* functions. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2000 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
#include "power.h"
#include "relational.h"
#include "symbol.h"
+#include "pseries.h"
#include "utils.h"
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx exp(x) -> exp(x)
return exp(x);
}
-REGISTER_FUNCTION(exp, exp_eval, exp_evalf, exp_diff, NULL);
+REGISTER_FUNCTION(exp, eval_func(exp_eval).
+ evalf_func(exp_evalf).
+ derivative_func(exp_deriv));
//////////
// 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(_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);
}
- // 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
-
+ GINAC_ASSERT(deriv_param==0);
+
// d/dx log(x) -> 1/x
return power(x, _ex_1());
}
-REGISTER_FUNCTION(log, log_eval, log_evalf, log_diff, NULL);
+static ex log_series(const ex &x, const relational &rel, int order)
+{
+ 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).
+ evalf_func(log_evalf).
+ derivative_func(log_deriv).
+ series_func(log_series));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx sin(x) -> cos(x)
return cos(x);
}
-REGISTER_FUNCTION(sin, sin_eval, sin_evalf, sin_diff, NULL);
+REGISTER_FUNCTION(sin, eval_func(sin_eval).
+ evalf_func(sin_evalf).
+ derivative_func(sin_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx cos(x) -> -sin(x)
return _ex_1()*sin(x);
}
-REGISTER_FUNCTION(cos, cos_eval, cos_evalf, cos_diff, NULL);
+REGISTER_FUNCTION(cos, eval_func(cos_eval).
+ evalf_func(cos_evalf).
+ derivative_func(cos_deriv));
//////////
// 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;
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 tan(x).hold();
}
-static ex tan_diff(ex const & x, unsigned diff_param)
+static ex tan_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx tan(x) -> 1+tan(x)^2;
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 relational &rel, int order)
{
// method:
- // Taylor series where there is no pole falls back to tan_diff.
+ // Taylor series where there is no pole falls back to tan_deriv.
// 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(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(s, point, order+2);
+ return (sin(x)/cos(x)).series(rel, order+2);
}
-REGISTER_FUNCTION(tan, tan_eval, tan_evalf, tan_diff, tan_series);
+REGISTER_FUNCTION(tan, eval_func(tan_eval).
+ evalf_func(tan_evalf).
+ derivative_func(tan_deriv).
+ series_func(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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx asin(x) -> 1/sqrt(1-x^2)
return power(1-power(x,_ex2()),_ex_1_2());
}
-REGISTER_FUNCTION(asin, asin_eval, asin_evalf, asin_diff, NULL);
+REGISTER_FUNCTION(asin, eval_func(asin_eval).
+ evalf_func(asin_evalf).
+ derivative_func(asin_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx acos(x) -> -1/sqrt(1-x^2)
return _ex_1()*power(1-power(x,_ex2()),_ex_1_2());
}
-REGISTER_FUNCTION(acos, acos_eval, acos_evalf, acos_diff, NULL);
+REGISTER_FUNCTION(acos, eval_func(acos_eval).
+ evalf_func(acos_evalf).
+ derivative_func(acos_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx atan(x) -> 1/(1+x^2)
return power(_ex1()+power(x,_ex2()), _ex_1());
}
-REGISTER_FUNCTION(atan, atan_eval, atan_evalf, atan_diff, NULL);
+REGISTER_FUNCTION(atan, eval_func(atan_eval).
+ evalf_func(atan_evalf).
+ derivative_func(atan_deriv));
//////////
// 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_deriv(const ex & y, const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param<2);
+ GINAC_ASSERT(deriv_param<2);
- if (diff_param==0) {
+ if (deriv_param==0) {
// d/dy atan(y,x)
return x*power(power(x,_ex2())+power(y,_ex2()),_ex_1());
}
return -y*power(power(x,_ex2())+power(y,_ex2()),_ex_1());
}
-REGISTER_FUNCTION(atan2, atan2_eval, atan2_evalf, atan2_diff, NULL);
+REGISTER_FUNCTION(atan2, eval_func(atan2_eval).
+ evalf_func(atan2_evalf).
+ derivative_func(atan2_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx sinh(x) -> cosh(x)
return cosh(x);
}
-REGISTER_FUNCTION(sinh, sinh_eval, sinh_evalf, sinh_diff, NULL);
+REGISTER_FUNCTION(sinh, eval_func(sinh_eval).
+ evalf_func(sinh_evalf).
+ derivative_func(sinh_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx cosh(x) -> sinh(x)
return sinh(x);
}
-REGISTER_FUNCTION(cosh, cosh_eval, cosh_evalf, cosh_diff, NULL);
+REGISTER_FUNCTION(cosh, eval_func(cosh_eval).
+ evalf_func(cosh_evalf).
+ derivative_func(cosh_deriv));
+
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx tanh(x) -> 1-tanh(x)^2
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 relational &rel, int order)
{
// method:
- // Taylor series where there is no pole falls back to tanh_diff.
+ // Taylor series where there is no pole falls back to tanh_deriv.
// 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(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(s, point, order+2);
+ return (sinh(x)/cosh(x)).series(rel, order+2);
}
-REGISTER_FUNCTION(tanh, tanh_eval, tanh_evalf, tanh_diff, tanh_series);
+REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
+ evalf_func(tanh_evalf).
+ derivative_func(tanh_deriv).
+ series_func(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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx asinh(x) -> 1/sqrt(1+x^2)
return power(_ex1()+power(x,_ex2()),_ex_1_2());
}
-REGISTER_FUNCTION(asinh, asinh_eval, asinh_evalf, asinh_diff, NULL);
+REGISTER_FUNCTION(asinh, eval_func(asinh_eval).
+ evalf_func(asinh_evalf).
+ derivative_func(asinh_deriv));
//////////
// 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_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx acosh(x) -> 1/(sqrt(x-1)*sqrt(x+1))
return power(x+_ex_1(),_ex_1_2())*power(x+_ex1(),_ex_1_2());
}
-REGISTER_FUNCTION(acosh, acosh_eval, acosh_evalf, acosh_diff, NULL);
+REGISTER_FUNCTION(acosh, eval_func(acosh_eval).
+ evalf_func(acosh_evalf).
+ derivative_func(acosh_deriv));
//////////
// 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
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);
return atanh(x).hold();
}
-static ex atanh_diff(ex const & x, unsigned diff_param)
+static ex atanh_deriv(const ex & x, unsigned deriv_param)
{
- GINAC_ASSERT(diff_param==0);
+ GINAC_ASSERT(deriv_param==0);
// d/dx atanh(x) -> 1/(1-x^2)
return power(_ex1()-power(x,_ex2()),_ex_1());
}
-REGISTER_FUNCTION(atanh, atanh_eval, atanh_evalf, atanh_diff, NULL);
+REGISTER_FUNCTION(atanh, eval_func(atanh_eval).
+ evalf_func(atanh_evalf).
+ derivative_func(atanh_deriv));
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff