]> www.ginac.de Git - ginac.git/blobdiff - ginac/numeric.cpp
* Added output-support for Python bindings and LaTeX printing for
[ginac.git] / ginac / numeric.cpp
index 3af060d0cba27415d1e3beb4623425490f8e2fac..01c58453363e508d4321362ac663f09219991037 100644 (file)
 #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 "numeric.h"
 #include "ex.h"
 #include "print.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "tostring.h"
 #include "utils.h"
 
 // CLN should pollute the global namespace as little as possible.  Hence, we
@@ -69,14 +62,12 @@ namespace GiNaC {
 GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
 
 //////////
-// default ctor, dtor, copy ctor assignment
-// operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
 /** default ctor. Numerically it initializes to an integer zero. */
 numeric::numeric() : basic(TINFO_numeric)
 {
-       debugmsg("numeric default ctor", LOGLEVEL_CONSTRUCT);
        value = cln::cl_I(0);
        setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -97,7 +88,6 @@ DEFAULT_DESTROY(numeric)
 
 numeric::numeric(int i) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor 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.  However, if the integer is small enough, 
@@ -113,7 +103,6 @@ numeric::numeric(int i) : basic(TINFO_numeric)
 
 numeric::numeric(unsigned int i) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor 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.  However, if the integer is small enough, 
@@ -129,7 +118,6 @@ numeric::numeric(unsigned int i) : basic(TINFO_numeric)
 
 numeric::numeric(long i) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor from long",LOGLEVEL_CONSTRUCT);
        value = cln::cl_I(i);
        setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -137,7 +125,6 @@ numeric::numeric(long i) : basic(TINFO_numeric)
 
 numeric::numeric(unsigned long i) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor from ulong",LOGLEVEL_CONSTRUCT);
        value = cln::cl_I(i);
        setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -147,7 +134,6 @@ numeric::numeric(unsigned long i) : basic(TINFO_numeric)
  *  @exception overflow_error (division by zero) */
 numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor from long/long",LOGLEVEL_CONSTRUCT);
        if (!denom)
                throw std::overflow_error("division by zero");
        value = cln::cl_I(numer) / cln::cl_I(denom);
@@ -157,7 +143,6 @@ numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
 
 numeric::numeric(double d) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor 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:
@@ -170,40 +155,47 @@ numeric::numeric(double d) : basic(TINFO_numeric)
  *  notation like "2+5*I". */
 numeric::numeric(const char *s) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor from string",LOGLEVEL_CONSTRUCT);
        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;
                }
-               if (term.find(".") != std::string::npos) {
+               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
@@ -214,33 +206,25 @@ numeric::numeric(const char *s) : basic(TINFO_numeric)
                        // 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)
+                       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
-#if defined(HAVE_SSTREAM)
-                       std::ostringstream buf;
-                       buf << unsigned(Digits) << std::ends;
-                       term += "_" + buf.str();
-#else
-                       char buf[14];
-                       std::ostrstream(buf,sizeof(buf)) << unsigned(Digits) << std::ends;
-                       term += "_" + std::string(buf);
-#endif
+                       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 {
-                       // not a floating point number...
+                       // 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);
+       } while (delim != std::string::npos);
        value = ctorval;
        setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -250,7 +234,6 @@ numeric::numeric(const char *s) : basic(TINFO_numeric)
  *  only. */
 numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
 {
-       debugmsg("numeric ctor from cl_N", LOGLEVEL_CONSTRUCT);
        value = z;
        setflag(status_flags::evaluated | status_flags::expanded);
 }
@@ -261,17 +244,12 @@ numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
 
 numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-       debugmsg("numeric ctor from archive_node", LOGLEVEL_CONSTRUCT);
        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
                cln::cl_idecoded_float re, im;
                char c;
                s.get(c);
@@ -301,12 +279,7 @@ 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 << cln::the<cln::cl_N>(value);
        else {
@@ -324,19 +297,13 @@ void numeric::archive(archive_node &n) const
                        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
 //////////
 
 /** Helper function to print a real number in a nicer way than is CLN's
@@ -346,20 +313,28 @@ DEFAULT_UNARCHIVE(numeric)
  *  want to visibly distinguish from cl_LF.
  *
  *  @see numeric::print() */
-static void print_real_number(std::ostream &os, const cln::cl_R &num)
+static void print_real_number(const print_context & c, const cln::cl_R &x)
 {
        cln::cl_print_flags ourflags;
-       if (cln::instanceof(num, cln::cl_RA_ring)) {
-               // case 1: integer or rational, nothing special to do:
-               cln::print_real(os, ourflags, num);
+       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
+                       c.s << "\\frac{";
+                       cln::print_real(c.s, ourflags, 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>(num));
-               cln::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
@@ -368,41 +343,39 @@ static void print_real_number(std::ostream &os, const cln::cl_R &num)
  *  @see print_real_number() */
 void numeric::print(const print_context & c, unsigned level) const
 {
-       debugmsg("numeric print", LOGLEVEL_PRINT);
-
-       if (is_of_type(c, print_tree)) {
+       if (is_a<print_tree>(c)) {
 
                c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
                    << " (" << class_name() << ")"
                    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
                    << std::endl;
 
-       } else if (is_of_type(c, print_csrc)) {
+       } else if (is_a<print_csrc>(c)) {
 
                std::ios::fmtflags oldflags = c.s.flags();
                c.s.setf(std::ios::scientific);
                if (this->is_rational() && !this->is_integer()) {
-                       if (compare(_num0()) > 0) {
+                       if (compare(_num0) > 0) {
                                c.s << "(";
-                               if (is_of_type(c, print_csrc_cl_N))
+                               if (is_a<print_csrc_cl_N>(c))
                                        c.s << "cln::cl_F(\"" << numer().evalf() << "\")";
                                else
                                        c.s << numer().to_double();
                        } else {
                                c.s << "-(";
-                               if (is_of_type(c, print_csrc_cl_N))
+                               if (is_a<print_csrc_cl_N>(c))
                                        c.s << "cln::cl_F(\"" << -numer().evalf() << "\")";
                                else
                                        c.s << -numer().to_double();
                        }
                        c.s << "/";
-                       if (is_of_type(c, print_csrc_cl_N))
+                       if (is_a<print_csrc_cl_N>(c))
                                c.s << "cln::cl_F(\"" << denom().evalf() << "\")";
                        else
                                c.s << denom().to_double();
                        c.s << ")";
                } else {
-                       if (is_of_type(c, print_csrc_cl_N))
+                       if (is_a<print_csrc_cl_N>(c))
                                c.s << "cln::cl_F(\"" << evalf() << "\")";
                        else
                                c.s << to_double();
@@ -410,30 +383,32 @@ void numeric::print(const print_context & c, unsigned level) const
                c.s.flags(oldflags);
 
        } else {
-               const std::string par_open  = is_of_type(c, print_latex) ? "{(" : "(";
-               const std::string par_close = is_of_type(c, print_latex) ? ")}" : ")";
-               const std::string imag_sym  = is_of_type(c, print_latex) ? "i" : "I";
-               const std::string mul_sym   = is_of_type(c, print_latex) ? " " : "*";
+               const std::string par_open  = is_a<print_latex>(c) ? "{(" : "(";
+               const std::string par_close = is_a<print_latex>(c) ? ")}" : ")";
+               const std::string imag_sym  = is_a<print_latex>(c) ? "i" : "I";
+               const std::string mul_sym   = is_a<print_latex>(c) ? " " : "*";
                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 (is_a<print_python_repr>(c))
+                       c.s << class_name() << "('";
                if (cln::zerop(i)) {
                        // case 1, real:  x  or  -x
-                       if ((precedence <= level) && (!this->is_nonneg_integer())) {
+                       if ((precedence() <= level) && (!this->is_nonneg_integer())) {
                                c.s << par_open;
-                               print_real_number(c.s, r);
+                               print_real_number(c, r);
                                c.s << par_close;
                        } else {
-                               print_real_number(c.s, r);
+                               print_real_number(c, r);
                        }
                } else {
                        if (cln::zerop(r)) {
                                // case 2, imaginary:  y*I  or  -y*I
-                               if ((precedence <= level) && (i < 0)) {
+                               if ((precedence() <= level) && (i < 0)) {
                                        if (i == -1) {
                                                c.s << par_open+imag_sym+par_close;
                                        } else {
                                                c.s << par_open;
-                                               print_real_number(c.s, i);
+                                               print_real_number(c, i);
                                                c.s << mul_sym+imag_sym+par_close;
                                        }
                                } else {
@@ -443,21 +418,21 @@ void numeric::print(const print_context & c, unsigned level) const
                                                if (i == -1) {
                                                        c.s << "-" << imag_sym;
                                                } else {
-                                                       print_real_number(c.s, i);
+                                                       print_real_number(c, i);
                                                        c.s << mul_sym+imag_sym;
                                                }
                                        }
                                }
                        } else {
                                // case 3, complex:  x+y*I  or  x-y*I  or  -x+y*I  or  -x-y*I
-                               if (precedence <= level)
+                               if (precedence() <= level)
                                        c.s << par_open;
-                               print_real_number(c.s, r);
+                               print_real_number(c, r);
                                if (i < 0) {
                                        if (i == -1) {
                                                c.s << "-"+imag_sym;
                                        } else {
-                                               print_real_number(c.s, i);
+                                               print_real_number(c, i);
                                                c.s << mul_sym+imag_sym;
                                        }
                                } else {
@@ -465,14 +440,16 @@ void numeric::print(const print_context & c, unsigned level) const
                                                c.s << "+"+imag_sym;
                                        } else {
                                                c.s << "+";
-                                               print_real_number(c.s, i);
+                                               print_real_number(c, i);
                                                c.s << mul_sym+imag_sym;
                                        }
                                }
-                               if (precedence <= level)
+                               if (precedence() <= level)
                                        c.s << par_close;
                        }
                }
+               if (is_a<print_python_repr>(c))
+                       c.s << "')";
        }
 }
 
@@ -529,9 +506,9 @@ bool numeric::info(unsigned inf) const
  *  sign as a multiplicative factor. */
 bool numeric::has(const ex &other) const
 {
-       if (!is_exactly_of_type(*other.bp, numeric))
+       if (!is_ex_exactly_of_type(other, numeric))
                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
@@ -575,8 +552,8 @@ ex numeric::evalf(int level) const
 
 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));
+       GINAC_ASSERT(is_exactly_a<numeric>(other));
+       const numeric &o = static_cast<const numeric &>(other);
        
        return this->compare(o);
 }
@@ -584,10 +561,10 @@ int numeric::compare_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);
 }
 
 
@@ -618,10 +595,9 @@ unsigned numeric::calchash(void) const
 const numeric numeric::add(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral element by pointer.
-       static const numeric * _num0p = &_num0();
-       if (this==_num0p)
+       if (this==_num0_p)
                return other;
-       else if (&other==_num0p)
+       else if (&other==_num0_p)
                return *this;
        
        return numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value));
@@ -641,10 +617,9 @@ const numeric numeric::sub(const numeric &other) const
 const numeric numeric::mul(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral element by pointer.
-       static const numeric * _num1p = &_num1();
-       if (this==_num1p)
+       if (this==_num1_p)
                return other;
-       else if (&other==_num1p)
+       else if (&other==_num1_p)
                return *this;
        
        return numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value));
@@ -668,8 +643,7 @@ const numeric numeric::div(const numeric &other) const
 const numeric numeric::power(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral exponent by pointer.
-       static const numeric * _num1p = &_num1();
-       if (&other==_num1p)
+       if (&other==_num1_p)
                return *this;
        
        if (cln::zerop(cln::the<cln::cl_N>(value))) {
@@ -680,7 +654,7 @@ const numeric numeric::power(const numeric &other) const
                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(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value)));
 }
@@ -689,10 +663,9 @@ const numeric numeric::power(const numeric &other) const
 const numeric &numeric::add_dyn(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral element by pointer.
-       static const numeric * _num0p = &_num0();
-       if (this==_num0p)
+       if (this==_num0_p)
                return other;
-       else if (&other==_num0p)
+       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)))->
@@ -710,10 +683,9 @@ const numeric &numeric::sub_dyn(const numeric &other) const
 const numeric &numeric::mul_dyn(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral element by pointer.
-       static const numeric * _num1p = &_num1();
-       if (this==_num1p)
+       if (this==_num1_p)
                return other;
-       else if (&other==_num1p)
+       else if (&other==_num1_p)
                return *this;
        
        return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value)))->
@@ -733,8 +705,7 @@ const numeric &numeric::div_dyn(const numeric &other) const
 const numeric &numeric::power_dyn(const numeric &other) const
 {
        // Efficiency shortcut: trap the neutral exponent by pointer.
-       static const numeric * _num1p=&_num1();
-       if (&other==_num1p)
+       if (&other==_num1_p)
                return *this;
        
        if (cln::zerop(cln::the<cln::cl_N>(value))) {
@@ -745,7 +716,7 @@ const numeric &numeric::power_dyn(const numeric &other) const
                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(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value))))->
                                             setflag(status_flags::dynallocated));
@@ -938,13 +909,13 @@ bool numeric::is_real(void) const
 
 bool numeric::operator==(const numeric &other) const
 {
-       return equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+       return cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
 }
 
 
 bool numeric::operator!=(const numeric &other) const
 {
-       return !equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+       return !cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
 }
 
 
@@ -1112,16 +1083,16 @@ const numeric numeric::numer(void) const
 const numeric numeric::denom(void) const
 {
        if (this->is_integer())
-               return _num1();
+               return _num1;
        
-       if (instanceof(value, cln::cl_RA_ring))
+       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(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();
+                       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))
@@ -1130,7 +1101,7 @@ const numeric numeric::denom(void) const
                        return numeric(cln::lcm(cln::denominator(r), cln::denominator(i)));
        }
        // at least one float encountered
-       return _num1();
+       return _num1;
 }
 
 
@@ -1148,15 +1119,6 @@ int numeric::int_length(void) const
                return 0;
 }
 
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned numeric::precedence = 30;
-
 //////////
 // global constants
 //////////
@@ -1243,7 +1205,7 @@ 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 cln::atan(x.to_cl_N());
 }
@@ -1394,7 +1356,7 @@ static cln::cl_N Li2_projection(const cln::cl_N &x,
 const numeric Li2(const numeric &x)
 {
        if (x.is_zero())
-               return _num0();
+               return _num0;
        
        // what is the desired float format?
        // first guess: default format
@@ -1433,10 +1395,7 @@ const numeric zeta(const numeric &x)
                if (cln::zerop(x.to_cl_N()-aux))
                        return cln::zeta(aux);
        }
-       std::clog << "zeta(" << x
-                         << "): Does anybody know a good way to calculate this numerically?"
-                         << std::endl;
-       return numeric(0);
+       throw dunno();
 }
 
 
@@ -1444,17 +1403,11 @@ const numeric zeta(const numeric &x)
  *  This is only a stub! */
 const numeric lgamma(const numeric &x)
 {
-       std::clog << "lgamma(" << x
-                 << "): Does anybody know a good way to calculate this numerically?"
-                 << std::endl;
-       return numeric(0);
+       throw dunno();
 }
 const numeric tgamma(const numeric &x)
 {
-       std::clog << "tgamma(" << x
-                 << "): Does anybody know a good way to calculate this numerically?"
-                 << std::endl;
-       return numeric(0);
+       throw dunno();
 }
 
 
@@ -1462,10 +1415,7 @@ const numeric tgamma(const numeric &x)
  *  This is only a stub! */
 const numeric psi(const numeric &x)
 {
-       std::clog << "psi(" << x
-                 << "): Does anybody know a good way to calculate this numerically?"
-                 << std::endl;
-       return numeric(0);
+       throw dunno();
 }
 
 
@@ -1473,10 +1423,7 @@ const numeric psi(const numeric &x)
  *  This is only a stub! */
 const numeric psi(const numeric &n, const numeric &x)
 {
-       std::clog << "psi(" << n << "," << x
-                 << "): Does anybody know a good way to calculate this numerically?"
-                 << std::endl;
-       return numeric(0);
+       throw dunno();
 }
 
 
@@ -1500,8 +1447,8 @@ const numeric factorial(const numeric &n)
  *  @exception range_error (argument must be integer >= -1) */
 const numeric doublefactorial(const numeric &n)
 {
-       if (n.is_equal(_num_1()))
-               return _num1();
+       if (n.is_equal(_num_1))
+               return _num1;
        
        if (!n.is_nonneg_integer())
                throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
@@ -1518,12 +1465,12 @@ 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)
+                       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);
                }
        }
        
@@ -1574,16 +1521,16 @@ const numeric bernoulli(const numeric &nn)
        // we don't use it.)
        
        // the special cases not covered by the algorithm below
-       if (nn.is_equal(_num1()))
-               return _num_1_2();
+       if (nn.is_equal(_num1))
+               return _num_1_2;
        if (nn.is_odd())
-               return _num0();
+               return _num0;
        
        // store nonvanishing Bernoulli numbers here
        static std::vector< cln::cl_RA > results;
        static int highest_result = 0;
        // algorithm not applicable to B(0), so just store it
-       if (results.size()==0)
+       if (results.empty())
                results.push_back(cln::cl_RA(1));
        
        int n = nn.to_long();
@@ -1635,7 +1582,7 @@ 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);
@@ -1687,7 +1634,7 @@ const numeric mod(const numeric &a, const numeric &b)
                return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
                                cln::the<cln::cl_I>(b.to_cl_N()));
        else
-               return _num0();
+               return _num0;
 }
 
 
@@ -1702,7 +1649,7 @@ const numeric smod(const numeric &a, const numeric &b)
                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();
+               return _num0;
 }
 
 
@@ -1718,7 +1665,7 @@ const numeric irem(const numeric &a, const numeric &b)
                return cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
                                cln::the<cln::cl_I>(b.to_cl_N()));
        else
-               return _num0();
+               return _num0;
 }
 
 
@@ -1737,8 +1684,8 @@ const numeric irem(const numeric &a, const numeric &b, numeric &q)
                q = rem_quo.quotient;
                return rem_quo.remainder;
        } else {
-               q = _num0();
-               return _num0();
+               q = _num0;
+               return _num0;
        }
 }
 
@@ -1750,10 +1697,10 @@ const numeric irem(const numeric &a, const numeric &b, numeric &q)
 const numeric iquo(const numeric &a, const numeric &b)
 {
        if (a.is_integer() && b.is_integer())
-               return truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
-                            cln::the<cln::cl_I>(b.to_cl_N()));
+               return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
+                                 cln::the<cln::cl_I>(b.to_cl_N()));
        else
-               return _num0();
+               return _num0;
 }
 
 
@@ -1771,8 +1718,8 @@ const numeric iquo(const numeric &a, const numeric &b, numeric &r)
                r = rem_quo.remainder;
                return rem_quo.quotient;
        } else {
-               r = _num0();
-               return _num0();
+               r = _num0;
+               return _num0;
        }
 }
 
@@ -1787,7 +1734,7 @@ const numeric gcd(const numeric &a, const numeric &b)
                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;
 }
 
 
@@ -1827,7 +1774,7 @@ const numeric isqrt(const numeric &x)
                cln::isqrt(cln::the<cln::cl_I>(x.to_cl_N()), &root);
                return root;
        } else
-               return _num0();
+               return _num0;
 }
 
 
@@ -1886,7 +1833,6 @@ _numeric_digits::operator long()
 /** Append global Digits object to ostream. */
 void _numeric_digits::print(std::ostream &os) const
 {
-       debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
        os << digits;
 }