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estimators.rs
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/
estimators.rs
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use std::cmp;
pub type CounterType = u8;
pub fn counts(registers: &[CounterType], q: usize) -> Vec<u16> {
let mut counts = vec![0; q + 2];
for k in registers {
counts[*k as usize] += 1;
}
counts
}
#[allow(clippy::many_single_char_names)]
pub fn mle(counts: &[u16], p: usize, q: usize, relerr: f64) -> f64 {
let m = 1 << p;
if counts[q + 1] == m {
return std::f64::INFINITY;
}
let (k_min, _) = counts.iter().enumerate().find(|(_, v)| **v != 0).unwrap();
let k_min_prime = cmp::max(1, k_min);
let (k_max, _) = counts
.iter()
.enumerate()
.rev()
.find(|(_, v)| **v != 0)
.unwrap();
let k_max_prime = cmp::min(q, k_max as usize);
let mut z = 0.;
for i in num_iter::range_step_inclusive(k_max_prime as i32, k_min_prime as i32, -1) {
z = 0.5 * z + counts[i as usize] as f64;
}
// ldexp(x, i) = x * (2 ** i)
z *= 2f64.powi(-(k_min_prime as i32));
let mut c_prime = counts[q + 1];
if q >= 1 {
c_prime += counts[k_max_prime];
}
let mut g_prev = 0.;
let a = z + (counts[0] as f64);
let b = z + (counts[q + 1] as f64) * 2f64.powi(-(q as i32));
let m_prime = (m - counts[0]) as f64;
let mut x = if b <= 1.5 * a {
// weak lower bound (47)
m_prime / (0.5 * b + a)
} else {
// strong lower bound (46)
m_prime / (b * (1. + b / a).ln())
};
let mut delta_x = x;
let del = relerr / (m as f64).sqrt();
while delta_x > x * del {
// secant method iteration
let kappa: usize = az::saturating_cast(2. + x.log2().floor());
// x_prime in [0, 0.25]
let mut x_prime = x * 2f64.powi(-(cmp::max(k_max_prime, kappa) as i32) - 1);
let x_pp = x_prime * x_prime;
// Taylor approximation (58)
let mut h = x_prime - (x_pp / 3.) + (x_pp * x_pp) * (1. / 45. - x_pp / 472.5);
// Calculate h(x/2^k), see (56), at this point x_prime = x / (2^(k+2))
for _k in num_iter::range_step_inclusive(kappa as i32 - 1, k_max_prime as i32, -1) {
let h_prime = 1. - h;
h = (x_prime + h * h_prime) / (x_prime + h_prime);
x_prime += x_prime;
}
// compare (53)
let mut g = c_prime as f64 * h;
for k in num_iter::range_step_inclusive(k_max_prime as i32 - 1, k_min_prime as i32, -1) {
let h_prime = 1. - h;
// Calculate h(x/2^k), see (56), at this point x_prime = x / (2^(k+2))
h = (x_prime + h * h_prime) / (x_prime + h_prime);
g += counts[k as usize] as f64 * h;
x_prime += x_prime;
}
g += x * a;
delta_x = if (g > g_prev) | (m_prime >= g) {
// see (54)
delta_x * (m_prime - g) / (g - g_prev)
} else {
0.
};
x += delta_x;
g_prev = g
}
m as f64 * x
}
/// Calculate the joint maximum likelihood of A and B.
///
/// Returns a tuple (only in A, only in B, intersection)
pub fn joint_mle(
k1: &[CounterType],
k2: &[CounterType],
p: usize,
q: usize,
) -> (usize, usize, usize) {
let mut c1 = vec![0; q + 2];
let mut c2 = vec![0; q + 2];
let mut cu = vec![0; q + 2];
let mut cg1 = vec![0; q + 2];
let mut cg2 = vec![0; q + 2];
let mut ceq = vec![0; q + 2];
for (k1_, k2_) in k1.iter().zip(k2.iter()) {
match k1_.cmp(k2_) {
cmp::Ordering::Less => {
c1[*k1_ as usize] += 1;
cg2[*k2_ as usize] += 1;
}
cmp::Ordering::Greater => {
cg1[*k1_ as usize] += 1;
c2[*k2_ as usize] += 1;
}
cmp::Ordering::Equal => {
ceq[*k1_ as usize] += 1;
}
}
cu[*cmp::max(k1_, k2_) as usize] += 1;
}
for (i, (v, u)) in cg1.iter().zip(ceq.iter()).enumerate() {
c1[i] += v + u;
}
for (i, (v, u)) in cg2.iter().zip(ceq.iter()).enumerate() {
c2[i] += v + u;
}
let c_ax = mle(&c1, p, q, 0.01);
let c_bx = mle(&c2, p, q, 0.01);
let c_abx = mle(&cu, p, q, 0.01);
let mut counts_axb_half = vec![0u16; q + 2];
let mut counts_bxa_half = vec![0u16; q + 2];
counts_axb_half[q] = k1.len() as u16;
counts_bxa_half[q] = k2.len() as u16;
for _q in 0..q {
counts_axb_half[_q] = cg1[_q] + ceq[_q] + cg2[_q + 1];
debug_assert!(counts_axb_half[q] >= counts_axb_half[_q]);
counts_axb_half[q] -= counts_axb_half[_q];
counts_bxa_half[_q] = cg2[_q] + ceq[_q] + cg1[_q + 1];
debug_assert!(counts_bxa_half[q] >= counts_bxa_half[_q]);
counts_bxa_half[q] -= counts_bxa_half[_q];
}
let c_axb_half = mle(&counts_axb_half, p, q - 1, 0.01);
let c_bxa_half = mle(&counts_bxa_half, p, q - 1, 0.01);
let cx1 = 1.5 * c_bx + 1.5 * c_ax - c_bxa_half - c_axb_half;
let cx2 = 2. * (c_bxa_half + c_axb_half) - 3. * c_abx;
(
(c_abx - c_bx) as usize,
(c_abx - c_ax) as usize,
cmp::max(0, (0.5 * (cx1 + cx2)) as usize),
)
}