From d03584e8b6562b6b53e38af5eda2a172d45b812a Mon Sep 17 00:00:00 2001 From: jbb01 <32650546+jbb01@users.noreply.github.com> Date: Wed, 10 Sep 2025 11:30:54 +0200 Subject: [PATCH] add 05_what_the_bf.rs --- src/bin/05_what_the_bf.rs | 5354 +++++++++++++++++++++++++++++++++++++ 1 file changed, 5354 insertions(+) create mode 100644 src/bin/05_what_the_bf.rs diff --git a/src/bin/05_what_the_bf.rs b/src/bin/05_what_the_bf.rs new file mode 100644 index 0000000..7cac38a --- /dev/null +++ b/src/bin/05_what_the_bf.rs @@ -0,0 +1,5354 @@ +#![allow(dead_code)] +use lib::compute_async; + +const N0: u128 = 11538000000u128; +const X0: u128 = 540610237213u128; + +fn main() { + let d = 1000000000000 - N0 - 1; + + let n = N0 + d; + let x = f_n(100 * d); + + println!("n = {n}"); + println!("x = {x}"); +} + +fn main_cycle_detection() { + compute_async(|tx| { + // brent's algorithm + let mut power: u128 = 1; + let mut lam: u128 = 1; + let mut tortoise = X0; + let mut hare = f(X0); + + // button problem + let mut i: u128 = 1; + let mut n = N0; + + while tortoise != hare { + // time to start a new power of two? + if power == lam { + tortoise = hare; + power *= 2; + lam = 0; + } + hare = f(hare); + lam += 1; + + // button problem + i += 1; + if i % 100 == 0 { + n += 1; + + if n % 1_000_000 == 0 { + tx.send((n, hare)).unwrap(); + } + } + } + + // Find the position of the first repetition of length lambda + tortoise = X0; + hare = X0; + for _ in 0..lam { + hare = f(hare) + } + // the distance between the hare and tortoise is now lambda + + // next, the hare and tortoise move at same speed until they agree + let mut mu = 0; + while tortoise != hare { + tortoise = f(tortoise); + hare = f(hare); + mu += 1; + } + + println!("mu = {mu}"); + println!("lam = {lam}"); + }); +} + + +const A: u128 = 909_090_909_091u128; // (10 * b + 1) / 11 +const B: u128 = 1_000_000_000_000u128; // 10^12 +const C: u128 = 999_999_999_989u128; // b - 11 +const D: u128 = 999_999_999_999u128; // b - 1 +fn f(mut x: u128) -> u128 { + x = x * A % B; + x = (x * C + D) / B; + x +} + + +const MU: u128 = 0; +const LAM: u128 = 249_999_999_997; +/// Computes `f(f(...f(X0)...))` where `f` is applied `n` times. +fn f_n(n: u128) -> u128 { + let n = n % LAM; + + let search = N0 + n / 100; + let (idx, value) = match F_DATA.binary_search_by_key(&search, |(n, _)| *n) { + Ok(i) => F_DATA[i], + Err(i) => F_DATA[i - 1], + }; + + let mut value = value; + let limit = 100 * N0 + n - 100 * idx; + for _ in 0..limit { + value = f(value); + } + + value +} + +const F_DATA: &[(u128, u128)] = &[ + (11538000000, 540610237213), + (11539000000, 525319061659), + (11540000000, 411624296534), + (11541000000, 854355037022), + (11542000000, 184063696259), + (11543000000, 906009215077), + (11544000000, 178353134835), + (11545000000, 240067837204), + (11546000000, 475846971706), + (11547000000, 860976969332), + (11548000000, 333912885718), + (11549000000, 479252441539), + (11550000000, 873095279736), + (11551000000, 225104858304), + 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