- unsigned result = 0;
- symbol x("x");
- ex chk;
-
- chk = asin(1)-acos(0);
- if (!chk.is_zero()) {
- clog << "asin(1)-acos(0) erroneously returned " << chk
- << " instead of 0" << endl;
- ++result;
- }
-
- // arbitrary check of type sin(f(x)):
- chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
- - (1+pow(x,2))*pow(sin(atan(x)),2);
- if (chk != 1-pow(x,2)) {
- clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
- << "erroneously returned " << chk << " instead of 1-x^2" << endl;
- ++result;
- }
-
- // arbitrary check of type cos(f(x)):
- chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
- - (1+pow(x,2))*pow(cos(atan(x)),2);
- if (!chk.is_zero()) {
- clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
- << "erroneously returned " << chk << " instead of 0" << endl;
- ++result;
- }
-
- // arbitrary check of type tan(f(x)):
- chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
- if (chk != 1-x) {
- clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
- << "erroneously returned " << chk << " instead of -x+1" << endl;
- ++result;
- }
-
- // arbitrary check of type sinh(f(x)):
- chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
- - pow(sinh(asinh(x)),2);
- if (!chk.is_zero()) {
- clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
- << "erroneously returned " << chk << " instead of 0" << endl;
- ++result;
- }
-
- // arbitrary check of type cosh(f(x)):
- chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
- * pow(cosh(atanh(x)),2);
- if (chk != 1) {
- clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
- << "erroneously returned " << chk << " instead of 1" << endl;
- ++result;
- }
-
- // arbitrary check of type tanh(f(x)):
- chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
- * pow(tanh(atanh(x)),2);
- if (chk != 2) {
- clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
- << "erroneously returned " << chk << " instead of 2" << endl;
- ++result;
- }
-
- return result;
+ unsigned result = 0;
+ symbol x("x");
+ ex chk;
+
+ chk = asin(1)-acos(0);
+ if (!chk.is_zero()) {
+ clog << "asin(1)-acos(0) erroneously returned " << chk
+ << " instead of 0" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type sin(f(x)):
+ chk = pow(sin(acos(x)),2) + pow(sin(asin(x)),2)
+ - (1+pow(x,2))*pow(sin(atan(x)),2);
+ if (chk != 1-pow(x,2)) {
+ clog << "sin(acos(x))^2 + sin(asin(x))^2 - (1+x^2)*sin(atan(x))^2 "
+ << "erroneously returned " << chk << " instead of 1-x^2" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type cos(f(x)):
+ chk = pow(cos(acos(x)),2) + pow(cos(asin(x)),2)
+ - (1+pow(x,2))*pow(cos(atan(x)),2);
+ if (!chk.is_zero()) {
+ clog << "cos(acos(x))^2 + cos(asin(x))^2 - (1+x^2)*cos(atan(x))^2 "
+ << "erroneously returned " << chk << " instead of 0" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type tan(f(x)):
+ chk = tan(acos(x))*tan(asin(x)) - tan(atan(x));
+ if (chk != 1-x) {
+ clog << "tan(acos(x))*tan(asin(x)) - tan(atan(x)) "
+ << "erroneously returned " << chk << " instead of -x+1" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type sinh(f(x)):
+ chk = -pow(sinh(acosh(x)),2).expand()*pow(sinh(atanh(x)),2)
+ - pow(sinh(asinh(x)),2);
+ if (!chk.is_zero()) {
+ clog << "expand(-(sinh(acosh(x)))^2)*(sinh(atanh(x))^2) - sinh(asinh(x))^2 "
+ << "erroneously returned " << chk << " instead of 0" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type cosh(f(x)):
+ chk = (pow(cosh(asinh(x)),2) - 2*pow(cosh(acosh(x)),2))
+ * pow(cosh(atanh(x)),2);
+ if (chk != 1) {
+ clog << "(cosh(asinh(x))^2 - 2*cosh(acosh(x))^2) * cosh(atanh(x))^2 "
+ << "erroneously returned " << chk << " instead of 1" << endl;
+ ++result;
+ }
+
+ // arbitrary check of type tanh(f(x)):
+ chk = (pow(tanh(asinh(x)),-2) - pow(tanh(acosh(x)),2)).expand()
+ * pow(tanh(atanh(x)),2);
+ if (chk != 2) {
+ clog << "expand(tanh(acosh(x))^2 - tanh(asinh(x))^(-2)) * tanh(atanh(x))^2 "
+ << "erroneously returned " << chk << " instead of 2" << endl;
+ ++result;
+ }
+
+ // check consistency of log and eta phases:
+ for (int r1=-1; r1<=1; ++r1) {
+ for (int i1=-1; i1<=1; ++i1) {
+ ex x1 = r1+I*i1;
+ if (x1.is_zero())
+ continue;
+ for (int r2=-1; r2<=1; ++r2) {
+ for (int i2=-1; i2<=1; ++i2) {
+ ex x2 = r2+I*i2;
+ if (x2.is_zero())
+ continue;
+ if (abs(evalf(eta(x1,x2)-log(x1*x2)+log(x1)+log(x2)))>.1e-12) {
+ clog << "either eta(x,y), log(x), log(y) or log(x*y) is wrong"
+ << " at x==" << x1 << ", y==" << x2 << endl;
+ ++result;
+ }
+ }
+ }
+ }
+ }
+
+ return result;