* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 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"
setflag(status_flags::evaluated | status_flags::expanded);
}
+
//////////
// archiving
//////////
// 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
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(cln::the<cln::cl_N>(value));
- const cln::cl_R i = cln::imagpart(cln::the<cln::cl_N>(value));
+ const cln::cl_R r = cln::realpart(value);
+ const cln::cl_R i = cln::imagpart(value);
if (cln::zerop(i)) {
else
c.s << "float>(";
- print_real_csrc(c, cln::realpart(cln::the<cln::cl_N>(value)));
+ print_real_csrc(c, cln::realpart(value));
c.s << ",";
- print_real_csrc(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+ print_real_csrc(c, cln::imagpart(value));
c.s << ")";
}
// Complex number
c.s << "cln::complex(";
- print_real_cl_N(c, cln::realpart(cln::the<cln::cl_N>(value)));
+ print_real_cl_N(c, cln::realpart(value));
c.s << ",";
- print_real_cl_N(c, cln::imagpart(cln::the<cln::cl_N>(value)));
+ 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, ' ') << cln::the<cln::cl_N>(value)
+ c.s << std::string(level, ' ') << value
<< " (" << class_name() << ")" << " @" << this
<< std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
<< std::endl;
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
// 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_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));
}
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_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() 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))
const numeric numeric::denom() const
{
if (cln::instanceof(value, cln::cl_I_ring))
- return _num1; // integer case
+ 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;
}
/** 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;
}
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;
}
git://www.ginac.de / ginac.git / blobdiff