Vectorize log PDF calculation

[not522]

Calculating the log PDF is a computationally intensive task within TPE, and improving its performance is crucial. This PR addresses the issue by preventing branching operations from occurring during these heavy computations, thereby achieving speed improvements.

Benchmark

• master

n_params  n_trials    total [ms]  per trial [us]
      40       500         410.3         820.5
      40      1000        1457.6        1457.6
      40      2000        5691.5        2845.7

• PR

n_params  n_trials    total [ms]  per trial [us]
      40       500         260.1         520.1
      40      1000         867.1         867.1
      40      2000        3334.2        1667.1

Details

use std::hint::black_box;
use std::time::{Duration, Instant};

use rustuna_core::storage::InMemoryStorage;
use rustuna_core::study::{create_study, Direction};
use rustuna_core::Result;
use rustuna_sampler::tpe::TpeSampler;

const N_TRIALS: [usize; 3] = [500, 1000, 2000];
const N_PARAMS: [usize; 1] = [40];

fn run_study(n_trials: usize, n_params: usize) -> Result<Duration> {
    let storage = InMemoryStorage::new();
    let study = create_study(
        "tpe-benchmark",
        storage,
        TpeSampler::seed_from_u64(0),
        vec![Direction::Minimize],
    )?;

    let start = Instant::now();
    study.optimize(
        |mut trial| {
            let mut value = 0.0;
            for i in 0..n_params {
                let x = trial.suggest_float(&format!("x{i}"), -10.0, 10.0)?;
                value += x * x;
            }
            Ok(vec![black_box(value)])
        },
        n_trials,
    )?;
    Ok(start.elapsed())
}

fn main() -> Result<()> {
    println!(
        "{:>8}  {:>8}  {:>12}  {:>12}",
        "n_params", "n_trials", "total [ms]", "per trial [us]"
    );
    for n_params in N_PARAMS {
        for n_trials in N_TRIALS {
            let duration = run_study(n_trials, n_params)?;
            println!(
                "{:>8}  {:>8}  {:>12.1}  {:>12.1}",
                n_params,
                n_trials,
                duration.as_secs_f64() * 1e3,
                duration.as_secs_f64() * 1e6 / n_trials as f64,
            );
        }
    }
    Ok(())
}

[c-bata]

@y0z Could you review this PR?