* Its most important design principle is to completely hide the inner
* working of that other package from the user of GiNaC. It must either
* provide implementation of arithmetic operators and numerical evaluation
- * of special functions or implement the interface to the bignum package.
- *
+ * of special functions or implement the interface to the bignum package. */
+
+/*
* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
#include <vector>
#include <stdexcept>
-#include "ginac.h"
+#include "numeric.h"
+#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:
#include <cln.h>
#endif
+#ifndef NO_GINAC_NAMESPACE
+namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
+
// linker has no problems finding text symbols for numerator or denominator
//#define SANE_LINKER
// public
/** default ctor. Numerically it initializes to an integer zero. */
-numeric::numeric() : basic(TINFO_NUMERIC)
+numeric::numeric() : basic(TINFO_numeric)
{
debugmsg("numeric default constructor", LOGLEVEL_CONSTRUCT);
value = new cl_N;
// public
-numeric::numeric(int i) : basic(TINFO_NUMERIC)
+numeric::numeric(int i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT);
// Not the whole int-range is available if we don't cast to long
status_flags::hash_calculated);
}
-numeric::numeric(unsigned int i) : basic(TINFO_NUMERIC)
+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
status_flags::hash_calculated);
}
-numeric::numeric(long i) : basic(TINFO_NUMERIC)
+numeric::numeric(long i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from long",LOGLEVEL_CONSTRUCT);
value = new cl_I(i);
status_flags::hash_calculated);
}
-numeric::numeric(unsigned long i) : basic(TINFO_NUMERIC)
+numeric::numeric(unsigned long i) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from ulong",LOGLEVEL_CONSTRUCT);
value = new cl_I(i);
/** Ctor for rational numerics a/b.
*
* @exception overflow_error (division by zero) */
-numeric::numeric(long numer, long denom) : basic(TINFO_NUMERIC)
+numeric::numeric(long numer, long denom) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from long/long",LOGLEVEL_CONSTRUCT);
if (!denom)
status_flags::hash_calculated);
}
-numeric::numeric(double d) : basic(TINFO_NUMERIC)
+numeric::numeric(double d) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from double",LOGLEVEL_CONSTRUCT);
// We really want to explicitly use the type cl_LF instead of the
status_flags::hash_calculated);
}
-numeric::numeric(char const *s) : basic(TINFO_NUMERIC)
+numeric::numeric(char const *s) : basic(TINFO_numeric)
{ // MISSING: treatment of complex and ints and rationals.
debugmsg("numeric constructor from string",LOGLEVEL_CONSTRUCT);
if (strchr(s, '.'))
/** 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(cl_N const & z) : basic(TINFO_numeric)
{
debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT);
value = new cl_N(z);
void numeric::print(ostream & os, unsigned upper_precedence) const
{
debugmsg("numeric print", LOGLEVEL_PRINT);
- if (is_real()) {
+ if (is_real()) {
// case 1, real: x or -x
if ((precedence<=upper_precedence) && (!is_pos_integer())) {
os << "(" << *value << ")";
}
}
+void numeric::printtree(ostream & os, unsigned indent) const
+{
+ debugmsg("numeric printtree", LOGLEVEL_PRINT);
+ os << string(indent,' ') << *value
+ << " (numeric): "
+ << "hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")"
+ << ", 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 (compare(_num0()) > 0) {
+ os << "(";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << numer().evalf() << "\")";
+ else
+ os << numer().to_double();
+ } else {
+ os << "-(";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << -numer().evalf() << "\")";
+ else
+ os << -numer().to_double();
+ }
+ os << "/";
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << denom().evalf() << "\")";
+ else
+ os << denom().to_double();
+ os << ")";
+ } else {
+ if (type == csrc_types::ctype_cl_N)
+ os << "cl_F(\"" << evalf() << "\")";
+ else
+ os << to_double();
+ }
+ os.flags(oldflags);
+}
+
bool numeric::info(unsigned inf) const
{
switch (inf) {
case info_flags::rational:
case info_flags::rational_polynomial:
return is_rational();
+ case info_flags::crational:
+ case info_flags::crational_polynomial:
+ return is_crational();
case info_flags::integer:
case info_flags::integer_polynomial:
return is_integer();
+ case info_flags::cinteger:
+ case info_flags::cinteger_polynomial:
+ return is_cinteger();
case info_flags::positive:
return is_positive();
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:
* currently set.
*
* @param level ignored, but needed for overriding basic::evalf.
- * @return an ex-handle to a numeric. */
+ * @return an ex-handle to a numeric. */
ex numeric::evalf(int level) const
{
// level can safely be discarded for numeric objects.
int numeric::compare_same_type(basic const & other) const
{
- ASSERT(is_exactly_of_type(other, numeric));
+ GINAC_ASSERT(is_exactly_of_type(other, numeric));
numeric const & o = static_cast<numeric &>(const_cast<basic &>(other));
if (*value == *o.value) {
bool numeric::is_equal_same_type(basic const & other) const
{
- ASSERT(is_exactly_of_type(other,numeric));
+ GINAC_ASSERT(is_exactly_of_type(other,numeric));
numeric const *o = static_cast<numeric const *>(&other);
return is_equal(*o);
* result as a new numeric object. */
numeric numeric::mul(numeric const & 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));
* @exception overflow_error (division by zero) */
numeric numeric::div(numeric const & other) const
{
- if (zerop(*other.value))
+ if (::zerop(*other.value))
throw (std::overflow_error("division by zero"));
return numeric((*value)/(*other.value));
}
numeric numeric::power(numeric const & 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)))
+ if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value)))
throw (std::overflow_error("division by zero"));
- return numeric(expt(*value,*other.value));
+ return numeric(::expt(*value,*other.value));
}
/** Inverse of a number. */
numeric numeric::inverse(void) const
{
- return numeric(recip(*value)); // -> CLN
+ return numeric(::recip(*value)); // -> CLN
}
numeric const & numeric::add_dyn(numeric const & other) const
numeric const & numeric::mul_dyn(numeric const & 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)))->
numeric const & numeric::div_dyn(numeric const & other) const
{
- if (zerop(*other.value))
+ if (::zerop(*other.value))
throw (std::overflow_error("division by zero"));
return static_cast<numeric const &>((new numeric((*value)/(*other.value)))->
setflag(status_flags::dynallocated));
numeric const & numeric::power_dyn(numeric const & other) const
{
- static const numeric * numONEp=&numONE();
- if (&other==numONEp) {
+ static const numeric * _num1p=&_num1();
+ if (&other==_num1p)
return *this;
- }
- // The ifs are only a workaround for a bug in CLN. It gets stuck otherwise:
- if ( !other.is_integer() &&
- other.is_rational() &&
- (*this).is_nonneg_integer() ) {
- if ( !zerop(*value) ) {
- return static_cast<numeric const &>((new numeric(exp(*other.value * log(*value))))->
- setflag(status_flags::dynallocated));
- } else {
- if ( !zerop(*other.value) ) { // 0^(n/m)
- return static_cast<numeric const &>((new numeric(0))->
- setflag(status_flags::dynallocated));
- } else { // raise FPE (0^0 requested)
- return static_cast<numeric const &>((new numeric(1/(*other.value)))->
- setflag(status_flags::dynallocated));
- }
- }
- } else { // default -> CLN
- return static_cast<numeric const &>((new numeric(expt(*value,*other.value)))->
- setflag(status_flags::dynallocated));
- }
+ 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)))->
+ setflag(status_flags::dynallocated));
}
numeric const & numeric::operator=(int i)
return operator=(numeric(s));
}
+/** Return the complex half-plane (left or right) in which the number lies.
+ * 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) */
+int numeric::csgn(void) const
+{
+ if (is_zero())
+ return 0;
+ if (!::zerop(realpart(*value))) {
+ if (::plusp(realpart(*value)))
+ return 1;
+ else
+ return -1;
+ } else {
+ if (::plusp(imagpart(*value)))
+ return 1;
+ else
+ return -1;
+ }
+}
+
/** This method establishes a canonical order on all numbers. For complex
* numbers this is not possible in a mathematically consistent way but we need
* to establish some order and it ought to be fast. So we simply define it
- * similar to Maple's csgn. */
+ * to be compatible with our method csgn.
+ *
+ * @return csgn(*this-other)
+ * @see numeric::csgn(void) */
int numeric::compare(numeric const & other) const
{
// Comparing two real numbers?
if (is_real() && other.is_real())
// Yes, just compare them
- return cl_compare(The(cl_R)(*value), The(cl_R)(*other.value));
+ 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 zero. */
bool numeric::is_zero(void) const
{
- return zerop(*value); // -> CLN
+ return ::zerop(*value); // -> CLN
}
/** True if object is not complex and greater than zero. */
bool numeric::is_positive(void) const
{
- if (is_real()) {
- return plusp(The(cl_R)(*value)); // -> CLN
- }
+ if (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()) {
- return minusp(The(cl_R)(*value)); // -> CLN
- }
+ if (is_real())
+ return ::minusp(The(cl_R)(*value)); // -> CLN
return false;
}
/** True if object is a non-complex integer. */
bool numeric::is_integer(void) const
{
- return (bool)instanceof(*value, cl_I_ring); // -> CLN
+ return ::instanceof(*value, cl_I_ring); // -> CLN
}
/** 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 (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 (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 (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 (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 (is_integer() && ::isprobprime(The(cl_I)(*value))); // -> CLN
}
/** True if object is an exact rational number, may even be complex
* (denominator may be unity). */
bool numeric::is_rational(void) const
{
- 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) )
- return true;
- }
- return false;
+ 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 (bool)instanceof(*value, cl_R_ring); // -> CLN
+ return ::instanceof(*value, cl_R_ring); // -> CLN
}
bool numeric::operator==(numeric const & other) const
return (*value != *other.value); // -> CLN
}
+/** True if object is element of the domain of integers extended by I, i.e. is
+ * of the form a+b*I, where a and b are integers. */
+bool numeric::is_cinteger(void) const
+{
+ 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))
+ return true;
+ }
+ return false;
+}
+
+/** True if object is an exact rational number, may even be complex
+ * (denominator may be unity). */
+bool numeric::is_crational(void) const
+{
+ 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))
+ return true;
+ }
+ return false;
+}
+
/** Numerical comparison: less.
*
* @exception invalid_argument (complex inequality) */
bool numeric::operator<(numeric const & other) const
{
- if ( is_real() && other.is_real() ) {
+ if (is_real() && other.is_real())
return (bool)(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<=(numeric const & other) const
{
- if ( is_real() && other.is_real() ) {
+ if (is_real() && other.is_real())
return (bool)(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>(numeric const & other) const
{
- if ( is_real() && other.is_real() ) {
+ if (is_real() && other.is_real())
return (bool)(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>=(numeric const & other) const
{
- if ( is_real() && other.is_real() ) {
+ if (is_real() && other.is_real())
return (bool)(The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN
- }
throw (std::invalid_argument("numeric::operator>=(): complex inequality"));
return false; // make compiler shut up
}
* if the number is really an integer before calling this method. */
int numeric::to_int(void) const
{
- ASSERT(is_integer());
- return cl_I_to_int(The(cl_I)(*value));
+ GINAC_ASSERT(is_integer());
+ return ::cl_I_to_int(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
{
- ASSERT(is_real());
- return cl_double_approx(realpart(*value));
+ GINAC_ASSERT(is_real());
+ return ::cl_double_approx(realpart(*value)); // -> CLN
}
/** Real part of a number. */
numeric numeric::real(void) const
{
- return numeric(realpart(*value)); // -> CLN
+ return numeric(::realpart(*value)); // -> CLN
}
/** Imaginary part of a number. */
numeric numeric::imag(void) const
{
- return numeric(imagpart(*value)); // -> CLN
+ return numeric(::imagpart(*value)); // -> CLN
}
#ifndef SANE_LINKER
/** Numerator. Computes the numerator of rational numbers, rationalized
* 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 itself in all other cases. */
+ * (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
{
if (is_integer()) {
return numeric(*this);
}
#ifdef SANE_LINKER
- else if (instanceof(*value, cl_RA_ring)) {
- return numeric(numerator(The(cl_RA)(*value)));
+ else if (::instanceof(*value, cl_RA_ring)) {
+ return numeric(::numerator(The(cl_RA)(*value)));
}
else if (!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))
+ 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))));
- 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)) {
- 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))))));
+ 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))
+ 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)))),
+ ::numerator(The(cl_RA)(i))*(exquo(s,::denominator(The(cl_RA)(i))))));
}
}
#else
numeric numeric::denom(void) const
{
if (is_integer()) {
- return numONE();
+ return _num1();
}
#ifdef SANE_LINKER
if (instanceof(*value, cl_RA_ring)) {
- return numeric(denominator(The(cl_RA)(*value)));
+ 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 (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
- return numONE();
- 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))
- 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))));
+ if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring))
+ 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))
+ 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))));
}
#else
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(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
* in two's complement if it is an integer, 0 otherwise. */
int numeric::int_length(void) const
{
- if (is_integer()) {
- return integer_length(The(cl_I)(*value)); // -> CLN
- } else {
+ if (is_integer())
+ return ::integer_length(The(cl_I)(*value)); // -> CLN
+ else
return 0;
- }
}
type_info const & 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 = (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;
-}
+const numeric I = numeric(complex(cl_I(0),cl_I(1)));
/** Exponential function.
*
* @return arbitrary precision numerical exp(x). */
numeric exp(numeric const & x)
{
- return exp(*x.value); // -> CLN
+ return ::exp(*x.value); // -> CLN
}
/** Natural logarithm.
{
if (z.is_zero())
throw (std::overflow_error("log(): logarithmic singularity"));
- return log(*z.value); // -> CLN
+ return ::log(*z.value); // -> CLN
}
/** Numeric sine (trigonometric function).
* @return arbitrary precision numerical sin(x). */
numeric sin(numeric const & x)
{
- return sin(*x.value); // -> CLN
+ return ::sin(*x.value); // -> CLN
}
/** Numeric cosine (trigonometric function).
* @return arbitrary precision numerical cos(x). */
numeric cos(numeric const & x)
{
- return cos(*x.value); // -> CLN
+ return ::cos(*x.value); // -> CLN
}
/** Numeric tangent (trigonometric function).
* @return arbitrary precision numerical tan(x). */
numeric tan(numeric const & x)
{
- return tan(*x.value); // -> CLN
+ return ::tan(*x.value); // -> CLN
}
/** Numeric inverse sine (trigonometric function).
* @return arbitrary precision numerical asin(x). */
numeric asin(numeric const & x)
{
- return asin(*x.value); // -> CLN
+ return ::asin(*x.value); // -> CLN
}
/** Numeric inverse cosine (trigonometric function).
* @return arbitrary precision numerical acos(x). */
numeric acos(numeric const & x)
{
- return acos(*x.value); // -> CLN
+ return ::acos(*x.value); // -> CLN
}
/** Arcustangents.
{
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
+ return ::atan(*x.value); // -> CLN
}
/** Arcustangents.
numeric atan(numeric const & y, numeric const & 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"));
}
* @return arbitrary precision numerical sinh(x). */
numeric sinh(numeric const & x)
{
- return sinh(*x.value); // -> CLN
+ return ::sinh(*x.value); // -> CLN
}
/** Numeric hyperbolic cosine (trigonometric function).
* @return arbitrary precision numerical cosh(x). */
numeric cosh(numeric const & x)
{
- return cosh(*x.value); // -> CLN
+ return ::cosh(*x.value); // -> CLN
}
/** Numeric hyperbolic tangent (trigonometric function).
* @return arbitrary precision numerical tanh(x). */
numeric tanh(numeric const & x)
{
- return tanh(*x.value); // -> CLN
+ return ::tanh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic sine (trigonometric function).
* @return arbitrary precision numerical asinh(x). */
numeric asinh(numeric const & x)
{
- return asinh(*x.value); // -> CLN
+ return ::asinh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic cosine (trigonometric function).
* @return arbitrary precision numerical acosh(x). */
numeric acosh(numeric const & x)
{
- return acosh(*x.value); // -> CLN
+ return ::acosh(*x.value); // -> CLN
}
/** Numeric inverse hyperbolic tangent (trigonometric function).
* @return arbitrary precision numerical atanh(x). */
numeric atanh(numeric const & x)
{
- return atanh(*x.value); // -> CLN
+ return ::atanh(*x.value); // -> CLN
+}
+
+/** Numeric evaluation of Riemann's Zeta function. Currently works only for
+ * integer arguments. */
+numeric zeta(numeric const & 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
+ // cascades down to zeta(3.0).evalf(). The trick is to rely on 3.0-3
+ // 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)));
+ if (zerop(*x.value-aux))
+ return ::cl_zeta(aux); // -> CLN
+ }
+ clog << "zeta(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
+ return numeric(0);
}
/** The gamma function.
- * stub stub stub stub stub stub! */
+ * This is only a stub! */
numeric gamma(numeric const & x)
{
- clog << "gamma(): Nobody expects the Spanish inquisition" << endl;
+ clog << "gamma(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
+ return numeric(0);
+}
+
+/** The psi function (aka polygamma function).
+ * This is only a stub! */
+numeric psi(numeric const & x)
+{
+ clog << "psi(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
+ return numeric(0);
+}
+
+/** The psi functions (aka polygamma functions).
+ * This is only a stub! */
+numeric psi(numeric const & n, numeric const & x)
+{
+ clog << "psi(" << n << "," << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
return numeric(0);
}
* @exception range_error (argument must be integer >= 0) */
numeric factorial(numeric const & nn)
{
- if ( !nn.is_nonneg_integer() ) {
+ if (!nn.is_nonneg_integer())
throw (std::range_error("numeric::factorial(): argument must be integer >= 0"));
- }
-
- return numeric(factorial(nn.to_int())); // -> CLN
+ return numeric(::factorial(nn.to_int())); // -> CLN
}
/** The double factorial combinatorial function. (Scarcely used, but still
* @exception range_error (argument must be integer >= -1) */
numeric doublefactorial(numeric const & 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
static vector<numeric> oddresults;
static int highest_oddresult = -1;
- if ( nn == numeric(-1) ) {
- return numONE();
+ if (nn == numeric(-1)) {
+ return _num1();
}
- if ( !nn.is_nonneg_integer() ) {
+ 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 ) {
+ if (nn.is_even()) {
+ int n = nn.div(_num2()).to_int();
+ if (n <= highest_evenresult) {
return evenresults[n];
}
- if ( evenresults.capacity() < (unsigned)(n+1) ) {
+ if (evenresults.capacity() < (unsigned)(n+1)) {
evenresults.reserve(n+1);
}
- if ( highest_evenresult < 0 ) {
- evenresults.push_back(numONE());
+ if (highest_evenresult < 0) {
+ evenresults.push_back(_num1());
highest_evenresult=0;
}
for (int i=highest_evenresult+1; i<=n; i++) {
highest_evenresult=n;
return evenresults[n];
} else {
- int n = nn.sub(numONE()).div(numTWO()).to_int();
- if ( n <= highest_oddresult ) {
+ int n = nn.sub(_num1()).div(_num2()).to_int();
+ if (n <= highest_oddresult) {
return oddresults[n];
}
- if ( oddresults.capacity() < (unsigned)n ) {
+ if (oddresults.capacity() < (unsigned)n) {
oddresults.reserve(n+1);
}
- if ( highest_oddresult < 0 ) {
- oddresults.push_back(numONE());
+ if (highest_oddresult < 0) {
+ oddresults.push_back(_num1());
highest_oddresult=0;
}
for (int i=highest_oddresult+1; i<=n; i++) {
}
}
-/** The Binomial function. It computes the binomial coefficients. If the
- * arguments are both nonnegative integers and 0 <= k <= n, then
- * binomial(n, k) = n!/k!/(n-k)! which is the number of ways of choosing k
- * objects from n distinct objects. If k > n, then binomial(n,k) returns 0. */
+/** 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)
{
- if (n.is_nonneg_integer() && k.is_nonneg_integer()) {
- return numeric(binomial(n.to_int(),k.to_int())); // -> CLN
- } else {
- // should really be gamma(n+1)/(gamma(r+1)/gamma(n-r+1)
- return numeric(0);
+ if (n.is_integer() && k.is_integer()) {
+ if (n.is_nonneg_integer()) {
+ if (k.compare(n)!=1 && k.compare(_num0())!=-1)
+ return numeric(::binomial(n.to_int(),k.to_int())); // -> CLN
+ else
+ return _num0();
+ } else {
+ return _num_1().power(k)*binomial(k-n-_num1(),k);
+ }
}
- // return factorial(n).div(factorial(k).mul(factorial(n.sub(k))));
+
+ // should really be gamma(n+1)/(gamma(r+1)/gamma(n-r+1) or a suitable limit
+ 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(numeric const & nn)
+{
+ if (!nn.is_integer() || nn.is_negative())
+ throw (std::range_error("numeric::bernoulli(): argument must be integer >= 0"));
+ if (nn.is_zero())
+ return _num1();
+ if (!nn.compare(_num1()))
+ return numeric(-1,2);
+ if (nn.is_odd())
+ 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
+ // B(nn) == - 1/(nn+1) * sum_{k=0}^{nn-1}(binomial(nn+1,k)*B(k))
+ // whith B(0) == 1.
+ static vector<numeric> results;
+ static int highest_result = -1;
+ int n = nn.sub(_num2()).div(_num2()).to_int();
+ if (n <= highest_result)
+ return results[n];
+ if (results.capacity() < (unsigned)(n+1))
+ results.reserve(n+1);
+
+ numeric tmp; // used to store the sum
+ for (int i=highest_result+1; i<=n; ++i) {
+ // the first two elements:
+ tmp = numeric(-2*i-1,2);
+ // accumulate the remaining elements:
+ for (int j=0; j<i; ++j)
+ tmp += binomial(numeric(2*i+3),numeric(j*2+2))*results[j];
+ // divide by -(nn+1) and store result:
+ results.push_back(-tmp/numeric(2*i+3));
+ }
+ highest_result=n;
+ return results[n];
}
/** Absolute value. */
numeric abs(numeric const & x)
{
- return abs(*x.value); // -> CLN
+ return ::abs(*x.value); // -> CLN
}
/** Modulus (in positive representation).
* integer, 0 otherwise. */
numeric mod(numeric const & a, numeric const & 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?
- }
+ if (a.is_integer() && b.is_integer())
+ return ::mod(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
+ else
+ return _num0(); // Throw?
}
/** Modulus (in symmetric representation).
* @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */
numeric smod(numeric const & a, numeric const & 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 ::mod(The(cl_I)(*a.value) + b2, The(cl_I)(*b.value)) - b2;
+ } else
+ return _num0(); // Throw?
}
/** Numeric integer remainder.
* @return remainder of a/b if both are integer, 0 otherwise. */
numeric irem(numeric const & a, numeric const & 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?
- }
+ if (a.is_integer() && b.is_integer())
+ return ::rem(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
+ else
+ return _num0(); // Throw?
}
/** Numeric integer remainder.
return rem_quo.remainder;
}
else {
- q = numZERO();
- return numZERO(); // Throw?
+ q = _num0();
+ return _num0(); // Throw?
}
}
* @return truncated quotient of a/b if both are integer, 0 otherwise. */
numeric iquo(numeric const & a, numeric const & b)
{
- if (a.is_integer() && b.is_integer()) {
+ if (a.is_integer() && b.is_integer())
return truncate1(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
- } else {
- return numZERO(); // Throw?
- }
+ else
+ return _num0(); // Throw?
}
/** Numeric integer quotient.
r = rem_quo.remainder;
return rem_quo.quotient;
} else {
- r = numZERO();
- return numZERO(); // Throw?
+ r = _num0();
+ return _num0(); // Throw?
}
}
* where imag(z)>0. */
numeric sqrt(numeric const & z)
{
- return sqrt(*z.value); // -> CLN
+ return ::sqrt(*z.value); // -> CLN
}
/** Integer numeric square root. */
numeric isqrt(numeric const & x)
{
- if (x.is_integer()) {
- cl_I root;
- isqrt(The(cl_I)(*x.value), &root); // -> CLN
- return root;
- } else
- return numZERO(); // Throw?
+ if (x.is_integer()) {
+ cl_I root;
+ ::isqrt(The(cl_I)(*x.value), &root); // -> CLN
+ return root;
+ } else
+ return _num0(); // Throw?
}
/** Greatest Common Divisor.
numeric gcd(numeric const & a, numeric const & b)
{
if (a.is_integer() && b.is_integer())
- return gcd(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
+ return ::gcd(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
- return numONE();
+ return _num1();
}
/** Least Common Multiple.
numeric lcm(numeric const & a, numeric const & b)
{
if (a.is_integer() && b.is_integer())
- return lcm(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
+ return ::lcm(The(cl_I)(*a.value), The(cl_I)(*b.value)); // -> CLN
else
return *a.value * *b.value;
}
/** 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
+} // namespace GiNaC
+#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff