* 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
#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 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)
//////////
-// default constructor, destructor, copy constructor assignment
-// operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
//////////
-// 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;
+ value = cln::cl_I(0);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-// protected
-
-void numeric::copy(const numeric & other)
+void numeric::copy(const numeric &other)
{
- basic::copy(other);
- value = new ::cl_N(*other.value);
+ inherited::copy(other);
+ value = other.value;
}
-void numeric::destroy(bool call_parent)
-{
- delete value;
- if (call_parent) basic::destroy(call_parent);
-}
+DEFAULT_DESTROY(numeric)
//////////
-// other constructors
+// other ctors
//////////
// public
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 < (1U<<cl_value_len-1))
+ value = cln::cl_I(i);
+ else
+ value = cln::cl_I((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((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.
* @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);
}
+
/** ctor from C-style string. It also accepts complex numbers in GiNaC
* 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::expanded |
- 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)
{
- 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);
-}
-
-/** Unarchive the object. */
-ex numeric::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated);
+ value = ctorval;
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-/** 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
-{
- debugmsg("numeric print", LOGLEVEL_PRINT);
- if (this->is_real()) {
- // case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
- os << "(";
- print_real_number(os, The(::cl_R)(*value));
- os << ")";
+/** 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)
+{
+ // 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 {
- print_real_number(os, The(::cl_R)(*value));
+ c.s << "-(";
+ print_integer_csrc(c, -numer);
}
+ c.s << "/";
+ print_integer_csrc(c, denom);
+ c.s << ")";
+
} 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";
- }
- }
- }
- } 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";
- } else {
- print_real_number(os, The(::cl_R)(::imagpart(*value)));
- os << "*I";
- }
- } else {
- if (::imagpart(*value) == 1) {
- os << "+I";
- } else {
- os << "+";
- print_real_number(os, The(::cl_R)(::imagpart(*value)));
- os << "*I";
- }
- }
- if (precedence <= upper_precedence)
- os << ")";
- }
+
+ // Anything else
+ c.s << cln::double_approx(x);
}
}
-
-void numeric::printraw(std::ostream & os) const
+/** 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)
{
- // 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 << ")";
-}
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+ // Integer number
+ c.s << "cln::cl_I(\"";
+ print_real_number(c, x);
+ c.s << "\")";
-void numeric::printtree(std::ostream & os, unsigned indent) const
-{
- debugmsg("numeric printtree", LOGLEVEL_PRINT);
- os << std::string(indent,' ') << *value
- << " (numeric): "
- << "hash=" << hashvalue
- << " (0x" << std::hex << hashvalue << std::dec << ")"
- << ", flags=" << flags << std::endl;
-}
+ } 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::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+/** 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(const print_context & 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();
+ 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_a<print_csrc_cl_N>(c)) {
+
+ // CLN output
+ if (this->is_real()) {
+
+ // Real number
+ print_real_cl_N(c, cln::the<cln::cl_R>(value));
+
} else {
- os << "-(";
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << -numer().evalf() << "\")";
- else
- os << -numer().to_double();
+
+ // 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 << ")";
}
- os << "/";
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << denom().evalf() << "\")";
+
+ } else if (is_a<print_csrc>(c)) {
+
+ // C++ source output
+ 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(16);
else
- os << denom().to_double();
- os << ")";
+ c.s.precision(7);
+
+ if (this->is_real()) {
+
+ // Real number
+ print_real_csrc(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "std::complex<";
+ if (is_a<print_csrc_double>(c))
+ c.s << "double>(";
+ else
+ c.s << "float>(";
+
+ print_real_csrc(c, cln::realpart(cln::the<cln::cl_N>(value)));
+ c.s << ",";
+ print_real_csrc(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+ c.s << ")";
+ }
+
+ c.s.flags(oldflags);
+ c.s.precision(oldprec);
+
} else {
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << evalf() << "\")";
- else
- os << to_double();
+
+ 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())) {
+ c.s << par_open;
+ print_real_number(c, r);
+ c.s << par_close;
+ } else {
+ print_real_number(c, r);
+ }
+ } else {
+ if (cln::zerop(r)) {
+ // case 2, imaginary: y*I or -y*I
+ if (i==1)
+ c.s << imag_sym;
+ else {
+ if (precedence()<=level)
+ c.s << par_open;
+ if (i == -1)
+ c.s << "-" << imag_sym;
+ else {
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
+ if (precedence()<=level)
+ c.s << par_close;
+ }
+ } else {
+ // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
+ if (precedence() <= level)
+ c.s << par_open;
+ print_real_number(c, r);
+ if (i < 0) {
+ if (i == -1) {
+ c.s << "-"+imag_sym;
+ } else {
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
+ } else {
+ if (i == 1) {
+ c.s << "+"+imag_sym;
+ } else {
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
+ }
+ if (precedence() <= level)
+ c.s << par_close;
+ }
+ }
+ if (is_a<print_python_repr>(c))
+ c.s << "')";
}
- os.flags(oldflags);
}
-
bool numeric::info(unsigned inf) const
{
switch (inf) {
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_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
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
-{
- return _ex0();
-}
-
-
-int numeric::compare_same_type(const basic & other) 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));
-
- 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);
}
// 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);
+ setflag(status_flags::hash_calculated);
+ return (hashvalue = cln::equal_hashcode(cln::the<cln::cl_N>(value)) | 0x80000000U);
}
// 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));
+ // Efficiency shortcut: trap the neutral element by pointer.
+ if (this==_num0_p)
+ return other;
+ else if (&other==_num0_p)
+ return *this;
+
+ 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) {
+ // Efficiency shortcut: trap the neutral element by pointer.
+ if (this==_num1_p)
return other;
- } else if (&other==_num1p) {
+ else if (&other==_num1_p)
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)
+ // Efficiency shortcut: trap the neutral exponent by pointer.
+ if (&other==_num1_p)
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
+const numeric &numeric::add_dyn(const numeric &other) const
{
- return static_cast<const numeric &>((new numeric((*value)+(*other.value)))->
+ // Efficiency shortcut: trap the neutral element by pointer.
+ 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
+
+const numeric &numeric::sub_dyn(const numeric &other) const
{
- return static_cast<const numeric &>((new numeric((*value)-(*other.value)))->
+ 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
+
+const numeric &numeric::mul_dyn(const numeric &other) const
{
- static const numeric * _num1p=&_num1();
- if (this==_num1p) {
+ // Efficiency shortcut: trap the neutral element by pointer.
+ 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)))->
+
+ 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
+
+const numeric &numeric::div_dyn(const numeric &other) const
{
- if (::zerop(*other.value))
+ 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)))->
+ 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
+
+const numeric &numeric::power_dyn(const numeric &other) const
{
- static const numeric * _num1p=&_num1();
- if (&other==_num1p)
+ // Efficiency shortcut: trap the neutral exponent by pointer.
+ if (&other==_num1_p)
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(void) 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) */
+ * @see numeric::compare(const numeric &other) */
int numeric::csgn(void) 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
*
* @return csgn(*this-other)
* @see numeric::csgn(void) */
-int numeric::compare(const numeric & other) const
+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
{
- 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
{
if (this->is_real())
- return ::plusp(The(::cl_R)(*value)); // -> CLN
+ 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
{
if (this->is_real())
- return ::minusp(The(::cl_R)(*value)); // -> CLN
+ 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
{
- 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
{
- return (this->is_integer() && ::plusp(The(::cl_I)(*value))); // -> CLN
+ return (this->is_integer() && 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
{
- return (this->is_integer() && !::minusp(The(::cl_I)(*value))); // -> CLN
+ return (this->is_integer() && !cln::minusp(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact even integer. */
bool numeric::is_even(void) const
{
- return (this->is_integer() && ::evenp(The(::cl_I)(*value))); // -> CLN
+ return (this->is_integer() && cln::evenp(cln::the<cln::cl_I>(value)));
}
+
/** True if object is an exact odd integer. */
bool numeric::is_odd(void) const
{
- return (this->is_integer() && ::oddp(The(::cl_I)(*value))); // -> CLN
+ return (this->is_integer() && 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
{
- return (this->is_integer() && ::isprobprime(The(::cl_I)(*value))); // -> CLN
+ return (this->is_integer() && 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
{
- 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
{
- 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
{
- 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
{
- 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");
}
+
/** 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");
}
+
/** 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");
}
+
/** 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
{
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
{
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
{
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(void) const
+{
+ return cln::cl_N(cln::the<cln::cl_N>(value));
+}
+
+
/** Real part of a number. */
const numeric numeric::real(void) 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
{
- 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
* cases. */
const numeric numeric::numer(void) const
{
- if (this->is_integer()) {
+ 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);
- }
+
+ 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
{
- 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 (this->is_integer())
+ return _num1;
+
+ 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.
int numeric::int_length(void) const
{
if (this->is_integer())
- return ::integer_length(The(::cl_I)(*value)); // -> CLN
+ 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 std::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());
}
* @param z 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 &z)
{
if (z.is_zero())
throw pole_error("log(): logarithmic pole",0);
- return ::log(*z.value); // -> CLN
+ return cln::log(z.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());
}
* @param z complex number
* @return atan(z)
* @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());
}
* @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");
}
/** 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);
/** 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;
}
/** 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);
}
* 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
// 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();
}
*
* @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()));
}
* @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()));
}
* 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);
}
}
*
* @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
// 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;
+ }
+ 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));
}
- return results[n/2];
+ next_r = n+2;
+ return results[n/2-1];
}
* @param n an integer
* @return the nth Fibonacci number F(n) (an integer number)
* @exception range_error (argument must be an integer) */
-const numeric fibonacci(const numeric & n)
+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.
// 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;
}
}
// 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());
}
*
* @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;
}
* 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) >> 1)) - 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;
}
* 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;
}
* 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;
}
}
/** 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;
}
* 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;
}
*
* @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(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. */
+const numeric sqrt(const numeric &z)
+{
+ return cln::sqrt(z.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)
{
- 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)
{
- 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)
{
- 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;
* 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
git://www.ginac.de / ginac.git / blobdiff