From 3caf693ecf071eb8c018122236c0a01a88ef32b7 Mon Sep 17 00:00:00 2001
From: Hazel Levine <rose.hazel@protonmail.ch>
Date: Fri, 21 Feb 2020 15:38:59 -0500
Subject: [PATCH] problem 25

---
 Cargo.toml        |  1 +
 src/bin/prob25.rs | 35 +++++++++++++++++++++++++++++++++++
 2 files changed, 36 insertions(+)
 create mode 100644 src/bin/prob25.rs

diff --git a/Cargo.toml b/Cargo.toml
index ab780ff..b674eee 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -9,3 +9,4 @@ edition = "2018"
 [dependencies]
 num-bigint = "0.2"
 num-traits = "0.2"
+rug = "1.7.0"
diff --git a/src/bin/prob25.rs b/src/bin/prob25.rs
new file mode 100644
index 0000000..1923030
--- /dev/null
+++ b/src/bin/prob25.rs
@@ -0,0 +1,35 @@
+// Problem 25:
+//
+// What is the index of the first term in the Fibonacci sequence to contain
+// 1000 digits?
+
+extern crate rug;
+
+use rug::{ops::Pow, Float, Integer};
+
+const PHI: f64 = 1.618_033_988_749_895;
+
+// https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression
+// uses change of base as GMP doesn't implement log of a certain base
+fn fib_idx(n: Integer) -> Integer {
+    let phi = Float::with_val(64, PHI);
+
+    let to_ln: Float = n * Float::with_val(64, 5f64.sqrt()) + 0.5;
+    let ln_x: Float = to_ln.ln();
+    let ln_phi: Float = phi.ln();
+
+    (ln_x / ln_phi).floor().to_integer().unwrap() + 1
+}
+
+fn compute(n: u32) -> Integer {
+    let upper_limit: Integer = Integer::from(10).pow(n - 1);
+
+    fib_idx(upper_limit)
+}
+
+fn main() {
+    println!(
+        "the index of the smallest fibonacci number with 1000 digits is: {}",
+        compute(1000)
+    );
+}