.py 7",0.04077101800000005,0.008782824810351926,0.040449628000000015,0.029562500000000002,0.016093749999999997,0.028448878000000066,0.05205177800000005,7
"python ./pytest/timing.py 8",0.04834307800000006,0.008276160843853466,0.04665782800000007,0.041781250000000006,0.05874999999999999,0.03589267800000007,0.06276897800000003,8
"python ./pytest/timing.py 9",0.04610321800000006,0.01221144375440967,0.04276542800000005,0.004125000000000001,0.005593749999999997,0.031109278000000073,0.06754577800000006,9
"python ./pytest/timing.py 10",0.656881348,1.816322202089533,0.04675287800000005,0.02075,0.00915625,0.03219597800000007,5.8203265779999995,10
"python ./pytest/timing.py 11",0.04503963800000007,0.005758636203747479,0.04366842800000009,0.018906250000000003,0.029718749999999995,0.03824637800000008,0.056746278000000094,11
"python ./pytest/timing.py 12",0.06112314800000005,0.01715353160780924,0.05904557800000004,0.02146875,0.025031249999999994,0.03643177800000008,0.09102267800000008,12
"python ./pytest/timing.py 13",0.07466937800000005,0.040038996149254304,0.060930978000000025,0.040781250000000005,0.017656249999999995,0.03599187800000003,0.15105747800000002,13
"python ./pytest/timing.py 14",0.12913027800000004,0.16291293196519285,0.05922252800000005,0.10300000000000001,0.004249999999999999,0.035453378000000035,0.5145964780000001,14
"python ./pytest/timing.py 15",0.5586950680000001,0.7332788059539814,0.17217967800000006,0.500875,0.005593749999999997,0.03280447800000008,2.137246578,15
"python ./pytest/timing.py 16",2.576790488,2.687933192209969,1.668545078,2.5227499999999994,0.03284374999999999,0.041527578000000065,6.829759978,16
"python ./pytest/timing.py 17",5.479623618,7.132625194222096,3.4482901779999997,5.43184375,0.015874999999999993,0.05124057800000004,21.924067778,17
"python ./pytest/timing.py 18",34.976559767999994,45.33047970462983,1.2725040280000002,34.897749999999995,0.020562499999999994,0.03764907800000006,95.283775278,18
"python ./pytest/timing.py 19",100.16646647799999,143.37612065560103,1.117140078,100.04775,0.022343749999999996,0.036464678000000084,385.89288487799996,19
"python ./pytest/timing.py 20",253.70613178800005,435.7539383326962,75.73695792800001,253.42871875,0.047562499999999994,0.0477563780000001,1400.148915478,20
1 #command mean stddev median user system min max parameter_n
2 python ./pytest/timing.py 5 0.04581394800000006 0.00816270671734837 0.04668517800000005 0.026718750000000003 0.019218749999999996 0.032075278000000096 0.05514677800000001 5
3 python ./pytest/timing.py 6 0.042371348000000066 0.007327761603207661 0.04315997800000004 0.009812500000000002 0.010281249999999997 0.03199467800000011 0.05567727800000011 6
4 python ./pytest/timing.py 7 0.04077101800000005 0.008782824810351926 0.040449628000000015 0.029562500000000002 0.016093749999999997 0.028448878000000066 0.05205177800000005 7
5 python ./pytest/timing.py 8 0.04834307800000006 0.008276160843853466 0.04665782800000007 0.041781250000000006 0.05874999999999999 0.03589267800000007 0.06276897800000003 8
6 python ./pytest/timing.py 9 0.04610321800000006 0.01221144375440967 0.04276542800000005 0.004125000000000001 0.005593749999999997 0.031109278000000073 0.06754577800000006 9
7 python ./pytest/timing.py 10 0.656881348 1.816322202089533 0.04675287800000005 0.02075 0.00915625 0.03219597800000007 5.8203265779999995 10
8 python ./pytest/timing.py 11 0.04503963800000007 0.005758636203747479 0.04366842800000009 0.018906250000000003 0.029718749999999995 0.03824637800000008 0.056746278000000094 11
9 python ./pytest/timing.py 12 0.06112314800000005 0.01715353160780924 0.05904557800000004 0.02146875 0.025031249999999994 0.03643177800000008 0.09102267800000008 12
10 python ./pytest/timing.py 13 0.07466937800000005 0.040038996149254304 0.060930978000000025 0.040781250000000005 0.017656249999999995 0.03599187800000003 0.15105747800000002 13
11 python ./pytest/timing.py 14 0.12913027800000004 0.16291293196519285 0.05922252800000005 0.10300000000000001 0.004249999999999999 0.035453378000000035 0.5145964780000001 14
12 python ./pytest/timing.py 15 0.5586950680000001 0.7332788059539814 0.17217967800000006 0.500875 0.005593749999999997 0.03280447800000008 2.137246578 15
13 python ./pytest/timing.py 16 2.576790488 2.687933192209969 1.668545078 2.5227499999999994 0.03284374999999999 0.041527578000000065 6.829759978 16
14 python ./pytest/timing.py 17 5.479623618 7.132625194222096 3.4482901779999997 5.43184375 0.015874999999999993 0.05124057800000004 21.924067778 17
15 python ./pytest/timing.py 18 34.976559767999994 45.33047970462983 1.2725040280000002 34.897749999999995 0.020562499999999994 0.03764907800000006 95.283775278 18
16 python ./pytest/timing.py 19 100.16646647799999 143.37612065560103 1.117140078 100.04775 0.022343749999999996 0.036464678000000084 385.89288487799996 19
17 python ./pytest/timing.py 20 253.70613178800005 435.7539383326962 75.73695792800001 253.42871875 0.047562499999999994 0.0477563780000001 1400.148915478 20

596
hyperfine.json Normal file
View File

@ -0,0 +1,596 @@
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0,
0,
0
],
"parameters": {
"n": "17"
}
},
{
"command": "python ./pytest/timing.py 18",
"mean": 34.976559767999994,
"stddev": 45.33047970462983,
"median": 1.2725040280000002,
"user": 34.897749999999995,
"system": 0.020562499999999994,
"min": 0.03764907800000006,
"max": 95.283775278,
"times": [
65.275574278,
93.015606878,
93.44633337799999,
1.253816878,
1.291191178,
0.03791617800000002,
0.04903267800000011,
0.03764907800000006,
95.283775278,
0.07470187800000005
],
"exit_codes": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"parameters": {
"n": "18"
}
},
{
"command": "python ./pytest/timing.py 19",
"mean": 100.16646647799999,
"stddev": 143.37612065560103,
"median": 1.117140078,
"user": 100.04775,
"system": 0.022343749999999996,
"min": 0.036464678000000084,
"max": 385.89288487799996,
"times": [
385.89288487799996,
290.359225178,
0.036464678000000084,
0.19590917800000007,
0.046879778000000094,
161.21907277800003,
2.035711278,
0.04454757800000009,
161.635400578,
0.19856887800000012
],
"exit_codes": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"parameters": {
"n": "19"
}
},
{
"command": "python ./pytest/timing.py 20",
"mean": 253.70613178800005,
"stddev": 435.7539383326962,
"median": 75.73695792800001,
"user": 253.42871875,
"system": 0.047562499999999994,
"min": 0.0477563780000001,
"max": 1400.148915478,
"times": [
420.37908587799996,
0.07129847800000011,
422.945836478,
25.767745578000003,
125.706170278,
141.83330137800002,
0.06695817800000003,
1400.148915478,
0.094249778,
0.0477563780000001
],
"exit_codes": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"parameters": {
"n": "20"
}
}
]
}

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15
pytest/bounds.py Normal file
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@ -0,0 +1,15 @@
import adversary
from math import sqrt
prover = adversary.Prover(
"= (ham x) k", "= (ham y) (+ k 1)", "= ham (^ x y) p").hint_symmetric()
bounds = prover.find_bounds(16, 5, 8)
lower_bound = sqrt(bounds.min_x_relations *
bounds.min_y_relations / bounds.max_joint_relations)
print("m =", bounds.min_x_relations)
print(f"From x={bounds.single_bounding_x:b}")
print("m' =", bounds.min_y_relations)
print(f"From y={bounds.single_bounding_y:b}")
print("ℓ·ℓ' =", bounds.max_joint_relations)
print(f"From x={bounds.joint_bounding_x:012b} and y={bounds.joint_bounding_y:012b} and window={bounds.bounding_window:012b}")
print(f"Query lower bounds = {lower_bound}")

75
pytest/pure.py Normal file
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@ -0,0 +1,75 @@
import itertools
from math import inf
n = 16
k = 6
p = 2
def in_set_a(x):
return x.bit_count() == k
def in_set_b(y):
return y.bit_count() == k + 1
def related(a, b):
return (x ^ y).bit_count() == 1
m = inf
m_prime = inf
window = (1 << p) - 1
l = 0
l_prime = 0
# Look at all the `x`s, find the `x` with least number of relations, and
# what is the `x` with most relations (under the window condition)
for x in range(2**n):
if not in_set_a(x):
continue
relations_count = 0
for y in range(2**n):
if not in_set_b(y):
continue
if not related(x, y):
continue
relations_count += 1
if (x & window) != (y & window):
l += 1
# This `x` has less relations than all `x` we've looked at so far
if relations_count < m:
m = relations_count
for y in range(2**n):
if not in_set_b(y):
continue
relations_count = 0
for x in range(2**n):
if not in_set_a(x):
continue
if not related(x, y):
continue
relations_count += 1
if (x & window) != (y & window):
l_prime += 1
# This `y` has less relations than all `y` we've looked at so far
if relations_count < m_prime:
m_prime = relations_count
# Finally, see if we can get a better `l_max` under this window than
# what we've seen so far
l_max = l * l_prime
print(m, m_prime, l_max)

10
pytest/timing.py Normal file
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@ -0,0 +1,10 @@
import adversary
import random
import sys
n = int(sys.argv[1])
prover = adversary.Prover(
"= (ham x) k", "= (ham y) (+ k 1)", "= ham (^ x y) p").hint_symmetric()
k = random.randint(0, n)
p = random.randint(0, n)
bounds = prover.find_bounds(n, k, p)

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119
src/lib.rs
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@ -1,11 +1,12 @@
extern crate pest;
#[macro_use]
extern crate pest_derive;
#[macro_use]
extern crate bitflags;
mod vm;
pub mod vm;
use pyo3::prelude::*;
use vm::VmCode;
// We cache the A and B set up to a total of ~2Gb of memory,
// meaning ~ 10^7 elements in each set
@ -33,58 +34,64 @@ pub struct BoundsResult {
#[pyclass]
pub struct Prover {
a_description: VmCode,
b_description: VmCode,
relationship: VmCode,
a_description: vm::VmCode,
b_description: vm::VmCode,
relationship: vm::VmCode,
hints: ProofHints,
}
bitflags! {
struct ProofHints: u8 {
const SymmetricFn = 0b00000001;
}
}
struct CachedSetIterator<'code> {
cache: Vec<u64>,
filter: &'code VmCode,
filter: &'code vm::VmCode,
stack: vm::VmStack,
n: u32,
p: u32,
k: u32,
cached: bool,
counter: u64,
cache_counter: usize,
top: u64,
counter: usize,
top: usize,
is_x: bool,
}
impl<'code> CachedSetIterator<'code> {
fn create_x(filter: &'code VmCode, n: u32, p: u32, k: u32) -> Self {
fn create_x(filter: &'code vm::VmCode, n: u32, p: u32, k: u32) -> Self {
CachedSetIterator {
cache: Vec::with_capacity(CACHE_SIZE_LIMIT),
filter,
stack: vm::VmStack::from_code(filter),
n,
p,
k,
cached: false,
counter: 0,
cache_counter: 0,
top: 2_u64.pow(n as u32),
top: 2_usize.pow(n as u32),
is_x: true,
}
}
fn create_y(filter: &'code VmCode, n: u32, p: u32, k: u32) -> Self {
fn create_y(filter: &'code vm::VmCode, n: u32, p: u32, k: u32) -> Self {
CachedSetIterator {
cache: Vec::with_capacity(CACHE_SIZE_LIMIT),
filter,
stack: vm::VmStack::from_code(filter),
n,
p,
k,
cached: false,
counter: 0,
cache_counter: 0,
top: 2_u64.pow(n as u32),
top: 2_usize.pow(n as u32),
is_x: false,
}
}
fn reset(&mut self) {
self.counter = 0;
self.cache_counter = 0;
}
}
@ -93,12 +100,12 @@ impl<'code> Iterator for &mut CachedSetIterator<'code> {
fn next(&mut self) -> Option<Self::Item> {
if self.cached {
if self.cache_counter < self.cache.len() {
let result = self.cache[self.cache_counter];
self.cache_counter += 1;
if self.counter < self.cache.len() {
let result = self.cache[self.counter as usize];
self.counter += 1;
if self.cache_counter == CACHE_SIZE_LIMIT {
self.counter = self.cache.last().unwrap() + 1;
if self.counter == CACHE_SIZE_LIMIT {
self.counter = *self.cache.last().unwrap() as usize + 1;
}
return Some(result);
@ -118,24 +125,28 @@ impl<'code> Iterator for &mut CachedSetIterator<'code> {
let included = if self.is_x {
vm::Vm::load(
self.filter,
vm::Registers::load(self.counter, 0, self.n, self.p, self.k),
vm::Registers::load(self.counter as u64, 0, self.n, self.p, self.k),
&mut self.stack,
)
.run()
.unwrap_bool()
.output_bool()
.unwrap()
} else {
vm::Vm::load(
self.filter,
vm::Registers::load(0, self.counter, self.n, self.p, self.k),
vm::Registers::load(0, self.counter as u64, self.n, self.p, self.k),
&mut self.stack,
)
.run()
.unwrap_bool()
.output_bool()
.unwrap()
};
if !included {
self.counter += 1;
continue;
} else {
let result = self.counter;
let result = self.counter as u64;
if self.cache.len() < CACHE_SIZE_LIMIT {
self.cache.push(result);
}
@ -150,6 +161,7 @@ impl<'code> Iterator for &mut CachedSetIterator<'code> {
// See https://stackoverflow.com/a/27755938
// In turn from http://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation
struct FixedHammingWeight {
ones: u32,
permutation: u64,
top: u64,
exhausted: bool,
@ -158,11 +170,17 @@ struct FixedHammingWeight {
impl FixedHammingWeight {
fn new(bits: u32, ones: u32) -> Self {
FixedHammingWeight {
ones,
permutation: (1 << ones) - 1,
top: ((1 << ones) - 1) << (bits - ones),
exhausted: false,
}
}
fn reset(&mut self) {
self.permutation = (1 << self.ones) - 1;
self.exhausted = false;
}
}
impl Iterator for FixedHammingWeight {
@ -170,6 +188,7 @@ impl Iterator for FixedHammingWeight {
fn next(&mut self) -> Option<Self::Item> {
if self.exhausted {
self.reset();
return None;
}
let to_yield = self.permutation;
@ -263,9 +282,20 @@ impl Prover {
relationship,
a_description,
b_description,
hints: ProofHints::empty(),
})
}
/// Hints to the prover that the function in question is totally symmetric,
/// or, equivalently, that `a_description` only depends on the Hamming weight
/// of x, and `b_description` only depends on the Hamming weight of y.
///
/// If you l your results will lower bound the upper bound.
pub fn hint_symmetric<'s>(mut py_self: PyRefMut<'s, Self>, py: Python) -> PyRefMut<'s, Self> {
(*py_self).hints |= ProofHints::SymmetricFn;
py_self
}
/// Finds a lower bound to the query complexity according to the specified parameters.
///
/// Arguments:
@ -273,7 +303,7 @@ impl Prover {
/// belonging to either of the specified sets [int]
/// p The number of parallel queries [int]
/// k Parameter accepted in set specifications and relations [int]
pub fn find_bounds(&self, n: u32, p: u32, k: u32) -> PyResult<BoundsResult> {
pub fn find_bounds(&self, n: u32, k: u32, p: u32) -> PyResult<BoundsResult> {
if n > 63 {
return Err(pyo3::exceptions::PyValueError::new_err(
"More than 63 bits is not supported. (Because of `n` parameter.)",
@ -290,9 +320,10 @@ impl Prover {
));
}
let mut vm_stack = vm::VmStack::from_code(&self.relationship);
let mut a_set_iterator = CachedSetIterator::create_x(&self.a_description, n, p, k);
let mut b_set_iterator = CachedSetIterator::create_y(&self.b_description, n, p, k);
let window_iterator = FixedHammingWeight::new(n, p);
let mut min_x_relations = u64::MAX;
let mut min_y_relations = u64::MAX;
@ -303,7 +334,15 @@ impl Prover {
let mut joint_bounding_y = 0_u64;
let mut bounding_window = 0_u64;
for window in window_iterator {
let mut window_iterator = FixedHammingWeight::new(n, p).into_iter();
let mut first_entry = [(1_u64 << p) - 1].into_iter();
let effective_window_iterator = if self.hints.contains(ProofHints::SymmetricFn) {
&mut first_entry as &mut dyn Iterator<Item = u64>
} else {
&mut window_iterator as &mut dyn Iterator<Item = u64>
};
for window in effective_window_iterator {
let mut max_x_relations = 0_u64;
let mut max_y_relations = 0_u64;
let mut bounding_x_candidate = 0_u64;
@ -317,9 +356,11 @@ impl Prover {
let related = vm::Vm::load(
&self.relationship,
vm::Registers::load(x, y, n, p, k),
&mut vm_stack,
)
.run()
.unwrap_bool();
.output_bool()
.unwrap();
if related {
min_x_relations_candidate += 1;
@ -344,10 +385,14 @@ impl Prover {
let mut max_y_relations_candidate = 0_u64;
for x in &mut a_set_iterator {
let related =
vm::Vm::load(&self.relationship, vm::Registers::load(x, y, n, p, k))
.run()
.unwrap_bool();
let related = vm::Vm::load(
&self.relationship,
vm::Registers::load(x, y, n, p, k),
&mut vm_stack,
)
.run()
.output_bool()
.unwrap();
if related {
min_y_relations_candidate += 1;
@ -374,9 +419,9 @@ impl Prover {
joint_bounding_x = bounding_x_candidate;
joint_bounding_y = bounding_y_candidate;
bounding_window = window;
Python::with_gil(|py| py.check_signals())?;
}
Python::with_gil(|py| py.check_signals())?;
}
Ok(BoundsResult {
@ -437,4 +482,4 @@ fn test_full_run() {
.unwrap();
std::hint::black_box(obj.find_bounds(10, 5, 3)).expect("Success");
})
}
}

539
src/vm/mod.rs
View File

@ -4,7 +4,8 @@ use parsing::ast;
use crate::vm::parsing::ast::ComparisonOperator;
type Bytecode = (OpCode, usize);
// type Bytecode = (OpCode, usize);
type Bytecode = OpCode;
#[derive(Debug)]
pub struct VmCode {
@ -15,6 +16,13 @@ pub struct VmCode {
pub struct Vm<'code> {
code: &'code VmCode,
registers: Registers,
stack: &'code mut VmStack,
}
#[derive(Debug)]
pub struct VmStack {
boolean_stack: Vec<bool>,
arithmetic_stack: Vec<ArithmeticValue>,
}
#[derive(Debug)]
@ -26,11 +34,12 @@ pub struct Registers {
k: i64,
}
/*
#[derive(Debug)]
pub enum VmOutput {
Boolean(bool),
Arithmetic(ArithmeticValue),
}
} */
#[derive(Debug)]
pub enum ArithmeticValue {
@ -54,7 +63,23 @@ enum Expression {
Arithmetic(ast::ArithmeticExpression),
}
impl VmOutput {
impl VmStack {
pub fn from_code(code: &VmCode) -> Self {
// Each op_code can produce at most one value onto the stack
let code = &code.code;
VmStack {
boolean_stack: Vec::with_capacity(code.len()),
arithmetic_stack: Vec::with_capacity(code.len()),
}
}
fn reset(&mut self) {
self.boolean_stack.clear();
self.arithmetic_stack.clear();
}
}
/*impl VmOutput {
pub fn unwrap_bool(self) -> bool {
match self {
VmOutput::Boolean(value) => value,
@ -73,6 +98,7 @@ impl VmOutput {
}
}
}
*/
impl Registers {
pub fn load(x: u64, y: u64, n: u32, p: u32, k: u32) -> Self {
@ -101,7 +127,7 @@ pub fn compile_arithmetic(expression: ast::ArithmeticExpression) -> VmCode {
impl VmCode {
pub fn any<P: Fn(&OpCode) -> bool>(&self, predicate: P) -> bool {
for (opcode, _) in &self.code {
for opcode in &self.code {
if predicate(opcode) {
return true;
}
@ -111,242 +137,219 @@ impl VmCode {
}
impl<'code> Vm<'code> {
pub fn load(code: &'code VmCode, registers: Registers) -> Self {
Vm { code, registers }
pub fn load(code: &'code VmCode, registers: Registers, stack: &'code mut VmStack) -> Self {
Vm {
code,
registers,
stack,
}
}
pub fn run(&self) -> VmOutput {
pub fn run(&mut self) -> &mut Self {
// Arithmetic operations for `ArithmeticValue`s
fn operations_as_integer(
op: &ast::BinaryArithmeticOperator,
left_operand: i64,
right_operand: i64,
) -> ArithmeticValue {
match op {
ast::BinaryArithmeticOperator::Times => {
ArithmeticValue::Integer(left_operand * right_operand)
}
ast::BinaryArithmeticOperator::Divide => {
if left_operand % right_operand == 0 {
ArithmeticValue::Integer(left_operand / right_operand)
} else {
ArithmeticValue::Floating(left_operand as f64 / right_operand as f64)
}
}
ast::BinaryArithmeticOperator::Plus => {
ArithmeticValue::Integer(left_operand + right_operand)
}
ast::BinaryArithmeticOperator::Minus => {
ArithmeticValue::Integer(left_operand - right_operand)
}
ast::BinaryArithmeticOperator::Xor => {
ArithmeticValue::Integer(left_operand ^ right_operand)
}
ast::BinaryArithmeticOperator::Pow => {
if right_operand > 0 {
ArithmeticValue::Integer(left_operand.pow(right_operand as u32))
} else {
ArithmeticValue::Floating((left_operand as f64).powi(right_operand as i32))
}
}
}
}
fn operations_as_floating(
op: &ast::BinaryArithmeticOperator,
left_operand: f64,
right_operand: f64,
) -> ArithmeticValue {
match op {
ast::BinaryArithmeticOperator::Times => {
ArithmeticValue::Floating(left_operand * right_operand)
}
ast::BinaryArithmeticOperator::Divide => {
ArithmeticValue::Floating(left_operand as f64 / right_operand as f64)
}
ast::BinaryArithmeticOperator::Plus => {
ArithmeticValue::Floating(left_operand + right_operand)
}
ast::BinaryArithmeticOperator::Minus => {
ArithmeticValue::Floating(left_operand - right_operand)
}
ast::BinaryArithmeticOperator::Xor => {
ArithmeticValue::Integer(left_operand as i64 ^ right_operand as i64)
}
ast::BinaryArithmeticOperator::Pow => {
ArithmeticValue::Floating(left_operand.powf(right_operand))
}
}
}
fn comparison<T: std::cmp::PartialOrd>(
op: &ComparisonOperator,
left_operand: T,
right_operand: T,
) -> bool {
match op {
ast::ComparisonOperator::GreaterOrEqual => left_operand.ge(&right_operand),
ast::ComparisonOperator::LessOrEqual => left_operand.le(&right_operand),
ast::ComparisonOperator::GreaterThan => left_operand.gt(&right_operand),
ast::ComparisonOperator::LessThan => left_operand.lt(&right_operand),
ast::ComparisonOperator::NotEqual => left_operand.ne(&right_operand),
ast::ComparisonOperator::Equal => left_operand.eq(&right_operand),
}
}
// Alias for convenience
let code = &self.code.code;
let registers = &self.registers;
let stack = &mut self.stack;
struct Resolver<'f> {
f: &'f dyn Fn(&Resolver, usize) -> VmOutput,
}
stack.reset();
let resolver = Resolver {
f: &|resolver: &Resolver, op_index: usize| -> VmOutput {
let (opcode, offset) = &code[op_index];
match opcode {
OpCode::UnaryBooleanOperator(op) => match op {
for opcode in code.iter().rev() {
match opcode {
OpCode::UnaryBooleanOperator(op) => {
let operand = stack.boolean_stack.pop().unwrap();
match op {
ast::UnaryBooleanOperator::Not => {
let value = (resolver.f)(resolver, op_index + 1);
match value {
VmOutput::Arithmetic(_) => panic!("Bad bytecode! Unary operator is followed by arithmetic resolution."),
VmOutput::Boolean(value) => VmOutput::Boolean(!value),
}
}
},
OpCode::ComparisonOperator(op) => {
let left_operand = match (resolver.f)(resolver, op_index + 1) {
VmOutput::Arithmetic(value) => value,
VmOutput::Boolean(_) => panic!(
"Bad bytecode! Left operand of arithmetic operator is boolean."
),
};
let right_operand = match (resolver.f)(resolver, op_index + offset) {
VmOutput::Arithmetic(value) => value,
VmOutput::Boolean(_) => panic!(
"Bad bytecode! Right operand of arithmetic operator is boolean."
),
};
fn comparison<T: std::cmp::PartialOrd>(
op: &ComparisonOperator,
left_operand: T,
right_operand: T,
) -> VmOutput {
VmOutput::Boolean(match op {
ast::ComparisonOperator::GreaterOrEqual => {
left_operand.ge(&right_operand)
}
ast::ComparisonOperator::LessOrEqual => {
left_operand.le(&right_operand)
}
ast::ComparisonOperator::GreaterThan => {
left_operand.gt(&right_operand)
}
ast::ComparisonOperator::LessThan => {
left_operand.lt(&right_operand)
}
ast::ComparisonOperator::NotEqual => {
left_operand.ne(&right_operand)
}
ast::ComparisonOperator::Equal => left_operand.eq(&right_operand),
})
};
match left_operand {
ArithmeticValue::Integer(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
comparison(op, left_operand, right_operand)
}
ArithmeticValue::Floating(right_operand) => {
comparison(op, left_operand as f64, right_operand)
}
},
ArithmeticValue::Floating(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
comparison(op, left_operand, right_operand as f64)
}
ArithmeticValue::Floating(right_operand) => {
comparison(op, left_operand, right_operand)
}
},
stack.boolean_stack.push(!operand);
}
}
OpCode::BinaryArithmeticOperator(op) => {
let left_operand = match (resolver.f)(resolver, op_index + 1) {
VmOutput::Arithmetic(value) => value,
VmOutput::Boolean(_) => panic!(
"Bad bytecode! Left operand of arithmetic operator is boolean."
),
};
let right_operand = match (resolver.f)(resolver, op_index + offset) {
VmOutput::Arithmetic(value) => value,
VmOutput::Boolean(_) => panic!(
"Bad bytecode! Right operand of arithmetic operator is boolean."
),
};
let operations_as_integer = |left_operand: i64, right_operand: i64| match op
{
ast::BinaryArithmeticOperator::Times => {
ArithmeticValue::Integer(left_operand * right_operand)
}
ast::BinaryArithmeticOperator::Divide => {
if left_operand % right_operand == 0 {
ArithmeticValue::Integer(left_operand / right_operand)
} else {
ArithmeticValue::Floating(
left_operand as f64 / right_operand as f64,
)
}
}
ast::BinaryArithmeticOperator::Plus => {
ArithmeticValue::Integer(left_operand + right_operand)
}
ast::BinaryArithmeticOperator::Minus => {
ArithmeticValue::Integer(left_operand - right_operand)
}
ast::BinaryArithmeticOperator::Xor => {
ArithmeticValue::Integer(left_operand ^ right_operand)
}
ast::BinaryArithmeticOperator::Pow => {
if right_operand > 0 {
ArithmeticValue::Integer(left_operand.pow(right_operand as u32))
} else {
ArithmeticValue::Floating(
(left_operand as f64).powi(right_operand as i32),
)
}
}
};
let operations_as_floating =
|left_operand: f64, right_operand: f64| match op {
ast::BinaryArithmeticOperator::Times => {
ArithmeticValue::Floating(left_operand * right_operand)
}
ast::BinaryArithmeticOperator::Divide => ArithmeticValue::Floating(
left_operand as f64 / right_operand as f64,
),
ast::BinaryArithmeticOperator::Plus => {
ArithmeticValue::Floating(left_operand + right_operand)
}
ast::BinaryArithmeticOperator::Minus => {
ArithmeticValue::Floating(left_operand - right_operand)
}
ast::BinaryArithmeticOperator::Xor => ArithmeticValue::Integer(
left_operand as i64 ^ right_operand as i64,
),
ast::BinaryArithmeticOperator::Pow => {
ArithmeticValue::Floating(left_operand.powf(right_operand))
}
};
VmOutput::Arithmetic(match left_operand {
ArithmeticValue::Integer(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
operations_as_integer(left_operand, right_operand)
}
ArithmeticValue::Floating(right_operand) => {
operations_as_floating(left_operand as f64, right_operand)
}
},
ArithmeticValue::Floating(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
operations_as_floating(left_operand, right_operand as f64)
}
ArithmeticValue::Floating(right_operand) => {
operations_as_floating(left_operand, right_operand)
}
},
})
}
OpCode::UnaryArithmeticOperator(op) => {
let value = match (resolver.f)(resolver, op_index + 1) {
VmOutput::Arithmetic(value) => value,
VmOutput::Boolean(_) => panic!("Bad bytecode! Arithmetic unary operator followed by boolean resolution."),
};
VmOutput::Arithmetic(match op {
ast::UnaryArithmeticOperator::Negative => match value {
ArithmeticValue::Integer(value) => ArithmeticValue::Integer(-value),
ArithmeticValue::Floating(value) => {
ArithmeticValue::Floating(-value)
}
},
ast::UnaryArithmeticOperator::Ham => {
ArithmeticValue::Integer(match value {
ArithmeticValue::Integer(value) => value.count_ones() as i64,
ArithmeticValue::Floating(value) => {
(value as u64).count_ones() as i64
}
})
}
ast::UnaryArithmeticOperator::Sqrt => {
ArithmeticValue::Floating(match value {
ArithmeticValue::Integer(value) => (value as f64).sqrt(),
ArithmeticValue::Floating(value) => value.sqrt(),
})
}
})
}
OpCode::BinaryBooleanOperator(op) => {
let left_operand = match (resolver.f)(resolver, op_index + 1) {
VmOutput::Boolean(value) => value,
VmOutput::Arithmetic(_) => panic!(
"Bad bytecode! Left operand of boolean operator is arithmetic."
),
};
let right_operand = match (resolver.f)(resolver, op_index + offset) {
VmOutput::Boolean(value) => value,
VmOutput::Arithmetic(_) => panic!(
"Bad bytecode! Right operand of boolean operator is arithmetic."
),
};
VmOutput::Boolean(match op {
ast::BinaryBooleanOperator::And => left_operand & right_operand,
ast::BinaryBooleanOperator::Or => left_operand | right_operand,
ast::BinaryBooleanOperator::Xor => left_operand ^ right_operand,
})
}
OpCode::Variable(var) => {
VmOutput::Arithmetic(ArithmeticValue::Integer(match var {
ast::Variable::X => registers.x,
ast::Variable::Y => registers.y,
ast::Variable::N => registers.n,
ast::Variable::P => registers.p,
ast::Variable::K => registers.k,
}))
}
OpCode::Literal(lit) => VmOutput::Arithmetic(ArithmeticValue::Integer(*lit)),
}
},
};
OpCode::BinaryArithmeticOperator(op) => {
let left_operand = stack.arithmetic_stack.pop().unwrap();
let right_operand = stack.arithmetic_stack.pop().unwrap();
let value = match left_operand {
ArithmeticValue::Integer(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
operations_as_integer(op, left_operand, right_operand)
}
ArithmeticValue::Floating(right_operand) => {
operations_as_floating(op, left_operand as f64, right_operand)
}
},
ArithmeticValue::Floating(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
operations_as_floating(op, left_operand, right_operand as f64)
}
ArithmeticValue::Floating(right_operand) => {
operations_as_floating(op, left_operand, right_operand)
}
},
};
stack.arithmetic_stack.push(value);
}
OpCode::ComparisonOperator(op) => {
let left_operand = stack.arithmetic_stack.pop().unwrap();
let right_operand = stack.arithmetic_stack.pop().unwrap();
let value = match left_operand {
ArithmeticValue::Integer(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
comparison(op, left_operand, right_operand)
}
ArithmeticValue::Floating(right_operand) => {
comparison(op, left_operand as f64, right_operand)
}
},
ArithmeticValue::Floating(left_operand) => match right_operand {
ArithmeticValue::Integer(right_operand) => {
comparison(op, left_operand, right_operand as f64)
}
ArithmeticValue::Floating(right_operand) => {
comparison(op, left_operand, right_operand)
}
},
};
stack.boolean_stack.push(value);
}
OpCode::UnaryArithmeticOperator(op) => {
let operand = stack.arithmetic_stack.pop().unwrap();
let value = match op {
ast::UnaryArithmeticOperator::Negative => match operand {
ArithmeticValue::Integer(operand) => ArithmeticValue::Integer(-operand),
ArithmeticValue::Floating(operand) => {
ArithmeticValue::Floating(-operand)
}
},
ast::UnaryArithmeticOperator::Ham => {
ArithmeticValue::Integer(match operand {
ArithmeticValue::Integer(operand) => operand.count_ones() as i64,
ArithmeticValue::Floating(operand) => {
(operand.round() as i64).count_ones() as i64
}
})
}
ast::UnaryArithmeticOperator::Sqrt => {
ArithmeticValue::Floating(match operand {
ArithmeticValue::Integer(operand) => (operand as f64).sqrt(),
ArithmeticValue::Floating(operand) => operand.sqrt(),
})
}
};
stack.arithmetic_stack.push(value);
}
OpCode::BinaryBooleanOperator(op) => {
let left_operand = stack.boolean_stack.pop().unwrap();
let right_operand = stack.boolean_stack.pop().unwrap();
let value = match op {
ast::BinaryBooleanOperator::And => left_operand & right_operand,
ast::BinaryBooleanOperator::Or => left_operand | right_operand,
ast::BinaryBooleanOperator::Xor => left_operand ^ right_operand,
};
stack.boolean_stack.push(value);
}
OpCode::Variable(variable) => {
let value = ArithmeticValue::Integer(match variable {
ast::Variable::X => registers.x,
ast::Variable::Y => registers.y,
ast::Variable::N => registers.n,
ast::Variable::P => registers.p,
ast::Variable::K => registers.k,
});
stack.arithmetic_stack.push(value);
}
OpCode::Literal(literal) => {
stack
.arithmetic_stack
.push(ArithmeticValue::Integer(*literal));
}
}
}
self
}
(resolver.f)(&resolver, 0)
pub fn output_bool(&mut self) -> Result<bool, ()> {
self.stack.boolean_stack.pop().ok_or(())
}
#[allow(unused)]
pub fn output_arithmetic(&mut self) -> Result<ArithmeticValue, ()> {
self.stack.arithmetic_stack.pop().ok_or(())
}
}
@ -356,28 +359,32 @@ fn compile_expression(expression: Expression, code: &mut Vec<Bytecode>) -> usize
Expression::Boolean(expression) => match expression {
ast::BooleanExpression::BinaryBooleanConjunction(expression) => {
let expression = *expression;
code.push((OpCode::BinaryBooleanOperator(expression.operator), 0));
// code.push((OpCode::BinaryBooleanOperator(expression.operator), 0));
code.push(OpCode::BinaryBooleanOperator(expression.operator));
let index = code.len() - 1;
let left_operand_size =
compile_expression(Expression::Boolean(expression.left_operand), code);
let right_operand_size =
compile_expression(Expression::Boolean(expression.right_operand), code);
code[index].1 = left_operand_size + 1;
// code[index].1 = left_operand_size + 1;
return 1 + left_operand_size + right_operand_size;
}
ast::BooleanExpression::UnaryBooleanConjunction(expression) => {
let expression = *expression;
code.push((OpCode::UnaryBooleanOperator(expression.operator), 0));
// code.push((OpCode::UnaryBooleanOperator(expression.operator), 0));
code.push(OpCode::UnaryBooleanOperator(expression.operator));
let operand_size =
compile_expression(Expression::Boolean(expression.operand), code);
return 1 + operand_size;
}
ast::BooleanExpression::ComparisonConjunction(expression) => {
code.push((OpCode::ComparisonOperator(expression.operator), 0));
// code.push((OpCode::ComparisonOperator(expression.operator), 0));
code.push(OpCode::ComparisonOperator(expression.operator));
let index = code.len() - 1;
let left_operand_size = match expression.left_operand {
ast::ArithmeticOperand::Literal(literal) => {
code.push((OpCode::Literal(literal), 0));
// code.push((OpCode::Literal(literal), 0));
code.push(OpCode::Literal(literal));
1_usize
}
ast::ArithmeticOperand::Expression(expression) => {
@ -386,28 +393,32 @@ fn compile_expression(expression: Expression, code: &mut Vec<Bytecode>) -> usize
};
let right_operand_size = match expression.right_operand {
ast::ArithmeticOperand::Literal(literal) => {
code.push((OpCode::Literal(literal), 0));
// code.push((OpCode::Literal(literal), 0));
code.push(OpCode::Literal(literal));
1_usize
}
ast::ArithmeticOperand::Expression(expression) => {
compile_expression(Expression::Arithmetic(*expression), code)
}
};
code[index].1 = left_operand_size + 1;
// code[index].1 = left_operand_size + 1;
return 1 + left_operand_size + right_operand_size;
}
},
Expression::Arithmetic(expression) => match expression {
ast::ArithmeticExpression::Variable(variable) => {
code.push((OpCode::Variable(variable), 0));
// code.push((OpCode::Variable(variable), 0));
code.push(OpCode::Variable(variable));
return 1;
}
ast::ArithmeticExpression::UnaryArithmeticConjunction(expression) => {
let expression = *expression;
code.push((OpCode::UnaryArithmeticOperator(expression.operator), 0));
// code.push((OpCode::UnaryArithmeticOperator(expression.operator), 0));
code.push(OpCode::UnaryArithmeticOperator(expression.operator));
let operand_size = match expression.operand {
ast::ArithmeticOperand::Literal(literal) => {
code.push((OpCode::Literal(literal), 0));
// code.push((OpCode::Literal(literal), 0));
code.push(OpCode::Literal(literal));
1_usize
}
ast::ArithmeticOperand::Expression(expression) => {
@ -417,11 +428,13 @@ fn compile_expression(expression: Expression, code: &mut Vec<Bytecode>) -> usize
return 1 + operand_size;
}
ast::ArithmeticExpression::BinaryArithmeticConjunction(expression) => {
code.push((OpCode::BinaryArithmeticOperator(expression.operator), 0));
// code.push((OpCode::BinaryArithmeticOperator(expression.operator), 0));
code.push(OpCode::BinaryArithmeticOperator(expression.operator));
let index = code.len() - 1;
let left_operand_size = match expression.left_operand {
ast::ArithmeticOperand::Literal(literal) => {
code.push((OpCode::Literal(literal), 0));
// code.push((OpCode::Literal(literal), 0));
code.push(OpCode::Literal(literal));
1_usize
}
ast::ArithmeticOperand::Expression(expression) => {
@ -430,14 +443,15 @@ fn compile_expression(expression: Expression, code: &mut Vec<Bytecode>) -> usize
};
let right_operand_size = match expression.right_operand {
ast::ArithmeticOperand::Literal(literal) => {
code.push((OpCode::Literal(literal), 0));
// code.push((OpCode::Literal(literal), 0));
code.push(OpCode::Literal(literal));
1_usize
}
ast::ArithmeticOperand::Expression(expression) => {
compile_expression(Expression::Arithmetic(*expression), code)
}
};
code[index].1 = left_operand_size + 1;
// code[index].1 = left_operand_size + 1;
return 1 + left_operand_size + right_operand_size;
}
},
@ -452,13 +466,48 @@ fn boolean_compilation_test() {
}
#[test]
fn run_test() {
fn test_vm_simple() {
let expression = parsing::parse_relation("(= (ham (^ x y)) (ham 1))");
if let Err(e) = expression {
println!("{}", e);
panic!();
}
let code = compile_boolean(expression.unwrap());
let vm = Vm::load(&code, Registers::load(0b_1011, 0b_1111, 10, 2, 3));
println!("{:?}", vm.run());
let mut stack = VmStack::from_code(&code);
let mut vm = Vm::load(
&code,
Registers::load(0b_1011, 0b_1111, 10, 2, 3),
&mut stack,
);
let output = vm.run().output_bool().unwrap();
assert_eq!(output, true);
let mut vm = Vm::load(
&code,
Registers::load(0b_1011, 0b_1110, 10, 2, 3),
&mut stack,
);
let output = vm.run().output_bool().unwrap();
assert_eq!(output, false);
}
#[test]
fn test_vm_contrived() {
let expression = parsing::parse_relation("and (= (ham (^ x y)) (ham (+ 3 x))) (> (* x y) 5)");
if let Err(e) = expression {
println!("{}", e);
panic!();
}
let code = compile_boolean(expression.unwrap());
let mut stack = VmStack::from_code(&code);
let as_rust = |x: u64, y: u64| ((x + 3).count_ones() == (x ^ y).count_ones()) && (x * y > 5);
for x in 0..(1 << 4) {
for y in 0..(1 << 4) {
let mut vm = Vm::load(&code, Registers::load(x, y, 10, 2, 3), &mut stack);
let output = vm.run().output_bool().unwrap();
let expected = as_rust(x, y);
assert_eq!(output, expected);
}
}
}

15
src/vm/parsing/mod.rs
View File

@ -323,6 +323,19 @@ fn rule_as_text(rule: &Rule) -> &'static str {
}
}
#[test]
fn parse_bad() {
match parse_relation("< ham x cheese") {
Err(e) => {
println!("{}", e);
}
Ok(ast) => {
println!("{:?}", ast);
panic!();
}
}
}
#[test]
fn parse_test() {
match parse_relation("< ham x 3") {
@ -331,7 +344,7 @@ fn parse_test() {
panic!();
}
Ok(ast) => {
println!("{:?}", ast)
println!("{:#?}", ast)
}
}
}

13
test/bounds.py
View File

@ -1,13 +0,0 @@
import adversary
from math import sqrt
prover = adversary.Prover("= (ham x) k", "= (ham y) (+ k 1)", "<= ham (^ x y) p")
bounds = prover.find_bounds(16, 5, 3);
lower_bound = sqrt(bounds.min_x_relations * bounds.min_y_relations / bounds.max_joint_relations)
print("m =", bounds.min_x_relations)
print(f"From x={bounds.single_bounding_x:b}")
print("m' =", bounds.min_y_relations)
print(f"From y={bounds.single_bounding_y:b}")
print("ℓ·ℓ' =", bounds.max_joint_relations)
print(f"From x={bounds.joint_bounding_x:b} and y={bounds.joint_bounding_y:b} and window={bounds.bounding_window:b}")
print(f"Query lower bounds = {lower_bound}")

962
timing_scaling.svg Normal file
View File

@ -0,0 +1,962 @@
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,320.994)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,320.994)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,320.994)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 400</text>
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 600</text>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,265.65)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#a0a0a4" stroke-opacity="1" stroke-dasharray="0.5,1" stroke-dashoffset="0" stroke-width="0.5" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
<polyline fill="none" vector-effect="none" points="52.5,204.5 58.5,204.5 " />
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
</g>
<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 800</text>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,22.1375,211.313)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#a0a0a4" stroke-opacity="1" stroke-dasharray="0.5,1" stroke-dashoffset="0" stroke-width="0.5" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
<polyline fill="none" vector-effect="none" points="52.5,150.5 58.5,150.5 " />
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
</g>
<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 1000</text>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,155.969)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
</g>
<g fill="none" stroke="#a0a0a4" stroke-opacity="1" stroke-dasharray="0.5,1" stroke-dashoffset="0" stroke-width="0.5" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
<polyline fill="none" vector-effect="none" points="52.5,95.5 58.5,95.5 " />
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
</g>
<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 1200</text>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,101.631)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#a0a0a4" stroke-opacity="1" stroke-dasharray="0.5,1" stroke-dashoffset="0" stroke-width="0.5" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="Sans" font-size="9" font-weight="400" font-style="normal"
>
<text fill="#000000" fill-opacity="1" stroke="none" xml:space="preserve" x="0" y="0" font-family="Sans" font-size="9" font-weight="400" font-style="normal"
> 1400</text>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,15.0938,46.2875)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#000000" stroke-opacity="1" stroke-width="1" stroke-linecap="square" stroke-linejoin="bevel" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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<g fill="none" stroke="#a0a0a4" stroke-opacity="1" stroke-dasharray="0.5,1" stroke-dashoffset="0" stroke-width="0.5" stroke-linecap="round" stroke-linejoin="round" transform="matrix(1.00625,0,0,1.00625,0,0)"
font-family="MS Shell Dlg 2" font-size="8.25" font-weight="400" font-style="normal"
>
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