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// Requires clap and statrs
use statrs::function::gamma::ln_gamma;
use std::f64::consts::E;
use clap::Parser;
struct LnGammaCache {
n: usize,
k: usize,
n_log: f64,
// contains [0, k] which represents [1, k+1]
lk_tab: Vec<f64>,
// contains [n-k, n]
hk_tab: Vec<f64>,
}
impl LnGammaCache {
fn precompute_ktab(&mut self, n: usize) {
for k in 0..=self.k {
self.lk_tab[k] = ln_gamma((k + 1) as f64);
self.hk_tab[k] = ln_gamma((n - k + 1) as f64);
}
}
fn new(n: usize, k: usize) -> Self {
let mut cache = LnGammaCache {
n,
k,
n_log: (n as f64).ln(),
lk_tab: vec![0f64; k+1],
hk_tab: vec![0f64; k+1],
};
cache.precompute_ktab(n);
cache
}
unsafe fn ln_gamma_unchecked(&self, i: usize) -> f64 {
unsafe {
if i <= self.k + 1 {
debug_assert!(i > 0, "Uncached call to ln_gamma");
return *self.lk_tab.get_unchecked(i - 1)
} else {
debug_assert!(self.n - self.k <= i && i <= self.n + 1, "Uncached call to ln_gamma");
return *self.hk_tab.get_unchecked(self.n - (i - 1))
}
}
}
}
// The performance is dependent heavily on the execution time of this function
// After many optimizations, powf is the most computationally expensive unit in this routine
fn evaluate_probability_log_gamma(
partition: &[usize],
k: usize,
n: usize,
maxpart: usize,
cache: &LnGammaCache,
) -> f64 {
let mut c0 = 0;
for i in 0..maxpart {
c0 += partition[i];
}
c0 = n - c0;
let log_probability = unsafe {
let mut log_denominator = (k as f64) * cache.n_log + cache.ln_gamma_unchecked(c0 + 1);
let log_numerator = cache.ln_gamma_unchecked(n + 1) + cache.ln_gamma_unchecked(k + 1);
for i in 0..maxpart {
log_denominator += cache.ln_gamma_unchecked(partition[i] + 1);
log_denominator += (partition[i] as f64) * cache.ln_gamma_unchecked(i + 2);
}
log_numerator - log_denominator
};
E.powf(log_probability)
}
fn evaluate_probability(
partition: &[usize],
probdist: &mut [f64],
k: usize,
n: usize,
maxpart: usize,
cache: &LnGammaCache
) {
let mut collisions = 0usize;
for i in 1..maxpart {
collisions += i * partition[i];
}
probdist[collisions] += evaluate_probability_log_gamma(partition, k, n, maxpart, cache);
}
fn generate_partitions_dfs(
partition: &mut [usize],
probdist: &mut [f64],
k: usize,
n: usize,
n_collisions: usize,
collision_ub: usize,
level_ub: &[usize],
cache: &LnGammaCache,
) {
if n_collisions > collision_ub {
return;
}
generate_partitions_dfs(partition, probdist, k, n, n_collisions + 1, collision_ub, level_ub, cache);
let mut n_subcomb = partition[0] / n_collisions;
n_subcomb = std::cmp::min(n_subcomb, level_ub[n_collisions - 1]);
for i in 1..=n_subcomb {
partition[0] -= i * n_collisions;
partition[n_collisions- 1] += i;
evaluate_probability(partition, probdist, k, n, n_collisions, cache);
generate_partitions_dfs(partition, probdist, k, n, n_collisions + 1, collision_ub, level_ub, cache);
partition[0] += i * n_collisions;
partition[n_collisions - 1] -= i;
}
}
fn generate_partitions(
k: usize,
n: usize,
collision_ub: usize,
level_ub: &[usize],
) -> Vec<f64> {
let mut partitions = vec![0usize; k];
let mut probdist = vec![0f64; k];
partitions[0] = k;
let cache = LnGammaCache::new(n, k);
if collision_ub > 0 {
evaluate_probability(&partitions, &mut probdist, k, n, 1, &cache);
}
if collision_ub > 1 {
generate_partitions_dfs(&mut partitions, &mut probdist, k, n, 2, collision_ub, level_ub, &cache);
}
return probdist;
}
fn parse_max_level_collisions(s: &str) -> Vec<usize> {
let mut max_sizes = Vec::new();
let mut add_token = |token: &str| {
let sz = match token.parse::<usize>() {
Ok(res) => res,
Err(err) => {
eprintln!("Failed to parse max sizes: {}", err);
std::process::exit(1);
}
};
max_sizes.push(sz);
};
let mut i = 0usize;
while let Some(j) = s[i..].find(',') {
add_token(&s[i..i+j]);
i += j + 1;
}
add_token(&s[i..]);
max_sizes
}
#[derive(Parser,Debug)]
#[command(author, version, about)]
struct Args {
n: usize,
k: usize,
// Only consider collisions up until this bound (inclusive)
// For collision_ub=4, combinations of zero, one, two, three, and four
// collisions are calculated
collision_ub: Option<usize>,
// Only consider collisions up to level_ub_l collisions for level l.
// For example, if level_ub_3 = 10 this means we only consider scenarios
// in which three hashes co-collide up to 10 times
level_ub: Option<String>,
}
fn main() {
let args = Args::parse();
if args.n == 0 || args.k == 0 {
return;
}
if args.k >= args.n {
eprintln!("This computation is optimized for k < n.");
std::process::exit(1);
}
let collision_ub = match args.collision_ub {
Some(ub) => {
if ub > args.k {
eprintln!("collision_ub={} hashes cannot collide if only k={} values are hashed", ub, args.k);
}
ub
},
None => args.k
};
let level_ub: Vec<usize>;
if let Some(ub_spec) = args.level_ub {
level_ub = parse_max_level_collisions(&ub_spec[..]);
if level_ub.len() != collision_ub {
eprintln!("Please specify {} bounds for each level", collision_ub);
std::process::exit(1);
}
} else {
level_ub = vec![args.k; collision_ub + 1];
}
let probdist = generate_partitions(args.k, args.n, collision_ub, &level_ub[..]);
for i in 0..probdist.len() {
println!("{},{}", i, probdist[i]);
}
}
|
