/*
rational.cc -- implement Rational
-
+
source file of the Flower Library
- (c) 1997 Han-Wen Nienhuys <hanwen@stack.nl>
+ (c) 1997--2008 Han-Wen Nienhuys <hanwen@xs4all.nl>
*/
-#include <stdlib.h>
+
#include "rational.hh"
-#include "string.hh"
-#include "string-convert.hh"
-#include "libc-extension.hh"
-Rational::operator bool () const
-{
- return sign_;
-}
+#include <cmath>
+#include <cassert>
+#include <cstdlib>
+using namespace std;
-Rational::operator int () const
-{
- return sign_ * num_ / den_;
-}
+#include "string-convert.hh"
+#include "libc-extension.hh"
-Rational::operator double () const
+double
+Rational::to_double () const
{
- return (double)sign_ * num_ / den_;
+ if (sign_ == -1 || sign_ == 1 || sign_ == 0)
+ return ((double)sign_) * num_ / den_;
+ if (sign_ == -2)
+ return -HUGE_VAL;
+ else if (sign_ == 2)
+ return HUGE_VAL;
+ else
+ assert (false);
+
+ return 0.0;
}
+
+#ifdef STREAM_SUPPORT
ostream &
operator << (ostream &o, Rational r)
{
- o << r.str ();
+ o << r.string ();
return o;
}
+#endif
-
+Rational
+Rational::abs () const
+{
+ return Rational (num_, den_);
+}
Rational
-Rational::truncated () const
+Rational::trunc_rat () const
{
- return Rational(num_ - (num_ % den_), den_);
+ if (is_infinity())
+ return *this;
+ return Rational ((num_ - (num_ % den_)) * sign_, den_);
}
Rational::Rational ()
{
- sign_ = 1;
+ sign_ = 0;
num_ = den_ = 1;
}
-Rational::Rational (int n, int d)
+Rational::Rational (I64 n, I64 d)
{
sign_ = ::sign (n) * ::sign (d);
- num_ = abs (n);
- den_ = abs (d);
- normalise ();
+ num_ = ::abs (n);
+ den_ = ::abs (d);
+ normalize ();
}
+Rational::Rational (I64 n)
+{
+ sign_ = ::sign (n);
+ num_ = ::abs (n);
+ den_ = 1;
+}
-static
-int gcd (int a, int b)
+Rational::Rational (U64 n)
{
- int t;
- while ((t = a % b))
- {
- a = b;
- b = t;
- }
- return b;
+ sign_ = 1;
+ num_ = n;
+ den_ = 1;
}
-static
-int lcm (int a, int b)
+Rational::Rational (int n)
{
- return abs (a*b / gcd (a,b));
+ sign_ = ::sign (n);
+ num_ = ::abs (n);
+ den_ = 1;
}
+
void
Rational::set_infinite (int s)
{
- sign_ = ::sign (s) * 2;
+ sign_ = ::sign (s) * 2;
+ num_ = 1;
}
Rational
Rational::operator - () const
{
- Rational r(*this);
+ Rational r (*this);
r.negate ();
return r;
}
+Rational
+Rational::div_rat (Rational div) const
+{
+ Rational r (*this);
+ r /= div;
+ return r.trunc_rat ();
+}
+
+Rational
+Rational::mod_rat (Rational div) const
+{
+ Rational r (*this);
+ r = (r / div - r.div_rat (div)) * div;
+ return r;
+}
+
+
+/*
+ copy & paste from scm_gcd (GUILE).
+ */
+static I64
+gcd (I64 u, I64 v)
+{
+ I64 result = 0;
+ if (u == 0)
+ result = v;
+ else if (v == 0)
+ result = u;
+ else
+ {
+ I64 k = 1;
+ I64 t;
+ /* Determine a common factor 2^k */
+ while (!(1 & (u | v)))
+ {
+ k <<= 1;
+ u >>= 1;
+ v >>= 1;
+ }
+ /* Now, any factor 2^n can be eliminated */
+ if (u & 1)
+ t = -v;
+ else
+ {
+ t = u;
+ b3:
+ t = t >> 1;
+ }
+ if (!(1 & t))
+ goto b3;
+ if (t > 0)
+ u = t;
+ else
+ v = -t;
+ t = u - v;
+ if (t != 0)
+ goto b3;
+ result = u * k;
+ }
+
+ return result;
+}
+
+
void
-Rational::normalise ()
+Rational::normalize ()
{
if (!sign_)
{
den_ = 1;
num_ = 0;
- return ;
}
- if (!den_)
- sign_ = 2;
- if (!num_)
- sign_ = 0;
-
- int g = gcd (num_ , den_);
+ else if (!den_)
+ {
+ sign_ = 2;
+ num_ = 1;
+ }
+ else if (!num_)
+ {
+ sign_ = 0;
+ den_ = 1;
+ }
+ else
+ {
+ I64 g = gcd (num_, den_);
- num_ /= g;
- den_ /= g;
+ num_ /= g;
+ den_ /= g;
+ }
}
-
int
Rational::sign () const
{
return ::sign (sign_);
}
-bool
-Rational::infty_b () const
-{
- return abs (sign_) > 1;
-}
-
int
Rational::compare (Rational const &r, Rational const &s)
{
return -1;
else if (r.sign_ > s.sign_)
return 1;
- else if (r.infty_b ())
+ else if (r.is_infinity ())
return 0;
-
- return (r - s).sign ();
+ else if (r.sign_ == 0)
+ return 0;
+ return r.sign_ * ::sign ((I64) (r.num_ * s.den_) - (I64) (s.num_ * r.den_));
}
int
compare (Rational const &r, Rational const &s)
{
- return Rational::compare (r, s );
+ return Rational::compare (r, s);
+}
+
+Rational &
+Rational::operator %= (Rational r)
+{
+ *this = mod_rat (r);
+ return *this;
}
Rational &
Rational::operator += (Rational r)
{
- if (infty_b ())
+ if (is_infinity ())
;
- else if (r.infty_b ())
- {
- *this = r;
- }
- else
+ else if (r.is_infinity ())
+ *this = r;
+ else
{
- int n = sign_ * num_ *r.den_ + r.sign_ * den_ * r.num_;
- int d = den_ * r.den_;
- sign_ = ::sign (n) * ::sign(d);
- num_ = abs (n);
- den_ = abs (d);
- normalise ();
+ I64 lcm = (den_ / gcd (r.den_, den_)) * r.den_;
+ I64 n = sign_ * num_ * (lcm / den_) + r.sign_ * r.num_ * (lcm / r.den_);
+ I64 d = lcm;
+ sign_ = ::sign (n) * ::sign (d);
+ num_ = ::abs (n);
+ den_ = ::abs (d);
+ normalize ();
}
return *this;
}
-
/*
copied from libg++ 2.8.0
- */
-Rational::Rational(double x)
+*/
+Rational::Rational (double x)
{
- num_ = 0;
- den_ = 1;
if (x != 0.0)
{
sign_ = ::sign (x);
x *= sign_;
- const long shift = 15; // a safe shift per step
- const double width = 32768.0; // = 2^shift
- const int maxiter = 20; // ought not be necessary, but just in case,
- // max 300 bits of precision
int expt;
- double mantissa = frexp(x, &expt);
- long exponent = expt;
- double intpart;
- int k = 0;
- while (mantissa != 0.0 && k++ < maxiter)
- {
- mantissa *= width;
- mantissa = modf(mantissa, &intpart);
- num_ <<= shift;
- num_ += (long)intpart;
- exponent -= shift;
- }
- if (exponent > 0)
- num_ <<= exponent;
- else if (exponent < 0)
- den_ <<= -exponent;
- } else {
- sign_ = 0;
+ double mantissa = frexp (x, &expt);
+
+ const int FACT = 1 << 20;
+
+ /*
+ Thanks to Afie for this too simple idea.
+
+ do not blindly substitute by libg++ code, since that uses
+ arbitrary-size integers. The rationals would overflow too
+ easily.
+ */
+
+ num_ = (U64) (mantissa * FACT);
+ den_ = (U64) FACT;
+ normalize ();
+ if (expt < 0)
+ den_ <<= -expt;
+ else
+ num_ <<= expt;
+ normalize ();
+ }
+ else
+ {
+ num_ = 0;
+ den_ = 1;
+ sign_ = 0;
+ normalize ();
}
- normalise();
}
-
void
Rational::invert ()
{
- int r (num_);
- num_ = den_;
+ I64 r (num_);
+ num_ = den_;
den_ = r;
}
Rational::operator *= (Rational r)
{
sign_ *= ::sign (r.sign_);
- if (r.infty_b ())
- {
+ if (r.is_infinity ())
+ {
sign_ = sign () * 2;
goto exit_func;
}
num_ *= r.num_;
den_ *= r.den_;
- normalise ();
+ normalize ();
exit_func:
return *this;
}
-
+
Rational &
Rational::operator /= (Rational r)
{
sign_ *= -1;
}
-Rational&
+Rational &
Rational::operator -= (Rational r)
{
r.negate ();
return (*this += r);
}
-/*
- be paranoid about overiding libg++ stuff
- */
-Rational &
-Rational::operator = (Rational const &r)
-{
- copy (r);
- return *this;
-}
-
-Rational::Rational (Rational const &r)
-{
- copy (r);
-}
-
-Rational::operator String () const
+string
+Rational::to_string () const
{
- return str ();
-}
-
-String
-Rational::str () const
-{
- if (infty_b ())
+ if (is_infinity ())
{
- String s (sign_ > 0 ? "" : "-" );
- return String (s + "infinity");
+ string s (sign_ > 0 ? "" : "-");
+ return string (s + "infinity");
}
- String s (num ());
+
+ string s = ::to_string (num ());
if (den () != 1 && num ())
- s += "/" + String (den ());
+ s += "/" + ::to_string (den ());
return s;
}
+int
+Rational::to_int () const
+{
+ return (int) num () / den ();
+}
+
int
sign (Rational r)
{
return r.sign ();
}
+
+bool
+Rational::is_infinity () const
+{
+ return sign_ == 2 || sign_ == -2;
+}
projects / lilypond.git / blobdiff