// 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 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();
{
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();
/** 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;
-#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);
+ *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));
+ *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);
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;
- if (is_crational())
+#else
+ char buf[1024];
+ ostrstream s(buf, 1024);
+#endif
+ if (this->is_crational())
s << *value;
else {
// Non-rational numbers are written in an integer-decoded format
// to preserve the precision
- if (is_real()) {
+ 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)));
+ 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;
}
}
+#ifdef HAVE_SSTREAM
n.add_string("number", s.str());
#else
- // Write number as string
- char buf[1024];
- ostrstream f(buf, 1024);
- if (is_crational())
- f << *value << ends;
- else {
- // Non-rational numbers are written in an integer-decoded format
- // to preserve the precision
- if (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 (is_real()) {
+ if (this->is_real()) {
// case 1, real: x or -x
- if ((precedence<=upper_precedence) && (!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 (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 << "(";
+ print_real_number(os, The(cl_R)(::imagpart(*value)));
+ os << "*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";
+ 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 (imagpart(*value) < 0) {
- if (imagpart(*value) == -1) {
+ 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) {
+ 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 << ")";
}
}
}
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
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
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;
+ */
}
/*
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();
* @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 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. */
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
* (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 (!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;
* (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 (!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
}
* 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
}
* You may also consider checking the range first. */
long numeric::to_long(void) const
{
- GINAC_ASSERT(is_integer());
+ GINAC_ASSERT(this->is_integer());
return ::cl_I_to_long(The(cl_I)(*value)); // -> CLN
}
* 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. */
-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 (is_integer()) {
+ 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 (!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))
+ 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)))),
+ 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
- else if (instanceof(*value, cl_RA_ring)) {
+ 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);
- if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring))
+ 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));
- 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)) {
- cl_I s = lcm(TheRatio(r)->denominator, TheRatio(i)->denominator);
- return numeric(complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)),
+ 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))
+ 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)),
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 (is_integer()) {
+ 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 (!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 (!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_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))
- return numeric(lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))));
+ 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 (!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 (!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_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))
- return numeric(lcm(TheRatio(r)->denominator, TheRatio(i)->denominator));
+ if (instanceof(r, ::cl_RA_ring) && instanceof(i, ::cl_RA_ring))
+ 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.
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"));
}
// 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
}
}
-/** The gamma function.
+/** The Gamma function.
* This is only a stub! */
-const numeric gamma(const numeric & x)
+const numeric lgamma(const numeric & x)
{
- clog << "gamma(" << x
+ clog << "lgamma(" << x
+ << "): Does anybody know good way to calculate this numerically?"
+ << endl;
+ return numeric(0);
+}
+const numeric tgamma(const numeric & 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();
* @exception range_error (argument must be an integer) */
const numeric fibonacci(const numeric & n)
{
- if (!n.is_integer()) {
+ 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;
+ // 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);
- // 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);
+ 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);
}
* @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;
/** 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)
+/** Floating point evaluation of Euler's constant gamma. */
+ex EulerEvalf(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
}
{
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;
}
git://www.ginac.de / ginac.git / blobdiff