#include <vector>
#include <stdexcept>
#include <string>
-
-#if defined(HAVE_SSTREAM)
#include <sstream>
-#elif defined(HAVE_STRSTREAM)
-#include <strstream>
-#else
-#error Need either sstream or strstream
-#endif
#include "numeric.h"
#include "ex.h"
+#include "print.h"
#include "archive.h"
-#include "debugmsg.h"
+#include "tostring.h"
#include "utils.h"
// CLN should pollute the global namespace as little as possible. Hence, we
GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
//////////
-// default ctor, dtor, copy ctor assignment
-// operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
//////////
-// public
-
/** default ctor. Numerically it initializes to an integer zero. */
numeric::numeric() : basic(TINFO_numeric)
{
- debugmsg("numeric default ctor", LOGLEVEL_CONSTRUCT);
value = cln::cl_I(0);
setflag(status_flags::evaluated | status_flags::expanded);
}
-// protected
-
-/** For use by copy ctor and assignment operator. */
void numeric::copy(const numeric &other)
{
inherited::copy(other);
value = other.value;
}
-void numeric::destroy(bool call_parent)
-{
- if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_DESTROY(numeric)
//////////
// other ctors
numeric::numeric(int i) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from int",LOGLEVEL_CONSTRUCT);
// Not the whole int-range is available if we don't cast to long
// first. This is due to the behaviour of the cl_I-ctor, which
// emphasizes efficiency. However, if the integer is small enough,
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from uint",LOGLEVEL_CONSTRUCT);
// Not the whole uint-range is available if we don't cast to ulong
// first. This is due to the behaviour of the cl_I-ctor, which
// emphasizes efficiency. However, if the integer is small enough,
numeric::numeric(long i) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from long",LOGLEVEL_CONSTRUCT);
value = cln::cl_I(i);
setflag(status_flags::evaluated | status_flags::expanded);
}
numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from ulong",LOGLEVEL_CONSTRUCT);
value = cln::cl_I(i);
setflag(status_flags::evaluated | status_flags::expanded);
}
* @exception overflow_error (division by zero) */
numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from long/long",LOGLEVEL_CONSTRUCT);
if (!denom)
throw std::overflow_error("division by zero");
value = cln::cl_I(numer) / cln::cl_I(denom);
numeric::numeric(double d) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from double",LOGLEVEL_CONSTRUCT);
// We really want to explicitly use the type cl_LF instead of the
// more general cl_F, since that would give us a cl_DF only which
// will not be promoted to cl_LF if overflow occurs:
* notation like "2+5*I". */
numeric::numeric(const char *s) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from string",LOGLEVEL_CONSTRUCT);
cln::cl_N ctorval = 0;
// parse complex numbers (functional but not completely safe, unfortunately
// std::string does not understand regexpese):
// ss should represent a simple sum like 2+5*I
- std::string ss(s);
- // make it safe by adding explicit sign
+ std::string ss = s;
+ std::string::size_type delim;
+
+ // make this implementation safe by adding explicit sign
if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#')
ss = '+' + ss;
- std::string::size_type delim;
+
+ // We use 'E' as exponent marker in the output, but some people insist on
+ // writing 'e' at input, so let's substitute them right at the beginning:
+ while ((delim = ss.find("e"))!=std::string::npos)
+ ss.replace(delim,1,"E");
+
+ // main parser loop:
do {
// chop ss into terms from left to right
std::string term;
bool imaginary = false;
delim = ss.find_first_of(std::string("+-"),1);
// Do we have an exponent marker like "31.415E-1"? If so, hop on!
- if ((delim != std::string::npos) && (ss.at(delim-1) == 'E'))
+ if (delim!=std::string::npos && ss.at(delim-1)=='E')
delim = ss.find_first_of(std::string("+-"),delim+1);
term = ss.substr(0,delim);
- if (delim != std::string::npos)
+ if (delim!=std::string::npos)
ss = ss.substr(delim);
// is the term imaginary?
- if (term.find("I") != std::string::npos) {
+ if (term.find("I")!=std::string::npos) {
// erase 'I':
- term = term.replace(term.find("I"),1,"");
+ term.erase(term.find("I"),1);
// erase '*':
- if (term.find("*") != std::string::npos)
- term = term.replace(term.find("*"),1,"");
+ if (term.find("*")!=std::string::npos)
+ term.erase(term.find("*"),1);
// correct for trivial +/-I without explicit factor on I:
- if (term.size() == 1)
- term += "1";
+ if (term.size()==1)
+ term += '1';
imaginary = true;
}
- if (term.find(".") != std::string::npos) {
+ if (term.find('.')!=std::string::npos || term.find('E')!=std::string::npos) {
// CLN's short type cl_SF is not very useful within the GiNaC
// framework where we are mainly interested in the arbitrary
// precision type cl_LF. Hence we go straight to the construction
// 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;
setflag(status_flags::evaluated | status_flags::expanded);
}
* only. */
numeric::numeric(const cln::cl_N &z) : basic(TINFO_numeric)
{
- debugmsg("numeric ctor from cl_N", LOGLEVEL_CONSTRUCT);
value = z;
setflag(status_flags::evaluated | status_flags::expanded);
}
// archiving
//////////
-/** Construct object from archive_node. */
numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("numeric ctor from archive_node", LOGLEVEL_CONSTRUCT);
cln::cl_N ctorval = 0;
// Read number as string
std::string str;
if (n.find_string("number", str)) {
-#ifdef HAVE_SSTREAM
std::istringstream s(str);
-#else
- std::istrstream s(str.c_str(), str.size() + 1);
-#endif
cln::cl_idecoded_float re, im;
char c;
s.get(c);
setflag(status_flags::evaluated | status_flags::expanded);
}
-/** Unarchive the object. */
-ex numeric::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
void numeric::archive(archive_node &n) const
{
inherited::archive(n);
// Write number as string
-#ifdef HAVE_SSTREAM
std::ostringstream s;
-#else
- char buf[1024];
- std::ostrstream s(buf, 1024);
-#endif
if (this->is_crational())
s << 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
//////////
/** Helper function to print a real number in a nicer way than is CLN's
* want to visibly distinguish from cl_LF.
*
* @see numeric::print() */
-static void print_real_number(std::ostream &os, const cln::cl_R &num)
+static void print_real_number(const print_context & c, const cln::cl_R &x)
{
cln::cl_print_flags ourflags;
- if (cln::instanceof(num, cln::cl_RA_ring)) {
- // case 1: integer or rational, nothing special to do:
- cln::print_real(os, ourflags, num);
+ if (cln::instanceof(x, cln::cl_RA_ring)) {
+ // case 1: integer or rational
+ if (cln::instanceof(x, cln::cl_I_ring) ||
+ !is_a<print_latex>(c)) {
+ cln::print_real(c.s, ourflags, x);
+ } else { // rational output in LaTeX context
+ c.s << "\\frac{";
+ cln::print_real(c.s, ourflags, cln::numerator(cln::the<cln::cl_RA>(x)));
+ c.s << "}{";
+ cln::print_real(c.s, ourflags, cln::denominator(cln::the<cln::cl_RA>(x)));
+ c.s << '}';
+ }
} else {
// case 2: float
// make CLN believe this number has default_float_format, so it prints
// 'E' as exponent marker instead of 'L':
- ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(num));
- cln::print_real(os, ourflags, num);
+ ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(x));
+ cln::print_real(c.s, ourflags, x);
}
- return;
}
/** This method adds to the output so it blends more consistently together
* with the other routines and produces something compatible to ginsh input.
*
* @see print_real_number() */
-void numeric::print(std::ostream &os, unsigned upper_precedence) const
-{
- debugmsg("numeric print", LOGLEVEL_PRINT);
- 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, r);
- os << ")";
+void numeric::print(const print_context & c, unsigned level) const
+{
+ if (is_a<print_tree>(c)) {
+
+ c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
+ << " (" << class_name() << ")"
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+
+ } else if (is_a<print_csrc>(c)) {
+
+ std::ios::fmtflags oldflags = c.s.flags();
+ c.s.setf(std::ios::scientific);
+ if (this->is_rational() && !this->is_integer()) {
+ if (compare(_num0) > 0) {
+ c.s << "(";
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "cln::cl_F(\"" << numer().evalf() << "\")";
+ else
+ c.s << numer().to_double();
+ } else {
+ c.s << "-(";
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "cln::cl_F(\"" << -numer().evalf() << "\")";
+ else
+ c.s << -numer().to_double();
+ }
+ c.s << "/";
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "cln::cl_F(\"" << denom().evalf() << "\")";
+ else
+ c.s << denom().to_double();
+ c.s << ")";
} else {
- print_real_number(os, r);
+ if (is_a<print_csrc_cl_N>(c))
+ c.s << "cln::cl_F(\"" << evalf() << "\")";
+ else
+ c.s << to_double();
}
+ c.s.flags(oldflags);
+
} 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)";
- }
+ const std::string par_open = is_a<print_latex>(c) ? "{(" : "(";
+ const std::string par_close = is_a<print_latex>(c) ? ")}" : ")";
+ const std::string imag_sym = is_a<print_latex>(c) ? "i" : "I";
+ const std::string mul_sym = is_a<print_latex>(c) ? " " : "*";
+ const cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
+ const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+ if (is_a<print_python_repr>(c))
+ c.s << class_name() << "('";
+ if (cln::zerop(i)) {
+ // case 1, real: x or -x
+ if ((precedence() <= level) && (!this->is_nonneg_integer())) {
+ c.s << par_open;
+ print_real_number(c, r);
+ c.s << par_close;
} else {
- if (i == 1) {
- os << "I";
- } else {
+ print_real_number(c, r);
+ }
+ } else {
+ if (cln::zerop(r)) {
+ // case 2, imaginary: y*I or -y*I
+ if ((precedence() <= level) && (i < 0)) {
if (i == -1) {
- os << "-I";
+ c.s << par_open+imag_sym+par_close;
} else {
- print_real_number(os, i);
- os << "*I";
+ c.s << par_open;
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym+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 (i < 0) {
- if (i == -1) {
- os << "-I";
} else {
- print_real_number(os, i);
- os << "*I";
+ if (i == 1) {
+ c.s << imag_sym;
+ } else {
+ if (i == -1) {
+ c.s << "-" << imag_sym;
+ } else {
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
+ }
}
} else {
- if (i == 1) {
- os << "+I";
+ // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
+ if (precedence() <= level)
+ c.s << par_open;
+ print_real_number(c, r);
+ if (i < 0) {
+ if (i == -1) {
+ c.s << "-"+imag_sym;
+ } else {
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
} else {
- os << "+";
- print_real_number(os, i);
- os << "*I";
+ if (i == 1) {
+ c.s << "+"+imag_sym;
+ } else {
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym+imag_sym;
+ }
}
+ if (precedence() <= level)
+ c.s << par_close;
}
- if (precedence <= upper_precedence)
- os << ")";
}
+ if (is_a<print_python_repr>(c))
+ c.s << "')";
}
}
-
-void numeric::printraw(std::ostream &os) 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 << class_name() << "(" << cln::the<cln::cl_N>(value) << ")";
-}
-
-
-void numeric::printtree(std::ostream &os, unsigned indent) 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;
-}
-
-
-void numeric::printcsrc(std::ostream &os, unsigned type, unsigned upper_precedence) 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 << ")";
- } else {
- if (type == csrc_types::ctype_cl_N)
- os << "cln::cl_F(\"" << evalf() << "\")";
- else
- os << to_double();
- }
- os.flags(oldflags);
-}
-
-
bool numeric::info(unsigned inf) const
{
switch (inf) {
* sign as a multiplicative factor. */
bool numeric::has(const ex &other) const
{
- if (!is_exactly_of_type(*other.bp, numeric))
+ if (!is_ex_exactly_of_type(other, numeric))
return false;
- const numeric &o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
+ const numeric &o = ex_to<numeric>(other);
if (this->is_equal(o) || this->is_equal(-o))
return true;
if (o.imag().is_zero()) // e.g. scan for 3 in -3*I
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
{
- 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);
}
const numeric numeric::add(const numeric &other) const
{
// Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num0p = &_num0();
- if (this==_num0p)
+ if (this==_num0_p)
return other;
- else if (&other==_num0p)
+ else if (&other==_num0_p)
return *this;
return numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value));
const numeric numeric::mul(const numeric &other) const
{
// Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num1p = &_num1();
- if (this==_num1p)
+ if (this==_num1_p)
return other;
- else if (&other==_num1p)
+ else if (&other==_num1_p)
return *this;
return numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value));
const numeric numeric::power(const numeric &other) const
{
// Efficiency shortcut: trap the neutral exponent by pointer.
- static const numeric * _num1p = &_num1();
- if (&other==_num1p)
+ if (&other==_num1_p)
return *this;
if (cln::zerop(cln::the<cln::cl_N>(value))) {
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
{
// Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num0p = &_num0();
- if (this==_num0p)
+ if (this==_num0_p)
return other;
- else if (&other==_num0p)
+ else if (&other==_num0_p)
return *this;
return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value)))->
const numeric &numeric::mul_dyn(const numeric &other) const
{
// Efficiency shortcut: trap the neutral element by pointer.
- static const numeric * _num1p = &_num1();
- if (this==_num1p)
+ if (this==_num1_p)
return other;
- else if (&other==_num1p)
+ else if (&other==_num1_p)
return *this;
return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value)))->
const numeric &numeric::power_dyn(const numeric &other) const
{
// Efficiency shortcut: trap the neutral exponent by pointer.
- static const numeric * _num1p=&_num1();
- if (&other==_num1p)
+ if (&other==_num1_p)
return *this;
if (cln::zerop(cln::the<cln::cl_N>(value))) {
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));
bool numeric::operator==(const numeric &other) const
{
- return equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+ return cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
}
bool numeric::operator!=(const numeric &other) const
{
- return !equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+ return !cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
}
const numeric numeric::denom(void) const
{
if (this->is_integer())
- return _num1();
+ return _num1;
- if (instanceof(value, cln::cl_RA_ring))
+ if (cln::instanceof(value, cln::cl_RA_ring))
return numeric(cln::denominator(cln::the<cln::cl_RA>(value)));
if (!this->is_real()) { // complex case, handle Q(i):
const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(cln::the<cln::cl_N>(value)));
const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(cln::the<cln::cl_N>(value)));
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
- return _num1();
+ return _num1;
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
return numeric(cln::denominator(i));
if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
return numeric(cln::lcm(cln::denominator(r), cln::denominator(i)));
}
// at least one float encountered
- return _num1();
+ return _num1;
}
return 0;
}
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned numeric::precedence = 30;
-
//////////
// global constants
//////////
{
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());
}
const numeric Li2(const numeric &x)
{
if (x.is_zero())
- return _num0();
+ return _num0;
// what is the desired float format?
// first guess: default format
if (cln::zerop(x.to_cl_N()-aux))
return cln::zeta(aux);
}
- std::clog << "zeta(" << x
- << "): Does anybody know a good way to calculate this numerically?"
- << std::endl;
- return numeric(0);
+ throw dunno();
}
* This is only a stub! */
const numeric lgamma(const numeric &x)
{
- std::clog << "lgamma(" << x
- << "): Does anybody know a good way to calculate this numerically?"
- << std::endl;
- return numeric(0);
+ throw dunno();
}
const numeric tgamma(const numeric &x)
{
- std::clog << "tgamma(" << x
- << "): Does anybody know a good way to calculate this numerically?"
- << std::endl;
- return numeric(0);
+ throw dunno();
}
* This is only a stub! */
const numeric psi(const numeric &x)
{
- std::clog << "psi(" << x
- << "): Does anybody know a good way to calculate this numerically?"
- << std::endl;
- return numeric(0);
+ throw dunno();
}
* This is only a stub! */
const numeric psi(const numeric &n, const numeric &x)
{
- std::clog << "psi(" << n << "," << x
- << "): Does anybody know a good way to calculate this numerically?"
- << std::endl;
- return numeric(0);
+ throw dunno();
}
* @exception range_error (argument must be integer >= -1) */
const numeric doublefactorial(const numeric &n)
{
- if (n.is_equal(_num_1()))
- return _num1();
+ if (n.is_equal(_num_1))
+ return _num1;
if (!n.is_nonneg_integer())
throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
{
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);
}
}
{
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;
+ 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;
+ }
+ for (unsigned p=next_r; p<=n; p+=2) {
+ cln::cl_I c = 1;
+ cln::cl_RA b = cln::cl_RA(1-p)/2;
+ const unsigned p3 = p+3;
+ const unsigned p2 = p+2;
+ const unsigned pm = p-2;
+ unsigned i, k;
+ for (i=2, k=0; i <= pm; i += 2, k++) {
+ c = cln::exquo(c * ((p3 - i)*(p2 - i)), (i - 1)*i);
+ b = b + c * results[k];
}
- B = (1 - ((B+1)/(2*i+3))) / (cln::cl_I(1)<<(2*i+2));
- results.push_back(B);
- ++highest_result;
+ results.push_back(-b / (p+1));
+ next_r += 2;
}
- return results[n/2];
+ return results[n/2 - 1];
}
// 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 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;
}
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;
}
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;
}
q = rem_quo.quotient;
return rem_quo.remainder;
} else {
- q = _num0();
- return _num0();
+ q = _num0;
+ return _num0;
}
}
const numeric iquo(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer())
- return truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N()));
else
- return _num0();
+ return _num0;
}
r = rem_quo.remainder;
return rem_quo.quotient;
} else {
- r = _num0();
- return _num0();
+ r = _num0;
+ return _num0;
}
}
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;
}
cln::isqrt(cln::the<cln::cl_I>(x.to_cl_N()), &root);
return root;
} else
- return _num0();
+ return _num0;
}
/** Append global Digits object to ostream. */
void _numeric_digits::print(std::ostream &os) const
{
- debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
os << digits;
}
git://www.ginac.de / ginac.git / blobdiff