X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=bfa00af6a1b7e81432d3184ec3f4b0c3da70699c;hp=c189c3d7387faccacff265193f2d198dee8dfdcb;hb=d8452c110d6f725c569b8b151d3c78f6e8834536;hpb=6b3768e8c544739ae53321539cb4d1e3112ded1b diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp index c189c3d7..bfa00af6 100644 --- a/ginac/numeric.cpp +++ b/ginac/numeric.cpp @@ -6,22 +6,84 @@ * provide implementation of arithmetic operators and numerical evaluation * of special functions or implement the interface to the bignum package. */ +/* + * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + */ + +#include "config.h" + #include #include +#include -#include "ginac.h" +#if defined(HAVE_SSTREAM) +#include +#elif defined(HAVE_STRSTREAM) +#include +#else +#error Need either sstream or strstream +#endif + +#include "numeric.h" +#include "ex.h" +#include "archive.h" +#include "debugmsg.h" +#include "utils.h" // CLN should not pollute the global namespace, hence we include it here -// instead of in some header file where it would propagate to other parts: +// instead of in some header file where it would propagate to other parts. +// Also, we only need a subset of CLN, so we don't include the complete cln.h: #ifdef HAVE_CLN_CLN_H -#include -#else -#include -#endif +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#else // def HAVE_CLN_CLN_H +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#endif // def HAVE_CLN_CLN_H + +#ifndef NO_NAMESPACE_GINAC +namespace GiNaC { +#endif // ndef NO_NAMESPACE_GINAC // linker has no problems finding text symbols for numerator or denominator //#define SANE_LINKER +GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic) + ////////// // default constructor, destructor, copy constructor assignment // operator and helpers @@ -30,13 +92,14 @@ // public /** default ctor. Numerically it initializes to an integer zero. */ -numeric::numeric() : basic(TINFO_NUMERIC) +numeric::numeric() : basic(TINFO_numeric) { debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT); - value = new cl_N; - *value=cl_I(0); + value = new ::cl_N; + *value = ::cl_I(0); calchash(); - setflag(status_flags::evaluated| + setflag(status_flags::evaluated | + status_flags::expanded | status_flags::hash_calculated); } @@ -46,13 +109,13 @@ numeric::~numeric() destroy(0); } -numeric::numeric(numeric const & other) +numeric::numeric(const numeric & other) { debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT); copy(other); } -numeric const & numeric::operator=(numeric const & other) +const numeric & numeric::operator=(const numeric & other) { debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT); if (this != &other) { @@ -64,10 +127,10 @@ numeric const & numeric::operator=(numeric const & other) // protected -void numeric::copy(numeric const & other) +void numeric::copy(const numeric & other) { basic::copy(other); - value = new cl_N(*other.value); + value = new ::cl_N(*other.value); } void numeric::destroy(bool call_parent) @@ -82,43 +145,46 @@ void numeric::destroy(bool call_parent) // public -numeric::numeric(int i) : basic(TINFO_NUMERIC) +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 + // first. This is due to the behaviour of the cl_I-ctor, which // emphasizes efficiency: - value = new cl_I((long) i); + value = new ::cl_I((long) i); calchash(); setflag(status_flags::evaluated| status_flags::hash_calculated); } -numeric::numeric(unsigned int i) : basic(TINFO_NUMERIC) + +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 + // first. This is due to the behaviour of the cl_I-ctor, which // emphasizes efficiency: - value = new cl_I((unsigned long)i); + value = new ::cl_I((unsigned long)i); calchash(); setflag(status_flags::evaluated| status_flags::hash_calculated); } -numeric::numeric(long i) : basic(TINFO_NUMERIC) + +numeric::numeric(long i) : basic(TINFO_numeric) { debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT); - value = new cl_I(i); + value = new ::cl_I(i); calchash(); setflag(status_flags::evaluated| status_flags::hash_calculated); } -numeric::numeric(unsigned long i) : basic(TINFO_NUMERIC) + +numeric::numeric(unsigned long i) : basic(TINFO_numeric) { debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT); - value = new cl_I(i); + value = new ::cl_I(i); calchash(); setflag(status_flags::evaluated| status_flags::hash_calculated); @@ -127,19 +193,20 @@ numeric::numeric(unsigned long i) : basic(TINFO_NUMERIC) /** Ctor for rational numerics a/b. * * @exception overflow_error (division by zero) */ -numeric::numeric(long numer, long denom) : basic(TINFO_NUMERIC) +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); + 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); } -numeric::numeric(double d) : basic(TINFO_NUMERIC) + +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 @@ -152,13 +219,61 @@ numeric::numeric(double d) : basic(TINFO_NUMERIC) status_flags::hash_calculated); } -numeric::numeric(char const *s) : basic(TINFO_NUMERIC) -{ // MISSING: treatment of complex and ints and rationals. + +/** ctor from C-style string. It also accepts complex numbers in GiNaC + * notation like "2+5*I". */ +numeric::numeric(const char *s) : basic(TINFO_numeric) +{ debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT); - if (strchr(s, '.')) - value = new cl_LF(s); - else - value = new cl_I(s); + 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::hash_calculated); @@ -166,15 +281,102 @@ numeric::numeric(char const *s) : basic(TINFO_NUMERIC) /** Ctor from CLN types. This is for the initiated user or internal use * only. */ -numeric::numeric(cl_N const & z) : basic(TINFO_NUMERIC) +numeric::numeric(const cl_N & z) : basic(TINFO_numeric) { debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT); - value = new cl_N(z); + value = new ::cl_N(z); + calchash(); + setflag(status_flags::evaluated| + status_flags::hash_calculated); +} + +////////// +// archiving +////////// + +/** Construct object from archive_node. */ +numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +{ + debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT); + value = new ::cl_N; + + // Read number as string + std::string str; + if (n.find_string("number", str)) { +#ifdef HAVE_SSTREAM + std::istringstream s(str); +#else + std::istrstream s(str.c_str(), str.size() + 1); +#endif + ::cl_idecoded_float re, im; + 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); } +/** 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 << *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()); +#else + s << ends; + std::string str(buf); + n.add_string("number", str); +#endif +} + ////////// // functions overriding virtual functions from bases classes ////////// @@ -187,139 +389,260 @@ basic * numeric::duplicate() const return new numeric(*this); } -// The method printraw doesn't do much, it simply uses CLN's operator<<() for -// output, which is ugly but reliable. Examples: -// 2+2i -void numeric::printraw(ostream & os) const + +/** Helper function to print a real number in a nicer way than is CLN's + * default. Instead of printing 42.0L0 this just prints 42.0 to ostream os + * and instead of 3.99168L7 it prints 3.99168E7. This is fine in GiNaC as + * long as it only uses cl_LF and no other floating point types. + * + * @see numeric::print() */ +static void print_real_number(std::ostream & os, const cl_R & num) { - debugmsg("numeric printraw", LOGLEVEL_PRINT); - os << "numeric(" << *value << ")"; + 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; } -// The method print adds to the output so it blends more consistently together -// with the other routines. -void numeric::print(ostream & os, unsigned upper_precedence) const +/** This method adds to the output so it blends more consistently together + * with the other routines and produces something compatible to ginsh input. + * + * @see print_real_number() */ +void numeric::print(std::ostream & os, unsigned upper_precedence) const { debugmsg("numeric print", LOGLEVEL_PRINT); - if (is_real()) { + if (this->is_real()) { // case 1, real: x or -x - if ((realpart(*value) < 0) && (precedence <= upper_precedence)) { - os << "(" << *value << ")"; + if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) { + os << "("; + print_real_number(os, The(::cl_R)(*value)); + os << ")"; } else { - os << *value; + print_real_number(os, The(::cl_R)(*value)); } } else { // case 2, imaginary: y*I or -y*I - if (realpart(*value) == 0) { - if ((imagpart(*value) < 0) && (precedence <= upper_precedence)) { - if (imagpart(*value) == -1) { + if (::realpart(*value) == 0) { + if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) { + if (::imagpart(*value) == -1) { os << "(-I)"; } else { - os << "(" << imagpart(*value) << "*I)"; + os << "("; + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I)"; } } else { - if (imagpart(*value) == 1) { + if (::imagpart(*value) == 1) { os << "I"; } else { - if (imagpart (*value) == -1) { + if (::imagpart (*value) == -1) { os << "-I"; } else { - os << imagpart(*value) << "*I"; + 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 ((realpart(*value) < 0) && (precedence <= upper_precedence)) { - os << "(" << realpart(*value); - if (imagpart(*value) < 0) { - if (imagpart(*value) == -1) { - os << "-I)"; - } else { - os << imagpart(*value) << "*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 { - if (imagpart(*value) == 1) { - os << "+I)"; - } else { - os << "+" << imagpart(*value) << "*I)"; - } + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I"; } } else { - os << realpart(*value); - if (imagpart(*value) < 0) { - if (imagpart(*value) == -1) { - os << "-I"; - } else { - os << imagpart(*value) << "*I"; - } + if (::imagpart(*value) == 1) { + os << "+I"; } else { - if (imagpart(*value) == 1) { - os << "+I"; - } else { - os << "+" << imagpart(*value) << "*I"; - } + 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: + 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 + * single number. Also handles the imaginary unit. It ignores the sign on + * both this and the argument, which may lead to what might appear as funny + * results: (2+I).has(-2) -> true. But this is consistent, since we also + * would like to have (-2+I).has(2) -> true and we want to think about the + * sign as a multiplicative factor. */ +bool numeric::has(const ex & other) const +{ + if (!is_exactly_of_type(*other.bp, numeric)) + return false; + const numeric & o = static_cast(const_cast(*other.bp)); + if (this->is_equal(o) || this->is_equal(-o)) return true; - case info_flags::real: - return is_real(); - case info_flags::rational: - case info_flags::rational_polynomial: - return is_rational(); - case info_flags::integer: - case info_flags::integer_polynomial: - return is_integer(); - case info_flags::positive: - return is_positive(); - case info_flags::negative: - return is_negative(); - case info_flags::nonnegative: - return compare(numZERO())>=0; - case info_flags::posint: - return is_pos_integer(); - case info_flags::negint: - return is_integer() && (compare(numZERO())<0); - 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(); + 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(); +} + + /** 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. - * @return an ex-handle to a numeric. */ + * @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 + return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN } // protected -int numeric::compare_same_type(basic const & other) const +/** Implementation of ex::diff() for a numeric. It always returns 0. + * + * @see ex::diff */ +ex numeric::derivative(const symbol & s) const +{ + return _ex0(); +} + + +int numeric::compare_same_type(const basic & other) const { - ASSERT(is_exactly_of_type(other, numeric)); - numeric const & o = static_cast(const_cast(other)); + GINAC_ASSERT(is_exactly_of_type(other, numeric)); + const numeric & o = static_cast(const_cast(other)); if (*value == *o.value) { return 0; @@ -328,26 +651,23 @@ int numeric::compare_same_type(basic const & other) const return compare(o); } -bool numeric::is_equal_same_type(basic const & other) const + +bool numeric::is_equal_same_type(const basic & other) const { - ASSERT(is_exactly_of_type(other,numeric)); - numeric const *o = static_cast(&other); + GINAC_ASSERT(is_exactly_of_type(other,numeric)); + const numeric *o = static_cast(&other); - return is_equal(*o); + return this->is_equal(*o); } -/* + 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); } -*/ ////////// @@ -364,26 +684,26 @@ unsigned numeric::calchash(void) const /** Numerical addition method. Adds argument to *this and returns result as * a new numeric object. */ -numeric numeric::add(numeric const & other) const +numeric numeric::add(const numeric & other) const { return numeric((*value)+(*other.value)); } /** Numerical subtraction method. Subtracts argument from *this and returns * result as a new numeric object. */ -numeric numeric::sub(numeric const & other) const +numeric numeric::sub(const numeric & other) const { return numeric((*value)-(*other.value)); } /** Numerical multiplication method. Multiplies *this and argument and returns * result as a new numeric object. */ -numeric numeric::mul(numeric const & other) const +numeric numeric::mul(const numeric & other) const { - static const numeric * numONEp=&numONE(); - if (this==numONEp) { + static const numeric * _num1p=&_num1(); + if (this==_num1p) { return other; - } else if (&other==numONEp) { + } else if (&other==_num1p) { return *this; } return numeric((*value)*(*other.value)); @@ -393,141 +713,164 @@ numeric numeric::mul(numeric const & other) const * a new numeric object. * * @exception overflow_error (division by zero) */ -numeric numeric::div(numeric const & other) const +numeric numeric::div(const numeric & other) const { - if (zerop(*other.value)) - throw (std::overflow_error("division by zero")); + if (::zerop(*other.value)) + throw std::overflow_error("division by zero"); return numeric((*value)/(*other.value)); } -numeric numeric::power(numeric const & other) const +numeric numeric::power(const numeric & other) const { - static const numeric * numONEp=&numONE(); - if (&other==numONEp) { + 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(); } - if (zerop(*value) && other.is_real() && minusp(realpart(*other.value))) - throw (std::overflow_error("division by zero")); - return numeric(expt(*value,*other.value)); + return numeric(::expt(*value,*other.value)); } /** Inverse of a number. */ numeric numeric::inverse(void) const { - return numeric(recip(*value)); // -> CLN + return numeric(::recip(*value)); // -> CLN } -numeric const & numeric::add_dyn(numeric const & other) const +const numeric & numeric::add_dyn(const numeric & other) const { - return static_cast((new numeric((*value)+(*other.value)))-> + return static_cast((new numeric((*value)+(*other.value)))-> setflag(status_flags::dynallocated)); } -numeric const & numeric::sub_dyn(numeric const & other) const +const numeric & numeric::sub_dyn(const numeric & other) const { - return static_cast((new numeric((*value)-(*other.value)))-> + return static_cast((new numeric((*value)-(*other.value)))-> setflag(status_flags::dynallocated)); } -numeric const & numeric::mul_dyn(numeric const & other) const +const numeric & numeric::mul_dyn(const numeric & other) const { - static const numeric * numONEp=&numONE(); - if (this==numONEp) { + static const numeric * _num1p=&_num1(); + if (this==_num1p) { return other; - } else if (&other==numONEp) { + } else if (&other==_num1p) { return *this; } - return static_cast((new numeric((*value)*(*other.value)))-> + return static_cast((new numeric((*value)*(*other.value)))-> setflag(status_flags::dynallocated)); } -numeric const & numeric::div_dyn(numeric const & other) const +const numeric & numeric::div_dyn(const numeric & other) const { - if (zerop(*other.value)) - throw (std::overflow_error("division by zero")); - return static_cast((new numeric((*value)/(*other.value)))-> + if (::zerop(*other.value)) + throw std::overflow_error("division by zero"); + return static_cast((new numeric((*value)/(*other.value)))-> setflag(status_flags::dynallocated)); } -numeric const & numeric::power_dyn(numeric const & other) const +const numeric & numeric::power_dyn(const numeric & other) const { - static const numeric * numONEp=&numONE(); - if (&other==numONEp) { + 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(); } - // The ifs are only a workaround for a bug in CLN. It gets stuck otherwise: - if ( !other.is_integer() && - other.is_rational() && - (*this).is_nonneg_integer() ) { - if ( !zerop(*value) ) { - return static_cast((new numeric(exp(*other.value * log(*value))))-> - setflag(status_flags::dynallocated)); - } else { - if ( !zerop(*other.value) ) { // 0^(n/m) - return static_cast((new numeric(0))-> - setflag(status_flags::dynallocated)); - } else { // raise FPE (0^0 requested) - return static_cast((new numeric(1/(*other.value)))-> - setflag(status_flags::dynallocated)); - } - } - } else { // default -> CLN - return static_cast((new numeric(expt(*value,*other.value)))-> - setflag(status_flags::dynallocated)); - } + return static_cast((new numeric(::expt(*value,*other.value)))-> + setflag(status_flags::dynallocated)); } -numeric const & numeric::operator=(int i) +const numeric & numeric::operator=(int i) { return operator=(numeric(i)); } -numeric const & numeric::operator=(unsigned int i) +const numeric & numeric::operator=(unsigned int i) { return operator=(numeric(i)); } -numeric const & numeric::operator=(long i) +const numeric & numeric::operator=(long i) { return operator=(numeric(i)); } -numeric const & numeric::operator=(unsigned long i) +const numeric & numeric::operator=(unsigned long i) { return operator=(numeric(i)); } -numeric const & numeric::operator=(double d) +const numeric & numeric::operator=(double d) { return operator=(numeric(d)); } -numeric const & numeric::operator=(char const * s) +const numeric & numeric::operator=(const char * s) { return operator=(numeric(s)); } +/** Return the complex half-plane (left or right) in which the number lies. + * csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0, + * csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0. + * + * @see numeric::compare(const numeric & other) */ +int numeric::csgn(void) const +{ + if (this->is_zero()) + 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 * numbers this is not possible in a mathematically consistent way but we need * to establish some order and it ought to be fast. So we simply define it - * similar to Maple's csgn. */ -int numeric::compare(numeric const & other) const + * to be compatible with our method csgn. + * + * @return csgn(*this-other) + * @see numeric::csgn(void) */ +int numeric::compare(const numeric & other) const { // Comparing two real numbers? - if (is_real() && other.is_real()) + if (this->is_real() && other.is_real()) // Yes, just compare them - return cl_compare(The(cl_R)(*value), The(cl_R)(*other.value)); + 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)); + 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(numeric const & other) const +bool numeric::is_equal(const numeric & other) const { return (*value == *other.value); } @@ -535,59 +878,53 @@ bool numeric::is_equal(numeric const & other) const /** 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 (is_real()) { - return plusp(The(cl_R)(*value)); // -> CLN - } + 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 (is_real()) { - return minusp(The(cl_R)(*value)); // -> CLN - } + 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 (bool)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 (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 (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 (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 (is_integer() && - oddp(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && ::oddp(The(::cl_I)(*value))); // -> CLN } /** Probabilistic primality test. @@ -595,114 +932,140 @@ bool numeric::is_odd(void) const * @return true if object is exact integer and prime. */ bool numeric::is_prime(void) const { - return (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 { - if (instanceof(*value, cl_RA_ring)) { - return true; - } else if (!is_real()) { // complex case, handle Q(i): - if ( instanceof(realpart(*value), cl_RA_ring) && - instanceof(imagpart(*value), cl_RA_ring) ) - return true; - } - return false; + 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 (bool)instanceof(*value, cl_R_ring); // -> CLN + return ::instanceof(*value, ::cl_R_ring); // -> CLN } -bool numeric::operator==(numeric const & other) const +bool numeric::operator==(const numeric & other) const { return (*value == *other.value); // -> CLN } -bool numeric::operator!=(numeric const & other) const +bool numeric::operator!=(const numeric & other) const { 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; +} + +/** 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; +} + /** Numerical comparison: less. * * @exception invalid_argument (complex inequality) */ -bool numeric::operator<(numeric const & other) const +bool numeric::operator<(const numeric & other) const { - if ( is_real() && other.is_real() ) { - return (bool)(The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN - } - throw (std::invalid_argument("numeric::operator<(): complex inequality")); + 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: less or equal. * * @exception invalid_argument (complex inequality) */ -bool numeric::operator<=(numeric const & other) const +bool numeric::operator<=(const numeric & other) const { - if ( is_real() && other.is_real() ) { - return (bool)(The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN - } - throw (std::invalid_argument("numeric::operator<=(): complex inequality")); + 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>(numeric const & other) const +bool numeric::operator>(const numeric & other) const { - if ( is_real() && other.is_real() ) { - return (bool)(The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN - } - throw (std::invalid_argument("numeric::operator>(): complex inequality")); + 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 or equal. * * @exception invalid_argument (complex inequality) */ -bool numeric::operator>=(numeric const & other) const +bool numeric::operator>=(const numeric & other) const { - if ( is_real() && other.is_real() ) { - return (bool)(The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN - } - throw (std::invalid_argument("numeric::operator>=(): complex inequality")); + 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 } -/** Converts numeric types to machine's int. You should check with is_integer() - * if the number is really an integer before calling this method. */ +/** Converts numeric types to machine's int. You should check with + * is_integer() if the number is really an integer before calling this method. + * You may also consider checking the range first. */ int numeric::to_int(void) const { - ASSERT(is_integer()); - return cl_I_to_int(The(cl_I)(*value)); + 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 + * is_integer() if the number is really an integer before calling this method. + * You may also consider checking the range first. */ +long numeric::to_long(void) const +{ + GINAC_ASSERT(this->is_integer()); + return ::cl_I_to_long(The(::cl_I)(*value)); // -> CLN } /** 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 { - ASSERT(is_real()); - return cl_double_approx(realpart(*value)); + GINAC_ASSERT(this->is_real()); + return ::cl_double_approx(::realpart(*value)); // -> CLN } /** Real part of a number. */ -numeric numeric::real(void) const +const numeric numeric::real(void) const { - return numeric(realpart(*value)); // -> CLN + return numeric(::realpart(*value)); // -> CLN } /** Imaginary part of a number. */ -numeric numeric::imag(void) const +const numeric numeric::imag(void) const { - return numeric(imagpart(*value)); // -> CLN + return numeric(::imagpart(*value)); // -> CLN } #ifndef SANE_LINKER @@ -720,47 +1083,48 @@ inline cl_heap_ratio* TheRatio (const cl_N& obj) /** Numerator. Computes the numerator of rational numbers, rationalized * numerator of complex if real and imaginary part are both rational numbers - * (i.e numer(4/3+5/6*I) == 8+5*I), the number itself in all other cases. */ -numeric numeric::numer(void) const + * (i.e numer(4/3+5/6*I) == 8+5*I), the number carrying the sign in all other + * cases. */ +const numeric numeric::numer(void) const { - if (is_integer()) { + if (this->is_integer()) { return numeric(*this); } #ifdef SANE_LINKER - else if (instanceof(*value, cl_RA_ring)) { - return numeric(numerator(The(cl_RA)(*value))); + else if (::instanceof(*value, ::cl_RA_ring)) { + return numeric(::numerator(The(::cl_RA)(*value))); } - else if (!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)) + 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)))))); + 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)) { + else if (instanceof(*value, ::cl_RA_ring)) { return numeric(TheRatio(*value)->numerator); } - else if (!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)) + 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)), + 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)))); } } @@ -772,46 +1136,46 @@ numeric numeric::numer(void) const /** Denominator. Computes the denominator of rational numbers, common integer * denominator of complex if real and imaginary part are both rational numbers * (i.e denom(4/3+5/6*I) == 6), one in all other cases. */ -numeric numeric::denom(void) const +const numeric numeric::denom(void) const { - if (is_integer()) { - return numONE(); + if (this->is_integer()) { + return _num1(); } #ifdef SANE_LINKER - if (instanceof(*value, cl_RA_ring)) { - return numeric(denominator(The(cl_RA)(*value))); + if (instanceof(*value, ::cl_RA_ring)) { + return numeric(::denominator(The(::cl_RA)(*value))); } - if (!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 numONE(); - 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 (!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)) { + if (instanceof(*value, ::cl_RA_ring)) { return numeric(TheRatio(*value)->denominator); } - if (!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 numONE(); - if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring)) + 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)) + 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(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 numONE(); + return _num1(); } /** Size in binary notation. For integers, this is the smallest n >= 0 such @@ -822,11 +1186,10 @@ numeric numeric::denom(void) const * in two's complement if it is an integer, 0 otherwise. */ int numeric::int_length(void) const { - if (is_integer()) { - return integer_length(The(cl_I)(*value)); // -> CLN - } else { + if (this->is_integer()) + return ::integer_length(The(::cl_I)(*value)); // -> CLN + else return 0; - } } @@ -843,295 +1206,521 @@ unsigned numeric::precedence = 30; ////////// const numeric some_numeric; -type_info const & typeid_numeric=typeid(some_numeric); +const type_info & typeid_numeric=typeid(some_numeric); /** Imaginary unit. This is not a constant but a numeric since we are * natively handing complex numbers anyways. */ -const numeric I = (complex(cl_I(0),cl_I(1))); - -////////// -// global functions -////////// +const numeric I = numeric(::complex(cl_I(0),cl_I(1))); -numeric const & numZERO(void) -{ - const static ex eZERO = ex((new numeric(0))->setflag(status_flags::dynallocated)); - const static numeric * nZERO = static_cast(eZERO.bp); - return *nZERO; -} - -numeric const & numONE(void) -{ - const static ex eONE = ex((new numeric(1))->setflag(status_flags::dynallocated)); - const static numeric * nONE = static_cast(eONE.bp); - return *nONE; -} - -numeric const & numTWO(void) -{ - const static ex eTWO = ex((new numeric(2))->setflag(status_flags::dynallocated)); - const static numeric * nTWO = static_cast(eTWO.bp); - return *nTWO; -} - -numeric const & numTHREE(void) -{ - const static ex eTHREE = ex((new numeric(3))->setflag(status_flags::dynallocated)); - const static numeric * nTHREE = static_cast(eTHREE.bp); - return *nTHREE; -} - -numeric const & numMINUSONE(void) -{ - const static ex eMINUSONE = ex((new numeric(-1))->setflag(status_flags::dynallocated)); - const static numeric * nMINUSONE = static_cast(eMINUSONE.bp); - return *nMINUSONE; -} - -numeric const & numHALF(void) -{ - const static ex eHALF = ex((new numeric(1, 2))->setflag(status_flags::dynallocated)); - const static numeric * nHALF = static_cast(eHALF.bp); - return *nHALF; -} /** Exponential function. * * @return arbitrary precision numerical exp(x). */ -numeric exp(numeric const & x) +const numeric exp(const numeric & x) { - return exp(*x.value); // -> CLN + return ::exp(*x.value); // -> CLN } + /** Natural logarithm. * * @param z complex number * @return arbitrary precision numerical log(x). - * @exception overflow_error (logarithmic singularity) */ -numeric log(numeric const & z) + * @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 + throw pole_error("log(): logarithmic pole",0); + return ::log(*z.value); // -> CLN } + /** Numeric sine (trigonometric function). * * @return arbitrary precision numerical sin(x). */ -numeric sin(numeric const & x) +const numeric sin(const numeric & x) { - return sin(*x.value); // -> CLN + return ::sin(*x.value); // -> CLN } + /** Numeric cosine (trigonometric function). * * @return arbitrary precision numerical cos(x). */ -numeric cos(numeric const & x) +const numeric cos(const numeric & x) { - return cos(*x.value); // -> CLN + return ::cos(*x.value); // -> CLN } - + + /** Numeric tangent (trigonometric function). * * @return arbitrary precision numerical tan(x). */ -numeric tan(numeric const & 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). */ -numeric asin(numeric const & x) +const numeric asin(const numeric & x) { - return asin(*x.value); // -> CLN + return ::asin(*x.value); // -> CLN } - + + /** Numeric inverse cosine (trigonometric function). * * @return arbitrary precision numerical acos(x). */ -numeric acos(numeric const & x) +const numeric acos(const numeric & x) { - return acos(*x.value); // -> CLN + return ::acos(*x.value); // -> CLN } -/** Arcustangents. + +/** Arcustangent. * * @param z complex number * @return atan(z) - * @exception overflow_error (logarithmic singularity) */ -numeric atan(numeric const & x) + * @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(numONE())) - throw (std::overflow_error("atan(): logarithmic singularity")); - return atan(*x.value); // -> CLN + abs(x.imag()).is_equal(_num1())) + throw pole_error("atan(): logarithmic pole",0); + return ::atan(*x.value); // -> CLN } -/** Arcustangents. + +/** Arcustangent. * * @param x real number * @param y real number * @return atan(y/x) */ -numeric atan(numeric const & y, numeric const & x) +const numeric atan(const numeric & y, const numeric & x) { if (x.is_real() && y.is_real()) - return atan(realpart(*x.value), realpart(*y.value)); // -> CLN + return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN else - throw (std::invalid_argument("numeric::atan(): complex argument")); + throw std::invalid_argument("atan(): complex argument"); } + /** Numeric hyperbolic sine (trigonometric function). * * @return arbitrary precision numerical sinh(x). */ -numeric sinh(numeric const & x) +const numeric sinh(const numeric & x) { - return sinh(*x.value); // -> CLN + return ::sinh(*x.value); // -> CLN } + /** Numeric hyperbolic cosine (trigonometric function). * * @return arbitrary precision numerical cosh(x). */ -numeric cosh(numeric const & x) +const numeric cosh(const numeric & x) { - return cosh(*x.value); // -> CLN + return ::cosh(*x.value); // -> CLN } - + + /** Numeric hyperbolic tangent (trigonometric function). * * @return arbitrary precision numerical tanh(x). */ -numeric tanh(numeric const & 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). */ -numeric asinh(numeric const & x) +const numeric asinh(const numeric & x) { - return asinh(*x.value); // -> CLN + return ::asinh(*x.value); // -> CLN } + /** Numeric inverse hyperbolic cosine (trigonometric function). * * @return arbitrary precision numerical acosh(x). */ -numeric acosh(numeric const & x) +const numeric acosh(const numeric & x) { - return acosh(*x.value); // -> CLN + return ::acosh(*x.value); // -> CLN } + /** Numeric inverse hyperbolic tangent (trigonometric function). * * @return arbitrary precision numerical atanh(x). */ -numeric atanh(numeric const & x) +const numeric atanh(const numeric & x) +{ + 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) { - return atanh(*x.value); // -> CLN + 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); } -/** The gamma function. - * stub stub stub stub stub stub! */ -numeric gamma(numeric const & x) + +/** Numeric evaluation of Riemann's Zeta function. Currently works only for + * integer arguments. */ +const numeric zeta(const numeric & x) { - clog << "gamma(): Nobody expects the Spanish inquisition" << endl; + // 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); } + +/** The Gamma function. + * This is only a stub! */ +const numeric lgamma(const numeric & x) +{ + std::clog << "lgamma(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); +} +const numeric tgamma(const numeric & x) +{ + std::clog << "tgamma(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); +} + + +/** The psi function (aka polygamma function). + * This is only a stub! */ +const numeric psi(const numeric & x) +{ + std::clog << "psi(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); +} + + +/** The psi functions (aka polygamma functions). + * This is only a stub! */ +const numeric psi(const numeric & n, const numeric & x) +{ + std::clog << "psi(" << n << "," << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); +} + + /** Factorial combinatorial function. * + * @param n integer argument >= 0 * @exception range_error (argument must be integer >= 0) */ -numeric factorial(numeric const & nn) +const numeric factorial(const numeric & n) { - if ( !nn.is_nonneg_integer() ) { - throw (std::range_error("numeric::factorial(): argument must be integer >= 0")); - } - - return numeric(factorial(nn.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 } + /** The double factorial combinatorial function. (Scarcely used, but still - * useful in cases, like for exact results of Gamma(n+1/2) for instance.) + * useful in cases, like for exact results of tgamma(n+1/2) for instance.) * * @param n integer argument >= -1 - * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == 1 == (-1)!! + * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1 * @exception range_error (argument must be integer >= -1) */ -numeric doublefactorial(numeric const & nn) -{ - // We store the results separately for even and odd arguments. This has - // the advantage that we don't have to compute any even result at all if - // the function is always called with odd arguments and vice versa. There - // is no tradeoff involved in this, it is guaranteed to save time as well - // as memory. (If this is not enough justification consider the Gamma - // function of half integer arguments: it only needs odd doublefactorials.) - static vector evenresults; - static int highest_evenresult = -1; - static vector oddresults; - static int highest_oddresult = -1; - - if ( nn == numeric(-1) ) { - return numONE(); +const numeric doublefactorial(const numeric & n) +{ + if (n == numeric(-1)) { + return _num1(); } - if ( !nn.is_nonneg_integer() ) { - throw (std::range_error("numeric::doublefactorial(): argument must be integer >= -1")); + if (!n.is_nonneg_integer()) { + throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1"); } - if ( nn.is_even() ) { - int n = nn.div(numTWO()).to_int(); - if ( n <= highest_evenresult ) { - return evenresults[n]; - } - if ( evenresults.capacity() < (unsigned)(n+1) ) { - evenresults.reserve(n+1); - } - if ( highest_evenresult < 0 ) { - evenresults.push_back(numONE()); - highest_evenresult=0; - } - for (int i=highest_evenresult+1; i<=n; i++) { - evenresults.push_back(numeric(evenresults[i-1].mul(numeric(i*2)))); - } - highest_evenresult=n; - return evenresults[n]; - } else { - int n = nn.sub(numONE()).div(numTWO()).to_int(); - if ( n <= highest_oddresult ) { - return oddresults[n]; - } - if ( oddresults.capacity() < (unsigned)n ) { - oddresults.reserve(n+1); - } - if ( highest_oddresult < 0 ) { - oddresults.push_back(numONE()); - highest_oddresult=0; - } - for (int i=highest_oddresult+1; i<=n; i++) { - oddresults.push_back(numeric(oddresults[i-1].mul(numeric(i*2+1)))); + return numeric(::doublefactorial(n.to_int())); // -> CLN +} + + +/** The Binomial coefficients. It computes the binomial coefficients. For + * integer n and k and positive n this is the number of ways of choosing k + * objects from n distinct objects. If n is negative, the formula + * binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */ +const numeric binomial(const numeric & n, const numeric & k) +{ + 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); } - highest_oddresult=n; - return oddresults[n]; } + + // 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."); } -/** The Binomial function. It computes the binomial coefficients. If the - * arguments are both nonnegative integers and 0 <= k <= n, then - * binomial(n, k) = n!/k!/(n-k)! which is the number of ways of choosing k - * objects from n distinct objects. If k > n, then binomial(n,k) returns 0. */ -numeric binomial(numeric const & n, numeric const & k) + +/** Bernoulli number. The nth Bernoulli number is the coefficient of x^n/n! + * in the expansion of the function x/(e^x-1). + * + * @return the nth Bernoulli number (a rational number). + * @exception range_error (argument must be integer >= 0) */ +const numeric bernoulli(const numeric & nn) { - if (n.is_nonneg_integer() && k.is_nonneg_integer()) { - return numeric(binomial(n.to_int(),k.to_int())); // -> CLN - } else { - // should really be gamma(n+1)/(gamma(r+1)/gamma(n-r+1) - return numeric(0); + 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 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; i0; --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]; +} + + +/** Fibonacci number. The nth Fibonacci number F(n) is defined by the + * recurrence formula F(n)==F(n-1)+F(n-2) with F(0)==0 and F(1)==1. + * + * @param n an integer + * @return the nth Fibonacci number F(n) (an integer number) + * @exception range_error (argument must be an integer) */ +const numeric fibonacci(const numeric & n) +{ + 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; + } } - // return factorial(n).div(factorial(k).mul(factorial(n.sub(k)))); + 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(numeric const & x) +numeric abs(const numeric & x) { - return abs(*x.value); // -> CLN + return ::abs(*x.value); // -> CLN } + /** Modulus (in positive representation). * In general, mod(a,b) has the sign of b or is zero, and rem(a,b) has the * sign of a or is zero. This is different from Maple's modp, where the sign @@ -1139,46 +1728,44 @@ numeric abs(numeric const & x) * * @return a mod b in the range [0,abs(b)-1] with sign of b if both are * integer, 0 otherwise. */ -numeric mod(numeric const & a, numeric const & b) +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 numZERO(); // 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? } + /** Modulus (in symmetric representation). * Equivalent to Maple's mods. * * @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */ -numeric smod(numeric const & a, numeric const & b) +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 numZERO(); // Throw? - } + 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? } + /** Numeric integer remainder. * Equivalent to Maple's irem(a,b) as far as sign conventions are concerned. * In general, mod(a,b) has the sign of b or is zero, and irem(a,b) has the * sign of a or is zero. * * @return remainder of a/b if both are integer, 0 otherwise. */ -numeric irem(numeric const & a, numeric const & b) +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 numZERO(); // 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? } + /** Numeric integer remainder. * Equivalent to Maple's irem(a,b,'q') it obeyes the relation * irem(a,b,q) == a - q*b. In general, mod(a,b) has the sign of b or is zero, @@ -1186,50 +1773,52 @@ numeric irem(numeric const & a, numeric const & b) * * @return remainder of a/b and quotient stored in q if both are integer, * 0 otherwise. */ -numeric irem(numeric const & a, numeric const & b, numeric & q) +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)); + 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 = numZERO(); - return numZERO(); // Throw? + q = _num0(); + return _num0(); // Throw? } } + /** Numeric integer quotient. * Equivalent to Maple's iquo as far as sign conventions are concerned. * * @return truncated quotient of a/b if both are integer, 0 otherwise. */ -numeric iquo(numeric const & a, numeric const & b) +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 numZERO(); // 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? } + /** Numeric integer quotient. * Equivalent to Maple's iquo(a,b,'r') it obeyes the relation * r == a - iquo(a,b,r)*b. * * @return truncated quotient of a/b and remainder stored in r if both are * integer, 0 otherwise. */ -numeric iquo(numeric const & a, numeric const & b, numeric & r) +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)); + 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 = numZERO(); - return numZERO(); // Throw? + r = _num0(); + return _num0(); // Throw? } } + /** Numeric square root. * If possible, sqrt(z) should respect squares of exact numbers, i.e. sqrt(4) * should return integer 2. @@ -1238,61 +1827,71 @@ numeric iquo(numeric const & a, numeric const & b, numeric & r) * @return square root of z. Branch cut along negative real axis, the negative * real axis itself where imag(z)==0 and real(z)<0 belongs to the upper part * where imag(z)>0. */ -numeric sqrt(numeric const & z) +numeric sqrt(const numeric & z) { - return sqrt(*z.value); // -> CLN + return ::sqrt(*z.value); // -> CLN } + /** Integer numeric square root. */ -numeric isqrt(numeric const & x) +numeric isqrt(const numeric & x) { - if (x.is_integer()) { - cl_I root; - isqrt(The(cl_I)(*x.value), &root); // -> CLN - return root; - } else - return numZERO(); // Throw? + if (x.is_integer()) { + cl_I root; + ::isqrt(The(::cl_I)(*x.value), &root); // -> CLN + return root; + } else + return _num0(); // Throw? } + /** Greatest Common Divisor. * * @return The GCD of two numbers if both are integer, a numerical 1 * if they are not. */ -numeric gcd(numeric const & a, numeric const & b) +numeric gcd(const numeric & a, const numeric & b) { if (a.is_integer() && b.is_integer()) - return gcd(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN + return ::gcd(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN else - return numONE(); + return _num1(); } + /** Least Common Multiple. * * @return The LCM of two numbers if both are integer, the product of those * two numbers if they are not. */ -numeric lcm(numeric const & a, numeric const & b) +numeric lcm(const numeric & a, const numeric & b) { if (a.is_integer() && b.is_integer()) - return lcm(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN + return ::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 } -ex EulerGammaEvalf(void) + +/** 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 } + // It initializes to 17 digits, because in CLN cl_float_format(17) turns out to // be 61 (<64) while cl_float_format(18)=65. We want to have a cl_LF instead // of cl_SF, cl_FF or cl_DF but everything else is basically arbitrary. @@ -1301,28 +1900,32 @@ _numeric_digits::_numeric_digits() { assert(!too_late); too_late = true; - cl_default_float_format = cl_float_format(17); + 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); + cl_default_float_format = ::cl_float_format(prec); return *this; } + _numeric_digits::operator long() { 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; } -ostream& operator<<(ostream& os, _numeric_digits const & e) + +std::ostream& operator<<(std::ostream& os, const _numeric_digits & e) { e.print(os); return os; @@ -1336,6 +1939,11 @@ ostream& operator<<(ostream& os, _numeric_digits const & e) bool _numeric_digits::too_late = false; + /** Accuracy in decimal digits. Only object of this type! Can be set using * assignment from C++ unsigned ints and evaluated like any built-in type. */ _numeric_digits Digits; + +#ifndef NO_NAMESPACE_GINAC +} // namespace GiNaC +#endif // ndef NO_NAMESPACE_GINAC