From edcded21cbeb272ff206a92c693ab21bf33ebae6 Mon Sep 17 00:00:00 2001
From: Julian Weigt <juw@posteo.de>
Date: Tue, 23 Dec 2025 15:55:51 +0000
Subject: Define safe sums and products and finish exact version.

---
 ratio.c | 107 ++++++++++++++++++++++++++++++++++++++++++++++++++--------------
 1 file changed, 84 insertions(+), 23 deletions(-)

(limited to 'ratio.c')

diff --git a/ratio.c b/ratio.c
index 8c67538..70a198a 100644
--- a/ratio.c
+++ b/ratio.c
@@ -1,64 +1,125 @@
 #include <stdio.h>
 #include <stdlib.h>
 #include <math.h>
+#include <limits.h>
 
-typedef struct {long int n; long unsigned int d} rational;
+typedef unsigned long long num;
+
+typedef struct {bool s; num n; num d} rational;
+
+unsigned int safe_sum(num n1, num n2){
+	if(n2 > ULLONG_MAX-n1){
+		printf("Sum overflow: Adding %llu and %llu\n",n1,n2);
+		exit(1);
+	}
+	else {
+		return n1+n2;
+	}
+}
+
+num safe_product(num n1, num n2){
+	if(n1 != 0 && n2 > ULLONG_MAX/n1){
+		printf("Product overflow: Multiplying %llu by %llu\n",n1,n2);
+		exit(1);
+	}
+	else {
+		return n1*n2;
+	}
+}
 
 rational convert_int(int i){ 
-	rational r = {i,1};
+	rational r;
+	r.d = 1;
+	r.n = abs(i);
+	if(i >= 0) { r.s=false; } else { r.s=true; }
 	return r;
 }
 
-rational cancel(rational r){
-	long unsigned int a = abs(r.n), b = r.d, c;
+num gcd(num a, num b){
+	num c;
 	while (b) {
 		c = a % b;
 		a = b;
 		b = c;
 	}
-	rational res = {r.n/a,r.d/a};
+	return a;
+}
+
+rational cancel(rational r){
+	num a = gcd(r.n,r.d);
+	rational res = {r.s,r.n/a,r.d/a};
 	return res;
 }
 
 rational sum(rational r1, rational r2){
-	rational r = {r1.n*r2.d+r2.n*r1.d,r1.d*r2.d};
+	num a = gcd(r1.d,r2.d);
+	num r1da = r1.d/a;
+	num r2da = r2.d/a;
+	rational r;
+	r.d = safe_product(r1da,r2.d);
+	num n1 = safe_product(r1.n,r2da);
+	num n2 = safe_product(r2.n,r1da);
+	if(r1.s == r2.s){
+		r.n = safe_sum(n1,n2);
+		r.s = r1.s;
+	}
+	else {
+		if(n1 >= n2) {
+			r.n = n1 - n2;
+			r.s = r1.s;
+		}
+		else {
+			r.n = n2 - n1;
+			r.s = r2.s;
+		}
+	}
 	return cancel(r);
 }
 
 rational difference(rational r1, rational r2){
-	rational r = {r1.n*r2.d-r2.n*r1.d,r1.d*r2.d};
-	return cancel(r);
+	r2.s = !r2.s;
+	return sum(r1,r2);
 }
 
-bool is_greater(rational r1, rational r2){ return (difference(r1,r2).n > 0); }
+bool is_greater(rational r1, rational r2){ return !(difference(r1,r2).s); }
 
 rational product(rational r1, rational r2){
-	rational r = {r1.n*r2.n,r1.d*r2.d};
+	rational r;
+	rational s1 = {r1.s, r1.n, r2.d};
+	rational s2 = {r2.s, r2.n, r1.d};
+	rational t1 = cancel(s1);
+	rational t2 = cancel(s2);
+	r.s = t1.s^t2.s;
+	r.n = safe_product(t1.n,t2.n);
+	r.d = safe_product(t1.d,t2.d);
 	return cancel(r);
 }
 
 rational ratio(rational r1, rational r2){
-	rational r = {0,1};
-	if (r2.n>0){
-		rational r = {0,1};
-	}
-	else{
-		rational r = {-r1.n*r2.d,r1.d*(-r2.n)};
-	}
-	return cancel(r);
+	rational r2i = {r2.s,r2.d,r2.n};
+	return product(r1,r2i);
 }
 
-double to_double(rational r){ return ((double)r.n)/((double)r.d); }
-
 rational absolute(rational r){
-	rational s = {abs(r.n),r.d};
+	rational s = {false,r.n,r.d};
 	return s;
 }
 
 rational power(rational r, unsigned int p){
-	rational s = {1,1};
+	rational s = {0,1,1};
 	for(int i = 1; i<= p; i++){
-		rational s = product(r,s);
+		s = product(r,s);
 	}
 	return s;
 }
+
+double to_double(rational r){
+	double i;
+	if(r.s) { i=-1.0; } else { i=1.0; }
+	return i*((double)r.n)/((double)r.d);
+}
+
+bool to_string(char* s,rational r){
+	sprintf(s,"%llu / %llu",r.n,r.d);
+	return true;
+}
-- 
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