#include "debugmsg.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
+// 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>
#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
#endif // ndef NO_NAMESPACE_GINAC
-// linker has no problems finding text symbols for numerator or denominator
-//#define SANE_LINKER
-
GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
//////////
numeric::numeric() : basic(TINFO_numeric)
{
debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
- value = new ::cl_N;
- *value = ::cl_I(0);
+ value = cln::cl_I(0);
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
void numeric::copy(const numeric & other)
{
basic::copy(other);
- value = new ::cl_N(*other.value);
+ value = other.value;
}
void numeric::destroy(bool call_parent)
{
- delete value;
if (call_parent) basic::destroy(call_parent);
}
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);
+ // 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))
+ value = cln::cl_I(i);
+ else
+ value = cln::cl_I((long) i);
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
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);
+ // 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))
+ value = cln::cl_I(i);
+ else
+ value = cln::cl_I((unsigned long) i);
calchash();
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);
+ value = cln::cl_I(i);
calchash();
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);
+ value = cln::cl_I(i);
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
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);
+ value = cln::cl_I(numer) / cln::cl_I(denom);
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
// 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);
+ value = cln::cl_float(d, cln::default_float_format);
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
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
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) {
+ // 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
+#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
+ // 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 {
+ // 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);
+ ctorval = ctorval + cln::cl_R(term.c_str());
+ }
} while(delim != std::string::npos);
+ value = ctorval;
calchash();
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);
+ value = z;
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
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;
#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;
}
}
+ value = ctorval;
calchash();
setflag(status_flags::evaluated |
status_flags::expanded |
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;
/** 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)
+static void print_real_number(std::ostream & os, const cln::cl_R & num)
{
- cl_print_flags ourflags;
- if (::instanceof(num, ::cl_RA_ring)) {
+ cln::cl_print_flags ourflags;
+ if (cln::instanceof(num, cln::cl_RA_ring)) {
// case 1: integer or rational, nothing special to do:
- ::print_real(os, ourflags, num);
+ cln::print_real(os, ourflags, num);
} 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>(num));
+ cln::print_real(os, ourflags, num);
}
return;
}
void numeric::print(std::ostream & os, unsigned upper_precedence) const
{
debugmsg("numeric print", LOGLEVEL_PRINT);
- if (this->is_real()) {
+ cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
+ cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+ if (cln::zerop(i)) {
// case 1, real: x or -x
if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
os << "(";
- print_real_number(os, The(::cl_R)(*value));
+ print_real_number(os, r);
os << ")";
} else {
- print_real_number(os, The(::cl_R)(*value));
+ print_real_number(os, r);
}
} else {
- // case 2, imaginary: y*I or -y*I
- if (::realpart(*value) == 0) {
- if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) {
- if (::imagpart(*value) == -1) {
+ 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, The(::cl_R)(::imagpart(*value)));
+ print_real_number(os, i);
os << "*I)";
}
} else {
- if (::imagpart(*value) == 1) {
+ if (i == 1) {
os << "I";
} else {
- if (::imagpart (*value) == -1) {
+ if (i == -1) {
os << "-I";
} else {
- print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ print_real_number(os, i);
os << "*I";
}
}
// 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) {
+ print_real_number(os, r);
+ if (i < 0) {
+ if (i == -1) {
os << "-I";
} else {
- print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ print_real_number(os, i);
os << "*I";
}
} else {
- if (::imagpart(*value) == 1) {
+ if (i == 1) {
os << "+I";
} else {
os << "+";
- print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ print_real_number(os, i);
os << "*I";
}
}
// 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 << ")";
+ os << "numeric(" << cln::the<cln::cl_N>(value) << ")";
}
void numeric::printtree(std::ostream & os, unsigned indent) const
{
debugmsg("numeric printtree", LOGLEVEL_PRINT);
- os << std::string(indent,' ') << *value
+ os << std::string(indent,' ') << cln::the<cln::cl_N>(value)
<< " (numeric): "
<< "hash=" << hashvalue
<< " (0x" << std::hex << hashvalue << std::dec << ")"
void numeric::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
{
debugmsg("numeric print csrc", LOGLEVEL_PRINT);
- ios::fmtflags oldflags = os.flags();
- os.setf(ios::scientific);
+ 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 << "cl_F(\"" << numer().evalf() << "\")";
+ os << "cln::cl_F(\"" << numer().evalf() << "\")";
else
os << numer().to_double();
} else {
os << "-(";
if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << -numer().evalf() << "\")";
+ os << "cln::cl_F(\"" << -numer().evalf() << "\")";
else
os << -numer().to_double();
}
os << "/";
if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << denom().evalf() << "\")";
+ os << "cln::cl_F(\"" << denom().evalf() << "\")";
else
os << denom().to_double();
os << ")";
} else {
if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << evalf() << "\")";
+ os << "cln::cl_F(\"" << evalf() << "\")";
else
os << to_double();
}
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
{
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);
+
+ return this->compare(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);
+ return (hashvalue = cln::equal_hashcode(cln::the<cln::cl_N>(value)) | 0x80000000U);
}
/** Numerical addition method. Adds argument to *this and returns result as
* a new numeric object. */
-numeric numeric::add(const numeric & other) const
+const numeric numeric::add(const numeric & other) const
{
- return numeric((*value)+(*other.value));
+ // 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. */
-numeric numeric::sub(const numeric & other) const
+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
+const numeric numeric::mul(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
- if (this==_num1p) {
+ // Efficiency shortcut: trap the neutral element by pointer.
+ static const numeric * _num1p = &_num1();
+ if (this==_num1p)
return other;
- } else if (&other==_num1p) {
+ else if (&other==_num1p)
return *this;
- }
- return numeric((*value)*(*other.value));
+
+ return numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value));
}
+
/** Numerical division method. Divides *this by argument and returns result as
* a new numeric object.
*
* @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
+
+const numeric numeric::power(const numeric & other) const
{
+ // Efficiency shortcut: trap the neutral exponent by pointer.
static const numeric * _num1p = &_num1();
if (&other==_num1p)
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 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
{
- return static_cast<const numeric &>((new numeric((*value)+(*other.value)))->
+ // 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 static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value)))->
setflag(status_flags::dynallocated));
}
+
const numeric & numeric::sub_dyn(const numeric & other) const
{
- return static_cast<const numeric &>((new numeric((*value)-(*other.value)))->
+ return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value)))->
setflag(status_flags::dynallocated));
}
+
const numeric & numeric::mul_dyn(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
- if (this==_num1p) {
+ // Efficiency shortcut: trap the neutral element by pointer.
+ static const numeric * _num1p = &_num1();
+ if (this==_num1p)
return other;
- } else if (&other==_num1p) {
+ else if (&other==_num1p)
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
{
- 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
{
+ // Efficiency shortcut: trap the neutral exponent by pointer.
static const numeric * _num1p=&_num1();
if (&other==_num1p)
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 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)
{
return operator=(numeric(i));
}
+
const numeric & numeric::operator=(unsigned int i)
{
return operator=(numeric(i));
}
+
const numeric & numeric::operator=(long i)
{
return operator=(numeric(i));
}
+
const numeric & numeric::operator=(unsigned long i)
{
return operator=(numeric(i));
}
+
const numeric & numeric::operator=(double d)
{
return operator=(numeric(d));
}
+
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) */
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
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
{
- 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
{
- return (*value == *other.value); // -> CLN
+ return equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
}
+
bool numeric::operator!=(const numeric & other) const
{
- return (*value != *other.value); // -> CLN
+ return !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
{
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
{
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
{
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
{
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)));
}
+
/** 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()) {
+ 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 (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))
+ 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 (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));
+ 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();
}
+
/** 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;
}
+/** Returns a new CLN object of type cl_N, representing the value of *this.
+ * This method is useful for casting when mixing GiNaC and CLN in one project.
+ */
+numeric::operator cln::cl_N() const
+{
+ return cln::cl_N(cln::the<cln::cl_N>(value));
+}
+
+
//////////
// static member variables
//////////
//////////
const numeric some_numeric;
-const type_info & typeid_numeric=typeid(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)));
+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)
{
- return ::exp(*x.value); // -> CLN
+ return cln::exp(cln::cl_N(x));
}
{
if (z.is_zero())
throw pole_error("log(): logarithmic pole",0);
- return ::log(*z.value); // -> CLN
+ return cln::log(cln::cl_N(z));
}
* @return arbitrary precision numerical sin(x). */
const numeric sin(const numeric & x)
{
- return ::sin(*x.value); // -> CLN
+ return cln::sin(cln::cl_N(x));
}
* @return arbitrary precision numerical cos(x). */
const numeric cos(const numeric & x)
{
- return ::cos(*x.value); // -> CLN
+ return cln::cos(cln::cl_N(x));
}
* @return arbitrary precision numerical tan(x). */
const numeric tan(const numeric & x)
{
- return ::tan(*x.value); // -> CLN
+ return cln::tan(cln::cl_N(x));
}
* @return arbitrary precision numerical asin(x). */
const numeric asin(const numeric & x)
{
- return ::asin(*x.value); // -> CLN
+ return cln::asin(cln::cl_N(x));
}
* @return arbitrary precision numerical acos(x). */
const numeric acos(const numeric & x)
{
- return ::acos(*x.value); // -> CLN
+ return cln::acos(cln::cl_N(x));
}
x.real().is_zero() &&
abs(x.imag()).is_equal(_num1()))
throw pole_error("atan(): logarithmic pole",0);
- return ::atan(*x.value); // -> CLN
+ return cln::atan(cln::cl_N(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>(cln::cl_N(x)),
+ cln::the<cln::cl_R>(cln::cl_N(y)));
else
throw std::invalid_argument("atan(): complex argument");
}
* @return arbitrary precision numerical sinh(x). */
const numeric sinh(const numeric & x)
{
- return ::sinh(*x.value); // -> CLN
+ return cln::sinh(cln::cl_N(x));
}
* @return arbitrary precision numerical cosh(x). */
const numeric cosh(const numeric & x)
{
- return ::cosh(*x.value); // -> CLN
+ return cln::cosh(cln::cl_N(x));
}
* @return arbitrary precision numerical tanh(x). */
const numeric tanh(const numeric & x)
{
- return ::tanh(*x.value); // -> CLN
+ return cln::tanh(cln::cl_N(x));
}
* @return arbitrary precision numerical asinh(x). */
const numeric asinh(const numeric & x)
{
- return ::asinh(*x.value); // -> CLN
+ return cln::asinh(cln::cl_N(x));
}
* @return arbitrary precision numerical acosh(x). */
const numeric acosh(const numeric & x)
{
- return ::acosh(*x.value); // -> CLN
+ return cln::acosh(cln::cl_N(x));
}
* @return arbitrary precision numerical atanh(x). */
const numeric atanh(const numeric & x)
{
- return ::atanh(*x.value); // -> CLN
+ return cln::atanh(cln::cl_N(x));
}
-/*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);
}
* @return arbitrary precision numerical Li2(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 = cln::cl_N(x);
// 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(cln::cl_N(x), prec);
}
// 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>(cln::cl_N(x))));
+ if (cln::zerop(cln::cl_N(x)-aux))
+ return cln::zeta(aux);
}
std::clog << "zeta(" << x
<< "): Does anybody know good way to calculate this numerically?"
{
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()));
}
* @exception range_error (argument must be integer >= -1) */
const numeric doublefactorial(const numeric & n)
{
- if (n == numeric(-1)) {
+ if (n == numeric(-1))
return _num1();
- }
- if (!n.is_nonneg_integer()) {
+
+ 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()));
}
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
+ return numeric(cln::binomial(n.to_int(),k.to_int()));
else
return _num0();
} else {
return _num0();
// store nonvanishing Bernoulli numbers here
- static std::vector< ::cl_RA > results;
+ 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(::cl_RA(1));
+ results.push_back(cln::cl_RA(1));
int n = nn.to_long();
for (int i=highest_result; i<n/2; ++i) {
- ::cl_RA B = 0;
+ 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 = ::cl_I(n*m) * (B+results[j]) / (d1*d2);
+ 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))) / (::cl_I(1)<<(2*i+2));
+ B = (1 - ((B+1)/(2*i+3))) / (cln::cl_I(1)<<(2*i+2));
results.push_back(B);
++highest_result;
}
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.
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>(cln::cl_N(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(cln::cl_N(x));
}
*
* @return a mod b in the range [0,abs(b)-1] with sign of b if both are
* integer, 0 otherwise. */
-numeric mod(const numeric & a, const numeric & b)
+const numeric mod(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
- return ::mod(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ return cln::mod(cln::the<cln::cl_I>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
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>(cln::cl_N(b)) >> 1) - 1;
+ return cln::mod(cln::the<cln::cl_I>(cln::cl_N(a)) + b2,
+ cln::the<cln::cl_I>(cln::cl_N(b))) - b2;
} else
- return _num0(); // Throw?
+ return _num0();
}
* 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)
+const numeric irem(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
- return ::rem(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ return cln::rem(cln::the<cln::cl_I>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
else
- return _num0(); // Throw?
+ return _num0();
}
*
* @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)
+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 (a.is_integer() && b.is_integer()) {
+ const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
q = rem_quo.quotient;
return rem_quo.remainder;
} else {
q = _num0();
- return _num0(); // Throw?
+ return _num0();
}
}
* 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)
+const numeric iquo(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
- return truncate1(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ return truncate1(cln::the<cln::cl_I>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
else
- return _num0(); // Throw?
+ return _num0();
}
*
* @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)
+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 (a.is_integer() && b.is_integer()) {
+ const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
r = rem_quo.remainder;
return rem_quo.quotient;
} else {
r = _num0();
- return _num0(); // Throw?
+ 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>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
else
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>(cln::cl_N(a)),
+ cln::the<cln::cl_I>(cln::cl_N(b)));
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(cln::cl_N(z));
+}
+
+
+/** 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>(cln::cl_N(x)), &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::_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);
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;
}
+/** Append global Digits object to ostream. */
void _numeric_digits::print(std::ostream & os) const
{
debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
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