Reorganizing source code. Created util dir

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/util/inf_rational.cpp

@@ -0,0 +1,179 @@
+/*++
+Copyright (c) 2006 Microsoft Corporation
+
+Module Name:
+
+    inf_rational.cpp
+
+Abstract:
+
+    Rational numbers with infenitesimals
+
+Author:
+
+    Nikolaj Bjorner (nbjorner) 2006-12-05.
+
+Revision History:
+
+--*/
+#include"inf_rational.h"
+
+inf_rational inf_rational::m_zero(0);
+inf_rational inf_rational::m_one(1);
+inf_rational inf_rational::m_minus_one(-1);
+
+inf_rational inf_mult(inf_rational const& r1, inf_rational const& r2) 
+{
+    inf_rational result;
+    result.m_first = r1.m_first * r2.m_first;
+    result.m_second = (r1.m_first * r2.m_second) + (r1.m_second * r2.m_first);
+
+    if (r1.m_second.is_pos() && r2.m_second.is_neg()) {
+        --result.m_second;
+    }
+    else if (r1.m_second.is_neg() && r2.m_second.is_pos()) {
+        --result.m_second;
+    }
+    return result;
+}
+
+inf_rational sup_mult(inf_rational const& r1, inf_rational const& r2) 
+{
+    inf_rational result;
+    result.m_first = r1.m_first * r2.m_first;
+    result.m_second = (r1.m_first * r2.m_second) + (r1.m_second * r2.m_first);
+
+    if (r1.m_second.is_pos() && r2.m_second.is_pos()) {
+        ++result.m_second;
+    }
+    else if (r1.m_second.is_neg() && r2.m_second.is_neg()) {
+        ++result.m_second;
+    }
+    return result;
+}
+
+//
+// Find rationals c, x, such that c + epsilon*x <= r1/r2
+// 
+// let r1 = a + d_1
+// let r2 = b + d_2
+// 
+// suppose b != 0:
+//
+//      r1/b <= r1/r2 
+// <=> { if b > 0, then r2 > 0, and cross multiplication does not change the sign }
+//     { if b < 0, then r2 < 0, and cross multiplication changes sign twice }
+//      r1 * r2 <= b * r1 
+// <=>
+//      r1 * (b + d_2) <= r1 * b
+// <=>
+//      r1 * d_2 <= 0
+// 
+// if r1 * d_2 > 0, then r1/(b + sign_of(r1)*1/2*|b|) <= r1/r2
+// 
+// Not handled here:
+// if b = 0, then d_2 != 0
+//   if r1 * d_2 = 0 then it's 0.
+//   if r1 * d_2 > 0, then result is +oo
+//   if r1 * d_2 < 0, then result is -oo
+// 
+inf_rational inf_div(inf_rational const& r1, inf_rational const& r2) 
+{
+    SASSERT(!r2.m_first.is_zero());
+    inf_rational result;
+
+    if (r2.m_second.is_neg() && r1.is_neg()) {
+        result = r1 / (r2.m_first - (abs(r2.m_first)/rational(2)));
+    }
+    else if (r2.m_second.is_pos() && r1.is_pos()) {
+        result = r1 / (r2.m_first + (abs(r2.m_first)/rational(2)));
+    }
+    else {
+        result = r1 / r2.m_first;
+    }    
+    return result;
+}
+
+inf_rational sup_div(inf_rational const& r1, inf_rational const& r2) 
+{
+    SASSERT(!r2.m_first.is_zero());
+    inf_rational result;
+
+    if (r2.m_second.is_pos() && r1.is_neg()) {
+        result = r1 / (r2.m_first + (abs(r2.m_first)/rational(2)));
+    }
+    else if (r2.m_second.is_neg() && r1.is_pos()) {
+        result = r1 / (r2.m_first - (abs(r2.m_first)/rational(2)));
+    }
+    else {
+        result = r1 / r2.m_first;
+    }    
+    return result;
+
+}
+
+inf_rational inf_power(inf_rational const& r, unsigned n) 
+{
+    bool is_even = (0 == (n & 0x1));
+    inf_rational result;
+    if (n == 1) {
+        result = r;
+    }
+    else if ((r.m_second.is_zero()) ||
+        (r.m_first.is_pos() && r.m_second.is_pos()) ||
+        (r.m_first.is_neg() && r.m_second.is_neg() && is_even)) {
+        result.m_first = r.m_first.expt(n);
+    }
+    else if (is_even) {
+        // 0 will work.
+    }
+    else if (r.m_first.is_zero()) {
+        result.m_first = rational(-1);        
+    }
+    else if (r.m_first.is_pos()) {
+        result.m_first = rational(r.m_first - r.m_first/rational(2)).expt(n);
+    }
+    else {
+        result.m_first = rational(r.m_first + r.m_first/rational(2)).expt(n);
+    }
+    return result;
+}
+
+inf_rational sup_power(inf_rational const& r, unsigned n) 
+{
+    bool is_even = (0 == (n & 0x1));
+    inf_rational result;
+    if (n == 1) {
+        result = r;
+    }
+    else if (r.m_second.is_zero() ||
+        (r.m_first.is_pos() && r.m_second.is_neg()) ||
+        (r.m_first.is_neg() && r.m_second.is_pos() && is_even)) {
+        result.m_first = r.m_first.expt(n);
+    }
+    else if (r.m_first.is_zero() || (n == 0)) {
+        result.m_first = rational(1);        
+    }
+    else if (r.m_first.is_pos() || is_even) {
+        result.m_first = rational(r.m_first + r.m_first/rational(2)).expt(n);
+    }
+    else {
+        // r (r.m_first) is negative, n is odd.
+        result.m_first = rational(r.m_first - r.m_first/rational(2)).expt(n);
+    }
+    return result;
+}
+
+inf_rational inf_root(inf_rational const& r, unsigned n) 
+{
+    SASSERT(!r.is_neg());
+    // use 0
+    return inf_rational();
+}
+
+inf_rational sup_root(inf_rational const& r, unsigned n) 
+{
+    SASSERT(!r.is_neg());
+    // use r.
+    return r;
+}