// instead of in some header file where it would propagate to other parts.
// Also, we only need a subset of CLN, so we don't include the complete cln.h:
#ifdef HAVE_CLN_CLN_H
+#include <cln/cl_output.h>
#include <cln/cl_integer_io.h>
#include <cln/cl_integer_ring.h>
#include <cln/cl_rational_io.h>
#include <cln/cl_complex_ring.h>
#include <cln/cl_numtheory.h>
#else // def HAVE_CLN_CLN_H
+#include <cl_output.h>
#include <cl_integer_io.h>
#include <cl_integer_ring.h>
#include <cl_rational_io.h>
{
debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
value = new cl_N;
- *value=cl_I(0);
+ *value = cl_I(0);
calchash();
- setflag(status_flags::evaluated|
+ setflag(status_flags::evaluated |
+ status_flags::expanded |
status_flags::hash_calculated);
}
{
debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
value = new cl_N;
-#ifdef HAVE_SSTREAM
+
// Read number as string
string str;
if (n.find_string("number", str)) {
+#ifdef HAVE_SSTREAM
istringstream s(str);
+#else
+ istrstream s(str.c_str(), str.size() + 1);
+#endif
cl_idecoded_float re, im;
char c;
s.get(c);
switch (c) {
- case 'N': // Ordinary number
case 'R': // Integer-decoded real number
s >> re.sign >> re.mantissa >> re.exponent;
*value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent);
break;
}
}
-#else
- // Read number as string
- string str;
- if (n.find_string("number", str)) {
- istrstream f(str.c_str(), str.size() + 1);
- cl_idecoded_float re, im;
- char c;
- f.get(c);
- switch (c) {
- case 'R': // Integer-decoded real number
- f >> re.sign >> re.mantissa >> re.exponent;
- *value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent);
- break;
- case 'C': // Integer-decoded complex number
- f >> re.sign >> re.mantissa >> re.exponent;
- f >> im.sign >> im.mantissa >> im.exponent;
- *value = ::complex(re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent),
- im.sign * im.mantissa * ::expt(cl_float(2.0, cl_default_float_format), im.exponent));
- break;
- default: // Ordinary number
- f.putback(c);
- f >> *value;
- break;
- }
- }
-#endif
calchash();
setflag(status_flags::evaluated|
status_flags::hash_calculated);
void numeric::archive(archive_node &n) const
{
inherited::archive(n);
-#ifdef HAVE_SSTREAM
+
// Write number as string
+#ifdef HAVE_SSTREAM
ostringstream s;
+#else
+ char buf[1024];
+ ostrstream f(buf, 1024);
+#endif
if (this->is_crational())
s << *value;
else {
s << im.sign << " " << im.mantissa << " " << im.exponent;
}
}
+#ifdef HAVE_SSTREAM
n.add_string("number", s.str());
#else
- // Write number as string
- char buf[1024];
- ostrstream f(buf, 1024);
- if (this->is_crational())
- f << *value << ends;
- else {
- // Non-rational numbers are written in an integer-decoded format
- // to preserve the precision
- if (this->is_real()) {
- cl_idecoded_float re = integer_decode_float(The(cl_F)(*value));
- f << "R";
- f << re.sign << " " << re.mantissa << " " << re.exponent << ends;
- } else {
- cl_idecoded_float re = integer_decode_float(The(cl_F)(::realpart(*value)));
- cl_idecoded_float im = integer_decode_float(The(cl_F)(::imagpart(*value)));
- f << "C";
- f << re.sign << " " << re.mantissa << " " << re.exponent << " ";
- f << im.sign << " " << im.mantissa << " " << im.exponent << ends;
- }
- }
- string str(buf);
- n.add_string("number", str);
+ s << ends;
+ string str(buf);
+ n.add_string("number", str);
#endif
}
return new numeric(*this);
}
+
+/** Helper function to print a real number in a nicer way than is CLN's
+ * default. Instead of printing 42.0L0 this just prints 42.0 to ostream os
+ * and instead of 3.99168L7 it prints 3.99168E7. This is fine in GiNaC as
+ * long as it only uses cl_LF and no other floating point types.
+ *
+ * @see numeric::print() */
+void print_real_number(ostream & os, const cl_R & num)
+{
+ cl_print_flags ourflags;
+ if (::instanceof(num, ::cl_RA_ring)) {
+ // case 1: integer or rational, nothing special to do:
+ ::print_real(os, ourflags, num);
+ } else {
+ // case 2: float
+ // make CLN believe this number has default_float_format, so it prints
+ // 'E' as exponent marker instead of 'L':
+ ourflags.default_float_format = ::cl_float_format(The(cl_F)(num));
+ ::print_real(os, ourflags, num);
+ }
+ return;
+}
+
+/** 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(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 (this->is_real()) {
// case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!this->is_pos_integer())) {
- os << "(" << *value << ")";
+ if ((precedence<=upper_precedence) && (!this->is_nonneg_integer())) {
+ os << "(";
+ print_real_number(os, The(cl_R)(*value));
+ os << ")";
} else {
- os << *value;
+ print_real_number(os, The(cl_R)(*value));
}
} else {
// case 2, imaginary: y*I or -y*I
if (::imagpart(*value) == -1) {
os << "(-I)";
} else {
- os << "(" << ::imagpart(*value) << "*I)";
+ os << "(";
+ print_real_number(os, The(cl_R)(::imagpart(*value)));
+ os << "*I)";
}
} else {
if (::imagpart(*value) == 1) {
if (::imagpart (*value) == -1) {
os << "-I";
} else {
- os << ::imagpart(*value) << "*I";
+ print_real_number(os, The(cl_R)(::imagpart(*value)));
+ os << "*I";
}
}
}
} else {
// case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I
- if (precedence <= upper_precedence) os << "(";
- os << ::realpart(*value);
+ if (precedence <= upper_precedence)
+ os << "(";
+ print_real_number(os, The(cl_R)(::realpart(*value)));
if (::imagpart(*value) < 0) {
if (::imagpart(*value) == -1) {
os << "-I";
} else {
- os << ::imagpart(*value) << "*I";
+ print_real_number(os, The(cl_R)(::imagpart(*value)));
+ os << "*I";
}
} else {
if (::imagpart(*value) == 1) {
os << "+I";
} else {
- os << "+" << ::imagpart(*value) << "*I";
+ os << "+";
+ print_real_number(os, The(cl_R)(::imagpart(*value)));
+ os << "*I";
}
}
- if (precedence <= upper_precedence) os << ")";
+ if (precedence <= upper_precedence)
+ os << ")";
}
}
}
numeric numeric::power(const numeric & other) const
{
- static const numeric * _num1p=&_num1();
+ static const numeric * _num1p = &_num1();
if (&other==_num1p)
return *this;
if (::zerop(*value)) {
if (::zerop(*other.value))
throw (std::domain_error("numeric::eval(): pow(0,0) is undefined"));
- else if (other.is_real() && !::plusp(::realpart(*other.value)))
+ else if (::zerop(::realpart(*other.value)))
+ throw (std::domain_error("numeric::eval(): pow(0,I) is undefined"));
+ else if (::minusp(::realpart(*other.value)))
throw (std::overflow_error("numeric::eval(): division by zero"));
else
return _num0();
if (::zerop(*value)) {
if (::zerop(*other.value))
throw (std::domain_error("numeric::eval(): pow(0,0) is undefined"));
- else if (other.is_real() && !::plusp(::realpart(*other.value)))
+ else if (::zerop(::realpart(*other.value)))
+ throw (std::domain_error("numeric::eval(): pow(0,I) is undefined"));
+ else if (::minusp(::realpart(*other.value)))
throw (std::overflow_error("numeric::eval(): division by zero"));
else
return _num0();
/** True if object is a non-complex integer. */
bool numeric::is_integer(void) const
{
- return ::instanceof(*value, cl_I_ring); // -> CLN
+ return ::instanceof(*value, ::cl_I_ring); // -> CLN
}
/** True if object is an exact integer greater than zero. */
* (denominator may be unity). */
bool numeric::is_rational(void) const
{
- return ::instanceof(*value, cl_RA_ring); // -> CLN
+ return ::instanceof(*value, ::cl_RA_ring); // -> CLN
}
/** True if object is a real integer, rational or float (but not complex). */
bool numeric::is_real(void) const
{
- return ::instanceof(*value, cl_R_ring); // -> CLN
+ return ::instanceof(*value, ::cl_R_ring); // -> CLN
}
bool numeric::operator==(const numeric & other) const
* of the form a+b*I, where a and b are integers. */
bool numeric::is_cinteger(void) const
{
- if (::instanceof(*value, cl_I_ring))
+ if (::instanceof(*value, ::cl_I_ring))
return true;
else if (!this->is_real()) { // complex case, handle n+m*I
- if (::instanceof(::realpart(*value), cl_I_ring) &&
- ::instanceof(::imagpart(*value), cl_I_ring))
+ if (::instanceof(::realpart(*value), ::cl_I_ring) &&
+ ::instanceof(::imagpart(*value), ::cl_I_ring))
return true;
}
return false;
* (denominator may be unity). */
bool numeric::is_crational(void) const
{
- if (::instanceof(*value, cl_RA_ring))
+ if (::instanceof(*value, ::cl_RA_ring))
return true;
else if (!this->is_real()) { // complex case, handle Q(i):
- if (::instanceof(::realpart(*value), cl_RA_ring) &&
- ::instanceof(::imagpart(*value), cl_RA_ring))
+ if (::instanceof(::realpart(*value), ::cl_RA_ring) &&
+ ::instanceof(::imagpart(*value), ::cl_RA_ring))
return true;
}
return false;
}
/** Real part of a number. */
-numeric numeric::real(void) const
+const numeric numeric::real(void) const
{
return numeric(::realpart(*value)); // -> CLN
}
/** Imaginary part of a number. */
-numeric numeric::imag(void) const
+const numeric numeric::imag(void) const
{
return numeric(::imagpart(*value)); // -> CLN
}
* 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. */
-numeric numeric::numer(void) const
+const numeric numeric::numer(void) const
{
if (this->is_integer()) {
return numeric(*this);
}
#ifdef SANE_LINKER
- else if (::instanceof(*value, cl_RA_ring)) {
+ else if (::instanceof(*value, ::cl_RA_ring)) {
return numeric(::numerator(The(cl_RA)(*value)));
}
else if (!this->is_real()) { // complex case, handle Q(i):
cl_R r = ::realpart(*value);
cl_R i = ::imagpart(*value);
- if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring))
+ if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring))
return numeric(*this);
- if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_ring))
+ if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_RA_ring))
return numeric(::complex(r*::denominator(The(cl_RA)(i)), ::numerator(The(cl_RA)(i))));
- if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_I_ring))
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring))
return numeric(::complex(::numerator(The(cl_RA)(r)), i*::denominator(The(cl_RA)(r))));
- if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_RA_ring)) {
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring)) {
cl_I s = ::lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i)));
return numeric(::complex(::numerator(The(cl_RA)(r))*(exquo(s,::denominator(The(cl_RA)(r)))),
::numerator(The(cl_RA)(i))*(exquo(s,::denominator(The(cl_RA)(i))))));
}
}
#else
- else if (instanceof(*value, cl_RA_ring)) {
+ else if (instanceof(*value, ::cl_RA_ring)) {
return numeric(TheRatio(*value)->numerator);
}
else if (!this->is_real()) { // complex case, handle Q(i):
cl_R r = ::realpart(*value);
cl_R i = ::imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
+ if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
return numeric(*this);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
+ if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_RA_ring))
return numeric(::complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring))
return numeric(::complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator));
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring)) {
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring)) {
cl_I s = ::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator);
return numeric(::complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)),
TheRatio(i)->numerator*(exquo(s,TheRatio(i)->denominator))));
/** 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. */
-numeric numeric::denom(void) const
+const numeric numeric::denom(void) const
{
if (this->is_integer()) {
return _num1();
}
#ifdef SANE_LINKER
- if (instanceof(*value, cl_RA_ring)) {
+ if (instanceof(*value, ::cl_RA_ring)) {
return numeric(::denominator(The(cl_RA)(*value)));
}
if (!this->is_real()) { // complex case, handle Q(i):
cl_R r = ::realpart(*value);
cl_R i = ::imagpart(*value);
- if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring))
+ if (::instanceof(r, ::cl_I_ring) && ::instanceof(i, ::cl_I_ring))
return _num1();
- if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_ring))
+ 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))
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_I_ring))
return numeric(::denominator(The(cl_RA)(r)));
- if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_RA_ring))
+ if (::instanceof(r, ::cl_RA_ring) && ::instanceof(i, ::cl_RA_ring))
return numeric(::lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))));
}
#else
- if (instanceof(*value, cl_RA_ring)) {
+ if (instanceof(*value, ::cl_RA_ring)) {
return numeric(TheRatio(*value)->denominator);
}
if (!this->is_real()) { // complex case, handle Q(i):
cl_R r = ::realpart(*value);
cl_R i = ::imagpart(*value);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
+ if (instanceof(r, ::cl_I_ring) && instanceof(i, ::cl_I_ring))
return _num1();
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
+ 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))
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_I_ring))
return numeric(TheRatio(r)->denominator);
- if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring))
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring))
return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
}
#endif // def SANE_LINKER
}
-/** The gamma function.
+/** The Gamma function.
* This is only a stub! */
-const numeric gamma(const numeric & x)
+const numeric lgamma(const numeric & x)
+{
+ clog << "lgamma(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
+ return numeric(0);
+}
+const numeric tgamma(const numeric & x)
{
- clog << "gamma(" << x
+ clog << "tgamma(" << x
<< "): Does anybody know good way to calculate this numerically?"
<< endl;
return numeric(0);
/** The double factorial combinatorial function. (Scarcely used, but still
- * useful in cases, like for exact results of Gamma(n+1/2) for instance.)
+ * useful in cases, like for exact results of tgamma(n+1/2) for instance.)
*
* @param n integer argument >= -1
* @return n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1
return numeric(-1,2);
if (nn.is_odd())
return _num0();
- // Until somebody has the Blues and comes up with a much better idea and
+ // 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
+ // computes its results using the defining formula
// B(nn) == - 1/(nn+1) * sum_{k=0}^{nn-1}(binomial(nn+1,k)*B(k))
// whith B(0) == 1.
+ // Be warned, though: the Bernoulli numbers are computationally very
+ // expensive anyhow and you shouldn't expect miracles to happen.
static vector<numeric> results;
static int highest_result = -1;
int n = nn.sub(_num2()).div(_num2()).to_int();
}
-/** Floating point evaluation of Euler's constant Gamma. */
-ex EulerGammaEvalf(void)
+/** Floating point evaluation of Euler's constant gamma. */
+ex EulerEvalf(void)
{
return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN
}
git://www.ginac.de / ginac.git / blobdiff