X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=f8e4d93b406222046357042188ad12acb42ef9df;hp=af2d8effe25226ce2c7d5d33d4d6ec703ee9925c;hb=8dc09f48182574d792a2ed7c37b66831d9267a6c;hpb=7d10a252470cc6501b2c66bf9d6774c79b093761

diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp
index af2d8eff..f8e4d93b 100644
--- a/ginac/numeric.cpp
+++ b/ginac/numeric.cpp
@@ -7,7 +7,7 @@
  *  of special functions or implement the interface to the bignum package. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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
@@ -29,114 +29,54 @@
 #include <vector>
 #include <stdexcept>
 #include <string>
-
-#if defined(HAVE_SSTREAM)
 #include <sstream>
-#elif defined(HAVE_STRSTREAM)
-#include <strstream>
-#else
-#error Need either sstream or strstream
-#endif
+#include <limits>
 
 #include "numeric.h"
 #include "ex.h"
+#include "operators.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "tostring.h"
 #include "utils.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.
-// Also, we only need a subset of CLN, so we don't include the complete cln.h:
-#ifdef HAVE_CLN_CLN_H
-#include <cln/cl_output.h>
-#include <cln/cl_integer_io.h>
-#include <cln/cl_integer_ring.h>
-#include <cln/cl_rational_io.h>
-#include <cln/cl_rational_ring.h>
-#include <cln/cl_lfloat_class.h>
-#include <cln/cl_lfloat_io.h>
-#include <cln/cl_real_io.h>
-#include <cln/cl_real_ring.h>
-#include <cln/cl_complex_io.h>
-#include <cln/cl_complex_ring.h>
-#include <cln/cl_numtheory.h>
-#else  // def HAVE_CLN_CLN_H
-#include <cl_output.h>
-#include <cl_integer_io.h>
-#include <cl_integer_ring.h>
-#include <cl_rational_io.h>
-#include <cl_rational_ring.h>
-#include <cl_lfloat_class.h>
-#include <cl_lfloat_io.h>
-#include <cl_real_io.h>
-#include <cl_real_ring.h>
-#include <cl_complex_io.h>
-#include <cl_complex_ring.h>
-#include <cl_numtheory.h>
-#endif  // def HAVE_CLN_CLN_H
-
-#ifndef NO_NAMESPACE_GINAC
-namespace GiNaC {
-#endif  // ndef NO_NAMESPACE_GINAC
+// 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>
 
-// linker has no problems finding text symbols for numerator or denominator
-//#define SANE_LINKER
+namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
+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)
 {
-	debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
-	value = new ::cl_N;
-	*value = ::cl_I(0);
-	calchash();
-	setflag(status_flags::evaluated |
-	        status_flags::expanded |
-	        status_flags::hash_calculated);
-}
-
-numeric::~numeric()
-{
-	debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT);
-	destroy(false);
-}
-
-numeric::numeric(const numeric & other)
-{
-	debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT);
-	copy(other);
-}
-
-const numeric & numeric::operator=(const numeric & other)
-{
-	debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT);
-	if (this != &other) {
-		destroy(true);
-		copy(other);
-	}
-	return *this;
-}
-
-// protected
-
-void numeric::copy(const numeric & other)
-{
-	basic::copy(other);
-	value = new ::cl_N(*other.value);
-}
-
-void numeric::destroy(bool call_parent)
-{
-	delete value;
-	if (call_parent) basic::destroy(call_parent);
+	value = cln::cl_I(0);
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
 //////////
@@ -147,82 +87,67 @@ void numeric::destroy(bool call_parent)
 
 numeric::numeric(int i) : basic(TINFO_numeric)
 {
-	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::expanded |
-	        status_flags::hash_calculated);
+	// 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(unsigned int i) : basic(TINFO_numeric)
 {
-	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::expanded |
-	        status_flags::hash_calculated);
+	// 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 < (1U << (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::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::expanded |
-	        status_flags::hash_calculated);
+	value = cln::cl_I(i);
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
 
 numeric::numeric(unsigned long i) : basic(TINFO_numeric)
 {
-	debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
-	value = new ::cl_I(i);
-	calchash();
-	setflag(status_flags::evaluated |
-	        status_flags::expanded |
-	        status_flags::hash_calculated);
+	value = cln::cl_I(i);
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
-/** Ctor for rational numerics a/b.
+
+/** Constructor 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::expanded |
-	        status_flags::hash_calculated);
+	value = cln::cl_I(numer) / cln::cl_I(denom);
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
 
 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::expanded |
-	        status_flags::hash_calculated);
+	value = cln::cl_float(d, cln::default_float_format);
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
 
@@ -230,317 +155,407 @@ numeric::numeric(double d) : basic(TINFO_numeric)
  *  notation like "2+5*I". */
 numeric::numeric(const char *s) : basic(TINFO_numeric)
 {
-	debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
-	value = new ::cl_N(0);
+	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);
-	// make it safe by adding explicit sign
+	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;
-	std::string::size_type delim;
+
+	// 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')
+		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)
+		if (delim!=std::string::npos)
 			ss = ss.substr(delim);
 		// is the term imaginary?
-		if (term.find("I") != std::string::npos) {
+		if (term.find("I")!=std::string::npos) {
 			// erase 'I':
-			term = term.replace(term.find("I"),1,"");
+			term.erase(term.find("I"),1);
 			// erase '*':
-			if (term.find("*") != std::string::npos)
-				term = term.replace(term.find("*"),1,"");
+			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";
+			if (term.size()==1)
+				term += '1';
 			imaginary = true;
 		}
-		const char *cs = term.c_str();
-		// CLN's short types are not useful within the GiNaC framework, hence
-		// we go straight to the construction of a long float.  Simply using
-		// cl_N(s) would require us to use add a CLN exponent mark, otherwise
-		// we would not be save from over-/underflows.
-		if (strchr(cs, '.'))
+		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)
-				*value = *value + ::complex(cl_I(0),::cl_LF(cs));
+				ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_F(term.c_str()));
 			else
-				*value = *value + ::cl_LF(cs);
-		else
+				ctorval = ctorval + cln::cl_F(term.c_str());
+		} else {
+			// this is not a floating point number...
 			if (imaginary)
-				*value = *value + ::complex(cl_I(0),::cl_R(cs));
+				ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_R(term.c_str()));
 			else
-				*value = *value + ::cl_R(cs);
-	} while(delim != std::string::npos);
-	calchash();
-	setflag(status_flags::evaluated |
-	        status_flags::hash_calculated);
+				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 cl_N & z) : basic(TINFO_numeric)
+numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
 {
-	debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
-	value = new ::cl_N(z);
-	calchash();
-	setflag(status_flags::evaluated |
-	        status_flags::expanded |
-	        status_flags::hash_calculated);
+	value = z;
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
-	value = new ::cl_N;
+	cln::cl_N ctorval = 0;
 
 	// Read number as string
 	std::string str;
 	if (n.find_string("number", str)) {
-#ifdef HAVE_SSTREAM
 		std::istringstream s(str);
-#else
-		std::istrstream s(str.c_str(), str.size() + 1);
-#endif
-		::cl_idecoded_float re, im;
+		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;
-				*value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), 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;
-				*value = ::complex(re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent),
-								 im.sign * im.mantissa * ::expt(cl_float(2.0, cl_default_float_format), 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 >> *value;
+				s >> ctorval;
 				break;
 		}
 	}
-	calchash();
-	setflag(status_flags::evaluated |
-	        status_flags::expanded |
-	        status_flags::hash_calculated);
+	value = ctorval;
+	setflag(status_flags::evaluated | status_flags::expanded);
 }
 
-/** Unarchive the object. */
-ex numeric::unarchive(const archive_node &n, const lst &sym_lst)
-{
-	return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
 void numeric::archive(archive_node &n) const
 {
 	inherited::archive(n);
 
 	// Write number as string
-#ifdef HAVE_SSTREAM
 	std::ostringstream s;
-#else
-	char buf[1024];
-	std::ostrstream s(buf, 1024);
-#endif
 	if (this->is_crational())
-		s << *value;
+		s << cln::the<cln::cl_N>(value);
 	else {
 		// Non-rational numbers are written in an integer-decoded format
 		// to preserve the precision
 		if (this->is_real()) {
-			cl_idecoded_float re = integer_decode_float(The(::cl_F)(*value));
+			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 {
-			cl_idecoded_float re = integer_decode_float(The(::cl_F)(::realpart(*value)));
-			cl_idecoded_float im = integer_decode_float(The(::cl_F)(::imagpart(*value)));
+			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;
 		}
 	}
-#ifdef HAVE_SSTREAM
 	n.add_string("number", s.str());
-#else
-	s << ends;
-	std::string str(buf);
-	n.add_string("number", str);
-#endif
 }
 
+DEFAULT_UNARCHIVE(numeric)
+
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
-// public
-
-basic * numeric::duplicate() const
-{
-	debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE);
-	return new numeric(*this);
-}
-
-
 /** 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.
+ *  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(std::ostream & os, const cl_R & num)
-{
-	cl_print_flags ourflags;
-	if (::instanceof(num, ::cl_RA_ring)) {
-		// case 1: integer or rational, nothing special to do:
-		::print_real(os, ourflags, num);
+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 = ::cl_float_format(The(::cl_F)(num));
-		::print_real(os, ourflags, num);
+		ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(x));
+		cln::print_real(c.s, ourflags, x);
 	}
-	return;
 }
 
-/** This method adds to the output so it blends more consistently together
- *  with the other routines and produces something compatible to ginsh input.
- *  
- *  @see print_real_number() */
-void numeric::print(std::ostream & os, unsigned upper_precedence) const
+/** 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 print", LOGLEVEL_PRINT);
-	if (this->is_real()) {
+	// 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);
+}
+
+/** 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)
+{
+	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);
+	}
+}
+
+/** 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(cln::the<cln::cl_N>(value));
+	const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+
+	if (cln::zerop(i)) {
+
 		// case 1, real:  x  or  -x
-		if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
-			os << "(";
-			print_real_number(os, The(::cl_R)(*value));
-			os << ")";
+		if ((precedence() <= level) && (!this->is_nonneg_integer())) {
+			c.s << par_open;
+			print_real_number(c, r);
+			c.s << par_close;
 		} else {
-			print_real_number(os, The(::cl_R)(*value));
+			print_real_number(c, r);
 		}
+
 	} 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 << "(";
-					print_real_number(os, The(::cl_R)(::imagpart(*value)));
-					os << "*I)";
-				}
-			} else {
-				if (::imagpart(*value) == 1) {
-					os << "I";
-				} else {
-					if (::imagpart (*value) == -1) {
-						os << "-I";
-					} else {
-						print_real_number(os, The(::cl_R)(::imagpart(*value)));
-						os << "*I";
-					}
+		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 <= upper_precedence)
-				os << "(";
-			print_real_number(os, The(::cl_R)(::realpart(*value)));
-			if (::imagpart(*value) < 0) {
-				if (::imagpart(*value) == -1) {
-					os << "-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(os, The(::cl_R)(::imagpart(*value)));
-					os << "*I";
+					print_real_number(c, i);
+					c.s << mul_sym << imag_sym;
 				}
 			} else {
-				if (::imagpart(*value) == 1) {
-					os << "+I";
+				if (i == 1) {
+					c.s << "+" << imag_sym;
 				} else {
-					os << "+";
-					print_real_number(os, The(::cl_R)(::imagpart(*value)));
-					os << "*I";
+					c.s << "+";
+					print_real_number(c, i);
+					c.s << mul_sym << imag_sym;
 				}
 			}
-			if (precedence <= upper_precedence)
-				os << ")";
+			if (precedence() <= level)
+				c.s << par_close;
 		}
 	}
 }
 
-
-void numeric::printraw(std::ostream & os) const
+void numeric::do_print(const print_context & c, unsigned level) const
 {
-	// The method printraw doesn't do much, it simply uses CLN's operator<<()
-	// for output, which is ugly but reliable. e.g: 2+2i
-	debugmsg("numeric printraw", LOGLEVEL_PRINT);
-	os << "numeric(" << *value << ")";
+	print_numeric(c, "(", ")", "I", "*", level);
 }
 
-
-void numeric::printtree(std::ostream & os, unsigned indent) const
+void numeric::do_print_latex(const print_latex & c, unsigned level) const
 {
-	debugmsg("numeric printtree", LOGLEVEL_PRINT);
-	os << std::string(indent,' ') << *value
-	   << " (numeric): "
-	   << "hash=" << hashvalue
-	   << " (0x" << std::hex << hashvalue << std::dec << ")"
-	   << ", flags=" << flags << std::endl;
+	print_numeric(c, "{(", ")}", "i", " ", level);
 }
 
-
-void numeric::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+void numeric::do_print_csrc(const print_csrc & c, unsigned level) const
 {
-	debugmsg("numeric print csrc", LOGLEVEL_PRINT);
-	ios::fmtflags oldflags = os.flags();
-	os.setf(ios::scientific);
-	if (this->is_rational() && !this->is_integer()) {
-		if (compare(_num0()) > 0) {
-			os << "(";
-			if (type == csrc_types::ctype_cl_N)
-				os << "cl_F(\"" << numer().evalf() << "\")";
-			else
-				os << numer().to_double();
-		} else {
-			os << "-(";
-			if (type == csrc_types::ctype_cl_N)
-				os << "cl_F(\"" << -numer().evalf() << "\")";
-			else
-				os << -numer().to_double();
-		}
-		os << "/";
-		if (type == csrc_types::ctype_cl_N)
-			os << "cl_F(\"" << denom().evalf() << "\")";
-		else
-			os << denom().to_double();
-		os << ")";
+	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 {
-		if (type == csrc_types::ctype_cl_N)
-			os << "cl_F(\"" << evalf() << "\")";
+
+		// Complex number
+		c.s << "std::complex<";
+		if (is_a<print_csrc_double>(c))
+			c.s << "double>(";
 		else
-			os << to_double();
+			c.s << "float>(";
+
+		print_real_csrc(c, cln::realpart(cln::the<cln::cl_N>(value)));
+		c.s << ",";
+		print_real_csrc(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+		c.s << ")";
 	}
-	os.flags(oldflags);
+
+	c.s.flags(oldflags);
+	c.s.precision(oldprec);
 }
 
+void numeric::do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const
+{
+	if (this->is_real()) {
+
+		// 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(cln::the<cln::cl_N>(value)));
+		c.s << ",";
+		print_real_cl_N(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+		c.s << ")";
+	}
+}
+
+void numeric::do_print_tree(const print_tree & c, unsigned level) const
+{
+	c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
+	    << " (" << class_name() << ")" << " @" << this
+	    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+	    << std::endl;
+}
+
+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
 {
@@ -587,17 +602,32 @@ bool numeric::info(unsigned inf) const
 	return false;
 }
 
+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) const
+bool numeric::has(const ex &other) const
 {
-	if (!is_exactly_of_type(*other.bp, numeric))
+	if (!is_exactly_a<numeric>(other))
 		return false;
-	const numeric & o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
+	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
@@ -633,48 +663,39 @@ ex numeric::eval(int level) const
 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
+	return numeric(cln::cl_float(1.0, cln::default_float_format) *
+	               (cln::the<cln::cl_N>(value)));
 }
 
 // protected
 
-/** Implementation of ex::diff() for a numeric. It always returns 0.
- *
- *  @see ex::diff */
-ex numeric::derivative(const symbol & s) const
+int numeric::compare_same_type(const basic &other) const
 {
-	return _ex0();
-}
-
-
-int numeric::compare_same_type(const basic & other) const
-{
-	GINAC_ASSERT(is_exactly_of_type(other, numeric));
-	const numeric & o = static_cast<numeric &>(const_cast<basic &>(other));
-
-	if (*value == *o.value) {
-		return 0;
-	}
-
-	return compare(o);    
+	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(const basic & other) const
+bool numeric::is_equal_same_type(const basic &other) const
 {
-	GINAC_ASSERT(is_exactly_of_type(other,numeric));
-	const numeric *o = static_cast<const numeric *>(&other);
+	GINAC_ASSERT(is_exactly_a<numeric>(other));
+	const numeric &o = static_cast<const numeric &>(other);
 	
-	return this->is_equal(*o);
+	return this->is_equal(o);
 }
 
 
-unsigned numeric::calchash(void) const
+unsigned numeric::calchash() const
 {
-	// Use CLN's hashcode.  Warning: It 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.
-	return (hashvalue = cl_equal_hashcode(*value) | 0x80000000U);
+	// 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(cln::the<cln::cl_N>(value)));
+	return hashvalue;
 }
 
 
@@ -691,616 +712,649 @@ unsigned numeric::calchash(void) const
 // public
 
 /** Numerical addition method.  Adds argument to *this and returns result as
- *  a new numeric object. */
-numeric numeric::add(const numeric & other) const
+ *  a numeric object. */
+const numeric numeric::add(const numeric &other) const
 {
-	return numeric((*value)+(*other.value));
+	return numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value));
 }
 
+
 /** Numerical subtraction method.  Subtracts argument from *this and returns
- *  result as a new numeric object. */
-numeric numeric::sub(const numeric & other) const
+ *  result as a numeric object. */
+const numeric numeric::sub(const numeric &other) const
 {
-	return numeric((*value)-(*other.value));
+	return numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value));
 }
 
+
 /** Numerical multiplication method.  Multiplies *this and argument and returns
- *  result as a new numeric object. */
-numeric numeric::mul(const numeric & other) const
+ *  result as a numeric object. */
+const numeric numeric::mul(const numeric &other) const
 {
-	static const numeric * _num1p=&_num1();
-	if (this==_num1p) {
-		return other;
-	} else if (&other==_num1p) {
-		return *this;
-	}
-	return numeric((*value)*(*other.value));
+	return numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(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(const numeric & other) const
+const numeric numeric::div(const numeric &other) const
 {
-	if (::zerop(*other.value))
+	if (cln::zerop(cln::the<cln::cl_N>(other.value)))
 		throw std::overflow_error("numeric::div(): division by zero");
-	return numeric((*value)/(*other.value));
+	return numeric(cln::the<cln::cl_N>(value)/cln::the<cln::cl_N>(other.value));
 }
 
-numeric numeric::power(const numeric & 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 * _num1p = &_num1();
-	if (&other==_num1p)
+	// Shortcut for efficiency and numeric stability (as in 1.0 exponent):
+	// trap the neutral exponent.
+	if (&other==_num1_p || cln::equal(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
 		return *this;
-	if (::zerop(*value)) {
-		if (::zerop(*other.value))
+	
+	if (cln::zerop(cln::the<cln::cl_N>(value))) {
+		if (cln::zerop(cln::the<cln::cl_N>(other.value)))
 			throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
-		else if (::zerop(::realpart(*other.value)))
+		else if (cln::zerop(cln::realpart(cln::the<cln::cl_N>(other.value))))
 			throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
-		else if (::minusp(::realpart(*other.value)))
+		else if (cln::minusp(cln::realpart(cln::the<cln::cl_N>(other.value))))
 			throw std::overflow_error("numeric::eval(): division by zero");
 		else
-			return _num0();
+			return _num0;
 	}
-	return numeric(::expt(*value,*other.value));
+	return numeric(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value)));
 }
 
-/** Inverse of a number. */
-numeric numeric::inverse(void) const
-{
-	if (::zerop(*value))
-		throw std::overflow_error("numeric::inverse(): division by zero");
-	return numeric(::recip(*value));  // -> CLN
-}
 
-const numeric & numeric::add_dyn(const numeric & other) 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 static_cast<const numeric &>((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==_num0_p)
+		return other;
+	else if (&other==_num0_p)
+		return *this;
+	
+	return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value)))->
+	                                    setflag(status_flags::dynallocated));
 }
 
-const numeric & numeric::sub_dyn(const numeric & other) const
-{
-	return static_cast<const numeric &>((new numeric((*value)-(*other.value)))->
-										setflag(status_flags::dynallocated));
+
+/** 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
+{
+	// 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(cln::the<cln::cl_N>(other.value)))
+		return *this;
+	
+	return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value)))->
+	                                    setflag(status_flags::dynallocated));
 }
 
-const numeric & numeric::mul_dyn(const numeric & other) const
-{
-	static const numeric * _num1p=&_num1();
-	if (this==_num1p) {
+
+/** 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
+{
+	// 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==_num1p) {
+	else if (&other==_num1_p)
 		return *this;
-	}
-	return static_cast<const numeric &>((new numeric((*value)*(*other.value)))->
-										setflag(status_flags::dynallocated));
+	
+	return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value)))->
+	                                    setflag(status_flags::dynallocated));
 }
 
-const numeric & numeric::div_dyn(const numeric & 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
 {
-	if (::zerop(*other.value))
+	// 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));
+	return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)/cln::the<cln::cl_N>(other.value)))->
+	                                    setflag(status_flags::dynallocated));
 }
 
-const numeric & numeric::power_dyn(const numeric & 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
 {
-	static const numeric * _num1p=&_num1();
-	if (&other==_num1p)
+	// 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(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
 		return *this;
-	if (::zerop(*value)) {
-		if (::zerop(*other.value))
+	
+	if (cln::zerop(cln::the<cln::cl_N>(value))) {
+		if (cln::zerop(cln::the<cln::cl_N>(other.value)))
 			throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
-		else if (::zerop(::realpart(*other.value)))
+		else if (cln::zerop(cln::realpart(cln::the<cln::cl_N>(other.value))))
 			throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
-		else if (::minusp(::realpart(*other.value)))
+		else if (cln::minusp(cln::realpart(cln::the<cln::cl_N>(other.value))))
 			throw std::overflow_error("numeric::eval(): division by zero");
 		else
-			return _num0();
+			return _num0;
 	}
-	return static_cast<const numeric &>((new numeric(::expt(*value,*other.value)))->
-										setflag(status_flags::dynallocated));
+	return static_cast<const numeric &>((new numeric(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value))))->
+	                                     setflag(status_flags::dynallocated));
 }
 
-const numeric & numeric::operator=(int i)
+
+const numeric &numeric::operator=(int i)
 {
 	return operator=(numeric(i));
 }
 
-const numeric & numeric::operator=(unsigned int i)
+
+const numeric &numeric::operator=(unsigned int i)
 {
 	return operator=(numeric(i));
 }
 
-const numeric & numeric::operator=(long i)
+
+const numeric &numeric::operator=(long i)
 {
 	return operator=(numeric(i));
 }
 
-const numeric & numeric::operator=(unsigned long i)
+
+const numeric &numeric::operator=(unsigned long i)
 {
 	return operator=(numeric(i));
 }
 
-const numeric & numeric::operator=(double d)
+
+const numeric &numeric::operator=(double d)
 {
 	return operator=(numeric(d));
 }
 
-const numeric & numeric::operator=(const char * s)
+
+const numeric &numeric::operator=(const char * s)
 {
 	return operator=(numeric(s));
 }
 
+
+/** Inverse of a number. */
+const numeric numeric::inverse() const
+{
+	if (cln::zerop(cln::the<cln::cl_N>(value)))
+		throw std::overflow_error("numeric::inverse(): division by zero");
+	return numeric(cln::recip(cln::the<cln::cl_N>(value)));
+}
+
+
 /** 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(const numeric & other) */
-int numeric::csgn(void) const
+ *  @see numeric::compare(const numeric &other) */
+int numeric::csgn() const
 {
-	if (this->is_zero())
+	if (cln::zerop(cln::the<cln::cl_N>(value)))
 		return 0;
-	if (!::zerop(::realpart(*value))) {
-		if (::plusp(::realpart(*value)))
+	cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
+	if (!cln::zerop(r)) {
+		if (cln::plusp(r))
 			return 1;
 		else
 			return -1;
 	} else {
-		if (::plusp(::imagpart(*value)))
+		if (cln::plusp(cln::imagpart(cln::the<cln::cl_N>(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(const numeric & other) const
+ *  @see numeric::csgn() */
+int numeric::compare(const numeric &other) const
 {
 	// Comparing two real numbers?
-	if (this->is_real() && other.is_real())
-		// Yes, just compare them
-		return ::cl_compare(The(::cl_R)(*value), The(::cl_R)(*other.value));    
+	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 compare real parts
-		cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value));
+		// No, first cln::compare real parts...
+		cl_signean real_cmp = cln::compare(cln::realpart(cln::the<cln::cl_N>(value)), cln::realpart(cln::the<cln::cl_N>(other.value)));
 		if (real_cmp)
 			return real_cmp;
-
-		return ::cl_compare(::imagpart(*value), ::imagpart(*other.value));
+		// ...and then the imaginary parts.
+		return cln::compare(cln::imagpart(cln::the<cln::cl_N>(value)), cln::imagpart(cln::the<cln::cl_N>(other.value)));
 	}
 }
 
-bool numeric::is_equal(const numeric & other) const
+
+bool numeric::is_equal(const numeric &other) const
 {
-	return (*value == *other.value);
+	return cln::equal(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(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(cln::the<cln::cl_N>(value));
 }
 
+
 /** True if object is not complex and greater than zero. */
-bool numeric::is_positive(void) const
+bool numeric::is_positive() const
 {
-	if (this->is_real())
-		return ::plusp(The(::cl_R)(*value));  // -> CLN
+	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 (this->is_real())
-		return ::minusp(The(::cl_R)(*value));  // -> CLN
+	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 ::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 (this->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 (this->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 (this->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 (this->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 (this->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
 {
-	return ::instanceof(*value, ::cl_RA_ring);  // -> CLN
+	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 ::instanceof(*value, ::cl_R_ring);  // -> CLN
+	return cln::instanceof(value, cln::cl_R_ring);
 }
 
-bool numeric::operator==(const numeric & other) const
+
+bool numeric::operator==(const numeric &other) const
 {
-	return (*value == *other.value);  // -> CLN
+	return cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
 }
 
-bool numeric::operator!=(const numeric & other) const
+
+bool numeric::operator!=(const numeric &other) const
 {
-	return (*value != *other.value);  // -> CLN
+	return !cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(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(void) const
+bool numeric::is_cinteger() const
 {
-	if (::instanceof(*value, ::cl_I_ring))
+	if (cln::instanceof(value, cln::cl_I_ring))
 		return true;
 	else if (!this->is_real()) {  // complex case, handle n+m*I
-		if (::instanceof(::realpart(*value), ::cl_I_ring) &&
-		    ::instanceof(::imagpart(*value), ::cl_I_ring))
+		if (cln::instanceof(cln::realpart(cln::the<cln::cl_N>(value)), cln::cl_I_ring) &&
+		    cln::instanceof(cln::imagpart(cln::the<cln::cl_N>(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(void) const
+bool numeric::is_crational() const
 {
-	if (::instanceof(*value, ::cl_RA_ring))
+	if (cln::instanceof(value, cln::cl_RA_ring))
 		return true;
 	else if (!this->is_real()) {  // complex case, handle Q(i):
-		if (::instanceof(::realpart(*value), ::cl_RA_ring) &&
-		    ::instanceof(::imagpart(*value), ::cl_RA_ring))
+		if (cln::instanceof(cln::realpart(cln::the<cln::cl_N>(value)), cln::cl_RA_ring) &&
+		    cln::instanceof(cln::imagpart(cln::the<cln::cl_N>(value)), cln::cl_RA_ring))
 			return true;
 	}
 	return false;
 }
 
+
 /** Numerical comparison: less.
  *
  *  @exception invalid_argument (complex inequality) */ 
-bool numeric::operator<(const numeric & other) const
+bool numeric::operator<(const numeric &other) const
 {
 	if (this->is_real() && other.is_real())
-		return (The(::cl_R)(*value) < The(::cl_R)(*other.value));  // -> CLN
+		return (cln::the<cln::cl_R>(value) < cln::the<cln::cl_R>(other.value));
 	throw std::invalid_argument("numeric::operator<(): complex inequality");
-	return false;  // make compiler shut up
 }
 
+
 /** Numerical comparison: less or equal.
  *
  *  @exception invalid_argument (complex inequality) */ 
-bool numeric::operator<=(const numeric & other) const
+bool numeric::operator<=(const numeric &other) const
 {
 	if (this->is_real() && other.is_real())
-		return (The(::cl_R)(*value) <= The(::cl_R)(*other.value));  // -> CLN
+		return (cln::the<cln::cl_R>(value) <= cln::the<cln::cl_R>(other.value));
 	throw std::invalid_argument("numeric::operator<=(): complex inequality");
-	return false;  // make compiler shut up
 }
 
+
 /** Numerical comparison: greater.
  *
  *  @exception invalid_argument (complex inequality) */ 
-bool numeric::operator>(const numeric & other) const
+bool numeric::operator>(const numeric &other) const
 {
 	if (this->is_real() && other.is_real())
-		return (The(::cl_R)(*value) > The(::cl_R)(*other.value));  // -> CLN
+		return (cln::the<cln::cl_R>(value) > cln::the<cln::cl_R>(other.value));
 	throw std::invalid_argument("numeric::operator>(): complex inequality");
-	return false;  // make compiler shut up
 }
 
+
 /** Numerical comparison: greater or equal.
  *
  *  @exception invalid_argument (complex inequality) */  
-bool numeric::operator>=(const numeric & other) const
+bool numeric::operator>=(const numeric &other) const
 {
 	if (this->is_real() && other.is_real())
-		return (The(::cl_R)(*value) >= The(::cl_R)(*other.value));  // -> CLN
+		return (cln::the<cln::cl_R>(value) >= cln::the<cln::cl_R>(other.value));
 	throw std::invalid_argument("numeric::operator>=(): complex inequality");
-	return false;  // make compiler shut up
 }
 
+
 /** 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(void) const
+int numeric::to_int() const
 {
 	GINAC_ASSERT(this->is_integer());
-	return ::cl_I_to_int(The(::cl_I)(*value));  // -> CLN
+	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(void) const
+long numeric::to_long() const
 {
 	GINAC_ASSERT(this->is_integer());
-	return ::cl_I_to_long(The(::cl_I)(*value));  // -> CLN
+	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(this->is_real());
-	return ::cl_double_approx(::realpart(*value));  // -> CLN
+	return cln::double_approx(cln::realpart(cln::the<cln::cl_N>(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 cln::cl_N(cln::the<cln::cl_N>(value));
 }
 
+
 /** Real part of a number. */
-const numeric numeric::real(void) const
+const numeric numeric::real() const
 {
-	return numeric(::realpart(*value));  // -> CLN
+	return numeric(cln::realpart(cln::the<cln::cl_N>(value)));
 }
 
+
 /** Imaginary part of a number. */
-const numeric numeric::imag(void) const
+const numeric numeric::imag() const
 {
-	return numeric(::imagpart(*value));  // -> CLN
+	return numeric(cln::imagpart(cln::the<cln::cl_N>(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. */
-const numeric numeric::numer(void) const
+const numeric numeric::numer() const
 {
-	if (this->is_integer()) {
-		return numeric(*this);
-	}
-#ifdef SANE_LINKER
-	else if (::instanceof(*value, ::cl_RA_ring)) {
-		return numeric(::numerator(The(::cl_RA)(*value)));
-	}
-	else if (!this->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);
-	}
+	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):
-		cl_R r = ::realpart(*value);
-		cl_R i = ::imagpart(*value);
-		if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
+		const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(cln::the<cln::cl_N>(value)));
+		const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(cln::the<cln::cl_N>(value)));
+		if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::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))));
+		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)))));
 		}
 	}
-#endif // def SANE_LINKER
 	// 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. */
-const numeric numeric::denom(void) const
+const numeric numeric::denom() const
 {
-	if (this->is_integer()) {
-		return _num1();
-	}
-#ifdef SANE_LINKER
-	if (instanceof(*value, ::cl_RA_ring)) {
-		return numeric(::denominator(The(::cl_RA)(*value)));
-	}
-	if (!this->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 _num1();
-		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 (cln::instanceof(value, cln::cl_I_ring))
+		return _num1;  // 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):
-		cl_R r = ::realpart(*value);
-		cl_R i = ::imagpart(*value);
-		if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
-			return _num1();
-		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));
+		const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(cln::the<cln::cl_N>(value)));
+		const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(cln::the<cln::cl_N>(value)));
+		if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
+			return _num1;
+		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)));
 	}
-#endif // def SANE_LINKER
 	// at least one float encountered
-	return _num1();
+	return _num1;
 }
 
+
 /** 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 (this->is_integer())
-		return ::integer_length(The(::cl_I)(*value));  // -> CLN
+	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;
-const type_info & 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)));
+ *  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)));
 
 
 /** Exponential function.
  *
  *  @return  arbitrary precision numerical exp(x). */
-const numeric exp(const numeric & x)
+const numeric exp(const numeric &x)
 {
-	return ::exp(*x.value);  // -> CLN
+	return cln::exp(x.to_cl_N());
 }
 
 
 /** Natural logarithm.
  *
- *  @param z complex number
+ *  @param x complex number
  *  @return  arbitrary precision numerical log(x).
  *  @exception pole_error("log(): logarithmic pole",0) */
-const numeric log(const numeric & z)
+const numeric log(const numeric &x)
 {
-	if (z.is_zero())
+	if (x.is_zero())
 		throw pole_error("log(): logarithmic pole",0);
-	return ::log(*z.value);  // -> CLN
+	return cln::log(x.to_cl_N());
 }
 
 
 /** Numeric sine (trigonometric function).
  *
  *  @return  arbitrary precision numerical sin(x). */
-const numeric sin(const numeric & x)
+const numeric sin(const numeric &x)
 {
-	return ::sin(*x.value);  // -> CLN
+	return cln::sin(x.to_cl_N());
 }
 
 
 /** Numeric cosine (trigonometric function).
  *
  *  @return  arbitrary precision numerical cos(x). */
-const numeric cos(const numeric & x)
+const numeric cos(const numeric &x)
 {
-	return ::cos(*x.value);  // -> CLN
+	return cln::cos(x.to_cl_N());
 }
 
 
 /** Numeric tangent (trigonometric function).
  *
  *  @return  arbitrary precision numerical tan(x). */
-const numeric tan(const numeric & x)
+const numeric tan(const numeric &x)
 {
-	return ::tan(*x.value);  // -> CLN
+	return cln::tan(x.to_cl_N());
 }
 	
 
 /** Numeric inverse sine (trigonometric function).
  *
  *  @return  arbitrary precision numerical asin(x). */
-const numeric asin(const numeric & x)
+const numeric asin(const numeric &x)
 {
-	return ::asin(*x.value);  // -> CLN
+	return cln::asin(x.to_cl_N());
 }
 
 
 /** Numeric inverse cosine (trigonometric function).
  *
  *  @return  arbitrary precision numerical acos(x). */
-const numeric acos(const numeric & x)
+const numeric acos(const numeric &x)
 {
-	return ::acos(*x.value);  // -> CLN
+	return cln::acos(x.to_cl_N());
 }
 	
 
 /** Arcustangent.
  *
- *  @param z complex number
- *  @return atan(z)
+ *  @param x complex number
+ *  @return atan(x)
  *  @exception pole_error("atan(): logarithmic pole",0) */
-const numeric atan(const numeric & x)
+const numeric atan(const numeric &x)
 {
 	if (!x.is_real() &&
 	    x.real().is_zero() &&
-	    abs(x.imag()).is_equal(_num1()))
+	    abs(x.imag()).is_equal(_num1))
 		throw pole_error("atan(): logarithmic pole",0);
-	return ::atan(*x.value);  // -> CLN
+	return cln::atan(x.to_cl_N());
 }
 
 
@@ -1309,10 +1363,11 @@ const numeric atan(const numeric & x)
  *  @param x real number
  *  @param y real number
  *  @return atan(y/x) */
-const numeric atan(const numeric & y, const numeric & x)
+const numeric atan(const numeric &y, const numeric &x)
 {
 	if (x.is_real() && y.is_real())
-		return ::atan(::realpart(*x.value), ::realpart(*y.value));  // -> CLN
+		return 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");        
 }
@@ -1321,77 +1376,77 @@ const numeric atan(const numeric & y, const numeric & x)
 /** Numeric hyperbolic sine (trigonometric function).
  *
  *  @return  arbitrary precision numerical sinh(x). */
-const numeric sinh(const numeric & x)
+const numeric sinh(const numeric &x)
 {
-	return ::sinh(*x.value);  // -> CLN
+	return cln::sinh(x.to_cl_N());
 }
 
 
 /** Numeric hyperbolic cosine (trigonometric function).
  *
  *  @return  arbitrary precision numerical cosh(x). */
-const numeric cosh(const numeric & x)
+const numeric cosh(const numeric &x)
 {
-	return ::cosh(*x.value);  // -> CLN
+	return cln::cosh(x.to_cl_N());
 }
 
 
 /** Numeric hyperbolic tangent (trigonometric function).
  *
  *  @return  arbitrary precision numerical tanh(x). */
-const numeric tanh(const numeric & x)
+const numeric tanh(const numeric &x)
 {
-	return ::tanh(*x.value);  // -> CLN
+	return cln::tanh(x.to_cl_N());
 }
 	
 
 /** Numeric inverse hyperbolic sine (trigonometric function).
  *
  *  @return  arbitrary precision numerical asinh(x). */
-const numeric asinh(const numeric & x)
+const numeric asinh(const numeric &x)
 {
-	return ::asinh(*x.value);  // -> CLN
+	return cln::asinh(x.to_cl_N());
 }
 
 
 /** Numeric inverse hyperbolic cosine (trigonometric function).
  *
  *  @return  arbitrary precision numerical acosh(x). */
-const numeric acosh(const numeric & x)
+const numeric acosh(const numeric &x)
 {
-	return ::acosh(*x.value);  // -> CLN
+	return cln::acosh(x.to_cl_N());
 }
 
 
 /** Numeric inverse hyperbolic tangent (trigonometric function).
  *
  *  @return  arbitrary precision numerical atanh(x). */
-const numeric atanh(const numeric & x)
+const numeric atanh(const numeric &x)
 {
-	return ::atanh(*x.value);  // -> CLN
+	return cln::atanh(x.to_cl_N());
 }
 
 
-/*static ::cl_N Li2_series(const ::cl_N & x,
-                         const ::cl_float_format_t & prec)
+/*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!
-	::cl_N c1 = -::log(1-x);
-	::cl_N c2 = c1;
+	cln::cl_N c1 = -cln::log(1-x);
+	cln::cl_N c2 = c1;
 	// hard-wire the first two Bernoulli numbers
-	::cl_N acc = c1 - ::square(c1)/4;
-	::cl_N aug;
-	::cl_F pisq = ::square(::cl_pi(prec));  // pi^2
-	::cl_F piac = ::cl_float(1, prec);  // accumulator: pi^(2*i)
+	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 = ::square(c1);
+	c1 = cln::square(c1);
 	do {
 		c2 = c1 * c2;
 		piac = piac * pisq;
-		aug = c2 * (*(bernoulli(numeric(2*i)).clnptr())) / ::factorial(2*i+1);
-		// aug = c2 * ::cl_I(i%2 ? 1 : -1) / ::cl_I(2*i+1) * ::cl_zeta(2*i, prec) / piac / (::cl_I(1)<<(2*i-1));
+		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);
@@ -1400,13 +1455,13 @@ const numeric atanh(const numeric & x)
 
 /** Numeric evaluation of Dilogarithm within circle of convergence (unit
  *  circle) using a power series. */
-static ::cl_N Li2_series(const ::cl_N & x,
-                         const ::cl_float_format_t & prec)
+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
-	::cl_N aug, acc;
-	::cl_N num = ::complex(::cl_float(1, prec), 0);
-	::cl_I den = 0;
+	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;
@@ -1419,23 +1474,23 @@ static ::cl_N Li2_series(const ::cl_N & x,
 }
 
 /** Folds Li2's argument inside a small rectangle to enhance convergence. */
-static ::cl_N Li2_projection(const ::cl_N & x,
-                             const ::cl_float_format_t & prec)
+static cln::cl_N Li2_projection(const cln::cl_N &x,
+                                const cln::float_format_t &prec)
 {
-	const ::cl_R re = ::realpart(x);
-	const ::cl_R im = ::imagpart(x);
-	if (re > ::cl_F(".5"))
+	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(::cl_zeta(2)
+		return(cln::zeta(2)
 		       - Li2_series(1-x, prec)
-		       - ::log(x)*::log(1-x));
-	if ((re <= 0 && ::abs(im) > ::cl_F(".75")) || (re < ::cl_F("-.5")))
+		       - 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(- ::square(::log(1-x))/2
+		return(- cln::square(cln::log(1-x))/2
 		       - Li2_series(x/(x-1), prec));
-	if (re > 0 && ::abs(im) > ::cl_LF(".75"))
+	if (re > 0 && cln::abs(im) > cln::cl_LF(".75"))
 		// Li2(x^2)/2 - Li2(-x)
-		return(Li2_projection(::square(x), prec)/2
+		return(Li2_projection(cln::square(x), prec)/2
 		       - Li2_projection(-x, prec));
 	return Li2_series(x, prec);
 }
@@ -1445,36 +1500,37 @@ static ::cl_N Li2_projection(const ::cl_N & x,
  *  continuous with quadrant IV.
  *
  *  @return  arbitrary precision numerical Li2(x). */
-const numeric Li2(const numeric & x)
+const numeric Li2(const numeric &x)
 {
-	if (::zerop(*x.value))
-		return x;
+	if (x.is_zero())
+		return _num0;
 	
 	// what is the desired float format?
 	// first guess: default format
-	::cl_float_format_t prec = ::cl_default_float_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 (!::instanceof(::realpart(*x.value),cl_RA_ring))
-		prec = ::cl_float_format(The(::cl_F)(::realpart(*x.value)));
-	else if (!::instanceof(::imagpart(*x.value),cl_RA_ring))
-		prec = ::cl_float_format(The(::cl_F)(::imagpart(*x.value)));
+	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 (*x.value==1)  // may cause trouble with log(1-x)
-		return ::cl_zeta(2, prec);
+	if (cln::the<cln::cl_N>(value)==1)  // may cause trouble with log(1-x)
+		return cln::zeta(2, prec);
 	
-	if (::abs(*x.value) > 1)
+	if (cln::abs(value) > 1)
 		// -log(-x)^2 / 2 - zeta(2) - Li2(1/x)
-		return(- ::square(::log(-*x.value))/2
-		       - ::cl_zeta(2, prec)
-		       - Li2_projection(::recip(*x.value), prec));
+		return(- cln::square(cln::log(-value))/2
+		       - cln::zeta(2, prec)
+		       - Li2_projection(cln::recip(value), prec));
 	else
-		return Li2_projection(*x.value, prec);
+		return Li2_projection(x.to_cl_N(), prec);
 }
 
 
 /** Numeric evaluation of Riemann's Zeta function.  Currently works only for
  *  integer arguments. */
-const numeric zeta(const numeric & x)
+const numeric zeta(const numeric &x)
 {
 	// A dirty hack to allow for things like zeta(3.0), since CLN currently
 	// only knows about integer arguments and zeta(3).evalf() automatically
@@ -1482,54 +1538,39 @@ const numeric zeta(const numeric & x)
 	// 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()) {
-		int aux = (int)(::cl_double_approx(::realpart(*x.value)));
-		if (::zerop(*x.value-aux))
-			return ::cl_zeta(aux);  // -> CLN
+		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);
 	}
-	std::clog << "zeta(" << x
-			  << "): Does anybody know good way to calculate this numerically?"
-			  << std::endl;
-	return numeric(0);
+	throw dunno();
 }
 
 
 /** The Gamma function.
  *  This is only a stub! */
-const numeric lgamma(const numeric & x)
+const numeric lgamma(const numeric &x)
 {
-	std::clog << "lgamma(" << x
-	          << "): Does anybody know good way to calculate this numerically?"
-	          << std::endl;
-	return numeric(0);
+	throw dunno();
 }
-const numeric tgamma(const numeric & x)
+const numeric tgamma(const numeric &x)
 {
-	std::clog << "tgamma(" << x
-	          << "): Does anybody know good way to calculate this numerically?"
-	          << std::endl;
-	return numeric(0);
+	throw dunno();
 }
 
 
 /** The psi function (aka polygamma function).
  *  This is only a stub! */
-const numeric psi(const numeric & x)
+const numeric psi(const numeric &x)
 {
-	std::clog << "psi(" << x
-	          << "): Does anybody know good way to calculate this numerically?"
-	          << std::endl;
-	return numeric(0);
+	throw dunno();
 }
 
 
 /** The psi functions (aka polygamma functions).
  *  This is only a stub! */
-const numeric psi(const numeric & n, const numeric & x)
+const numeric psi(const numeric &n, const numeric &x)
 {
-	std::clog << "psi(" << n << "," << x
-	          << "): Does anybody know good way to calculate this numerically?"
-	          << std::endl;
-	return numeric(0);
+	throw dunno();
 }
 
 
@@ -1537,11 +1578,11 @@ const numeric psi(const numeric & n, const numeric & x)
  *
  *  @param n  integer argument >= 0
  *  @exception range_error (argument must be integer >= 0) */
-const numeric factorial(const numeric & n)
+const numeric factorial(const numeric &n)
 {
 	if (!n.is_nonneg_integer())
 		throw std::range_error("numeric::factorial(): argument must be integer >= 0");
-	return numeric(::factorial(n.to_int()));  // -> CLN
+	return numeric(cln::factorial(n.to_int()));
 }
 
 
@@ -1551,15 +1592,15 @@ const numeric factorial(const numeric & n)
  *  @param n  integer argument >= -1
  *  @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1
  *  @exception range_error (argument must be integer >= -1) */
-const numeric doublefactorial(const numeric & n)
+const numeric doublefactorial(const numeric &n)
 {
-	if (n == numeric(-1)) {
-		return _num1();
-	}
-	if (!n.is_nonneg_integer()) {
+	if (n.is_equal(_num_1))
+		return _num1;
+	
+	if (!n.is_nonneg_integer())
 		throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
-	}
-	return numeric(::doublefactorial(n.to_int()));  // -> CLN
+	
+	return numeric(cln::doublefactorial(n.to_int()));
 }
 
 
@@ -1567,16 +1608,16 @@ const numeric doublefactorial(const numeric & n)
  *  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. */
-const numeric binomial(const numeric & n, const numeric & k)
+const numeric binomial(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())!=-1)
-				return numeric(::binomial(n.to_int(),k.to_int()));  // -> CLN
+			if (k.compare(n)!=1 && k.compare(_num0)!=-1)
+				return numeric(cln::binomial(n.to_int(),k.to_int()));
 			else
-				return _num0();
+				return _num0;
 		} else {
-			return _num_1().power(k)*binomial(k-n-_num1(),k);
+			return _num_1.power(k)*binomial(k-n-_num1,k);
 		}
 	}
 	
@@ -1590,11 +1631,11 @@ const numeric binomial(const numeric & n, const numeric & k)
  *
  *  @return the nth Bernoulli number (a rational number).
  *  @exception range_error (argument must be integer >= 0) */
-const numeric bernoulli(const numeric & nn)
+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
@@ -1618,46 +1659,61 @@ const numeric bernoulli(const numeric & nn)
 	// 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 code below is adapted from Pari's function bernvec().
+	// 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 twice as fast as our
-	// implementation below, but it requires storing one such polynomial in
+	// 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 (nn.is_equal(_num1()))
-		return _num_1_2();
-	if (nn.is_odd())
-		return _num0();
-	
+	if (n & 1)
+		return (n==1) ? _num_1_2 : _num0;
+	if (!n)
+		 return _num1;
+
 	// store nonvanishing Bernoulli numbers here
-	static std::vector< ::cl_RA > results;
-	static int highest_result = 0;
-	// algorithm not applicable to B(0), so just store it
-	if (results.size()==0)
-		results.push_back(::cl_RA(1));
-	
-	int n = nn.to_long();
-	for (int i=highest_result; i<n/2; ++i) {
-		::cl_RA B = 0;
-		long n = 8;
-		long m = 5;
-		long d1 = i;
-		long d2 = 2*i-1;
-		for (int j=i; j>0; --j) {
-			B = ::cl_I(n*m) * (B+results[j]) / (d1*d2);
-			n += 4;
-			m += 2;
-			d1 -= 1;
-			d2 -= 2;
-		}
-		B = (1 - ((B+1)/(2*i+3))) / (::cl_I(1)<<(2*i+2));
-		results.push_back(B);
-		++highest_result;
+	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;
 	}
-	return results[n/2];
+	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(1-p)/2;
+		const unsigned p3 = p+3;
+		const unsigned pm = p-2;
+		unsigned i, k, p_2;
+		// test if intermediate unsigned int can be represented by immediate
+		// objects by CLN (i.e. < 2^29 for 32 Bit machines, see <cln/object.h>)
+		if (p < (1UL<<cl_value_len/2)) {
+			for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+				c = cln::exquo(c * ((p3-i) * p_2), (i-1)*k);
+				b = b + c*results[k-1];
+			}
+		} else {
+			for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+				c = cln::exquo((c * (p3-i)) * p_2, cln::cl_I(i-1)*k);
+				b = b + c*results[k-1];
+			}
+ 		}
+		results.push_back(-b/(p+1));
+	}
+	next_r = n+2;
+	return results[n/2-1];
 }
 
 
@@ -1667,16 +1723,12 @@ const numeric bernoulli(const numeric & nn)
  *  @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)
+const numeric fibonacci(const numeric &n)
 {
 	if (!n.is_integer())
 		throw std::range_error("numeric::fibonacci(): argument must be integer");
 	// Method:
 	//
-	// This is based on an implementation that can be found in CLN's example
-	// directory.  There, it is done recursively, which may be more elegant
-	// than our non-recursive implementation that has to resort to some bit-
-	// fiddling.  This is, however, a matter of taste.
 	// The following addition formula holds:
 	//
 	//      F(n+m)   = F(m-1)*F(n) + F(m)*F(n+1)  for m >= 1, n >= 0.
@@ -1692,26 +1744,26 @@ const numeric fibonacci(const numeric & n)
 	// hence
 	//      F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
 	if (n.is_zero())
-		return _num0();
+		return _num0;
 	if (n.is_negative())
 		if (n.is_even())
 			return -fibonacci(-n);
 		else
 			return fibonacci(-n);
 	
-	::cl_I u(0);
-	::cl_I v(1);
-	::cl_I m = The(::cl_I)(*n.value) >> 1L;  // floor(n/2);
-	for (uintL bit=::integer_length(m); bit>0; --bit) {
+	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.
-		::cl_I u2 = ::square(u);
-		::cl_I v2 = ::square(v);
-		if (::logbitp(bit-1, m)) {
-			v = ::square(u + v) - u2;
+		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 - ::square(v - u);
+			u = v2 - cln::square(v - u);
 			v = u2 + v2;
 		}
 	}
@@ -1720,14 +1772,14 @@ const numeric fibonacci(const numeric & n)
 		// is cheaper than two squarings.
 		return u * ((v << 1) - u);
 	else
-		return ::square(u) + ::square(v);    
+		return cln::square(u) + cln::square(v);    
 }
 
 
 /** Absolute value. */
-numeric abs(const numeric & x)
+const numeric abs(const numeric& x)
 {
-	return ::abs(*x.value);  // -> CLN
+	return cln::abs(x.to_cl_N());
 }
 
 
@@ -1738,12 +1790,13 @@ numeric abs(const numeric & x)
  *
  *  @return a mod b in the range [0,abs(b)-1] with sign of b if both are
  *  integer, 0 otherwise. */
-numeric mod(const numeric & a, const numeric & 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
+		return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
+		                cln::the<cln::cl_I>(b.to_cl_N()));
 	else
-		return _num0();  // Throw?
+		return _num0;
 }
 
 
@@ -1751,13 +1804,14 @@ numeric mod(const numeric & a, const numeric & b)
  *  Equivalent to Maple's mods.
  *
  *  @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
-numeric smod(const numeric & a, const numeric & b)
+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;
+		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();  // Throw?
+		return _num0;
 }
 
 
@@ -1766,32 +1820,40 @@ numeric smod(const numeric & a, const numeric & 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.
  *
- *  @return remainder of a/b if both are integer, 0 otherwise. */
-numeric irem(const numeric & a, const numeric & 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 (b.is_zero())
+		throw std::overflow_error("numeric::irem(): division by zero");
 	if (a.is_integer() && b.is_integer())
-		return ::rem(The(::cl_I)(*a.value), The(::cl_I)(*b.value));  // -> CLN
+		return cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
+		                cln::the<cln::cl_I>(b.to_cl_N()));
 	else
-		return _num0();  // Throw?
+		return _num0;
 }
 
 
 /** 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(const numeric & a, const numeric & 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));
+	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();
-		return _num0();  // Throw?
+		q = _num0;
+		return _num0;
 	}
 }
 
@@ -1799,13 +1861,17 @@ numeric irem(const numeric & a, const numeric & b, numeric & q)
 /** 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(const numeric & a, const numeric & 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 (b.is_zero())
+		throw std::overflow_error("numeric::iquo(): division by zero");
 	if (a.is_integer() && b.is_integer())
-		return truncate1(The(::cl_I)(*a.value), The(::cl_I)(*b.value));  // -> CLN
+		return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
+	                          cln::the<cln::cl_I>(b.to_cl_N()));
 	else
-		return _num0();  // Throw?
+		return _num0;
 }
 
 
@@ -1814,56 +1880,35 @@ numeric iquo(const numeric & a, const numeric & b)
  *  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(const numeric & a, const numeric & 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));
+	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();
-		return _num0();  // Throw?
+		r = _num0;
+		return _num0;
 	}
 }
 
 
-/** 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(const numeric & z)
-{
-	return ::sqrt(*z.value);  // -> CLN
-}
-
-
-/** Integer numeric square root. */
-numeric isqrt(const numeric & x)
-{
-	if (x.is_integer()) {
-		cl_I root;
-		::isqrt(The(::cl_I)(*x.value), &root);  // -> CLN
-		return root;
-	} else
-		return _num0();  // Throw?
-}
-
-
 /** Greatest Common Divisor.
  *   
  *  @return  The GCD of two numbers if both are integer, a numerical 1
  *  if they are not. */
-numeric gcd(const numeric & a, const numeric & 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
+		return cln::gcd(cln::the<cln::cl_I>(a.to_cl_N()),
+		                cln::the<cln::cl_I>(b.to_cl_N()));
 	else
-		return _num1();
+		return _num1;
 }
 
 
@@ -1871,70 +1916,102 @@ numeric gcd(const numeric & a, const numeric & b)
  *   
  *  @return  The LCM of two numbers if both are integer, the product of those
  *  two numbers if they are not. */
-numeric lcm(const numeric & a, const numeric & b)
+const numeric lcm(const numeric &a, const numeric &b)
 {
 	if (a.is_integer() && b.is_integer())
-		return ::lcm(The(::cl_I)(*a.value), The(::cl_I)(*b.value));  // -> CLN
+		return cln::lcm(cln::the<cln::cl_I>(a.to_cl_N()),
+		                cln::the<cln::cl_I>(b.to_cl_N()));
 	else
-		return *a.value * *b.value;
+		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)
+{
+	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;
 }
 
 
 /** Floating point evaluation of Archimedes' constant Pi. */
-ex PiEvalf(void)
+ex PiEvalf()
 { 
-	return numeric(::cl_pi(cl_default_float_format));  // -> CLN
+	return numeric(cln::pi(cln::default_float_format));
 }
 
 
 /** Floating point evaluation of Euler's constant gamma. */
-ex EulerEvalf(void)
+ex EulerEvalf()
 { 
-	return numeric(::cl_eulerconst(cl_default_float_format));  // -> CLN
+	return numeric(cln::eulerconst(cln::default_float_format));
 }
 
 
 /** Floating point evaluation of Catalan's constant. */
-ex CatalanEvalf(void)
+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)
 {
-	assert(!too_late);
+	// 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;
-	cl_default_float_format = ::cl_float_format(17);
+	cln::default_float_format = cln::float_format(17);
 }
 
 
+/** 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); 
+	digits = prec;
+	cln::default_float_format = cln::float_format(prec); 
 	return *this;
 }
 
 
+/** Convert global Digits object to native type long. */
 _numeric_digits::operator long()
 {
+	// BTW, this is approx. unsigned(cln::default_float_format*0.301)-1
 	return (long)digits;
 }
 
 
-void _numeric_digits::print(std::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;
 }
 
 
-std::ostream& operator<<(std::ostream& os, const _numeric_digits & e)
+std::ostream& operator<<(std::ostream &os, const _numeric_digits &e)
 {
 	e.print(os);
 	return os;
@@ -1953,6 +2030,4 @@ bool _numeric_digits::too_late = false;
  *  assignment from C++ unsigned ints and evaluated like any built-in type. */
 _numeric_digits Digits;
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC