* 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 <limits>
#include "numeric.h"
#include "ex.h"
+#include "operators.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
#include <cln/complex_ring.h>
#include <cln/numtheory.h>
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
-GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(numeric, basic,
+ print_func<print_context>(&numeric::do_print).
+ print_func<print_latex>(&numeric::do_print_latex).
+ print_func<print_csrc>(&numeric::do_print_csrc).
+ print_func<print_csrc_cl_N>(&numeric::do_print_csrc_cl_N).
+ print_func<print_tree>(&numeric::do_print_tree).
+ print_func<print_python_repr>(&numeric::do_print_python_repr))
//////////
-// default constructor, destructor, copy constructor assignment
-// operator and helpers
+// default constructor
//////////
-// public
-
/** default ctor. Numerically it initializes to an integer zero. */
numeric::numeric() : basic(TINFO_numeric)
{
- debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
value = cln::cl_I(0);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
-}
-
-numeric::~numeric()
-{
- debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT);
- destroy(false);
-}
-
-numeric::numeric(const numeric & other)
-{
- debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const numeric & numeric::operator=(const numeric & other)
-{
- debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(true);
- copy(other);
- }
- return *this;
-}
-
-// protected
-
-void numeric::copy(const numeric & other)
-{
- basic::copy(other);
- value = other.value;
-}
-
-void numeric::destroy(bool call_parent)
-{
- if (call_parent) basic::destroy(call_parent);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
//////////
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. However, if the integer is small enough,
- // i.e. satisfies cl_immediate_p(), we save space and dereferences by
- // using an immediate type:
- if (cln::cl_immediate_p(i))
+ // emphasizes efficiency. However, if the integer is small enough
+ // we save space and dereferences by using an immediate type.
+ // (C.f. <cln/object.h>)
+ if (i < (1L << (cl_value_len-1)) && i >= -(1L << (cl_value_len-1)))
value = cln::cl_I(i);
else
- value = cln::cl_I((long) i);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ value = cln::cl_I(static_cast<long>(i));
+ setflag(status_flags::evaluated | status_flags::expanded);
}
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
// Not the whole uint-range is available if we don't cast to ulong
// first. This is due to the behaviour of the cl_I-ctor, which
- // emphasizes efficiency. However, if the integer is small enough,
- // i.e. satisfies cl_immediate_p(), we save space and dereferences by
- // using an immediate type:
- if (cln::cl_immediate_p(i))
+ // 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);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ value = cln::cl_I(static_cast<unsigned long>(i));
+ setflag(status_flags::evaluated | status_flags::expanded);
}
numeric::numeric(long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
value = cln::cl_I(i);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
value = cln::cl_I(i);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
-/** Ctor for rational numerics a/b.
+
+/** Constructor for rational numerics a/b.
*
* @exception overflow_error (division by zero) */
numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
if (!denom)
throw std::overflow_error("division by zero");
value = cln::cl_I(numer) / cln::cl_I(denom);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ 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 = cln::cl_float(d, cln::default_float_format);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ 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);
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
// 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 += "_" + 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;
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
+
/** Ctor from CLN types. This is for the initiated user or internal use
* only. */
-numeric::numeric(const cln::cl_N & z) : basic(TINFO_numeric)
+numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
value = z;
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ setflag(status_flags::evaluated | status_flags::expanded);
}
//////////
// archiving
//////////
-/** Construct object from archive_node. */
-numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
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);
}
}
value = ctorval;
- 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);
+ 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 << cln::the<cln::cl_N>(value);
else {
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
* 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
+ if (x < 0)
+ c.s << "-";
+ c.s << "\\frac{";
+ cln::print_real(c.s, ourflags, cln::abs(cln::numerator(cln::the<cln::cl_RA>(x))));
+ c.s << "}{";
+ cln::print_real(c.s, ourflags, cln::denominator(cln::the<cln::cl_RA>(x)));
+ c.s << '}';
+ }
} else {
// case 2: float
// make CLN believe this number has default_float_format, so it prints
// 'E' as exponent marker instead of 'L':
- ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(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
- * with the other routines and produces something compatible to ginsh input.
- *
- * @see print_real_number() */
-void numeric::print(std::ostream & os, unsigned upper_precedence) const
+/** Helper function to print integer number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_integer_csrc(const print_context & c, const cln::cl_I & x)
{
- debugmsg("numeric print", LOGLEVEL_PRINT);
- cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
- cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+ // Print small numbers in compact float format, but larger numbers in
+ // scientific format
+ const int max_cln_int = 536870911; // 2^29-1
+ if (x >= cln::cl_I(-max_cln_int) && x <= cln::cl_I(max_cln_int))
+ c.s << cln::cl_I_to_int(x) << ".0";
+ else
+ c.s << cln::double_approx(x);
+}
+
+/** Helper function to print real number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_real_csrc(const print_context & c, const cln::cl_R & x)
+{
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+
+ // Integer number
+ print_integer_csrc(c, cln::the<cln::cl_I>(x));
+
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ const cln::cl_I numer = cln::numerator(cln::the<cln::cl_RA>(x));
+ const cln::cl_I denom = cln::denominator(cln::the<cln::cl_RA>(x));
+ if (cln::plusp(x) > 0) {
+ c.s << "(";
+ print_integer_csrc(c, numer);
+ } else {
+ c.s << "-(";
+ print_integer_csrc(c, -numer);
+ }
+ c.s << "/";
+ print_integer_csrc(c, denom);
+ c.s << ")";
+
+ } else {
+
+ // Anything else
+ c.s << cln::double_approx(x);
+ }
+}
+
+/** Helper function to print real number in C++ source format using cl_N types.
+ *
+ * @see numeric::print() */
+static void print_real_cl_N(const print_context & c, const cln::cl_R & x)
+{
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+
+ // Integer number
+ c.s << "cln::cl_I(\"";
+ print_real_number(c, x);
+ c.s << "\")";
+
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ cln::cl_print_flags ourflags;
+ c.s << "cln::cl_RA(\"";
+ cln::print_rational(c.s, ourflags, cln::the<cln::cl_RA>(x));
+ c.s << "\")";
+
+ } else {
+
+ // Anything else
+ c.s << "cln::cl_F(\"";
+ print_real_number(c, cln::cl_float(1.0, cln::default_float_format) * x);
+ c.s << "_" << Digits << "\")";
+ }
+}
+
+void numeric::print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const
+{
+ const cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
+ const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+
if (cln::zerop(i)) {
+
// case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
- os << "(";
- print_real_number(os, r);
- os << ")";
+ if ((precedence() <= level) && (!this->is_nonneg_integer())) {
+ c.s << par_open;
+ print_real_number(c, r);
+ c.s << par_close;
} else {
- print_real_number(os, r);
+ print_real_number(c, r);
}
+
} else {
if (cln::zerop(r)) {
+
// case 2, imaginary: y*I or -y*I
- if ((precedence<=upper_precedence) && (i < 0)) {
- if (i == -1) {
- os << "(-I)";
- } else {
- os << "(";
- print_real_number(os, i);
- os << "*I)";
- }
- } else {
- if (i == 1) {
- os << "I";
- } else {
- if (i == -1) {
- os << "-I";
- } else {
- print_real_number(os, i);
- os << "*I";
- }
+ if (i == 1)
+ c.s << imag_sym;
+ else {
+ if (precedence()<=level)
+ c.s << par_open;
+ if (i == -1)
+ c.s << "-" << imag_sym;
+ else {
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
}
+ if (precedence()<=level)
+ c.s << par_close;
}
+
} else {
+
// case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
- if (precedence <= upper_precedence)
- os << "(";
- print_real_number(os, r);
+ if (precedence() <= level)
+ c.s << par_open;
+ print_real_number(c, r);
if (i < 0) {
if (i == -1) {
- os << "-I";
+ c.s << "-" << imag_sym;
} else {
- print_real_number(os, i);
- os << "*I";
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
}
} else {
if (i == 1) {
- os << "+I";
+ c.s << "+" << imag_sym;
} else {
- os << "+";
- print_real_number(os, i);
- os << "*I";
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
}
}
- if (precedence <= upper_precedence)
- os << ")";
+ if (precedence() <= level)
+ c.s << par_close;
}
}
}
-
-void numeric::printraw(std::ostream & os) const
+void numeric::do_print(const print_context & c, unsigned level) const
{
- // The method printraw doesn't do much, it simply uses CLN's operator<<()
- // for output, which is ugly but reliable. e.g: 2+2i
- debugmsg("numeric printraw", LOGLEVEL_PRINT);
- os << "numeric(" << cln::the<cln::cl_N>(value) << ")";
+ print_numeric(c, "(", ")", "I", "*", level);
}
-
-void numeric::printtree(std::ostream & os, unsigned indent) const
+void numeric::do_print_latex(const print_latex & c, unsigned level) const
{
- debugmsg("numeric printtree", LOGLEVEL_PRINT);
- os << std::string(indent,' ') << cln::the<cln::cl_N>(value)
- << " (numeric): "
- << "hash=" << hashvalue
- << " (0x" << std::hex << hashvalue << std::dec << ")"
- << ", flags=" << flags << std::endl;
+ print_numeric(c, "{(", ")}", "i", " ", level);
}
-
-void numeric::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+void numeric::do_print_csrc(const print_csrc & c, unsigned level) const
{
- debugmsg("numeric print csrc", LOGLEVEL_PRINT);
- std::ios::fmtflags oldflags = os.flags();
- os.setf(std::ios::scientific);
- if (this->is_rational() && !this->is_integer()) {
- if (compare(_num0()) > 0) {
- os << "(";
- if (type == csrc_types::ctype_cl_N)
- os << "cln::cl_F(\"" << numer().evalf() << "\")";
- else
- os << numer().to_double();
- } else {
- os << "-(";
- if (type == csrc_types::ctype_cl_N)
- os << "cln::cl_F(\"" << -numer().evalf() << "\")";
- else
- os << -numer().to_double();
- }
- os << "/";
- if (type == csrc_types::ctype_cl_N)
- os << "cln::cl_F(\"" << denom().evalf() << "\")";
- else
- os << denom().to_double();
- os << ")";
+ std::ios::fmtflags oldflags = c.s.flags();
+ c.s.setf(std::ios::scientific);
+ int oldprec = c.s.precision();
+
+ // Set precision
+ if (is_a<print_csrc_double>(c))
+ c.s.precision(std::numeric_limits<double>::digits10 + 1);
+ else
+ c.s.precision(std::numeric_limits<float>::digits10 + 1);
+
+ if (this->is_real()) {
+
+ // Real number
+ print_real_csrc(c, cln::the<cln::cl_R>(value));
+
} else {
- if (type == csrc_types::ctype_cl_N)
- os << "cln::cl_F(\"" << evalf() << "\")";
+
+ // Complex number
+ c.s << "std::complex<";
+ if (is_a<print_csrc_double>(c))
+ c.s << "double>(";
else
- os << to_double();
+ c.s << "float>(";
+
+ print_real_csrc(c, cln::realpart(cln::the<cln::cl_N>(value)));
+ c.s << ",";
+ print_real_csrc(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+ c.s << ")";
+ }
+
+ c.s.flags(oldflags);
+ c.s.precision(oldprec);
+}
+
+void numeric::do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const
+{
+ if (this->is_real()) {
+
+ // Real number
+ print_real_cl_N(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "cln::complex(";
+ print_real_cl_N(c, cln::realpart(cln::the<cln::cl_N>(value)));
+ c.s << ",";
+ print_real_cl_N(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+ c.s << ")";
}
- os.flags(oldflags);
}
+void numeric::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
+ << " (" << class_name() << ")" << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+}
+
+void numeric::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << "('";
+ print_numeric(c, "(", ")", "I", "*", level);
+ c.s << "')";
+}
bool numeric::info(unsigned inf) const
{
return false;
}
+int numeric::degree(const ex & s) const
+{
+ return 0;
+}
+
+int numeric::ldegree(const ex & s) const
+{
+ return 0;
+}
+
+ex numeric::coeff(const ex & s, int n) const
+{
+ return n==0 ? *this : _ex0;
+}
+
/** Disassemble real part and imaginary part to scan for the occurrence of a
* single number. Also handles the imaginary unit. It ignores the sign on
* both this and the argument, which may lead to what might appear as funny
* results: (2+I).has(-2) -> true. But this is consistent, since we also
* would like to have (-2+I).has(2) -> true and we want to think about the
* sign as a multiplicative factor. */
-bool numeric::has(const ex & other) const
+bool numeric::has(const ex &other) const
{
- if (!is_exactly_of_type(*other.bp, numeric))
+ if (!is_exactly_a<numeric>(other))
return false;
- const numeric & o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
+ const numeric &o = ex_to<numeric>(other);
if (this->is_equal(o) || this->is_equal(-o))
return true;
if (o.imag().is_zero()) // e.g. scan for 3 in -3*I
{
// level can safely be discarded for numeric objects.
return numeric(cln::cl_float(1.0, cln::default_float_format) *
- (cln::the<cln::cl_N>(value)));
+ (cln::the<cln::cl_N>(value)));
}
// protected
-/** Implementation of ex::diff() for a numeric. It always returns 0.
- *
- * @see ex::diff */
-ex numeric::derivative(const symbol & s) const
+int numeric::compare_same_type(const basic &other) const
{
- return _ex0();
-}
-
-
-int numeric::compare_same_type(const basic & other) const
-{
- GINAC_ASSERT(is_exactly_of_type(other, numeric));
- const numeric & o = static_cast<numeric &>(const_cast<basic &>(other));
+ GINAC_ASSERT(is_exactly_a<numeric>(other));
+ const numeric &o = static_cast<const numeric &>(other);
return this->compare(o);
}
-bool numeric::is_equal_same_type(const basic & other) const
+bool numeric::is_equal_same_type(const basic &other) const
{
- GINAC_ASSERT(is_exactly_of_type(other,numeric));
- const numeric *o = static_cast<const numeric *>(&other);
+ GINAC_ASSERT(is_exactly_a<numeric>(other));
+ const numeric &o = static_cast<const numeric &>(other);
- return this->is_equal(*o);
+ return this->is_equal(o);
}
-unsigned numeric::calchash(void) const
+unsigned numeric::calchash() const
{
- // Use CLN's hashcode. Warning: It depends only on the number's value, not
- // its type or precision (i.e. a true equivalence relation on numbers). As
- // a consequence, 3 and 3.0 share the same hashvalue.
- return (hashvalue = cln::equal_hashcode(cln::the<cln::cl_N>(value)) | 0x80000000U);
+ // Base computation of hashvalue on CLN's hashcode. Note: That depends
+ // only on the number's value, not its type or precision (i.e. a true
+ // equivalence relation on numbers). As a consequence, 3 and 3.0 share
+ // the same hashvalue. That shouldn't really matter, though.
+ setflag(status_flags::hash_calculated);
+ hashvalue = golden_ratio_hash(cln::equal_hashcode(cln::the<cln::cl_N>(value)));
+ return hashvalue;
}
// public
/** Numerical addition method. Adds argument to *this and returns result as
- * a new numeric object. */
-const numeric numeric::add(const numeric & other) const
+ * a numeric object. */
+const numeric numeric::add(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num0p = &_num0();
- if (this==_num0p)
- return other;
- else if (&other==_num0p)
- 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. */
-const numeric numeric::sub(const numeric & other) const
+ * result as a numeric object. */
+const numeric numeric::sub(const numeric &other) const
{
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. */
-const numeric numeric::mul(const numeric & other) const
+ * result as a numeric object. */
+const numeric numeric::mul(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num1p = &_num1();
- if (this==_num1p)
- return other;
- else if (&other==_num1p)
- return *this;
-
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) */
-const numeric numeric::div(const numeric & other) const
+const numeric numeric::div(const numeric &other) const
{
if (cln::zerop(cln::the<cln::cl_N>(other.value)))
throw std::overflow_error("numeric::div(): division by zero");
}
-const 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
{
- // Efficiency shortcut: trap the neutral exponent by pointer.
- static const numeric * _num1p = &_num1();
- if (&other==_num1p)
+ // Shortcut for efficiency and numeric stability (as in 1.0 exponent):
+ // trap the neutral exponent.
+ if (&other==_num1_p || cln::equal(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
return *this;
if (cln::zerop(cln::the<cln::cl_N>(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(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value)));
}
-const numeric & numeric::add_dyn(const numeric & other) const
+
+/** Numerical addition method. Adds argument to *this and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping into
+ * an ex object, where the result would end up on the heap anyways. */
+const numeric &numeric::add_dyn(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num0p = &_num0();
- if (this==_num0p)
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (this==_num0_p)
return other;
- else if (&other==_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)))->
- setflag(status_flags::dynallocated));
+ setflag(status_flags::dynallocated));
}
-const numeric & numeric::sub_dyn(const numeric & other) const
-{
+/** Numerical subtraction method. Subtracts argument from *this and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
+const numeric &numeric::sub_dyn(const numeric &other) const
+{
+ // Efficiency shortcut: trap the neutral exponent (first by pointer). This
+ // hack is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num0_p || cln::zerop(cln::the<cln::cl_N>(other.value)))
+ return *this;
+
return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ setflag(status_flags::dynallocated));
}
-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)
+/** Numerical multiplication method. Multiplies *this and argument and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
+const numeric &numeric::mul_dyn(const numeric &other) const
+{
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (this==_num1_p)
return other;
- else if (&other==_num1p)
+ else if (&other==_num1_p)
return *this;
return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ setflag(status_flags::dynallocated));
}
-const numeric & numeric::div_dyn(const numeric & other) const
+/** Numerical division method. Divides *this by argument and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping
+ * into an ex object, where the result would end up on the heap
+ * anyways.
+ *
+ * @exception overflow_error (division by zero) */
+const numeric &numeric::div_dyn(const numeric &other) const
{
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num1_p)
+ return *this;
if (cln::zerop(cln::the<cln::cl_N>(other.value)))
throw std::overflow_error("division by zero");
return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)/cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ setflag(status_flags::dynallocated));
}
-const numeric & numeric::power_dyn(const numeric & other) const
+/** Numerical exponentiation. Raises *this to the power given as argument and
+ * returns result as a numeric object on the heap. Use internally only for
+ * direct wrapping into an ex object, where the result would end up on the
+ * heap anyways. */
+const numeric &numeric::power_dyn(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral exponent by pointer.
- static const numeric * _num1p=&_num1();
- if (&other==_num1p)
+ // Efficiency shortcut: trap the neutral exponent (first try by pointer, then
+ // try harder, since calls to cln::expt() below may return amazing results for
+ // floating point exponent 1.0).
+ if (&other==_num1_p || cln::equal(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
return *this;
if (cln::zerop(cln::the<cln::cl_N>(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(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
+const numeric numeric::inverse() const
{
if (cln::zerop(cln::the<cln::cl_N>(value)))
throw std::overflow_error("numeric::inverse(): division by zero");
* csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0,
* csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.
*
- * @see numeric::compare(const numeric & other) */
-int numeric::csgn(void) const
+ * @see numeric::compare(const numeric &other) */
+int numeric::csgn() const
{
if (cln::zerop(cln::the<cln::cl_N>(value)))
return 0;
* to be compatible with our method csgn.
*
* @return csgn(*this-other)
- * @see numeric::csgn(void) */
-int numeric::compare(const numeric & other) const
+ * @see numeric::csgn() */
+int numeric::compare(const numeric &other) const
{
// Comparing two real numbers?
if (cln::instanceof(value, cln::cl_R_ring) &&
}
-bool numeric::is_equal(const numeric & other) const
+bool numeric::is_equal(const numeric &other) const
{
return cln::equal(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value));
}
/** True if object is zero. */
-bool numeric::is_zero(void) const
+bool numeric::is_zero() const
{
return cln::zerop(cln::the<cln::cl_N>(value));
}
/** True if object is not complex and greater than zero. */
-bool numeric::is_positive(void) const
+bool numeric::is_positive() const
{
- if (this->is_real())
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
return cln::plusp(cln::the<cln::cl_R>(value));
return false;
}
/** True if object is not complex and less than zero. */
-bool numeric::is_negative(void) const
+bool numeric::is_negative() const
{
- if (this->is_real())
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
return cln::minusp(cln::the<cln::cl_R>(value));
return false;
}
/** True if object is a non-complex integer. */
-bool numeric::is_integer(void) const
+bool numeric::is_integer() const
{
return cln::instanceof(value, cln::cl_I_ring);
}
/** True if object is an exact integer greater than zero. */
-bool numeric::is_pos_integer(void) const
+bool numeric::is_pos_integer() const
{
- return (this->is_integer() && cln::plusp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::plusp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact integer greater or equal zero. */
-bool numeric::is_nonneg_integer(void) const
+bool numeric::is_nonneg_integer() const
{
- return (this->is_integer() && !cln::minusp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && !cln::minusp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact even integer. */
-bool numeric::is_even(void) const
+bool numeric::is_even() const
{
- return (this->is_integer() && cln::evenp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::evenp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact odd integer. */
-bool numeric::is_odd(void) const
+bool numeric::is_odd() const
{
- return (this->is_integer() && cln::oddp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::oddp(cln::the<cln::cl_I>(value)));
}
/** Probabilistic primality test.
*
* @return true if object is exact integer and prime. */
-bool numeric::is_prime(void) const
+bool numeric::is_prime() const
{
- return (this->is_integer() && cln::isprobprime(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) // integer?
+ && cln::plusp(cln::the<cln::cl_I>(value)) // positive?
+ && cln::isprobprime(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact rational number, may even be complex
* (denominator may be unity). */
-bool numeric::is_rational(void) const
+bool numeric::is_rational() const
{
return cln::instanceof(value, cln::cl_RA_ring);
}
/** True if object is a real integer, rational or float (but not complex). */
-bool numeric::is_real(void) const
+bool numeric::is_real() const
{
return cln::instanceof(value, cln::cl_R_ring);
}
-bool numeric::operator==(const numeric & other) 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
+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));
}
/** True if object is element of the domain of integers extended by I, i.e. is
* of the form a+b*I, where a and b are integers. */
-bool numeric::is_cinteger(void) const
+bool numeric::is_cinteger() const
{
if (cln::instanceof(value, cln::cl_I_ring))
return true;
/** True if object is an exact rational number, may even be complex
* (denominator may be unity). */
-bool numeric::is_crational(void) const
+bool numeric::is_crational() const
{
if (cln::instanceof(value, cln::cl_RA_ring))
return true;
/** 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 (cln::the<cln::cl_R>(value) < cln::the<cln::cl_R>(other.value));
/** 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 (cln::the<cln::cl_R>(value) <= cln::the<cln::cl_R>(other.value));
/** 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 (cln::the<cln::cl_R>(value) > cln::the<cln::cl_R>(other.value));
/** 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 (cln::the<cln::cl_R>(value) >= cln::the<cln::cl_R>(other.value));
/** Converts numeric types to machine's int. You should check with
* is_integer() if the number is really an integer before calling this method.
* You may also consider checking the range first. */
-int numeric::to_int(void) const
+int numeric::to_int() const
{
GINAC_ASSERT(this->is_integer());
return cln::cl_I_to_int(cln::the<cln::cl_I>(value));
/** Converts numeric types to machine's long. You should check with
* is_integer() if the number is really an integer before calling this method.
* You may also consider checking the range first. */
-long numeric::to_long(void) const
+long numeric::to_long() const
{
GINAC_ASSERT(this->is_integer());
return cln::cl_I_to_long(cln::the<cln::cl_I>(value));
/** Converts numeric types to machine's double. You should check with is_real()
* if the number is really not complex before calling this method. */
-double numeric::to_double(void) const
+double numeric::to_double() const
{
GINAC_ASSERT(this->is_real());
return 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
+cln::cl_N numeric::to_cl_N() const
{
return cln::cl_N(cln::the<cln::cl_N>(value));
}
/** Real part of a number. */
-const numeric numeric::real(void) const
+const numeric numeric::real() const
{
return numeric(cln::realpart(cln::the<cln::cl_N>(value)));
}
/** Imaginary part of a number. */
-const numeric numeric::imag(void) const
+const numeric numeric::imag() const
{
return numeric(cln::imagpart(cln::the<cln::cl_N>(value)));
}
* numerator of complex if real and imaginary part are both rational numbers
* (i.e numer(4/3+5/6*I) == 8+5*I), the number carrying the sign in all other
* cases. */
-const numeric numeric::numer(void) const
+const numeric numeric::numer() const
{
- if (this->is_integer())
- return numeric(*this);
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return numeric(*this); // integer case
else if (cln::instanceof(value, cln::cl_RA_ring))
return numeric(cln::numerator(cln::the<cln::cl_RA>(value)));
/** Denominator. Computes the denominator of rational numbers, common integer
* denominator of complex if real and imaginary part are both rational numbers
* (i.e denom(4/3+5/6*I) == 6), one in all other cases. */
-const numeric numeric::denom(void) const
+const numeric numeric::denom() const
{
- if (this->is_integer())
- return _num1();
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return _num1; // integer case
- 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))
return numeric(cln::lcm(cln::denominator(r), cln::denominator(i)));
}
// at least one float encountered
- return _num1();
+ return _num1;
}
*
* @return number of bits (excluding sign) needed to represent that number
* in two's complement if it is an integer, 0 otherwise. */
-int numeric::int_length(void) const
+int numeric::int_length() const
{
- if (this->is_integer())
+ if (cln::instanceof(value, cln::cl_I_ring))
return cln::integer_length(cln::the<cln::cl_I>(value));
else
return 0;
}
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned numeric::precedence = 30;
-
//////////
// global constants
//////////
-const numeric some_numeric;
-const 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. */
+ * 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 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);
/** Numeric sine (trigonometric function).
*
* @return arbitrary precision numerical sin(x). */
-const numeric sin(const numeric & x)
+const numeric sin(const numeric &x)
{
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 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 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 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 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 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 cln::atan(cln::the<cln::cl_R>(x.to_cl_N()),
/** Numeric hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical sinh(x). */
-const numeric sinh(const numeric & x)
+const numeric sinh(const numeric &x)
{
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 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 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 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 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 cln::atanh(x.to_cl_N());
}
-/*static cln::cl_N Li2_series(const ::cl_N & x,
- const ::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
/** Numeric evaluation of Dilogarithm within circle of convergence (unit
* circle) using a power series. */
-static cln::cl_N Li2_series(const cln::cl_N & x,
- const cln::float_format_t & prec)
+static cln::cl_N Li2_series(const cln::cl_N &x,
+ const cln::float_format_t &prec)
{
// Note: argument must be in the unit circle
cln::cl_N aug, acc;
}
/** Folds Li2's argument inside a small rectangle to enhance convergence. */
-static cln::cl_N Li2_projection(const cln::cl_N & x,
- const cln::float_format_t & prec)
+static cln::cl_N Li2_projection(const cln::cl_N &x,
+ const cln::float_format_t &prec)
{
const cln::cl_R re = cln::realpart(x);
const cln::cl_R im = cln::imagpart(x);
* continuous with quadrant IV.
*
* @return arbitrary precision numerical Li2(x). */
-const numeric Li2(const numeric & 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
/** 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
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");
* @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_equal(_num_1))
+ return _num1;
if (!n.is_nonneg_integer())
throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
* 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)
+ 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< cln::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(cln::cl_RA(1));
-
- int n = nn.to_long();
- for (int i=highest_result; i<n/2; ++i) {
- cln::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 = cln::cl_I(n*m) * (B+results[j]) / (d1*d2);
- n += 4;
- m += 2;
- d1 -= 1;
- d2 -= 2;
- }
- B = (1 - ((B+1)/(2*i+3))) / (cln::cl_I(1)<<(2*i+2));
- results.push_back(B);
- ++highest_result;
+ static unsigned next_r = 0;
+
+ // algorithm not applicable to B(2), so just store it
+ if (!next_r) {
+ results.push_back(cln::recip(cln::cl_RA(6)));
+ next_r = 4;
}
- return results[n/2];
+ if (n<next_r)
+ return results[n/2-1];
+
+ results.reserve(n/2);
+ for (unsigned p=next_r; p<=n; p+=2) {
+ cln::cl_I c = 1; // seed for binonmial coefficients
+ cln::cl_RA b = cln::cl_RA(1-p)/2;
+ const unsigned p3 = p+3;
+ const unsigned pm = p-2;
+ unsigned i, k, p_2;
+ // test if intermediate unsigned int can be represented by immediate
+ // objects by CLN (i.e. < 2^29 for 32 Bit machines, see <cln/object.h>)
+ if (p < (1UL<<cl_value_len/2)) {
+ for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+ c = cln::exquo(c * ((p3-i) * p_2), (i-1)*k);
+ b = b + c*results[k-1];
+ }
+ } else {
+ for (i=2, k=1, p_2=p/2; i<=pm; i+=2, ++k, --p_2) {
+ c = cln::exquo((c * (p3-i)) * p_2, cln::cl_I(i-1)*k);
+ b = b + c*results[k-1];
+ }
+ }
+ results.push_back(-b/(p+1));
+ }
+ next_r = n+2;
+ return results[n/2-1];
}
* @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");
// 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);
*
* @return a mod b in the range [0,abs(b)-1] with sign of b if both are
* integer, 0 otherwise. */
-const 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 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;
}
* Equivalent to Maple's mods.
*
* @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
-const numeric smod(const numeric & a, const numeric & b)
+const numeric smod(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer()) {
const cln::cl_I b2 = cln::ceiling1(cln::the<cln::cl_I>(b.to_cl_N()) >> 1) - 1;
return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
cln::the<cln::cl_I>(b.to_cl_N())) - b2;
} else
- return _num0();
+ 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. */
-const 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 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;
}
/** Numeric integer remainder.
* Equivalent to Maple's irem(a,b,'q') it obeyes the relation
* irem(a,b,q) == a - q*b. In general, mod(a,b) has the sign of b or is zero,
- * and irem(a,b) has the sign of a or is zero.
+ * and irem(a,b) has the sign of a or is zero.
*
* @return remainder of a/b and quotient stored in q if both are integer,
- * 0 otherwise. */
-const 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 (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();
+ 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. */
-const 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(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;
}
* r == a - iquo(a,b,r)*b.
*
* @return truncated quotient of a/b and remainder stored in r if both are
- * integer, 0 otherwise. */
-const 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 (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();
+ r = _num0;
+ return _num0;
}
}
*
* @return The GCD of two numbers if both are integer, a numerical 1
* if they are not. */
-const 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 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. */
-const 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 cln::lcm(cln::the<cln::cl_I>(a.to_cl_N()),
* @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)
+const numeric sqrt(const numeric &z)
{
return cln::sqrt(z.to_cl_N());
}
/** Integer numeric square root. */
-const numeric isqrt(const numeric & x)
+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();
+ return _num0;
}
/** Floating point evaluation of Archimedes' constant Pi. */
-ex PiEvalf(void)
+ex PiEvalf()
{
return numeric(cln::pi(cln::default_float_format));
}
/** Floating point evaluation of Euler's constant gamma. */
-ex EulerEvalf(void)
+ex EulerEvalf()
{
return numeric(cln::eulerconst(cln::default_float_format));
}
/** Floating point evaluation of Catalan's constant. */
-ex CatalanEvalf(void)
+ex CatalanEvalf()
{
return numeric(cln::catalanconst(cln::default_float_format));
}
+/** _numeric_digits default ctor, checking for singleton invariance. */
_numeric_digits::_numeric_digits()
: digits(17)
{
// It initializes to 17 digits, because in CLN float_format(17) turns out
// to be 61 (<64) while float_format(18)=65. The reason is we want to
// have a cl_LF instead of cl_SF, cl_FF or cl_DF.
- assert(!too_late);
+ if (too_late)
+ throw(std::runtime_error("I told you not to do instantiate me!"));
too_late = true;
cln::default_float_format = cln::float_format(17);
}
/** Append global Digits object to ostream. */
-void _numeric_digits::print(std::ostream & os) const
+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