X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=c23d46a2408700b83b78fd541c59b516cd0091b6;hp=bb2762a2e0cbfa58996689800f6aa077b0bd6579;hb=dbc2bb1dfa0377b3e314f91a3ec21bb08b09e226;hpb=52b8a6451d4d5f32e45e3dbf93c22369fc2f99c2 diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp index bb2762a2..c23d46a2 100644 --- a/ginac/numeric.cpp +++ b/ginac/numeric.cpp @@ -7,7 +7,7 @@ * of special functions or implement the interface to the bignum package. */ /* - * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany + * 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 @@ -26,25 +26,54 @@ #include #include +#include +#include //!! #include "numeric.h" #include "ex.h" #include "config.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 +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include #else -#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include #endif +#ifndef NO_GINAC_NAMESPACE namespace GiNaC { +#endif // ndef NO_GINAC_NAMESPACE // 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 @@ -69,13 +98,13 @@ 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) { @@ -87,7 +116,7 @@ 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); @@ -198,6 +227,60 @@ numeric::numeric(cl_N const & z) : basic(TINFO_numeric) 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; +#if 0 //!! + // This is how it should be implemented but we have no istringstream here... + string str; + if (n.find_string("number", str)) { + istringstream s(str); + s >> *value; + } +#else + // Workaround for the above: read from strstream + string str; + if (n.find_string("number", str)) { + istrstream f(str.c_str(), str.size() + 1); + f >> *value; + } +#endif + 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); +#if 0 //!! + // This is how it should be implemented but we have no ostringstream here... + ostringstream s; + s << *value; + n.add_string("number", s.str()); +#else + // Workaround for the above: write to strstream + char buf[1024]; + ostrstream f(buf, 1024); + f << *value << ends; + string str(buf); + n.add_string("number", str); +#endif +} + ////////// // functions overriding virtual functions from bases classes ////////// @@ -210,19 +293,11 @@ 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 -{ - debugmsg("numeric printraw", LOGLEVEL_PRINT); - os << "numeric(" << *value << ")"; -} - -// The method print adds to the output so it blends more consistently together -// with the other routines and produces something compatible to Maple input. void numeric::print(ostream & os, unsigned upper_precedence) const { + // The method print adds to the output so it blends more consistently + // together with the other routines and produces something compatible to + // ginsh input. debugmsg("numeric print", LOGLEVEL_PRINT); if (is_real()) { // case 1, real: x or -x @@ -273,6 +348,57 @@ void numeric::print(ostream & os, unsigned upper_precedence) const } } + +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 (is_rational() && !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) { @@ -285,19 +411,25 @@ bool numeric::info(unsigned inf) const 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 compare(numZERO())>=0; + return compare(_num0())>=0; case info_flags::posint: return is_pos_integer(); case info_flags::negint: - return is_integer() && (compare(numZERO())<0); + return is_integer() && (compare(_num0())<0); case info_flags::nonnegint: return is_nonneg_integer(); case info_flags::even: @@ -315,7 +447,7 @@ bool numeric::info(unsigned inf) const * currently set. * * @param level ignored, but needed for overriding basic::evalf. - * @return an ex-handle to a numeric. */ + * @return an ex-handle to a numeric. */ ex numeric::evalf(int level) const { // level can safely be discarded for numeric objects. @@ -327,7 +459,7 @@ ex numeric::evalf(int level) const int numeric::compare_same_type(basic const & other) const { GINAC_ASSERT(is_exactly_of_type(other, numeric)); - numeric const & o = static_cast(const_cast(other)); + const numeric & o = static_cast(const_cast(other)); if (*value == *o.value) { return 0; @@ -339,7 +471,7 @@ int numeric::compare_same_type(basic const & other) const bool numeric::is_equal_same_type(basic const & other) const { GINAC_ASSERT(is_exactly_of_type(other,numeric)); - numeric const *o = static_cast(&other); + const numeric *o = static_cast(&other); return is_equal(*o); } @@ -372,26 +504,26 @@ 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)); @@ -401,116 +533,98 @@ 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)) + 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) && other.is_real() && minusp(realpart(*other.value))) + 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)) + if (::zerop(*other.value)) throw (std::overflow_error("division by zero")); - return static_cast((new numeric((*value)/(*other.value)))-> + 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; - } - // 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)); - } + if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value))) + throw (std::overflow_error("division by zero")); + 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=(char const * s) { return operator=(numeric(s)); } @@ -519,18 +633,18 @@ numeric const & numeric::operator=(char const * s) * 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(numeric const & other) */ + * @see numeric::compare(const numeric & other) */ int numeric::csgn(void) const { if (is_zero()) return 0; - if (!zerop(realpart(*value))) { - if (plusp(realpart(*value))) + if (!::zerop(realpart(*value))) { + if (::plusp(realpart(*value))) return 1; else return -1; } else { - if (plusp(imagpart(*value))) + if (::plusp(imagpart(*value))) return 1; else return -1; @@ -544,23 +658,23 @@ int numeric::csgn(void) const * * @return csgn(*this-other) * @see numeric::csgn(void) */ -int numeric::compare(numeric const & other) const +int numeric::compare(const numeric & other) const { // Comparing two real numbers? if (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); } @@ -568,59 +682,53 @@ 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 (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 (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 (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 (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 (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 (is_integer() && ::oddp(The(cl_I)(*value))); // -> CLN } /** Probabilistic primality test. @@ -628,48 +736,67 @@ 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 (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 (!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 (!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() ) { + 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")); return false; // make compiler shut up } @@ -677,11 +804,10 @@ bool numeric::operator<(numeric const & other) const /** 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() ) { + 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")); return false; // make compiler shut up } @@ -689,11 +815,10 @@ bool numeric::operator<=(numeric const & other) const /** 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() ) { + 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")); return false; // make compiler shut up } @@ -701,11 +826,10 @@ bool numeric::operator>(numeric const & other) const /** 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() ) { + 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")); return false; // make compiler shut up } @@ -715,7 +839,7 @@ bool numeric::operator>=(numeric const & other) const int numeric::to_int(void) const { GINAC_ASSERT(is_integer()); - return cl_I_to_int(The(cl_I)(*value)); + return ::cl_I_to_int(The(cl_I)(*value)); // -> CLN } /** Converts numeric types to machine's double. You should check with is_real() @@ -723,19 +847,19 @@ int numeric::to_int(void) const double numeric::to_double(void) const { GINAC_ASSERT(is_real()); - return cl_double_approx(realpart(*value)); + return ::cl_double_approx(realpart(*value)); // -> CLN } /** Real part of a number. */ 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 { - return numeric(imagpart(*value)); // -> CLN + return numeric(::imagpart(*value)); // -> CLN } #ifndef SANE_LINKER @@ -761,22 +885,22 @@ numeric numeric::numer(void) const 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)) + 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 @@ -809,23 +933,23 @@ numeric numeric::numer(void) const numeric numeric::denom(void) const { if (is_integer()) { - return numONE(); + return _num1(); } #ifdef SANE_LINKER if (instanceof(*value, cl_RA_ring)) { - return numeric(denominator(The(cl_RA)(*value))); + 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 (::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)) { @@ -835,7 +959,7 @@ numeric numeric::denom(void) const cl_R r = realpart(*value); cl_R i = imagpart(*value); if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring)) - return numONE(); + 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)) @@ -845,7 +969,7 @@ numeric numeric::denom(void) const } #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 @@ -856,11 +980,10 @@ 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 (is_integer()) + return ::integer_length(The(cl_I)(*value)); // -> CLN + else return 0; - } } @@ -882,56 +1005,10 @@ type_info const & typeid_numeric=typeid(some_numeric); * natively handing complex numbers anyways. */ const numeric I = numeric(complex(cl_I(0),cl_I(1))); -////////// -// global functions -////////// - -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) +numeric exp(const numeric & x) { return ::exp(*x.value); // -> CLN } @@ -941,7 +1018,7 @@ numeric exp(numeric const & x) * @param z complex number * @return arbitrary precision numerical log(x). * @exception overflow_error (logarithmic singularity) */ -numeric log(numeric const & z) +numeric log(const numeric & z) { if (z.is_zero()) throw (std::overflow_error("log(): logarithmic singularity")); @@ -951,7 +1028,7 @@ numeric log(numeric const & z) /** Numeric sine (trigonometric function). * * @return arbitrary precision numerical sin(x). */ -numeric sin(numeric const & x) +numeric sin(const numeric & x) { return ::sin(*x.value); // -> CLN } @@ -959,7 +1036,7 @@ numeric sin(numeric const & x) /** Numeric cosine (trigonometric function). * * @return arbitrary precision numerical cos(x). */ -numeric cos(numeric const & x) +numeric cos(const numeric & x) { return ::cos(*x.value); // -> CLN } @@ -967,7 +1044,7 @@ numeric cos(numeric const & x) /** Numeric tangent (trigonometric function). * * @return arbitrary precision numerical tan(x). */ -numeric tan(numeric const & x) +numeric tan(const numeric & x) { return ::tan(*x.value); // -> CLN } @@ -975,7 +1052,7 @@ numeric tan(numeric const & x) /** Numeric inverse sine (trigonometric function). * * @return arbitrary precision numerical asin(x). */ -numeric asin(numeric const & x) +numeric asin(const numeric & x) { return ::asin(*x.value); // -> CLN } @@ -983,7 +1060,7 @@ numeric asin(numeric const & x) /** Numeric inverse cosine (trigonometric function). * * @return arbitrary precision numerical acos(x). */ -numeric acos(numeric const & x) +numeric acos(const numeric & x) { return ::acos(*x.value); // -> CLN } @@ -993,11 +1070,11 @@ numeric acos(numeric const & x) * @param z complex number * @return atan(z) * @exception overflow_error (logarithmic singularity) */ -numeric atan(numeric const & x) +numeric atan(const numeric & x) { if (!x.is_real() && x.real().is_zero() && - !abs(x.imag()).is_equal(numONE())) + !abs(x.imag()).is_equal(_num1())) throw (std::overflow_error("atan(): logarithmic singularity")); return ::atan(*x.value); // -> CLN } @@ -1007,7 +1084,7 @@ numeric atan(numeric const & x) * @param x real number * @param y real number * @return atan(y/x) */ -numeric atan(numeric const & y, numeric const & x) +numeric atan(const numeric & y, const numeric & x) { if (x.is_real() && y.is_real()) return ::atan(realpart(*x.value), realpart(*y.value)); // -> CLN @@ -1018,7 +1095,7 @@ numeric atan(numeric const & y, numeric const & x) /** Numeric hyperbolic sine (trigonometric function). * * @return arbitrary precision numerical sinh(x). */ -numeric sinh(numeric const & x) +numeric sinh(const numeric & x) { return ::sinh(*x.value); // -> CLN } @@ -1026,7 +1103,7 @@ numeric sinh(numeric const & x) /** Numeric hyperbolic cosine (trigonometric function). * * @return arbitrary precision numerical cosh(x). */ -numeric cosh(numeric const & x) +numeric cosh(const numeric & x) { return ::cosh(*x.value); // -> CLN } @@ -1034,7 +1111,7 @@ numeric cosh(numeric const & x) /** Numeric hyperbolic tangent (trigonometric function). * * @return arbitrary precision numerical tanh(x). */ -numeric tanh(numeric const & x) +numeric tanh(const numeric & x) { return ::tanh(*x.value); // -> CLN } @@ -1042,7 +1119,7 @@ numeric tanh(numeric const & x) /** Numeric inverse hyperbolic sine (trigonometric function). * * @return arbitrary precision numerical asinh(x). */ -numeric asinh(numeric const & x) +numeric asinh(const numeric & x) { return ::asinh(*x.value); // -> CLN } @@ -1050,7 +1127,7 @@ numeric asinh(numeric const & x) /** Numeric inverse hyperbolic cosine (trigonometric function). * * @return arbitrary precision numerical acosh(x). */ -numeric acosh(numeric const & x) +numeric acosh(const numeric & x) { return ::acosh(*x.value); // -> CLN } @@ -1058,47 +1135,68 @@ numeric acosh(numeric const & x) /** Numeric inverse hyperbolic tangent (trigonometric function). * * @return arbitrary precision numerical atanh(x). */ -numeric atanh(numeric const & x) +numeric atanh(const numeric & x) { return ::atanh(*x.value); // -> CLN } /** Numeric evaluation of Riemann's Zeta function. Currently works only for * integer arguments. */ -numeric zeta(numeric const & x) -{ - if (x.is_integer()) - return ::cl_zeta(x.to_int()); // -> CLN - else - clog << "zeta(): Does anybody know good way to calculate this numerically?" << endl; +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); } /** The gamma function. * This is only a stub! */ -numeric gamma(numeric const & x) +numeric gamma(const numeric & x) { - clog << "gamma(): Does anybody know good way to calculate this numerically?" << endl; + clog << "gamma(" << x + << "): Does anybody know good way to calculate this numerically?" + << endl; return numeric(0); } /** The psi function (aka polygamma function). * This is only a stub! */ -numeric psi(numeric const & n, numeric const & x) +numeric psi(const numeric & x) { - clog << "psi(): Does anybody know good way to calculate this numerically?" << endl; + clog << "psi(" << x + << "): Does anybody know good way to calculate this numerically?" + << endl; + return numeric(0); +} + +/** The psi functions (aka polygamma functions). + * This is only a stub! */ +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); } /** Factorial combinatorial function. * * @exception range_error (argument must be integer >= 0) */ -numeric factorial(numeric const & nn) +numeric factorial(const numeric & nn) { - if ( !nn.is_nonneg_integer() ) { + if (!nn.is_nonneg_integer()) throw (std::range_error("numeric::factorial(): argument must be integer >= 0")); - } - return numeric(::factorial(nn.to_int())); // -> CLN } @@ -1106,83 +1204,34 @@ numeric factorial(numeric const & nn) * useful in cases, like for exact results of Gamma(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) +numeric doublefactorial(const numeric & nn) { - // META-NOTE: The whole shit here will become obsolete and may be moved - // out once CLN learns about double factorial, which should be as soon as - // 1.0.3 rolls out! - - // 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(); + return _num1(); } if (!nn.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)))); - } - highest_oddresult=n; - return oddresults[n]; - } + return numeric(::doublefactorial(nn.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. */ -numeric binomial(numeric const & n, numeric const & k) +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(numZERO())!=-1) + if (k.compare(n)!=1 && k.compare(_num0())!=-1) return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN else - return numZERO(); + return _num0(); } else { - return numMINUSONE().power(k)*binomial(k-n-numONE(),k); - } + 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 @@ -1194,16 +1243,16 @@ numeric binomial(numeric const & n, numeric const & k) * * @return the nth Bernoulli number (a rational number). * @exception range_error (argument must be integer >= 0) */ -numeric bernoulli(numeric const & nn) +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 numONE(); - if (!nn.compare(numONE())) + return _num1(); + if (!nn.compare(_num1())) return numeric(-1,2); if (nn.is_odd()) - return numZERO(); + 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 formula @@ -1211,7 +1260,7 @@ numeric bernoulli(numeric const & nn) // whith B(0) == 1. static vector results; static int highest_result = -1; - int n = nn.sub(numTWO()).div(numTWO()).to_int(); + int n = nn.sub(_num2()).div(_num2()).to_int(); if (n <= highest_result) return results[n]; if (results.capacity() < (unsigned)(n+1)) @@ -1232,7 +1281,7 @@ numeric bernoulli(numeric const & nn) } /** Absolute value. */ -numeric abs(numeric const & x) +numeric abs(const numeric & x) { return ::abs(*x.value); // -> CLN } @@ -1244,28 +1293,26 @@ 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()) { + if (a.is_integer() && b.is_integer()) return ::mod(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN - } - else { - return numZERO(); // Throw? - } + 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) { + // FIXME: Should this become a member function? 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? - } + } else + return _num0(); // Throw? } /** Numeric integer remainder. @@ -1274,14 +1321,12 @@ numeric smod(numeric const & a, numeric const & b) * 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()) { + if (a.is_integer() && b.is_integer()) return ::rem(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN - } - else { - return numZERO(); // Throw? - } + else + return _num0(); // Throw? } /** Numeric integer remainder. @@ -1291,7 +1336,7 @@ 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)); @@ -1299,8 +1344,8 @@ numeric irem(numeric const & a, numeric const & b, numeric & q) return rem_quo.remainder; } else { - q = numZERO(); - return numZERO(); // Throw? + q = _num0(); + return _num0(); // Throw? } } @@ -1308,13 +1353,12 @@ numeric irem(numeric const & a, numeric const & b, numeric & q) * 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()) { + if (a.is_integer() && b.is_integer()) return truncate1(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN - } else { - return numZERO(); // Throw? - } + else + return _num0(); // Throw? } /** Numeric integer quotient. @@ -1323,15 +1367,15 @@ numeric iquo(numeric const & a, numeric const & 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)); r = rem_quo.remainder; return rem_quo.quotient; } else { - r = numZERO(); - return numZERO(); // Throw? + r = _num0(); + return _num0(); // Throw? } } @@ -1343,42 +1387,42 @@ 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 } /** 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; } @@ -1406,7 +1450,7 @@ _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) @@ -1445,4 +1489,6 @@ bool _numeric_digits::too_late = false; * assignment from C++ unsigned ints and evaluated like any built-in type. */ _numeric_digits Digits; +#ifndef NO_GINAC_NAMESPACE } // namespace GiNaC +#endif // ndef NO_GINAC_NAMESPACE