* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "config.h"
#include <stdexcept>
#include <string>
#include <sstream>
+#include <limits>
#include "numeric.h"
#include "ex.h"
-#include "print.h"
+#include "operators.h"
#include "archive.h"
#include "tostring.h"
#include "utils.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(numeric, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(numeric, basic,
+ print_func<print_context>(&numeric::do_print).
+ print_func<print_latex>(&numeric::do_print_latex).
+ print_func<print_csrc>(&numeric::do_print_csrc).
+ print_func<print_csrc_cl_N>(&numeric::do_print_csrc_cl_N).
+ print_func<print_tree>(&numeric::do_print_tree).
+ print_func<print_python_repr>(&numeric::do_print_python_repr))
//////////
-// default ctor, dtor, copy ctor, assignment operator and helpers
+// default constructor
//////////
/** default ctor. Numerically it initializes to an integer zero. */
setflag(status_flags::evaluated | status_flags::expanded);
}
-void numeric::copy(const numeric &other)
-{
- inherited::copy(other);
- value = other.value;
-}
-
-DEFAULT_DESTROY(numeric)
-
//////////
-// other ctors
+// other constructors
//////////
// public
// emphasizes efficiency. However, if the integer is small enough
// we save space and dereferences by using an immediate type.
// (C.f. <cln/object.h>)
- if (i < (1U<<cl_value_len-1))
+ if (i < (1L << (cl_value_len-1)) && i >= -(1L << (cl_value_len-1)))
value = cln::cl_I(i);
else
- value = cln::cl_I((long) i);
+ value = cln::cl_I(static_cast<long>(i));
setflag(status_flags::evaluated | status_flags::expanded);
}
// emphasizes efficiency. However, if the integer is small enough
// we save space and dereferences by using an immediate type.
// (C.f. <cln/object.h>)
- if (i < (1U<<cl_value_len-1))
+ if (i < (1U << (cl_value_len-1)))
value = cln::cl_I(i);
else
- value = cln::cl_I((unsigned long) i);
+ value = cln::cl_I(static_cast<unsigned long>(i));
setflag(status_flags::evaluated | status_flags::expanded);
}
setflag(status_flags::evaluated | status_flags::expanded);
}
-/** Ctor for rational numerics a/b.
+
+/** Constructor for rational numerics a/b.
*
* @exception overflow_error (division by zero) */
numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
setflag(status_flags::evaluated | status_flags::expanded);
}
+
//////////
// archiving
//////////
-numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
cln::cl_N ctorval = 0;
// Write number as string
std::ostringstream s;
if (this->is_crational())
- s << cln::the<cln::cl_N>(value);
+ s << value;
else {
// Non-rational numbers are written in an integer-decoded format
// to preserve the precision
* want to visibly distinguish from cl_LF.
*
* @see numeric::print() */
-static void print_real_number(const print_context & c, const cln::cl_R &x)
+static void print_real_number(const print_context & c, const cln::cl_R & x)
{
cln::cl_print_flags ourflags;
if (cln::instanceof(x, cln::cl_RA_ring)) {
!is_a<print_latex>(c)) {
cln::print_real(c.s, ourflags, x);
} else { // rational output in LaTeX context
+ if (x < 0)
+ c.s << "-";
c.s << "\\frac{";
- cln::print_real(c.s, ourflags, cln::numerator(cln::the<cln::cl_RA>(x)));
+ cln::print_real(c.s, ourflags, cln::abs(cln::numerator(cln::the<cln::cl_RA>(x))));
c.s << "}{";
cln::print_real(c.s, ourflags, cln::denominator(cln::the<cln::cl_RA>(x)));
c.s << '}';
}
}
-/** This method adds to the output so it blends more consistently together
- * with the other routines and produces something compatible to ginsh input.
- *
- * @see print_real_number() */
-void numeric::print(const print_context & c, unsigned level) const
+/** Helper function to print integer number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_integer_csrc(const print_context & c, const cln::cl_I & x)
{
- if (is_a<print_tree>(c)) {
+ // Print small numbers in compact float format, but larger numbers in
+ // scientific format
+ const int max_cln_int = 536870911; // 2^29-1
+ if (x >= cln::cl_I(-max_cln_int) && x <= cln::cl_I(max_cln_int))
+ c.s << cln::cl_I_to_int(x) << ".0";
+ else
+ c.s << cln::double_approx(x);
+}
- c.s << std::string(level, ' ') << cln::the<cln::cl_N>(value)
- << " (" << class_name() << ")"
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << std::endl;
+/** Helper function to print real number in C++ source format.
+ *
+ * @see numeric::print() */
+static void print_real_csrc(const print_context & c, const cln::cl_R & x)
+{
+ if (cln::instanceof(x, cln::cl_I_ring)) {
- } else if (is_a<print_csrc>(c)) {
+ // Integer number
+ print_integer_csrc(c, cln::the<cln::cl_I>(x));
- std::ios::fmtflags oldflags = c.s.flags();
- c.s.setf(std::ios::scientific);
- int oldprec = c.s.precision();
- if (is_a<print_csrc_double>(c))
- c.s.precision(16);
- else
- c.s.precision(7);
- if (is_a<print_csrc_cl_N>(c) && this->is_integer()) {
- c.s << "cln::cl_I(\"";
- const cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
- print_real_number(c,r);
- c.s << "\")";
- } else if (this->is_rational() && !this->is_integer()) {
- if (compare(_num0) > 0) {
- c.s << "(";
- if (is_a<print_csrc_cl_N>(c))
- c.s << "cln::cl_F(\"" << numer().evalf() << "\")";
- else
- c.s << numer().to_double();
- } else {
- c.s << "-(";
- if (is_a<print_csrc_cl_N>(c))
- c.s << "cln::cl_F(\"" << -numer().evalf() << "\")";
- else
- c.s << -numer().to_double();
- }
- c.s << "/";
- if (is_a<print_csrc_cl_N>(c))
- c.s << "cln::cl_F(\"" << denom().evalf() << "\")";
- else
- c.s << denom().to_double();
- c.s << ")";
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ const cln::cl_I numer = cln::numerator(cln::the<cln::cl_RA>(x));
+ const cln::cl_I denom = cln::denominator(cln::the<cln::cl_RA>(x));
+ if (cln::plusp(x) > 0) {
+ c.s << "(";
+ print_integer_csrc(c, numer);
} else {
- if (is_a<print_csrc_cl_N>(c))
- c.s << "cln::cl_F(\"" << evalf() << "_" << Digits << "\")";
- else
- c.s << to_double();
+ c.s << "-(";
+ print_integer_csrc(c, -numer);
}
- c.s.flags(oldflags);
- c.s.precision(oldprec);
+ c.s << "/";
+ print_integer_csrc(c, denom);
+ c.s << ")";
} else {
- const std::string par_open = is_a<print_latex>(c) ? "{(" : "(";
- const std::string par_close = is_a<print_latex>(c) ? ")}" : ")";
- const std::string imag_sym = is_a<print_latex>(c) ? "i" : "I";
- const std::string mul_sym = is_a<print_latex>(c) ? " " : "*";
- const cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
- const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
- if (is_a<print_python_repr>(c))
- c.s << class_name() << "('";
- if (cln::zerop(i)) {
- // case 1, real: x or -x
- if ((precedence() <= level) && (!this->is_nonneg_integer())) {
- c.s << par_open;
- print_real_number(c, r);
- c.s << par_close;
- } else {
- print_real_number(c, r);
- }
+
+ // Anything else
+ c.s << cln::double_approx(x);
+ }
+}
+
+/** Helper function to print real number in C++ source format using cl_N types.
+ *
+ * @see numeric::print() */
+static void print_real_cl_N(const print_context & c, const cln::cl_R & x)
+{
+ if (cln::instanceof(x, cln::cl_I_ring)) {
+
+ // Integer number
+ c.s << "cln::cl_I(\"";
+ print_real_number(c, x);
+ c.s << "\")";
+
+ } else if (cln::instanceof(x, cln::cl_RA_ring)) {
+
+ // Rational number
+ cln::cl_print_flags ourflags;
+ c.s << "cln::cl_RA(\"";
+ cln::print_rational(c.s, ourflags, cln::the<cln::cl_RA>(x));
+ c.s << "\")";
+
+ } else {
+
+ // Anything else
+ c.s << "cln::cl_F(\"";
+ print_real_number(c, cln::cl_float(1.0, cln::default_float_format) * x);
+ c.s << "_" << Digits << "\")";
+ }
+}
+
+void numeric::print_numeric(const print_context & c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const
+{
+ const cln::cl_R r = cln::realpart(value);
+ const cln::cl_R i = cln::imagpart(value);
+
+ if (cln::zerop(i)) {
+
+ // case 1, real: x or -x
+ if ((precedence() <= level) && (!this->is_nonneg_integer())) {
+ c.s << par_open;
+ print_real_number(c, r);
+ c.s << par_close;
} else {
- if (cln::zerop(r)) {
- // case 2, imaginary: y*I or -y*I
- if (i==1)
- c.s << imag_sym;
+ print_real_number(c, r);
+ }
+
+ } else {
+ if (cln::zerop(r)) {
+
+ // case 2, imaginary: y*I or -y*I
+ if (i == 1)
+ c.s << imag_sym;
+ else {
+ if (precedence()<=level)
+ c.s << par_open;
+ if (i == -1)
+ c.s << "-" << imag_sym;
else {
- if (precedence()<=level)
- c.s << par_open;
- if (i == -1)
- c.s << "-" << imag_sym;
- else {
- print_real_number(c, i);
- c.s << mul_sym+imag_sym;
- }
- if (precedence()<=level)
- c.s << par_close;
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ if (precedence()<=level)
+ c.s << par_close;
+ }
+
+ } else {
+
+ // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
+ if (precedence() <= level)
+ c.s << par_open;
+ print_real_number(c, r);
+ if (i < 0) {
+ if (i == -1) {
+ c.s << "-" << imag_sym;
+ } else {
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
}
} else {
- // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
- if (precedence() <= level)
- c.s << par_open;
- print_real_number(c, r);
- if (i < 0) {
- if (i == -1) {
- c.s << "-"+imag_sym;
- } else {
- print_real_number(c, i);
- c.s << mul_sym+imag_sym;
- }
+ if (i == 1) {
+ c.s << "+" << imag_sym;
} else {
- if (i == 1) {
- c.s << "+"+imag_sym;
- } else {
- c.s << "+";
- print_real_number(c, i);
- c.s << mul_sym+imag_sym;
- }
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
}
- if (precedence() <= level)
- c.s << par_close;
}
+ if (precedence() <= level)
+ c.s << par_close;
}
- if (is_a<print_python_repr>(c))
- c.s << "')";
}
}
+void numeric::do_print(const print_context & c, unsigned level) const
+{
+ print_numeric(c, "(", ")", "I", "*", level);
+}
+
+void numeric::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_numeric(c, "{(", ")}", "i", " ", level);
+}
+
+void numeric::do_print_csrc(const print_csrc & c, unsigned level) const
+{
+ std::ios::fmtflags oldflags = c.s.flags();
+ c.s.setf(std::ios::scientific);
+ int oldprec = c.s.precision();
+
+ // Set precision
+ if (is_a<print_csrc_double>(c))
+ c.s.precision(std::numeric_limits<double>::digits10 + 1);
+ else
+ c.s.precision(std::numeric_limits<float>::digits10 + 1);
+
+ if (this->is_real()) {
+
+ // Real number
+ print_real_csrc(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "std::complex<";
+ if (is_a<print_csrc_double>(c))
+ c.s << "double>(";
+ else
+ c.s << "float>(";
+
+ print_real_csrc(c, cln::realpart(value));
+ c.s << ",";
+ print_real_csrc(c, cln::imagpart(value));
+ c.s << ")";
+ }
+
+ c.s.flags(oldflags);
+ c.s.precision(oldprec);
+}
+
+void numeric::do_print_csrc_cl_N(const print_csrc_cl_N & c, unsigned level) const
+{
+ if (this->is_real()) {
+
+ // Real number
+ print_real_cl_N(c, cln::the<cln::cl_R>(value));
+
+ } else {
+
+ // Complex number
+ c.s << "cln::complex(";
+ print_real_cl_N(c, cln::realpart(value));
+ c.s << ",";
+ print_real_cl_N(c, cln::imagpart(value));
+ c.s << ")";
+ }
+}
+
+void numeric::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << value
+ << " (" << class_name() << ")" << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+}
+
+void numeric::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << "('";
+ print_numeric(c, "(", ")", "I", "*", level);
+ c.s << "')";
+}
+
bool numeric::info(unsigned inf) const
{
switch (inf) {
* sign as a multiplicative factor. */
bool numeric::has(const ex &other) const
{
- if (!is_ex_exactly_of_type(other, numeric))
+ if (!is_exactly_a<numeric>(other))
return false;
const numeric &o = ex_to<numeric>(other);
if (this->is_equal(o) || this->is_equal(-o))
return true;
- if (o.imag().is_zero()) // e.g. scan for 3 in -3*I
- return (this->real().is_equal(o) || this->imag().is_equal(o) ||
- this->real().is_equal(-o) || this->imag().is_equal(-o));
+ if (o.imag().is_zero()) { // e.g. scan for 3 in -3*I
+ if (!this->real().is_equal(*_num0_p))
+ if (this->real().is_equal(o) || this->real().is_equal(-o))
+ return true;
+ if (!this->imag().is_equal(*_num0_p))
+ if (this->imag().is_equal(o) || this->imag().is_equal(-o))
+ return true;
+ return false;
+ }
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));
+ if (!this->imag().is_equal(*_num0_p))
+ if (this->imag().is_equal(o*I) || this->imag().is_equal(-o*I))
+ return true;
}
return false;
}
ex numeric::evalf(int level) const
{
// level can safely be discarded for numeric objects.
- return numeric(cln::cl_float(1.0, cln::default_float_format) *
- (cln::the<cln::cl_N>(value)));
+ return numeric(cln::cl_float(1.0, cln::default_float_format) * value);
+}
+
+ex numeric::conjugate() const
+{
+ if (is_real()) {
+ return *this;
+ }
+ return numeric(cln::conjugate(this->value));
}
// protected
}
-unsigned numeric::calchash(void) const
+unsigned numeric::calchash() 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.
+ // Base computation of hashvalue on CLN's hashcode. Note: That 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. That shouldn't really matter, though.
setflag(status_flags::hash_calculated);
- return (hashvalue = cln::equal_hashcode(cln::the<cln::cl_N>(value)) | 0x80000000U);
+ hashvalue = golden_ratio_hash(cln::equal_hashcode(value));
+ return hashvalue;
}
* a numeric object. */
const numeric numeric::add(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
- if (this==_num0_p)
- return other;
- else if (&other==_num0_p)
- return *this;
-
- return numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value));
+ return numeric(value + other.value);
}
* result as a numeric object. */
const numeric numeric::sub(const numeric &other) const
{
- return numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value));
+ return numeric(value - other.value);
}
* result as a numeric object. */
const numeric numeric::mul(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
- if (this==_num1_p)
- return other;
- else if (&other==_num1_p)
- return *this;
-
- return numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value));
+ return numeric(value * other.value);
}
* @exception overflow_error (division by zero) */
const numeric numeric::div(const numeric &other) const
{
- if (cln::zerop(cln::the<cln::cl_N>(other.value)))
+ if (cln::zerop(other.value))
throw std::overflow_error("numeric::div(): division by zero");
- return numeric(cln::the<cln::cl_N>(value)/cln::the<cln::cl_N>(other.value));
+ return numeric(value / other.value);
}
* returns result as a numeric object. */
const numeric numeric::power(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral exponent by pointer.
- if (&other==_num1_p)
+ // Shortcut for efficiency and numeric stability (as in 1.0 exponent):
+ // trap the neutral exponent.
+ if (&other==_num1_p || cln::equal(other.value,_num1_p->value))
return *this;
- if (cln::zerop(cln::the<cln::cl_N>(value))) {
- if (cln::zerop(cln::the<cln::cl_N>(other.value)))
+ if (cln::zerop(value)) {
+ if (cln::zerop(other.value))
throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
- else if (cln::zerop(cln::realpart(cln::the<cln::cl_N>(other.value))))
+ else if (cln::zerop(cln::realpart(other.value)))
throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
- else if (cln::minusp(cln::realpart(cln::the<cln::cl_N>(other.value))))
+ else if (cln::minusp(cln::realpart(other.value)))
throw std::overflow_error("numeric::eval(): division by zero");
else
- return _num0;
+ return *_num0_p;
}
- return numeric(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value)));
+ return numeric(cln::expt(value, other.value));
}
+
+/** Numerical addition method. Adds argument to *this and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping into
+ * an ex object, where the result would end up on the heap anyways. */
const numeric &numeric::add_dyn(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
if (this==_num0_p)
return other;
else if (&other==_num0_p)
return *this;
- return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)+cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ return static_cast<const numeric &>((new numeric(value + other.value))->
+ setflag(status_flags::dynallocated));
}
+/** Numerical subtraction method. Subtracts argument from *this and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
const numeric &numeric::sub_dyn(const numeric &other) const
{
- return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ // Efficiency shortcut: trap the neutral exponent (first by pointer). This
+ // hack is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num0_p || cln::zerop(other.value))
+ return *this;
+
+ return static_cast<const numeric &>((new numeric(value - other.value))->
+ setflag(status_flags::dynallocated));
}
+/** Numerical multiplication method. Multiplies *this and argument and returns
+ * result as a numeric object on the heap. Use internally only for direct
+ * wrapping into an ex object, where the result would end up on the heap
+ * anyways. */
const numeric &numeric::mul_dyn(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral element by pointer.
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
if (this==_num1_p)
return other;
else if (&other==_num1_p)
return *this;
- return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)*cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ return static_cast<const numeric &>((new numeric(value * other.value))->
+ setflag(status_flags::dynallocated));
}
+/** Numerical division method. Divides *this by argument and returns result as
+ * a numeric object on the heap. Use internally only for direct wrapping
+ * into an ex object, where the result would end up on the heap
+ * anyways.
+ *
+ * @exception overflow_error (division by zero) */
const numeric &numeric::div_dyn(const numeric &other) const
{
+ // Efficiency shortcut: trap the neutral element by pointer. This hack
+ // is supposed to keep the number of distinct numeric objects low.
+ if (&other==_num1_p)
+ return *this;
if (cln::zerop(cln::the<cln::cl_N>(other.value)))
throw std::overflow_error("division by zero");
- return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)/cln::the<cln::cl_N>(other.value)))->
- setflag(status_flags::dynallocated));
+ return static_cast<const numeric &>((new numeric(value / other.value))->
+ setflag(status_flags::dynallocated));
}
+/** Numerical exponentiation. Raises *this to the power given as argument and
+ * returns result as a numeric object on the heap. Use internally only for
+ * direct wrapping into an ex object, where the result would end up on the
+ * heap anyways. */
const numeric &numeric::power_dyn(const numeric &other) const
{
- // Efficiency shortcut: trap the neutral exponent by pointer.
- if (&other==_num1_p)
+ // Efficiency shortcut: trap the neutral exponent (first try by pointer, then
+ // try harder, since calls to cln::expt() below may return amazing results for
+ // floating point exponent 1.0).
+ if (&other==_num1_p || cln::equal(other.value, _num1_p->value))
return *this;
- if (cln::zerop(cln::the<cln::cl_N>(value))) {
- if (cln::zerop(cln::the<cln::cl_N>(other.value)))
+ if (cln::zerop(value)) {
+ if (cln::zerop(other.value))
throw std::domain_error("numeric::eval(): pow(0,0) is undefined");
- else if (cln::zerop(cln::realpart(cln::the<cln::cl_N>(other.value))))
+ else if (cln::zerop(cln::realpart(other.value)))
throw std::domain_error("numeric::eval(): pow(0,I) is undefined");
- else if (cln::minusp(cln::realpart(cln::the<cln::cl_N>(other.value))))
+ else if (cln::minusp(cln::realpart(other.value)))
throw std::overflow_error("numeric::eval(): division by zero");
else
- return _num0;
+ return *_num0_p;
}
- return static_cast<const numeric &>((new numeric(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value))))->
+ return static_cast<const numeric &>((new numeric(cln::expt(value, other.value)))->
setflag(status_flags::dynallocated));
}
/** Inverse of a number. */
-const numeric numeric::inverse(void) const
+const numeric numeric::inverse() const
{
- if (cln::zerop(cln::the<cln::cl_N>(value)))
+ if (cln::zerop(value))
throw std::overflow_error("numeric::inverse(): division by zero");
- return numeric(cln::recip(cln::the<cln::cl_N>(value)));
+ return numeric(cln::recip(value));
}
* csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.
*
* @see numeric::compare(const numeric &other) */
-int numeric::csgn(void) const
+int numeric::csgn() const
{
- if (cln::zerop(cln::the<cln::cl_N>(value)))
+ if (cln::zerop(value))
return 0;
- cln::cl_R r = cln::realpart(cln::the<cln::cl_N>(value));
+ cln::cl_R r = cln::realpart(value);
if (!cln::zerop(r)) {
if (cln::plusp(r))
return 1;
else
return -1;
} else {
- if (cln::plusp(cln::imagpart(cln::the<cln::cl_N>(value))))
+ if (cln::plusp(cln::imagpart(value)))
return 1;
else
return -1;
* to be compatible with our method csgn.
*
* @return csgn(*this-other)
- * @see numeric::csgn(void) */
+ * @see numeric::csgn() */
int numeric::compare(const numeric &other) const
{
// Comparing two real numbers?
return cln::compare(cln::the<cln::cl_R>(value), cln::the<cln::cl_R>(other.value));
else {
// No, first cln::compare real parts...
- cl_signean real_cmp = cln::compare(cln::realpart(cln::the<cln::cl_N>(value)), cln::realpart(cln::the<cln::cl_N>(other.value)));
+ cl_signean real_cmp = cln::compare(cln::realpart(value), cln::realpart(other.value));
if (real_cmp)
return real_cmp;
// ...and then the imaginary parts.
- return cln::compare(cln::imagpart(cln::the<cln::cl_N>(value)), cln::imagpart(cln::the<cln::cl_N>(other.value)));
+ return cln::compare(cln::imagpart(value), cln::imagpart(other.value));
}
}
bool numeric::is_equal(const numeric &other) const
{
- return cln::equal(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value));
+ return cln::equal(value, other.value);
}
/** True if object is zero. */
-bool numeric::is_zero(void) const
+bool numeric::is_zero() const
{
- return cln::zerop(cln::the<cln::cl_N>(value));
+ return cln::zerop(value);
}
/** True if object is not complex and greater than zero. */
-bool numeric::is_positive(void) const
+bool numeric::is_positive() const
{
- if (this->is_real())
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
return cln::plusp(cln::the<cln::cl_R>(value));
return false;
}
/** True if object is not complex and less than zero. */
-bool numeric::is_negative(void) const
+bool numeric::is_negative() const
{
- if (this->is_real())
+ if (cln::instanceof(value, cln::cl_R_ring)) // real?
return cln::minusp(cln::the<cln::cl_R>(value));
return false;
}
/** True if object is a non-complex integer. */
-bool numeric::is_integer(void) const
+bool numeric::is_integer() const
{
return cln::instanceof(value, cln::cl_I_ring);
}
/** True if object is an exact integer greater than zero. */
-bool numeric::is_pos_integer(void) const
+bool numeric::is_pos_integer() const
{
- return (this->is_integer() && cln::plusp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::plusp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact integer greater or equal zero. */
-bool numeric::is_nonneg_integer(void) const
+bool numeric::is_nonneg_integer() const
{
- return (this->is_integer() && !cln::minusp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && !cln::minusp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact even integer. */
-bool numeric::is_even(void) const
+bool numeric::is_even() const
{
- return (this->is_integer() && cln::evenp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::evenp(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact odd integer. */
-bool numeric::is_odd(void) const
+bool numeric::is_odd() const
{
- return (this->is_integer() && cln::oddp(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) && cln::oddp(cln::the<cln::cl_I>(value)));
}
/** Probabilistic primality test.
*
* @return true if object is exact integer and prime. */
-bool numeric::is_prime(void) const
+bool numeric::is_prime() const
{
- return (this->is_integer() && cln::isprobprime(cln::the<cln::cl_I>(value)));
+ return (cln::instanceof(value, cln::cl_I_ring) // integer?
+ && cln::plusp(cln::the<cln::cl_I>(value)) // positive?
+ && cln::isprobprime(cln::the<cln::cl_I>(value)));
}
/** True if object is an exact rational number, may even be complex
* (denominator may be unity). */
-bool numeric::is_rational(void) const
+bool numeric::is_rational() const
{
return cln::instanceof(value, cln::cl_RA_ring);
}
/** True if object is a real integer, rational or float (but not complex). */
-bool numeric::is_real(void) const
+bool numeric::is_real() const
{
return cln::instanceof(value, cln::cl_R_ring);
}
bool numeric::operator==(const numeric &other) const
{
- return cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+ return cln::equal(value, other.value);
}
bool numeric::operator!=(const numeric &other) const
{
- return !cln::equal(cln::the<cln::cl_N>(value), cln::the<cln::cl_N>(other.value));
+ return !cln::equal(value, other.value);
}
/** 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
+bool numeric::is_cinteger() const
{
if (cln::instanceof(value, cln::cl_I_ring))
return true;
else if (!this->is_real()) { // complex case, handle n+m*I
- if (cln::instanceof(cln::realpart(cln::the<cln::cl_N>(value)), cln::cl_I_ring) &&
- cln::instanceof(cln::imagpart(cln::the<cln::cl_N>(value)), cln::cl_I_ring))
+ if (cln::instanceof(cln::realpart(value), cln::cl_I_ring) &&
+ cln::instanceof(cln::imagpart(value), cln::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
+bool numeric::is_crational() const
{
if (cln::instanceof(value, cln::cl_RA_ring))
return true;
else if (!this->is_real()) { // complex case, handle Q(i):
- if (cln::instanceof(cln::realpart(cln::the<cln::cl_N>(value)), cln::cl_RA_ring) &&
- cln::instanceof(cln::imagpart(cln::the<cln::cl_N>(value)), cln::cl_RA_ring))
+ if (cln::instanceof(cln::realpart(value), cln::cl_RA_ring) &&
+ cln::instanceof(cln::imagpart(value), cln::cl_RA_ring))
return true;
}
return false;
/** Converts numeric types to machine's int. You should check with
* is_integer() if the number is really an integer before calling this method.
* You may also consider checking the range first. */
-int numeric::to_int(void) const
+int numeric::to_int() const
{
GINAC_ASSERT(this->is_integer());
return cln::cl_I_to_int(cln::the<cln::cl_I>(value));
/** Converts numeric types to machine's long. You should check with
* is_integer() if the number is really an integer before calling this method.
* You may also consider checking the range first. */
-long numeric::to_long(void) const
+long numeric::to_long() const
{
GINAC_ASSERT(this->is_integer());
return cln::cl_I_to_long(cln::the<cln::cl_I>(value));
/** 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
+double numeric::to_double() const
{
GINAC_ASSERT(this->is_real());
- return cln::double_approx(cln::realpart(cln::the<cln::cl_N>(value)));
+ return cln::double_approx(cln::realpart(value));
}
/** Returns a new CLN object of type cl_N, representing the value of *this.
* This method may be used when mixing GiNaC and CLN in one project.
*/
-cln::cl_N numeric::to_cl_N(void) const
+cln::cl_N numeric::to_cl_N() const
{
- return cln::cl_N(cln::the<cln::cl_N>(value));
+ return value;
}
/** Real part of a number. */
-const numeric numeric::real(void) const
+const numeric numeric::real() const
{
- return numeric(cln::realpart(cln::the<cln::cl_N>(value)));
+ return numeric(cln::realpart(value));
}
/** Imaginary part of a number. */
-const numeric numeric::imag(void) const
+const numeric numeric::imag() const
{
- return numeric(cln::imagpart(cln::the<cln::cl_N>(value)));
+ return numeric(cln::imagpart(value));
}
* numerator of complex if real and imaginary part are both rational numbers
* (i.e numer(4/3+5/6*I) == 8+5*I), the number carrying the sign in all other
* cases. */
-const numeric numeric::numer(void) const
+const numeric numeric::numer() const
{
- if (this->is_integer())
- return numeric(*this);
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return numeric(*this); // integer case
else if (cln::instanceof(value, cln::cl_RA_ring))
return numeric(cln::numerator(cln::the<cln::cl_RA>(value)));
else if (!this->is_real()) { // complex case, handle Q(i):
- const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(cln::the<cln::cl_N>(value)));
- const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(cln::the<cln::cl_N>(value)));
+ const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(value));
+ const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(value));
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
return numeric(*this);
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
/** Denominator. Computes the denominator of rational numbers, common integer
* denominator of complex if real and imaginary part are both rational numbers
* (i.e denom(4/3+5/6*I) == 6), one in all other cases. */
-const numeric numeric::denom(void) const
+const numeric numeric::denom() const
{
- if (this->is_integer())
- return _num1;
+ if (cln::instanceof(value, cln::cl_I_ring))
+ return *_num1_p; // integer case
if (cln::instanceof(value, cln::cl_RA_ring))
return numeric(cln::denominator(cln::the<cln::cl_RA>(value)));
if (!this->is_real()) { // complex case, handle Q(i):
- const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(cln::the<cln::cl_N>(value)));
- const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(cln::the<cln::cl_N>(value)));
+ const cln::cl_RA r = cln::the<cln::cl_RA>(cln::realpart(value));
+ const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(value));
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
- return _num1;
+ return *_num1_p;
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
return numeric(cln::denominator(i));
if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
return numeric(cln::lcm(cln::denominator(r), cln::denominator(i)));
}
// at least one float encountered
- return _num1;
+ return *_num1_p;
}
*
* @return number of bits (excluding sign) needed to represent that number
* in two's complement if it is an integer, 0 otherwise. */
-int numeric::int_length(void) const
+int numeric::int_length() const
{
- if (this->is_integer())
+ if (cln::instanceof(value, cln::cl_I_ring))
return cln::integer_length(cln::the<cln::cl_I>(value));
else
return 0;
/** Natural logarithm.
*
- * @param z complex number
+ * @param x complex number
* @return arbitrary precision numerical log(x).
* @exception pole_error("log(): logarithmic pole",0) */
-const numeric log(const numeric &z)
+const numeric log(const numeric &x)
{
- if (z.is_zero())
+ if (x.is_zero())
throw pole_error("log(): logarithmic pole",0);
- return cln::log(z.to_cl_N());
+ return cln::log(x.to_cl_N());
}
/** Arcustangent.
*
- * @param z complex number
- * @return atan(z)
+ * @param x complex number
+ * @return atan(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))
+ abs(x.imag()).is_equal(*_num1_p))
throw pole_error("atan(): logarithmic pole",0);
return cln::atan(x.to_cl_N());
}
const numeric Li2(const numeric &x)
{
if (x.is_zero())
- return _num0;
+ return *_num0_p;
// what is the desired float format?
// first guess: default format
else if (!x.imag().is_rational())
prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(value)));
- if (cln::the<cln::cl_N>(value)==1) // may cause trouble with log(1-x)
+ if (value==1) // may cause trouble with log(1-x)
return cln::zeta(2, prec);
if (cln::abs(value) > 1)
* @exception range_error (argument must be integer >= -1) */
const numeric doublefactorial(const numeric &n)
{
- if (n.is_equal(_num_1))
- return _num1;
+ if (n.is_equal(*_num_1_p))
+ return *_num1_p;
if (!n.is_nonneg_integer())
throw std::range_error("numeric::doublefactorial(): argument must be integer >= -1");
{
if (n.is_integer() && k.is_integer()) {
if (n.is_nonneg_integer()) {
- if (k.compare(n)!=1 && k.compare(_num0)!=-1)
+ if (k.compare(n)!=1 && k.compare(*_num0_p)!=-1)
return numeric(cln::binomial(n.to_int(),k.to_int()));
else
- return _num0;
+ return *_num0_p;
} else {
- return _num_1.power(k)*binomial(k-n-_num1,k);
+ return _num_1_p->power(k)*binomial(k-n-(*_num1_p),k);
}
}
- // should really be gamma(n+1)/gamma(r+1)/gamma(n-r+1) or a suitable limit
- throw std::range_error("numeric::binomial(): donยดt know how to evaluate that.");
+ // should really be gamma(n+1)/gamma(k+1)/gamma(n-k+1) or a suitable limit
+ throw std::range_error("numeric::binomial(): don't know how to evaluate that.");
}
// the special cases not covered by the algorithm below
if (n & 1)
- return (n==1) ? _num_1_2 : _num0;
+ return (n==1) ? (*_num_1_2_p) : (*_num0_p);
if (!n)
- return _num1;
+ return *_num1_p;
// store nonvanishing Bernoulli numbers here
static std::vector< cln::cl_RA > results;
// hence
// F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
if (n.is_zero())
- return _num0;
+ return *_num0_p;
if (n.is_negative())
if (n.is_even())
return -fibonacci(-n);
return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
else
- return _num0;
+ return *_num0_p;
}
/** 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)]. */
+ * @return a mod b in the range [-iquo(abs(b)-1,2), iquo(abs(b),2)]. */
const numeric smod(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer()) {
return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
cln::the<cln::cl_I>(b.to_cl_N())) - b2;
} else
- return _num0;
+ return *_num0_p;
}
return cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
else
- return _num0;
+ return *_num0_p;
}
/** Numeric integer remainder.
* Equivalent to Maple's irem(a,b,'q') it obeyes the relation
* irem(a,b,q) == a - q*b. In general, mod(a,b) has the sign of b or is zero,
- * and irem(a,b) has the sign of a or is zero.
+ * and irem(a,b) has the sign of a or is zero.
*
* @return remainder of a/b and quotient stored in q if both are integer,
* 0 otherwise.
q = rem_quo.quotient;
return rem_quo.remainder;
} else {
- q = _num0;
- return _num0;
+ q = *_num0_p;
+ return *_num0_p;
}
}
return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
else
- return _num0;
+ return *_num0_p;
}
r = rem_quo.remainder;
return rem_quo.quotient;
} else {
- r = _num0;
- return _num0;
+ r = *_num0_p;
+ return *_num0_p;
}
}
return cln::gcd(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
else
- return _num1;
+ return *_num1_p;
}
/** Numeric square root.
- * If possible, sqrt(z) should respect squares of exact numbers, i.e. sqrt(4)
+ * If possible, sqrt(x) should respect squares of exact numbers, i.e. sqrt(4)
* should return integer 2.
*
- * @param z numeric argument
- * @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. */
-const numeric sqrt(const numeric &z)
+ * @param x numeric argument
+ * @return square root of x. Branch cut along negative real axis, the negative
+ * real axis itself where imag(x)==0 and real(x)<0 belongs to the upper part
+ * where imag(x)>0. */
+const numeric sqrt(const numeric &x)
{
- return cln::sqrt(z.to_cl_N());
+ return cln::sqrt(x.to_cl_N());
}
cln::isqrt(cln::the<cln::cl_I>(x.to_cl_N()), &root);
return root;
} else
- return _num0;
+ return *_num0_p;
}
/** Floating point evaluation of Archimedes' constant Pi. */
-ex PiEvalf(void)
+ex PiEvalf()
{
return numeric(cln::pi(cln::default_float_format));
}
/** Floating point evaluation of Euler's constant gamma. */
-ex EulerEvalf(void)
+ex EulerEvalf()
{
return numeric(cln::eulerconst(cln::default_float_format));
}
/** Floating point evaluation of Catalan's constant. */
-ex CatalanEvalf(void)
+ex CatalanEvalf()
{
return numeric(cln::catalanconst(cln::default_float_format));
}
git://www.ginac.de / ginac.git / blobdiff