From 6e3c04a810ca0041bcc99bb297c9c2fa1b0da097 Mon Sep 17 00:00:00 2001
From: Andrew Kubera <andrewkubera@gmail.com>
Date: Fri, 28 Jul 2023 14:23:56 -0400
Subject: [PATCH] Reimplement ten_to_the

---
 src/lib.rs | 47 ++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 36 insertions(+), 11 deletions(-)

diff --git a/src/lib.rs b/src/lib.rs
index a1c23dc..9bd1170 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -102,27 +102,52 @@ mod parsing;
 pub mod rounding;
 pub use rounding::RoundingMode;
 
-#[inline(always)]
+/// Return 10^pow
+///
+/// Try to calculate this with fewest number of allocations
+///
 fn ten_to_the(pow: u64) -> BigInt {
     if pow < 20 {
-        BigInt::from(10u64.pow(pow as u32))
-    } else {
-        let (half, rem) = pow.div_rem(&16);
+        return BigInt::from(10u64.pow(pow as u32));
+    }
+
+    // linear case of 10^pow = 10^(19 * count + rem)
+    if pow < 590 {
+        let ten_to_nineteen = 10u64.pow(19);
 
-        let mut x = ten_to_the(half);
+        // count factors of 19
+        let (count, rem) = pow.div_rem(&19);
 
-        for _ in 0..4 {
-            x = &x * &x;
+        let mut res = BigInt::from(ten_to_nineteen);
+
+        for _ in 1..count {
+            res *= ten_to_nineteen;
         }
 
-        if rem == 0 {
-            x
-        } else {
-            x * ten_to_the(rem)
+        if rem != 0 {
+            res *= 10u64.pow(rem as u32);
         }
+
+        return res;
+    }
+
+    // use recursive algorithm where linear case might be too slow
+    let (quoteint, rem) = pow.div_rem(&16);
+    let x = ten_to_the(quoteint);
+
+    let x2 = &x * &x;
+    let x4 = &x2 * &x2;
+    let x8 = &x4 * &x4;
+    let res = &x8 * &x8;
+
+    if rem == 0 {
+        res
+    } else {
+        res * 10u64.pow(rem as u32)
     }
 }
 
+
 #[inline(always)]
 fn count_decimal_digits(int: &BigInt) -> u64 {
     if int.is_zero() {