Data update

Task/Arithmetic-Rational/Ballerina/arithmetic-rational.ballerina

@@ -0,0 +1,156 @@
+import ballerina/io;
+
+function gcd(int num, int den) returns int {
+    int n = num;  // make mutable
+    int d = den;  // ditto
+    while d != 0 {
+        int t = d;
+        d = n % d;
+        n = t;
+    }
+    return n;
+}
+
+class Frac {
+    int num;
+    int den;
+
+    function init(int num, int den) {
+        int n = num;  // make mutable
+        int d = den;  // ditto
+        if n == 0 {
+            d = 1;
+        } else if d < 0 {
+            n = -n;
+            d = -d;
+        }
+        int g = gcd(n, d).abs();
+        if g > 1 {
+            n /= g;
+            d /= g;
+        }
+        self.num = n;
+        self.den = d;
+    }
+
+    function fromInt(int i) returns Frac {
+        return new Frac(i, 1);
+    }
+
+    function neg() returns Frac {
+        return new Frac(-self.num, self.den);
+    }
+
+    function inv() returns Frac {
+        return new Frac(self.den, self.num);
+    }
+
+    function copy() returns Frac {
+        return new Frac(self.num, self.den);
+    }
+
+    function abs() returns Frac {
+        if self.num >= 0 { return self.copy(); }
+        return self.neg();
+    }
+
+    function add(Frac other) returns Frac {
+        return new Frac(self.num * other.den + self.den * other.num, self.den * other.den);
+    }
+
+    function sub(Frac other) returns Frac {
+        return self.add(other.neg());
+    }
+
+    function mul(Frac other) returns Frac {
+        return new Frac(self.num * other.num, self.den * other.den);
+    }
+
+    function div(Frac other) returns Frac {
+        return new Frac(self.num * other.den, self.den * other.num);
+    }
+
+    function toFloat() returns float {
+        return <float>self.num / <float>self.den;
+    }
+
+    function toInt() returns int {
+        float f = self.toFloat();
+        f = f >= 0.0 ? f.floor() : f.ceiling();
+        return <int>f;
+    }
+
+    function idiv(Frac other) returns Frac {
+        return new Frac(self.toInt(), 1);
+    }
+
+    function mod(Frac other) returns Frac {
+        return self.sub(self.idiv(other).mul(other));
+    }
+
+    function lt(Frac other) returns boolean {
+        return self.toFloat() < other.toFloat();
+    }
+
+    function le(Frac other) returns boolean {
+        return self.toFloat() <= other.toFloat();
+    }
+
+    function gt(Frac other) returns boolean {
+        return self.toFloat() > other.toFloat();
+    }
+
+    function ge(Frac other) returns boolean {
+        return self.toFloat() >= other.toFloat();
+    }
+
+    function eq(Frac other) returns boolean {
+        return self.toFloat() == other.toFloat();
+    }
+
+    function ne(Frac other) returns boolean {
+        return self.toFloat() != other.toFloat();
+    }
+
+    function toString() returns string {
+        return string `${self.num} / ${self.den}`;
+    }
+}
+
+function divisors(int n) returns int[] {
+    if n < 1 { return []; }
+    int[] divisors  = [];
+    int[] divisors2 = [];
+    int i = 1;
+    int k = n % 2 == 0 ? 1 : 2;
+    while i * i <= n {
+        if n % i == 0 {
+            divisors.push(i);
+            int j = n / i;
+            if j != i { divisors2.push(j); }
+        }
+        i += k;
+    }
+    if divisors2.length() > 0 {
+        divisors.push(...divisors2.reverse());
+    }
+    return divisors;
+}
+
+function properDivisors(int n) returns int[] {
+    int[] d = divisors(n);
+    int c = d.length();
+    return c <= 1 ? [] : d.slice(0, c - 1);
+}
+
+public function main() {
+    final Frac one = new Frac(1, 1);
+    io:println("The following numbers (less than 2^19) are perfect:");
+    foreach int i in 2..<(<int>1<<19) {
+        var sum = new Frac(1, i);
+        foreach int j in properDivisors(i).slice(1) {
+            sum = sum.add(new Frac(1, j));
+        }
+        if sum.eq(one) { io:println("  ", i); }
+    }
+}

Task/Arithmetic-Rational/REXX/arithmetic-rational.rexx

@@ -1,6 +1,8 @@
 include Settings
 
-say version; say 'Rational arithmetic'; say
+say 'RATIONAL ARITHMETIC - 2 Mar 2025'
+say version
+say
 a = '1 2'; b = '-3 4'; c = '5 -6'; d = '-7 -8'; e = 3; f = 1.666666666
 say 'VALUES'
 say 'a =' Rlst2form(a)