abacus: bignum: add order comparisons

src/bignum/bignum.cc

@@ -38,6 +38,19 @@ bool BigNum::equal(BigNum const& rhs) const {
     return digits_ == rhs.digits_;
 }
 
+bool BigNum::less_than(BigNum const& rhs) const {
+    assert(is_canonicalized());
+    assert(rhs.is_canonicalized());
+
+    if (sign_ != rhs.sign_) {
+        return sign_ < rhs.sign_;
+    }
+
+    return std::lexicographical_compare(digits_.rbegin(), digits_.rend(),
+                                        rhs.digits_.rbegin(),
+                                        rhs.digits_.rend());
+}
+
 void BigNum::canonicalize() {
     auto const it = std::find_if(digits_.rbegin(), digits_.rend(),
                                  [](auto v) { return v != 0; });

src/bignum/bignum.hh

@@ -18,8 +18,25 @@ public:
         return !(lhs == rhs);
     }
 
+    friend bool operator<(BigNum const& lhs, BigNum const& rhs) {
+        return lhs.less_than(rhs);
+    }
+
+    friend bool operator>(BigNum const& lhs, BigNum const& rhs) {
+        return rhs < lhs;
+    }
+
+    friend bool operator<=(BigNum const& lhs, BigNum const& rhs) {
+        return !(lhs > rhs);
+    }
+
+    friend bool operator>=(BigNum const& lhs, BigNum const& rhs) {
+        return !(lhs < rhs);
+    }
+
 private:
     bool equal(BigNum const& rhs) const;
+    bool less_than(BigNum const& rhs) const;
 
     void canonicalize();
     bool is_canonicalized() const;