* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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
#include "numeric.h"
#include "ex.h"
-#include "print.h"
#include "operators.h"
#include "archive.h"
#include "tostring.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 constructor
// 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
}
}
-/** 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
+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
{
- if (is_a<print_tree>(c)) {
+ const cln::cl_R r = cln::realpart(value);
+ const cln::cl_R i = cln::imagpart(value);
- 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;
+ if (cln::zerop(i)) {
- } else if (is_a<print_csrc_cl_N>(c)) {
+ // 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);
+ }
- // CLN output
- if (this->is_real()) {
+ } else {
+ if (cln::zerop(r)) {
- // Real number
- print_real_cl_N(c, cln::the<cln::cl_R>(value));
+ // 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 {
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ if (precedence()<=level)
+ c.s << par_close;
+ }
} else {
- // Complex number
- c.s << "cln::complex(";
- print_real_cl_N(c, cln::realpart(cln::the<cln::cl_N>(value)));
- c.s << ",";
- print_real_cl_N(c, cln::imagpart(cln::the<cln::cl_N>(value)));
- c.s << ")";
+ // 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 {
+ if (i == 1) {
+ c.s << "+" << imag_sym;
+ } else {
+ c.s << "+";
+ print_real_number(c, i);
+ c.s << mul_sym << imag_sym;
+ }
+ }
+ if (precedence() <= level)
+ c.s << par_close;
}
+ }
+}
- } else if (is_a<print_csrc>(c)) {
+void numeric::do_print(const print_context & c, unsigned level) const
+{
+ print_numeric(c, "(", ")", "I", "*", level);
+}
- // C++ source output
- std::ios::fmtflags oldflags = c.s.flags();
- c.s.setf(std::ios::scientific);
- int oldprec = c.s.precision();
+void numeric::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_numeric(c, "{(", ")}", "i", " ", level);
+}
- // 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);
+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();
- if (this->is_real()) {
+ // 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);
- // Real number
- print_real_csrc(c, cln::the<cln::cl_R>(value));
+ if (this->is_real()) {
- } else {
+ // Real number
+ print_real_csrc(c, cln::the<cln::cl_R>(value));
- // Complex number
- c.s << "std::complex<";
- if (is_a<print_csrc_double>(c))
- c.s << "double>(";
- else
- c.s << "float>(";
+ } else {
- print_real_csrc(c, cln::realpart(cln::the<cln::cl_N>(value)));
- c.s << ",";
- print_real_csrc(c, cln::imagpart(cln::the<cln::cl_N>(value)));
- c.s << ")";
- }
+ // Complex number
+ c.s << "std::complex<";
+ if (is_a<print_csrc_double>(c))
+ c.s << "double>(";
+ else
+ c.s << "float>(";
- c.s.flags(oldflags);
- c.s.precision(oldprec);
+ 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 {
- 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);
- }
- } 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 {
- 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 {
- if (i == 1) {
- c.s << "+"+imag_sym;
- } else {
- c.s << "+";
- print_real_number(c, i);
- c.s << mul_sym+imag_sym;
- }
- }
- if (precedence() <= level)
- c.s << par_close;
- }
- }
- if (is_a<print_python_repr>(c))
- c.s << "')";
+ // 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) {
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
// 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);
- hashvalue = golden_ratio_hash(cln::equal_hashcode(cln::the<cln::cl_N>(value)));
+ hashvalue = golden_ratio_hash(cln::equal_hashcode(value));
return hashvalue;
}
* a numeric object. */
const numeric numeric::add(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::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
{
- 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);
}
{
// Shortcut for efficiency and numeric stability (as in 1.0 exponent):
// trap the neutral exponent.
- if (&other==_num1_p || cln::equal(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
+ if (&other==_num1_p || cln::equal(other.value,_num1.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 numeric(cln::expt(cln::the<cln::cl_N>(value),cln::the<cln::cl_N>(other.value)));
+ return numeric(cln::expt(value, other.value));
}
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)))->
+ return static_cast<const numeric &>((new numeric(value + 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(cln::the<cln::cl_N>(other.value)))
+ if (&other==_num0_p || cln::zerop(other.value))
return *this;
- return static_cast<const numeric &>((new numeric(cln::the<cln::cl_N>(value)-cln::the<cln::cl_N>(other.value)))->
+ return static_cast<const numeric &>((new numeric(value - other.value))->
setflag(status_flags::dynallocated));
}
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)))->
+ return static_cast<const numeric &>((new numeric(value * other.value))->
setflag(status_flags::dynallocated));
}
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)))->
+ return static_cast<const numeric &>((new numeric(value / other.value))->
setflag(status_flags::dynallocated));
}
// 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(cln::the<cln::cl_N>(other.value),cln::the<cln::cl_N>(_num1.value)))
+ if (&other==_num1_p || cln::equal(other.value, _num1.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 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() 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));
}
* @see numeric::compare(const numeric &other) */
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;
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() const
{
- return cln::zerop(cln::the<cln::cl_N>(value));
+ return cln::zerop(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);
}
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);
}
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;
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;
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));
}
*/
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() 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() const
{
- return numeric(cln::imagpart(cln::the<cln::cl_N>(value)));
+ return numeric(cln::imagpart(value));
}
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))
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;
if (cln::instanceof(r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
/** 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)
{
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)
/** 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()) {
/** 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());
}
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