* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include "config.h"
+
#include <vector>
#include <stdexcept>
#include <string>
-#include <strstream> //!!
+
+#if defined(HAVE_SSTREAM)
+#include <sstream>
+#elif defined(HAVE_STRSTREAM)
+#include <strstream>
+#else
+#error Need either sstream or strstream
+#endif
#include "numeric.h"
#include "ex.h"
-#include "config.h"
#include "archive.h"
#include "debugmsg.h"
#include "utils.h"
#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
+#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
// linker has no problems finding text symbols for numerator or denominator
//#define SANE_LINKER
{
debugmsg("numeric constructor 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
+ // first. This is due to the behaviour of the cl_I-ctor, which
// emphasizes efficiency:
value = new cl_I((long) i);
calchash();
status_flags::hash_calculated);
}
+
numeric::numeric(unsigned int i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor 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
+ // first. This is due to the behaviour of the cl_I-ctor, which
// emphasizes efficiency:
value = new cl_I((unsigned long)i);
calchash();
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);
/** Ctor from CLN types. This is for the initiated user or internal use
* only. */
-numeric::numeric(cl_N const & z) : basic(TINFO_numeric)
+numeric::numeric(const cl_N & z) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
value = new cl_N(z);
{
debugmsg("numeric constructor from archive_node", LOGLEVEL_CONSTRUCT);
value = new cl_N;
-#if 0 //!!
- // This is how it should be implemented but we have no istringstream here...
+#ifdef HAVE_SSTREAM
+ // Read number as string
string str;
if (n.find_string("number", str)) {
istringstream s(str);
- s >> *value;
+ 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;
+ case 'C': // Integer-decoded complex number
+ s >> re.sign >> re.mantissa >> re.exponent;
+ s >> 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
+ s.putback(c);
+ s >> *value;
+ break;
+ }
}
#else
- // Workaround for the above: read from strstream
+ // Read number as string
string str;
if (n.find_string("number", str)) {
istrstream f(str.c_str(), str.size() + 1);
- f >> *value;
+ 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();
void numeric::archive(archive_node &n) const
{
inherited::archive(n);
-#if 0 //!!
- // This is how it should be implemented but we have no ostringstream here...
+#ifdef HAVE_SSTREAM
+ // Write number as string
ostringstream s;
- s << *value;
+ if (this->is_crational())
+ s << *value;
+ 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));
+ s << "R";
+ s << re.sign << " " << re.mantissa << " " << re.exponent;
+ } 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)));
+ s << "C";
+ s << re.sign << " " << re.mantissa << " " << re.exponent << " ";
+ s << im.sign << " " << im.mantissa << " " << im.exponent;
+ }
+ }
n.add_string("number", s.str());
#else
- // Workaround for the above: write to strstream
+ // Write number as string
char buf[1024];
ostrstream f(buf, 1024);
- f << *value << ends;
+ 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);
#endif
// together with the other routines and produces something compatible to
// ginsh input.
debugmsg("numeric print", LOGLEVEL_PRINT);
- if (is_real()) {
+ if (this->is_real()) {
// case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!is_pos_integer())) {
+ if ((precedence<=upper_precedence) && (!this->is_pos_integer())) {
os << "(" << *value << ")";
} else {
os << *value;
}
} else {
// case 2, imaginary: y*I or -y*I
- if (realpart(*value) == 0) {
- if ((precedence<=upper_precedence) && (imagpart(*value) < 0)) {
- if (imagpart(*value) == -1) {
+ if (::realpart(*value) == 0) {
+ if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) {
+ if (::imagpart(*value) == -1) {
os << "(-I)";
} else {
- os << "(" << imagpart(*value) << "*I)";
+ os << "(" << ::imagpart(*value) << "*I)";
}
} else {
- if (imagpart(*value) == 1) {
+ if (::imagpart(*value) == 1) {
os << "I";
} else {
- if (imagpart (*value) == -1) {
+ if (::imagpart (*value) == -1) {
os << "-I";
} else {
- os << imagpart(*value) << "*I";
+ os << ::imagpart(*value) << "*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 (imagpart(*value) < 0) {
- if (imagpart(*value) == -1) {
+ os << ::realpart(*value);
+ if (::imagpart(*value) < 0) {
+ if (::imagpart(*value) == -1) {
os << "-I";
} else {
- os << imagpart(*value) << "*I";
+ os << ::imagpart(*value) << "*I";
}
} else {
- if (imagpart(*value) == 1) {
+ if (::imagpart(*value) == 1) {
os << "+I";
} else {
- os << "+" << imagpart(*value) << "*I";
+ os << "+" << ::imagpart(*value) << "*I";
}
}
if (precedence <= upper_precedence) os << ")";
debugmsg("numeric printraw", LOGLEVEL_PRINT);
os << "numeric(" << *value << ")";
}
+
+
void numeric::printtree(ostream & os, unsigned indent) const
{
debugmsg("numeric printtree", LOGLEVEL_PRINT);
<< ", flags=" << flags << endl;
}
+
void numeric::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
{
debugmsg("numeric print csrc", LOGLEVEL_PRINT);
ios::fmtflags oldflags = os.flags();
os.setf(ios::scientific);
- if (is_rational() && !is_integer()) {
+ if (this->is_rational() && !this->is_integer()) {
if (compare(_num0()) > 0) {
os << "(";
if (type == csrc_types::ctype_cl_N)
os.flags(oldflags);
}
+
bool numeric::info(unsigned inf) const
{
switch (inf) {
case info_flags::negative:
return is_negative();
case info_flags::nonnegative:
- return compare(_num0())>=0;
+ return !is_negative();
case info_flags::posint:
return is_pos_integer();
case info_flags::negint:
- return is_integer() && (compare(_num0())<0);
+ return is_integer() && is_negative();
case info_flags::nonnegint:
return is_nonneg_integer();
case info_flags::even:
return false;
}
+/** Disassemble real part and imaginary part to scan for the occurrence of a
+ * single number. Also handles the imaginary unit. It ignores the sign on
+ * both this and the argument, which may lead to what might appear as funny
+ * results: (2+I).has(-2) -> true. But this is consistent, since we also
+ * would like to have (-2+I).has(2) -> true and we want to think about the
+ * sign as a multiplicative factor. */
+bool numeric::has(const ex & other) const
+{
+ if (!is_exactly_of_type(*other.bp, numeric))
+ return false;
+ const numeric & o = static_cast<numeric &>(const_cast<basic &>(*other.bp));
+ 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));
+ 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));
+ }
+ return false;
+}
+
+
+/** Evaluation of numbers doesn't do anything at all. */
+ex numeric::eval(int level) const
+{
+ // Warning: if this is ever gonna do something, the ex ctors from all kinds
+ // of numbers should be checking for status_flags::evaluated.
+ return this->hold();
+}
+
+
/** Cast numeric into a floating-point object. For example exact numeric(1) is
* returned as a 1.0000000000000000000000 and so on according to how Digits is
* currently set.
ex numeric::evalf(int level) const
{
// level can safely be discarded for numeric objects.
- return numeric(cl_float(1.0, cl_default_float_format) * (*value)); // -> CLN
+ return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN
}
// protected
+/** Implementation of ex::diff() for a numeric. It always returns 0.
+ *
+ * @see ex::diff */
+ex numeric::derivative(const symbol & s) const
+{
+ return _ex0();
+}
+
+
int numeric::compare_same_type(const basic & other) const
{
GINAC_ASSERT(is_exactly_of_type(other, numeric));
return compare(o);
}
+
bool numeric::is_equal_same_type(const basic & other) const
{
GINAC_ASSERT(is_exactly_of_type(other,numeric));
const numeric *o = static_cast<const numeric *>(&other);
- return is_equal(*o);
+ return this->is_equal(*o);
+}
+
+unsigned numeric::calchash(void) const
+{
+ return (hashvalue=cl_equal_hashcode(*value) | 0x80000000U);
+ /*
+ cout << *value << "->" << hashvalue << endl;
+ hashvalue=HASHVALUE_NUMERIC+1000U;
+ return HASHVALUE_NUMERIC+1000U;
+ */
}
/*
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"));
+ 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)))
+ throw (std::overflow_error("numeric::eval(): division by zero"));
+ else
+ return _num0();
+ }
return numeric(::expt(*value,*other.value));
}
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"));
+ 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)))
+ throw (std::overflow_error("numeric::eval(): division by zero"));
+ else
+ return _num0();
+ }
return static_cast<const numeric &>((new numeric(::expt(*value,*other.value)))->
setflag(status_flags::dynallocated));
}
* @see numeric::compare(const numeric & other) */
int numeric::csgn(void) const
{
- if (is_zero())
+ if (this->is_zero())
return 0;
- if (!::zerop(realpart(*value))) {
- if (::plusp(realpart(*value)))
+ if (!::zerop(::realpart(*value))) {
+ if (::plusp(::realpart(*value)))
return 1;
else
return -1;
} else {
- if (::plusp(imagpart(*value)))
+ if (::plusp(::imagpart(*value)))
return 1;
else
return -1;
int numeric::compare(const numeric & other) const
{
// Comparing two real numbers?
- if (is_real() && other.is_real())
+ if (this->is_real() && other.is_real())
// Yes, just compare them
return ::cl_compare(The(cl_R)(*value), The(cl_R)(*other.value));
else {
// No, first compare real parts
- cl_signean real_cmp = ::cl_compare(realpart(*value), realpart(*other.value));
+ cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value));
if (real_cmp)
return real_cmp;
- return ::cl_compare(imagpart(*value), imagpart(*other.value));
+ return ::cl_compare(::imagpart(*value), ::imagpart(*other.value));
}
}
/** True if object is not complex and greater than zero. */
bool numeric::is_positive(void) const
{
- if (is_real())
+ if (this->is_real())
return ::plusp(The(cl_R)(*value)); // -> CLN
return false;
}
/** True if object is not complex and less than zero. */
bool numeric::is_negative(void) const
{
- if (is_real())
+ if (this->is_real())
return ::minusp(The(cl_R)(*value)); // -> CLN
return false;
}
/** True if object is an exact integer greater than zero. */
bool numeric::is_pos_integer(void) const
{
- return (is_integer() && ::plusp(The(cl_I)(*value))); // -> CLN
+ return (this->is_integer() && ::plusp(The(cl_I)(*value))); // -> CLN
}
/** True if object is an exact integer greater or equal zero. */
bool numeric::is_nonneg_integer(void) const
{
- return (is_integer() && !::minusp(The(cl_I)(*value))); // -> CLN
+ return (this->is_integer() && !::minusp(The(cl_I)(*value))); // -> CLN
}
/** True if object is an exact even integer. */
bool numeric::is_even(void) const
{
- return (is_integer() && ::evenp(The(cl_I)(*value))); // -> CLN
+ return (this->is_integer() && ::evenp(The(cl_I)(*value))); // -> CLN
}
/** True if object is an exact odd integer. */
bool numeric::is_odd(void) const
{
- return (is_integer() && ::oddp(The(cl_I)(*value))); // -> CLN
+ return (this->is_integer() && ::oddp(The(cl_I)(*value))); // -> CLN
}
/** Probabilistic primality test.
* @return true if object is exact integer and prime. */
bool numeric::is_prime(void) const
{
- return (is_integer() && ::isprobprime(The(cl_I)(*value))); // -> CLN
+ return (this->is_integer() && ::isprobprime(The(cl_I)(*value))); // -> CLN
}
/** True if object is an exact rational number, may even be complex
{
if (::instanceof(*value, cl_I_ring))
return true;
- else if (!is_real()) { // complex case, handle n+m*I
- if (::instanceof(realpart(*value), cl_I_ring) &&
- ::instanceof(imagpart(*value), cl_I_ring))
+ else if (!this->is_real()) { // complex case, handle n+m*I
+ if (::instanceof(::realpart(*value), cl_I_ring) &&
+ ::instanceof(::imagpart(*value), cl_I_ring))
return true;
}
return false;
{
if (::instanceof(*value, cl_RA_ring))
return true;
- else if (!is_real()) { // complex case, handle Q(i):
- if (::instanceof(realpart(*value), cl_RA_ring) &&
- ::instanceof(imagpart(*value), cl_RA_ring))
+ else if (!this->is_real()) { // complex case, handle Q(i):
+ if (::instanceof(::realpart(*value), cl_RA_ring) &&
+ ::instanceof(::imagpart(*value), cl_RA_ring))
return true;
}
return false;
* @exception invalid_argument (complex inequality) */
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
+ if (this->is_real() && other.is_real())
+ return (The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN
throw (std::invalid_argument("numeric::operator<(): complex inequality"));
return false; // make compiler shut up
}
* @exception invalid_argument (complex inequality) */
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
+ if (this->is_real() && other.is_real())
+ return (The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN
throw (std::invalid_argument("numeric::operator<=(): complex inequality"));
return false; // make compiler shut up
}
* @exception invalid_argument (complex inequality) */
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
+ if (this->is_real() && other.is_real())
+ return (The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN
throw (std::invalid_argument("numeric::operator>(): complex inequality"));
return false; // make compiler shut up
}
* @exception invalid_argument (complex inequality) */
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
+ if (this->is_real() && other.is_real())
+ return (The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN
throw (std::invalid_argument("numeric::operator>=(): complex inequality"));
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());
+ GINAC_ASSERT(this->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(this->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
{
- GINAC_ASSERT(is_real());
- return ::cl_double_approx(realpart(*value)); // -> CLN
+ GINAC_ASSERT(this->is_real());
+ return ::cl_double_approx(::realpart(*value)); // -> CLN
}
/** Real part of a number. */
* cases. */
numeric numeric::numer(void) const
{
- if (is_integer()) {
+ if (this->is_integer()) {
return numeric(*this);
}
#ifdef SANE_LINKER
else if (::instanceof(*value, cl_RA_ring)) {
return numeric(::numerator(The(cl_RA)(*value)));
}
- else if (!is_real()) { // complex case, handle Q(i):
+ 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))
return numeric(*this);
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))));
+ 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))
- return numeric(complex(::numerator(The(cl_RA)(r)), i*::denominator(The(cl_RA)(r))));
+ 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)) {
- 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)))),
+ 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 if (instanceof(*value, cl_RA_ring)) {
return numeric(TheRatio(*value)->numerator);
}
- else if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*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))
return numeric(*this);
if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring))
- return numeric(complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator));
+ return numeric(::complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator));
if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring))
- return numeric(complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator));
+ return numeric(::complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator));
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)),
+ 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))));
}
}
* (i.e denom(4/3+5/6*I) == 6), one in all other cases. */
numeric numeric::denom(void) const
{
- if (is_integer()) {
+ if (this->is_integer()) {
return _num1();
}
#ifdef SANE_LINKER
if (instanceof(*value, cl_RA_ring)) {
return numeric(::denominator(The(cl_RA)(*value)));
}
- if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*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))
return _num1();
if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_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))
- return numeric(lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))));
+ return numeric(::lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))));
}
#else
if (instanceof(*value, cl_RA_ring)) {
return numeric(TheRatio(*value)->denominator);
}
- if (!is_real()) { // complex case, handle Q(i):
- cl_R r = realpart(*value);
- cl_R i = imagpart(*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))
return _num1();
if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_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))
- return numeric(lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
+ return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
}
#endif // def SANE_LINKER
// at least one float encountered
* in two's complement if it is an integer, 0 otherwise. */
int numeric::int_length(void) const
{
- if (is_integer())
+ if (this->is_integer())
return ::integer_length(The(cl_I)(*value)); // -> CLN
else
return 0;
const type_info & typeid_numeric=typeid(some_numeric);
/** Imaginary unit. This is not a constant but a numeric since we are
* natively handing complex numbers anyways. */
-const numeric I = numeric(complex(cl_I(0),cl_I(1)));
+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
+ return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN
else
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
// being an exact zero for CLN, which can be tested and then we can just
// pass the number casted to an int:
if (x.is_real()) {
- int aux = (int)(::cl_double_approx(realpart(*x.value)));
+ int aux = (int)(::cl_double_approx(::realpart(*x.value)));
if (zerop(*x.value-aux))
return ::cl_zeta(aux); // -> CLN
}
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"));
+ // The following addition formula holds:
+ // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0.
+ // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence
+ // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values
+ // agree.)
+ // Replace m by m+1:
+ // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0
+ // Now put in m = n, to get
+ // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n))
+ // F(2n+1) = F(n)^2 + F(n+1)^2
+ // hence
+ // F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
+ if (n.is_zero())
+ return _num0();
+ if (n.is_negative())
+ if (n.is_even())
+ return -fibonacci(-n);
+ else
+ return fibonacci(-n);
+
+ cl_I u(0);
+ cl_I v(1);
+ cl_I m = The(cl_I)(*n.value) >> 1L; // floor(n/2);
+ for (uintL bit=::integer_length(m); bit>0; --bit) {
+ // Since a squaring is cheaper than a multiplication, better use
+ // three squarings instead of one multiplication and two squarings.
+ cl_I u2 = ::square(u);
+ cl_I v2 = ::square(v);
+ if (::logbitp(bit-1, m)) {
+ v = ::square(u + v) - u2;
+ u = u2 + v2;
+ } else {
+ u = v2 - ::square(v - u);
+ v = u2 + v2;
+ }
+ }
+ if (n.is_even())
+ // Here we don't use the squaring formula because one multiplication
+ // is cheaper than two squarings.
+ return u * ((v << 1) - u);
+ else
+ return ::square(u) + ::square(v);
+}
+
+
/** 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 a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
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;
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
+ 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
+ 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
+ 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.
{
assert(!too_late);
too_late = true;
- cl_default_float_format = cl_float_format(17);
+ cl_default_float_format = ::cl_float_format(17);
}
+
_numeric_digits& _numeric_digits::operator=(long prec)
{
digits=prec;
- cl_default_float_format = cl_float_format(prec);
+ cl_default_float_format = ::cl_float_format(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);
bool _numeric_digits::too_late = false;
+
/** Accuracy in decimal digits. Only object of this type! Can be set using
* assignment from C++ unsigned ints and evaluated like any built-in type. */
_numeric_digits Digits;
-#ifndef NO_GINAC_NAMESPACE
+#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
+#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff