static ex log_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
+ if (x.is_equal(_ex0())) // log(0) -> infinity
+ throw(std::domain_error("log_eval(): log(0)"));
+ if (x.info(info_flags::real) && x.info(info_flags::negative))
+ return (log(-x)+I*Pi);
if (x.is_equal(_ex1())) // log(1) -> 0
return _ex0();
- if (x.is_equal(_ex_1())) // log(-1) -> I*Pi
- return (I*Pi);
if (x.is_equal(I)) // log(I) -> Pi*I/2
return (Pi*I*_num1_2());
if (x.is_equal(-I)) // log(-I) -> -Pi*I/2
return (Pi*I*_num_1_2());
- if (x.is_equal(_ex0())) // log(0) -> infinity
- throw(std::domain_error("log_eval(): log(0)"));
// log(float)
if (!x.info(info_flags::crational))
return log_evalf(x);
static ex log_deriv(const ex & x, unsigned deriv_param)
{
GINAC_ASSERT(deriv_param==0);
-
+
// d/dx log(x) -> 1/x
return power(x, _ex_1());
}
-static ex log_series(const ex &x, const relational &r, int order)
+static ex log_series(const ex &x, const relational &rel, int order)
{
- if (x.subs(r).is_zero()) {
- epvector seq;
- seq.push_back(expair(log(x), _ex0()));
- return pseries(r, seq);
- } else
- throw do_taylor();
+ const ex x_pt = x.subs(rel);
+ if (!x_pt.info(info_flags::negative) && !x_pt.is_zero())
+ throw do_taylor(); // caught by function::series()
+ // now we either have to care for the branch cut or the branch point:
+ if (x_pt.is_zero()) { // branch point: return a plain log(x).
+ epvector seq;
+ seq.push_back(expair(log(x), _ex0()));
+ return pseries(rel, seq);
+ } // on the branch cut:
+ const ex point = rel.rhs();
+ const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+ const symbol foo;
+ // compute the formal series:
+ ex replx = series(log(x),*s==foo,order).subs(foo==point);
+ epvector seq;
+ seq.push_back(expair(-I*csgn(x*I)*Pi,_ex0()));
+ seq.push_back(expair(Order(_ex1()),order));
+ return series(replx - I*Pi + pseries(rel, seq),rel,order);
}
REGISTER_FUNCTION(log, eval_func(log_eval).
if (z.is_equal(_num25())) // tan(5/12*Pi) -> 2+sqrt(3)
return sign*(power(_ex3(),_ex1_2())+_ex2());
if (z.is_equal(_num30())) // tan(Pi/2) -> infinity
- throw (std::domain_error("tan_eval(): infinity"));
+ throw (std::domain_error("tan_eval(): simple pole"));
}
if (is_ex_exactly_of_type(x, function)) {
return (_ex1()+power(tan(x),_ex2()));
}
-static ex tan_series(const ex &x, const relational &r, int order)
+static ex tan_series(const ex &x, const relational &rel, int order)
{
// method:
// Taylor series where there is no pole falls back to tan_deriv.
// On a pole simply expand sin(x)/cos(x).
- const ex x_pt = x.subs(r);
+ const ex x_pt = x.subs(rel);
if (!(2*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sin(x)/cos(x)).series(r, order+2);
+ return (sin(x)/cos(x)).series(rel, order+2);
}
REGISTER_FUNCTION(tan, eval_func(tan_eval).
return _ex1()-power(tanh(x),_ex2());
}
-static ex tanh_series(const ex &x, const relational &r, int order)
+static ex tanh_series(const ex &x, const relational &rel, int order)
{
// method:
// Taylor series where there is no pole falls back to tanh_deriv.
// On a pole simply expand sinh(x)/cosh(x).
- const ex x_pt = x.subs(r);
+ const ex x_pt = x.subs(rel);
if (!(2*I*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sinh(x)/cosh(x)).series(r, order+2);
+ return (sinh(x)/cosh(x)).series(rel, order+2);
}
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
if (x.is_zero())
return _ex0();
// atanh({+|-}1) -> throw
- if (x.is_equal(_ex1()) || x.is_equal(_ex1()))
- throw (std::domain_error("atanh_eval(): infinity"));
+ if (x.is_equal(_ex1()) || x.is_equal(_ex_1()))
+ throw (std::domain_error("atanh_eval(): logarithmic pole"));
// atanh(float) -> float
if (!x.info(info_flags::crational))
return atanh_evalf(x);