+ << f << " instead of simplifying to 0." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned exam_expand_power()
+{
+ unsigned result = 0;
+ symbol x("x"), a("a"), b("b");
+ ex e;
+
+ e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand();
+
+ if (e != 1) {
+ clog << "e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand(); erroneously returned "
+ << e << " instead of simplifying to 1." << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned exam_sqrfree()
+{
+ unsigned result = 0;
+ symbol x("x"), y("y");
+ ex e1, e2;
+
+ e1 = (1+x)*pow((2+x),2)*pow((3+x),3)*pow((4+x),4);
+ e2 = sqrfree(expand(e1),lst{x});
+ if (e1 != e2) {
+ clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
+ << e2 << endl;
+ ++result;
+ }
+
+ e1 = (x+y)*pow((x+2*y),2)*pow((x+3*y),3)*pow((x+4*y),4);
+ e2 = sqrfree(expand(e1));
+ if (e1 != e2) {
+ clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
+ << e2 << endl;
+ ++result;
+ }
+ e2 = sqrfree(expand(e1),lst{x});
+ if (e1 != e2) {
+ clog << "sqrfree(expand(" << e1 << "),[x]) erroneously returned "
+ << e2 << endl;
+ ++result;
+ }
+ e2 = sqrfree(expand(e1),lst{y});
+ if (e1 != e2) {
+ clog << "sqrfree(expand(" << e1 << "),[y]) erroneously returned "
+ << e2 << endl;
+ ++result;
+ }
+ e2 = sqrfree(expand(e1),lst{x,y});
+ if (e1 != e2) {
+ clog << "sqrfree(expand(" << e1 << "),[x,y]) erroneously returned "
+ << e2 << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+/* Arithmetic Operators should behave just as one expects from built-in types.
+ * When somebody screws up the operators this routine will most probably fail
+ * to compile. Unfortunately we can only test the stuff that is allowed, not
+ * what is forbidden (e.g. e1+e2 = 42) since that must not compile. :-( */
+static unsigned exam_operator_semantics()
+{
+ unsigned result = 0;
+ ex e1, e2;
+ int i1, i2;
+
+ // Assignment should not return const ex though it may be obfuscated:
+ e1 = 7; e2 = 4;
+ i1 = 7; i2 = 4;
+ (e1 = e2) = 2;
+ (i1 = i2) = 2;
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of ex::operator=() screwed." << endl;
+ ++result;
+ }
+ (e1 += e2) = 2;
+ (i1 += i2) = 2;
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of ex::operator=() screwed." << endl;
+ ++result;
+ }
+ (e1 -= e2) = 2;
+ (i1 -= i2) = 2;
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of ex::operator=() screwed." << endl;
+ ++result;
+ }
+
+ // Prefix/postfix increment/decrement behavior:
+ e1 = 7; e2 = 4;
+ i1 = 7; i2 = 4;
+ e1 = (--e2 = 2)++;
+ i1 = (--i2 = 2)++;
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of increment/decrement operators screwed." << endl;
+ ++result;
+ }
+ e1 = (++e2 = 2)--;
+ i1 = (++i2 = 2)--;
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of increment/decrement operators screwed." << endl;
+ ++result;
+ }
+
+ // prefix increment/decrement must return an lvalue (contrary to postfix):
+ e1 = 7; e2 = 4;
+ i1 = 7; i2 = 4;
+ --++----e1; ++(++++++++(++++e2));
+ --++----i1; ++(++++++++(++++i2));
+ if (e1!=i1 || e2!=i2) {
+ clog << "Semantics of prefix increment/decrement operators screwed." << endl;
+ ++result;
+ }
+
+ // This one has a good chance of detecting problems in self-assignment:
+ // (which incidentally was severely broken from version 0.7.3 to 0.8.2).
+ ex selfprobe = numeric("65536");
+ selfprobe = selfprobe;
+ if (!is_exactly_a<numeric>(selfprobe)) {
+ clog << "ex (of numeric) after self-assignment became " << selfprobe << endl;