* fixed printing defaults for functions.
* removed functions "numerical <functionname>(const numeric& x)". For the
internally used abs, factorial and binomial functions static members of the
respective classes have been added.
--- /dev/null
+/** @file check_numeric.cpp
+ *
+ * These exams creates some numbers and check the result of several boolean
+ * tests on these numbers like is_integer() etc... */
+
+/*
+ * GiNaC Copyright (C) 1999-2005 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
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+#include "checks.h"
+
+/* Simple and maybe somewhat pointless consistency tests of assorted tests and
+ * conversions. */
+static unsigned check_numeric1()
+{
+ unsigned result = 0;
+ bool errorflag = false;
+ int re_q, im_q;
+
+ // Check some numerator and denominator calculations:
+ for (int rep=0; rep<200; ++rep) {
+ do { re_q = rand(); } while (re_q == 0);
+ do { im_q = rand(); } while (im_q == 0);
+ numeric r(rand()-RAND_MAX/2, re_q);
+ numeric i(rand()-RAND_MAX/2, im_q);
+ numeric z = r + I*i;
+ numeric p = numer(z);
+ numeric q = denom(z);
+ numeric res = p/q;
+ if (res != z) {
+ clog << z << " erroneously transformed into "
+ << p << "/" << q << " by numer() and denom()" << endl;
+ errorflag = true;
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
+}
+
+static unsigned check_numeric2()
+{
+ unsigned result = 0;
+ bool errorflag = false;
+ int i_num, i_den;
+
+ // Check non-nested radicals (n/d)^(m/n) in ex wrapper class:
+ for (int i=0; i<200; ++i) {
+ for (int j=2; j<13; ++j) {
+ // construct an exponent 1/j...
+ numeric nm(1,j);
+ nm += numeric(int(20.0*rand()/(RAND_MAX+1.0))-10);
+ // ...a numerator...
+ do {
+ i_num = rand();
+ } while (i_num<=0);
+ numeric num(i_num);
+ // ...and a denominator.
+ do {
+ i_den = (rand())/100;
+ } while (i_den<=0);
+ numeric den(i_den);
+ // construct the radicals:
+ ex radical = pow(ex(num)/ex(den),ex(nm));
+ numeric floating = pow(num/den,nm);
+ // test the result:
+ if (is_a<numeric>(radical)) {
+ // This is very improbable with decent random numbers but it
+ // still can happen, so we better check if it is correct:
+ if (pow(radical,inverse(nm))==num/den) {
+ // Aha! We drew some lucky numbers. Nothing to see here...
+ } else {
+ clog << "(" << num << "/" << den << ")^(" << nm
+ << ") should have been a product, instead it's "
+ << radical << endl;
+ errorflag = true;
+ }
+ }
+ numeric ratio = abs_function::eval_numeric(ex_to<numeric>(evalf(radical))/floating);
+ if (ratio>1.0001 && ratio<0.9999) {
+ clog << "(" << num << "/" << den << ")^(" << nm
+ << ") erroneously evaluated to " << radical;
+ errorflag = true;
+ }
+ }
+ }
+ if (errorflag)
+ ++result;
+
+ return result;
+}
+
+unsigned check_numeric()
+{
+ unsigned result = 0;
+
+ cout << "checking consistency of numeric types" << flush;
+ clog << "---------consistency of numeric types:" << endl;
+
+ result += check_numeric1(); cout << '.' << flush;
+ result += check_numeric2(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
+}
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(function, exprseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(function, exprseq,
+ print_func<print_context>(&function::do_print).
+ print_func<print_latex>(&function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
function::function(const archive_node& n, lst& sym_lst) : inherited(n, sym_lst)
{
ex function::expand(unsigned options) const
{
return setflag(status_flags::expanded);
-//TODO??
-// // Only expand arguments when asked to do so
-// if (options & expand_options::expand_function_args)
-// return inherited::expand(options);
-// else
-// return (options == 0) ? setflag(status_flags::expanded) : *this;
}
bool function::info(unsigned inf) const
}
}
-void function::print(const print_context& c, unsigned level) const
-{
- const std::vector<print_functor>& pdt = get_class_info().options.get_print_dispatch_table();
- unsigned id = c.get_class_info().options.get_id();
- if (id >= pdt.size() || !(pdt[id].is_valid())) {
- if (is_a<print_tree>(c)) {
- c.s << std::string(level, ' ') << class_name()
- << " @" << this
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << ", nops=" << nops()
- << std::endl;
- unsigned delta_indent = static_cast<const print_tree&>(c).delta_indent;
- for (size_t i=0; i<seq.size(); ++i) {
- seq[i].print(c, level + delta_indent);
- }
- c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
- } else if (is_a<print_latex>(c)) {
- c.s << "\\mbox{" << class_name() << "}";
- inherited::do_print(c,level);
- } else {
- std::string classname(class_name());
- c.s << classname.erase(classname.find("_function",0),9);
- inherited::do_print(c,level);
- }
- } else {
- pdt[id](*this, c, level);
+void function::do_print(const print_context& c, unsigned level) const
+{
+ std::string classname(class_name());
+ c.s << classname;
+ inherited::do_print(c,level);
+}
+
+void function::do_print_cmath(const print_context& c, unsigned level) const
+{
+ std::string classname(class_name());
+ c.s << classname.erase(classname.find("_function",0),9);
+ inherited::do_print(c, level);
+}
+
+void function::do_print_cmath_latex(const print_context& c, unsigned level) const
+{
+ c.s << "\\";
+ do_print_cmath(c, level);
+}
+
+void function::do_print_latex(const print_context& c, unsigned level) const
+{
+ c.s << "\\mbox{" << class_name() << "}";
+ inherited::do_print(c, level);
+}
+
+void function::do_print_tree(const print_context& c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name()
+ << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << ", nops=" << nops()
+ << std::endl;
+ unsigned delta_indent = static_cast<const print_tree&>(c).delta_indent;
+ for (size_t i=0; i<seq.size(); ++i) {
+ seq[i].print(c, level + delta_indent);
}
+ c.s << std::string(level + delta_indent, ' ') << "=====" << std::endl;
}
} // namespace GiNaC
virtual ex power_law(const ex& exp) const;
public:
virtual bool info(unsigned inf) const;
- virtual void print(const print_context& c, unsigned level = 0) const;
+public:
+ void do_print_cmath(const print_context & c, unsigned level) const;
+ void do_print_cmath_latex(const print_context & c, unsigned level) const;
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_context & c, unsigned level) const;
+ void do_print_tree(const print_context & c, unsigned level) const;
public:
function() { }
function(tinfo_t ti) { tinfo_key = ti; }
GiNaC::registered_class_info classname::reg_info = GiNaC::registered_class_info(GiNaC::registered_class_options(#classname, "function", &classname::tinfo_static, &classname::unarchive).func_factory(&classname::factory).options); \
const tinfo_static_t classname::tinfo_static = {};
-/** Exception class thrown by classes which provide their own series expansion
- * to signal that ordinary Taylor expansion is safe. */
-class do_taylor {};
-
} // namespace GiNaC
#endif // ifndef __GINAC_FUNCTION_H__
/** @file inifcns.cpp
*
- * Implementation of GiNaC's initially known functions. */
+ * Implementation of GiNaC's initially known basic functions. */
/*
* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
#include "symmetry.h"
#include "utils.h"
+#include <cln/cln.h>
#include <stdexcept>
#include <vector>
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(abs_function,
+ print_func<print_context>(&function::do_print_cmath).
print_func<print_csrc_float>(&abs_function::do_print_csrc_float).
- print_func<print_latex>(&abs_function::do_print_latex))
+ print_func<print_latex>(&abs_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex abs_function::conjugate() const
{
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg))
- return abs(ex_to<numeric>(arg));
+ return eval_numeric(ex_to<numeric>(arg));
else
return this->hold();
}
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg)) {
- return abs(ex_to<numeric>(arg));
+ return eval_numeric(ex_to<numeric>(arg));
}
return this->hold();
return power(abs(arg), exp).hold();
}
+numeric abs_function::eval_numeric(const numeric& x)
+{
+ return cln::abs(x.to_cl_N());
+}
+
void abs_function::do_print_csrc_float(const print_context& c, unsigned level) const
{
c.s << "fabs("; seq[0].print(c); c.s << ")";
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(conjugate_function,
- print_func<print_latex>(&conjugate_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&conjugate_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex conjugate_function::conjugate() const
{
void conjugate_function::do_print_latex(const print_context& c, unsigned level) const
{
const ex& arg = seq[0];
- c.s << "\\bar{"; arg.print(c); c.s << "}";
+ if (is_exactly_a<symbol>(arg)) {
+ c.s << "{" << arg << "^\\ast}";
+ } else {
+ c.s << "{\\left(" << arg << "\\right)}^\\ast}";
+ }
}
//////////
// Complex sign
//////////
-GINAC_IMPLEMENT_FUNCTION(csgn_function)
+GINAC_IMPLEMENT_FUNCTION(csgn)
-ex csgn_function::conjugate() const
+ex csgn::conjugate() const
{
return *this;
}
-ex csgn_function::eval(int level) const
+ex csgn::eval(int level) const
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg))
- return csgn(ex_to<numeric>(arg));
+ return ex_to<numeric>(arg).csgn();
else if (is_exactly_a<mul>(arg) &&
is_exactly_a<numeric>(arg.op(arg.nops()-1))) {
return this->hold();
}
-ex csgn_function::evalf(int level) const
+ex csgn::evalf(int level) const
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg))
- return csgn(ex_to<numeric>(arg));
+ return ex_to<numeric>(arg).csgn();
return this->hold();
}
-ex csgn_function::power_law(const ex& exp) const
+ex csgn::power_law(const ex& exp) const
{
const ex& arg = seq[0];
if (is_a<numeric>(exp) && exp.info(info_flags::positive) && ex_to<numeric>(exp).is_integer()) {
return power(*this, exp).hold();
}
-ex csgn_function::series(const relational& r, int order, unsigned options) const
+ex csgn::series(const relational& r, int order, unsigned options) const
{
const ex& arg = seq[0];
const ex arg_pt = arg.subs(r, subs_options::no_pattern);
// Step function
//////////
-GINAC_IMPLEMENT_FUNCTION(step_function)
+GINAC_IMPLEMENT_FUNCTION(step)
-ex step_function::conjugate() const
+ex step::conjugate() const
{
return *this;
}
-ex step_function::eval(int level) const
+ex step::eval(int level) const
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg))
- return step(ex_to<numeric>(arg));
+ return ex_to<numeric>(arg).step();
else if (is_exactly_a<mul>(arg) &&
is_exactly_a<numeric>(arg.op(arg.nops()-1))) {
return this->hold();
}
-ex step_function::evalf(int level) const
+ex step::evalf(int level) const
{
const ex& arg = seq[0];
if (is_exactly_a<numeric>(arg))
- return step(ex_to<numeric>(arg));
+ return ex_to<numeric>(arg).step();
return this->hold();
}
-ex step_function::series(const relational& rel, int order, unsigned options) const
+ex step::series(const relational& rel, int order, unsigned options) const
{
const ex& arg = seq[0];
const ex arg_pt = arg.subs(rel, subs_options::no_pattern);
// factorial
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(factorial_function,
- print_func<print_dflt>(&factorial_function::do_print_dflt_latex).
- print_func<print_latex>(&factorial_function::do_print_dflt_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(factorial,
+ print_func<print_dflt>(&factorial::do_print_dflt_latex).
+ print_func<print_latex>(&factorial::do_print_dflt_latex))
-ex factorial_function::conjugate() const
+ex factorial::conjugate() const
{
return *this;
}
-ex factorial_function::eval(int level) const
+ex factorial::eval(int level) const
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return factorial(ex_to<numeric>(x));
+ return eval_numeric(ex_to<numeric>(x));
else
return this->hold();
}
-ex factorial_function::evalf(int level) const
+ex factorial::evalf(int level) const
{
return this->hold();
}
-void factorial_function::do_print_dflt_latex(const print_context& c, unsigned level) const
+numeric factorial::eval_numeric(const numeric& x)
+{
+ if (!x.is_nonneg_integer())
+ throw std::range_error("numeric::factorial(): argument must be integer >= 0");
+ return numeric(cln::factorial(x.to_int()));
+}
+
+void factorial::do_print_dflt_latex(const print_context& c, unsigned level) const
{
const ex& x = seq[0];
if (is_exactly_a<symbol>(x) || is_exactly_a<constant>(x) || is_exactly_a<function>(x)) {
// binomial
//////////
-GINAC_IMPLEMENT_FUNCTION(binomial_function)
+GINAC_IMPLEMENT_FUNCTION_OPT(binomial,
+ print_func<print_latex>(&binomial::do_print_latex))
// At the moment the numeric evaluation of a binomail function always
// gives a real number, but if this would be implemented using the gamma
// function, also complex conjugation should be changed (or rather, deleted).
-ex binomial_function::conjugate() const
+ex binomial::conjugate() const
{
return *this;
}
-ex binomial_function::sym(const ex& x, const numeric& y) const
+ex binomial::eval(int level) const
+{
+ const ex& x = seq[0];
+ const ex& y = seq[1];
+ if (is_exactly_a<numeric>(y)) {
+ if (is_exactly_a<numeric>(x) && ex_to<numeric>(x).is_integer())
+ return eval_numeric(ex_to<numeric>(x), ex_to<numeric>(y));
+ else
+ return sym(x, ex_to<numeric>(y));
+ } else
+ return this->hold();
+}
+
+ex binomial::evalf(int level) const
+{
+ return this->hold();
+}
+
+/** The Binomial coefficients. It computes the binomial coefficients. For
+ * integer n and k and positive n this is the number of ways of choosing k
+ * objects from n distinct objects. If n is negative, the formula
+ * binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */
+numeric binomial::eval_numeric(const numeric& n, const numeric& k)
+{
+ if (n.is_integer() && k.is_integer()) {
+ if (n.is_nonneg_integer()) {
+ if (k.compare(n)!=1 && k.compare(*_num0_p)!=-1)
+ return numeric(cln::binomial(n.to_int(),k.to_int()));
+ else
+ return *_num0_p;
+ } else {
+ return _num_1_p->power(k)*eval_numeric(k-n-(*_num1_p),k);
+ }
+ }
+
+ // should really be gamma(n+1)/gamma(k+1)/gamma(n-k+1) or a suitable limit
+ throw std::range_error("binomial::eval_numeric(): don't know how to evaluate that.");
+}
+
+ex binomial::sym(const ex& x, const numeric& y) const
{
if (y.is_integer()) {
if (y.is_nonneg_integer()) {
return this->hold();
}
-ex binomial_function::eval(int level) const
-{
- const ex& x = seq[0];
- const ex& y = seq[1];
- if (is_exactly_a<numeric>(y)) {
- if (is_exactly_a<numeric>(x) && ex_to<numeric>(x).is_integer())
- return binomial(ex_to<numeric>(x), ex_to<numeric>(y));
- else
- return sym(x, ex_to<numeric>(y));
- } else
- return this->hold();
-}
-
-ex binomial_function::evalf(int level) const
+void binomial::do_print_latex(const print_context& c, unsigned level) const
{
- return this->hold();
+ c.s << "{ {" << seq[0] << "} \\choose {" << seq[1] << "} }";
}
//////////
// Order term function (for truncated power series)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(Order_function,
- print_func<print_latex>(&Order_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(Order,
+ print_func<print_latex>(&Order::do_print_latex))
-ex Order_function::conjugate() const
+ex Order::conjugate() const
{
return *this;
}
-ex Order_function::derivative(const symbol& s) const
+ex Order::derivative(const symbol& s) const
{
return Order(seq[0].diff(s));
}
-ex Order_function::eval(int level) const
+ex Order::eval(int level) const
{
const ex& x = op(0);
if (is_exactly_a<numeric>(x)) {
return this->hold();
}
-ex Order_function::series(const relational& r, int order, unsigned options) const
+ex Order::series(const relational& r, int order, unsigned options) const
{
const ex& x = op(0);
// Just wrap the function into a pseries object
return pseries(r, new_seq);
}
-void Order_function::do_print_latex(const print_context& c, unsigned level) const
+void Order::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\mathcal{O}";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// Abstract derivative of functions
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(function_derivative_function,
- print_func<print_dflt>(&function_derivative_function::do_print_dflt).
- print_func<print_tree>(&function_derivative_function::do_print_tree))
+GINAC_IMPLEMENT_FUNCTION_OPT(function_derivative,
+ print_func<print_dflt>(&function_derivative::do_print_dflt).
+ print_func<print_latex>(&function_derivative::do_print_latex).
+ print_func<print_tree>(&function_derivative::do_print_tree))
/** Implementation of ex::diff() for derivatives. It applies the chain rule.
* @see ex::diff */
-ex function_derivative_function::derivative(const symbol& s) const
+ex function_derivative::derivative(const symbol& s) const
{
GINAC_ASSERT(seq[0].size() == 2);
GINAC_ASSERT(is_a<lst>(seq[0]));
return result;
}
-ex function_derivative_function::eval(int level) const
+ex function_derivative::eval(int level) const
{
if (level > 1) {
// first evaluate children, then we will end up here again
- return function_derivative_function(evalchildren(level));
+ return function_derivative(evalchildren(level));
}
const ex& params = seq[0];
return this->hold();
}
-void function_derivative_function::do_print_dflt(const print_context& c, unsigned level) const
+void function_derivative::do_print_dflt(const print_context& c, unsigned level) const
{
c.s << "D[";
const lst& params = ex_to<lst>(seq[0]);
c.s << *i << "](" << seq[1] << ")";
}
-void function_derivative_function::do_print_tree(const print_tree& c, unsigned level) const
+void function_derivative::do_print_latex(const print_context& c, unsigned level) const
+{
+ c.s << "\\mbox{D}[";
+ const lst& params = ex_to<lst>(seq[0]);
+ lst::const_iterator i = params.begin(), end = params.end();
+ --end;
+ while (i != end) {
+ c.s << *i++ << ",";
+ }
+ c.s << *i << "](" << seq[1] << ")";
+}
+
+void function_derivative::do_print_tree(const print_tree& c, unsigned level) const
{
c.s << std::string(level, ' ') << class_name() << " "
<< ex_to<function>(seq[1]).class_name() << " @" << this
/** @file inifcns.h
*
- * Interface to GiNaC's initially known functions. */
+ * Interface to GiNaC's initially known basic functions. */
/*
* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
virtual ex power_law(const ex& exp) const;
+public:
+ static numeric eval_numeric(const numeric& x);
protected:
void do_print_csrc_float(const print_context& c, unsigned level) const;
void do_print_latex(const print_context& c, unsigned level) const;
inline abs_function abs(float x1) { return abs_function(x1); }
/** Complex conjugate. */
-GINAC_FUNCTION_1P(conjugate,
- GINAC_FUNCTION_conjugate
- GINAC_FUNCTION_eval
- GINAC_FUNCTION_evalf
- GINAC_FUNCTION_print_latex)
+class conjugate_function : public function
+{
+ GINAC_DECLARE_FUNCTION_1P(conjugate_function)
+public:
+ virtual ex conjugate() const;
+ virtual ex eval(int level = 0) const;
+ virtual ex evalf(int level = 0) const;
+protected:
+ void do_print_latex(const print_context& c, unsigned level) const;
+};
+
+template<typename T1> inline conjugate_function conjugate(const T1& x1) { return conjugate_function(x1); }
/** Complex sign. */
-GINAC_FUNCTION_1P(csgn,
- GINAC_FUNCTION_conjugate
- GINAC_FUNCTION_eval
- GINAC_FUNCTION_evalf
- GINAC_FUNCTION_power_law
- GINAC_FUNCTION_series)
+class csgn : public function
+{
+ GINAC_DECLARE_FUNCTION_1P(csgn)
+public:
+ virtual ex conjugate() const;
+ virtual ex eval(int level = 0) const;
+ virtual ex evalf(int level = 0) const;
+ virtual ex power_law(const ex& exp) const;
+ virtual ex series(const relational& r, int order, unsigned options = 0) const;
+};
/** Step function. */
-class step_function : public function
+class step : public function
{
- GINAC_DECLARE_FUNCTION_1P(step_function)
+ GINAC_DECLARE_FUNCTION_1P(step)
public:
virtual ex conjugate() const;
virtual ex eval(int level = 0) const;
virtual ex series(const relational& r, int order, unsigned options = 0) const;
};
-template<typename T1> inline step_function step(const T1& x1) { return step_function(x1); }
-
/** Factorial function. */
-class factorial_function : public function
+class factorial : public function
{
- GINAC_DECLARE_FUNCTION_1P(factorial_function)
+ GINAC_DECLARE_FUNCTION_1P(factorial)
public:
virtual ex conjugate() const;
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
+public:
+ static numeric eval_numeric(const numeric& x);
protected:
void do_print_dflt_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline factorial_function factorial(const T1& x1) { return factorial_function(x1); }
-
/** Binomial function. */
-class binomial_function : public function
+class binomial : public function
{
- GINAC_DECLARE_FUNCTION_2P(binomial_function)
+ GINAC_DECLARE_FUNCTION_2P(binomial)
public:
virtual ex conjugate() const;
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
+public:
+ static numeric eval_numeric(const numeric& n, const numeric& k);
protected:
ex sym(const ex& x, const numeric& y) const;
+protected:
+ void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1, typename T2> inline binomial_function binomial(const T1& x1, const T2& x2) { return binomial_function(x1, x2); }
-
/** Order term function (for truncated power series). */
-class Order_function : public function
+class Order : public function
{
- GINAC_DECLARE_FUNCTION_1P(Order_function)
+ GINAC_DECLARE_FUNCTION_1P(Order)
public:
virtual ex conjugate() const;
virtual ex derivative(const symbol& s) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline Order_function Order(const T1& x1) { return Order_function(x1); }
-
/** Abstract derivative of functions. */
-class function_derivative_function : public function
+class function_derivative : public function
{
- GINAC_DECLARE_FUNCTION_2P(function_derivative_function)
+ GINAC_DECLARE_FUNCTION_2P(function_derivative)
public:
virtual ex derivative(const symbol& s) const;
virtual ex eval(int level = 0) const;
protected:
void do_print_dflt(const print_context& c, unsigned level) const;
+ void do_print_latex(const print_context& c, unsigned level) const;
void do_print_tree(const print_tree& c, unsigned level) const;
};
-template<typename T1, typename T2>
-inline function_derivative_function function_derivative(const T1& x1, const T2& x2) { return function_derivative_function(x1, x2); }
-
ex lsolve(const ex& eqns, const ex& symbols, unsigned options = solve_algo::automatic);
/** Find a real root of real-valued function f(x) numerically within a given
/** @file inifcns_exp.cpp
*
- * Implementation of TODO
- * functions. */
+ * Implementation of GiNaC's initially known exponential and related functions. */
/*
* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
namespace GiNaC {
-GINAC_IMPLEMENT_FUNCTION_OPT(eta_function,
- print_func<print_latex>(&eta_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(eta,
+ print_func<print_latex>(&eta::do_print_latex))
-ex eta_function::conjugate() const
+ex eta::conjugate() const
{
return -eta(seq[0], seq[1]);
}
-ex eta_function::eval(int level) const
+ex eta::eval(int level) const
{
// Canonicalize argument order according to the symmetry properties
exvector v = seq;
cut -= 4;
if (nxy.is_real() && nxy.is_negative())
cut += 4;
- return (I/4)*Pi*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
- (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
+ return (I/4)*Pi*(((-imag(nx)).csgn()+1)*((-imag(ny)).csgn()+1)*((imag(nxy)).csgn()+1)-
+ ((imag(nx)).csgn()+1)*((imag(ny)).csgn()+1)*((-imag(nxy)).csgn()+1)+cut);
}
return this->hold();
}
-ex eta_function::evalf(int level) const
+ex eta::evalf(int level) const
{
const ex& x = seq[0];
const ex& y = seq[1];
cut -= 4;
if (nxy.is_real() && nxy.is_negative())
cut += 4;
- return GiNaC::evalf(I/4*Pi)*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
- (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
+ return GiNaC::evalf(I/4*Pi)*(((-imag(nx)).csgn()+1)*((-imag(ny)).csgn()+1)*((imag(nxy)).csgn()+1)-
+ ((imag(nx)).csgn()+1)*((imag(ny)).csgn()+1)*((-imag(nxy)).csgn()+1)+cut);
}
return this->hold();
}
-ex eta_function::series(const relational& rel, int order, unsigned options) const
+ex eta::series(const relational& rel, int order, unsigned options) const
{
const ex& x = seq[0];
const ex& y = seq[1];
if ((x_pt.info(info_flags::numeric) && x_pt.info(info_flags::negative)) ||
(y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) ||
((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
- throw (std::domain_error("eta_series(): on discontinuity"));
+ throw (std::domain_error("eta::series(): on discontinuity"));
epvector seq;
seq.push_back(expair(eta(x_pt,y_pt), _ex0));
return pseries(rel, seq);
}
-void eta_function::do_print_latex(const print_context& c, unsigned level) const
+void eta::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\eta";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(exp_function,
+ print_func<print_context>(&function::do_print_cmath).
print_func<print_csrc_float>(&exp_function::do_print_csrc_float).
- print_func<print_latex>(&exp_function::do_print_latex))
+ print_func<print_latex>(&exp_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex exp_function::eval(int level) const
{
// exp(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return exp(ex_to<numeric>(x));
+ return numeric(cln::exp(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return exp(ex_to<numeric>(x));
+ return numeric(cln::exp(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
void exp_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\exp";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(log_function,
+ print_func<print_context>(&function::do_print_cmath).
print_func<print_csrc_float>(&log_function::do_print_csrc_float).
- print_func<print_latex>(&log_function::do_print_latex))
+ print_func<print_latex>(&log_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex log_function::eval(int level) const
{
// log(float) -> float
if (!x.info(info_flags::crational))
- return log(ex_to<numeric>(x));
+ return numeric(cln::log(ex_to<numeric>(x).to_cl_N()));
}
// log(exp(t)) -> t (if -Pi < t.imag() <= Pi):
ex log_function::evalf(int level) const
{
const ex& x = seq[0];
- if (is_exactly_a<numeric>(x))
- return log(ex_to<numeric>(x));
-
+ if (is_exactly_a<numeric>(x)) {
+ const numeric& xn = ex_to<numeric>(x);
+ if (xn.is_zero())
+ throw pole_error("log(): logarithmic pole",0);
+ return numeric(cln::log(xn.to_cl_N()));
+ }
+
return this->hold();
}
void log_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\log";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// Logarithm of Gamma function
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(lgamma_function,
- print_func<print_latex>(&lgamma_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(lgamma,
+ print_func<print_latex>(&lgamma::do_print_latex))
/** Evaluation of lgamma(x), the natural logarithm of the Gamma function.
* Knows about integer arguments and that's it. Somebody ought to provide
* some good numerical evaluation some day...
*
* @exception GiNaC::pole_error("lgamma_eval(): logarithmic pole",0) */
-ex lgamma_function::eval(int level) const
+ex lgamma::eval(int level) const
{
const ex& x = seq[0];
if (x.info(info_flags::numeric)) {
return this->hold();
}
-ex lgamma_function::evalf(int level) const
+ex lgamma::evalf(int level) const
{
- const ex& x = seq[0];
- if (is_exactly_a<numeric>(x)) {
- try {
- return lgamma(ex_to<numeric>(x));
- } catch (const dunno& e) { }
- }
-
return this->hold();
}
-ex lgamma_function::pderivative(unsigned deriv_param) const
+ex lgamma::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
GINAC_ASSERT(deriv_param==0);
return psi(x);
}
-ex lgamma_function::series(const relational& rel, int order, unsigned options) const
+ex lgamma::series(const relational& rel, int order, unsigned options) const
{
const ex& arg = seq[0];
// method:
return (lgamma(arg+m+_ex1)-recur).series(rel, order, options);
}
-void lgamma_function::do_print_latex(const print_context& c, unsigned level) const
+void lgamma::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\log \\Gamma";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// true Gamma function
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(tgamma_function,
- print_func<print_latex>(&tgamma_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(tgamma,
+ print_func<print_latex>(&tgamma::do_print_latex))
/** Evaluation of tgamma(x), the true Gamma function. Knows about integer
* arguments, half-integer arguments and that's it. Somebody ought to provide
* some good numerical evaluation some day...
*
* @exception pole_error("tgamma_eval(): simple pole",0) */
-ex tgamma_function::eval(int level) const
+ex tgamma::eval(int level) const
{
const ex& x = seq[0];
if (x.info(info_flags::numeric)) {
if (two_x.is_even()) {
// tgamma(n) -> (n-1)! for postitive n
if (two_x.is_positive()) {
- return factorial(ex_to<numeric>(x).sub(*_num1_p));
+ return factorial::eval_numeric(ex_to<numeric>(x).sub(*_num1_p));
} else {
throw (pole_error("tgamma_eval(): simple pole",1));
}
} else {
// trap negative x==(-n+1/2)
// tgamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
- const numeric n = abs(ex_to<numeric>(x).sub(*_num1_2_p));
+ const numeric n = abs_function::eval_numeric(ex_to<numeric>(x).sub(*_num1_2_p));
return (pow(*_num_2_p, n).div(doublefactorial(n.mul(*_num2_p).sub(*_num1_p))))*sqrt(Pi);
}
}
return this->hold();
}
-ex tgamma_function::evalf(int level) const
+ex tgamma::evalf(int level) const
{
- const ex& x = seq[0];
- if (is_exactly_a<numeric>(x)) {
- try {
- return tgamma(ex_to<numeric>(x));
- } catch (const dunno &e) { }
- }
-
return this->hold();
}
-ex tgamma_function::pderivative(unsigned deriv_param) const
+ex tgamma::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
GINAC_ASSERT(deriv_param==0);
return psi(x)*tgamma(x);
}
-ex tgamma_function::series(const relational& rel, int order, unsigned options) const
+ex tgamma::series(const relational& rel, int order, unsigned options) const
{
const ex& arg = seq[0];
// method:
return (tgamma(arg+m+_ex1)/ser_denom).series(rel, order, options);
}
-void tgamma_function::do_print_latex(const print_context& c, unsigned level) const
+void tgamma::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\Gamma";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// beta-function
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(beta_function,
- print_func<print_latex>(&beta_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(beta,
+ print_func<print_latex>(&beta::do_print_latex))
-ex beta_function::eval(int level) const
+ex beta::eval(int level) const
{
// Canonicalize argument order according to the symmetry properties
exvector v = seq;
return this->hold();
}
-ex beta_function::evalf(int level) const
+ex beta::evalf(int level) const
{
- const ex& x = seq[0];
- const ex& y = seq[1];
- if (is_exactly_a<numeric>(x) && is_exactly_a<numeric>(y)) {
- try {
- return tgamma(ex_to<numeric>(x))*tgamma(ex_to<numeric>(y))/tgamma(ex_to<numeric>(x+y));
- } catch (const dunno &e) { }
- }
-
return this->hold();
}
-ex beta_function::pderivative(unsigned deriv_param) const
+ex beta::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
return retval;
}
-ex beta_function::series(const relational& rel, int order, unsigned options) const
+ex beta::series(const relational& rel, int order, unsigned options) const
{
const ex& arg1 = seq[0];
const ex& arg2 = seq[1];
return (arg1_ser*arg2_ser/arg1arg2_ser).series(rel, order, options).expand();
}
-void beta_function::do_print_latex(const print_context& c, unsigned level) const
+void beta::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\mbox{B}";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// Psi-function (aka digamma-function)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(psi1_function,
- print_func<print_latex>(&psi1_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(psi1,
+ print_func<print_latex>(&psi1::do_print_latex))
/** Evaluation of digamma-function psi(x).
* Somebody ought to provide some good numerical evaluation some day... */
-ex psi1_function::eval(int level) const
+ex psi1::eval(int level) const
{
const ex& x = seq[0];
if (x.info(info_flags::numeric)) {
return this->hold();
}
-ex psi1_function::evalf(int level) const
+ex psi1::evalf(int level) const
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x)) {
return this->hold();
}
-ex psi1_function::pderivative(unsigned deriv_param) const
+ex psi1::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
GINAC_ASSERT(deriv_param==0);
return psi(_ex1, x);
}
-ex psi1_function::series(const relational& rel, int order, unsigned options) const
+ex psi1::series(const relational& rel, int order, unsigned options) const
{
const ex& arg = seq[0];
// method:
return (psi(arg+m+_ex1)-recur).series(rel, order, options);
}
-void psi1_function::do_print_latex(const print_context& c, unsigned level) const
+void psi1::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\psi";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
// Psi-functions (aka polygamma-functions) psi(0,x)==psi(x)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(psi2_function,
- print_func<print_latex>(&psi2_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(psi2,
+ print_func<print_latex>(&psi2::do_print_latex))
/** Evaluation of polygamma-function psi(n,x).
* Somebody ought to provide some good numerical evaluation some day... */
-ex psi2_function::eval(int eval) const
+ex psi2::eval(int eval) const
{
const ex& n = seq[0];
const ex& x = seq[1];
// integer case
if (nx.is_equal(*_num1_p))
// use psi(n,1) == (-)^(n+1) * n! * zeta(n+1)
- return pow(*_num_1_p,nn+(*_num1_p))*factorial(nn)*zeta_function(nn+(*_num1_p));
+ return pow(*_num_1_p,nn+(*_num1_p))*factorial::eval_numeric(nn)*zeta_function(nn+(*_num1_p));
if (nx.is_positive()) {
// use the recurrence relation
// psi(n,m) == psi(n,m+1) - (-)^n * n! / m^(n+1)
numeric recur = 0;
for (numeric p = 1; p<nx; ++p)
recur += pow(p, -nn+(*_num_1_p));
- recur *= factorial(nn)*pow((*_num_1_p), nn);
+ recur *= factorial::eval_numeric(nn)*pow((*_num_1_p), nn);
return recur+psi(n,_ex1);
} else {
// for non-positive integers there is a pole:
// half integer case
if (nx.is_equal(*_num1_2_p))
// use psi(n,1/2) == (-)^(n+1) * n! * (2^(n+1)-1) * zeta(n+1)
- return pow(*_num_1_p,nn+(*_num1_p))*factorial(nn)*(pow(*_num2_p,nn+(*_num1_p)) + (*_num_1_p))*zeta_function(nn+(*_num1_p));
+ return pow(*_num_1_p,nn+(*_num1_p))*factorial::eval_numeric(nn)*(pow(*_num2_p,nn+(*_num1_p)) + (*_num_1_p))*zeta_function(nn+(*_num1_p));
if (nx.is_positive()) {
const numeric m = nx - (*_num1_2_p);
// use the multiplication formula
numeric recur = 0;
for (numeric p = nx; p<0; ++p)
recur += pow(p, -nn+(*_num_1_p));
- recur *= factorial(nn)*pow(*_num_1_p, nn+(*_num_1_p));
+ recur *= factorial::eval_numeric(nn)*pow(*_num_1_p, nn+(*_num_1_p));
return recur+psi(n,_ex1_2);
}
}
return this->hold();
}
-ex psi2_function::evalf(int eval) const
+ex psi2::evalf(int eval) const
{
const ex& n = seq[0];
const ex& x = seq[1];
return this->hold();
}
-ex psi2_function::pderivative(unsigned deriv_param) const
+ex psi2::pderivative(unsigned deriv_param) const
{
const ex& n = seq[0];
const ex& x = seq[1];
return psi(n+_ex1, x);
}
-ex psi2_function::series(const relational& rel, int order, unsigned options) const
+ex psi2::series(const relational& rel, int order, unsigned options) const
{
const ex& n = seq[0];
const ex& arg = seq[1];
return (psi(n, arg+m+_ex1)-recur).series(rel, order, options);
}
-void psi2_function::do_print_latex(const print_context& c, unsigned level) const
+void psi2::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\psi";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
} // namespace GiNaC
/** @file inifcns_exp.h
*
- * Interface to GiNaC's TODO */
+ * Interface to GiNaC's initially known exponential and related functions. */
/*
* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
// This function is closely related to the unwinding number K, sometimes found
// in modern literature: K(z) == (z-log(exp(z)))/(2*Pi*I).
//////////
-class eta_function : public function
+class eta : public function
{
- GINAC_DECLARE_FUNCTION_2P(eta_function)
+ GINAC_DECLARE_FUNCTION_2P(eta)
public:
virtual ex conjugate() const;
virtual ex eval(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1, typename T2> inline eta_function eta(const T1& x1, const T2& x2) { return eta_function(x1, x2); }
-
/** Exponential function. */
class exp_function : public function
{
inline log_function log(float x1) { return log_function(x1); }
/** Log-Gamma-function. */
-class lgamma_function : public function
+class lgamma : public function
{
- GINAC_DECLARE_FUNCTION_1P(lgamma_function)
+ GINAC_DECLARE_FUNCTION_1P(lgamma)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline lgamma_function lgamma(const T1& x1) { return lgamma_function(x1); }
-
/** Gamma-function. */
-class tgamma_function : public function
+class tgamma : public function
{
- GINAC_DECLARE_FUNCTION_1P(tgamma_function)
+ GINAC_DECLARE_FUNCTION_1P(tgamma)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline tgamma_function tgamma(const T1& x1) { return tgamma_function(x1); }
-
/** Beta-function. */
-class beta_function : public function
+class beta : public function
{
- GINAC_DECLARE_FUNCTION_2P(beta_function)
+ GINAC_DECLARE_FUNCTION_2P(beta)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1, typename T2> inline beta_function beta(const T1& x1, const T2& x2) { return beta_function(x1, x2); }
-
/** Psi-function (aka digamma-function). */
-class psi1_function : public function
+class psi1 : public function
{
- GINAC_DECLARE_FUNCTION_1P(psi1_function)
+ GINAC_DECLARE_FUNCTION_1P(psi1)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline psi1_function psi(const T1& x1) { return psi1_function(x1); }
+template<typename T1> inline psi1 psi(const T1& x1) { return psi1(x1); }
/** Derivatives of Psi-function (aka polygamma-functions). */
-class psi2_function : public function
+class psi2 : public function
{
- GINAC_DECLARE_FUNCTION_2P(psi2_function)
+ GINAC_DECLARE_FUNCTION_2P(psi2)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1, typename T2> inline psi2_function psi(const T1& x1, const T2& x2) { return psi2_function(x1, x2); }
+template<typename T1, typename T2> inline psi2 psi(const T1& x1, const T2& x2) { return psi2(x1, x2); }
} // namespace GiNaC
/** @file inifcns_polylog.cpp
*
- * Implementation of some special functions that have a representation as nested sums. TODO
+ * Implementation of GiNaC's initially known polylogarithmic functions.
*
* The functions are:
* classical polylogarithm Li(n,x)
#include <vector>
#include <cln/cln.h>
-
#include "inifcns.h"
#include "inifcns_exp.h"
#include "add.h"
// [Kol] (2.22)
return -(1-cln::expt(cln::cl_I(2),1-n)) * cln::zeta(n);
}
- if (abs(x.real()) < 0.4 && abs(abs(x)-1) < 0.01) {
+ if (abs_function::eval_numeric(x.real()) < 0.4 && abs_function::eval_numeric(abs_function::eval_numeric(x)-1) < 0.01) {
cln::cl_N x_ = ex_to<numeric>(x).to_cl_N();
cln::cl_N result = -cln::expt(cln::log(x_), n-1) * cln::log(1-x_) / cln::factorial(n-1);
for (int j=0; j<n-1; j++) {
// G({1,...,1};y) -> G({1};y)^k / k!
if (all_ones && a.size() > 1) {
- return pow(G_eval1(a.front(),scale), count_ones) / factorial(count_ones);
+ return pow(G_eval1(a.front(),scale), count_ones) / factorial::eval_numeric(count_ones);
}
// G({0,...,0};y) -> log(y)^k / k!
if (all_zero) {
- return pow(log(gsyms[std::abs(scale)]), a.size()) / factorial(a.size());
+ return pow(log(gsyms[std::abs(scale)]), a.size()) / factorial::eval_numeric(a.size());
}
// no special cases anymore -> convert it into Li
//
//////////////////////////////////////////////////////////////////////
-GINAC_IMPLEMENT_FUNCTION(G_function)
+GINAC_IMPLEMENT_FUNCTION_OPT(G_function,
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex G_function::eval(int level) const
{
s.append(+1);
}
if (all_zero) {
- return pow(log(y), x.nops()) / factorial(x.nops());
+ return pow(log(y), x.nops()) / factorial::eval_numeric(x.nops());
}
if (!y.info(info_flags::crational)) {
crational = false;
}
}
if (all_zero) {
- return pow(log(y), x.nops()) / factorial(x.nops());
+ return pow(log(y), x.nops()) / factorial::eval_numeric(x.nops());
}
if (!y.info(info_flags::crational)) {
crational = false;
s.append(+1);
}
if (all_zero) {
- return pow(log(y), x.nops()) / factorial(x.nops());
+ return pow(log(y), x.nops()) / factorial::eval_numeric(x.nops());
}
return G_numeric(x, s, y);
} else {
}
}
if (all_zero) {
- return pow(log(y), x.nops()) / factorial(x.nops());
+ return pow(log(y), x.nops()) / factorial::eval_numeric(x.nops());
}
return G_numeric(x, sn, y);
}
//////////////////////////////////////////////////////////////////////
GINAC_IMPLEMENT_FUNCTION_OPT(Li_function,
- print_func<print_latex>(&Li_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&Li_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex Li_function::eval(int level) const
{
// method:
// This is the branch cut: assemble the primitive series manually
// and then add the corresponding complex step function.
- const symbol &s = ex_to<symbol>(rel.lhs());
+ const symbol& s = ex_to<symbol>(rel.lhs());
const ex point = rel.rhs();
const symbol foo;
epvector seq;
//////////////////////////////////////////////////////////////////////
GINAC_IMPLEMENT_FUNCTION_OPT(S_function,
- print_func<print_latex>(&S_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&S_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex S_function::eval(int level) const
{
it++;
}
if (it == parameter.end()) {
- return pow(log(arg),parameter.nops()) / factorial(parameter.nops());
+ return pow(log(arg),parameter.nops()) / factorial::eval_numeric(parameter.nops());
}
//
if (allthesame) {
map_trafo_H_mult unify;
return unify((pow(H(lst(-1),1/arg).hold() - H(lst(0),1/arg).hold(), parameter.nops())
- / factorial(parameter.nops())).expand());
+ / factorial::eval_numeric(parameter.nops())).expand());
}
} else {
for (int i=1; i<parameter.nops(); i++) {
if (allthesame) {
map_trafo_H_mult unify;
return unify((pow(H(lst(1),1/arg).hold() + H(lst(0),1/arg).hold() + H_polesign, parameter.nops())
- / factorial(parameter.nops())).expand());
+ / factorial::eval_numeric(parameter.nops())).expand());
}
}
if (allthesame) {
map_trafo_H_mult unify;
ex res = unify((pow(-H(lst(1),(1-arg)/(1+arg)).hold() - H(lst(-1),(1-arg)/(1+arg)).hold(), parameter.nops())
- / factorial(parameter.nops())).expand());
+ / factorial::eval_numeric(parameter.nops())).expand());
return res;
}
} else if (parameter.op(0) == -1) {
if (allthesame) {
map_trafo_H_mult unify;
ex res = unify((pow(log(2) - H(lst(-1),(1-arg)/(1+arg)).hold(), parameter.nops())
- / factorial(parameter.nops())).expand());
+ / factorial::eval_numeric(parameter.nops())).expand());
return res;
}
} else {
if (allthesame) {
map_trafo_H_mult unify;
ex res = unify((pow(-log(2) - H(lst(0),(1-arg)/(1+arg)).hold() + H(lst(-1),(1-arg)/(1+arg)).hold(), parameter.nops())
- / factorial(parameter.nops())).expand());
+ / factorial::eval_numeric(parameter.nops())).expand());
return res;
}
}
//////////////////////////////////////////////////////////////////////
GINAC_IMPLEMENT_FUNCTION_OPT(H_function,
- print_func<print_latex>(&H_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&H_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex H_function::eval(int level) const
{
if (x == _ex0) {
return this->hold();
}
- return pow(log(x), m.nops()) / factorial(m.nops());
+ return pow(log(x), m.nops()) / factorial::eval_numeric(m.nops());
} else {
// all (minus) one
- return pow(-pos1*log(1-pos1*x), m.nops()) / factorial(m.nops());
+ return pow(-pos1*log(1-pos1*x), m.nops()) / factorial::eval_numeric(m.nops());
}
} else if ((step == 1) && (pos1 == _ex0)){
// convertible to S
//////////////////////////////////////////////////////////////////////
GINAC_IMPLEMENT_FUNCTION_OPT(zeta_function,
- print_func<print_latex>(&zeta_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&zeta_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex zeta_function::eval(int level) const
{
if (y.info(info_flags::odd)) {
return this->hold();
} else {
- return abs(bernoulli(y)) * pow(Pi, y) * pow(*_num2_p, y-(*_num1_p)) / factorial(y);
+ return abs_function::eval_numeric(bernoulli(y)) * pow(Pi, y) * pow(*_num2_p, y-(*_num1_p)) / factorial::eval_numeric(y);
}
} else {
if (y.info(info_flags::odd)) {
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(zetaderiv_function,
- print_func<print_latex>(&zetaderiv_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&zetaderiv_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex zetaderiv_function::eval(int level) const
{
/** @file inifcns_polylog.h
*
- * Interface to GiNaC's TODO */
+ * Interface to GiNaC's initially known polylogarithmic functions. */
/*
* GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
#include "pseries.h"
#include "utils.h"
+#include <cln/cln.h>
#include <stdexcept>
#include <string>
////////////////////////////////////////////////////////////////////////////////
GINAC_IMPLEMENT_FUNCTION_OPT(sin_function,
- print_func<print_latex>(&sin_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex sin_function::eval(int level) const
{
// sin(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return sin(ex_to<numeric>(x));
+ return numeric(cln::sin(ex_to<numeric>(x).to_cl_N()));
// sin() is odd
if (x.info(info_flags::negative))
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return sin(ex_to<numeric>(x));
-
+ return numeric(cln::sin(ex_to<numeric>(x).to_cl_N()));
+
return this->hold();
}
return cos(seq[0]);
}
-void sin_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\sin";
- inherited::do_print(c,level);
-}
-
//////////
// cosine (trigonometric function)
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(cos_function,
- print_func<print_latex>(&cos_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex cos_function::eval(int level) const
{
// cos(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return cos(ex_to<numeric>(x));
+ return numeric(cln::cos(ex_to<numeric>(x).to_cl_N()));
// cos() is even
if (x.info(info_flags::negative))
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return cos(ex_to<numeric>(x));
+ return numeric(cln::cos(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
return -sin(seq[0]);
}
-void cos_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\cos";
- inherited::do_print(c,level);
-}
-
//////////
// tangent (trigonometric function)
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(tan_function,
- print_func<print_latex>(&tan_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex tan_function::eval(int level) const
{
// tan(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) {
- return tan(ex_to<numeric>(x));
+ return numeric(cln::tan(ex_to<numeric>(x).to_cl_N()));
}
// tan() is odd
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return tan(ex_to<numeric>(x));
+ return numeric(cln::tan(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
return (sin(x)/cos(x)).series(rel, order, options);
}
-void tan_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\tan";
- inherited::do_print(c,level);
-}
-
//////////
// inverse sine (arc sine)
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(asin_function,
- print_func<print_latex>(&asin_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&asin_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex asin_function::eval(int level) const
{
// asin(float) -> float
if (!x.info(info_flags::crational))
- return asin(ex_to<numeric>(x));
+ return numeric(cln::asin(ex_to<numeric>(x).to_cl_N()));
// asin() is odd
if (x.info(info_flags::negative))
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return asin(ex_to<numeric>(x));
+ return numeric(cln::asin(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
void asin_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\arcsin";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(acos_function,
- print_func<print_latex>(&acos_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&acos_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex acos_function::eval(int level) const
{
// acos(float) -> float
if (!x.info(info_flags::crational))
- return acos(ex_to<numeric>(x));
+ return numeric(cln::acos(ex_to<numeric>(x).to_cl_N()));
// acos(-x) -> Pi-acos(x)
if (x.info(info_flags::negative))
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return acos(ex_to<numeric>(x));
+ return numeric(cln::acos(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
void acos_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\arccos";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(atan_function,
- print_func<print_latex>(&atan_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&atan_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex atan_function::eval(int level) const
{
// atan(float) -> float
if (!x.info(info_flags::crational))
- return atan(ex_to<numeric>(x));
+ return evalf(level);
// atan() is odd
if (x.info(info_flags::negative))
ex atan_function::evalf(int level) const
{
- const ex& x = seq[0];
- if (is_exactly_a<numeric>(x))
- return atan(ex_to<numeric>(x));
+ const ex& x_ = seq[0];
+ if (is_exactly_a<numeric>(x_)) {
+ const numeric& x = ex_to<numeric>(x_);
+ if (!x.is_real() && x.real().is_zero() && abs(x.imag()).is_equal(*_num1_p))
+ throw pole_error("atan(): logarithmic pole", 0);
+ return numeric(cln::atan(ex_to<numeric>(x).to_cl_N()));
+ }
return this->hold();
}
void atan_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\arctan";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(atan2_function,
- print_func<print_latex>(&atan2_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&atan2_function::do_print_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex atan2_function::eval(int level) const
{
// atan(float, float) -> float
if (!y.info(info_flags::crational) && !x.info(info_flags::crational))
- return atan(ex_to<numeric>(y), ex_to<numeric>(x));
+ return evalf(level);
// atan(real, real) -> atan(y/x) +/- Pi
if (y.info(info_flags::real) && x.info(info_flags::real)) {
ex atan2_function::evalf(int level) const
{
- const ex& y = seq[0];
- const ex& x = seq[1];
- if (is_exactly_a<numeric>(y) && is_exactly_a<numeric>(x))
- return atan(ex_to<numeric>(y), ex_to<numeric>(x));
-
+ const ex& y_ = seq[0];
+ const ex& x_ = seq[1];
+ if (is_exactly_a<numeric>(y_) && is_exactly_a<numeric>(x_)) {
+ const numeric& y = ex_to<numeric>(y_);
+ const numeric& x = ex_to<numeric>(x_);
+ if (x.is_real() && y.is_real())
+ return numeric(cln::atan(cln::the<cln::cl_R>(x.to_cl_N()), cln::the<cln::cl_R>(y.to_cl_N())));
+ else
+ throw std::invalid_argument("atan(): complex argument");
+ }
+
return this->hold();
}
void atan2_function::do_print_latex(const print_context& c, unsigned level) const
{
c.s << "\\arctan_2";
- inherited::do_print(c,level);
+ exprseq::do_print(c,level);
}
//////////
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(sinh_function,
- print_func<print_latex>(&sinh_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex sinh_function::eval(int level) const
{
// sinh(float) -> float
if (!x.info(info_flags::crational))
- return sinh(ex_to<numeric>(x));
+ return numeric(cln::sinh(ex_to<numeric>(x).to_cl_N()));
// sinh() is odd
if (x.info(info_flags::negative))
ex_to<numeric>(x/Pi).real().is_zero()) // sinh(I*x) -> I*sin(x)
return I*sin(x/I);
- const ex& t = x.op(0);
- if (is_exactly_a<asinh_function>(x)) {
+ if (is_exactly_a<asinh>(x)) {
// sinh(asinh(x)) -> x
- return t;
- } else if (is_exactly_a<acosh_function>(x)) {
+ return x.op(0);
+ } else if (is_exactly_a<acosh>(x)) {
// sinh(acosh(x)) -> sqrt(x-1) * sqrt(x+1)
+ const ex& t = x.op(0);
return sqrt(t-_ex1)*sqrt(t+_ex1);
- } else if (is_exactly_a<atanh_function>(x)) {
+ } else if (is_exactly_a<atanh>(x)) {
// sinh(atanh(x)) -> x/sqrt(1-x^2)
+ const ex& t = x.op(0);
return t*power::power(_ex1-power::power(t,_ex2),_ex_1_2);
}
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return sinh(ex_to<numeric>(x));
+ return numeric(cln::sinh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
return cosh(x);
}
-void sinh_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\arcsin";
- inherited::do_print(c,level);
-}
-
//////////
// hyperbolic cosine (trigonometric function)
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(cosh_function,
- print_func<print_latex>(&cosh_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex cosh_function::eval(int level) const
{
// cosh(float) -> float
if (!x.info(info_flags::crational))
- return cosh(ex_to<numeric>(x));
+ return numeric(cln::cosh(ex_to<numeric>(x).to_cl_N()));
// cosh() is even
if (x.info(info_flags::negative))
ex_to<numeric>(x/Pi).real().is_zero()) // cosh(I*x) -> cos(x)
return cos(x/I);
- if (is_exactly_a<acosh_function>(x)) {
+ if (is_exactly_a<acosh>(x)) {
// cosh(acosh(x)) -> x
return x.op(0);
- } else if (is_exactly_a<asinh_function>(x)) {
+ } else if (is_exactly_a<asinh>(x)) {
// cosh(asinh(x)) -> sqrt(1+x^2)
return sqrt(_ex1+power::power(x.op(0),_ex2));
- } else if (is_exactly_a<atanh_function>(x)) {
+ } else if (is_exactly_a<atanh>(x)) {
// cosh(atanh(x)) -> 1/sqrt(1-x^2)
return power::power(_ex1-power::power(x.op(0),_ex2),_ex_1_2);
}
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return cosh(ex_to<numeric>(x));
+ return numeric(cln::cosh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
return sinh(x);
}
-void cosh_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\arccos";
- inherited::do_print(c,level);
-}
-
//////////
// hyperbolic tangent (trigonometric function)
//////////
GINAC_IMPLEMENT_FUNCTION_OPT(tanh_function,
- print_func<print_latex>(&tanh_function::do_print_latex))
+ print_func<print_context>(&function::do_print_cmath).
+ print_func<print_latex>(&function::do_print_cmath_latex).
+ print_func<print_tree>(&function::do_print_tree))
ex tanh_function::eval(int level) const
{
// tanh(float) -> float
if (!x.info(info_flags::crational))
- return tanh(ex_to<numeric>(x));
+ return numeric(cln::tanh(ex_to<numeric>(x).to_cl_N()));
// tanh() is odd
if (x.info(info_flags::negative))
ex_to<numeric>(x/Pi).real().is_zero()) // tanh(I*x) -> I*tan(x);
return I*tan(x/I);
- if (is_exactly_a<atanh_function>(x)) {
+ if (is_exactly_a<atanh>(x)) {
// tanh(atanh(x)) -> x
return x.op(0);
- } else if (is_exactly_a<asinh_function>(x)) {
+ } else if (is_exactly_a<asinh>(x)) {
// tanh(asinh(x)) -> x/sqrt(1+x^2)
const ex& t = x.op(0);
return t*power::power(_ex1+power::power(t,_ex2),_ex_1_2);
- } else if (is_exactly_a<acosh_function>(x)) {
+ } else if (is_exactly_a<acosh>(x)) {
// tanh(acosh(x)) -> sqrt(x-1)*sqrt(x+1)/x
const ex& t = x.op(0);
return sqrt(t-_ex1)*sqrt(t+_ex1)*power::power(t,_ex_1);
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return tanh(ex_to<numeric>(x));
+ return numeric(cln::tanh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
return (sinh(x)/cosh(x)).series(rel, order, options);
}
-void tanh_function::do_print_latex(const print_context& c, unsigned level) const
-{
- c.s << "\\arctan";
- inherited::do_print(c,level);
-}
-
//////////
// inverse hyperbolic sine (trigonometric function)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(asinh_function,
- print_func<print_latex>(&asinh_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(asinh,
+ print_func<print_latex>(&asinh::do_print_latex))
-ex asinh_function::eval(int level) const
+ex asinh::eval(int level) const
{
const ex& x = seq[0];
// asinh(float) -> float
if (!x.info(info_flags::crational))
- return asinh(ex_to<numeric>(x));
+ return numeric(cln::asinh(ex_to<numeric>(x).to_cl_N()));
// asinh() is odd
if (x.info(info_flags::negative))
return this->hold();
}
-ex asinh_function::evalf(int level) const
+ex asinh::evalf(int level) const
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return asinh(ex_to<numeric>(x));
+ return numeric(cln::asinh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
-ex asinh_function::pderivative(unsigned deriv_param) const
+ex asinh::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
return power::power(_ex1+power::power(x,_ex2),_ex_1_2);
}
-void asinh_function::do_print_latex(const print_context& c, unsigned level) const
+void asinh::do_print_latex(const print_context& c, unsigned level) const
{
- c.s << "\\arcsinh";
- inherited::do_print(c,level);
+ c.s << "\\mbox{arcsinh}";
+ exprseq::do_print(c,level);
}
//////////
// inverse hyperbolic cosine (trigonometric function)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(acosh_function,
- print_func<print_latex>(&acosh_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(acosh,
+ print_func<print_latex>(&acosh::do_print_latex))
-ex acosh_function::eval(int level) const
+ex acosh::eval(int level) const
{
const ex& x = seq[0];
// acosh(float) -> float
if (!x.info(info_flags::crational))
- return acosh(ex_to<numeric>(x));
+ return numeric(cln::acosh(ex_to<numeric>(x).to_cl_N()));
// acosh(-x) -> Pi*I-acosh(x)
if (x.info(info_flags::negative))
return this->hold();
}
-ex acosh_function::evalf(int level) const
+ex acosh::evalf(int level) const
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return acosh(ex_to<numeric>(x));
+ return numeric(cln::acosh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
-ex acosh_function::pderivative(unsigned deriv_param) const
+ex acosh::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
return power::power(x+_ex_1,_ex_1_2)*power::power(x+_ex1,_ex_1_2);
}
-void acosh_function::do_print_latex(const print_context& c, unsigned level) const
+void acosh::do_print_latex(const print_context& c, unsigned level) const
{
- c.s << "\\arccosh";
- inherited::do_print(c,level);
+ c.s << "\\mbox{arccosh}";
+ exprseq::do_print(c,level);
}
//////////
// inverse hyperbolic tangent (trigonometric function)
//////////
-GINAC_IMPLEMENT_FUNCTION_OPT(atanh_function,
- print_func<print_latex>(&atanh_function::do_print_latex))
+GINAC_IMPLEMENT_FUNCTION_OPT(atanh,
+ print_func<print_latex>(&atanh::do_print_latex))
-ex atanh_function::eval(int level) const
+ex atanh::eval(int level) const
{
const ex& x = seq[0];
if (x.info(info_flags::numeric)) {
// atanh(float) -> float
if (!x.info(info_flags::crational))
- return atanh(ex_to<numeric>(x));
+ return numeric(cln::atanh(ex_to<numeric>(x).to_cl_N()));
// atanh() is odd
if (x.info(info_flags::negative))
return this->hold();
}
-ex atanh_function::evalf(int level) const
+ex atanh::evalf(int level) const
{
const ex& x = seq[0];
if (is_exactly_a<numeric>(x))
- return atanh(ex_to<numeric>(x));
+ return numeric(cln::atanh(ex_to<numeric>(x).to_cl_N()));
return this->hold();
}
-ex atanh_function::pderivative(unsigned deriv_param) const
+ex atanh::pderivative(unsigned deriv_param) const
{
const ex& x = seq[0];
GINAC_ASSERT(deriv_param==0);
return power::power(_ex1-power::power(x,_ex2),_ex_1);
}
-ex atanh_function::series(const relational& rel, int order, unsigned options) const
+ex atanh::series(const relational& rel, int order, unsigned options) const
{
const ex& arg = seq[0];
return basic::series(rel, order, options);
}
-void atanh_function::do_print_latex(const print_context& c, unsigned level) const
+void atanh::do_print_latex(const print_context& c, unsigned level) const
{
- c.s << "\\arctanh";
- inherited::do_print(c,level);
+ c.s << "\\mbox{arctanh}";
+ exprseq::do_print(c,level);
}
} // namespace GiNaC
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline sin_function sin(const T1& x1) { return sin_function(x1); }
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline cos_function cos(const T1& x1) { return cos_function(x1); }
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
virtual ex series(const relational & r, int order, unsigned options = 0) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline tan_function tan(const T1& x1) { return tan_function(x1); }
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline sinh_function sinh(const T1& x1) { return sinh_function(x1); }
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline cosh_function cosh(const T1& x1) { return cosh_function(x1); }
virtual ex evalf(int level = 0) const;
virtual ex pderivative(unsigned diff_param) const;
virtual ex series(const relational & r, int order, unsigned options = 0) const;
-protected:
- void do_print_latex(const print_context& c, unsigned level) const;
};
template<typename T1> inline tanh_function tanh(const T1& x1) { return tanh_function(x1); }
/** Inverse hyperbolic Sine (area hyperbolic sine). */
-class asinh_function : public function
+class asinh : public function
{
- GINAC_DECLARE_FUNCTION_1P(asinh_function)
+ GINAC_DECLARE_FUNCTION_1P(asinh)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline asinh_function asinh(const T1& x1) { return asinh_function(x1); }
-inline asinh_function asinh(double x1);
-inline asinh_function asinh(float x1);
-
/** Inverse hyperbolic Cosine (area hyperbolic cosine). */
-class acosh_function : public function
+class acosh : public function
{
- GINAC_DECLARE_FUNCTION_1P(acosh_function)
+ GINAC_DECLARE_FUNCTION_1P(acosh)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline acosh_function acosh(const T1& x1) { return acosh_function(x1); }
-inline acosh_function acosh(double x1);
-inline acosh_function acosh(float x1);
-
/** Inverse hyperbolic Tangent (area hyperbolic tangent). */
-class atanh_function : public function
+class atanh : public function
{
- GINAC_DECLARE_FUNCTION_1P(atanh_function)
+ GINAC_DECLARE_FUNCTION_1P(atanh)
public:
virtual ex eval(int level = 0) const;
virtual ex evalf(int level = 0) const;
void do_print_latex(const print_context& c, unsigned level) const;
};
-template<typename T1> inline atanh_function atanh(const T1& x1) { return atanh_function(x1); }
-inline atanh_function atanh(double x1);
-inline atanh_function atanh(float x1);
-
} // namespace GiNaC
#endif // ifndef __GINAC_INIFCNS_TRIG_H__
ex nu7 = svec[i];
int nu8 = lvec[i];
--i;
- if (abs(ex_to<numeric>(s1+s2-nu7)) <= nu6)
+ if (abs_function::eval_numeric(ex_to<numeric>(s1+s2-nu7)) <= nu6)
app+=(s1+s2);
else {
if (nu8>=integral::max_integration_level)
#include "lst.h"
#include "idx.h"
#include "indexed.h"
+#include "inifcns.h"
#include "add.h"
#include "power.h"
#include "symbol.h"
// search largest element in column co beginning at row ro
GINAC_ASSERT(is_exactly_a<numeric>(this->m[k*col+co]));
unsigned kmax = k+1;
- numeric mmax = abs(ex_to<numeric>(m[kmax*col+co]));
+ numeric mmax = abs_function::eval_numeric(ex_to<numeric>(m[kmax*col+co]));
while (kmax<row) {
GINAC_ASSERT(is_exactly_a<numeric>(this->m[kmax*col+co]));
numeric tmp = ex_to<numeric>(this->m[kmax*col+co]);
- if (abs(tmp) > mmax) {
+ if (abs_function::eval_numeric(tmp) > mmax) {
mmax = tmp;
k = kmax;
}
numeric numeric::integer_content() const
{
- return abs(*this);
+ return abs_function::eval_numeric(*this);
}
numeric add::integer_content() const
}
#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
- return abs(ex_to<numeric>(overall_coeff));
+ return abs_function::eval_numeric(ex_to<numeric>(overall_coeff));
}
if (is_exactly_a<numeric>(*this)) {
if (info(info_flags::negative)) {
u = _ex_1;
- c = abs(ex_to<numeric>(*this));
+ c = abs_function::eval_numeric(ex_to<numeric>(*this));
} else {
u = _ex1;
c = *this;
numeric numeric::max_coefficient() const
{
- return abs(*this);
+ return abs_function::eval_numeric(*this);
}
numeric add::max_coefficient() const
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
- numeric cur_max = abs(ex_to<numeric>(overall_coeff));
+ numeric cur_max = abs_function::eval_numeric(ex_to<numeric>(overall_coeff));
while (it != itend) {
numeric a;
GINAC_ASSERT(!is_exactly_a<numeric>(it->rest));
- a = abs(ex_to<numeric>(it->coeff));
+ a = abs_function::eval_numeric(ex_to<numeric>(it->coeff));
if (a > cur_max)
cur_max = a;
it++;
}
#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
- return abs(ex_to<numeric>(overall_coeff));
+ return abs_function::eval_numeric(ex_to<numeric>(overall_coeff));
}
* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
+#include "config.h"
+
#include <vector>
#include <stdexcept>
+#include <string>
+#include <sstream>
+#include <limits>
#include "numeric.h"
#include "ex.h"
-#include "config.h"
-#include "debugmsg.h"
-
-// CLN should not pollute the global namespace, hence we include it here
-// instead of in some header file where it would propagate to other parts:
-#ifdef HAVE_CLN_CLN_H
-#include <CLN/cln.h>
-#else
-#include <cln.h>
-#endif
+#include "inifcns.h"
+#include "operators.h"
+#include "archive.h"
+#include "tostring.h"
+#include "utils.h"
+
+// CLN should pollute the global namespace as little as possible. Hence, we
+// include most of it here and include only the part needed for properly
+// declaring cln::cl_number in numeric.h. This can only be safely done in
+// namespaced versions of CLN, i.e. version > 1.1.0. Also, we only need a
+// subset of CLN, so we don't include the complete <cln/cln.h> but only the
+// essential stuff:
+#include <cln/output.h>
+#include <cln/integer_io.h>
+#include <cln/integer_ring.h>
+#include <cln/rational_io.h>
+#include <cln/rational_ring.h>
+#include <cln/lfloat_class.h>
+#include <cln/lfloat_io.h>
+#include <cln/real_io.h>
+#include <cln/real_ring.h>
+#include <cln/complex_io.h>
+#include <cln/complex_ring.h>
+#include <cln/numtheory.h>
namespace GiNaC {
-// linker has no problems finding text symbols for numerator or denominator
-//#define SANE_LINKER
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(numeric, basic,
+ print_func<print_context>(&numeric::do_print).
+ print_func<print_latex>(&numeric::do_print_latex).
+ print_func<print_csrc>(&numeric::do_print_csrc).
+ print_func<print_csrc_cl_N>(&numeric::do_print_csrc_cl_N).
+ print_func<print_tree>(&numeric::do_print_tree).
+ print_func<print_python_repr>(&numeric::do_print_python_repr))
//////////
-// default constructor, destructor, copy constructor assignment
-// operator and helpers
+// default constructor
//////////
-// public
-
/** default ctor. Numerically it initializes to an integer zero. */
-numeric::numeric() : basic(TINFO_numeric)
+numeric::numeric() : basic(&numeric::tinfo_static)
{
- debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
- value = new cl_N;
- *value=cl_I(0);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ value = cln::cl_I(0);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-numeric::~numeric()
+//////////
+// other constructors
+//////////
+
+// public
+
+numeric::numeric(int i) : basic(&numeric::tinfo_static)
{
- debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT);
- destroy(0);
+ // Not the whole int-range is available if we don't cast to long
+ // first. This is due to the behaviour of the cl_I-ctor, which
+ // emphasizes efficiency. However, if the integer is small enough
+ // we save space and dereferences by using an immediate type.
+ // (C.f. <cln/object.h>)
+ if (i < (1L << (cl_value_len-1)) && i >= -(1L << (cl_value_len-1)))
+ value = cln::cl_I(i);
+ else
+ value = cln::cl_I(static_cast<long>(i));
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-numeric::numeric(numeric const & other)
+
+numeric::numeric(unsigned int i) : basic(&numeric::tinfo_static)
{
- debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT);
- copy(other);
+ // Not the whole uint-range is available if we don't cast to ulong
+ // first. This is due to the behaviour of the cl_I-ctor, which
+ // emphasizes efficiency. However, if the integer is small enough
+ // we save space and dereferences by using an immediate type.
+ // (C.f. <cln/object.h>)
+ if (i < (1UL << (cl_value_len-1)))
+ value = cln::cl_I(i);
+ else
+ value = cln::cl_I(static_cast<unsigned long>(i));
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-numeric const & numeric::operator=(numeric const & other)
+
+numeric::numeric(long i) : basic(&numeric::tinfo_static)
{
- debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ value = cln::cl_I(i);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-// protected
-void numeric::copy(numeric const & other)
+numeric::numeric(unsigned long i) : basic(&numeric::tinfo_static)
{
- basic::copy(other);
- value = new cl_N(*other.value);
+ value = cln::cl_I(i);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-void numeric::destroy(bool call_parent)
+
+/** Constructor for rational numerics a/b.
+ *
+ * @exception overflow_error (division by zero) */
+numeric::numeric(long numer, long denom) : basic(&numeric::tinfo_static)
+{
+ if (!denom)
+ throw std::overflow_error("division by zero");
+ value = cln::cl_I(numer) / cln::cl_I(denom);
+ setflag(status_flags::evaluated | status_flags::expanded);
+}
+
+
+numeric::numeric(double d) : basic(&numeric::tinfo_static)
+{
+ // We really want to explicitly use the type cl_LF instead of the
+ // more general cl_F, since that would give us a cl_DF only which
+ // will not be promoted to cl_LF if overflow occurs:
+ value = cln::cl_float(d, cln::default_float_format);
+ setflag(status_flags::evaluated | status_flags::expanded);
+}
+
+
+/** ctor from C-style string. It also accepts complex numbers in GiNaC
+ * notation like "2+5*I". */
+numeric::numeric(const char *s) : basic(&numeric::tinfo_static)
+{
+ cln::cl_N ctorval = 0;
+ // parse complex numbers (functional but not completely safe, unfortunately
+ // std::string does not understand regexpese):
+ // ss should represent a simple sum like 2+5*I
+ std::string ss = s;
+ std::string::size_type delim;
+
+ // make this implementation safe by adding explicit sign
+ if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#')
+ ss = '+' + ss;
+
+ // We use 'E' as exponent marker in the output, but some people insist on
+ // writing 'e' at input, so let's substitute them right at the beginning:
+ while ((delim = ss.find("e"))!=std::string::npos)
+ ss.replace(delim,1,"E");
+
+ // main parser loop:
+ do {
+ // chop ss into terms from left to right
+ std::string term;
+ bool imaginary = false;
+ delim = ss.find_first_of(std::string("+-"),1);
+ // Do we have an exponent marker like "31.415E-1"? If so, hop on!
+ if (delim!=std::string::npos && ss.at(delim-1)=='E')
+ delim = ss.find_first_of(std::string("+-"),delim+1);
+ term = ss.substr(0,delim);
+ if (delim!=std::string::npos)
+ ss = ss.substr(delim);
+ // is the term imaginary?
+ if (term.find("I")!=std::string::npos) {
+ // erase 'I':
+ term.erase(term.find("I"),1);
+ // erase '*':
+ if (term.find("*")!=std::string::npos)
+ term.erase(term.find("*"),1);
+ // correct for trivial +/-I without explicit factor on I:
+ if (term.size()==1)
+ term += '1';
+ imaginary = true;
+ }
+ if (term.find('.')!=std::string::npos || term.find('E')!=std::string::npos) {
+ // CLN's short type cl_SF is not very useful within the GiNaC
+ // framework where we are mainly interested in the arbitrary
+ // precision type cl_LF. Hence we go straight to the construction
+ // of generic floats. In order to create them we have to convert
+ // our own floating point notation used for output and construction
+ // from char * to CLN's generic notation:
+ // 3.14 --> 3.14e0_<Digits>
+ // 31.4E-1 --> 31.4e-1_<Digits>
+ // and s on.
+ // No exponent marker? Let's add a trivial one.
+ if (term.find("E")==std::string::npos)
+ term += "E0";
+ // E to lower case
+ term = term.replace(term.find("E"),1,"e");
+ // append _<Digits> to term
+ term += "_" + ToString((unsigned)Digits);
+ // construct float using cln::cl_F(const char *) ctor.
+ if (imaginary)
+ ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_F(term.c_str()));
+ else
+ ctorval = ctorval + cln::cl_F(term.c_str());
+ } else {
+ // this is not a floating point number...
+ if (imaginary)
+ ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_R(term.c_str()));
+ else
+ ctorval = ctorval + cln::cl_R(term.c_str());
+ }
+ } while (delim != std::string::npos);
+ value = ctorval;
+ setflag(status_flags::evaluated | status_flags::expanded);
+}
+
+
+/** Ctor from CLN types. This is for the initiated user or internal use
+ * only. */
+numeric::numeric(const cln::cl_N &z) : basic(&numeric::tinfo_static)
{
- delete value;
- if (call_parent) basic::destroy(call_parent);
+ value = z;
+ setflag(status_flags::evaluated | status_flags::expanded);
}
+
//////////
-// other constructors
+// archiving
//////////
-// public
+numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+{
+ cln::cl_N ctorval = 0;
+
+ // Read number as string
+ std::string str;
+ if (n.find_string("number", str)) {
+ std::istringstream s(str);
+ cln::cl_idecoded_float re, im;
+ char c;
+ s.get(c);
+ switch (c) {
+ case 'R': // Integer-decoded real number
+ s >> re.sign >> re.mantissa >> re.exponent;
+ ctorval = re.sign * re.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), re.exponent);
+ break;
+ case 'C': // Integer-decoded complex number
+ s >> re.sign >> re.mantissa >> re.exponent;
+ s >> im.sign >> im.mantissa >> im.exponent;
+ ctorval = cln::complex(re.sign * re.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), re.exponent),
+ im.sign * im.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), im.exponent));
+ break;
+ default: // Ordinary number
+ s.putback(c);
+ s >> ctorval;
+ break;
+ }
+ }
+ value = ctorval;
+ setflag(status_flags::evaluated | status_flags::expanded);
+}
+
+void numeric::archive(archive_node &n) const
+{
+ inherited::archive(n);
+
+ // Write number as string
+ std::ostringstream s;
+ if (this->is_crational())
+ s << value;
+ else {
+ // Non-rational numbers are written in an integer-decoded format
+ // to preserve the precision
+ if (this->is_real()) {
+ cln::cl_idecoded_float re = cln::integer_decode_float(cln::the<cln::cl_F>(value));
+ s << "R";
+ s << re.sign << " " << re.mantissa << " " << re.exponent;
+ } else {
+ cln::cl_idecoded_float re = cln::integer_decode_float(cln::the<cln::cl_F>(cln::realpart(cln::the<cln::cl_N>(value))));
+ cln::cl_idecoded_float im = cln::integer_decode_float(cln::the<cln::cl_F>(cln::imagpart(cln::the<cln::cl_N>(value))));
+ s << "C";
+ s << re.sign << " " << re.mantissa << " " << re.exponent << " ";
+ s << im.sign << " " << im.mantissa << " " << im.exponent;
+ }
+ }
+ n.add_string("number", s.str());
+}
+
+DEFAULT_UNARCHIVE(numeric)
+
+//////////
+// functions overriding virtual functions from base classes
+//////////
-numeric::numeric(int i) : basic(TINFO_numeric)
+/** Helper function to print a real number in a nicer way than is CLN's
+ * default. Instead of printing 42.0L0 this just prints 42.0 to ostream os
+ * and instead of 3.99168L7 it prints 3.99168E7. This is fine in GiNaC as
+ * long as it only uses cl_LF and no other floating point types that we might
+ * want to visibly distinguish from cl_LF.
+ *
+ * @see numeric::print() */
+static void print_real_number(const print_context & c, const cln::cl_R & x)
+{
+ cln::cl_print_flags ourflags;
+ if (cln::instanceof(x, cln::cl_RA_ring)) {
+ // case 1: integer or rational
+ if (cln::instanceof(x, cln::cl_I_ring) ||
+ !is_a<print_latex>(c)) {
+ cln::print_real(c.s, ourflags, x);
+ } else { // rational output in LaTeX context
+ if (x < 0)
+ c.s << "-";
+ c.s << "\\frac{";
+ cln::print_real(c.s, ourflags, cln::abs(cln::numerator(cln::the<cln::cl_RA>(x))));
+ c.s << "}{";
+ cln::print_real(c.s, ourflags, cln::denominator(cln::the<cln::cl_RA>(x)));
+ c.s << '}';
+ }
+ } else {
+ // case 2: float
+ // make CLN believe this number has default_float_format, so it prints
+ // 'E' as exponent marker instead of 'L':
+ ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(x));
+ cln::print_real(c.s, ourflags, x);
+ }
+}
+
+/** Helper function to print integer number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_integer_csrc(const print_context & c, const cln::cl_I & x)
{
- debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT);
- // Not the whole int-range is available if we don't cast to long
- // first. This is due to the behaviour of the cl_I-ctor, which
- // emphasizes efficiency:
- value = new cl_I((long) i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ // Print small numbers in compact float format, but larger numbers in
+ // scientific format
+ const int max_cln_int = 536870911; // 2^29-1
+ if (x >= cln::cl_I(-max_cln_int) && x <= cln::cl_I(max_cln_int))
+ c.s << cln::cl_I_to_int(x) << ".0";
+ else
+ c.s << cln::double_approx(x);
}
-numeric::numeric(unsigned int i) : basic(TINFO_numeric)
+/** Helper function to print real number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_real_csrc(const print_context & c, const cln::cl_R & x)
{
- debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
- // Not the whole uint-range is available if we don't cast to ulong
- // first. This is due to the behaviour of the cl_I-ctor, which
- // emphasizes efficiency:
- value = new cl_I((unsigned long)i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+
+ // Integer number
+ print_integer_csrc(c, cln::the<cln::cl_I>(x));
+
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ const cln::cl_I numer = cln::numerator(cln::the<cln::cl_RA>(x));
+ const cln::cl_I denom = cln::denominator(cln::the<cln::cl_RA>(x));
+ if (cln::plusp(x) > 0) {
+ c.s << "(";
+ print_integer_csrc(c, numer);
+ } else {
+ c.s << "-(";
+ print_integer_csrc(c, -numer);
+ }
+ c.s << "/";
+ print_integer_csrc(c, denom);
+ c.s << ")";
+
+ } else {
+
+ // Anything else
+ c.s << cln::double_approx(x);
+ }
}
-numeric::numeric(long i) : basic(TINFO_numeric)
-{
- debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
- value = new cl_I(i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+/** Helper function to print real number in C++ source format using cl_N types.
+ *
+ * @see numeric::print() */
+static void print_real_cl_N(const print_context & c, const cln::cl_R & x)
+{
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+
+ // Integer number
+ c.s << "cln::cl_I(\"";
+ print_real_number(c, x);
+ c.s << "\")";
+
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ cln::cl_print_flags ourflags;
+ c.s << "cln::cl_RA(\"";
+ cln::print_rational(c.s, ourflags, cln::the<cln::cl_RA>(x));
+ c.s << "\")";
+
+ } else {
+
+ // Anything else
+ c.s << "cln::cl_F(\"";
+ print_real_number(c, cln::cl_float(1.0, cln::default_float_format) * x);
+ c.s << "_" << Digits << "\")";
+ }
+}
+
+void numeric::print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const
+{
+ const cln::cl_R r = cln::realpart(value);
+ const cln::cl_R i = cln::imagpart(value);
+
+ if (cln::zerop(i)) {
+
+ // case 1, real: x or -x
+ if ((precedence() <= level) && (!this->is_nonneg_integer())) {
+ c.s << par_open;
+ print_real_number(c, r);
+ c.s << par_close;
+ } else {
+ print_real_number(c, r);
+ }
+
+ } else {
+ if (cln::zerop(r)) {
+
+ // case 2, imaginary: y*I or -y*I
+ if (i == 1)
+ c.s << imag_sym;
+ else {
+ if (precedence()<=level)
+ c.s << par_open;
+ if (i == -1)
+ c.s << "-" << imag_sym;
+ else {
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ if (precedence()<=level)
+ c.s << par_close;
+ }
+
+ } else {
+
+ // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
+ if (precedence() <= level)
+ c.s << par_open;
+ print_real_number(c, r);
+ if (i < 0) {
+ if (i == -1) {
+ c.s << "-" << imag_sym;
+ } else {
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ } else {
+ if (i == 1) {
+ c.s << "+" << imag_sym;
+ } else {
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ }
+ if (precedence() <= level)
+ c.s << par_close;
+ }
+ }
}
-numeric::numeric(unsigned long i) : basic(TINFO_numeric)
+void numeric::do_print(const print_context & c, unsigned level) const
{
- debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
- value = new cl_I(i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ print_numeric(c, "(", ")", "I", "*", level);
}
-/** Ctor for rational numerics a/b.
- *
- * @exception overflow_error (division by zero) */
-numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
-{
- debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
- if (!denom)
- throw (std::overflow_error("division by zero"));
- value = new cl_I(numer);
- *value = *value / cl_I(denom);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
-}
-
-numeric::numeric(double d) : basic(TINFO_numeric)
-{
- debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
- // We really want to explicitly use the type cl_LF instead of the
- // more general cl_F, since that would give us a cl_DF only which
- // will not be promoted to cl_LF if overflow occurs:
- value = new cl_N;
- *value = cl_float(d, cl_default_float_format);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
-}
-
-numeric::numeric(char const *s) : basic(TINFO_numeric)
-{ // MISSING: treatment of complex and ints and rationals.
- debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
- if (strchr(s, '.'))
- value = new cl_LF(s);
- else
- value = new cl_I(s);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+void numeric::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_numeric(c, "{(", ")}", "i", " ", level);
}
-/** Ctor from CLN types. This is for the initiated user or internal use
- * only. */
-numeric::numeric(cl_N const & z) : basic(TINFO_numeric)
+void numeric::do_print_csrc(const print_csrc & c, unsigned level) const
{
- debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
- value = new cl_N(z);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ std::ios::fmtflags oldflags = c.s.flags();
+ c.s.setf(std::ios::scientific);
+ int oldprec = c.s.precision();
+
+ // Set precision
+ if (is_a<print_csrc_double>(c))
+ c.s.precision(std::numeric_limits<double>::digits10 + 1);
+ else
+ c.s.precision(std::numeric_limits<float>::digits10 + 1);
+
+ if (this->is_real()) {
+
+ // Real number
+ print_real_csrc(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "std::complex<";
+ if (is_a<print_csrc_double>(c))
+ c.s << "double>(";
+ else
+ c.s << "float>(";
+
+ print_real_csrc(c, cln::realpart(value));
+ c.s << ",";
+ print_real_csrc(c, cln::imagpart(value));
+ c.s << ")";
+ }
+
+ c.s.flags(oldflags);
+ c.s.precision(oldprec);
}
-//////////
-// functions overriding virtual functions from bases classes
-//////////
+void numeric::do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const
+{
+ if (this->is_real()) {
-// public
+ // Real number
+ print_real_cl_N(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "cln::complex(";
+ print_real_cl_N(c, cln::realpart(value));
+ c.s << ",";
+ print_real_cl_N(c, cln::imagpart(value));
+ c.s << ")";
+ }
+}
+
+void numeric::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << value
+ << " (" << class_name() << ")" << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+}
-basic * numeric::duplicate() const
-{
- debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE);
- return new numeric(*this);
-}
-
-// The method printraw doesn't do much, it simply uses CLN's operator<<() for
-// output, which is ugly but reliable. Examples:
-// 2+2i
-void numeric::printraw(ostream & os) const
-{
- debugmsg("numeric printraw", LOGLEVEL_PRINT);
- os << "numeric(" << *value << ")";
-}
-
-// The method print adds to the output so it blends more consistently together
-// with the other routines and produces something compatible to Maple input.
-void numeric::print(ostream & os, unsigned upper_precedence) const
-{
- debugmsg("numeric print", LOGLEVEL_PRINT);
- if (is_real()) {
- // case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!is_pos_integer())) {
- os << "(" << *value << ")";
- } else {
- os << *value;
- }
- } else {
- // case 2, imaginary: y*I or -y*I
- if (realpart(*value) == 0) {
- if ((precedence<=upper_precedence) && (imagpart(*value) < 0)) {
- if (imagpart(*value) == -1) {
- os << "(-I)";
- } else {
- os << "(" << imagpart(*value) << "*I)";
- }
- } else {
- if (imagpart(*value) == 1) {
- os << "I";
- } else {
- if (imagpart (*value) == -1) {
- os << "-I";
- } else {
- os << imagpart(*value) << "*I";
- }
- }
- }
- } else {
- // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
- if (precedence <= upper_precedence) os << "(";
- os << realpart(*value);
- if (imagpart(*value) < 0) {
- if (imagpart(*value) == -1) {
- os << "-I";
- } else {
- os << imagpart(*value) << "*I";
- }
- } else {
- if (imagpart(*value) == 1) {
- os << "+I";
- } else {
- os << "+" << imagpart(*value) << "*I";
- }
- }
- if (precedence <= upper_precedence) os << ")";
- }
- }
+void numeric::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << "('";
+ print_numeric(c, "(", ")", "I", "*", level);
+ c.s << "')";
}
bool numeric::info(unsigned inf) const
{
- switch (inf) {
- case info_flags::numeric:
- case info_flags::polynomial:
- case info_flags::rational_function:
- return true;
- case info_flags::real:
- return is_real();
- case info_flags::rational:
- case info_flags::rational_polynomial:
- return is_rational();
- case info_flags::integer:
- case info_flags::integer_polynomial:
- return is_integer();
- case info_flags::positive:
- return is_positive();
- case info_flags::negative:
- return is_negative();
- case info_flags::nonnegative:
- return compare(numZERO())>=0;
- case info_flags::posint:
- return is_pos_integer();
- case info_flags::negint:
- return is_integer() && (compare(numZERO())<0);
- case info_flags::nonnegint:
- return is_nonneg_integer();
- case info_flags::even:
- return is_even();
- case info_flags::odd:
- return is_odd();
- case info_flags::prime:
- return is_prime();
- }
- return false;
+ switch (inf) {
+ case info_flags::numeric:
+ case info_flags::polynomial:
+ case info_flags::rational_function:
+ return true;
+ case info_flags::real:
+ return is_real();
+ case info_flags::rational:
+ case info_flags::rational_polynomial:
+ return is_rational();
+ case info_flags::crational:
+ case info_flags::crational_polynomial:
+ return is_crational();
+ case info_flags::integer:
+ case info_flags::integer_polynomial:
+ return is_integer();
+ case info_flags::cinteger:
+ case info_flags::cinteger_polynomial:
+ return is_cinteger();
+ case info_flags::positive:
+ return is_positive();
+ case info_flags::negative:
+ return is_negative();
+ case info_flags::nonnegative:
+ return !is_negative();
+ case info_flags::posint:
+ return is_pos_integer();
+ case info_flags::negint:
+ return is_integer() && is_negative();
+ case info_flags::nonnegint:
+ return is_nonneg_integer();
+ case info_flags::even:
+ return is_even();
+ case info_flags::odd:
+ return is_odd();
+ case info_flags::prime:
+ return is_prime();
+ case info_flags::algebraic:
+ return !is_real();
+ }
+ return false;
+}
+
+bool numeric::is_polynomial(const ex & var) const
+{
+ return true;
+}
+
+int numeric::degree(const ex & s) const
+{
+ return 0;
+}
+
+int numeric::ldegree(const ex & s) const
+{
+ return 0;
+}
+
+ex numeric::coeff(const ex & s, int n) const
+{
+ return n==0 ? *this : _ex0;
+}
+
+/** Disassemble real part and imaginary part to scan for the occurrence of a
+ * single number. Also handles the imaginary unit. It ignores the sign on
+ * both this and the argument, which may lead to what might appear as funny
+ * results: (2+I).has(-2) -> true. But this is consistent, since we also
+ * would like to have (-2+I).has(2) -> true and we want to think about the
+ * sign as a multiplicative factor. */
+bool numeric::has(const ex &other, unsigned options) const
+{
+ if (!is_exactly_a<numeric>(other))
+ return false;
+ const numeric &o = ex_to<numeric>(other);
+ if (this->is_equal(o) || this->is_equal(-o))
+ return true;
+ if (o.imag().is_zero()) { // e.g. scan for 3 in -3*I
+ if (!this->real().is_equal(*_num0_p))
+ if (this->real().is_equal(o) || this->real().is_equal(-o))
+ return true;
+ if (!this->imag().is_equal(*_num0_p))
+ if (this->imag().is_equal(o) || this->imag().is_equal(-o))
+ return true;
+ return false;
+ }
+ else {
+ if (o.is_equal(I)) // e.g scan for I in 42*I
+ return !this->is_real();
+ if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1
+ if (!this->imag().is_equal(*_num0_p))
+ if (this->imag().is_equal(o*I) || this->imag().is_equal(-o*I))
+ return true;
+ }
+ return false;
+}
+
+
+/** Evaluation of numbers doesn't do anything at all. */
+ex numeric::eval(int level) const
+{
+ // Warning: if this is ever gonna do something, the ex ctors from all kinds
+ // of numbers should be checking for status_flags::evaluated.
+ return this->hold();
}
+
/** Cast numeric into a floating-point object. For example exact numeric(1) is
* returned as a 1.0000000000000000000000 and so on according to how Digits is
- * currently set.
+ * currently set. In case the object already was a floating point number the
+ * precision is trimmed to match the currently set default.
*
- * @param level ignored, but needed for overriding basic::evalf.
- * @return an ex-handle to a numeric. */
+ * @param level ignored, only needed for overriding basic::evalf.
+ * @return an ex-handle to a numeric. */
ex numeric::evalf(int level) const
{
- // level can safely be discarded for numeric objects.
- return numeric(cl_float(1.0, cl_default_float_format) * (*value)); // -> CLN
+ // level can safely be discarded for numeric objects.
+ return numeric(cln::cl_float(1.0, cln::default_float_format) * value);
}
-// protected
-
-int numeric::compare_same_type(basic const & other) const
+ex numeric::conjugate() const
{
- GINAC_ASSERT(is_exactly_of_type(other, numeric));
- numeric const & o = static_cast<numeric &>(const_cast<basic &>(other));
+ if (is_real()) {
+ return *this;
+ }
+ return numeric(cln::conjugate(this->value));
+}
- if (*value == *o.value) {
- return 0;
- }
+// protected
- return compare(o);
+int numeric::compare_same_type(const basic &other) const
+{
+ GINAC_ASSERT(is_exactly_a<numeric>(other));
+ const numeric &o = static_cast<const numeric &>(other);
+
+ return this->compare(o);
}
-bool numeric::is_equal_same_type(basic const & other) const
+
+bool numeric::is_equal_same_type(const basic &other) const
{
- GINAC_ASSERT(is_exactly_of_type(other,numeric));
- numeric const *o = static_cast<numeric const *>(&other);
-
- return is_equal(*o);
+ GINAC_ASSERT(is_exactly_a<numeric>(other));
+ const numeric &o = static_cast<const numeric &>(other);
+
+ return this->is_equal(o);
}
-/*
-unsigned numeric::calchash(void) const
+
+unsigned numeric::calchash() const
{
- double d=to_double();
- int s=d>0 ? 1 : -1;
- d=fabs(d);
- if (d>0x07FF0000) {
- d=0x07FF0000;
- }
- return 0x88000000U+s*unsigned(d/0x07FF0000);
+ // Base computation of hashvalue on CLN's hashcode. Note: That depends
+ // only on the number's value, not its type or precision (i.e. a true
+ // equivalence relation on numbers). As a consequence, 3 and 3.0 share
+ // the same hashvalue. That shouldn't really matter, though.
+ setflag(status_flags::hash_calculated);
+ hashvalue = golden_ratio_hash(cln::equal_hashcode(value));
+ return hashvalue;
}
-*/
//////////
// public
/** Numerical addition method. Adds argument to *this and returns result as
- * a new numeric object. */
-numeric numeric::add(numeric const & other) const
+ * a numeric object. */
+const numeric numeric::add(const numeric &other) const
{
- return numeric((*value)+(*other.value));
+ return numeric(value + other.value);
}
+
/** Numerical subtraction method. Subtracts argument from *this and returns
- * result as a new numeric object. */
-numeric numeric::sub(numeric const & other) const
+ * result as a numeric object. */
+const numeric numeric::sub(const numeric &other) const
{
- return numeric((*value)-(*other.value));
+ return numeric(value - other.value);
}
+
/** Numerical multiplication method. Multiplies *this and argument and returns
- * result as a new numeric object. */
-numeric numeric::mul(numeric const & other) const
+ * result as a numeric object. */
+const numeric numeric::mul(const numeric &other) const
{
- static const numeric * numONEp=&numONE();
- if (this==numONEp) {
- return other;
- } else if (&other==numONEp) {
- return *this;
- }
- return numeric((*value)*(*other.value));
+ return numeric(value * other.value);
}
+
/** Numerical division method. Divides *this by argument and returns result as
- * a new numeric object.
+ * a numeric object.
*
* @exception overflow_error (division by zero) */
-numeric numeric::div(numeric const & other) const
+const numeric numeric::div(const numeric &other) const
{
- if (zerop(*other.value))
- throw (std::overflow_error("division by zero"));
- return numeric((*value)/(*other.value));
+ if (cln::zerop(other.value))
+ throw std::overflow_error("numeric::div(): division by zero");
+ return numeric(value / other.value);
}
-numeric numeric::power(numeric const & other) const
+
+/** Numerical exponentiation. Raises *this to the power given as argument and
+ * returns result as a numeric object. */
+const numeric numeric::power(const numeric &other) const
{
- static const numeric * numONEp=&numONE();
- if (&other==numONEp) {
- return *this;
- }
- if (zerop(*value) && other.is_real() && minusp(realpart(*other.value)))
- throw (std::overflow_error("division by zero"));
- return numeric(expt(*value,*other.value));
+ // Shortcut for efficiency and numeric stability (as in 1.0 exponent):
+ // trap the neutral exponent.
+ if (&other==_num1_p || cln::equal(other.value,_num1_p->value))
+ return *this;
+
+ if (cln::zerop(value)) {
+ if (cln::zerop(other.value))
+ throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
+ else if (cln::zerop(cln::realpart(other.value)))
+ throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
+ else if (cln::minusp(cln::realpart(other.value)))
+ throw std::overflow_error("numeric::eval(): division by zero");
+ else
+ return *_num0_p;
+ }
+ return numeric(cln::expt(value, other.value));
}
-/** Inverse of a number. */
-numeric numeric::inverse(void) const
+
+
+/** Numerical addition method. Adds argument to *this and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping into
+ * an ex object, where the result would end up on the heap anyways. */
+const numeric &numeric::add_dyn(const numeric &other) const
{
- return numeric(recip(*value)); // -> CLN
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (this==_num0_p)
+ return other;
+ else if (&other==_num0_p)
+ return *this;
+
+ return static_cast<const numeric &>((new numeric(value + other.value))->
+ setflag(status_flags::dynallocated));
}
-numeric const & numeric::add_dyn(numeric const & other) const
+
+/** Numerical subtraction method. Subtracts argument from *this and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
+const numeric &numeric::sub_dyn(const numeric &other) const
{
- return static_cast<numeric const &>((new numeric((*value)+(*other.value)))->
- setflag(status_flags::dynallocated));
+ // Efficiency shortcut: trap the neutral exponent (first by pointer). This
+ // hack is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num0_p || cln::zerop(other.value))
+ return *this;
+
+ return static_cast<const numeric &>((new numeric(value - other.value))->
+ setflag(status_flags::dynallocated));
}
-numeric const & numeric::sub_dyn(numeric const & other) const
+
+/** Numerical multiplication method. Multiplies *this and argument and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
+const numeric &numeric::mul_dyn(const numeric &other) const
{
- return static_cast<numeric const &>((new numeric((*value)-(*other.value)))->
- setflag(status_flags::dynallocated));
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (this==_num1_p)
+ return other;
+ else if (&other==_num1_p)
+ return *this;
+
+ return static_cast<const numeric &>((new numeric(value * other.value))->
+ setflag(status_flags::dynallocated));
}
-numeric const & numeric::mul_dyn(numeric const & other) const
+
+/** Numerical division method. Divides *this by argument and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping
+ * into an ex object, where the result would end up on the heap
+ * anyways.
+ *
+ * @exception overflow_error (division by zero) */
+const numeric &numeric::div_dyn(const numeric &other) const
{
- static const numeric * numONEp=&numONE();
- if (this==numONEp) {
- return other;
- } else if (&other==numONEp) {
- return *this;
- }
- return static_cast<numeric const &>((new numeric((*value)*(*other.value)))->
- setflag(status_flags::dynallocated));
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num1_p)
+ return *this;
+ if (cln::zerop(cln::the<cln::cl_N>(other.value)))
+ throw std::overflow_error("division by zero");
+ return static_cast<const numeric &>((new numeric(value / other.value))->
+ setflag(status_flags::dynallocated));
}
-numeric const & numeric::div_dyn(numeric const & other) const
+
+/** Numerical exponentiation. Raises *this to the power given as argument and
+ * returns result as a numeric object on the heap. Use internally only for
+ * direct wrapping into an ex object, where the result would end up on the
+ * heap anyways. */
+const numeric &numeric::power_dyn(const numeric &other) const
{
- if (zerop(*other.value))
- throw (std::overflow_error("division by zero"));
- return static_cast<numeric const &>((new numeric((*value)/(*other.value)))->
- setflag(status_flags::dynallocated));
+ // Efficiency shortcut: trap the neutral exponent (first try by pointer, then
+ // try harder, since calls to cln::expt() below may return amazing results for
+ // floating point exponent 1.0).
+ if (&other==_num1_p || cln::equal(other.value, _num1_p->value))
+ return *this;
+
+ if (cln::zerop(value)) {
+ if (cln::zerop(other.value))
+ throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
+ else if (cln::zerop(cln::realpart(other.value)))
+ throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
+ else if (cln::minusp(cln::realpart(other.value)))
+ throw std::overflow_error("numeric::eval(): division by zero");
+ else
+ return *_num0_p;
+ }
+ return static_cast<const numeric &>((new numeric(cln::expt(value, other.value)))->
+ setflag(status_flags::dynallocated));
}
-numeric const & numeric::power_dyn(numeric const & other) const
+
+const numeric &numeric::operator=(int i)
{
- static const numeric * numONEp=&numONE();
- if (&other==numONEp) {
- return *this;
- }
- // The ifs are only a workaround for a bug in CLN. It gets stuck otherwise:
- if ( !other.is_integer() &&
- other.is_rational() &&
- (*this).is_nonneg_integer() ) {
- if ( !zerop(*value) ) {
- return static_cast<numeric const &>((new numeric(exp(*other.value * log(*value))))->
- setflag(status_flags::dynallocated));
- } else {
- if ( !zerop(*other.value) ) { // 0^(n/m)
- return static_cast<numeric const &>((new numeric(0))->
- setflag(status_flags::dynallocated));
- } else { // raise FPE (0^0 requested)
- return static_cast<numeric const &>((new numeric(1/(*other.value)))->
- setflag(status_flags::dynallocated));
- }
- }
- } else { // default -> CLN
- return static_cast<numeric const &>((new numeric(expt(*value,*other.value)))->
- setflag(status_flags::dynallocated));
- }
+ return operator=(numeric(i));
}
-numeric const & numeric::operator=(int i)
+
+const numeric &numeric::operator=(unsigned int i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
-numeric const & numeric::operator=(unsigned int i)
+
+const numeric &numeric::operator=(long i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
-numeric const & numeric::operator=(long i)
+
+const numeric &numeric::operator=(unsigned long i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
-numeric const & numeric::operator=(unsigned long i)
+
+const numeric &numeric::operator=(double d)
{
- return operator=(numeric(i));
+ return operator=(numeric(d));
}
-numeric const & numeric::operator=(double d)
+
+const numeric &numeric::operator=(const char * s)
{
- return operator=(numeric(d));
+ return operator=(numeric(s));
}
-numeric const & numeric::operator=(char const * s)
+
+/** Inverse of a number. */
+const numeric numeric::inverse() const
{
- return operator=(numeric(s));
+ if (cln::zerop(value))
+ throw std::overflow_error("numeric::inverse(): division by zero");
+ return numeric(cln::recip(value));
+}
+
+/** Return the step function of a numeric. The imaginary part of it is
+ * ignored because the step function is generally considered real but
+ * a numeric may develop a small imaginary part due to rounding errors.
+ */
+numeric numeric::step() const
+{ cln::cl_R r = cln::realpart(value);
+ if(cln::zerop(r))
+ return numeric(1,2);
+ if(cln::plusp(r))
+ return 1;
+ return 0;
}
/** Return the complex half-plane (left or right) in which the number lies.
* csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0,
* csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.
*
- * @see numeric::compare(numeric const & other) */
-int numeric::csgn(void) const
-{
- if (is_zero())
- return 0;
- if (!zerop(realpart(*value))) {
- if (plusp(realpart(*value)))
- return 1;
- else
- return -1;
- } else {
- if (plusp(imagpart(*value)))
- return 1;
- else
- return -1;
- }
+ * @see numeric::compare(const numeric &other) */
+int numeric::csgn() const
+{
+ if (cln::zerop(value))
+ return 0;
+ cln::cl_R r = cln::realpart(value);
+ if (!cln::zerop(r)) {
+ if (cln::plusp(r))
+ return 1;
+ else
+ return -1;
+ } else {
+ if (cln::plusp(cln::imagpart(value)))
+ return 1;
+ else
+ return -1;
+ }
}
+
/** This method establishes a canonical order on all numbers. For complex
* numbers this is not possible in a mathematically consistent way but we need
* to establish some order and it ought to be fast. So we simply define it
* to be compatible with our method csgn.
*
* @return csgn(*this-other)
- * @see numeric::csgn(void) */
-int numeric::compare(numeric const & other) const
+ * @see numeric::csgn() */
+int numeric::compare(const numeric &other) const
{
- // Comparing two real numbers?
- if (is_real() && other.is_real())
- // Yes, just compare them
- return cl_compare(The(cl_R)(*value), The(cl_R)(*other.value));
- else {
- // No, first compare real parts
- cl_signean real_cmp = cl_compare(realpart(*value), realpart(*other.value));
- if (real_cmp)
- return real_cmp;
-
- return cl_compare(imagpart(*value), imagpart(*other.value));
- }
+ // Comparing two real numbers?
+ if (cln::instanceof(value, cln::cl_R_ring) &&
+ cln::instanceof(other.value, cln::cl_R_ring))
+ // Yes, so just cln::compare them
+ return cln::compare(cln::the<cln::cl_R>(value), cln::the<cln::cl_R>(other.value));
+ else {
+ // No, first cln::compare real parts...
+ cl_signean real_cmp = cln::compare(cln::realpart(value), cln::realpart(other.value));
+ if (real_cmp)
+ return real_cmp;
+ // ...and then the imaginary parts.
+ return cln::compare(cln::imagpart(value), cln::imagpart(other.value));
+ }
}
-bool numeric::is_equal(numeric const & other) const
+
+bool numeric::is_equal(const numeric &other) const
{
- return (*value == *other.value);
+ return cln::equal(value, other.value);
}
+
/** True if object is zero. */
-bool numeric::is_zero(void) const
+bool numeric::is_zero() const
{
- return zerop(*value); // -> CLN
+ return cln::zerop(value);
}
+
/** True if object is not complex and greater than zero. */
-bool numeric::is_positive(void) const
+bool numeric::is_positive() const
{
- if (is_real()) {
- return plusp(The(cl_R)(*value)); // -> CLN
- }
- return false;
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
+ return cln::plusp(cln::the<cln::cl_R>(value));
+ return false;
}
+
/** True if object is not complex and less than zero. */
-bool numeric::is_negative(void) const
+bool numeric::is_negative() const
{
- if (is_real()) {
- return minusp(The(cl_R)(*value)); // -> CLN
- }
- return false;
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
+ return cln::minusp(cln::the<cln::cl_R>(value));
+ return false;
}
+
/** True if object is a non-complex integer. */
-bool numeric::is_integer(void) const
+bool numeric::is_integer() const
{
- return (bool)instanceof(*value, cl_I_ring); // -> CLN
+ return cln::instanceof(value, cln::cl_I_ring);
}
+
/** True if object is an exact integer greater than zero. */
-bool numeric::is_pos_integer(void) const
+bool numeric::is_pos_integer() const
{
- return (is_integer() &&
- plusp(The(cl_I)(*value))); // -> CLN
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::plusp(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact integer greater or equal zero. */
-bool numeric::is_nonneg_integer(void) const
+bool numeric::is_nonneg_integer() const
{
- return (is_integer() &&
- !minusp(The(cl_I)(*value))); // -> CLN
+ return (cln::instanceof(value, cln::cl_I_ring) && !cln::minusp(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact even integer. */
-bool numeric::is_even(void) const
+bool numeric::is_even() const
{
- return (is_integer() &&
- evenp(The(cl_I)(*value))); // -> CLN
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::evenp(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact odd integer. */
-bool numeric::is_odd(void) const
+bool numeric::is_odd() const
{
- return (is_integer() &&
- oddp(The(cl_I)(*value))); // -> CLN
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::oddp(cln::the<cln::cl_I>(value)));
}
+
/** Probabilistic primality test.
*
* @return true if object is exact integer and prime. */
-bool numeric::is_prime(void) const
+bool numeric::is_prime() const
{
- return (is_integer() &&
- isprobprime(The(cl_I)(*value))); // -> CLN
+ return (cln::instanceof(value, cln::cl_I_ring) // integer?
+ && cln::plusp(cln::the<cln::cl_I>(value)) // positive?
+ && cln::isprobprime(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact rational number, may even be complex
* (denominator may be unity). */
-bool numeric::is_rational(void) const
+bool numeric::is_rational() const
{
- if (instanceof(*value, cl_RA_ring)) {
- return true;
- } else if (!is_real()) { // complex case, handle Q(i):
- if ( instanceof(realpart(*value), cl_RA_ring) &&
- instanceof(imagpart(*value), cl_RA_ring) )
- return true;
- }
- return false;
+ return cln::instanceof(value, cln::cl_RA_ring);
}
+
/** True if object is a real integer, rational or float (but not complex). */
-bool numeric::is_real(void) const
+bool numeric::is_real() const
{
- return (bool)instanceof(*value, cl_R_ring); // -> CLN
+ return cln::instanceof(value, cln::cl_R_ring);
}
-bool numeric::operator==(numeric const & other) const
+
+bool numeric::operator==(const numeric &other) const
{
- return (*value == *other.value); // -> CLN
+ return cln::equal(value, other.value);
}
-bool numeric::operator!=(numeric const & other) const
+
+bool numeric::operator!=(const numeric &other) const
{
- return (*value != *other.value); // -> CLN
+ return !cln::equal(value, other.value);
}
+
+/** True if object is element of the domain of integers extended by I, i.e. is
+ * of the form a+b*I, where a and b are integers. */
+bool numeric::is_cinteger() const
+{
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return true;
+ else if (!this->is_real()) { // complex case, handle n+m*I
+ if (cln::instanceof(cln::realpart(value), cln::cl_I_ring) &&
+ cln::instanceof(cln::imagpart(value), cln::cl_I_ring))
+ return true;
+ }
+ return false;
+}
+
+
+/** True if object is an exact rational number, may even be complex
+ * (denominator may be unity). */
+bool numeric::is_crational() const
+{
+ if (cln::instanceof(value, cln::cl_RA_ring))
+ return true;
+ else if (!this->is_real()) { // complex case, handle Q(i):
+ if (cln::instanceof(cln::realpart(value), cln::cl_RA_ring) &&
+ cln::instanceof(cln::imagpart(value), cln::cl_RA_ring))
+ return true;
+ }
+ return false;
+}
+
+
/** Numerical comparison: less.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator<(numeric const & other) const
+bool numeric::operator<(const numeric &other) const
{
- if ( is_real() && other.is_real() ) {
- return (bool)(The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN
- }
- throw (std::invalid_argument("numeric::operator<(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (cln::the<cln::cl_R>(value) < cln::the<cln::cl_R>(other.value));
+ throw std::invalid_argument("numeric::operator<(): complex inequality");
}
+
/** Numerical comparison: less or equal.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator<=(numeric const & other) const
+bool numeric::operator<=(const numeric &other) const
{
- if ( is_real() && other.is_real() ) {
- return (bool)(The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN
- }
- throw (std::invalid_argument("numeric::operator<=(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (cln::the<cln::cl_R>(value) <= cln::the<cln::cl_R>(other.value));
+ throw std::invalid_argument("numeric::operator<=(): complex inequality");
}
+
/** Numerical comparison: greater.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator>(numeric const & other) const
+bool numeric::operator>(const numeric &other) const
{
- if ( is_real() && other.is_real() ) {
- return (bool)(The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN
- }
- throw (std::invalid_argument("numeric::operator>(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (cln::the<cln::cl_R>(value) > cln::the<cln::cl_R>(other.value));
+ throw std::invalid_argument("numeric::operator>(): complex inequality");
}
+
/** Numerical comparison: greater or equal.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator>=(numeric const & other) const
+bool numeric::operator>=(const numeric &other) const
{
- if ( is_real() && other.is_real() ) {
- return (bool)(The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN
- }
- throw (std::invalid_argument("numeric::operator>=(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (cln::the<cln::cl_R>(value) >= cln::the<cln::cl_R>(other.value));
+ throw std::invalid_argument("numeric::operator>=(): complex inequality");
}
-/** Converts numeric types to machine's int. You should check with is_integer()
- * if the number is really an integer before calling this method. */
-int numeric::to_int(void) const
+
+/** Converts numeric types to machine's int. You should check with
+ * is_integer() if the number is really an integer before calling this method.
+ * You may also consider checking the range first. */
+int numeric::to_int() const
{
- GINAC_ASSERT(is_integer());
- return cl_I_to_int(The(cl_I)(*value));
+ GINAC_ASSERT(this->is_integer());
+ return cln::cl_I_to_int(cln::the<cln::cl_I>(value));
}
+
+/** Converts numeric types to machine's long. You should check with
+ * is_integer() if the number is really an integer before calling this method.
+ * You may also consider checking the range first. */
+long numeric::to_long() const
+{
+ GINAC_ASSERT(this->is_integer());
+ return cln::cl_I_to_long(cln::the<cln::cl_I>(value));
+}
+
+
/** Converts numeric types to machine's double. You should check with is_real()
* if the number is really not complex before calling this method. */
-double numeric::to_double(void) const
+double numeric::to_double() const
{
- GINAC_ASSERT(is_real());
- return cl_double_approx(realpart(*value));
+ GINAC_ASSERT(this->is_real());
+ return cln::double_approx(cln::realpart(value));
}
+
+/** Returns a new CLN object of type cl_N, representing the value of *this.
+ * This method may be used when mixing GiNaC and CLN in one project.
+ */
+cln::cl_N numeric::to_cl_N() const
+{
+ return value;
+}
+
+
/** Real part of a number. */
-numeric numeric::real(void) const
+const numeric numeric::real() const
{
- return numeric(realpart(*value)); // -> CLN
+ return numeric(cln::realpart(value));
}
+
/** Imaginary part of a number. */
-numeric numeric::imag(void) const
+const numeric numeric::imag() const
{
- return numeric(imagpart(*value)); // -> CLN
+ return numeric(cln::imagpart(value));
}
-#ifndef SANE_LINKER
-// Unfortunately, CLN did not provide an official way to access the numerator
-// or denominator of a rational number (cl_RA). Doing some excavations in CLN
-// one finds how it works internally in src/rational/cl_RA.h:
-struct cl_heap_ratio : cl_heap {
- cl_I numerator;
- cl_I denominator;
-};
-
-inline cl_heap_ratio* TheRatio (const cl_N& obj)
-{ return (cl_heap_ratio*)(obj.pointer); }
-#endif // ndef SANE_LINKER
/** Numerator. Computes the numerator of rational numbers, rationalized
* numerator of complex if real and imaginary part are both rational numbers
* (i.e numer(4/3+5/6*I) == 8+5*I), the number carrying the sign in all other
* cases. */
-numeric numeric::numer(void) const
-{
- if (is_integer()) {
- return numeric(*this);
- }
-#ifdef SANE_LINKER
- else if (instanceof(*value, cl_RA_ring)) {
- return numeric(numerator(The(cl_RA)(*value)));
- }
- else if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numeric(*this);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
- return numeric(complex(r*denominator(The(cl_RA)(i)), numerator(The(cl_RA)(i))));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
- return numeric(complex(numerator(The(cl_RA)(r)), i*denominator(The(cl_RA)(r))));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring)) {
- cl_I s = lcm(denominator(The(cl_RA)(r)), denominator(The(cl_RA)(i)));
- return numeric(complex(numerator(The(cl_RA)(r))*(exquo(s,denominator(The(cl_RA)(r)))),
- numerator(The(cl_RA)(i))*(exquo(s,denominator(The(cl_RA)(i))))));
- }
- }
-#else
- else if (instanceof(*value, cl_RA_ring)) {
- return numeric(TheRatio(*value)->numerator);
- }
- else if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numeric(*this);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
- return numeric(complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
- return numeric(complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring)) {
- cl_I s = lcm(TheRatio(r)->denominator, TheRatio(i)->denominator);
- return numeric(complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)),
- TheRatio(i)->numerator*(exquo(s,TheRatio(i)->denominator))));
- }
- }
-#endif // def SANE_LINKER
- // at least one float encountered
- return numeric(*this);
+const numeric numeric::numer() const
+{
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return numeric(*this); // integer case
+
+ else if (cln::instanceof(value, cln::cl_RA_ring))
+ return numeric(cln::numerator(cln::the<cln::cl_RA>(value)));
+
+ else if (!this->is_real()) { // complex case, handle Q(i):
+ const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(value));
+ const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(value));
+ if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
+ return numeric(*this);
+ if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
+ return numeric(cln::complex(r*cln::denominator(i), cln::numerator(i)));
+ if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
+ return numeric(cln::complex(cln::numerator(r), i*cln::denominator(r)));
+ if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_RA_ring)) {
+ const cln::cl_I s = cln::lcm(cln::denominator(r), cln::denominator(i));
+ return numeric(cln::complex(cln::numerator(r)*(cln::exquo(s,cln::denominator(r))),
+ cln::numerator(i)*(cln::exquo(s,cln::denominator(i)))));
+ }
+ }
+ // at least one float encountered
+ return numeric(*this);
}
+
/** Denominator. Computes the denominator of rational numbers, common integer
* denominator of complex if real and imaginary part are both rational numbers
* (i.e denom(4/3+5/6*I) == 6), one in all other cases. */
-numeric numeric::denom(void) const
-{
- if (is_integer()) {
- return numONE();
- }
-#ifdef SANE_LINKER
- if (instanceof(*value, cl_RA_ring)) {
- return numeric(denominator(The(cl_RA)(*value)));
- }
- if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numONE();
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
- return numeric(denominator(The(cl_RA)(i)));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
- return numeric(denominator(The(cl_RA)(r)));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring))
- return numeric(lcm(denominator(The(cl_RA)(r)), denominator(The(cl_RA)(i))));
- }
-#else
- if (instanceof(*value, cl_RA_ring)) {
- return numeric(TheRatio(*value)->denominator);
- }
- if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numONE();
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
- return numeric(TheRatio(i)->denominator);
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
- return numeric(TheRatio(r)->denominator);
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring))
- return numeric(lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
- }
-#endif // def SANE_LINKER
- // at least one float encountered
- return numONE();
+const numeric numeric::denom() const
+{
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return *_num1_p; // integer case
+
+ if (cln::instanceof(value, cln::cl_RA_ring))
+ return numeric(cln::denominator(cln::the<cln::cl_RA>(value)));
+
+ if (!this->is_real()) { // complex case, handle Q(i):
+ const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(value));
+ const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(value));
+ if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
+ return *_num1_p;
+ if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
+ return numeric(cln::denominator(i));
+ if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
+ return numeric(cln::denominator(r));
+ if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_RA_ring))
+ return numeric(cln::lcm(cln::denominator(r), cln::denominator(i)));
+ }
+ // at least one float encountered
+ return *_num1_p;
}
+
/** Size in binary notation. For integers, this is the smallest n >= 0 such
* that -2^n <= x < 2^n. If x > 0, this is the unique n > 0 such that
* 2^(n-1) <= x < 2^n.
*
* @return number of bits (excluding sign) needed to represent that number
* in two's complement if it is an integer, 0 otherwise. */
-int numeric::int_length(void) const
+int numeric::int_length() const
{
- if (is_integer()) {
- return integer_length(The(cl_I)(*value)); // -> CLN
- } else {
- return 0;
- }
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return cln::integer_length(cln::the<cln::cl_I>(value));
+ else
+ return 0;
}
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned numeric::precedence = 30;
-
//////////
// global constants
//////////
-const numeric some_numeric;
-type_info const & typeid_numeric=typeid(some_numeric);
/** Imaginary unit. This is not a constant but a numeric since we are
- * natively handing complex numbers anyways. */
-const numeric I = numeric(complex(cl_I(0),cl_I(1)));
-
-//////////
-// global functions
-//////////
-
-numeric const & numZERO(void)
-{
- const static ex eZERO = ex((new numeric(0))->setflag(status_flags::dynallocated));
- const static numeric * nZERO = static_cast<const numeric *>(eZERO.bp);
- return *nZERO;
-}
-
-numeric const & numONE(void)
-{
- const static ex eONE = ex((new numeric(1))->setflag(status_flags::dynallocated));
- const static numeric * nONE = static_cast<const numeric *>(eONE.bp);
- return *nONE;
-}
-
-numeric const & numTWO(void)
-{
- const static ex eTWO = ex((new numeric(2))->setflag(status_flags::dynallocated));
- const static numeric * nTWO = static_cast<const numeric *>(eTWO.bp);
- return *nTWO;
-}
-
-numeric const & numTHREE(void)
-{
- const static ex eTHREE = ex((new numeric(3))->setflag(status_flags::dynallocated));
- const static numeric * nTHREE = static_cast<const numeric *>(eTHREE.bp);
- return *nTHREE;
-}
-
-numeric const & numMINUSONE(void)
-{
- const static ex eMINUSONE = ex((new numeric(-1))->setflag(status_flags::dynallocated));
- const static numeric * nMINUSONE = static_cast<const numeric *>(eMINUSONE.bp);
- return *nMINUSONE;
-}
-
-numeric const & numHALF(void)
-{
- const static ex eHALF = ex((new numeric(1, 2))->setflag(status_flags::dynallocated));
- const static numeric * nHALF = static_cast<const numeric *>(eHALF.bp);
- return *nHALF;
-}
-
-/** Exponential function.
- *
- * @return arbitrary precision numerical exp(x). */
-numeric exp(numeric const & x)
-{
- return ::exp(*x.value); // -> CLN
-}
-
-/** Natural logarithm.
- *
- * @param z complex number
- * @return arbitrary precision numerical log(x).
- * @exception overflow_error (logarithmic singularity) */
-numeric log(numeric const & z)
-{
- if (z.is_zero())
- throw (std::overflow_error("log(): logarithmic singularity"));
- return ::log(*z.value); // -> CLN
-}
-
-/** Numeric sine (trigonometric function).
+ * natively handing complex numbers anyways, so in each expression containing
+ * an I it is automatically eval'ed away anyhow. */
+const numeric I = numeric(cln::complex(cln::cl_I(0),cln::cl_I(1)));
+
+/*static cln::cl_N Li2_series(const ::cl_N &x,
+ const ::float_format_t &prec)
+{
+ // Note: argument must be in the unit circle
+ // This is very inefficient unless we have fast floating point Bernoulli
+ // numbers implemented!
+ cln::cl_N c1 = -cln::log(1-x);
+ cln::cl_N c2 = c1;
+ // hard-wire the first two Bernoulli numbers
+ cln::cl_N acc = c1 - cln::square(c1)/4;
+ cln::cl_N aug;
+ cln::cl_F pisq = cln::square(cln::cl_pi(prec)); // pi^2
+ cln::cl_F piac = cln::cl_float(1, prec); // accumulator: pi^(2*i)
+ unsigned i = 1;
+ c1 = cln::square(c1);
+ do {
+ c2 = c1 * c2;
+ piac = piac * pisq;
+ aug = c2 * (*(bernoulli(numeric(2*i)).clnptr())) / cln::factorial(2*i+1);
+ // aug = c2 * cln::cl_I(i%2 ? 1 : -1) / cln::cl_I(2*i+1) * cln::cl_zeta(2*i, prec) / piac / (cln::cl_I(1)<<(2*i-1));
+ acc = acc + aug;
+ ++i;
+ } while (acc != acc+aug);
+ return acc;
+}*/
+
+/** Numeric evaluation of Dilogarithm within circle of convergence (unit
+ * circle) using a power series. */
+static cln::cl_N Li2_series(const cln::cl_N &x,
+ const cln::float_format_t &prec)
+{
+ // Note: argument must be in the unit circle
+ cln::cl_N aug, acc;
+ cln::cl_N num = cln::complex(cln::cl_float(1, prec), 0);
+ cln::cl_I den = 0;
+ unsigned i = 1;
+ do {
+ num = num * x;
+ den = den + i; // 1, 4, 9, 16, ...
+ i += 2;
+ aug = num / den;
+ acc = acc + aug;
+ } while (acc != acc+aug);
+ return acc;
+}
+
+/** Folds Li2's argument inside a small rectangle to enhance convergence. */
+static cln::cl_N Li2_projection(const cln::cl_N &x,
+ const cln::float_format_t &prec)
+{
+ const cln::cl_R re = cln::realpart(x);
+ const cln::cl_R im = cln::imagpart(x);
+ if (re > cln::cl_F(".5"))
+ // zeta(2) - Li2(1-x) - log(x)*log(1-x)
+ return(cln::zeta(2)
+ - Li2_series(1-x, prec)
+ - cln::log(x)*cln::log(1-x));
+ if ((re <= 0 && cln::abs(im) > cln::cl_F(".75")) || (re < cln::cl_F("-.5")))
+ // -log(1-x)^2 / 2 - Li2(x/(x-1))
+ return(- cln::square(cln::log(1-x))/2
+ - Li2_series(x/(x-1), prec));
+ if (re > 0 && cln::abs(im) > cln::cl_LF(".75"))
+ // Li2(x^2)/2 - Li2(-x)
+ return(Li2_projection(cln::square(x), prec)/2
+ - Li2_projection(-x, prec));
+ return Li2_series(x, prec);
+}
+
+/** Numeric evaluation of Dilogarithm. The domain is the entire complex plane,
+ * the branch cut lies along the positive real axis, starting at 1 and
+ * continuous with quadrant IV.
*
- * @return arbitrary precision numerical sin(x). */
-numeric sin(numeric const & x)
-{
- return ::sin(*x.value); // -> CLN
+ * @return arbitrary precision numerical Li2(x). */
+const numeric Li2(const numeric &x)
+{
+ if (x.is_zero())
+ return *_num0_p;
+
+ // what is the desired float format?
+ // first guess: default format
+ cln::float_format_t prec = cln::default_float_format;
+ const cln::cl_N value = x.to_cl_N();
+ // second guess: the argument's format
+ if (!x.real().is_rational())
+ prec = cln::float_format(cln::the<cln::cl_F>(cln::realpart(value)));
+ else if (!x.imag().is_rational())
+ prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(value)));
+
+ if (value==1) // may cause trouble with log(1-x)
+ return cln::zeta(2, prec);
+
+ if (cln::abs(value) > 1)
+ // -log(-x)^2 / 2 - zeta(2) - Li2(1/x)
+ return(- cln::square(cln::log(-value))/2
+ - cln::zeta(2, prec)
+ - Li2_projection(cln::recip(value), prec));
+ else
+ return Li2_projection(x.to_cl_N(), prec);
}
-/** Numeric cosine (trigonometric function).
- *
- * @return arbitrary precision numerical cos(x). */
-numeric cos(numeric const & x)
-{
- return ::cos(*x.value); // -> CLN
-}
-
-/** Numeric tangent (trigonometric function).
- *
- * @return arbitrary precision numerical tan(x). */
-numeric tan(numeric const & x)
-{
- return ::tan(*x.value); // -> CLN
-}
-
-/** Numeric inverse sine (trigonometric function).
- *
- * @return arbitrary precision numerical asin(x). */
-numeric asin(numeric const & x)
-{
- return ::asin(*x.value); // -> CLN
-}
-
-/** Numeric inverse cosine (trigonometric function).
- *
- * @return arbitrary precision numerical acos(x). */
-numeric acos(numeric const & x)
-{
- return ::acos(*x.value); // -> CLN
-}
-
-/** Arcustangents.
- *
- * @param z complex number
- * @return atan(z)
- * @exception overflow_error (logarithmic singularity) */
-numeric atan(numeric const & x)
-{
- if (!x.is_real() &&
- x.real().is_zero() &&
- !abs(x.imag()).is_equal(numONE()))
- throw (std::overflow_error("atan(): logarithmic singularity"));
- return ::atan(*x.value); // -> CLN
-}
-
-/** Arcustangents.
- *
- * @param x real number
- * @param y real number
- * @return atan(y/x) */
-numeric atan(numeric const & y, numeric const & x)
-{
- if (x.is_real() && y.is_real())
- return ::atan(realpart(*x.value), realpart(*y.value)); // -> CLN
- else
- throw (std::invalid_argument("numeric::atan(): complex argument"));
-}
-
-/** Numeric hyperbolic sine (trigonometric function).
- *
- * @return arbitrary precision numerical sinh(x). */
-numeric sinh(numeric const & x)
-{
- return ::sinh(*x.value); // -> CLN
-}
-
-/** Numeric hyperbolic cosine (trigonometric function).
- *
- * @return arbitrary precision numerical cosh(x). */
-numeric cosh(numeric const & x)
-{
- return ::cosh(*x.value); // -> CLN
-}
-
-/** Numeric hyperbolic tangent (trigonometric function).
- *
- * @return arbitrary precision numerical tanh(x). */
-numeric tanh(numeric const & x)
-{
- return ::tanh(*x.value); // -> CLN
-}
-
-/** Numeric inverse hyperbolic sine (trigonometric function).
- *
- * @return arbitrary precision numerical asinh(x). */
-numeric asinh(numeric const & x)
-{
- return ::asinh(*x.value); // -> CLN
-}
-
-/** Numeric inverse hyperbolic cosine (trigonometric function).
- *
- * @return arbitrary precision numerical acosh(x). */
-numeric acosh(numeric const & x)
-{
- return ::acosh(*x.value); // -> CLN
-}
-
-/** Numeric inverse hyperbolic tangent (trigonometric function).
- *
- * @return arbitrary precision numerical atanh(x). */
-numeric atanh(numeric const & x)
-{
- return ::atanh(*x.value); // -> CLN
-}
/** Numeric evaluation of Riemann's Zeta function. Currently works only for
* integer arguments. */
-numeric zeta(numeric const & x)
+const numeric zeta(const numeric &x)
{
- if (x.is_integer())
- return ::cl_zeta(x.to_int()); // -> CLN
- else
- clog << "zeta(): Does anybody know good way to calculate this numerically?" << endl;
- return numeric(0);
+ // A dirty hack to allow for things like zeta(3.0), since CLN currently
+ // only knows about integer arguments and zeta(3).evalf() automatically
+ // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3
+ // being an exact zero for CLN, which can be tested and then we can just
+ // pass the number casted to an int:
+ if (x.is_real()) {
+ const int aux = (int)(cln::double_approx(cln::the<cln::cl_R>(x.to_cl_N())));
+ if (cln::zerop(x.to_cl_N()-aux))
+ return cln::zeta(aux);
+ }
+ throw dunno();
}
-/** The gamma function.
- * This is only a stub! */
-numeric gamma(numeric const & x)
-{
- clog << "gamma(): Does anybody know good way to calculate this numerically?" << endl;
- return numeric(0);
-}
-
-/** The psi function (aka polygamma function).
- * This is only a stub! */
-numeric psi(numeric const & n, numeric const & x)
-{
- clog << "psi(): Does anybody know good way to calculate this numerically?" << endl;
- return numeric(0);
-}
-
-/** Factorial combinatorial function.
- *
- * @exception range_error (argument must be integer >= 0) */
-numeric factorial(numeric const & nn)
-{
- if ( !nn.is_nonneg_integer() ) {
- throw (std::range_error("numeric::factorial(): argument must be integer >= 0"));
- }
-
- return numeric(::factorial(nn.to_int())); // -> CLN
-}
/** The double factorial combinatorial function. (Scarcely used, but still
- * useful in cases, like for exact results of Gamma(n+1/2) for instance.)
+ * useful in cases, like for exact results of tgamma(n+1/2) for instance.)
*
* @param n integer argument >= -1
- * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == 1 == (-1)!!
+ * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1
* @exception range_error (argument must be integer >= -1) */
-numeric doublefactorial(numeric const & nn)
-{
- // META-NOTE: The whole shit here will become obsolete and may be moved
- // out once CLN learns about double factorial, which should be as soon as
- // 1.0.3 rolls out!
-
- // We store the results separately for even and odd arguments. This has
- // the advantage that we don't have to compute any even result at all if
- // the function is always called with odd arguments and vice versa. There
- // is no tradeoff involved in this, it is guaranteed to save time as well
- // as memory. (If this is not enough justification consider the Gamma
- // function of half integer arguments: it only needs odd doublefactorials.)
- static vector<numeric> evenresults;
- static int highest_evenresult = -1;
- static vector<numeric> oddresults;
- static int highest_oddresult = -1;
-
- if (nn == numeric(-1)) {
- return numONE();
- }
- if (!nn.is_nonneg_integer()) {
- throw (std::range_error("numeric::doublefactorial(): argument must be integer >= -1"));
- }
- if (nn.is_even()) {
- int n = nn.div(numTWO()).to_int();
- if (n <= highest_evenresult) {
- return evenresults[n];
- }
- if (evenresults.capacity() < (unsigned)(n+1)) {
- evenresults.reserve(n+1);
- }
- if (highest_evenresult < 0) {
- evenresults.push_back(numONE());
- highest_evenresult=0;
- }
- for (int i=highest_evenresult+1; i<=n; i++) {
- evenresults.push_back(numeric(evenresults[i-1].mul(numeric(i*2))));
- }
- highest_evenresult=n;
- return evenresults[n];
- } else {
- int n = nn.sub(numONE()).div(numTWO()).to_int();
- if (n <= highest_oddresult) {
- return oddresults[n];
- }
- if (oddresults.capacity() < (unsigned)n) {
- oddresults.reserve(n+1);
- }
- if (highest_oddresult < 0) {
- oddresults.push_back(numONE());
- highest_oddresult=0;
- }
- for (int i=highest_oddresult+1; i<=n; i++) {
- oddresults.push_back(numeric(oddresults[i-1].mul(numeric(i*2+1))));
- }
- highest_oddresult=n;
- return oddresults[n];
- }
-}
-
-/** The Binomial coefficients. It computes the binomial coefficients. For
- * integer n and k and positive n this is the number of ways of choosing k
- * objects from n distinct objects. If n is negative, the formula
- * binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */
-numeric binomial(numeric const & n, numeric const & k)
-{
- if (n.is_integer() && k.is_integer()) {
- if (n.is_nonneg_integer()) {
- if (k.compare(n)!=1 && k.compare(numZERO())!=-1)
- return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN
- else
- return numZERO();
- } else {
- return numMINUSONE().power(k)*binomial(k-n-numONE(),k);
- }
- }
-
- // should really be gamma(n+1)/(gamma(r+1)/gamma(n-r+1) or a suitable limit
- throw (std::range_error("numeric::binomial(): don´t know how to evaluate that."));
+const numeric doublefactorial(const numeric &n)
+{
+ if (n.is_equal(*_num_1_p))
+ return *_num1_p;
+
+ if (!n.is_nonneg_integer())
+ throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
+
+ return numeric(cln::doublefactorial(n.to_int()));
}
+
/** Bernoulli number. The nth Bernoulli number is the coefficient of x^n/n!
* in the expansion of the function x/(e^x-1).
*
* @return the nth Bernoulli number (a rational number).
* @exception range_error (argument must be integer >= 0) */
-numeric bernoulli(numeric const & nn)
-{
- if (!nn.is_integer() || nn.is_negative())
- throw (std::range_error("numeric::bernoulli(): argument must be integer >= 0"));
- if (nn.is_zero())
- return numONE();
- if (!nn.compare(numONE()))
- return numeric(-1,2);
- if (nn.is_odd())
- return numZERO();
- // Until somebody has the Blues and comes up with a much better idea and
- // codes it (preferably in CLN) we make this a remembering function which
- // computes its results using the formula
- // B(nn) == - 1/(nn+1) * sum_{k=0}^{nn-1}(binomial(nn+1,k)*B(k))
- // whith B(0) == 1.
- static vector<numeric> results;
- static int highest_result = -1;
- int n = nn.sub(numTWO()).div(numTWO()).to_int();
- if (n <= highest_result)
- return results[n];
- if (results.capacity() < (unsigned)(n+1))
- results.reserve(n+1);
-
- numeric tmp; // used to store the sum
- for (int i=highest_result+1; i<=n; ++i) {
- // the first two elements:
- tmp = numeric(-2*i-1,2);
- // accumulate the remaining elements:
- for (int j=0; j<i; ++j)
- tmp += binomial(numeric(2*i+3),numeric(j*2+2))*results[j];
- // divide by -(nn+1) and store result:
- results.push_back(-tmp/numeric(2*i+3));
- }
- highest_result=n;
- return results[n];
-}
-
-/** Absolute value. */
-numeric abs(numeric const & x)
-{
- return ::abs(*x.value); // -> CLN
-}
+const numeric bernoulli(const numeric &nn)
+{
+ if (!nn.is_integer() || nn.is_negative())
+ throw std::range_error("numeric::bernoulli(): argument must be integer >= 0");
+
+ // Method:
+ //
+ // The Bernoulli numbers are rational numbers that may be computed using
+ // the relation
+ //
+ // B_n = - 1/(n+1) * sum_{k=0}^{n-1}(binomial(n+1,k)*B_k)
+ //
+ // with B(0) = 1. Since the n'th Bernoulli number depends on all the
+ // previous ones, the computation is necessarily very expensive. There are
+ // several other ways of computing them, a particularly good one being
+ // cl_I s = 1;
+ // cl_I c = n+1;
+ // cl_RA Bern = 0;
+ // for (unsigned i=0; i<n; i++) {
+ // c = exquo(c*(i-n),(i+2));
+ // Bern = Bern + c*s/(i+2);
+ // s = s + expt_pos(cl_I(i+2),n);
+ // }
+ // return Bern;
+ //
+ // But if somebody works with the n'th Bernoulli number she is likely to
+ // also need all previous Bernoulli numbers. So we need a complete remember
+ // table and above divide and conquer algorithm is not suited to build one
+ // up. The formula below accomplishes this. It is a modification of the
+ // defining formula above but the computation of the binomial coefficients
+ // is carried along in an inline fashion. It also honors the fact that
+ // B_n is zero when n is odd and greater than 1.
+ //
+ // (There is an interesting relation with the tangent polynomials described
+ // in `Concrete Mathematics', which leads to a program a little faster as
+ // our implementation below, but it requires storing one such polynomial in
+ // addition to the remember table. This doubles the memory footprint so
+ // we don't use it.)
+
+ const unsigned n = nn.to_int();
+
+ // the special cases not covered by the algorithm below
+ if (n & 1)
+ return (n==1) ? (*_num_1_2_p) : (*_num0_p);
+ if (!n)
+ return *_num1_p;
+
+ // store nonvanishing Bernoulli numbers here
+ static std::vector< cln::cl_RA > results;
+ static unsigned next_r = 0;
+
+ // algorithm not applicable to B(2), so just store it
+ if (!next_r) {
+ results.push_back(cln::recip(cln::cl_RA(6)));
+ next_r = 4;
+ }
+ if (n<next_r)
+ return results[n/2-1];
+
+ results.reserve(n/2);
+ for (unsigned p=next_r; p<=n; p+=2) {
+ cln::cl_I c = 1; // seed for binonmial coefficients
+ cln::cl_RA b = cln::cl_RA(p-1)/-2;
+ // The CLN manual says: "The conversion from `unsigned int' works only
+ // if the argument is < 2^29" (This is for 32 Bit machines. More
+ // generally, cl_value_len is the limiting exponent of 2. We must make
+ // sure that no intermediates are created which exceed this value. The
+ // largest intermediate is (p+3-2*k)*(p/2-k+1) <= (p^2+p)/2.
+ if (p < (1UL<<cl_value_len/2)) {
+ for (unsigned k=1; k<=p/2-1; ++k) {
+ c = cln::exquo(c * ((p+3-2*k) * (p/2-k+1)), (2*k-1)*k);
+ b = b + c*results[k-1];
+ }
+ } else {
+ for (unsigned k=1; k<=p/2-1; ++k) {
+ c = cln::exquo((c * (p+3-2*k)) * (p/2-k+1), cln::cl_I(2*k-1)*k);
+ b = b + c*results[k-1];
+ }
+ }
+ results.push_back(-b/(p+1));
+ }
+ next_r = n+2;
+ return results[n/2-1];
+}
+
+
+/** Fibonacci number. The nth Fibonacci number F(n) is defined by the
+ * recurrence formula F(n)==F(n-1)+F(n-2) with F(0)==0 and F(1)==1.
+ *
+ * @param n an integer
+ * @return the nth Fibonacci number F(n) (an integer number)
+ * @exception range_error (argument must be an integer) */
+const numeric fibonacci(const numeric &n)
+{
+ if (!n.is_integer())
+ throw std::range_error("numeric::fibonacci(): argument must be integer");
+ // Method:
+ //
+ // The following addition formula holds:
+ //
+ // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0.
+ //
+ // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence
+ // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values
+ // agree.)
+ // Replace m by m+1:
+ // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0
+ // Now put in m = n, to get
+ // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n))
+ // F(2n+1) = F(n)^2 + F(n+1)^2
+ // hence
+ // F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
+ if (n.is_zero())
+ return *_num0_p;
+ if (n.is_negative())
+ if (n.is_even())
+ return -fibonacci(-n);
+ else
+ return fibonacci(-n);
+
+ cln::cl_I u(0);
+ cln::cl_I v(1);
+ cln::cl_I m = cln::the<cln::cl_I>(n.to_cl_N()) >> 1L; // floor(n/2);
+ for (uintL bit=cln::integer_length(m); bit>0; --bit) {
+ // Since a squaring is cheaper than a multiplication, better use
+ // three squarings instead of one multiplication and two squarings.
+ cln::cl_I u2 = cln::square(u);
+ cln::cl_I v2 = cln::square(v);
+ if (cln::logbitp(bit-1, m)) {
+ v = cln::square(u + v) - u2;
+ u = u2 + v2;
+ } else {
+ u = v2 - cln::square(v - u);
+ v = u2 + v2;
+ }
+ }
+ if (n.is_even())
+ // Here we don't use the squaring formula because one multiplication
+ // is cheaper than two squarings.
+ return u * ((v << 1) - u);
+ else
+ return cln::square(u) + cln::square(v);
+}
+
+
+///** Absolute value. */
+//const numeric abs(const numeric& x)
+//{
+// return cln::abs(x.to_cl_N());
+//}
+
/** Modulus (in positive representation).
* In general, mod(a,b) has the sign of b or is zero, and rem(a,b) has the
*
* @return a mod b in the range [0,abs(b)-1] with sign of b if both are
* integer, 0 otherwise. */
-numeric mod(numeric const & a, numeric const & b)
+const numeric mod(const numeric &a, const numeric &b)
{
- if (a.is_integer() && b.is_integer()) {
- return ::mod(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- }
- else {
- return numZERO(); // Throw?
- }
+ if (a.is_integer() && b.is_integer())
+ return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ else
+ return *_num0_p;
}
+
/** Modulus (in symmetric representation).
* Equivalent to Maple's mods.
*
- * @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
-numeric smod(numeric const & a, numeric const & b)
+ * @return a mod b in the range [-iquo(abs(b)-1,2), iquo(abs(b),2)]. */
+const numeric smod(const numeric &a, const numeric &b)
{
- if (a.is_integer() && b.is_integer()) {
- cl_I b2 = The(cl_I)(ceiling1(The(cl_I)(*b.value) / 2)) - 1;
- return ::mod(The(cl_I)(*a.value) + b2, The(cl_I)(*b.value)) - b2;
- } else {
- return numZERO(); // Throw?
- }
+ if (a.is_integer() && b.is_integer()) {
+ const cln::cl_I b2 = cln::ceiling1(cln::the<cln::cl_I>(b.to_cl_N()) >> 1) - 1;
+ return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
+ cln::the<cln::cl_I>(b.to_cl_N())) - b2;
+ } else
+ return *_num0_p;
}
+
/** Numeric integer remainder.
* Equivalent to Maple's irem(a,b) as far as sign conventions are concerned.
* In general, mod(a,b) has the sign of b or is zero, and irem(a,b) has the
* sign of a or is zero.
*
- * @return remainder of a/b if both are integer, 0 otherwise. */
-numeric irem(numeric const & a, numeric const & b)
+ * @return remainder of a/b if both are integer, 0 otherwise.
+ * @exception overflow_error (division by zero) if b is zero. */
+const numeric irem(const numeric &a, const numeric &b)
{
- if (a.is_integer() && b.is_integer()) {
- return ::rem(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- }
- else {
- return numZERO(); // Throw?
- }
+ if (b.is_zero())
+ throw std::overflow_error("numeric::irem(): division by zero");
+ if (a.is_integer() && b.is_integer())
+ return cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ else
+ return *_num0_p;
}
+
/** Numeric integer remainder.
* Equivalent to Maple's irem(a,b,'q') it obeyes the relation
* irem(a,b,q) == a - q*b. In general, mod(a,b) has the sign of b or is zero,
- * and irem(a,b) has the sign of a or is zero.
+ * and irem(a,b) has the sign of a or is zero.
*
* @return remainder of a/b and quotient stored in q if both are integer,
- * 0 otherwise. */
-numeric irem(numeric const & a, numeric const & b, numeric & q)
+ * 0 otherwise.
+ * @exception overflow_error (division by zero) if b is zero. */
+const numeric irem(const numeric &a, const numeric &b, numeric &q)
{
- if (a.is_integer() && b.is_integer()) { // -> CLN
- cl_I_div_t rem_quo = truncate2(The(cl_I)(*a.value), The(cl_I)(*b.value));
- q = rem_quo.quotient;
- return rem_quo.remainder;
- }
- else {
- q = numZERO();
- return numZERO(); // Throw?
- }
+ if (b.is_zero())
+ throw std::overflow_error("numeric::irem(): division by zero");
+ if (a.is_integer() && b.is_integer()) {
+ const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ q = rem_quo.quotient;
+ return rem_quo.remainder;
+ } else {
+ q = *_num0_p;
+ return *_num0_p;
+ }
}
+
/** Numeric integer quotient.
* Equivalent to Maple's iquo as far as sign conventions are concerned.
*
- * @return truncated quotient of a/b if both are integer, 0 otherwise. */
-numeric iquo(numeric const & a, numeric const & b)
+ * @return truncated quotient of a/b if both are integer, 0 otherwise.
+ * @exception overflow_error (division by zero) if b is zero. */
+const numeric iquo(const numeric &a, const numeric &b)
{
- if (a.is_integer() && b.is_integer()) {
- return truncate1(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- } else {
- return numZERO(); // Throw?
- }
+ if (b.is_zero())
+ throw std::overflow_error("numeric::iquo(): division by zero");
+ if (a.is_integer() && b.is_integer())
+ return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ else
+ return *_num0_p;
}
+
/** Numeric integer quotient.
* Equivalent to Maple's iquo(a,b,'r') it obeyes the relation
* r == a - iquo(a,b,r)*b.
*
* @return truncated quotient of a/b and remainder stored in r if both are
- * integer, 0 otherwise. */
-numeric iquo(numeric const & a, numeric const & b, numeric & r)
+ * integer, 0 otherwise.
+ * @exception overflow_error (division by zero) if b is zero. */
+const numeric iquo(const numeric &a, const numeric &b, numeric &r)
{
- if (a.is_integer() && b.is_integer()) { // -> CLN
- cl_I_div_t rem_quo = truncate2(The(cl_I)(*a.value), The(cl_I)(*b.value));
- r = rem_quo.remainder;
- return rem_quo.quotient;
- } else {
- r = numZERO();
- return numZERO(); // Throw?
- }
+ if (b.is_zero())
+ throw std::overflow_error("numeric::iquo(): division by zero");
+ if (a.is_integer() && b.is_integer()) {
+ const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ r = rem_quo.remainder;
+ return rem_quo.quotient;
+ } else {
+ r = *_num0_p;
+ return *_num0_p;
+ }
}
-/** Numeric square root.
- * If possible, sqrt(z) should respect squares of exact numbers, i.e. sqrt(4)
- * should return integer 2.
- *
- * @param z numeric argument
- * @return square root of z. Branch cut along negative real axis, the negative
- * real axis itself where imag(z)==0 and real(z)<0 belongs to the upper part
- * where imag(z)>0. */
-numeric sqrt(numeric const & z)
-{
- return ::sqrt(*z.value); // -> CLN
-}
-
-/** Integer numeric square root. */
-numeric isqrt(numeric const & x)
-{
- if (x.is_integer()) {
- cl_I root;
- ::isqrt(The(cl_I)(*x.value), &root); // -> CLN
- return root;
- } else
- return numZERO(); // Throw?
-}
/** Greatest Common Divisor.
*
* @return The GCD of two numbers if both are integer, a numerical 1
* if they are not. */
-numeric gcd(numeric const & a, numeric const & b)
+const numeric gcd(const numeric &a, const numeric &b)
{
- if (a.is_integer() && b.is_integer())
- return ::gcd(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- else
- return numONE();
+ if (a.is_integer() && b.is_integer())
+ return cln::gcd(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ else
+ return *_num1_p;
}
+
/** Least Common Multiple.
*
* @return The LCM of two numbers if both are integer, the product of those
* two numbers if they are not. */
-numeric lcm(numeric const & a, numeric const & b)
+const numeric lcm(const numeric &a, const numeric &b)
+{
+ if (a.is_integer() && b.is_integer())
+ return cln::lcm(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
+ else
+ return a.mul(b);
+}
+
+
+/** Numeric square root.
+ * If possible, sqrt(x) should respect squares of exact numbers, i.e. sqrt(4)
+ * should return integer 2.
+ *
+ * @param x numeric argument
+ * @return square root of x. Branch cut along negative real axis, the negative
+ * real axis itself where imag(x)==0 and real(x)<0 belongs to the upper part
+ * where imag(x)>0. */
+const numeric sqrt(const numeric &x)
{
- if (a.is_integer() && b.is_integer())
- return ::lcm(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- else
- return *a.value * *b.value;
+ return cln::sqrt(x.to_cl_N());
+}
+
+
+/** Integer numeric square root. */
+const numeric isqrt(const numeric &x)
+{
+ if (x.is_integer()) {
+ cln::cl_I root;
+ cln::isqrt(cln::the<cln::cl_I>(x.to_cl_N()), &root);
+ return root;
+ } else
+ return *_num0_p;
}
-ex PiEvalf(void)
+
+/** Floating point evaluation of Archimedes' constant Pi. */
+ex PiEvalf()
{
- return numeric(cl_pi(cl_default_float_format)); // -> CLN
+ return numeric(cln::pi(cln::default_float_format));
}
-ex EulerGammaEvalf(void)
+
+/** Floating point evaluation of Euler's constant gamma. */
+ex EulerEvalf()
{
- return numeric(cl_eulerconst(cl_default_float_format)); // -> CLN
+ return numeric(cln::eulerconst(cln::default_float_format));
}
-ex CatalanEvalf(void)
+
+/** Floating point evaluation of Catalan's constant. */
+ex CatalanEvalf()
{
- return numeric(cl_catalanconst(cl_default_float_format)); // -> CLN
+ return numeric(cln::catalanconst(cln::default_float_format));
}
-// It initializes to 17 digits, because in CLN cl_float_format(17) turns out to
-// be 61 (<64) while cl_float_format(18)=65. We want to have a cl_LF instead
-// of cl_SF, cl_FF or cl_DF but everything else is basically arbitrary.
+
+/** _numeric_digits default ctor, checking for singleton invariance. */
_numeric_digits::_numeric_digits()
- : digits(17)
+ : digits(17)
{
- assert(!too_late);
- too_late = true;
- cl_default_float_format = cl_float_format(17);
+ // It initializes to 17 digits, because in CLN float_format(17) turns out
+ // to be 61 (<64) while float_format(18)=65. The reason is we want to
+ // have a cl_LF instead of cl_SF, cl_FF or cl_DF.
+ if (too_late)
+ throw(std::runtime_error("I told you not to do instantiate me!"));
+ too_late = true;
+ cln::default_float_format = cln::float_format(17);
+
+ // add callbacks for built-in functions
+ // like ... add_callback(Li_lookuptable);
}
+
+/** Assign a native long to global Digits object. */
_numeric_digits& _numeric_digits::operator=(long prec)
{
- digits=prec;
- cl_default_float_format = cl_float_format(prec);
- return *this;
+ long digitsdiff = prec - digits;
+ digits = prec;
+ cln::default_float_format = cln::float_format(prec);
+
+ // call registered callbacks
+ std::vector<digits_changed_callback>::const_iterator it = callbacklist.begin(), end = callbacklist.end();
+ for (; it != end; ++it) {
+ (*it)(digitsdiff);
+ }
+
+ return *this;
}
+
+/** Convert global Digits object to native type long. */
_numeric_digits::operator long()
{
- return (long)digits;
+ // BTW, this is approx. unsigned(cln::default_float_format*0.301)-1
+ return (long)digits;
}
-void _numeric_digits::print(ostream & os) const
+
+/** Append global Digits object to ostream. */
+void _numeric_digits::print(std::ostream &os) const
{
- debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
- os << digits;
+ os << digits;
}
-ostream& operator<<(ostream& os, _numeric_digits const & e)
+
+/** Add a new callback function. */
+void _numeric_digits::add_callback(digits_changed_callback callback)
{
- e.print(os);
- return os;
+ callbacklist.push_back(callback);
+}
+
+
+std::ostream& operator<<(std::ostream &os, const _numeric_digits &e)
+{
+ e.print(os);
+ return os;
}
//////////
bool _numeric_digits::too_late = false;
+
/** Accuracy in decimal digits. Only object of this type! Can be set using
* assignment from C++ unsigned ints and evaluated like any built-in type. */
_numeric_digits Digits;
* Makes the interface to the underlying bignum package available. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef __GINAC_NUMERIC_H__
#define __GINAC_NUMERIC_H__
-#include <strstream>
-#include <ginac/basic.h>
-#include <ginac/ex.h>
+#include "basic.h"
+#include "ex.h"
-class cl_N; // We want to include cln.h only in numeric.cpp in order to
- // avoid namespace pollution and keep compile-time low.
+#include <stdexcept>
+#include <vector>
+
+#include <cln/complex.h>
+
+#if defined(G__CINTVERSION) && !defined(__MAKECINT__)
+// Cint @$#$! doesn't like forward declaring classes used for casting operators
+// so we have to include the definition of cln::cl_N here, but it is enough to
+// do so for the compiler, hence the !defined(__MAKECINT__).
+ #include <cln/complex_class.h>
+#endif
namespace GiNaC {
-#define HASHVALUE_NUMERIC 0x80000001U
+/** Function pointer to implement callbacks in the case 'Digits' gets changed.
+ * Main purpose of such callbacks is to adjust look-up tables of certain
+ * functions to the new precision. Parameter contains the signed difference
+ * between new Digits and old Digits. */
+typedef void (* digits_changed_callback)(long);
-/** This class is used to instantiate a global object Digits which
- * behaves just like Maple's Digits. We need an object rather than a
- * dumber basic type since as a side-effect we let it change
+/** This class is used to instantiate a global singleton object Digits
+ * which behaves just like Maple's Digits. We need an object rather
+ * than a dumber basic type since as a side-effect we let it change
* cl_default_float_format when it gets changed. The only other
* meaningful thing to do with it is converting it to an unsigned,
* for temprary storing its value e.g. The user must not create an
{
// member functions
public:
- _numeric_digits();
- _numeric_digits& operator=(long prec);
- operator long();
- void print(ostream & os) const;
+ _numeric_digits();
+ _numeric_digits& operator=(long prec);
+ operator long();
+ void print(std::ostream& os) const;
+ void add_callback(digits_changed_callback callback);
// member variables
private:
- long digits;
- static bool too_late;
+ long digits; ///< Number of decimal digits
+ static bool too_late; ///< Already one object present
+ // Holds a list of functions that get called when digits is changed.
+ std::vector<digits_changed_callback> callbacklist;
+};
+
+
+/** Exception class thrown when a singularity is encountered. */
+class pole_error : public std::domain_error {
+public:
+ explicit pole_error(const std::string& what_arg, int degree);
+ int degree() const;
+private:
+ int deg;
};
+
/** This class is a wrapper around CLN-numbers within the GiNaC class
* hierarchy. Objects of this type may directly be created by the user.*/
class numeric : public basic
{
-// friends
- friend numeric exp(numeric const & x);
- friend numeric log(numeric const & x);
- friend numeric sin(numeric const & x);
- friend numeric cos(numeric const & x);
- friend numeric tan(numeric const & x);
- friend numeric asin(numeric const & x);
- friend numeric acos(numeric const & x);
- friend numeric atan(numeric const & x);
- friend numeric atan(numeric const & y, numeric const & x);
- friend numeric sinh(numeric const & x);
- friend numeric cosh(numeric const & x);
- friend numeric tanh(numeric const & x);
- friend numeric asinh(numeric const & x);
- friend numeric acosh(numeric const & x);
- friend numeric atanh(numeric const & x);
- friend numeric bernoulli(numeric const & n);
- friend numeric abs(numeric const & x);
- friend numeric mod(numeric const & a, numeric const & b);
- friend numeric smod(numeric const & a, numeric const & b);
- friend numeric irem(numeric const & a, numeric const & b);
- friend numeric irem(numeric const & a, numeric const & b, numeric & q);
- friend numeric iquo(numeric const & a, numeric const & b);
- friend numeric iquo(numeric const & a, numeric const & b, numeric & r);
- friend numeric sqrt(numeric const & x);
- friend numeric isqrt(numeric const & x);
- friend numeric gcd(numeric const & a, numeric const & b);
- friend numeric lcm(numeric const & a, numeric const & b);
- friend numeric const & numZERO(void);
- friend numeric const & numONE(void);
- friend numeric const & numTWO(void);
- friend numeric const & numTHREE(void);
- friend numeric const & numMINUSONE(void);
- friend numeric const & numHALF(void);
-
+ GINAC_DECLARE_REGISTERED_CLASS(numeric, basic)
+
// member functions
-
- // default constructor, destructor, copy constructor assignment
- // operator and helpers
-public:
- numeric();
- ~numeric();
- numeric(numeric const & other);
- numeric const & operator=(numeric const & other);
-protected:
- void copy(numeric const & other);
- void destroy(bool call_parent);
-
- // other constructors
+
+ // other constructors
public:
- explicit numeric(int i);
- explicit numeric(unsigned int i);
- explicit numeric(long i);
- explicit numeric(unsigned long i);
- explicit numeric(long numer, long denom);
- explicit numeric(double d);
- explicit numeric(char const *);
- numeric(cl_N const & z);
-
- // functions overriding virtual functions from bases classes
+ numeric(int i);
+ numeric(unsigned int i);
+ numeric(long i);
+ numeric(unsigned long i);
+ numeric(long numer, long denom);
+ numeric(double d);
+ numeric(const char *);
+
+ // functions overriding virtual functions from base classes
public:
- basic * duplicate() const;
- void printraw(ostream & os) const;
- void printtree(ostream & os, unsigned indent) const;
- void print(ostream & os, unsigned precedence=0) const;
- void printcsrc(ostream & os, unsigned type, unsigned precedence=0) const;
- bool info(unsigned inf) const;
- ex evalf(int level=0) const;
- ex diff(symbol const & s) const;
- ex normal(lst &sym_lst, lst &repl_lst, int level=0) const;
- numeric integer_content(void) const;
- ex smod(numeric const &xi) const;
- numeric max_coefficient(void) const;
+ unsigned precedence() const {return 30;}
+ bool info(unsigned inf) const;
+ bool is_polynomial(const ex & var) const;
+ int degree(const ex & s) const;
+ int ldegree(const ex & s) const;
+ ex coeff(const ex & s, int n = 1) const;
+ bool has(const ex &other, unsigned options = 0) const;
+ ex eval(int level = 0) const;
+ ex evalf(int level = 0) const;
+ ex subs(const exmap & m, unsigned options = 0) const { return subs_one_level(m, options); } // overwrites basic::subs() for performance reasons
+ ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
+ ex to_rational(exmap & repl) const;
+ ex to_polynomial(exmap & repl) const;
+ numeric integer_content() const;
+ ex smod(const numeric &xi) const;
+ numeric max_coefficient() const;
+ ex conjugate() const;
protected:
- int compare_same_type(basic const & other) const;
- bool is_equal_same_type(basic const & other) const;
- unsigned calchash(void) const {
- hashvalue=HASHVALUE_NUMERIC;
- return HASHVALUE_NUMERIC;
- }
-
- // new virtual functions which can be overridden by derived classes
- // (none)
-
- // non-virtual functions in this class
+ /** Implementation of ex::diff for a numeric always returns 0.
+ * @see ex::diff */
+ ex derivative(const symbol &s) const { return 0; }
+ bool is_equal_same_type(const basic &other) const;
+ unsigned calchash() const;
+
+ // new virtual functions which can be overridden by derived classes
+ // (none)
+
+ // non-virtual functions in this class
public:
- numeric add(numeric const & other) const;
- numeric sub(numeric const & other) const;
- numeric mul(numeric const & other) const;
- numeric div(numeric const & other) const;
- numeric power(numeric const & other) const;
- numeric const & add_dyn(numeric const & other) const;
- numeric const & sub_dyn(numeric const & other) const;
- numeric const & mul_dyn(numeric const & other) const;
- numeric const & div_dyn(numeric const & other) const;
- numeric const & power_dyn(numeric const & other) const;
- numeric const & operator=(int i);
- numeric const & operator=(unsigned int i);
- numeric const & operator=(long i);
- numeric const & operator=(unsigned long i);
- numeric const & operator=(double d);
- numeric const & operator=(char const * s);
- /*
- numeric add_dyn(numeric const & other) const { return add(other); }
- numeric sub_dyn(numeric const & other) const { return sub(other); }
- numeric mul_dyn(numeric const & other) const { return mul(other); }
- numeric div_dyn(numeric const & other) const { return div(other); }
- numeric power_dyn(numeric const & other) const { return power(other); }
- */
- numeric inverse(void) const;
- int csgn(void) const;
- int compare(numeric const & other) const;
- bool is_equal(numeric const & other) const;
- bool is_zero(void) const;
- bool is_positive(void) const;
- bool is_negative(void) const;
- bool is_integer(void) const;
- bool is_pos_integer(void) const;
- bool is_nonneg_integer(void) const;
- bool is_even(void) const;
- bool is_odd(void) const;
- bool is_prime(void) const;
- bool is_rational(void) const;
- bool is_real(void) const;
- bool operator==(numeric const & other) const;
- bool operator!=(numeric const & other) const;
- bool operator<(numeric const & other) const;
- bool operator<=(numeric const & other) const;
- bool operator>(numeric const & other) const;
- bool operator>=(numeric const & other) const;
- int to_int(void) const;
- double to_double(void) const;
- numeric real(void) const;
- numeric imag(void) const;
- numeric numer(void) const;
- numeric denom(void) const;
- int int_length(void) const;
+ const numeric add(const numeric &other) const;
+ const numeric sub(const numeric &other) const;
+ const numeric mul(const numeric &other) const;
+ const numeric div(const numeric &other) const;
+ const numeric power(const numeric &other) const;
+ const numeric & add_dyn(const numeric &other) const;
+ const numeric & sub_dyn(const numeric &other) const;
+ const numeric & mul_dyn(const numeric &other) const;
+ const numeric & div_dyn(const numeric &other) const;
+ const numeric & power_dyn(const numeric &other) const;
+ const numeric & operator=(int i);
+ const numeric & operator=(unsigned int i);
+ const numeric & operator=(long i);
+ const numeric & operator=(unsigned long i);
+ const numeric & operator=(double d);
+ const numeric & operator=(const char *s);
+ const numeric inverse() const;
+ numeric step() const;
+ int csgn() const;
+ int compare(const numeric &other) const;
+ bool is_equal(const numeric &other) const;
+ bool is_zero() const;
+ bool is_positive() const;
+ bool is_negative() const;
+ bool is_integer() const;
+ bool is_pos_integer() const;
+ bool is_nonneg_integer() const;
+ bool is_even() const;
+ bool is_odd() const;
+ bool is_prime() const;
+ bool is_rational() const;
+ bool is_real() const;
+ bool is_cinteger() const;
+ bool is_crational() const;
+ bool operator==(const numeric &other) const;
+ bool operator!=(const numeric &other) const;
+ bool operator<(const numeric &other) const;
+ bool operator<=(const numeric &other) const;
+ bool operator>(const numeric &other) const;
+ bool operator>=(const numeric &other) const;
+ int to_int() const;
+ long to_long() const;
+ double to_double() const;
+ cln::cl_N to_cl_N() const;
+ const numeric real() const;
+ const numeric imag() const;
+ const numeric numer() const;
+ const numeric denom() const;
+ int int_length() const;
+ // converting routines for interfacing with CLN:
+ numeric(const cln::cl_N &z);
+
+protected:
+ void print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const;
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_latex(const print_latex & c, unsigned level) const;
+ void do_print_csrc(const print_csrc & c, unsigned level) const;
+ void do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const;
+ void do_print_tree(const print_tree & c, unsigned level) const;
+ void do_print_python_repr(const print_python_repr & c, unsigned level) const;
// member variables
protected:
- static unsigned precedence;
- cl_N *value;
+ cln::cl_N value;
};
+
// global constants
-extern const numeric some_numeric;
extern const numeric I;
-extern type_info const & typeid_numeric;
extern _numeric_digits Digits;
-#define is_a_numeric_hash(x) ((x)==HASHVALUE_NUMERIC)
-// may have to be changed to ((x)>=0x80000000U)
-
// global functions
-numeric const & numZERO(void);
-numeric const & numONE(void);
-numeric const & numTWO(void);
-numeric const & numMINUSONE(void);
-numeric const & numHALF(void);
-
-numeric exp(numeric const & x);
-numeric log(numeric const & x);
-numeric sin(numeric const & x);
-numeric cos(numeric const & x);
-numeric tan(numeric const & x);
-numeric asin(numeric const & x);
-numeric acos(numeric const & x);
-numeric atan(numeric const & x);
-numeric atan(numeric const & y, numeric const & x);
-numeric sinh(numeric const & x);
-numeric cosh(numeric const & x);
-numeric tanh(numeric const & x);
-numeric asinh(numeric const & x);
-numeric acosh(numeric const & x);
-numeric atanh(numeric const & x);
-numeric zeta(numeric const & x);
-numeric gamma(numeric const & x);
-numeric psi(numeric const & n, numeric const & x);
-numeric factorial(numeric const & n);
-numeric doublefactorial(numeric const & n);
-numeric binomial(numeric const & n, numeric const & k);
-numeric bernoulli(numeric const & n);
-
-numeric abs(numeric const & x);
-numeric mod(numeric const & a, numeric const & b);
-numeric smod(numeric const & a, numeric const & b);
-numeric irem(numeric const & a, numeric const & b);
-numeric irem(numeric const & a, numeric const & b, numeric & q);
-numeric iquo(numeric const & a, numeric const & b);
-numeric iquo(numeric const & a, numeric const & b, numeric & r);
-numeric sqrt(numeric const & x);
-numeric isqrt(numeric const & x);
-
-numeric gcd(numeric const & a, numeric const & b);
-numeric lcm(numeric const & a, numeric const & b);
-
-/** Exception thrown by numeric members to signal failure */
-struct numeric_fail
-{
- int failval;
- numeric_fail(int n) { failval = n; }
-};
+//-- to go ...
+const numeric Li2(const numeric &x);
+const numeric zeta(const numeric &x);
+const numeric doublefactorial(const numeric &n);
+const numeric bernoulli(const numeric &n);
+const numeric fibonacci(const numeric &n);
+//--
+const numeric isqrt(const numeric &x);
+const numeric sqrt(const numeric &x);
+const numeric mod(const numeric &a, const numeric &b);
+const numeric smod(const numeric &a, const numeric &b);
+const numeric irem(const numeric &a, const numeric &b);
+const numeric irem(const numeric &a, const numeric &b, numeric &q);
+const numeric iquo(const numeric &a, const numeric &b);
+const numeric iquo(const numeric &a, const numeric &b, numeric &r);
+const numeric gcd(const numeric &a, const numeric &b);
+const numeric lcm(const numeric &a, const numeric &b);
// wrapper functions around member functions
-inline numeric inverse(numeric const & x)
-{ return x.inverse(); }
+inline const numeric pow(const numeric &x, const numeric &y)
+{ return x.power(y); }
-inline bool csgn(numeric const & x)
-{ return x.csgn(); }
+inline const numeric inverse(const numeric &x)
+{ return x.inverse(); }
-inline bool is_zero(numeric const & x)
+inline bool is_zero(const numeric &x)
{ return x.is_zero(); }
-inline bool is_positive(numeric const & x)
+inline bool is_positive(const numeric &x)
{ return x.is_positive(); }
-inline bool is_integer(numeric const & x)
+inline bool is_integer(const numeric &x)
{ return x.is_integer(); }
-inline bool is_pos_integer(numeric const & x)
+inline bool is_pos_integer(const numeric &x)
{ return x.is_pos_integer(); }
-inline bool is_nonneg_integer(numeric const & x)
+inline bool is_nonneg_integer(const numeric &x)
{ return x.is_nonneg_integer(); }
-inline bool is_even(numeric const & x)
+inline bool is_even(const numeric &x)
{ return x.is_even(); }
-inline bool is_odd(numeric const & x)
+inline bool is_odd(const numeric &x)
{ return x.is_odd(); }
-inline bool is_prime(numeric const & x)
+inline bool is_prime(const numeric &x)
{ return x.is_prime(); }
-inline bool is_rational(numeric const & x)
+inline bool is_rational(const numeric &x)
{ return x.is_rational(); }
-inline bool is_real(numeric const & x)
+inline bool is_real(const numeric &x)
{ return x.is_real(); }
-inline numeric real(numeric const & x)
+inline bool is_cinteger(const numeric &x)
+{ return x.is_cinteger(); }
+
+inline bool is_crational(const numeric &x)
+{ return x.is_crational(); }
+
+inline int to_int(const numeric &x)
+{ return x.to_int(); }
+
+inline long to_long(const numeric &x)
+{ return x.to_long(); }
+
+inline double to_double(const numeric &x)
+{ return x.to_double(); }
+
+inline const numeric real(const numeric &x)
{ return x.real(); }
-inline numeric imag(numeric const & x)
+inline const numeric imag(const numeric &x)
{ return x.imag(); }
-inline numeric numer(numeric const & x)
+inline const numeric numer(const numeric &x)
{ return x.numer(); }
-inline numeric denom(numeric const & x)
+inline const numeric denom(const numeric &x)
{ return x.denom(); }
-ex IEvalf(void);
-ex PiEvalf(void);
-ex EulerGammaEvalf(void);
-ex CatalanEvalf(void);
+// numeric evaluation functions for class constant objects:
+
+ex PiEvalf();
+ex EulerEvalf();
+ex CatalanEvalf();
-// utility functions
-inline const numeric &ex_to_numeric(const ex &e)
-{
- return static_cast<const numeric &>(*e.bp);
-}
} // namespace GiNaC
+#ifdef __MAKECINT__
+#pragma link off defined_in cln/number.h;
+#pragma link off defined_in cln/complex_class.h;
+#endif
+
#endif // ndef __GINAC_NUMERIC_H__
#include "numeric.h"
#include "constant.h"
#include "operators.h"
+#include "inifcns.h" // for binomial()
#include "inifcns_exp.h" // for log() in power::derivative()
#include "matrix.h"
#include "indexed.h"
if (is_exactly_a<numeric>(sub_exponent)) {
const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
GINAC_ASSERT(num_sub_exponent!=numeric(1));
- if (num_exponent->is_integer() || (abs(num_sub_exponent) - (*_num1_p)).is_negative())
+ if (num_exponent->is_integer() || (abs_function::eval_numeric(num_sub_exponent) - (*_num1_p)).is_negative())
return power(sub_basis,num_sub_exponent.mul(*num_exponent));
}
}
mulp->clearflag(status_flags::evaluated);
mulp->clearflag(status_flags::hash_calculated);
return (new mul(power(*mulp,exponent),
- power(abs(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
+ power(abs_function::eval_numeric(num_coeff),*num_exponent)))->setflag(status_flags::dynallocated);
}
}
}
// i.e. the number of unordered arrangements of m nonnegative integers
// which sum up to n. It is frequently written as C_n(m) and directly
// related with binomial coefficients:
- result.reserve(binomial(numeric(n+m-1), numeric(m-1)).to_int());
+ result.reserve(binomial::eval_numeric(numeric(n+m-1), numeric(m-1)).to_int());
intvector k(m-1);
intvector k_cum(m-1); // k_cum[l]:=sum(i=0,l,k[l]);
intvector upper_limit(m-1);
else
term.push_back(power(b,n-k_cum[m-2]));
- numeric f = binomial(numeric(n),numeric(k[0]));
+ numeric f = binomial::eval_numeric(numeric(n),numeric(k[0]));
for (l=1; l<m-1; ++l)
- f *= binomial(numeric(n-k_cum[l-1]),numeric(k[l]));
+ f *= binomial::eval_numeric(numeric(n-k_cum[l-1]),numeric(k[l]));
term.push_back(f);
if (i != seq.begin())
c.s << '+';
- if (!is_exactly_a<Order_function>(i->rest)) {
+ if (!is_exactly_a<Order>(i->rest)) {
// print 'rest', i.e. the expansion coefficient
if (i->rest.info(info_flags::numeric) &&
if (i >= seq.size())
throw (std::out_of_range("op() out of range"));
- if (is_exactly_a<Order_function>(seq[i].rest))
+ if (is_exactly_a<Order>(seq[i].rest))
return Order(power(var-point, seq[i].coeff));
return seq[i].rest * power(var - point, seq[i].coeff);
}
// FIXME: coeff might depend on var
while (it != itend) {
- if (is_exactly_a<Order_function>(it->rest)) {
+ if (is_exactly_a<Order>(it->rest)) {
new_seq.push_back(expair(it->rest, it->coeff - 1));
} else {
ex c = it->rest * it->coeff;
} else {
while (it != itend) {
- if (is_exactly_a<Order_function>(it->rest)) {
+ if (is_exactly_a<Order>(it->rest)) {
new_seq.push_back(*it);
} else {
ex c = it->rest.diff(s);
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- if (is_exactly_a<Order_function>(it->rest)) {
+ if (is_exactly_a<Order>(it->rest)) {
if (!no_order)
e += Order(power(var - point, it->coeff));
} else
bool pseries::is_terminating() const
{
- return seq.empty() || !is_exactly_a<Order_function>((seq.end()-1)->rest);
+ return seq.empty() || !is_exactly_a<Order>((seq.end()-1)->rest);
}
ex pseries::coeffop(size_t i) const
if (pow_a < pow_b) {
// a has lesser power, get coefficient from a
new_seq.push_back(*a);
- if (is_exactly_a<Order_function>((*a).rest))
+ if (is_exactly_a<Order>((*a).rest))
break;
++a;
} else if (pow_b < pow_a) {
// b has lesser power, get coefficient from b
new_seq.push_back(*b);
- if (is_exactly_a<Order_function>((*b).rest))
+ if (is_exactly_a<Order>((*b).rest))
break;
++b;
} else {
// Add coefficient of a and b
- if (is_exactly_a<Order_function>((*a).rest) || is_exactly_a<Order_function>((*b).rest)) {
+ if (is_exactly_a<Order>((*a).rest) || is_exactly_a<Order>((*b).rest)) {
new_seq.push_back(expair(Order(_ex1), (*a).coeff));
break; // Order term ends the sequence
} else {
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- if (!is_exactly_a<Order_function>(it->rest))
+ if (!is_exactly_a<Order>(it->rest))
new_seq.push_back(expair(it->rest * other, it->coeff));
else
new_seq.push_back(*it);
int higher_order_a = INT_MAX;
int higher_order_b = INT_MAX;
- if (is_exactly_a<Order_function>(coeff(var, a_max)))
+ if (is_exactly_a<Order>(coeff(var, a_max)))
higher_order_a = a_max + b_min;
- if (is_exactly_a<Order_function>(other.coeff(var, b_max)))
+ if (is_exactly_a<Order>(other.coeff(var, b_max)))
higher_order_b = b_max + a_min;
int higher_order_c = std::min(higher_order_a, higher_order_b);
if (cdeg_max >= higher_order_c)
for (int i=a_min; cdeg-i>=b_min; ++i) {
ex a_coeff = coeff(var, i);
ex b_coeff = other.coeff(var, cdeg-i);
- if (!is_exactly_a<Order_function>(a_coeff) && !is_exactly_a<Order_function>(b_coeff))
+ if (!is_exactly_a<Order>(a_coeff) && !is_exactly_a<Order>(b_coeff))
co += a_coeff * b_coeff;
}
if (!co.is_zero())
}
// O(x^n)^(-m) is undefined
- if (seq.size() == 1 && is_exactly_a<Order_function>(seq[0].rest) && p.real().is_negative())
+ if (seq.size() == 1 && is_exactly_a<Order>(seq[0].rest) && p.real().is_negative())
throw pole_error("pseries::power_const(): division by zero",1);
// Compute coefficients of the powered series
ex sum = _ex0;
for (int j=1; j<=i; ++j) {
ex c = coeff(var, j + ldeg);
- if (is_exactly_a<Order_function>(c)) {
+ if (is_exactly_a<Order>(c)) {
co.push_back(Order(_ex1));
break;
} else
for (int i=0; i<numcoeff; ++i) {
if (!co[i].is_zero())
new_seq.push_back(expair(co[i], p * ldeg + i));
- if (is_exactly_a<Order_function>(co[i])) {
+ if (is_exactly_a<Order>(co[i])) {
higher_order = true;
break;
}
fseries = f.series(x == (a.subs(r)), order, options);
for (size_t i=0; i<fseries.nops(); ++i) {
ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
- if (is_exactly_a<Order_function>(currcoeff))
+ if (is_exactly_a<Order>(currcoeff))
break;
ex currexpon = ex_to<pseries>(fseries).exponop(i);
int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
fseries = f.series(x == (b.subs(r)), order, options);
for (size_t i=0; i<fseries.nops(); ++i) {
ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
- if (is_exactly_a<Order_function>(currcoeff))
+ if (is_exactly_a<Order>(currcoeff))
break;
ex currexpon = ex_to<pseries>(fseries).exponop(i);
int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
ex symbol::conjugate() const
{
if (this->domain == domain::complex) {
- return GiNaC::conjugate(*this);
+ return GiNaC::conjugate(*this).hold();
} else {
return *this;
}
delete[] iv;
delete[] iv2;
- return sum / factorial(numeric(num));
+ return sum / factorial::eval_numeric(numeric(num));
}
ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)