X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=2fc8acc16326913b2f544f9cbed6df4ca8d7eecd;hp=bfa00af6a1b7e81432d3184ec3f4b0c3da70699c;hb=d4a2b696653478859882c13d585ad03549403fa7;hpb=d8452c110d6f725c569b8b151d3c78f6e8834536 diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp index bfa00af6..2fc8acc1 100644 --- a/ginac/numeric.cpp +++ b/ginac/numeric.cpp @@ -79,9 +79,6 @@ 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) ////////// @@ -94,49 +91,49 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic) /** default ctor. Numerically it initializes to an integer zero. */ numeric::numeric() : basic(TINFO_numeric) { - debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT); - value = new ::cl_N; - *value = ::cl_I(0); - calchash(); - setflag(status_flags::evaluated | - status_flags::expanded | - status_flags::hash_calculated); + debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT); + value = new ::cl_N; + *value = ::cl_I(0); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } numeric::~numeric() { - debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT); - destroy(0); + debugmsg("numeric destructor" ,LOGLEVEL_DESTRUCT); + destroy(false); } numeric::numeric(const numeric & other) { - debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT); - copy(other); + debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT); + copy(other); } const numeric & numeric::operator=(const numeric & other) { - debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT); - if (this != &other) { - destroy(1); - copy(other); - } - return *this; + debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT); + if (this != &other) { + destroy(true); + copy(other); + } + return *this; } // protected void numeric::copy(const numeric & other) { - basic::copy(other); - value = new ::cl_N(*other.value); + basic::copy(other); + value = new ::cl_N(*other.value); } void numeric::destroy(bool call_parent) { - delete value; - if (call_parent) basic::destroy(call_parent); + delete value; + if (call_parent) basic::destroy(call_parent); } ////////// @@ -147,47 +144,51 @@ void numeric::destroy(bool call_parent) numeric::numeric(int i) : basic(TINFO_numeric) { - debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT); - // Not the whole int-range is available if we don't cast to long - // first. This is due to the behaviour of the cl_I-ctor, which - // emphasizes efficiency: - value = new ::cl_I((long) i); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT); + // Not the whole int-range is available if we don't cast to long + // first. This is due to the behaviour of the cl_I-ctor, which + // emphasizes efficiency: + value = new ::cl_I((long) i); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } numeric::numeric(unsigned int i) : basic(TINFO_numeric) { - debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT); - // Not the whole uint-range is available if we don't cast to ulong - // first. This is due to the behaviour of the cl_I-ctor, which - // emphasizes efficiency: - value = new ::cl_I((unsigned long)i); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT); + // Not the whole uint-range is available if we don't cast to ulong + // first. This is due to the behaviour of the cl_I-ctor, which + // emphasizes efficiency: + value = new ::cl_I((unsigned long)i); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } numeric::numeric(long i) : basic(TINFO_numeric) { - debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT); - value = new ::cl_I(i); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT); + value = new ::cl_I(i); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } numeric::numeric(unsigned long i) : basic(TINFO_numeric) { - debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT); - value = new ::cl_I(i); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT); + value = new ::cl_I(i); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } /** Ctor for rational numerics a/b. @@ -195,99 +196,101 @@ numeric::numeric(unsigned long i) : basic(TINFO_numeric) * @exception overflow_error (division by zero) */ numeric::numeric(long numer, long denom) : basic(TINFO_numeric) { - debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT); - if (!denom) - throw std::overflow_error("division by zero"); - value = new ::cl_I(numer); - *value = *value / ::cl_I(denom); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT); + if (!denom) + throw std::overflow_error("division by zero"); + value = new ::cl_I(numer); + *value = *value / ::cl_I(denom); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } numeric::numeric(double d) : basic(TINFO_numeric) { - debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT); - // We really want to explicitly use the type cl_LF instead of the - // more general cl_F, since that would give us a cl_DF only which - // will not be promoted to cl_LF if overflow occurs: - value = new cl_N; - *value = cl_float(d, cl_default_float_format); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT); + // We really want to explicitly use the type cl_LF instead of the + // more general cl_F, since that would give us a cl_DF only which + // will not be promoted to cl_LF if overflow occurs: + value = new cl_N; + *value = cl_float(d, cl_default_float_format); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } - /** ctor from C-style string. It also accepts complex numbers in GiNaC * notation like "2+5*I". */ numeric::numeric(const char *s) : basic(TINFO_numeric) { - debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT); - value = new ::cl_N(0); - // parse complex numbers (functional but not completely safe, unfortunately - // std::string does not understand regexpese): - // ss should represent a simple sum like 2+5*I - std::string ss(s); - // make it safe by adding explicit sign - if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#') - ss = '+' + ss; - std::string::size_type delim; - do { - // chop ss into terms from left to right - std::string term; - bool imaginary = false; - delim = ss.find_first_of(std::string("+-"),1); - // Do we have an exponent marker like "31.415E-1"? If so, hop on! - if (delim != std::string::npos && - ss.at(delim-1) == 'E') - delim = ss.find_first_of(std::string("+-"),delim+1); - term = ss.substr(0,delim); - if (delim != std::string::npos) - ss = ss.substr(delim); - // is the term imaginary? - if (term.find("I") != std::string::npos) { - // erase 'I': - term = term.replace(term.find("I"),1,""); - // erase '*': - if (term.find("*") != std::string::npos) - term = term.replace(term.find("*"),1,""); - // correct for trivial +/-I without explicit factor on I: - if (term.size() == 1) - term += "1"; - imaginary = true; - } - const char *cs = term.c_str(); - // CLN's short types are not useful within the GiNaC framework, hence - // we go straight to the construction of a long float. Simply using - // cl_N(s) would require us to use add a CLN exponent mark, otherwise - // we would not be save from over-/underflows. - if (strchr(cs, '.')) - if (imaginary) - *value = *value + ::complex(cl_I(0),::cl_LF(cs)); - else - *value = *value + ::cl_LF(cs); - else - if (imaginary) - *value = *value + ::complex(cl_I(0),::cl_R(cs)); - else - *value = *value + ::cl_R(cs); - } while(delim != std::string::npos); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT); + value = new ::cl_N(0); + // parse complex numbers (functional but not completely safe, unfortunately + // std::string does not understand regexpese): + // ss should represent a simple sum like 2+5*I + std::string ss(s); + // make it safe by adding explicit sign + if (ss.at(0) != '+' && ss.at(0) != '-' && ss.at(0) != '#') + ss = '+' + ss; + std::string::size_type delim; + do { + // chop ss into terms from left to right + std::string term; + bool imaginary = false; + delim = ss.find_first_of(std::string("+-"),1); + // Do we have an exponent marker like "31.415E-1"? If so, hop on! + if ((delim != std::string::npos) && (ss.at(delim-1) == 'E')) + delim = ss.find_first_of(std::string("+-"),delim+1); + term = ss.substr(0,delim); + if (delim != std::string::npos) + ss = ss.substr(delim); + // is the term imaginary? + if (term.find("I") != std::string::npos) { + // erase 'I': + term = term.replace(term.find("I"),1,""); + // erase '*': + if (term.find("*") != std::string::npos) + term = term.replace(term.find("*"),1,""); + // correct for trivial +/-I without explicit factor on I: + if (term.size() == 1) + term += "1"; + imaginary = true; + } + const char *cs = term.c_str(); + // CLN's short types are not useful within the GiNaC framework, hence + // we go straight to the construction of a long float. Simply using + // cl_N(s) would require us to use add a CLN exponent mark, otherwise + // we would not be save from over-/underflows. + if (strchr(cs, '.')) + if (imaginary) + *value = *value + ::complex(cl_I(0),::cl_LF(cs)); + else + *value = *value + ::cl_LF(cs); + else + if (imaginary) + *value = *value + ::complex(cl_I(0),::cl_R(cs)); + else + *value = *value + ::cl_R(cs); + } while(delim != std::string::npos); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } /** Ctor from CLN types. This is for the initiated user or internal use * only. */ numeric::numeric(const cl_N & z) : basic(TINFO_numeric) { - debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT); - value = new ::cl_N(z); - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT); + value = new ::cl_N(z); + calchash(); + setflag(status_flags::evaluated | + status_flags::expanded | + status_flags::hash_calculated); } ////////// @@ -297,83 +300,84 @@ numeric::numeric(const cl_N & z) : basic(TINFO_numeric) /** Construct object from archive_node. */ numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) { - debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT); - value = new ::cl_N; + debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT); + value = new ::cl_N; - // Read number as string - std::string str; - if (n.find_string("number", str)) { + // Read number as string + std::string str; + if (n.find_string("number", str)) { #ifdef HAVE_SSTREAM - std::istringstream s(str); + std::istringstream s(str); #else - std::istrstream s(str.c_str(), str.size() + 1); + std::istrstream s(str.c_str(), str.size() + 1); #endif - ::cl_idecoded_float re, im; - char c; - s.get(c); - switch (c) { - case 'R': // Integer-decoded real number - s >> re.sign >> re.mantissa >> re.exponent; - *value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent); - break; - case 'C': // Integer-decoded complex number - s >> re.sign >> re.mantissa >> re.exponent; - s >> im.sign >> im.mantissa >> im.exponent; - *value = ::complex(re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent), - im.sign * im.mantissa * ::expt(cl_float(2.0, cl_default_float_format), im.exponent)); - break; - default: // Ordinary number - s.putback(c); - s >> *value; - break; - } - } - calchash(); - setflag(status_flags::evaluated| - status_flags::hash_calculated); + ::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::expanded | + status_flags::hash_calculated); } /** Unarchive the object. */ ex numeric::unarchive(const archive_node &n, const lst &sym_lst) { - return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated); + return (new numeric(n, sym_lst))->setflag(status_flags::dynallocated); } /** Archive the object. */ void numeric::archive(archive_node &n) const { - inherited::archive(n); + inherited::archive(n); - // Write number as string + // Write number as string #ifdef HAVE_SSTREAM - std::ostringstream s; + std::ostringstream s; #else - char buf[1024]; - std::ostrstream s(buf, 1024); + char buf[1024]; + std::ostrstream s(buf, 1024); #endif - if (this->is_crational()) - s << *value; - else { - // Non-rational numbers are written in an integer-decoded format - // to preserve the precision - if (this->is_real()) { - cl_idecoded_float re = integer_decode_float(The(::cl_F)(*value)); - s << "R"; - s << re.sign << " " << re.mantissa << " " << re.exponent; - } else { - cl_idecoded_float re = integer_decode_float(The(::cl_F)(::realpart(*value))); - cl_idecoded_float im = integer_decode_float(The(::cl_F)(::imagpart(*value))); - s << "C"; - s << re.sign << " " << re.mantissa << " " << re.exponent << " "; - s << im.sign << " " << im.mantissa << " " << im.exponent; - } - } + if (this->is_crational()) + s << *value; + else { + // Non-rational numbers are written in an integer-decoded format + // to preserve the precision + if (this->is_real()) { + cl_idecoded_float re = integer_decode_float(The(::cl_F)(*value)); + s << "R"; + s << re.sign << " " << re.mantissa << " " << re.exponent; + } else { + cl_idecoded_float re = integer_decode_float(The(::cl_F)(::realpart(*value))); + cl_idecoded_float im = integer_decode_float(The(::cl_F)(::imagpart(*value))); + s << "C"; + s << re.sign << " " << re.mantissa << " " << re.exponent << " "; + s << im.sign << " " << im.mantissa << " " << im.exponent; + } + } #ifdef HAVE_SSTREAM - n.add_string("number", s.str()); + n.add_string("number", s.str()); #else - s << ends; - std::string str(buf); - n.add_string("number", str); + s << ends; + std::string str(buf); + n.add_string("number", str); #endif } @@ -385,8 +389,8 @@ void numeric::archive(archive_node &n) const basic * numeric::duplicate() const { - debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE); - return new numeric(*this); + debugmsg("numeric duplicate", LOGLEVEL_DUPLICATE); + return new numeric(*this); } @@ -398,18 +402,18 @@ basic * numeric::duplicate() const * @see numeric::print() */ static void print_real_number(std::ostream & os, const cl_R & num) { - cl_print_flags ourflags; - if (::instanceof(num, ::cl_RA_ring)) { - // case 1: integer or rational, nothing special to do: - ::print_real(os, ourflags, num); - } else { - // case 2: float - // make CLN believe this number has default_float_format, so it prints - // 'E' as exponent marker instead of 'L': - ourflags.default_float_format = ::cl_float_format(The(::cl_F)(num)); - ::print_real(os, ourflags, num); - } - return; + cl_print_flags ourflags; + if (::instanceof(num, ::cl_RA_ring)) { + // case 1: integer or rational, nothing special to do: + ::print_real(os, ourflags, num); + } else { + // case 2: float + // make CLN believe this number has default_float_format, so it prints + // 'E' as exponent marker instead of 'L': + ourflags.default_float_format = ::cl_float_format(The(::cl_F)(num)); + ::print_real(os, ourflags, num); + } + return; } /** This method adds to the output so it blends more consistently together @@ -418,165 +422,165 @@ static void print_real_number(std::ostream & os, const cl_R & num) * @see print_real_number() */ void numeric::print(std::ostream & os, unsigned upper_precedence) const { - debugmsg("numeric print", LOGLEVEL_PRINT); - if (this->is_real()) { - // case 1, real: x or -x - if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) { - os << "("; - print_real_number(os, The(::cl_R)(*value)); - os << ")"; - } else { - print_real_number(os, The(::cl_R)(*value)); - } - } else { - // case 2, imaginary: y*I or -y*I - if (::realpart(*value) == 0) { - if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) { - if (::imagpart(*value) == -1) { - os << "(-I)"; - } else { - os << "("; - print_real_number(os, The(::cl_R)(::imagpart(*value))); - os << "*I)"; - } - } else { - if (::imagpart(*value) == 1) { - os << "I"; - } else { - if (::imagpart (*value) == -1) { - os << "-I"; - } else { - print_real_number(os, The(::cl_R)(::imagpart(*value))); - os << "*I"; - } - } - } - } else { - // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I - if (precedence <= upper_precedence) - os << "("; - print_real_number(os, The(::cl_R)(::realpart(*value))); - if (::imagpart(*value) < 0) { - if (::imagpart(*value) == -1) { - os << "-I"; - } else { - print_real_number(os, The(::cl_R)(::imagpart(*value))); - os << "*I"; - } - } else { - if (::imagpart(*value) == 1) { - os << "+I"; - } else { - os << "+"; - print_real_number(os, The(::cl_R)(::imagpart(*value))); - os << "*I"; - } - } - if (precedence <= upper_precedence) - os << ")"; - } - } + debugmsg("numeric print", LOGLEVEL_PRINT); + if (this->is_real()) { + // case 1, real: x or -x + if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) { + os << "("; + print_real_number(os, The(::cl_R)(*value)); + os << ")"; + } else { + print_real_number(os, The(::cl_R)(*value)); + } + } else { + // case 2, imaginary: y*I or -y*I + if (::realpart(*value) == 0) { + if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) { + if (::imagpart(*value) == -1) { + os << "(-I)"; + } else { + os << "("; + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I)"; + } + } else { + if (::imagpart(*value) == 1) { + os << "I"; + } else { + if (::imagpart (*value) == -1) { + os << "-I"; + } else { + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I"; + } + } + } + } else { + // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I + if (precedence <= upper_precedence) + os << "("; + print_real_number(os, The(::cl_R)(::realpart(*value))); + if (::imagpart(*value) < 0) { + if (::imagpart(*value) == -1) { + os << "-I"; + } else { + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I"; + } + } else { + if (::imagpart(*value) == 1) { + os << "+I"; + } else { + os << "+"; + print_real_number(os, The(::cl_R)(::imagpart(*value))); + os << "*I"; + } + } + if (precedence <= upper_precedence) + os << ")"; + } + } } void numeric::printraw(std::ostream & os) const { - // The method printraw doesn't do much, it simply uses CLN's operator<<() - // for output, which is ugly but reliable. e.g: 2+2i - debugmsg("numeric printraw", LOGLEVEL_PRINT); - os << "numeric(" << *value << ")"; + // 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; + 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); + debugmsg("numeric print csrc", LOGLEVEL_PRINT); + ios::fmtflags oldflags = os.flags(); + os.setf(ios::scientific); + if (this->is_rational() && !this->is_integer()) { + if (compare(_num0()) > 0) { + os << "("; + if (type == csrc_types::ctype_cl_N) + os << "cl_F(\"" << numer().evalf() << "\")"; + else + os << numer().to_double(); + } else { + os << "-("; + if (type == csrc_types::ctype_cl_N) + os << "cl_F(\"" << -numer().evalf() << "\")"; + else + os << -numer().to_double(); + } + os << "/"; + if (type == csrc_types::ctype_cl_N) + os << "cl_F(\"" << denom().evalf() << "\")"; + else + os << denom().to_double(); + os << ")"; + } else { + if (type == csrc_types::ctype_cl_N) + os << "cl_F(\"" << evalf() << "\")"; + else + os << to_double(); + } + os.flags(oldflags); } bool numeric::info(unsigned inf) const { - switch (inf) { - case info_flags::numeric: - case info_flags::polynomial: - case info_flags::rational_function: - return true; - case info_flags::real: - return is_real(); - case info_flags::rational: - case info_flags::rational_polynomial: - return is_rational(); - case info_flags::crational: - case info_flags::crational_polynomial: - return is_crational(); - case info_flags::integer: - case info_flags::integer_polynomial: - return is_integer(); - case info_flags::cinteger: - case info_flags::cinteger_polynomial: - return is_cinteger(); - case info_flags::positive: - return is_positive(); - case info_flags::negative: - return is_negative(); - case info_flags::nonnegative: - return !is_negative(); - case info_flags::posint: - return is_pos_integer(); - case info_flags::negint: - return is_integer() && is_negative(); - case info_flags::nonnegint: - return is_nonneg_integer(); - case info_flags::even: - return is_even(); - case info_flags::odd: - return is_odd(); - case info_flags::prime: - return is_prime(); - case info_flags::algebraic: - return !is_real(); - } - return false; + switch (inf) { + case info_flags::numeric: + case info_flags::polynomial: + case info_flags::rational_function: + return true; + case info_flags::real: + return is_real(); + case info_flags::rational: + case info_flags::rational_polynomial: + return is_rational(); + case info_flags::crational: + case info_flags::crational_polynomial: + return is_crational(); + case info_flags::integer: + case info_flags::integer_polynomial: + return is_integer(); + case info_flags::cinteger: + case info_flags::cinteger_polynomial: + return is_cinteger(); + case info_flags::positive: + return is_positive(); + case info_flags::negative: + return is_negative(); + case info_flags::nonnegative: + return !is_negative(); + case info_flags::posint: + return is_pos_integer(); + case info_flags::negint: + return is_integer() && is_negative(); + case info_flags::nonnegint: + return is_nonneg_integer(); + case info_flags::even: + return is_even(); + case info_flags::odd: + return is_odd(); + case info_flags::prime: + return is_prime(); + case info_flags::algebraic: + return !is_real(); + } + return false; } /** Disassemble real part and imaginary part to scan for the occurrence of a @@ -587,31 +591,31 @@ bool numeric::info(unsigned inf) const * 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; - if (o.imag().is_zero()) // e.g. scan for 3 in -3*I - return (this->real().is_equal(o) || this->imag().is_equal(o) || - this->real().is_equal(-o) || this->imag().is_equal(-o)); - else { - if (o.is_equal(I)) // e.g scan for I in 42*I - return !this->is_real(); - if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1 - return (this->real().has(o*I) || this->imag().has(o*I) || - this->real().has(-o*I) || this->imag().has(-o*I)); - } - return false; + if (!is_exactly_of_type(*other.bp, numeric)) + return false; + const numeric & o = static_cast(const_cast(*other.bp)); + if (this->is_equal(o) || this->is_equal(-o)) + return true; + if (o.imag().is_zero()) // e.g. scan for 3 in -3*I + return (this->real().is_equal(o) || this->imag().is_equal(o) || + this->real().is_equal(-o) || this->imag().is_equal(-o)); + else { + if (o.is_equal(I)) // e.g scan for I in 42*I + return !this->is_real(); + if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1 + return (this->real().has(o*I) || this->imag().has(o*I) || + this->real().has(-o*I) || this->imag().has(-o*I)); + } + return false; } /** Evaluation of numbers doesn't do anything at all. */ ex numeric::eval(int level) const { - // Warning: if this is ever gonna do something, the ex ctors from all kinds - // of numbers should be checking for status_flags::evaluated. - return this->hold(); + // Warning: if this is ever gonna do something, the ex ctors from all kinds + // of numbers should be checking for status_flags::evaluated. + return this->hold(); } @@ -624,8 +628,8 @@ ex numeric::eval(int level) const * @return an ex-handle to a numeric. */ ex numeric::evalf(int level) const { - // level can safely be discarded for numeric objects. - return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN + // level can safely be discarded for numeric objects. + return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN } // protected @@ -635,38 +639,38 @@ ex numeric::evalf(int level) const * @see ex::diff */ ex numeric::derivative(const symbol & s) const { - return _ex0(); + return _ex0(); } int numeric::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_exactly_of_type(other, numeric)); - const numeric & o = static_cast(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; - } + if (*value == *o.value) { + return 0; + } - return compare(o); + return compare(o); } bool numeric::is_equal_same_type(const basic & other) const { - GINAC_ASSERT(is_exactly_of_type(other,numeric)); - const numeric *o = static_cast(&other); - - return this->is_equal(*o); + GINAC_ASSERT(is_exactly_of_type(other,numeric)); + const numeric *o = static_cast(&other); + + return this->is_equal(*o); } unsigned numeric::calchash(void) const { - // 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); + // 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); } @@ -686,27 +690,27 @@ unsigned numeric::calchash(void) const * a new numeric object. */ numeric numeric::add(const numeric & other) const { - return numeric((*value)+(*other.value)); + return numeric((*value)+(*other.value)); } /** Numerical subtraction method. Subtracts argument from *this and returns * result as a new numeric object. */ numeric numeric::sub(const numeric & other) const { - return numeric((*value)-(*other.value)); + return numeric((*value)-(*other.value)); } /** Numerical multiplication method. Multiplies *this and argument and returns * result as a new numeric object. */ numeric numeric::mul(const numeric & other) const { - static const numeric * _num1p=&_num1(); - if (this==_num1p) { - return other; - } else if (&other==_num1p) { - return *this; - } - return numeric((*value)*(*other.value)); + static const numeric * _num1p=&_num1(); + if (this==_num1p) { + return other; + } else if (&other==_num1p) { + return *this; + } + return numeric((*value)*(*other.value)); } /** Numerical division method. Divides *this by argument and returns result as @@ -715,114 +719,116 @@ numeric numeric::mul(const numeric & other) const * @exception overflow_error (division by zero) */ numeric numeric::div(const numeric & other) const { - if (::zerop(*other.value)) - throw std::overflow_error("division by zero"); - return numeric((*value)/(*other.value)); + if (::zerop(*other.value)) + throw std::overflow_error("numeric::div(): division by zero"); + return numeric((*value)/(*other.value)); } numeric numeric::power(const numeric & other) const { - static const numeric * _num1p = &_num1(); - if (&other==_num1p) - return *this; - if (::zerop(*value)) { - if (::zerop(*other.value)) - throw std::domain_error("numeric::eval(): pow(0,0) is undefined"); - else if (::zerop(::realpart(*other.value))) - throw std::domain_error("numeric::eval(): pow(0,I) is undefined"); - else if (::minusp(::realpart(*other.value))) - throw std::overflow_error("numeric::eval(): division by zero"); - else - return _num0(); - } - return numeric(::expt(*value,*other.value)); + static const numeric * _num1p = &_num1(); + if (&other==_num1p) + return *this; + if (::zerop(*value)) { + if (::zerop(*other.value)) + throw std::domain_error("numeric::eval(): pow(0,0) is undefined"); + else if (::zerop(::realpart(*other.value))) + throw std::domain_error("numeric::eval(): pow(0,I) is undefined"); + else if (::minusp(::realpart(*other.value))) + throw std::overflow_error("numeric::eval(): division by zero"); + else + return _num0(); + } + return numeric(::expt(*value,*other.value)); } /** Inverse of a number. */ numeric numeric::inverse(void) const { - return numeric(::recip(*value)); // -> CLN + if (::zerop(*value)) + throw std::overflow_error("numeric::inverse(): division by zero"); + return numeric(::recip(*value)); // -> CLN } const numeric & numeric::add_dyn(const numeric & other) const { - return static_cast((new numeric((*value)+(*other.value)))-> - setflag(status_flags::dynallocated)); + return static_cast((new numeric((*value)+(*other.value)))-> + setflag(status_flags::dynallocated)); } const numeric & numeric::sub_dyn(const numeric & other) const { - return static_cast((new numeric((*value)-(*other.value)))-> - setflag(status_flags::dynallocated)); + return static_cast((new numeric((*value)-(*other.value)))-> + setflag(status_flags::dynallocated)); } const numeric & numeric::mul_dyn(const numeric & other) const { - static const numeric * _num1p=&_num1(); - if (this==_num1p) { - return other; - } else if (&other==_num1p) { - return *this; - } - return static_cast((new numeric((*value)*(*other.value)))-> - setflag(status_flags::dynallocated)); + static const numeric * _num1p=&_num1(); + if (this==_num1p) { + return other; + } else if (&other==_num1p) { + return *this; + } + return static_cast((new numeric((*value)*(*other.value)))-> + setflag(status_flags::dynallocated)); } const numeric & numeric::div_dyn(const numeric & other) const { - if (::zerop(*other.value)) - throw std::overflow_error("division by zero"); - return static_cast((new numeric((*value)/(*other.value)))-> - setflag(status_flags::dynallocated)); + if (::zerop(*other.value)) + throw std::overflow_error("division by zero"); + return static_cast((new numeric((*value)/(*other.value)))-> + setflag(status_flags::dynallocated)); } const numeric & numeric::power_dyn(const numeric & other) const { - static const numeric * _num1p=&_num1(); - if (&other==_num1p) - return *this; - if (::zerop(*value)) { - if (::zerop(*other.value)) - throw std::domain_error("numeric::eval(): pow(0,0) is undefined"); - else if (::zerop(::realpart(*other.value))) - throw std::domain_error("numeric::eval(): pow(0,I) is undefined"); - else if (::minusp(::realpart(*other.value))) - throw std::overflow_error("numeric::eval(): division by zero"); - else - return _num0(); - } - return static_cast((new numeric(::expt(*value,*other.value)))-> - setflag(status_flags::dynallocated)); + static const numeric * _num1p=&_num1(); + if (&other==_num1p) + return *this; + if (::zerop(*value)) { + if (::zerop(*other.value)) + throw std::domain_error("numeric::eval(): pow(0,0) is undefined"); + else if (::zerop(::realpart(*other.value))) + throw std::domain_error("numeric::eval(): pow(0,I) is undefined"); + else if (::minusp(::realpart(*other.value))) + throw std::overflow_error("numeric::eval(): division by zero"); + else + return _num0(); + } + return static_cast((new numeric(::expt(*value,*other.value)))-> + setflag(status_flags::dynallocated)); } const numeric & numeric::operator=(int i) { - return operator=(numeric(i)); + return operator=(numeric(i)); } const numeric & numeric::operator=(unsigned int i) { - return operator=(numeric(i)); + return operator=(numeric(i)); } const numeric & numeric::operator=(long i) { - return operator=(numeric(i)); + return operator=(numeric(i)); } const numeric & numeric::operator=(unsigned long i) { - return operator=(numeric(i)); + return operator=(numeric(i)); } const numeric & numeric::operator=(double d) { - return operator=(numeric(d)); + return operator=(numeric(d)); } const numeric & numeric::operator=(const char * s) { - return operator=(numeric(s)); + return operator=(numeric(s)); } /** Return the complex half-plane (left or right) in which the number lies. @@ -832,19 +838,19 @@ const numeric & numeric::operator=(const char * s) * @see numeric::compare(const numeric & other) */ int numeric::csgn(void) const { - if (this->is_zero()) - return 0; - if (!::zerop(::realpart(*value))) { - if (::plusp(::realpart(*value))) - return 1; - else - return -1; - } else { - if (::plusp(::imagpart(*value))) - return 1; - else - return -1; - } + if (this->is_zero()) + return 0; + if (!::zerop(::realpart(*value))) { + if (::plusp(::realpart(*value))) + return 1; + else + return -1; + } else { + if (::plusp(::imagpart(*value))) + return 1; + else + return -1; + } } /** This method establishes a canonical order on all numbers. For complex @@ -856,75 +862,75 @@ int numeric::csgn(void) const * @see numeric::csgn(void) */ int numeric::compare(const numeric & other) const { - // Comparing two real numbers? - if (this->is_real() && other.is_real()) - // Yes, just compare them - return ::cl_compare(The(::cl_R)(*value), The(::cl_R)(*other.value)); - else { - // No, first compare real parts - cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value)); - if (real_cmp) - return real_cmp; + // Comparing two real numbers? + if (this->is_real() && other.is_real()) + // Yes, just compare them + return ::cl_compare(The(::cl_R)(*value), The(::cl_R)(*other.value)); + else { + // No, first compare real parts + cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value)); + if (real_cmp) + return real_cmp; - return ::cl_compare(::imagpart(*value), ::imagpart(*other.value)); - } + return ::cl_compare(::imagpart(*value), ::imagpart(*other.value)); + } } bool numeric::is_equal(const numeric & other) const { - return (*value == *other.value); + return (*value == *other.value); } /** True if object is zero. */ bool numeric::is_zero(void) const { - return ::zerop(*value); // -> CLN + return ::zerop(*value); // -> CLN } /** True if object is not complex and greater than zero. */ bool numeric::is_positive(void) const { - if (this->is_real()) - return ::plusp(The(::cl_R)(*value)); // -> CLN - return false; + if (this->is_real()) + return ::plusp(The(::cl_R)(*value)); // -> CLN + return false; } /** True if object is not complex and less than zero. */ bool numeric::is_negative(void) const { - if (this->is_real()) - return ::minusp(The(::cl_R)(*value)); // -> CLN - return false; + if (this->is_real()) + return ::minusp(The(::cl_R)(*value)); // -> CLN + return false; } /** True if object is a non-complex integer. */ bool numeric::is_integer(void) const { - return ::instanceof(*value, ::cl_I_ring); // -> CLN + return ::instanceof(*value, ::cl_I_ring); // -> CLN } /** True if object is an exact integer greater than zero. */ bool numeric::is_pos_integer(void) const { - return (this->is_integer() && ::plusp(The(::cl_I)(*value))); // -> CLN + return (this->is_integer() && ::plusp(The(::cl_I)(*value))); // -> CLN } /** True if object is an exact integer greater or equal zero. */ bool numeric::is_nonneg_integer(void) const { - return (this->is_integer() && !::minusp(The(::cl_I)(*value))); // -> CLN + return (this->is_integer() && !::minusp(The(::cl_I)(*value))); // -> CLN } /** True if object is an exact even integer. */ bool numeric::is_even(void) const { - return (this->is_integer() && ::evenp(The(::cl_I)(*value))); // -> CLN + return (this->is_integer() && ::evenp(The(::cl_I)(*value))); // -> CLN } /** True if object is an exact odd integer. */ bool numeric::is_odd(void) const { - return (this->is_integer() && ::oddp(The(::cl_I)(*value))); // -> CLN + return (this->is_integer() && ::oddp(The(::cl_I)(*value))); // -> CLN } /** Probabilistic primality test. @@ -932,58 +938,58 @@ bool numeric::is_odd(void) const * @return true if object is exact integer and prime. */ bool numeric::is_prime(void) const { - return (this->is_integer() && ::isprobprime(The(::cl_I)(*value))); // -> CLN + return (this->is_integer() && ::isprobprime(The(::cl_I)(*value))); // -> CLN } /** True if object is an exact rational number, may even be complex * (denominator may be unity). */ bool numeric::is_rational(void) const { - return ::instanceof(*value, ::cl_RA_ring); // -> CLN + return ::instanceof(*value, ::cl_RA_ring); // -> CLN } /** True if object is a real integer, rational or float (but not complex). */ bool numeric::is_real(void) const { - return ::instanceof(*value, ::cl_R_ring); // -> CLN + return ::instanceof(*value, ::cl_R_ring); // -> CLN } bool numeric::operator==(const numeric & other) const { - return (*value == *other.value); // -> CLN + return (*value == *other.value); // -> CLN } bool numeric::operator!=(const numeric & other) const { - return (*value != *other.value); // -> CLN + return (*value != *other.value); // -> CLN } /** True if object is element of the domain of integers extended by I, i.e. is * of the form a+b*I, where a and b are integers. */ bool numeric::is_cinteger(void) const { - if (::instanceof(*value, ::cl_I_ring)) - return true; - else if (!this->is_real()) { // complex case, handle n+m*I - if (::instanceof(::realpart(*value), ::cl_I_ring) && - ::instanceof(::imagpart(*value), ::cl_I_ring)) - return true; - } - return false; + if (::instanceof(*value, ::cl_I_ring)) + return true; + else if (!this->is_real()) { // complex case, handle n+m*I + if (::instanceof(::realpart(*value), ::cl_I_ring) && + ::instanceof(::imagpart(*value), ::cl_I_ring)) + return true; + } + return false; } /** True if object is an exact rational number, may even be complex * (denominator may be unity). */ bool numeric::is_crational(void) const { - if (::instanceof(*value, ::cl_RA_ring)) - return true; - else if (!this->is_real()) { // complex case, handle Q(i): - if (::instanceof(::realpart(*value), ::cl_RA_ring) && - ::instanceof(::imagpart(*value), ::cl_RA_ring)) - return true; - } - return false; + if (::instanceof(*value, ::cl_RA_ring)) + return true; + else if (!this->is_real()) { // complex case, handle Q(i): + if (::instanceof(::realpart(*value), ::cl_RA_ring) && + ::instanceof(::imagpart(*value), ::cl_RA_ring)) + return true; + } + return false; } /** Numerical comparison: less. @@ -991,10 +997,9 @@ bool numeric::is_crational(void) const * @exception invalid_argument (complex inequality) */ bool numeric::operator<(const numeric & other) const { - if (this->is_real() && other.is_real()) - return (The(::cl_R)(*value) < The(::cl_R)(*other.value)); // -> CLN - throw std::invalid_argument("numeric::operator<(): complex inequality"); - return false; // make compiler shut up + if (this->is_real() && other.is_real()) + return (The(::cl_R)(*value) < The(::cl_R)(*other.value)); // -> CLN + throw std::invalid_argument("numeric::operator<(): complex inequality"); } /** Numerical comparison: less or equal. @@ -1002,10 +1007,10 @@ bool numeric::operator<(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator<=(const numeric & other) const { - if (this->is_real() && other.is_real()) - return (The(::cl_R)(*value) <= The(::cl_R)(*other.value)); // -> CLN - throw std::invalid_argument("numeric::operator<=(): complex inequality"); - return false; // make compiler shut up + if (this->is_real() && other.is_real()) + return (The(::cl_R)(*value) <= The(::cl_R)(*other.value)); // -> CLN + throw std::invalid_argument("numeric::operator<=(): complex inequality"); + return false; // make compiler shut up } /** Numerical comparison: greater. @@ -1013,10 +1018,9 @@ bool numeric::operator<=(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator>(const numeric & other) const { - if (this->is_real() && other.is_real()) - return (The(::cl_R)(*value) > The(::cl_R)(*other.value)); // -> CLN - throw std::invalid_argument("numeric::operator>(): complex inequality"); - return false; // make compiler shut up + if (this->is_real() && other.is_real()) + return (The(::cl_R)(*value) > The(::cl_R)(*other.value)); // -> CLN + throw std::invalid_argument("numeric::operator>(): complex inequality"); } /** Numerical comparison: greater or equal. @@ -1024,10 +1028,9 @@ bool numeric::operator>(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator>=(const numeric & other) const { - if (this->is_real() && other.is_real()) - return (The(::cl_R)(*value) >= The(::cl_R)(*other.value)); // -> CLN - throw std::invalid_argument("numeric::operator>=(): complex inequality"); - return false; // make compiler shut up + if (this->is_real() && other.is_real()) + return (The(::cl_R)(*value) >= The(::cl_R)(*other.value)); // -> CLN + throw std::invalid_argument("numeric::operator>=(): complex inequality"); } /** Converts numeric types to machine's int. You should check with @@ -1035,8 +1038,8 @@ bool numeric::operator>=(const numeric & other) const * You may also consider checking the range first. */ int numeric::to_int(void) const { - GINAC_ASSERT(this->is_integer()); - return ::cl_I_to_int(The(::cl_I)(*value)); // -> CLN + GINAC_ASSERT(this->is_integer()); + return ::cl_I_to_int(The(::cl_I)(*value)); // -> CLN } /** Converts numeric types to machine's long. You should check with @@ -1044,42 +1047,30 @@ int numeric::to_int(void) const * You may also consider checking the range first. */ long numeric::to_long(void) const { - GINAC_ASSERT(this->is_integer()); - return ::cl_I_to_long(The(::cl_I)(*value)); // -> CLN + GINAC_ASSERT(this->is_integer()); + return ::cl_I_to_long(The(::cl_I)(*value)); // -> CLN } /** Converts numeric types to machine's double. You should check with is_real() * if the number is really not complex before calling this method. */ double numeric::to_double(void) const { - GINAC_ASSERT(this->is_real()); - return ::cl_double_approx(::realpart(*value)); // -> CLN + GINAC_ASSERT(this->is_real()); + return ::cl_double_approx(::realpart(*value)); // -> CLN } /** Real part of a number. */ const numeric numeric::real(void) const { - return numeric(::realpart(*value)); // -> CLN + return numeric(::realpart(*value)); // -> CLN } /** Imaginary part of a number. */ const numeric numeric::imag(void) const { - return numeric(::imagpart(*value)); // -> CLN + return numeric(::imagpart(*value)); // -> CLN } -#ifndef SANE_LINKER -// Unfortunately, CLN did not provide an official way to access the numerator -// or denominator of a rational number (cl_RA). Doing some excavations in CLN -// one finds how it works internally in src/rational/cl_RA.h: -struct cl_heap_ratio : cl_heap { - cl_I numerator; - cl_I denominator; -}; - -inline cl_heap_ratio* TheRatio (const cl_N& obj) -{ return (cl_heap_ratio*)(obj.pointer); } -#endif // ndef SANE_LINKER /** Numerator. Computes the numerator of rational numbers, rationalized * numerator of complex if real and imaginary part are both rational numbers @@ -1087,50 +1078,29 @@ inline cl_heap_ratio* TheRatio (const cl_N& obj) * cases. */ const numeric numeric::numer(void) const { - if (this->is_integer()) { - return numeric(*this); - } -#ifdef SANE_LINKER - else if (::instanceof(*value, ::cl_RA_ring)) { - return numeric(::numerator(The(::cl_RA)(*value))); - } - else if (!this->is_real()) { // complex case, handle Q(i): - cl_R r = ::realpart(*value); - cl_R i = ::imagpart(*value); - if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring)) - return numeric(*this); - if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring)) - return numeric(::complex(r*::denominator(The(::cl_RA)(i)), ::numerator(The(::cl_RA)(i)))); - if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring)) - return numeric(::complex(::numerator(The(::cl_RA)(r)), i*::denominator(The(::cl_RA)(r)))); - if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring)) { - cl_I s = ::lcm(::denominator(The(::cl_RA)(r)), ::denominator(The(::cl_RA)(i))); - return numeric(::complex(::numerator(The(::cl_RA)(r))*(exquo(s,::denominator(The(::cl_RA)(r)))), - ::numerator(The(::cl_RA)(i))*(exquo(s,::denominator(The(::cl_RA)(i)))))); - } - } -#else - else if (instanceof(*value, ::cl_RA_ring)) { - return numeric(TheRatio(*value)->numerator); - } - else if (!this->is_real()) { // complex case, handle Q(i): - cl_R r = ::realpart(*value); - cl_R i = ::imagpart(*value); - if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring)) - return numeric(*this); - if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_RA_ring)) - return numeric(::complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator)); - if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring)) - return numeric(::complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator)); - if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring)) { - cl_I s = ::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator); - return numeric(::complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)), - TheRatio(i)->numerator*(exquo(s,TheRatio(i)->denominator)))); - } - } -#endif // def SANE_LINKER - // at least one float encountered - return numeric(*this); + if (this->is_integer()) + return numeric(*this); + + else if (::instanceof(*value, ::cl_RA_ring)) + return numeric(::numerator(The(::cl_RA)(*value))); + + else if (!this->is_real()) { // complex case, handle Q(i): + cl_R r = ::realpart(*value); + cl_R i = ::imagpart(*value); + if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring)) + return numeric(*this); + if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring)) + return numeric(::complex(r*::denominator(The(::cl_RA)(i)), ::numerator(The(::cl_RA)(i)))); + if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring)) + return numeric(::complex(::numerator(The(::cl_RA)(r)), i*::denominator(The(::cl_RA)(r)))); + if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring)) { + cl_I s = ::lcm(::denominator(The(::cl_RA)(r)), ::denominator(The(::cl_RA)(i))); + return numeric(::complex(::numerator(The(::cl_RA)(r))*(exquo(s,::denominator(The(::cl_RA)(r)))), + ::numerator(The(::cl_RA)(i))*(exquo(s,::denominator(The(::cl_RA)(i)))))); + } + } + // at least one float encountered + return numeric(*this); } /** Denominator. Computes the denominator of rational numbers, common integer @@ -1138,44 +1108,26 @@ const numeric numeric::numer(void) const * (i.e denom(4/3+5/6*I) == 6), one in all other cases. */ const numeric numeric::denom(void) const { - if (this->is_integer()) { - return _num1(); - } -#ifdef SANE_LINKER - if (instanceof(*value, ::cl_RA_ring)) { - return numeric(::denominator(The(::cl_RA)(*value))); - } - if (!this->is_real()) { // complex case, handle Q(i): - cl_R r = ::realpart(*value); - cl_R i = ::imagpart(*value); - if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring)) - return _num1(); - if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring)) - return numeric(::denominator(The(::cl_RA)(i))); - if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring)) - return numeric(::denominator(The(::cl_RA)(r))); - if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring)) - return numeric(::lcm(::denominator(The(::cl_RA)(r)), ::denominator(The(::cl_RA)(i)))); - } -#else - if (instanceof(*value, ::cl_RA_ring)) { - return numeric(TheRatio(*value)->denominator); - } - if (!this->is_real()) { // complex case, handle Q(i): - cl_R r = ::realpart(*value); - cl_R i = ::imagpart(*value); - if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring)) - return _num1(); - if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_RA_ring)) - return numeric(TheRatio(i)->denominator); - if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring)) - return numeric(TheRatio(r)->denominator); - if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring)) - return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator)); - } -#endif // def SANE_LINKER - // at least one float encountered - return _num1(); + if (this->is_integer()) + return _num1(); + + if (instanceof(*value, ::cl_RA_ring)) + return numeric(::denominator(The(::cl_RA)(*value))); + + if (!this->is_real()) { // complex case, handle Q(i): + cl_R r = ::realpart(*value); + cl_R i = ::imagpart(*value); + if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring)) + return _num1(); + if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring)) + return numeric(::denominator(The(::cl_RA)(i))); + if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring)) + return numeric(::denominator(The(::cl_RA)(r))); + if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring)) + return numeric(::lcm(::denominator(The(::cl_RA)(r)), ::denominator(The(::cl_RA)(i)))); + } + // at least one float encountered + return _num1(); } /** Size in binary notation. For integers, this is the smallest n >= 0 such @@ -1186,10 +1138,10 @@ const numeric numeric::denom(void) const * in two's complement if it is an integer, 0 otherwise. */ int numeric::int_length(void) const { - if (this->is_integer()) - return ::integer_length(The(::cl_I)(*value)); // -> CLN - else - return 0; + if (this->is_integer()) + return ::integer_length(The(::cl_I)(*value)); // -> CLN + else + return 0; } @@ -1206,7 +1158,7 @@ unsigned numeric::precedence = 30; ////////// const numeric some_numeric; -const type_info & typeid_numeric=typeid(some_numeric); +const std::type_info & typeid_numeric = typeid(some_numeric); /** Imaginary unit. This is not a constant but a numeric since we are * natively handing complex numbers anyways. */ const numeric I = numeric(::complex(cl_I(0),cl_I(1))); @@ -1217,7 +1169,7 @@ const numeric I = numeric(::complex(cl_I(0),cl_I(1))); * @return arbitrary precision numerical exp(x). */ const numeric exp(const numeric & x) { - return ::exp(*x.value); // -> CLN + return ::exp(*x.value); // -> CLN } @@ -1228,9 +1180,9 @@ const numeric exp(const numeric & x) * @exception pole_error("log(): logarithmic pole",0) */ const numeric log(const numeric & z) { - if (z.is_zero()) - throw pole_error("log(): logarithmic pole",0); - return ::log(*z.value); // -> CLN + if (z.is_zero()) + throw pole_error("log(): logarithmic pole",0); + return ::log(*z.value); // -> CLN } @@ -1239,7 +1191,7 @@ const numeric log(const numeric & z) * @return arbitrary precision numerical sin(x). */ const numeric sin(const numeric & x) { - return ::sin(*x.value); // -> CLN + return ::sin(*x.value); // -> CLN } @@ -1248,7 +1200,7 @@ const numeric sin(const numeric & x) * @return arbitrary precision numerical cos(x). */ const numeric cos(const numeric & x) { - return ::cos(*x.value); // -> CLN + return ::cos(*x.value); // -> CLN } @@ -1257,16 +1209,16 @@ const numeric cos(const numeric & x) * @return arbitrary precision numerical tan(x). */ const numeric tan(const numeric & x) { - return ::tan(*x.value); // -> CLN + return ::tan(*x.value); // -> CLN } - + /** Numeric inverse sine (trigonometric function). * * @return arbitrary precision numerical asin(x). */ const numeric asin(const numeric & x) { - return ::asin(*x.value); // -> CLN + return ::asin(*x.value); // -> CLN } @@ -1275,9 +1227,9 @@ const numeric asin(const numeric & x) * @return arbitrary precision numerical acos(x). */ const numeric acos(const numeric & x) { - return ::acos(*x.value); // -> CLN + return ::acos(*x.value); // -> CLN } - + /** Arcustangent. * @@ -1286,11 +1238,11 @@ const numeric acos(const numeric & 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(_num1())) - throw pole_error("atan(): logarithmic pole",0); - return ::atan(*x.value); // -> CLN + if (!x.is_real() && + x.real().is_zero() && + abs(x.imag()).is_equal(_num1())) + throw pole_error("atan(): logarithmic pole",0); + return ::atan(*x.value); // -> CLN } @@ -1301,10 +1253,10 @@ const numeric atan(const numeric & x) * @return atan(y/x) */ const numeric atan(const numeric & y, const numeric & x) { - if (x.is_real() && y.is_real()) - return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN - else - throw std::invalid_argument("atan(): complex argument"); + if (x.is_real() && y.is_real()) + return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN + else + throw std::invalid_argument("atan(): complex argument"); } @@ -1313,7 +1265,7 @@ const numeric atan(const numeric & y, const numeric & x) * @return arbitrary precision numerical sinh(x). */ const numeric sinh(const numeric & x) { - return ::sinh(*x.value); // -> CLN + return ::sinh(*x.value); // -> CLN } @@ -1322,7 +1274,7 @@ const numeric sinh(const numeric & x) * @return arbitrary precision numerical cosh(x). */ const numeric cosh(const numeric & x) { - return ::cosh(*x.value); // -> CLN + return ::cosh(*x.value); // -> CLN } @@ -1331,16 +1283,16 @@ const numeric cosh(const numeric & x) * @return arbitrary precision numerical tanh(x). */ const numeric tanh(const numeric & x) { - return ::tanh(*x.value); // -> CLN + return ::tanh(*x.value); // -> CLN } - + /** Numeric inverse hyperbolic sine (trigonometric function). * * @return arbitrary precision numerical asinh(x). */ const numeric asinh(const numeric & x) { - return ::asinh(*x.value); // -> CLN + return ::asinh(*x.value); // -> CLN } @@ -1349,7 +1301,7 @@ const numeric asinh(const numeric & x) * @return arbitrary precision numerical acosh(x). */ const numeric acosh(const numeric & x) { - return ::acosh(*x.value); // -> CLN + return ::acosh(*x.value); // -> CLN } @@ -1358,34 +1310,34 @@ const numeric acosh(const numeric & x) * @return arbitrary precision numerical atanh(x). */ const numeric atanh(const numeric & x) { - return ::atanh(*x.value); // -> CLN + return ::atanh(*x.value); // -> CLN } /*static ::cl_N Li2_series(const ::cl_N & x, const ::cl_float_format_t & prec) { - // Note: argument must be in the unit circle - // This is very inefficient unless we have fast floating point Bernoulli - // numbers implemented! - ::cl_N c1 = -::log(1-x); - ::cl_N c2 = c1; - // hard-wire the first two Bernoulli numbers - ::cl_N acc = c1 - ::square(c1)/4; - ::cl_N aug; - ::cl_F pisq = ::square(::cl_pi(prec)); // pi^2 - ::cl_F piac = ::cl_float(1, prec); // accumulator: pi^(2*i) - unsigned i = 1; - c1 = ::square(c1); - do { - c2 = c1 * c2; - piac = piac * pisq; - aug = c2 * (*(bernoulli(numeric(2*i)).clnptr())) / ::factorial(2*i+1); - // aug = c2 * ::cl_I(i%2 ? 1 : -1) / ::cl_I(2*i+1) * ::cl_zeta(2*i, prec) / piac / (::cl_I(1)<<(2*i-1)); - acc = acc + aug; - ++i; - } while (acc != acc+aug); - return acc; + // 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 @@ -1393,41 +1345,41 @@ const numeric atanh(const numeric & x) 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; + // 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); + 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, @@ -1437,28 +1389,28 @@ static ::cl_N Li2_projection(const ::cl_N & x, * @return arbitrary precision numerical Li2(x). */ const numeric Li2(const numeric & x) { - if (::zerop(*x.value)) - return x; - - // what is the desired float format? - // first guess: default format - ::cl_float_format_t prec = ::cl_default_float_format; - // second guess: the argument's format - if (!::instanceof(::realpart(*x.value),cl_RA_ring)) - prec = ::cl_float_format(The(::cl_F)(::realpart(*x.value))); - else if (!::instanceof(::imagpart(*x.value),cl_RA_ring)) - prec = ::cl_float_format(The(::cl_F)(::imagpart(*x.value))); - - if (*x.value==1) // may cause trouble with log(1-x) - return ::cl_zeta(2, prec); - - if (::abs(*x.value) > 1) - // -log(-x)^2 / 2 - zeta(2) - Li2(1/x) - return(-::square(::log(-*x.value))/2 - - ::cl_zeta(2, prec) - - Li2_projection(::recip(*x.value), prec)); - else - return Li2_projection(*x.value, prec); + 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); } @@ -1466,20 +1418,20 @@ const numeric Li2(const numeric & x) * integer arguments. */ const numeric zeta(const numeric & x) { - // A dirty hack to allow for things like zeta(3.0), since CLN currently - // only knows about integer arguments and zeta(3).evalf() automatically - // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3 - // being an exact zero for CLN, which can be tested and then we can just - // pass the number casted to an int: - if (x.is_real()) { - int aux = (int)(::cl_double_approx(::realpart(*x.value))); - if (::zerop(*x.value-aux)) - return ::cl_zeta(aux); // -> CLN - } - std::clog << "zeta(" << x - << "): Does anybody know good way to calculate this numerically?" - << std::endl; - return numeric(0); + // A dirty hack to allow for things like zeta(3.0), since CLN currently + // only knows about integer arguments and zeta(3).evalf() automatically + // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3 + // being an exact zero for CLN, which can be tested and then we can just + // pass the number casted to an int: + if (x.is_real()) { + int aux = (int)(::cl_double_approx(::realpart(*x.value))); + if (::zerop(*x.value-aux)) + return ::cl_zeta(aux); // -> CLN + } + std::clog << "zeta(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); } @@ -1487,17 +1439,17 @@ const numeric zeta(const numeric & x) * 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); + 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); + std::clog << "tgamma(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); } @@ -1505,10 +1457,10 @@ const numeric tgamma(const numeric & x) * 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); + std::clog << "psi(" << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); } @@ -1516,10 +1468,10 @@ const numeric psi(const numeric & x) * 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); + std::clog << "psi(" << n << "," << x + << "): Does anybody know good way to calculate this numerically?" + << std::endl; + return numeric(0); } @@ -1529,9 +1481,9 @@ const numeric psi(const numeric & n, const numeric & x) * @exception range_error (argument must be integer >= 0) */ const numeric factorial(const numeric & n) { - if (!n.is_nonneg_integer()) - throw std::range_error("numeric::factorial(): argument must be integer >= 0"); - return numeric(::factorial(n.to_int())); // -> CLN + if (!n.is_nonneg_integer()) + throw std::range_error("numeric::factorial(): argument must be integer >= 0"); + return numeric(::factorial(n.to_int())); // -> CLN } @@ -1543,13 +1495,13 @@ const numeric factorial(const numeric & n) * @exception range_error (argument must be integer >= -1) */ const numeric doublefactorial(const numeric & n) { - if (n == numeric(-1)) { - return _num1(); - } - if (!n.is_nonneg_integer()) { - throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1"); - } - return numeric(::doublefactorial(n.to_int())); // -> CLN + if (n == numeric(-1)) { + return _num1(); + } + if (!n.is_nonneg_integer()) { + throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1"); + } + return numeric(::doublefactorial(n.to_int())); // -> CLN } @@ -1559,19 +1511,19 @@ const numeric doublefactorial(const numeric & n) * binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */ const numeric binomial(const numeric & n, const numeric & k) { - if (n.is_integer() && k.is_integer()) { - if (n.is_nonneg_integer()) { - if (k.compare(n)!=1 && k.compare(_num0())!=-1) - return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN - else - return _num0(); - } else { - return _num_1().power(k)*binomial(k-n-_num1(),k); - } - } - - // should really be gamma(n+1)/gamma(r+1)/gamma(n-r+1) or a suitable limit - throw std::range_error("numeric::binomial(): don´t know how to evaluate that."); + if (n.is_integer() && k.is_integer()) { + if (n.is_nonneg_integer()) { + if (k.compare(n)!=1 && k.compare(_num0())!=-1) + return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN + else + return _num0(); + } else { + return _num_1().power(k)*binomial(k-n-_num1(),k); + } + } + + // should really be gamma(n+1)/gamma(r+1)/gamma(n-r+1) or a suitable limit + throw std::range_error("numeric::binomial(): don´t know how to evaluate that."); } @@ -1582,72 +1534,72 @@ const numeric binomial(const numeric & n, const numeric & k) * @exception range_error (argument must be integer >= 0) */ const numeric bernoulli(const numeric & nn) { - if (!nn.is_integer() || nn.is_negative()) - throw std::range_error("numeric::bernoulli(): argument must be integer >= 0"); - - // 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]; + 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]; } @@ -1659,65 +1611,65 @@ const numeric bernoulli(const numeric & nn) * @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; - } - } - if (n.is_even()) - // Here we don't use the squaring formula because one multiplication - // is cheaper than two squarings. - return u * ((v << 1) - u); - else - return ::square(u) + ::square(v); + if (!n.is_integer()) + throw std::range_error("numeric::fibonacci(): argument must be integer"); + // Method: + // + // This is based on an implementation that can be found in CLN's example + // directory. There, it is done recursively, which may be more elegant + // than our non-recursive implementation that has to resort to some bit- + // fiddling. This is, however, a matter of taste. + // The following addition formula holds: + // + // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0. + // + // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence + // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values + // agree.) + // Replace m by m+1: + // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0 + // Now put in m = n, to get + // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n)) + // F(2n+1) = F(n)^2 + F(n+1)^2 + // hence + // F(2n+2) = F(n+1)*(2*F(n) + F(n+1)) + if (n.is_zero()) + return _num0(); + if (n.is_negative()) + if (n.is_even()) + return -fibonacci(-n); + else + return fibonacci(-n); + + ::cl_I u(0); + ::cl_I v(1); + ::cl_I m = The(::cl_I)(*n.value) >> 1L; // floor(n/2); + for (uintL bit=::integer_length(m); bit>0; --bit) { + // Since a squaring is cheaper than a multiplication, better use + // three squarings instead of one multiplication and two squarings. + ::cl_I u2 = ::square(u); + ::cl_I v2 = ::square(v); + if (::logbitp(bit-1, m)) { + v = ::square(u + v) - u2; + u = u2 + v2; + } else { + u = v2 - ::square(v - u); + v = u2 + v2; + } + } + if (n.is_even()) + // Here we don't use the squaring formula because one multiplication + // is cheaper than two squarings. + return u * ((v << 1) - u); + else + return ::square(u) + ::square(v); } /** Absolute value. */ numeric abs(const numeric & x) { - return ::abs(*x.value); // -> CLN + return ::abs(*x.value); // -> CLN } @@ -1730,10 +1682,10 @@ numeric abs(const numeric & x) * integer, 0 otherwise. */ numeric mod(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) - return ::mod(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN - else - return _num0(); // Throw? + if (a.is_integer() && b.is_integer()) + return ::mod(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN + else + return _num0(); // Throw? } @@ -1743,11 +1695,11 @@ numeric mod(const numeric & a, const numeric & b) * @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */ numeric smod(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) { - cl_I b2 = The(::cl_I)(ceiling1(The(::cl_I)(*b.value) / 2)) - 1; - return ::mod(The(::cl_I)(*a.value) + b2, The(::cl_I)(*b.value)) - b2; - } else - return _num0(); // Throw? + if (a.is_integer() && b.is_integer()) { + cl_I b2 = The(::cl_I)(ceiling1(The(::cl_I)(*b.value) >> 1)) - 1; + return ::mod(The(::cl_I)(*a.value) + b2, The(::cl_I)(*b.value)) - b2; + } else + return _num0(); // Throw? } @@ -1759,10 +1711,10 @@ numeric smod(const numeric & a, const numeric & b) * @return remainder of a/b if both are integer, 0 otherwise. */ numeric irem(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) - return ::rem(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN - else - return _num0(); // Throw? + if (a.is_integer() && b.is_integer()) + return ::rem(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN + else + return _num0(); // Throw? } @@ -1775,15 +1727,14 @@ numeric irem(const numeric & a, const numeric & b) * 0 otherwise. */ numeric irem(const numeric & a, const numeric & b, numeric & q) { - if (a.is_integer() && b.is_integer()) { // -> CLN - cl_I_div_t rem_quo = truncate2(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); - q = rem_quo.quotient; - return rem_quo.remainder; - } - else { - q = _num0(); - return _num0(); // Throw? - } + if (a.is_integer() && b.is_integer()) { // -> CLN + cl_I_div_t rem_quo = truncate2(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); + q = rem_quo.quotient; + return rem_quo.remainder; + } else { + q = _num0(); + return _num0(); // Throw? + } } @@ -1793,10 +1744,10 @@ numeric irem(const numeric & a, const numeric & b, numeric & q) * @return truncated quotient of a/b if both are integer, 0 otherwise. */ numeric iquo(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) - return truncate1(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN - else - return _num0(); // Throw? + if (a.is_integer() && b.is_integer()) + return truncate1(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN + else + return _num0(); // Throw? } @@ -1808,14 +1759,14 @@ numeric iquo(const numeric & a, const numeric & b) * integer, 0 otherwise. */ numeric iquo(const numeric & a, const numeric & b, numeric & r) { - if (a.is_integer() && b.is_integer()) { // -> CLN - cl_I_div_t rem_quo = truncate2(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); - r = rem_quo.remainder; - return rem_quo.quotient; - } else { - r = _num0(); - return _num0(); // Throw? - } + if (a.is_integer() && b.is_integer()) { // -> CLN + cl_I_div_t rem_quo = truncate2(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); + r = rem_quo.remainder; + return rem_quo.quotient; + } else { + r = _num0(); + return _num0(); // Throw? + } } @@ -1829,19 +1780,19 @@ numeric iquo(const numeric & a, const numeric & b, numeric & r) * where imag(z)>0. */ numeric sqrt(const numeric & z) { - return ::sqrt(*z.value); // -> CLN + return ::sqrt(*z.value); // -> CLN } /** Integer numeric square root. */ numeric isqrt(const numeric & x) { - if (x.is_integer()) { - cl_I root; - ::isqrt(The(::cl_I)(*x.value), &root); // -> CLN - return root; - } else - return _num0(); // Throw? + if (x.is_integer()) { + cl_I root; + ::isqrt(The(::cl_I)(*x.value), &root); // -> CLN + return root; + } else + return _num0(); // Throw? } @@ -1851,10 +1802,10 @@ numeric isqrt(const numeric & x) * if they are not. */ numeric gcd(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) - return ::gcd(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN - else - return _num1(); + if (a.is_integer() && b.is_integer()) + return ::gcd(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN + else + return _num1(); } @@ -1864,31 +1815,31 @@ numeric gcd(const numeric & a, const numeric & b) * two numbers if they are not. */ numeric lcm(const numeric & a, const numeric & b) { - if (a.is_integer() && b.is_integer()) - return ::lcm(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN - else - return *a.value * *b.value; + if (a.is_integer() && b.is_integer()) + return ::lcm(The(::cl_I)(*a.value), The(::cl_I)(*b.value)); // -> CLN + else + return *a.value * *b.value; } /** Floating point evaluation of Archimedes' constant Pi. */ ex PiEvalf(void) { - return numeric(::cl_pi(cl_default_float_format)); // -> CLN + return numeric(::cl_pi(cl_default_float_format)); // -> CLN } /** Floating point evaluation of Euler's constant gamma. */ ex EulerEvalf(void) { - return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN + return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN } /** Floating point evaluation of Catalan's constant. */ ex CatalanEvalf(void) { - return numeric(::cl_catalanconst(cl_default_float_format)); // -> CLN + return numeric(::cl_catalanconst(cl_default_float_format)); // -> CLN } @@ -1896,39 +1847,39 @@ ex CatalanEvalf(void) // be 61 (<64) while cl_float_format(18)=65. We want to have a cl_LF instead // of cl_SF, cl_FF or cl_DF but everything else is basically arbitrary. _numeric_digits::_numeric_digits() - : digits(17) + : digits(17) { - assert(!too_late); - too_late = true; - cl_default_float_format = ::cl_float_format(17); + assert(!too_late); + too_late = true; + cl_default_float_format = ::cl_float_format(17); } _numeric_digits& _numeric_digits::operator=(long prec) { - digits=prec; - cl_default_float_format = ::cl_float_format(prec); - return *this; + digits=prec; + cl_default_float_format = ::cl_float_format(prec); + return *this; } _numeric_digits::operator long() { - return (long)digits; + return (long)digits; } void _numeric_digits::print(std::ostream & os) const { - debugmsg("_numeric_digits print", LOGLEVEL_PRINT); - os << digits; + debugmsg("_numeric_digits print", LOGLEVEL_PRINT); + os << digits; } std::ostream& operator<<(std::ostream& os, const _numeric_digits & e) { - e.print(os); - return os; + e.print(os); + return os; } //////////