From 9b0903f5d63f99a06efd1732010947eebd3b7669 Mon Sep 17 00:00:00 2001
From: kishanshukla-2307 <2307kishanshukla@gmail.com>
Date: Mon, 2 Mar 2020 23:36:55 +0530
Subject: [PATCH 1/2] Modified multiplication function. Base INT_MAX now works
 for multiplication

---
 include/real/exact_number.hpp | 36 +++++++++++++++++++++++++----------
 1 file changed, 26 insertions(+), 10 deletions(-)

diff --git a/include/real/exact_number.hpp b/include/real/exact_number.hpp
index 5080259..7e07aca 100644
--- a/include/real/exact_number.hpp
+++ b/include/real/exact_number.hpp
@@ -145,6 +145,20 @@ namespace boost {
                 this->normalize();
             }
 
+            // returns (a+b)%mod
+            T addn(T a, T b, T mod){
+            	T min = std::min(a, b);
+            	T max = std::max(a, b);
+            	if(max<(mod-min)){
+            		return (max+min);
+            	}
+            	if(mod%2==0){
+            		return (max-mod/2)-(mod/2-min);
+            	}else{
+            		return (max-mod/2)-(mod/2-min)-1;
+            	}
+            }
+
             //Returns (a*b)%mod
             T mulmod(T a, T b, T mod) 
             { 
@@ -154,10 +168,10 @@ namespace boost {
                 { 
                     // If b is odd, add 'a' to result 
                     if (b % 2 == 1) 
-                        res = (res + a) % mod; 
+                        res = addn(res, a, mod); 
             
                     // Multiply 'a' with 2 
-                    a = (a * 2) % mod; 
+                    a = addn(a, a, mod); 
             
                     // Divide b by 2 
                     b /= 2; 
@@ -175,17 +189,19 @@ namespace boost {
                 // a < c, rem < c.
                 while (b != 0) {
                     if (b & 1) {
-                        rem += a;
-                        if (rem >= c) {
-                            rem -= c;
-                            res++;
+                        if(rem >= (c-a)){
+                        	rem = addn(rem, a, c);
+                        	res++;
+                        }else{
+                        	rem = rem + a;
                         }
                     }
                     b /= 2;
-                    a *= 2;
-                    if (a >= c) {
-                        a -= c;
-                        res += b;
+                    if(a >= (c-a)){
+                    	a = addn(a, a, c);
+                    	res += b;
+                    }else{
+                    	a *= 2;
                     }
                 }
                 return res;

From 56020cfdb88c4e1517b7064ee79d3e0c3f68a321 Mon Sep 17 00:00:00 2001
From: kishanshukla-2307 <2307kishanshukla@gmail.com>
Date: Thu, 12 Mar 2020 19:33:40 +0530
Subject: [PATCH 2/2] added test file to check overflow in multiplication at
 base=INT_MAX

---
 test/real_overflow_multiplication_test.cpp | 48 ++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 test/real_overflow_multiplication_test.cpp

diff --git a/test/real_overflow_multiplication_test.cpp b/test/real_overflow_multiplication_test.cpp
new file mode 100644
index 0000000..f21efd6
--- /dev/null
+++ b/test/real_overflow_multiplication_test.cpp
@@ -0,0 +1,48 @@
+#include <catch2/catch.hpp>
+// #include <map>
+
+#include <real/real.hpp>
+#include <test_helpers.hpp>
+
+TEST_CASE("Overflow in Multiplication check") {
+	SECTION("A"){
+	    boost::real::real <int> a1("2123643646");
+	    boost::real::real <int> b1("2147471816");
+	    boost::real::real <int> c1;
+	    boost::real::real <int> d1("4560464877012481136");
+	    c1 = a1*b1;
+    	CHECK(d1 == c1);
+	}
+	SECTION("B"){
+	    boost::real::real <int> a2("2320102120234");
+	    boost::real::real <int> b2("1201320452302");
+	    boost::real::real <int> c2;
+	    boost::real::real <int> d2("2787186128466338066078668");
+	    c2 = a2*b2;
+	    CHECK(d2 == c2);
+	}
+	SECTION("C"){
+	    boost::real::real <int> a3("4524435689");
+	    boost::real::real <int> b3("6870530492");
+	    boost::real::real <int> c3;
+	    boost::real::real <int> d3("31085273360367528988");
+	    c3 = a3*b3;
+    	CHECK(d3 == c3);
+	}
+	SECTION("D"){
+	    boost::real::real <int> a4("7869349424036");
+	    boost::real::real <int> b4("3435469507547");
+	    boost::real::real <int> c4;
+	    boost::real::real <int> d4("27034909990508225005199692");
+	    c4 = a4*b4;
+	    CHECK(d4 == c4);
+	}
+	SECTION("E"){
+	    boost::real::real <int> a5("2123453646");
+	    boost::real::real <int> b5("2147482316");
+	    boost::real::real <int> c5;
+	    boost::real::real <int> d5("4560079153630724136");
+	    c5 = a5*b5;
+	    CHECK(d5 == c5);
+	}
+}
\ No newline at end of file