// exponential function
//////////
-static ex exp_evalf(ex const & x)
+static ex exp_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return exp(ex_to_numeric(x)); // -> numeric exp(numeric)
}
-static ex exp_eval(ex const & x)
+static ex exp_eval(const ex & x)
{
// exp(0) -> 1
if (x.is_zero()) {
return exp(x).hold();
}
-static ex exp_diff(ex const & x, unsigned diff_param)
+static ex exp_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// natural logarithm
//////////
-static ex log_evalf(ex const & x)
+static ex log_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return log(ex_to_numeric(x)); // -> numeric log(numeric)
}
-static ex log_eval(ex const & x)
+static ex log_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.is_equal(_ex1())) // log(1) -> 0
if (!x.info(info_flags::crational))
return log_evalf(x);
}
- // log(exp(t)) -> t (for real-valued t):
+ // log(exp(t)) -> t (if -Pi < t.imag() <= Pi):
if (is_ex_the_function(x, exp)) {
ex t = x.op(0);
- if (t.info(info_flags::real))
- return t;
+ if (t.info(info_flags::numeric)) {
+ numeric nt = ex_to_numeric(t);
+ if (nt.is_real())
+ return t;
+ }
}
return log(x).hold();
}
-static ex log_diff(ex const & x, unsigned diff_param)
+static ex log_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// sine (trigonometric function)
//////////
-static ex sin_evalf(ex const & x)
+static ex sin_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return sin(ex_to_numeric(x)); // -> numeric sin(numeric)
}
-static ex sin_eval(ex const & x)
+static ex sin_eval(const ex & x)
{
// sin(n/d*Pi) -> { all known non-nested radicals }
ex SixtyExOverPi = _ex60()*x/Pi;
return sin(x).hold();
}
-static ex sin_diff(ex const & x, unsigned diff_param)
+static ex sin_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// cosine (trigonometric function)
//////////
-static ex cos_evalf(ex const & x)
+static ex cos_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return cos(ex_to_numeric(x)); // -> numeric cos(numeric)
}
-static ex cos_eval(ex const & x)
+static ex cos_eval(const ex & x)
{
// cos(n/d*Pi) -> { all known non-nested radicals }
ex SixtyExOverPi = _ex60()*x/Pi;
return cos(x).hold();
}
-static ex cos_diff(ex const & x, unsigned diff_param)
+static ex cos_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// tangent (trigonometric function)
//////////
-static ex tan_evalf(ex const & x)
+static ex tan_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return tan(ex_to_numeric(x));
}
-static ex tan_eval(ex const & x)
+static ex tan_eval(const ex & x)
{
// tan(n/d*Pi) -> { all known non-nested radicals }
ex SixtyExOverPi = _ex60()*x/Pi;
return tan(x).hold();
}
-static ex tan_diff(ex const & x, unsigned diff_param)
+static ex tan_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
return (_ex1()+power(tan(x),_ex2()));
}
-static ex tan_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex tan_series(const ex & x, const symbol & s, const ex & pt, int order)
{
// method:
// Taylor series where there is no pole falls back to tan_diff.
// On a pole simply expand sin(x)/cos(x).
- ex xpoint = x.subs(s==point);
- if (!(2*xpoint/Pi).info(info_flags::odd))
+ const ex x_pt = x.subs(s==pt);
+ 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(s, point, order+2);
+ return (sin(x)/cos(x)).series(s, pt, order+2);
}
REGISTER_FUNCTION(tan, tan_eval, tan_evalf, tan_diff, tan_series);
// inverse sine (arc sine)
//////////
-static ex asin_evalf(ex const & x)
+static ex asin_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return asin(ex_to_numeric(x)); // -> numeric asin(numeric)
}
-static ex asin_eval(ex const & x)
+static ex asin_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// asin(0) -> 0
return asin(x).hold();
}
-static ex asin_diff(ex const & x, unsigned diff_param)
+static ex asin_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// inverse cosine (arc cosine)
//////////
-static ex acos_evalf(ex const & x)
+static ex acos_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return acos(ex_to_numeric(x)); // -> numeric acos(numeric)
}
-static ex acos_eval(ex const & x)
+static ex acos_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// acos(1) -> 0
return acos(x).hold();
}
-static ex acos_diff(ex const & x, unsigned diff_param)
+static ex acos_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// inverse tangent (arc tangent)
//////////
-static ex atan_evalf(ex const & x)
+static ex atan_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return atan(ex_to_numeric(x)); // -> numeric atan(numeric)
}
-static ex atan_eval(ex const & x)
+static ex atan_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// atan(0) -> 0
return atan(x).hold();
}
-static ex atan_diff(ex const & x, unsigned diff_param)
+static ex atan_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// inverse tangent (atan2(y,x))
//////////
-static ex atan2_evalf(ex const & y, ex const & x)
+static ex atan2_evalf(const ex & y, const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(y,numeric)
return atan(ex_to_numeric(y),ex_to_numeric(x)); // -> numeric atan(numeric)
}
-static ex atan2_eval(ex const & y, ex const & x)
+static ex atan2_eval(const ex & y, const ex & x)
{
if (y.info(info_flags::numeric) && !y.info(info_flags::crational) &&
x.info(info_flags::numeric) && !x.info(info_flags::crational)) {
return atan2(y,x).hold();
}
-static ex atan2_diff(ex const & y, ex const & x, unsigned diff_param)
+static ex atan2_diff(const ex & y, const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param<2);
// hyperbolic sine (trigonometric function)
//////////
-static ex sinh_evalf(ex const & x)
+static ex sinh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return sinh(ex_to_numeric(x)); // -> numeric sinh(numeric)
}
-static ex sinh_eval(ex const & x)
+static ex sinh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.is_zero()) // sinh(0) -> 0
return sinh(x).hold();
}
-static ex sinh_diff(ex const & x, unsigned diff_param)
+static ex sinh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// hyperbolic cosine (trigonometric function)
//////////
-static ex cosh_evalf(ex const & x)
+static ex cosh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return cosh(ex_to_numeric(x)); // -> numeric cosh(numeric)
}
-static ex cosh_eval(ex const & x)
+static ex cosh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.is_zero()) // cosh(0) -> 1
return cosh(x).hold();
}
-static ex cosh_diff(ex const & x, unsigned diff_param)
+static ex cosh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// hyperbolic tangent (trigonometric function)
//////////
-static ex tanh_evalf(ex const & x)
+static ex tanh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return tanh(ex_to_numeric(x)); // -> numeric tanh(numeric)
}
-static ex tanh_eval(ex const & x)
+static ex tanh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
if (x.is_zero()) // tanh(0) -> 0
return tanh(x).hold();
}
-static ex tanh_diff(ex const & x, unsigned diff_param)
+static ex tanh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
return _ex1()-power(tanh(x),_ex2());
}
-static ex tanh_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex tanh_series(const ex & x, const symbol & s, const ex & pt, int order)
{
// method:
// Taylor series where there is no pole falls back to tanh_diff.
// On a pole simply expand sinh(x)/cosh(x).
- ex xpoint = x.subs(s==point);
- if (!(2*I*xpoint/Pi).info(info_flags::odd))
+ const ex x_pt = x.subs(s==pt);
+ 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(s, point, order+2);
+ return (sinh(x)/cosh(x)).series(s, pt, order+2);
}
REGISTER_FUNCTION(tanh, tanh_eval, tanh_evalf, tanh_diff, tanh_series);
// inverse hyperbolic sine (trigonometric function)
//////////
-static ex asinh_evalf(ex const & x)
+static ex asinh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return asinh(ex_to_numeric(x)); // -> numeric asinh(numeric)
}
-static ex asinh_eval(ex const & x)
+static ex asinh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// asinh(0) -> 0
return asinh(x).hold();
}
-static ex asinh_diff(ex const & x, unsigned diff_param)
+static ex asinh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// inverse hyperbolic cosine (trigonometric function)
//////////
-static ex acosh_evalf(ex const & x)
+static ex acosh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return acosh(ex_to_numeric(x)); // -> numeric acosh(numeric)
}
-static ex acosh_eval(ex const & x)
+static ex acosh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// acosh(0) -> Pi*I/2
return acosh(x).hold();
}
-static ex acosh_diff(ex const & x, unsigned diff_param)
+static ex acosh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);
// inverse hyperbolic tangent (trigonometric function)
//////////
-static ex atanh_evalf(ex const & x)
+static ex atanh_evalf(const ex & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return atanh(ex_to_numeric(x)); // -> numeric atanh(numeric)
}
-static ex atanh_eval(ex const & x)
+static ex atanh_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// atanh(0) -> 0
return atanh(x).hold();
}
-static ex atanh_diff(ex const & x, unsigned diff_param)
+static ex atanh_diff(const ex & x, unsigned diff_param)
{
GINAC_ASSERT(diff_param==0);