From a8de0cfa88249679a152f25fd2c54f9157424515 Mon Sep 17 00:00:00 2001
From: Timothy Warren <twarren@nabancard.com>
Date: Wed, 11 Mar 2020 10:52:49 -0400
Subject: [PATCH] Add borrowing for subtraction

---
 src/bigint.rs | 57 ++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 50 insertions(+), 7 deletions(-)

diff --git a/src/bigint.rs b/src/bigint.rs
index 6f4a7f6..3e8b78b 100644
--- a/src/bigint.rs
+++ b/src/bigint.rs
@@ -1,6 +1,7 @@
 #![allow(unused_variables)]
 //! \[WIP\] Arbitrarily large integers
 use crate::num::*;
+use crate::num::Sign::*;
 use core::ops::{
     Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Not, Rem, RemAssign, Sub, SubAssign,
 };
@@ -100,6 +101,10 @@ impl Add for BigInt {
 
     fn add(self, rhs: Self) -> Self::Output {
         // @TODO: handle signs
+        if self.sign == Positive && rhs.sign == Negative {
+            return self - -rhs;
+        }
+
         let mut out = BigInt::new_empty();
 
         let u_digits = self.inner.len();
@@ -153,16 +158,37 @@ impl Sub for BigInt {
             let a = *self.inner.get(i).unwrap_or(&0usize);
             let b = *rhs.inner.get(i).unwrap_or(&0usize);
 
-            if a > b {
-                out.inner.push(a - b - borrow);
+            if a == 0 && b == 0 {
+                continue;
+            }
+
+            if a > 0 && (a - borrow) >= b {
+                let res = a - b - borrow;
+
+                // Don't add an extra zero if you borrowed everything
+                // from the most significant digit
+                if res == 0 && digits > 0 && i == digits -1 {
+                    return out;
+                }
+
+                out.inner.push(res);
                 borrow = 0;
-            } else if a < b {
-                todo!();
-            } else {
-                todo!();
+            } else  {
+                // To prevent subtraction overflow, the max borrowed
+                // value is usize::MAX. The rest of the borrowed value
+                // will be added on afterwords.
+                // In base ten, this would be like:
+                // 18 - 9 = 9-9 + 9
+                let rem = (a + 1) - borrow;
+                let res = (core::usize::MAX - b) + rem;
+                out.inner.push(res);
+
+                borrow = 1;
             }
         }
 
+        out.trim_zeros();
+
         out
     }
 }
@@ -368,9 +394,26 @@ mod tests {
 
         let diff = a - b;
         assert_eq!(
-            diff.inner[0],
+            diff.clone().inner[0],
             core::usize::MAX - core::u16::MAX as usize
         );
+        assert_eq!(diff.inner.len(), 1);
+    }
+
+    #[test]
+    fn test_sub_borrow() {
+        let a = BigInt {
+            inner: vec![0, 1],
+            sign: Positive
+        };
+
+        let b = BigInt::from(2);
+        let diff = a - b;
+        assert_eq!(diff.clone().inner.len(), 1, "{:#?}", diff.clone());
+        assert_eq!(
+            diff.inner[0],
+            core::usize::MAX - 1
+        );
     }
 
     #[test]