* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "ex.h"
#include "config.h"
#include "debugmsg.h"
+#include "utils.h"
// CLN should not pollute the global namespace, hence we include it here
// instead of in some header file where it would propagate to other parts:
destroy(0);
}
-numeric::numeric(numeric const & other)
+numeric::numeric(const numeric & other)
{
debugmsg("numeric copy constructor", LOGLEVEL_CONSTRUCT);
copy(other);
}
-numeric const & numeric::operator=(numeric const & other)
+const numeric & numeric::operator=(const numeric & other)
{
debugmsg("numeric operator=", LOGLEVEL_ASSIGNMENT);
if (this != &other) {
// protected
-void numeric::copy(numeric const & other)
+void numeric::copy(const numeric & other)
{
basic::copy(other);
value = new cl_N(*other.value);
numeric::numeric(int i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor 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:
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor 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:
numeric::numeric(long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor from long",LOGLEVEL_CONSTRUCT);
value = new cl_I(i);
calchash();
setflag(status_flags::evaluated|
numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor from ulong",LOGLEVEL_CONSTRUCT);
value = new cl_I(i);
calchash();
setflag(status_flags::evaluated|
* @exception overflow_error (division by zero) */
numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor from long/long",LOGLEVEL_CONSTRUCT);
if (!denom)
throw (std::overflow_error("division by zero"));
value = new cl_I(numer);
numeric::numeric(double d) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor 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:
numeric::numeric(char const *s) : basic(TINFO_numeric)
{ // MISSING: treatment of complex and ints and rationals.
- debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor from string",LOGLEVEL_CONSTRUCT);
if (strchr(s, '.'))
value = new cl_LF(s);
else
* only. */
numeric::numeric(cl_N const & z) : basic(TINFO_numeric)
{
- debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
+ debugmsg("const numericructor from cl_N", LOGLEVEL_CONSTRUCT);
value = new cl_N(z);
calchash();
setflag(status_flags::evaluated|
return new numeric(*this);
}
-// The method printraw doesn't do much, it simply uses CLN's operator<<() for
-// output, which is ugly but reliable. Examples:
-// 2+2i
-void numeric::printraw(ostream & os) const
-{
- debugmsg("numeric printraw", LOGLEVEL_PRINT);
- os << "numeric(" << *value << ")";
-}
-
-// The method print adds to the output so it blends more consistently together
-// with the other routines and produces something compatible to Maple input.
void numeric::print(ostream & os, unsigned upper_precedence) const
{
+ // The method print adds to the output so it blends more consistently
+ // together with the other routines and produces something compatible to
+ // ginsh input.
debugmsg("numeric print", LOGLEVEL_PRINT);
if (is_real()) {
// case 1, real: x or -x
}
}
+
+void numeric::printraw(ostream & os) const
+{
+ // The method printraw doesn't do much, it simply uses CLN's operator<<()
+ // for output, which is ugly but reliable. e.g: 2+2i
+ debugmsg("numeric printraw", LOGLEVEL_PRINT);
+ os << "numeric(" << *value << ")";
+}
void numeric::printtree(ostream & os, unsigned indent) const
{
debugmsg("numeric printtree", LOGLEVEL_PRINT);
ios::fmtflags oldflags = os.flags();
os.setf(ios::scientific);
if (is_rational() && !is_integer()) {
- if (compare(numZERO()) > 0) {
+ if (compare(_num0()) > 0) {
os << "(";
if (type == csrc_types::ctype_cl_N)
os << "cl_F(\"" << numer().evalf() << "\")";
case info_flags::negative:
return is_negative();
case info_flags::nonnegative:
- return compare(numZERO())>=0;
+ return compare(_num0())>=0;
case info_flags::posint:
return is_pos_integer();
case info_flags::negint:
- return is_integer() && (compare(numZERO())<0);
+ return is_integer() && (compare(_num0())<0);
case info_flags::nonnegint:
return is_nonneg_integer();
case info_flags::even:
int numeric::compare_same_type(basic const & other) const
{
GINAC_ASSERT(is_exactly_of_type(other, numeric));
- numeric const & o = static_cast<numeric &>(const_cast<basic &>(other));
+ const numeric & o = static_cast<numeric &>(const_cast<basic &>(other));
if (*value == *o.value) {
return 0;
bool numeric::is_equal_same_type(basic const & other) const
{
GINAC_ASSERT(is_exactly_of_type(other,numeric));
- numeric const *o = static_cast<numeric const *>(&other);
+ const numeric *o = static_cast<const numeric *>(&other);
return is_equal(*o);
}
/** Numerical addition method. Adds argument to *this and returns result as
* a new numeric object. */
-numeric numeric::add(numeric const & other) const
+numeric numeric::add(const numeric & other) const
{
return numeric((*value)+(*other.value));
}
/** Numerical subtraction method. Subtracts argument from *this and returns
* result as a new numeric object. */
-numeric numeric::sub(numeric const & other) const
+numeric numeric::sub(const numeric & other) const
{
return numeric((*value)-(*other.value));
}
/** Numerical multiplication method. Multiplies *this and argument and returns
* result as a new numeric object. */
-numeric numeric::mul(numeric const & other) const
+numeric numeric::mul(const numeric & other) const
{
- static const numeric * numONEp=&numONE();
- if (this==numONEp) {
+ static const numeric * _num1p=&_num1();
+ if (this==_num1p) {
return other;
- } else if (&other==numONEp) {
+ } else if (&other==_num1p) {
return *this;
}
return numeric((*value)*(*other.value));
* a new numeric object.
*
* @exception overflow_error (division by zero) */
-numeric numeric::div(numeric const & other) const
+numeric numeric::div(const numeric & other) const
{
if (::zerop(*other.value))
throw (std::overflow_error("division by zero"));
return numeric((*value)/(*other.value));
}
-numeric numeric::power(numeric const & other) const
+numeric numeric::power(const numeric & other) const
{
- static const numeric * numONEp=&numONE();
- if (&other==numONEp)
+ static const numeric * _num1p=&_num1();
+ if (&other==_num1p)
return *this;
if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value)))
throw (std::overflow_error("division by zero"));
return numeric(::recip(*value)); // -> CLN
}
-numeric const & numeric::add_dyn(numeric const & other) const
+const numeric & numeric::add_dyn(const numeric & other) const
{
- return static_cast<numeric const &>((new numeric((*value)+(*other.value)))->
+ return static_cast<const numeric &>((new numeric((*value)+(*other.value)))->
setflag(status_flags::dynallocated));
}
-numeric const & numeric::sub_dyn(numeric const & other) const
+const numeric & numeric::sub_dyn(const numeric & other) const
{
- return static_cast<numeric const &>((new numeric((*value)-(*other.value)))->
+ return static_cast<const numeric &>((new numeric((*value)-(*other.value)))->
setflag(status_flags::dynallocated));
}
-numeric const & numeric::mul_dyn(numeric const & other) const
+const numeric & numeric::mul_dyn(const numeric & other) const
{
- static const numeric * numONEp=&numONE();
- if (this==numONEp) {
+ static const numeric * _num1p=&_num1();
+ if (this==_num1p) {
return other;
- } else if (&other==numONEp) {
+ } else if (&other==_num1p) {
return *this;
}
- return static_cast<numeric const &>((new numeric((*value)*(*other.value)))->
+ return static_cast<const numeric &>((new numeric((*value)*(*other.value)))->
setflag(status_flags::dynallocated));
}
-numeric const & numeric::div_dyn(numeric const & other) const
+const numeric & numeric::div_dyn(const numeric & other) const
{
if (::zerop(*other.value))
throw (std::overflow_error("division by zero"));
- return static_cast<numeric const &>((new numeric((*value)/(*other.value)))->
+ return static_cast<const numeric &>((new numeric((*value)/(*other.value)))->
setflag(status_flags::dynallocated));
}
-numeric const & numeric::power_dyn(numeric const & other) const
+const numeric & numeric::power_dyn(const numeric & other) const
{
- static const numeric * numONEp=&numONE();
- if (&other==numONEp)
+ static const numeric * _num1p=&_num1();
+ if (&other==_num1p)
return *this;
if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value)))
throw (std::overflow_error("division by zero"));
- return static_cast<numeric const &>((new numeric(::expt(*value,*other.value)))->
+ return static_cast<const numeric &>((new numeric(::expt(*value,*other.value)))->
setflag(status_flags::dynallocated));
}
-numeric const & numeric::operator=(int i)
+const numeric & numeric::operator=(int i)
{
return operator=(numeric(i));
}
-numeric const & numeric::operator=(unsigned int i)
+const numeric & numeric::operator=(unsigned int i)
{
return operator=(numeric(i));
}
-numeric const & numeric::operator=(long i)
+const numeric & numeric::operator=(long i)
{
return operator=(numeric(i));
}
-numeric const & numeric::operator=(unsigned long i)
+const numeric & numeric::operator=(unsigned long i)
{
return operator=(numeric(i));
}
-numeric const & numeric::operator=(double d)
+const numeric & numeric::operator=(double d)
{
return operator=(numeric(d));
}
-numeric const & numeric::operator=(char const * s)
+const numeric & numeric::operator=(char const * s)
{
return operator=(numeric(s));
}
* csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0,
* csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.
*
- * @see numeric::compare(numeric const & other) */
+ * @see numeric::compare(const numeric & other) */
int numeric::csgn(void) const
{
if (is_zero())
*
* @return csgn(*this-other)
* @see numeric::csgn(void) */
-int numeric::compare(numeric const & other) const
+int numeric::compare(const numeric & other) const
{
// Comparing two real numbers?
if (is_real() && other.is_real())
}
}
-bool numeric::is_equal(numeric const & other) const
+bool numeric::is_equal(const numeric & other) const
{
return (*value == *other.value);
}
return ::instanceof(*value, cl_R_ring); // -> CLN
}
-bool numeric::operator==(numeric const & other) const
+bool numeric::operator==(const numeric & other) const
{
return (*value == *other.value); // -> CLN
}
-bool numeric::operator!=(numeric const & other) const
+bool numeric::operator!=(const numeric & other) const
{
return (*value != *other.value); // -> CLN
}
/** Numerical comparison: less.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator<(numeric const & other) const
+bool numeric::operator<(const numeric & other) const
{
if (is_real() && other.is_real())
return (bool)(The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN
/** Numerical comparison: less or equal.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator<=(numeric const & other) const
+bool numeric::operator<=(const numeric & other) const
{
if (is_real() && other.is_real())
return (bool)(The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN
/** Numerical comparison: greater.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator>(numeric const & other) const
+bool numeric::operator>(const numeric & other) const
{
if (is_real() && other.is_real())
return (bool)(The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN
/** Numerical comparison: greater or equal.
*
* @exception invalid_argument (complex inequality) */
-bool numeric::operator>=(numeric const & other) const
+bool numeric::operator>=(const numeric & other) const
{
if (is_real() && other.is_real())
return (bool)(The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN
numeric numeric::denom(void) const
{
if (is_integer()) {
- return numONE();
+ return _num1();
}
#ifdef SANE_LINKER
if (instanceof(*value, cl_RA_ring)) {
cl_R r = realpart(*value);
cl_R i = imagpart(*value);
if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring))
- return numONE();
+ return _num1();
if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_ring))
return numeric(::denominator(The(cl_RA)(i)));
if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_I_ring))
cl_R r = realpart(*value);
cl_R i = imagpart(*value);
if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numONE();
+ return _num1();
if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
return numeric(TheRatio(i)->denominator);
if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
}
#endif // def SANE_LINKER
// at least one float encountered
- return numONE();
+ return _num1();
}
/** Size in binary notation. For integers, this is the smallest n >= 0 such
* natively handing complex numbers anyways. */
const numeric I = numeric(complex(cl_I(0),cl_I(1)));
-//////////
-// global functions
-//////////
-
-numeric const & numZERO(void)
-{
- const static ex eZERO = ex((new numeric(0))->setflag(status_flags::dynallocated));
- const static numeric * nZERO = static_cast<const numeric *>(eZERO.bp);
- return *nZERO;
-}
-
-numeric const & numONE(void)
-{
- const static ex eONE = ex((new numeric(1))->setflag(status_flags::dynallocated));
- const static numeric * nONE = static_cast<const numeric *>(eONE.bp);
- return *nONE;
-}
-
-numeric const & numTWO(void)
-{
- const static ex eTWO = ex((new numeric(2))->setflag(status_flags::dynallocated));
- const static numeric * nTWO = static_cast<const numeric *>(eTWO.bp);
- return *nTWO;
-}
-
-numeric const & numTHREE(void)
-{
- const static ex eTHREE = ex((new numeric(3))->setflag(status_flags::dynallocated));
- const static numeric * nTHREE = static_cast<const numeric *>(eTHREE.bp);
- return *nTHREE;
-}
-
-numeric const & numMINUSONE(void)
-{
- const static ex eMINUSONE = ex((new numeric(-1))->setflag(status_flags::dynallocated));
- const static numeric * nMINUSONE = static_cast<const numeric *>(eMINUSONE.bp);
- return *nMINUSONE;
-}
-
-numeric const & numHALF(void)
-{
- const static ex eHALF = ex((new numeric(1, 2))->setflag(status_flags::dynallocated));
- const static numeric * nHALF = static_cast<const numeric *>(eHALF.bp);
- return *nHALF;
-}
-
/** Exponential function.
*
* @return arbitrary precision numerical exp(x). */
-numeric exp(numeric const & x)
+numeric exp(const numeric & x)
{
return ::exp(*x.value); // -> CLN
}
* @param z complex number
* @return arbitrary precision numerical log(x).
* @exception overflow_error (logarithmic singularity) */
-numeric log(numeric const & z)
+numeric log(const numeric & z)
{
if (z.is_zero())
throw (std::overflow_error("log(): logarithmic singularity"));
/** Numeric sine (trigonometric function).
*
* @return arbitrary precision numerical sin(x). */
-numeric sin(numeric const & x)
+numeric sin(const numeric & x)
{
return ::sin(*x.value); // -> CLN
}
/** Numeric cosine (trigonometric function).
*
* @return arbitrary precision numerical cos(x). */
-numeric cos(numeric const & x)
+numeric cos(const numeric & x)
{
return ::cos(*x.value); // -> CLN
}
/** Numeric tangent (trigonometric function).
*
* @return arbitrary precision numerical tan(x). */
-numeric tan(numeric const & x)
+numeric tan(const numeric & x)
{
return ::tan(*x.value); // -> CLN
}
/** Numeric inverse sine (trigonometric function).
*
* @return arbitrary precision numerical asin(x). */
-numeric asin(numeric const & x)
+numeric asin(const numeric & x)
{
return ::asin(*x.value); // -> CLN
}
/** Numeric inverse cosine (trigonometric function).
*
* @return arbitrary precision numerical acos(x). */
-numeric acos(numeric const & x)
+numeric acos(const numeric & x)
{
return ::acos(*x.value); // -> CLN
}
* @param z complex number
* @return atan(z)
* @exception overflow_error (logarithmic singularity) */
-numeric atan(numeric const & x)
+numeric atan(const numeric & x)
{
if (!x.is_real() &&
x.real().is_zero() &&
- !abs(x.imag()).is_equal(numONE()))
+ !abs(x.imag()).is_equal(_num1()))
throw (std::overflow_error("atan(): logarithmic singularity"));
return ::atan(*x.value); // -> CLN
}
* @param x real number
* @param y real number
* @return atan(y/x) */
-numeric atan(numeric const & y, numeric const & x)
+numeric atan(const numeric & y, const numeric & x)
{
if (x.is_real() && y.is_real())
return ::atan(realpart(*x.value), realpart(*y.value)); // -> CLN
/** Numeric hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical sinh(x). */
-numeric sinh(numeric const & x)
+numeric sinh(const numeric & x)
{
return ::sinh(*x.value); // -> CLN
}
/** Numeric hyperbolic cosine (trigonometric function).
*
* @return arbitrary precision numerical cosh(x). */
-numeric cosh(numeric const & x)
+numeric cosh(const numeric & x)
{
return ::cosh(*x.value); // -> CLN
}
/** Numeric hyperbolic tangent (trigonometric function).
*
* @return arbitrary precision numerical tanh(x). */
-numeric tanh(numeric const & x)
+numeric tanh(const numeric & x)
{
return ::tanh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical asinh(x). */
-numeric asinh(numeric const & x)
+numeric asinh(const numeric & x)
{
return ::asinh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic cosine (trigonometric function).
*
* @return arbitrary precision numerical acosh(x). */
-numeric acosh(numeric const & x)
+numeric acosh(const numeric & x)
{
return ::acosh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic tangent (trigonometric function).
*
* @return arbitrary precision numerical atanh(x). */
-numeric atanh(numeric const & x)
+numeric atanh(const numeric & x)
{
return ::atanh(*x.value); // -> CLN
}
/** Numeric evaluation of Riemann's Zeta function. Currently works only for
* integer arguments. */
-numeric zeta(numeric const & x)
+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
/** The gamma function.
* This is only a stub! */
-numeric gamma(numeric const & x)
+numeric gamma(const numeric & x)
{
clog << "gamma(" << x
<< "): Does anybody know good way to calculate this numerically?"
/** The psi function (aka polygamma function).
* This is only a stub! */
-numeric psi(numeric const & x)
+numeric psi(const numeric & x)
{
clog << "psi(" << x
<< "): Does anybody know good way to calculate this numerically?"
/** The psi functions (aka polygamma functions).
* This is only a stub! */
-numeric psi(numeric const & n, numeric const & x)
+numeric psi(const numeric & n, const numeric & x)
{
clog << "psi(" << n << "," << x
<< "): Does anybody know good way to calculate this numerically?"
/** Factorial combinatorial function.
*
* @exception range_error (argument must be integer >= 0) */
-numeric factorial(numeric const & nn)
+numeric factorial(const numeric & nn)
{
if (!nn.is_nonneg_integer())
throw (std::range_error("numeric::factorial(): argument must be integer >= 0"));
* useful in cases, like for exact results of Gamma(n+1/2) for instance.)
*
* @param n integer argument >= -1
- * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == 1 == (-1)!!
+ * @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1
* @exception range_error (argument must be integer >= -1) */
-numeric doublefactorial(numeric const & nn)
+numeric doublefactorial(const numeric & nn)
{
- // META-NOTE: The whole shit here will become obsolete and may be moved
- // out once CLN learns about double factorial, which should be as soon as
- // 1.0.3 rolls out!
-
- // We store the results separately for even and odd arguments. This has
- // the advantage that we don't have to compute any even result at all if
- // the function is always called with odd arguments and vice versa. There
- // is no tradeoff involved in this, it is guaranteed to save time as well
- // as memory. (If this is not enough justification consider the Gamma
- // function of half integer arguments: it only needs odd doublefactorials.)
- static vector<numeric> evenresults;
- static int highest_evenresult = -1;
- static vector<numeric> oddresults;
- static int highest_oddresult = -1;
-
if (nn == numeric(-1)) {
- return numONE();
+ return _num1();
}
if (!nn.is_nonneg_integer()) {
throw (std::range_error("numeric::doublefactorial(): argument must be integer >= -1"));
}
- if (nn.is_even()) {
- int n = nn.div(numTWO()).to_int();
- if (n <= highest_evenresult) {
- return evenresults[n];
- }
- if (evenresults.capacity() < (unsigned)(n+1)) {
- evenresults.reserve(n+1);
- }
- if (highest_evenresult < 0) {
- evenresults.push_back(numONE());
- highest_evenresult=0;
- }
- for (int i=highest_evenresult+1; i<=n; i++) {
- evenresults.push_back(numeric(evenresults[i-1].mul(numeric(i*2))));
- }
- highest_evenresult=n;
- return evenresults[n];
- } else {
- int n = nn.sub(numONE()).div(numTWO()).to_int();
- if (n <= highest_oddresult) {
- return oddresults[n];
- }
- if (oddresults.capacity() < (unsigned)n) {
- oddresults.reserve(n+1);
- }
- if (highest_oddresult < 0) {
- oddresults.push_back(numONE());
- highest_oddresult=0;
- }
- for (int i=highest_oddresult+1; i<=n; i++) {
- oddresults.push_back(numeric(oddresults[i-1].mul(numeric(i*2+1))));
- }
- highest_oddresult=n;
- return oddresults[n];
- }
+ return numeric(::doublefactorial(nn.to_int())); // -> CLN
}
/** The Binomial coefficients. It computes the binomial coefficients. For
* integer n and k and positive n this is the number of ways of choosing k
* objects from n distinct objects. If n is negative, the formula
* binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */
-numeric binomial(numeric const & n, numeric const & k)
+numeric binomial(const numeric & n, const numeric & k)
{
if (n.is_integer() && k.is_integer()) {
if (n.is_nonneg_integer()) {
- if (k.compare(n)!=1 && k.compare(numZERO())!=-1)
+ if (k.compare(n)!=1 && k.compare(_num0())!=-1)
return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN
else
- return numZERO();
+ return _num0();
} else {
- return numMINUSONE().power(k)*binomial(k-n-numONE(),k);
+ return _num_1().power(k)*binomial(k-n-_num1(),k);
}
}
*
* @return the nth Bernoulli number (a rational number).
* @exception range_error (argument must be integer >= 0) */
-numeric bernoulli(numeric const & nn)
+numeric bernoulli(const numeric & nn)
{
if (!nn.is_integer() || nn.is_negative())
throw (std::range_error("numeric::bernoulli(): argument must be integer >= 0"));
if (nn.is_zero())
- return numONE();
- if (!nn.compare(numONE()))
+ return _num1();
+ if (!nn.compare(_num1()))
return numeric(-1,2);
if (nn.is_odd())
- return numZERO();
+ return _num0();
// Until somebody has the Blues and comes up with a much better idea and
// codes it (preferably in CLN) we make this a remembering function which
// computes its results using the formula
// whith B(0) == 1.
static vector<numeric> results;
static int highest_result = -1;
- int n = nn.sub(numTWO()).div(numTWO()).to_int();
+ int n = nn.sub(_num2()).div(_num2()).to_int();
if (n <= highest_result)
return results[n];
if (results.capacity() < (unsigned)(n+1))
}
/** Absolute value. */
-numeric abs(numeric const & x)
+numeric abs(const numeric & x)
{
return ::abs(*x.value); // -> CLN
}
*
* @return a mod b in the range [0,abs(b)-1] with sign of b if both are
* integer, 0 otherwise. */
-numeric mod(numeric const & a, numeric const & b)
+numeric mod(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
return ::mod(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
- return numZERO(); // Throw?
+ return _num0(); // Throw?
}
/** Modulus (in symmetric representation).
* Equivalent to Maple's mods.
*
* @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
-numeric smod(numeric const & a, numeric const & b)
+numeric smod(const numeric & a, const numeric & b)
{
+ // FIXME: Should this become a member function?
if (a.is_integer() && b.is_integer()) {
cl_I b2 = The(cl_I)(ceiling1(The(cl_I)(*b.value) / 2)) - 1;
return ::mod(The(cl_I)(*a.value) + b2, The(cl_I)(*b.value)) - b2;
} else
- return numZERO(); // Throw?
+ return _num0(); // Throw?
}
/** Numeric integer remainder.
* sign of a or is zero.
*
* @return remainder of a/b if both are integer, 0 otherwise. */
-numeric irem(numeric const & a, numeric const & b)
+numeric irem(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
return ::rem(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
- return numZERO(); // Throw?
+ return _num0(); // Throw?
}
/** Numeric integer remainder.
*
* @return remainder of a/b and quotient stored in q if both are integer,
* 0 otherwise. */
-numeric irem(numeric const & a, numeric const & b, numeric & q)
+numeric irem(const numeric & a, const numeric & b, numeric & q)
{
if (a.is_integer() && b.is_integer()) { // -> CLN
cl_I_div_t rem_quo = truncate2(The(cl_I)(*a.value), The(cl_I)(*b.value));
return rem_quo.remainder;
}
else {
- q = numZERO();
- return numZERO(); // Throw?
+ q = _num0();
+ return _num0(); // Throw?
}
}
* Equivalent to Maple's iquo as far as sign conventions are concerned.
*
* @return truncated quotient of a/b if both are integer, 0 otherwise. */
-numeric iquo(numeric const & a, numeric const & b)
+numeric iquo(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
return truncate1(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
- return numZERO(); // Throw?
+ return _num0(); // Throw?
}
/** Numeric integer quotient.
*
* @return truncated quotient of a/b and remainder stored in r if both are
* integer, 0 otherwise. */
-numeric iquo(numeric const & a, numeric const & b, numeric & r)
+numeric iquo(const numeric & a, const numeric & b, numeric & r)
{
if (a.is_integer() && b.is_integer()) { // -> CLN
cl_I_div_t rem_quo = truncate2(The(cl_I)(*a.value), The(cl_I)(*b.value));
r = rem_quo.remainder;
return rem_quo.quotient;
} else {
- r = numZERO();
- return numZERO(); // Throw?
+ r = _num0();
+ return _num0(); // Throw?
}
}
* @return square root of z. Branch cut along negative real axis, the negative
* real axis itself where imag(z)==0 and real(z)<0 belongs to the upper part
* where imag(z)>0. */
-numeric sqrt(numeric const & z)
+numeric sqrt(const numeric & z)
{
return ::sqrt(*z.value); // -> CLN
}
/** Integer numeric square root. */
-numeric isqrt(numeric const & x)
+numeric isqrt(const numeric & x)
{
if (x.is_integer()) {
cl_I root;
::isqrt(The(cl_I)(*x.value), &root); // -> CLN
return root;
} else
- return numZERO(); // Throw?
+ return _num0(); // Throw?
}
/** Greatest Common Divisor.
*
* @return The GCD of two numbers if both are integer, a numerical 1
* if they are not. */
-numeric gcd(numeric const & a, numeric const & b)
+numeric gcd(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
return ::gcd(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
- return numONE();
+ return _num1();
}
/** Least Common Multiple.
*
* @return The LCM of two numbers if both are integer, the product of those
* two numbers if they are not. */
-numeric lcm(numeric const & a, numeric const & b)
+numeric lcm(const numeric & a, const numeric & b)
{
if (a.is_integer() && b.is_integer())
return ::lcm(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
git://www.ginac.de / ginac.git / blobdiff