index d91c02c0178346ccaed73f77d8976b3d2f5bce4b..96ea9cc7cd4a3feb8e3750d45eba145b062ea6a5 100644 (file)
@@ -4,7 +4,7 @@
*  functions. */

/*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
*
*  This program is free software; you can redistribute it and/or modify
*  it under the terms of the GNU General Public License as published by
/* Assorted tests on other transcendental functions. */
static unsigned inifcns_consist_trans(void)
{
-    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;
}

-/* Simple tests on the Gamma function.  We stuff in arguments where the results
+/* Simple tests on the tgamma function.  We stuff in arguments where the results
* exists in closed form and check if it's ok. */
static unsigned inifcns_consist_gamma(void)
{
-    unsigned result = 0;
-    ex e;
-
-    e = gamma(ex(1));
-    for (int i=2; i<8; ++i)
-        e += gamma(ex(i));
-    if (e != numeric(874)) {
-        clog << "gamma(1)+...+gamma(7) erroneously returned "
-             << e << " instead of 874" << endl;
-        ++result;
-    }
-
-    e = gamma(ex(1));
-    for (int i=2; i<8; ++i)
-        e *= gamma(ex(i));
-    if (e != numeric(24883200)) {
-        clog << "gamma(1)*...*gamma(7) erroneously returned "
-             << e << " instead of 24883200" << endl;
-        ++result;
-    }
-
-    e = gamma(ex(numeric(5, 2)))*gamma(ex(numeric(9, 2)))*64;
-    if (e != 315*Pi) {
-        clog << "64*gamma(5/2)*gamma(9/2) erroneously returned "
-             << e << " instead of 315*Pi" << endl;
-        ++result;
-    }
-
-    e = gamma(ex(numeric(-13, 2)));
-    for (int i=-13; i<7; i=i+2)
-        e += gamma(ex(numeric(i, 2)));
-    e = (e*gamma(ex(numeric(15, 2)))*numeric(512));
-    if (e != numeric(633935)*Pi) {
-        clog << "512*(gamma(-13/2)+...+gamma(5/2))*gamma(15/2) erroneously returned "
-             << e << " instead of 633935*Pi" << endl;
-        ++result;
-    }
-
-    return result;
+       unsigned result = 0;
+       ex e;
+
+       e = tgamma(1);
+       for (int i=2; i<8; ++i)
+               e += tgamma(ex(i));
+       if (e != numeric(874)) {
+               clog << "tgamma(1)+...+tgamma(7) erroneously returned "
+                    << e << " instead of 874" << endl;
+               ++result;
+       }
+
+       e = tgamma(1);
+       for (int i=2; i<8; ++i)
+               e *= tgamma(ex(i));
+       if (e != numeric(24883200)) {
+               clog << "tgamma(1)*...*tgamma(7) erroneously returned "
+                    << e << " instead of 24883200" << endl;
+               ++result;
+       }
+
+       e = tgamma(ex(numeric(5, 2)))*tgamma(ex(numeric(9, 2)))*64;
+       if (e != 315*Pi) {
+               clog << "64*tgamma(5/2)*tgamma(9/2) erroneously returned "
+                    << e << " instead of 315*Pi" << endl;
+               ++result;
+       }
+
+       e = tgamma(ex(numeric(-13, 2)));
+       for (int i=-13; i<7; i=i+2)
+               e += tgamma(ex(numeric(i, 2)));
+       e = (e*tgamma(ex(numeric(15, 2)))*numeric(512));
+       if (e != numeric(633935)*Pi) {
+               clog << "512*(tgamma(-13/2)+...+tgamma(5/2))*tgamma(15/2) erroneously returned "
+                    << e << " instead of 633935*Pi" << endl;
+               ++result;
+       }
+
+       return result;
}

/* Simple tests on the Psi-function (aka polygamma-function).  We stuff in
arguments where the result exists in closed form and check if it's ok. */
static unsigned inifcns_consist_psi(void)
{
-    unsigned result = 0;
-    symbol x;
-    ex e, f;
-
-    // We check psi(1) and psi(1/2) implicitly by calculating the curious
-    // little identity gamma(1)'/gamma(1) - gamma(1/2)'/gamma(1/2) == 2*log(2).
-    e += (gamma(x).diff(x)/gamma(x)).subs(x==numeric(1));
-    e -= (gamma(x).diff(x)/gamma(x)).subs(x==numeric(1,2));
-    if (e!=2*log(2)) {
-        clog << "gamma(1)'/gamma(1) - gamma(1/2)'/gamma(1/2) erroneously returned "
-             << e << " instead of 2*log(2)" << endl;
-        ++result;
-    }
-
-    return result;
+       unsigned result = 0;
+       symbol x;
+       ex e, f;
+
+       // We check psi(1) and psi(1/2) implicitly by calculating the curious
+       // little identity tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) == 2*log(2).
+       e += (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1));
+       e -= (tgamma(x).diff(x)/tgamma(x)).subs(x==numeric(1,2));
+       if (e!=2*log(2)) {
+               clog << "tgamma(1)'/tgamma(1) - tgamma(1/2)'/tgamma(1/2) erroneously returned "
+                    << e << " instead of 2*log(2)" << endl;
+               ++result;
+       }
+
+       return result;
}

/* Simple tests on the Riemann Zeta function.  We stuff in arguments where the
@@ -164,47 +185,47 @@ static unsigned inifcns_consist_psi(void)
* the Bernoulli numbers as a side effect. */
static unsigned inifcns_consist_zeta(void)
{
-    unsigned result = 0;
-    ex e;
-
-    for (int i=0; i<13; i+=2)
-        e += zeta(i)/pow(Pi,i);
-    if (e!=numeric(-204992279,638512875)) {
-        clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
-             << e << " instead of -204992279/638512875" << endl;
-        ++result;
-    }
-
-    e = 0;
-    for (int i=-1; i>-16; i--)
-        e += zeta(i);
-    if (e!=numeric(487871,1633632)) {
-        clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
-             << e << " instead of 487871/1633632" << endl;
-        ++result;
-    }
-
-    return result;
+       unsigned result = 0;
+       ex e;
+
+       for (int i=0; i<13; i+=2)
+               e += zeta(i)/pow(Pi,i);
+       if (e!=numeric(-204992279,638512875)) {
+               clog << "zeta(0) + zeta(2) + ... + zeta(12) erroneously returned "
+                    << e << " instead of -204992279/638512875" << endl;
+               ++result;
+       }
+
+       e = 0;
+       for (int i=-1; i>-16; i--)
+               e += zeta(i);
+       if (e!=numeric(487871,1633632)) {
+               clog << "zeta(-1) + zeta(-2) + ... + zeta(-15) erroneously returned "
+                    << e << " instead of 487871/1633632" << endl;
+               ++result;
+       }
+
+       return result;
}

unsigned exam_inifcns(void)
{
-    unsigned result = 0;
-
-    cout << "examining consistency of symbolic functions" << flush;
-    clog << "----------consistency of symbolic functions:" << endl;
-
-    result += inifcns_consist_trans();  cout << '.' << flush;
-    result += inifcns_consist_gamma();  cout << '.' << flush;
-    result += inifcns_consist_psi();  cout << '.' << flush;
-    result += inifcns_consist_zeta();  cout << '.' << flush;
-
-    if (!result) {
-        cout << " passed " << endl;
-        clog << "(no output)" << endl;
-    } else {
-        cout << " failed " << endl;
-    }
-
-    return result;
+       unsigned result = 0;
+
+       cout << "examining consistency of symbolic functions" << flush;
+       clog << "----------consistency of symbolic functions:" << endl;
+
+       result += inifcns_consist_trans();  cout << '.' << flush;
+       result += inifcns_consist_gamma();  cout << '.' << flush;
+       result += inifcns_consist_psi();  cout << '.' << flush;
+       result += inifcns_consist_zeta();  cout << '.' << flush;
+
+       if (!result) {
+               cout << " passed " << endl;
+               clog << "(no output)" << endl;
+       } else {
+               cout << " failed " << endl;
+       }
+
+       return result;
}