fix #2548 fix #2530

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/util/rational.cpp

@@ -85,3 +85,48 @@ void rational::finalize() {
     DEALLOC_MUTEX(g_powers_of_two);
 }
 
+bool rational::limit_denominator(rational &num, rational const& limit) {
+    rational n, d;
+    n = numerator(num);
+    d = denominator(num);
+    if (d < limit) return false;
+    
+    /*
+      Iteratively computes approximation using continuous fraction
+      decomposition
+      
+      p(-1) = 0, p(0) = 1
+      p(j) = t(j)*p(j-1) + p(j-2)
+      
+      q(-1) = 1, q(0) = 0
+      q(j) = t(j)*q(j-1) + q(j-2)
+      
+      cf[t1; t2, ..., tr] =  p(r) / q(r) for r >= 1
+      reference: https://www.math.u-bordeaux.fr/~pjaming/M1/exposes/MA2.pdf
+    */
+    
+    rational p0(0), p1(1);
+    rational q0(1), q1(0);
+    
+    while (!d.is_zero()) {
+        rational tj(0), rem(0);
+        rational p2(0), q2(0);
+        tj = div(n, d);
+        
+        q2 = tj * q1 + q0;
+        p2 = tj * p1 + p0;
+        if (q2 >= limit) {
+            num = p2/q2;
+            return true;
+        }
+        rem = n - tj * d;
+        p0 = p1;
+        p1 = p2;
+        q0 = q1;
+        q1 = q2;
+        n = d;
+        d = rem;
+    }
+    return false;
+}
+

src/util/rational.h

@@ -421,6 +421,8 @@ public:
         }
         return num_bits;
     }
+
+    static bool limit_denominator(rational &num, rational const& limit);
 };
 
 inline bool operator!=(rational const & r1, rational const & r2) {