#include <cln/cl_complex_io.h>
#include <cln/cl_complex_ring.h>
#include <cln/cl_numtheory.h>
-#else
+#else // def HAVE_CLN_CLN_H
#include <cl_integer_io.h>
#include <cl_integer_ring.h>
#include <cl_rational_io.h>
#include <cl_complex_io.h>
#include <cl_complex_ring.h>
#include <cl_numtheory.h>
-#endif
+#endif // def HAVE_CLN_CLN_H
#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_GINAC_NAMESPACE
// linker has no problems finding text symbols for numerator or denominator
//#define SANE_LINKER
status_flags::hash_calculated);
}
+
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT);
status_flags::hash_calculated);
}
+
numeric::numeric(long i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
status_flags::hash_calculated);
}
+
numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
status_flags::hash_calculated);
}
+
numeric::numeric(double d) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
status_flags::hash_calculated);
}
+
numeric::numeric(const char *s) : basic(TINFO_numeric)
{ // MISSING: treatment of complex and ints and rationals.
debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
return false; // make compiler shut up
}
-/** Converts numeric types to machine's int. You should check with is_integer()
- * if the number is really an integer before calling this method. */
+/** 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
{
GINAC_ASSERT(is_integer());
return ::cl_I_to_int(The(cl_I)(*value)); // -> CLN
}
+/** 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
+{
+ GINAC_ASSERT(is_integer());
+ return ::cl_I_to_long(The(cl_I)(*value)); // -> CLN
+}
+
/** Converts numeric types to machine's double. You should check with is_real()
* if the number is really not complex before calling this method. */
double numeric::to_double(void) const
* natively handing complex numbers anyways. */
const numeric I = numeric(complex(cl_I(0),cl_I(1)));
+
/** Exponential function.
*
* @return arbitrary precision numerical exp(x). */
-numeric exp(const numeric & x)
+const numeric exp(const numeric & x)
{
return ::exp(*x.value); // -> CLN
}
+
/** Natural logarithm.
*
* @param z complex number
* @return arbitrary precision numerical log(x).
* @exception overflow_error (logarithmic singularity) */
-numeric log(const numeric & z)
+const numeric log(const numeric & z)
{
if (z.is_zero())
throw (std::overflow_error("log(): logarithmic singularity"));
return ::log(*z.value); // -> CLN
}
+
/** Numeric sine (trigonometric function).
*
* @return arbitrary precision numerical sin(x). */
-numeric sin(const numeric & x)
+const numeric sin(const numeric & x)
{
return ::sin(*x.value); // -> CLN
}
+
/** Numeric cosine (trigonometric function).
*
* @return arbitrary precision numerical cos(x). */
-numeric cos(const numeric & x)
+const numeric cos(const numeric & x)
{
return ::cos(*x.value); // -> CLN
}
-
+
+
/** Numeric tangent (trigonometric function).
*
* @return arbitrary precision numerical tan(x). */
-numeric tan(const numeric & x)
+const numeric tan(const numeric & x)
{
return ::tan(*x.value); // -> CLN
}
+
/** Numeric inverse sine (trigonometric function).
*
* @return arbitrary precision numerical asin(x). */
-numeric asin(const numeric & x)
+const numeric asin(const numeric & x)
{
return ::asin(*x.value); // -> CLN
}
-
+
+
/** Numeric inverse cosine (trigonometric function).
*
* @return arbitrary precision numerical acos(x). */
-numeric acos(const numeric & x)
+const numeric acos(const numeric & x)
{
return ::acos(*x.value); // -> CLN
}
-/** Arcustangents.
+
+/** Arcustangent.
*
* @param z complex number
* @return atan(z)
* @exception overflow_error (logarithmic singularity) */
-numeric atan(const numeric & x)
+const numeric atan(const numeric & x)
{
if (!x.is_real() &&
x.real().is_zero() &&
return ::atan(*x.value); // -> CLN
}
-/** Arcustangents.
+
+/** Arcustangent.
*
* @param x real number
* @param y real number
* @return atan(y/x) */
-numeric atan(const numeric & y, const numeric & x)
+const numeric atan(const numeric & y, const numeric & x)
{
if (x.is_real() && y.is_real())
return ::atan(realpart(*x.value), realpart(*y.value)); // -> CLN
throw (std::invalid_argument("numeric::atan(): complex argument"));
}
+
/** Numeric hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical sinh(x). */
-numeric sinh(const numeric & x)
+const numeric sinh(const numeric & x)
{
return ::sinh(*x.value); // -> CLN
}
+
/** Numeric hyperbolic cosine (trigonometric function).
*
* @return arbitrary precision numerical cosh(x). */
-numeric cosh(const numeric & x)
+const numeric cosh(const numeric & x)
{
return ::cosh(*x.value); // -> CLN
}
-
+
+
/** Numeric hyperbolic tangent (trigonometric function).
*
* @return arbitrary precision numerical tanh(x). */
-numeric tanh(const numeric & x)
+const numeric tanh(const numeric & x)
{
return ::tanh(*x.value); // -> CLN
}
+
/** Numeric inverse hyperbolic sine (trigonometric function).
*
* @return arbitrary precision numerical asinh(x). */
-numeric asinh(const numeric & x)
+const numeric asinh(const numeric & x)
{
return ::asinh(*x.value); // -> CLN
}
+
/** Numeric inverse hyperbolic cosine (trigonometric function).
*
* @return arbitrary precision numerical acosh(x). */
-numeric acosh(const numeric & x)
+const numeric acosh(const numeric & x)
{
return ::acosh(*x.value); // -> CLN
}
+
/** Numeric inverse hyperbolic tangent (trigonometric function).
*
* @return arbitrary precision numerical atanh(x). */
-numeric atanh(const numeric & x)
+const 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(const numeric & x)
+const numeric zeta(const numeric & x)
{
// A dirty hack to allow for things like zeta(3.0), since CLN currently
// only knows about integer arguments and zeta(3).evalf() automatically
return numeric(0);
}
+
/** The gamma function.
* This is only a stub! */
-numeric gamma(const numeric & x)
+const numeric gamma(const numeric & x)
{
clog << "gamma(" << x
<< "): Does anybody know good way to calculate this numerically?"
return numeric(0);
}
+
/** The psi function (aka polygamma function).
* This is only a stub! */
-numeric psi(const numeric & x)
+const numeric psi(const numeric & x)
{
clog << "psi(" << x
<< "): Does anybody know good way to calculate this numerically?"
return numeric(0);
}
+
/** The psi functions (aka polygamma functions).
* This is only a stub! */
-numeric psi(const numeric & n, const numeric & x)
+const numeric psi(const numeric & n, const numeric & x)
{
clog << "psi(" << n << "," << x
<< "): Does anybody know good way to calculate this numerically?"
return numeric(0);
}
+
/** Factorial combinatorial function.
*
+ * @param n integer argument >= 0
* @exception range_error (argument must be integer >= 0) */
-numeric factorial(const numeric & nn)
+const numeric factorial(const numeric & n)
{
- if (!nn.is_nonneg_integer())
+ if (!n.is_nonneg_integer())
throw (std::range_error("numeric::factorial(): argument must be integer >= 0"));
- return numeric(::factorial(nn.to_int())); // -> CLN
+ return numeric(::factorial(n.to_int())); // -> CLN
}
+
/** The double factorial combinatorial function. (Scarcely used, but still
* 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
* @exception range_error (argument must be integer >= -1) */
-numeric doublefactorial(const numeric & nn)
+const numeric doublefactorial(const numeric & n)
{
- if (nn == numeric(-1)) {
+ if (n == numeric(-1)) {
return _num1();
}
- if (!nn.is_nonneg_integer()) {
+ if (!n.is_nonneg_integer()) {
throw (std::range_error("numeric::doublefactorial(): argument must be integer >= -1"));
}
- return numeric(::doublefactorial(nn.to_int())); // -> CLN
+ return numeric(::doublefactorial(n.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(const numeric & n, const numeric & k)
+const numeric binomial(const numeric & n, const numeric & k)
{
if (n.is_integer() && k.is_integer()) {
if (n.is_nonneg_integer()) {
throw (std::range_error("numeric::binomial(): don´t know how to evaluate that."));
}
+
/** Bernoulli number. The nth Bernoulli number is the coefficient of x^n/n!
* in the expansion of the function x/(e^x-1).
*
* @return the nth Bernoulli number (a rational number).
* @exception range_error (argument must be integer >= 0) */
-numeric bernoulli(const numeric & nn)
+const numeric bernoulli(const numeric & nn)
{
if (!nn.is_integer() || nn.is_negative())
throw (std::range_error("numeric::bernoulli(): argument must be integer >= 0"));
return results[n];
}
+
+/** Fibonacci number. The nth Fibonacci number F(n) is defined by the
+ * recurrence formula F(n)==F(n-1)+F(n-2) with F(0)==0 and F(1)==1.
+ *
+ * @param n an integer
+ * @return the nth Fibonacci number F(n) (an integer number)
+ * @exception range_error (argument must be an integer) */
+const numeric fibonacci(const numeric & n)
+{
+ if (!n.is_integer()) {
+ throw (std::range_error("numeric::fibonacci(): argument must be integer"));
+ }
+ // For positive arguments compute the nearest integer to
+ // ((1+sqrt(5))/2)^n/sqrt(5). For negative arguments, apply an additional
+ // sign. Note that we are falling back to longs, but this should suffice
+ // for all times.
+ int sig = 1;
+ const long nn = ::abs(n.to_double());
+ if (n.is_negative() && n.is_even())
+ sig =-1;
+
+ // Need a precision of ((1+sqrt(5))/2)^-n.
+ cl_float_format_t prec = ::cl_float_format((int)(0.208987641*nn+5));
+ cl_R sqrt5 = ::sqrt(::cl_float(5,prec));
+ cl_R phi = (1+sqrt5)/2;
+ return numeric(::round1(::expt(phi,nn)/sqrt5)*sig);
+}
+
+
/** Absolute value. */
numeric abs(const numeric & x)
{
return ::abs(*x.value); // -> CLN
}
+
/** Modulus (in positive representation).
* In general, mod(a,b) has the sign of b or is zero, and rem(a,b) has the
* sign of a or is zero. This is different from Maple's modp, where the sign
return _num0(); // Throw?
}
+
/** Modulus (in symmetric representation).
* Equivalent to Maple's mods.
*
return _num0(); // Throw?
}
+
/** Numeric integer remainder.
* Equivalent to Maple's irem(a,b) as far as sign conventions are concerned.
* In general, mod(a,b) has the sign of b or is zero, and irem(a,b) has the
return _num0(); // Throw?
}
+
/** 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,
}
}
+
/** Numeric integer quotient.
* Equivalent to Maple's iquo as far as sign conventions are concerned.
*
return _num0(); // Throw?
}
+
/** Numeric integer quotient.
* Equivalent to Maple's iquo(a,b,'r') it obeyes the relation
* r == a - iquo(a,b,r)*b.
}
}
+
/** Numeric square root.
* If possible, sqrt(z) should respect squares of exact numbers, i.e. sqrt(4)
* should return integer 2.
return ::sqrt(*z.value); // -> CLN
}
+
/** Integer numeric square root. */
numeric isqrt(const numeric & x)
{
return _num0(); // Throw?
}
+
/** Greatest Common Divisor.
*
* @return The GCD of two numbers if both are integer, a numerical 1
return _num1();
}
+
/** Least Common Multiple.
*
* @return The LCM of two numbers if both are integer, the product of those
return *a.value * *b.value;
}
+
+/** Floating point evaluation of Archimedes' constant Pi. */
ex PiEvalf(void)
{
return numeric(cl_pi(cl_default_float_format)); // -> CLN
}
+
+/** Floating point evaluation of Euler's constant Gamma. */
ex EulerGammaEvalf(void)
{
return numeric(cl_eulerconst(cl_default_float_format)); // -> CLN
}
+
+/** Floating point evaluation of Catalan's constant. */
ex CatalanEvalf(void)
{
return numeric(cl_catalanconst(cl_default_float_format)); // -> CLN
}
+
// It initializes to 17 digits, because in CLN cl_float_format(17) turns out to
// be 61 (<64) while cl_float_format(18)=65. We want to have a cl_LF instead
// of cl_SF, cl_FF or cl_DF but everything else is basically arbitrary.
cl_default_float_format = cl_float_format(17);
}
+
_numeric_digits& _numeric_digits::operator=(long prec)
{
digits=prec;
return *this;
}
+
_numeric_digits::operator long()
{
return (long)digits;
}
+
void _numeric_digits::print(ostream & os) const
{
debugmsg("_numeric_digits print", LOGLEVEL_PRINT);
os << digits;
}
+
ostream& operator<<(ostream& os, const _numeric_digits & e)
{
e.print(os);
git://www.ginac.de / ginac.git / blobdiff