/** default ctor. Numerically it initializes to an integer zero. */
numeric::numeric() : basic(TINFO_numeric)
{
- debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
- value = new cl_N;
- *value = cl_I(0);
- calchash();
- setflag(status_flags::evaluated |
- status_flags::expanded |
- status_flags::hash_calculated);
+ debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
+ value = new ::cl_N;
+ *value = ::cl_I(0);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
numeric::~numeric()
{
- debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT);
- destroy(0);
+ debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT);
+ destroy(false);
}
numeric::numeric(const numeric & other)
{
- debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT);
- copy(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(1);
- copy(other);
- }
- return *this;
+ 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 = new cl_N(*other.value);
+ basic::copy(other);
+ value = new ::cl_N(*other.value);
}
void numeric::destroy(bool call_parent)
{
- delete value;
- if (call_parent) basic::destroy(call_parent);
+ delete value;
+ if (call_parent) basic::destroy(call_parent);
}
//////////
numeric::numeric(int i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT);
- // Not the whole int-range is available if we don't cast to long
- // first. This is due to the behaviour of the cl_I-ctor, which
- // emphasizes efficiency:
- value = new cl_I((long) i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT);
+ // Not the whole int-range is available if we don't cast to long
+ // first. This is due to the behaviour of the cl_I-ctor, which
+ // emphasizes efficiency:
+ value = new ::cl_I((long) i);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
- // Not the whole uint-range is available if we don't cast to ulong
- // first. This is due to the behaviour of the cl_I-ctor, which
- // emphasizes efficiency:
- value = new cl_I((unsigned long)i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
+ // Not the whole uint-range is available if we don't cast to ulong
+ // first. This is due to the behaviour of the cl_I-ctor, which
+ // emphasizes efficiency:
+ value = new ::cl_I((unsigned long)i);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
numeric::numeric(long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
- value = new cl_I(i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
+ value = new ::cl_I(i);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
- value = new cl_I(i);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
+ value = new ::cl_I(i);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
/** Ctor for rational numerics a/b.
* @exception overflow_error (division by zero) */
numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
- if (!denom)
- throw (std::overflow_error("division by zero"));
- value = new cl_I(numer);
- *value = *value / cl_I(denom);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
+ if (!denom)
+ throw std::overflow_error("division by zero");
+ value = new ::cl_I(numer);
+ *value = *value / ::cl_I(denom);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
numeric::numeric(double d) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
- // We really want to explicitly use the type cl_LF instead of the
- // more general cl_F, since that would give us a cl_DF only which
- // will not be promoted to cl_LF if overflow occurs:
- value = new cl_N;
- *value = cl_float(d, cl_default_float_format);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
+ // We really want to explicitly use the type cl_LF instead of the
+ // more general cl_F, since that would give us a cl_DF only which
+ // will not be promoted to cl_LF if overflow occurs:
+ value = new cl_N;
+ *value = cl_float(d, cl_default_float_format);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
-
+/** 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)
-{ // MISSING: treatment of complex numbers
- debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
- if (strchr(s, '.'))
- value = new cl_LF(s);
- else
- value = new cl_R(s);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+{
+ debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
+ value = new ::cl_N(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
+ if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#')
+ ss = '+' + ss;
+ std::string::size_type delim;
+ 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'))
+ delim = ss.find_first_of(std::string("+-"),delim+1);
+ term = ss.substr(0,delim);
+ if (delim != std::string::npos)
+ ss = ss.substr(delim);
+ // is the term imaginary?
+ if (term.find("I") != std::string::npos) {
+ // erase 'I':
+ term = term.replace(term.find("I"),1,"");
+ // erase '*':
+ if (term.find("*") != std::string::npos)
+ term = term.replace(term.find("*"),1,"");
+ // correct for trivial +/-I without explicit factor on I:
+ if (term.size() == 1)
+ term += "1";
+ imaginary = true;
+ }
+ const char *cs = term.c_str();
+ // CLN's short types are not useful within the GiNaC framework, hence
+ // we go straight to the construction of a long float. Simply using
+ // cl_N(s) would require us to use add a CLN exponent mark, otherwise
+ // we would not be save from over-/underflows.
+ if (strchr(cs, '.'))
+ if (imaginary)
+ *value = *value + ::complex(cl_I(0),::cl_LF(cs));
+ else
+ *value = *value + ::cl_LF(cs);
+ else
+ if (imaginary)
+ *value = *value + ::complex(cl_I(0),::cl_R(cs));
+ else
+ *value = *value + ::cl_R(cs);
+ } while(delim != std::string::npos);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
/** Ctor from CLN types. This is for the initiated user or internal use
* only. */
numeric::numeric(const cl_N & z) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
- value = new cl_N(z);
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
+ value = new ::cl_N(z);
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
//////////
/** Construct object from archive_node. */
numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
- value = new cl_N;
+ debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
+ value = new ::cl_N;
- // Read number as string
- string str;
- if (n.find_string("number", str)) {
+ // Read number as string
+ std::string str;
+ if (n.find_string("number", str)) {
#ifdef HAVE_SSTREAM
- istringstream s(str);
+ std::istringstream s(str);
#else
- istrstream s(str.c_str(), str.size() + 1);
+ std::istrstream s(str.c_str(), str.size() + 1);
#endif
- 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);
- 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));
- break;
- default: // Ordinary number
+ ::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);
+ 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));
+ break;
+ default: // Ordinary number
s.putback(c);
- s >> *value;
- break;
- }
- }
- calchash();
- setflag(status_flags::evaluated|
- status_flags::hash_calculated);
+ s >> *value;
+ break;
+ }
+ }
+ calchash();
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
+ status_flags::hash_calculated);
}
/** Unarchive the object. */
ex numeric::unarchive(const archive_node &n, const lst &sym_lst)
{
- return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated);
+ return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated);
}
/** Archive the object. */
void numeric::archive(archive_node &n) const
{
- inherited::archive(n);
+ inherited::archive(n);
- // Write number as string
+ // Write number as string
#ifdef HAVE_SSTREAM
- ostringstream s;
+ std::ostringstream s;
#else
- char buf[1024];
- ostrstream s(buf, 1024);
+ char buf[1024];
+ std::ostrstream s(buf, 1024);
#endif
- if (this->is_crational())
- s << *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));
- 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)));
- s << "C";
- s << re.sign << " " << re.mantissa << " " << re.exponent << " ";
- s << im.sign << " " << im.mantissa << " " << im.exponent;
- }
- }
+ if (this->is_crational())
+ s << *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));
+ 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)));
+ s << "C";
+ s << re.sign << " " << re.mantissa << " " << re.exponent << " ";
+ s << im.sign << " " << im.mantissa << " " << im.exponent;
+ }
+ }
#ifdef HAVE_SSTREAM
- n.add_string("number", s.str());
+ n.add_string("number", s.str());
#else
s << ends;
- string str(buf);
+ std::string str(buf);
n.add_string("number", str);
#endif
}
basic * numeric::duplicate() const
{
- debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE);
- return new numeric(*this);
+ debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE);
+ return new numeric(*this);
}
* long as it only uses cl_LF and no other floating point types.
*
* @see numeric::print() */
-void print_real_number(ostream & os, const cl_R & num)
-{
- cl_print_flags ourflags;
- if (::instanceof(num, ::cl_RA_ring)) {
- // case 1: integer or rational, nothing special to do:
- ::print_real(os, ourflags, num);
- } 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);
- }
- return;
+static void print_real_number(std::ostream & os, const cl_R & num)
+{
+ cl_print_flags ourflags;
+ if (::instanceof(num, ::cl_RA_ring)) {
+ // case 1: integer or rational, nothing special to do:
+ ::print_real(os, ourflags, num);
+ } 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);
+ }
+ 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(ostream & os, unsigned upper_precedence) const
-{
- debugmsg("numeric print", LOGLEVEL_PRINT);
- if (this->is_real()) {
- // case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
- os << "(";
- print_real_number(os, The(cl_R)(*value));
- os << ")";
- } else {
- print_real_number(os, The(cl_R)(*value));
- }
- } else {
- // case 2, imaginary: y*I or -y*I
- if (::realpart(*value) == 0) {
- if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) {
- if (::imagpart(*value) == -1) {
- os << "(-I)";
- } else {
- os << "(";
- print_real_number(os, The(cl_R)(::imagpart(*value)));
- os << "*I)";
- }
- } else {
- if (::imagpart(*value) == 1) {
- os << "I";
- } else {
- if (::imagpart (*value) == -1) {
- os << "-I";
- } else {
- print_real_number(os, The(cl_R)(::imagpart(*value)));
- os << "*I";
- }
- }
- }
- } else {
- // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
- if (precedence <= upper_precedence)
- os << "(";
- print_real_number(os, The(cl_R)(::realpart(*value)));
- if (::imagpart(*value) < 0) {
- if (::imagpart(*value) == -1) {
- os << "-I";
- } else {
- print_real_number(os, The(cl_R)(::imagpart(*value)));
- os << "*I";
- }
- } else {
- if (::imagpart(*value) == 1) {
- os << "+I";
- } else {
- os << "+";
- print_real_number(os, The(cl_R)(::imagpart(*value)));
- os << "*I";
- }
- }
- if (precedence <= upper_precedence)
- os << ")";
- }
- }
-}
-
-
-void numeric::printraw(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 << "numeric(" << *value << ")";
-}
-
-
-void numeric::printtree(ostream & os, unsigned indent) const
-{
- debugmsg("numeric printtree", LOGLEVEL_PRINT);
- os << string(indent,' ') << *value
- << " (numeric): "
- << "hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")"
- << ", flags=" << flags << endl;
-}
-
-
-void numeric::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
-{
- debugmsg("numeric print csrc", LOGLEVEL_PRINT);
- ios::fmtflags oldflags = os.flags();
- os.setf(ios::scientific);
- if (this->is_rational() && !this->is_integer()) {
- if (compare(_num0()) > 0) {
- os << "(";
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << numer().evalf() << "\")";
- else
- os << numer().to_double();
- } else {
- os << "-(";
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << -numer().evalf() << "\")";
- else
- os << -numer().to_double();
- }
- os << "/";
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << denom().evalf() << "\")";
- else
- os << denom().to_double();
- os << ")";
- } else {
- if (type == csrc_types::ctype_cl_N)
- os << "cl_F(\"" << evalf() << "\")";
- else
- os << to_double();
- }
- os.flags(oldflags);
+void numeric::print(std::ostream & os, unsigned upper_precedence) const
+{
+ debugmsg("numeric print", LOGLEVEL_PRINT);
+ if (this->is_real()) {
+ // case 1, real: x or -x
+ if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
+ os << "(";
+ print_real_number(os, The(::cl_R)(*value));
+ os << ")";
+ } else {
+ print_real_number(os, The(::cl_R)(*value));
+ }
+ } else {
+ // case 2, imaginary: y*I or -y*I
+ if (::realpart(*value) == 0) {
+ if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) {
+ if (::imagpart(*value) == -1) {
+ os << "(-I)";
+ } else {
+ os << "(";
+ print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ os << "*I)";
+ }
+ } else {
+ if (::imagpart(*value) == 1) {
+ os << "I";
+ } else {
+ if (::imagpart (*value) == -1) {
+ os << "-I";
+ } else {
+ print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ os << "*I";
+ }
+ }
+ }
+ } else {
+ // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
+ if (precedence <= upper_precedence)
+ os << "(";
+ print_real_number(os, The(::cl_R)(::realpart(*value)));
+ if (::imagpart(*value) < 0) {
+ if (::imagpart(*value) == -1) {
+ os << "-I";
+ } else {
+ print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ os << "*I";
+ }
+ } else {
+ if (::imagpart(*value) == 1) {
+ os << "+I";
+ } else {
+ os << "+";
+ print_real_number(os, The(::cl_R)(::imagpart(*value)));
+ os << "*I";
+ }
+ }
+ if (precedence <= upper_precedence)
+ os << ")";
+ }
+ }
+}
+
+
+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 << "numeric(" << *value << ")";
+}
+
+
+void numeric::printtree(std::ostream & os, unsigned indent) const
+{
+ debugmsg("numeric printtree", LOGLEVEL_PRINT);
+ os << std::string(indent,' ') << *value
+ << " (numeric): "
+ << "hash=" << hashvalue
+ << " (0x" << std::hex << hashvalue << std::dec << ")"
+ << ", flags=" << flags << std::endl;
+}
+
+
+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);
+ if (this->is_rational() && !this->is_integer()) {
+ if (compare(_num0()) > 0) {
+ os << "(";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << numer().evalf() << "\")";
+ else
+ os << numer().to_double();
+ } else {
+ os << "-(";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << -numer().evalf() << "\")";
+ else
+ os << -numer().to_double();
+ }
+ os << "/";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << denom().evalf() << "\")";
+ else
+ os << denom().to_double();
+ os << ")";
+ } else {
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << evalf() << "\")";
+ else
+ os << to_double();
+ }
+ os.flags(oldflags);
}
bool numeric::info(unsigned inf) const
{
- switch (inf) {
- case info_flags::numeric:
- case info_flags::polynomial:
- case info_flags::rational_function:
- return true;
- case info_flags::real:
- return is_real();
- case info_flags::rational:
- case info_flags::rational_polynomial:
- return is_rational();
- case info_flags::crational:
- case info_flags::crational_polynomial:
- return is_crational();
- case info_flags::integer:
- case info_flags::integer_polynomial:
- return is_integer();
- case info_flags::cinteger:
- case info_flags::cinteger_polynomial:
- return is_cinteger();
- case info_flags::positive:
- return is_positive();
- case info_flags::negative:
- return is_negative();
- case info_flags::nonnegative:
- return !is_negative();
- case info_flags::posint:
- return is_pos_integer();
- case info_flags::negint:
- return is_integer() && is_negative();
- case info_flags::nonnegint:
- return is_nonneg_integer();
- case info_flags::even:
- return is_even();
- case info_flags::odd:
- return is_odd();
- case info_flags::prime:
- return is_prime();
- case info_flags::algebraic:
- return !is_real();
- }
- return false;
+ switch (inf) {
+ case info_flags::numeric:
+ case info_flags::polynomial:
+ case info_flags::rational_function:
+ return true;
+ case info_flags::real:
+ return is_real();
+ case info_flags::rational:
+ case info_flags::rational_polynomial:
+ return is_rational();
+ case info_flags::crational:
+ case info_flags::crational_polynomial:
+ return is_crational();
+ case info_flags::integer:
+ case info_flags::integer_polynomial:
+ return is_integer();
+ case info_flags::cinteger:
+ case info_flags::cinteger_polynomial:
+ return is_cinteger();
+ case info_flags::positive:
+ return is_positive();
+ case info_flags::negative:
+ return is_negative();
+ case info_flags::nonnegative:
+ return !is_negative();
+ case info_flags::posint:
+ return is_pos_integer();
+ case info_flags::negint:
+ return is_integer() && is_negative();
+ case info_flags::nonnegint:
+ return is_nonneg_integer();
+ case info_flags::even:
+ return is_even();
+ case info_flags::odd:
+ return is_odd();
+ case info_flags::prime:
+ return is_prime();
+ case info_flags::algebraic:
+ return !is_real();
+ }
+ return false;
}
/** Disassemble real part and imaginary part to scan for the occurrence of a
* sign as a multiplicative factor. */
bool numeric::has(const ex & other) const
{
- if (!is_exactly_of_type(*other.bp, numeric))
- return false;
- const numeric & o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
- if (this->is_equal(o) || this->is_equal(-o))
- return true;
- if (o.imag().is_zero()) // e.g. scan for 3 in -3*I
- return (this->real().is_equal(o) || this->imag().is_equal(o) ||
- this->real().is_equal(-o) || this->imag().is_equal(-o));
- else {
- if (o.is_equal(I)) // e.g scan for I in 42*I
- return !this->is_real();
- if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1
- return (this->real().has(o*I) || this->imag().has(o*I) ||
- this->real().has(-o*I) || this->imag().has(-o*I));
- }
- return false;
+ if (!is_exactly_of_type(*other.bp, numeric))
+ return false;
+ const numeric & o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
+ if (this->is_equal(o) || this->is_equal(-o))
+ return true;
+ if (o.imag().is_zero()) // e.g. scan for 3 in -3*I
+ return (this->real().is_equal(o) || this->imag().is_equal(o) ||
+ this->real().is_equal(-o) || this->imag().is_equal(-o));
+ else {
+ if (o.is_equal(I)) // e.g scan for I in 42*I
+ return !this->is_real();
+ if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1
+ return (this->real().has(o*I) || this->imag().has(o*I) ||
+ this->real().has(-o*I) || this->imag().has(-o*I));
+ }
+ return false;
}
/** Evaluation of numbers doesn't do anything at all. */
ex numeric::eval(int level) const
{
- // Warning: if this is ever gonna do something, the ex ctors from all kinds
- // of numbers should be checking for status_flags::evaluated.
- return this->hold();
+ // Warning: if this is ever gonna do something, the ex ctors from all kinds
+ // of numbers should be checking for status_flags::evaluated.
+ return this->hold();
}
/** Cast numeric into a floating-point object. For example exact numeric(1) is
* returned as a 1.0000000000000000000000 and so on according to how Digits is
- * currently set.
+ * currently set. In case the object already was a floating point number the
+ * precision is trimmed to match the currently set default.
*
- * @param level ignored, but needed for overriding basic::evalf.
+ * @param level ignored, only needed for overriding basic::evalf.
* @return an ex-handle to a numeric. */
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
+ // level can safely be discarded for numeric objects.
+ return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN
}
// protected
* @see ex::diff */
ex numeric::derivative(const symbol & s) const
{
- return _ex0();
+ 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_of_type(other, numeric));
+ const numeric & o = static_cast<numeric &>(const_cast<basic &>(other));
- if (*value == *o.value) {
- return 0;
- }
+ if (*value == *o.value) {
+ return 0;
+ }
- return compare(o);
+ return 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);
-
- return this->is_equal(*o);
+ GINAC_ASSERT(is_exactly_of_type(other,numeric));
+ const numeric *o = static_cast<const numeric *>(&other);
+
+ return this->is_equal(*o);
}
-unsigned numeric::calchash(void) const
-{
- return (hashvalue=cl_equal_hashcode(*value) | 0x80000000U);
- /*
- cout << *value << "->" << hashvalue << endl;
- hashvalue=HASHVALUE_NUMERIC+1000U;
- return HASHVALUE_NUMERIC+1000U;
- */
-}
-/*
unsigned numeric::calchash(void) const
{
- double d=to_double();
- int s=d>0 ? 1 : -1;
- d=fabs(d);
- if (d>0x07FF0000) {
- d=0x07FF0000;
- }
- return 0x88000000U+s*unsigned(d/0x07FF0000);
+ // 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);
}
-*/
//////////
* a new numeric object. */
numeric numeric::add(const numeric & other) const
{
- return numeric((*value)+(*other.value));
+ return numeric((*value)+(*other.value));
}
/** Numerical subtraction method. Subtracts argument from *this and returns
* result as a new numeric object. */
numeric numeric::sub(const numeric & other) const
{
- return numeric((*value)-(*other.value));
+ return numeric((*value)-(*other.value));
}
/** Numerical multiplication method. Multiplies *this and argument and returns
* result as a new numeric object. */
numeric numeric::mul(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
- if (this==_num1p) {
- return other;
- } else if (&other==_num1p) {
- return *this;
- }
- return numeric((*value)*(*other.value));
+ static const numeric * _num1p=&_num1();
+ if (this==_num1p) {
+ return other;
+ } else if (&other==_num1p) {
+ return *this;
+ }
+ return numeric((*value)*(*other.value));
}
/** Numerical division method. Divides *this by argument and returns result as
* @exception overflow_error (division by zero) */
numeric numeric::div(const numeric & other) const
{
- if (::zerop(*other.value))
- throw (std::overflow_error("division by zero"));
- return numeric((*value)/(*other.value));
+ if (::zerop(*other.value))
+ throw std::overflow_error("numeric::div(): division by zero");
+ return numeric((*value)/(*other.value));
}
numeric numeric::power(const numeric & other) const
{
- static const numeric * _num1p = &_num1();
- if (&other==_num1p)
- return *this;
- if (::zerop(*value)) {
- if (::zerop(*other.value))
- throw (std::domain_error("numeric::eval(): pow(0,0) is undefined"));
- else if (::zerop(::realpart(*other.value)))
- throw (std::domain_error("numeric::eval(): pow(0,I) is undefined"));
- else if (::minusp(::realpart(*other.value)))
- throw (std::overflow_error("numeric::eval(): division by zero"));
- else
- return _num0();
- }
- return numeric(::expt(*value,*other.value));
+ static const numeric * _num1p = &_num1();
+ if (&other==_num1p)
+ return *this;
+ if (::zerop(*value)) {
+ if (::zerop(*other.value))
+ throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
+ else if (::zerop(::realpart(*other.value)))
+ throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
+ else if (::minusp(::realpart(*other.value)))
+ throw std::overflow_error("numeric::eval(): division by zero");
+ else
+ return _num0();
+ }
+ return numeric(::expt(*value,*other.value));
}
/** Inverse of a number. */
numeric numeric::inverse(void) const
{
- return numeric(::recip(*value)); // -> CLN
+ 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)))->
- setflag(status_flags::dynallocated));
+ return static_cast<const numeric &>((new numeric((*value)+(*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)))->
- setflag(status_flags::dynallocated));
+ return static_cast<const numeric &>((new numeric((*value)-(*other.value)))->
+ setflag(status_flags::dynallocated));
}
const numeric & numeric::mul_dyn(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
- if (this==_num1p) {
- return other;
- } else if (&other==_num1p) {
- return *this;
- }
- return static_cast<const numeric &>((new numeric((*value)*(*other.value)))->
- setflag(status_flags::dynallocated));
+ static const numeric * _num1p=&_num1();
+ if (this==_num1p) {
+ return other;
+ } else if (&other==_num1p) {
+ return *this;
+ }
+ return static_cast<const numeric &>((new numeric((*value)*(*other.value)))->
+ setflag(status_flags::dynallocated));
}
const numeric & numeric::div_dyn(const numeric & other) const
{
- if (::zerop(*other.value))
- throw (std::overflow_error("division by zero"));
- return static_cast<const numeric &>((new numeric((*value)/(*other.value)))->
- setflag(status_flags::dynallocated));
+ if (::zerop(*other.value))
+ throw std::overflow_error("division by zero");
+ return static_cast<const numeric &>((new numeric((*value)/(*other.value)))->
+ setflag(status_flags::dynallocated));
}
const numeric & numeric::power_dyn(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
- if (&other==_num1p)
- return *this;
- if (::zerop(*value)) {
- if (::zerop(*other.value))
- throw (std::domain_error("numeric::eval(): pow(0,0) is undefined"));
- else if (::zerop(::realpart(*other.value)))
- throw (std::domain_error("numeric::eval(): pow(0,I) is undefined"));
- else if (::minusp(::realpart(*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));
+ static const numeric * _num1p=&_num1();
+ if (&other==_num1p)
+ return *this;
+ if (::zerop(*value)) {
+ if (::zerop(*other.value))
+ throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
+ else if (::zerop(::realpart(*other.value)))
+ throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
+ else if (::minusp(::realpart(*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));
}
const numeric & numeric::operator=(int i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
const numeric & numeric::operator=(unsigned int i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
const numeric & numeric::operator=(long i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
const numeric & numeric::operator=(unsigned long i)
{
- return operator=(numeric(i));
+ return operator=(numeric(i));
}
const numeric & numeric::operator=(double d)
{
- return operator=(numeric(d));
+ return operator=(numeric(d));
}
const numeric & numeric::operator=(const char * s)
{
- return operator=(numeric(s));
+ return operator=(numeric(s));
}
/** Return the complex half-plane (left or right) in which the number lies.
* @see numeric::compare(const numeric & other) */
int numeric::csgn(void) const
{
- if (this->is_zero())
- return 0;
- if (!::zerop(::realpart(*value))) {
- if (::plusp(::realpart(*value)))
- return 1;
- else
- return -1;
- } else {
- if (::plusp(::imagpart(*value)))
- return 1;
- else
- return -1;
- }
+ if (this->is_zero())
+ return 0;
+ if (!::zerop(::realpart(*value))) {
+ if (::plusp(::realpart(*value)))
+ return 1;
+ else
+ return -1;
+ } else {
+ if (::plusp(::imagpart(*value)))
+ return 1;
+ else
+ return -1;
+ }
}
/** This method establishes a canonical order on all numbers. For complex
* @see numeric::csgn(void) */
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));
- else {
- // No, first compare real parts
- cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value));
- if (real_cmp)
- return real_cmp;
+ // 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));
+ else {
+ // No, first compare real parts
+ cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value));
+ if (real_cmp)
+ return real_cmp;
- return ::cl_compare(::imagpart(*value), ::imagpart(*other.value));
- }
+ return ::cl_compare(::imagpart(*value), ::imagpart(*other.value));
+ }
}
bool numeric::is_equal(const numeric & other) const
{
- return (*value == *other.value);
+ return (*value == *other.value);
}
/** True if object is zero. */
bool numeric::is_zero(void) const
{
- return ::zerop(*value); // -> CLN
+ return ::zerop(*value); // -> CLN
}
/** 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 false;
+ if (this->is_real())
+ return ::plusp(The(::cl_R)(*value)); // -> CLN
+ 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 false;
+ if (this->is_real())
+ return ::minusp(The(::cl_R)(*value)); // -> CLN
+ return false;
}
/** True if object is a non-complex integer. */
bool numeric::is_integer(void) const
{
- return ::instanceof(*value, ::cl_I_ring); // -> CLN
+ return ::instanceof(*value, ::cl_I_ring); // -> CLN
}
/** 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() && ::plusp(The(::cl_I)(*value))); // -> CLN
}
/** 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() && !::minusp(The(::cl_I)(*value))); // -> CLN
}
/** 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() && ::evenp(The(::cl_I)(*value))); // -> CLN
}
/** 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() && ::oddp(The(::cl_I)(*value))); // -> CLN
}
/** 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() && ::isprobprime(The(::cl_I)(*value))); // -> CLN
}
/** 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 ::instanceof(*value, ::cl_RA_ring); // -> CLN
}
/** 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 ::instanceof(*value, ::cl_R_ring); // -> CLN
}
bool numeric::operator==(const numeric & other) const
{
- return (*value == *other.value); // -> CLN
+ return (*value == *other.value); // -> CLN
}
bool numeric::operator!=(const numeric & other) const
{
- return (*value != *other.value); // -> CLN
+ return (*value != *other.value); // -> CLN
}
/** 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))
- 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))
- return true;
- }
- return false;
+ if (::instanceof(*value, ::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))
+ 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))
- 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))
- return true;
- }
- return false;
+ if (::instanceof(*value, ::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))
+ 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
- throw (std::invalid_argument("numeric::operator<(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (The(::cl_R)(*value) < The(::cl_R)(*other.value)); // -> CLN
+ 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
- throw (std::invalid_argument("numeric::operator<=(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (The(::cl_R)(*value) <= The(::cl_R)(*other.value)); // -> CLN
+ 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
- throw (std::invalid_argument("numeric::operator>(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (The(::cl_R)(*value) > The(::cl_R)(*other.value)); // -> CLN
+ 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
- throw (std::invalid_argument("numeric::operator>=(): complex inequality"));
- return false; // make compiler shut up
+ if (this->is_real() && other.is_real())
+ return (The(::cl_R)(*value) >= The(::cl_R)(*other.value)); // -> CLN
+ throw std::invalid_argument("numeric::operator>=(): complex inequality");
}
/** Converts numeric types to machine's int. You should check with
* 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
+ GINAC_ASSERT(this->is_integer());
+ return ::cl_I_to_int(The(::cl_I)(*value)); // -> CLN
}
/** Converts numeric types to machine's long. You should check with
* 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
+ GINAC_ASSERT(this->is_integer());
+ return ::cl_I_to_long(The(::cl_I)(*value)); // -> CLN
}
/** 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
+ GINAC_ASSERT(this->is_real());
+ return ::cl_double_approx(::realpart(*value)); // -> CLN
}
/** Real part of a number. */
const numeric numeric::real(void) const
{
- return numeric(::realpart(*value)); // -> CLN
+ return numeric(::realpart(*value)); // -> CLN
}
/** Imaginary part of a number. */
const numeric numeric::imag(void) const
{
- return numeric(::imagpart(*value)); // -> CLN
+ return numeric(::imagpart(*value)); // -> CLN
}
#ifndef SANE_LINKER
// 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;
+ cl_I numerator;
+ cl_I denominator;
};
inline cl_heap_ratio* TheRatio (const cl_N& obj)
* cases. */
const numeric numeric::numer(void) const
{
- if (this->is_integer()) {
- return numeric(*this);
- }
+ 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 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 (!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*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))));
- }
- }
+ else if (instanceof(*value, ::cl_RA_ring)) {
+ return numeric(TheRatio(*value)->numerator);
+ }
+ 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*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))));
+ }
+ }
#endif // def SANE_LINKER
- // at least one float encountered
- return numeric(*this);
+ // at least one float encountered
+ return numeric(*this);
}
/** Denominator. Computes the denominator of rational numbers, common integer
* (i.e denom(4/3+5/6*I) == 6), one in all other cases. */
const numeric numeric::denom(void) const
{
- if (this->is_integer()) {
- return _num1();
- }
+ 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))));
- }
+ if (instanceof(*value, ::cl_RA_ring)) {
+ return numeric(::denominator(The(::cl_RA)(*value)));
+ }
+ if (!this->is_real()) { // complex case, handle Q(i):
+ cl_R r = ::realpart(*value);
+ cl_R i = ::imagpart(*value);
+ if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring))
+ return _num1();
+ if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring))
+ return numeric(::denominator(The(::cl_RA)(i)));
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring))
+ return numeric(::denominator(The(::cl_RA)(r)));
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring))
+ return numeric(::lcm(::denominator(The(::cl_RA)(r)), ::denominator(The(::cl_RA)(i))));
+ }
#else
- if (instanceof(*value, ::cl_RA_ring)) {
- return numeric(TheRatio(*value)->denominator);
- }
- if (!this->is_real()) { // complex case, handle Q(i):
- cl_R r = ::realpart(*value);
- cl_R i = ::imagpart(*value);
- if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
- return _num1();
- if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_RA_ring))
- return numeric(TheRatio(i)->denominator);
- if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring))
- return numeric(TheRatio(r)->denominator);
- if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring))
- return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
- }
+ if (instanceof(*value, ::cl_RA_ring)) {
+ return numeric(TheRatio(*value)->denominator);
+ }
+ if (!this->is_real()) { // complex case, handle Q(i):
+ cl_R r = ::realpart(*value);
+ cl_R i = ::imagpart(*value);
+ if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
+ return _num1();
+ if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_RA_ring))
+ return numeric(TheRatio(i)->denominator);
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring))
+ return numeric(TheRatio(r)->denominator);
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring))
+ return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
+ }
#endif // def SANE_LINKER
- // at least one float encountered
- return _num1();
+ // at least one float encountered
+ return _num1();
}
/** Size in binary notation. For integers, this is the smallest n >= 0 such
* in two's complement if it is an integer, 0 otherwise. */
int numeric::int_length(void) const
{
- if (this->is_integer())
- return ::integer_length(The(cl_I)(*value)); // -> CLN
- else
- return 0;
+ if (this->is_integer())
+ return ::integer_length(The(::cl_I)(*value)); // -> CLN
+ else
+ return 0;
}
* @return arbitrary precision numerical exp(x). */
const numeric exp(const numeric & x)
{
- return ::exp(*x.value); // -> CLN
+ return ::exp(*x.value); // -> CLN
}
*
* @param z complex number
* @return arbitrary precision numerical log(x).
- * @exception overflow_error (logarithmic singularity) */
+ * @exception pole_error("log(): logarithmic pole",0) */
const numeric log(const numeric & z)
{
- if (z.is_zero())
- throw (std::overflow_error("log(): logarithmic singularity"));
- return ::log(*z.value); // -> CLN
+ if (z.is_zero())
+ throw pole_error("log(): logarithmic pole",0);
+ return ::log(*z.value); // -> CLN
}
* @return arbitrary precision numerical sin(x). */
const numeric sin(const numeric & x)
{
- return ::sin(*x.value); // -> CLN
+ return ::sin(*x.value); // -> CLN
}
* @return arbitrary precision numerical cos(x). */
const numeric cos(const numeric & x)
{
- return ::cos(*x.value); // -> CLN
+ return ::cos(*x.value); // -> CLN
}
* @return arbitrary precision numerical tan(x). */
const numeric tan(const numeric & x)
{
- return ::tan(*x.value); // -> CLN
+ return ::tan(*x.value); // -> CLN
}
-
+
/** Numeric inverse sine (trigonometric function).
*
* @return arbitrary precision numerical asin(x). */
const numeric asin(const numeric & x)
{
- return ::asin(*x.value); // -> CLN
+ return ::asin(*x.value); // -> CLN
}
* @return arbitrary precision numerical acos(x). */
const numeric acos(const numeric & x)
{
- return ::acos(*x.value); // -> CLN
+ return ::acos(*x.value); // -> CLN
}
-
+
/** Arcustangent.
*
* @param z complex number
* @return atan(z)
- * @exception overflow_error (logarithmic singularity) */
+ * @exception pole_error("atan(): logarithmic pole",0) */
const numeric atan(const numeric & x)
{
- if (!x.is_real() &&
- x.real().is_zero() &&
- !abs(x.imag()).is_equal(_num1()))
- throw (std::overflow_error("atan(): logarithmic singularity"));
- return ::atan(*x.value); // -> CLN
+ if (!x.is_real() &&
+ x.real().is_zero() &&
+ abs(x.imag()).is_equal(_num1()))
+ throw pole_error("atan(): logarithmic pole",0);
+ return ::atan(*x.value); // -> CLN
}
* @return atan(y/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
- else
- throw (std::invalid_argument("numeric::atan(): complex argument"));
+ if (x.is_real() && y.is_real())
+ return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN
+ 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 ::sinh(*x.value); // -> CLN
}
* @return arbitrary precision numerical cosh(x). */
const numeric cosh(const numeric & x)
{
- return ::cosh(*x.value); // -> CLN
+ return ::cosh(*x.value); // -> CLN
}
* @return arbitrary precision numerical tanh(x). */
const numeric tanh(const numeric & x)
{
- return ::tanh(*x.value); // -> CLN
+ return ::tanh(*x.value); // -> CLN
}
-
+
/** Numeric inverse hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical asinh(x). */
const numeric asinh(const numeric & x)
{
- return ::asinh(*x.value); // -> CLN
+ return ::asinh(*x.value); // -> CLN
}
* @return arbitrary precision numerical acosh(x). */
const numeric acosh(const numeric & x)
{
- return ::acosh(*x.value); // -> CLN
+ return ::acosh(*x.value); // -> CLN
}
* @return arbitrary precision numerical atanh(x). */
const numeric atanh(const numeric & x)
{
- return ::atanh(*x.value); // -> CLN
+ return ::atanh(*x.value); // -> CLN
+}
+
+
+/*static ::cl_N Li2_series(const ::cl_N & x,
+ const ::cl_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;
+ // 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)
+ unsigned i = 1;
+ c1 = ::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));
+ acc = acc + aug;
+ ++i;
+ } while (acc != acc+aug);
+ return acc;
+}*/
+
+/** 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)
+{
+ // 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;
+ unsigned i = 1;
+ do {
+ num = num * x;
+ den = den + i; // 1, 4, 9, 16, ...
+ i += 2;
+ aug = num / den;
+ acc = acc + aug;
+ } while (acc != acc+aug);
+ return acc;
+}
+
+/** 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)
+{
+ const ::cl_R re = ::realpart(x);
+ const ::cl_R im = ::imagpart(x);
+ if (re > ::cl_F(".5"))
+ // zeta(2) - Li2(1-x) - log(x)*log(1-x)
+ return(::cl_zeta(2)
+ - Li2_series(1-x, prec)
+ - ::log(x)*::log(1-x));
+ if ((re <= 0 && ::abs(im) > ::cl_F(".75")) || (re < ::cl_F("-.5")))
+ // -log(1-x)^2 / 2 - Li2(x/(x-1))
+ return(- ::square(::log(1-x))/2
+ - Li2_series(x/(x-1), prec));
+ if (re > 0 && ::abs(im) > ::cl_LF(".75"))
+ // Li2(x^2)/2 - Li2(-x)
+ return(Li2_projection(::square(x), prec)/2
+ - Li2_projection(-x, prec));
+ return Li2_series(x, prec);
+}
+
+/** Numeric evaluation of Dilogarithm. The domain is the entire complex plane,
+ * the branch cut lies along the positive real axis, starting at 1 and
+ * continuous with quadrant IV.
+ *
+ * @return arbitrary precision numerical Li2(x). */
+const numeric Li2(const numeric & x)
+{
+ if (::zerop(*x.value))
+ return x;
+
+ // what is the desired float format?
+ // first guess: default format
+ ::cl_float_format_t prec = ::cl_default_float_format;
+ // 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.value==1) // may cause trouble with log(1-x)
+ return ::cl_zeta(2, prec);
+
+ if (::abs(*x.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));
+ else
+ return Li2_projection(*x.value, prec);
}
* integer arguments. */
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
- // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3
- // 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
- }
- clog << "zeta(" << x
- << "): Does anybody know good way to calculate this numerically?"
- << endl;
- return numeric(0);
+ // A dirty hack to allow for things like zeta(3.0), since CLN currently
+ // only knows about integer arguments and zeta(3).evalf() automatically
+ // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3
+ // 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
+ }
+ std::clog << "zeta(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << std::endl;
+ return numeric(0);
}
* This is only a stub! */
const numeric lgamma(const numeric & x)
{
- clog << "lgamma(" << x
- << "): Does anybody know good way to calculate this numerically?"
- << endl;
- return numeric(0);
+ std::clog << "lgamma(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << std::endl;
+ return numeric(0);
}
const numeric tgamma(const numeric & x)
{
- clog << "tgamma(" << x
- << "): Does anybody know good way to calculate this numerically?"
- << endl;
- return numeric(0);
+ std::clog << "tgamma(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << std::endl;
+ return numeric(0);
}
* This is only a stub! */
const numeric psi(const numeric & x)
{
- clog << "psi(" << x
- << "): Does anybody know good way to calculate this numerically?"
- << endl;
- return numeric(0);
+ std::clog << "psi(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << std::endl;
+ return numeric(0);
}
* This is only a stub! */
const numeric psi(const numeric & n, const numeric & x)
{
- clog << "psi(" << n << "," << x
- << "): Does anybody know good way to calculate this numerically?"
- << endl;
- return numeric(0);
+ std::clog << "psi(" << n << "," << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << std::endl;
+ return numeric(0);
}
* @exception range_error (argument must be integer >= 0) */
const numeric factorial(const numeric & n)
{
- if (!n.is_nonneg_integer())
- throw (std::range_error("numeric::factorial(): argument must be integer >= 0"));
- return numeric(::factorial(n.to_int())); // -> CLN
+ if (!n.is_nonneg_integer())
+ throw std::range_error("numeric::factorial(): argument must be integer >= 0");
+ return numeric(::factorial(n.to_int())); // -> CLN
}
* @exception range_error (argument must be integer >= -1) */
const numeric doublefactorial(const numeric & n)
{
- if (n == numeric(-1)) {
- return _num1();
- }
- if (!n.is_nonneg_integer()) {
- throw (std::range_error("numeric::doublefactorial(): argument must be integer >= -1"));
- }
- return numeric(::doublefactorial(n.to_int())); // -> CLN
+ if (n == numeric(-1)) {
+ return _num1();
+ }
+ if (!n.is_nonneg_integer()) {
+ throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
+ }
+ return numeric(::doublefactorial(n.to_int())); // -> CLN
}
* 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)
{
- 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
- else
- return _num0();
- } else {
- return _num_1().power(k)*binomial(k-n-_num1(),k);
- }
- }
-
- // should really be gamma(n+1)/(gamma(r+1)/gamma(n-r+1) or a suitable limit
- throw (std::range_error("numeric::binomial(): don´t know how to evaluate that."));
+ 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
+ else
+ return _num0();
+ } else {
+ return _num_1().power(k)*binomial(k-n-_num1(),k);
+ }
+ }
+
+ // should really be gamma(n+1)/gamma(r+1)/gamma(n-r+1) or a suitable limit
+ throw std::range_error("numeric::binomial(): don´t know how to evaluate that.");
}
* @exception range_error (argument must be integer >= 0) */
const numeric bernoulli(const numeric & nn)
{
- if (!nn.is_integer() || nn.is_negative())
- throw (std::range_error("numeric::bernoulli(): argument must be integer >= 0"));
- if (nn.is_zero())
- return _num1();
- if (!nn.compare(_num1()))
- return numeric(-1,2);
- if (nn.is_odd())
- return _num0();
- // Until somebody has the blues and comes up with a much better idea and
- // codes it (preferably in CLN) we make this a remembering function which
- // computes its results using the defining formula
- // B(nn) == - 1/(nn+1) * sum_{k=0}^{nn-1}(binomial(nn+1,k)*B(k))
- // whith B(0) == 1.
- // Be warned, though: the Bernoulli numbers are computationally very
- // expensive anyhow and you shouldn't expect miracles to happen.
- static vector<numeric> results;
- static int highest_result = -1;
- int n = nn.sub(_num2()).div(_num2()).to_int();
- if (n <= highest_result)
- return results[n];
- if (results.capacity() < (unsigned)(n+1))
- results.reserve(n+1);
-
- numeric tmp; // used to store the sum
- for (int i=highest_result+1; i<=n; ++i) {
- // the first two elements:
- tmp = numeric(-2*i-1,2);
- // accumulate the remaining elements:
- for (int j=0; j<i; ++j)
- tmp += binomial(numeric(2*i+3),numeric(j*2+2))*results[j];
- // divide by -(nn+1) and store result:
- results.push_back(-tmp/numeric(2*i+3));
- }
- highest_result=n;
- return results[n];
+ 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
+ // the relation
+ //
+ // B_n = - 1/(n+1) * sum_{k=0}^{n-1}(binomial(n+1,k)*B_k)
+ //
+ // with B(0) = 1. Since the n'th Bernoulli number depends on all the
+ // previous ones, the computation is necessarily very expensive. There are
+ // several other ways of computing them, a particularly good one being
+ // cl_I s = 1;
+ // cl_I c = n+1;
+ // cl_RA Bern = 0;
+ // for (unsigned i=0; i<n; i++) {
+ // c = exquo(c*(i-n),(i+2));
+ // Bern = Bern + c*s/(i+2);
+ // s = s + expt_pos(cl_I(i+2),n);
+ // }
+ // return Bern;
+ //
+ // 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().
+ //
+ // (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
+ // addition to the remember table. This doubles the memory footprint so
+ // we don't use it.)
+
+ // the special cases not covered by the algorithm below
+ if (nn.is_equal(_num1()))
+ return _num_1_2();
+ if (nn.is_odd())
+ return _num0();
+
+ // store nonvanishing Bernoulli numbers here
+ static std::vector< ::cl_RA > results;
+ static int highest_result = 0;
+ // algorithm not applicable to B(0), so just store it
+ if (results.size()==0)
+ results.push_back(::cl_RA(1));
+
+ int n = nn.to_long();
+ for (int i=highest_result; i<n/2; ++i) {
+ ::cl_RA B = 0;
+ long n = 8;
+ long m = 5;
+ long d1 = i;
+ long d2 = 2*i-1;
+ for (int j=i; j>0; --j) {
+ B = ::cl_I(n*m) * (B+results[j]) / (d1*d2);
+ n += 4;
+ m += 2;
+ d1 -= 1;
+ d2 -= 2;
+ }
+ B = (1 - ((B+1)/(2*i+3))) / (::cl_I(1)<<(2*i+2));
+ results.push_back(B);
+ ++highest_result;
+ }
+ return results[n/2];
}
* @exception range_error (argument must be an integer) */
const numeric fibonacci(const numeric & n)
{
- if (!n.is_integer())
- throw (std::range_error("numeric::fibonacci(): argument must be integer"));
- // The following addition formula holds:
- // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0.
- // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence
- // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values
- // agree.)
- // Replace m by m+1:
- // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0
- // Now put in m = n, to get
- // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n))
- // F(2n+1) = F(n)^2 + F(n+1)^2
- // hence
- // F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
- if (n.is_zero())
- return _num0();
- if (n.is_negative())
- if (n.is_even())
- return -fibonacci(-n);
- else
- return fibonacci(-n);
-
- cl_I u(0);
- cl_I v(1);
- cl_I m = The(cl_I)(*n.value) >> 1L; // floor(n/2);
- for (uintL bit=::integer_length(m); bit>0; --bit) {
- // 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;
- u = u2 + v2;
- } else {
- u = v2 - ::square(v - u);
- v = u2 + v2;
- }
- }
- if (n.is_even())
- // Here we don't use the squaring formula because one multiplication
- // is cheaper than two squarings.
- return u * ((v << 1) - u);
- else
- return ::square(u) + ::square(v);
+ if (!n.is_integer())
+ throw std::range_error("numeric::fibonacci(): argument must be integer");
+ // Method:
+ //
+ // This is based on an implementation that can be found in CLN's example
+ // directory. There, it is done recursively, which may be more elegant
+ // than our non-recursive implementation that has to resort to some bit-
+ // fiddling. This is, however, a matter of taste.
+ // The following addition formula holds:
+ //
+ // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0.
+ //
+ // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence
+ // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values
+ // agree.)
+ // Replace m by m+1:
+ // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0
+ // Now put in m = n, to get
+ // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n))
+ // F(2n+1) = F(n)^2 + F(n+1)^2
+ // hence
+ // F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
+ if (n.is_zero())
+ return _num0();
+ if (n.is_negative())
+ if (n.is_even())
+ return -fibonacci(-n);
+ else
+ return fibonacci(-n);
+
+ ::cl_I u(0);
+ ::cl_I v(1);
+ ::cl_I m = The(::cl_I)(*n.value) >> 1L; // floor(n/2);
+ for (uintL bit=::integer_length(m); bit>0; --bit) {
+ // 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;
+ u = u2 + v2;
+ } else {
+ u = v2 - ::square(v - u);
+ v = u2 + v2;
+ }
+ }
+ if (n.is_even())
+ // Here we don't use the squaring formula because one multiplication
+ // is cheaper than two squarings.
+ return u * ((v << 1) - u);
+ else
+ return ::square(u) + ::square(v);
}
/** Absolute value. */
numeric abs(const numeric & x)
{
- return ::abs(*x.value); // -> CLN
+ return ::abs(*x.value); // -> CLN
}
* integer, 0 otherwise. */
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
- else
- return _num0(); // Throw?
+ if (a.is_integer() && b.is_integer())
+ return ::mod(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ else
+ return _num0(); // Throw?
}
* @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
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) / 2)) - 1;
- return ::mod(The(cl_I)(*a.value) + b2, The(cl_I)(*b.value)) - b2;
- } else
- return _num0(); // Throw?
+ 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;
+ } else
+ return _num0(); // Throw?
}
* @return remainder of a/b if both are integer, 0 otherwise. */
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
- else
- return _num0(); // Throw?
+ if (a.is_integer() && b.is_integer())
+ return ::rem(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ else
+ return _num0(); // Throw?
}
* 0 otherwise. */
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));
- q = rem_quo.quotient;
- return rem_quo.remainder;
- }
- else {
- q = _num0();
- return _num0(); // Throw?
- }
+ 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));
+ q = rem_quo.quotient;
+ return rem_quo.remainder;
+ } else {
+ q = _num0();
+ return _num0(); // Throw?
+ }
}
* @return truncated quotient of a/b if both are integer, 0 otherwise. */
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
- else
- return _num0(); // Throw?
+ if (a.is_integer() && b.is_integer())
+ return truncate1(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ else
+ return _num0(); // Throw?
}
* integer, 0 otherwise. */
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));
- r = rem_quo.remainder;
- return rem_quo.quotient;
- } else {
- r = _num0();
- return _num0(); // Throw?
- }
+ 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));
+ r = rem_quo.remainder;
+ return rem_quo.quotient;
+ } else {
+ r = _num0();
+ return _num0(); // Throw?
+ }
}
* where imag(z)>0. */
numeric sqrt(const numeric & z)
{
- return ::sqrt(*z.value); // -> CLN
+ 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?
+ if (x.is_integer()) {
+ cl_I root;
+ ::isqrt(The(::cl_I)(*x.value), &root); // -> CLN
+ return root;
+ } else
+ return _num0(); // Throw?
}
* if they are not. */
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
- else
- return _num1();
+ if (a.is_integer() && b.is_integer())
+ return ::gcd(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ else
+ return _num1();
}
* two numbers if they are not. */
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
- else
- return *a.value * *b.value;
+ if (a.is_integer() && b.is_integer())
+ return ::lcm(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN
+ else
+ return *a.value * *b.value;
}
/** Floating point evaluation of Archimedes' constant Pi. */
ex PiEvalf(void)
{
- return numeric(::cl_pi(cl_default_float_format)); // -> CLN
+ return numeric(::cl_pi(cl_default_float_format)); // -> CLN
}
/** Floating point evaluation of Euler's constant gamma. */
ex EulerEvalf(void)
{
- return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN
+ return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN
}
/** Floating point evaluation of Catalan's constant. */
ex CatalanEvalf(void)
{
- return numeric(::cl_catalanconst(cl_default_float_format)); // -> CLN
+ return numeric(::cl_catalanconst(cl_default_float_format)); // -> CLN
}
// 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)
+ : digits(17)
{
- assert(!too_late);
- too_late = true;
- cl_default_float_format = ::cl_float_format(17);
+ assert(!too_late);
+ too_late = true;
+ cl_default_float_format = ::cl_float_format(17);
}
_numeric_digits& _numeric_digits::operator=(long prec)
{
- digits=prec;
- cl_default_float_format = ::cl_float_format(prec);
- return *this;
+ digits=prec;
+ cl_default_float_format = ::cl_float_format(prec);
+ return *this;
}
_numeric_digits::operator long()
{
- return (long)digits;
+ return (long)digits;
}
-void _numeric_digits::print(ostream & os) const
+void _numeric_digits::print(std::ostream & os) const
{
- debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
- os << digits;
+ debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
+ os << digits;
}
-ostream& operator<<(ostream& os, const _numeric_digits & e)
+std::ostream& operator<<(std::ostream& os, const _numeric_digits & e)
{
- e.print(os);
- return os;
+ e.print(os);
+ return os;
}
//////////
git://www.ginac.de / ginac.git / blobdiff