GEMini Atari/GEMini_Atari_CD-ROM_Walnut_Creek_December_1993.iso/files/gnu/g__lib/rational.cc

C/C++ Source or Header | 1993-07-23 | 6KB | 379 lines

/*
Copyright (C) 1988 Free Software Foundation
    written by Doug Lea ([e-mail])

This file is part of GNU CC.

GNU CC is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY.  No author or distributor
accepts responsibility to anyone for the consequences of using it
or for whether it serves any particular purpose or works at all,
unless he says so in writing.  Refer to the GNU CC General Public
License for full details.

Everyone is granted permission to copy, modify and redistribute
GNU CC, but only under the conditions described in the
GNU CC General Public License.   A copy of this license is
supposed to have been given to you along with GNU CC so you
can know your rights and responsibilities.  It should be in a
file named COPYING.  Among other things, the copyright notice
and this notice must be preserved on all copies.
*/

#include <Rational.h>
#include <std.h>
#include <math.h>
#include "libconfig.h"



void Rational::error(char* msg)
{
  (*lib_error_handler)("Rational", msg);
}

static Integer _Int_One(1);

void Rational::normalize()
{
  int s = sign(den);
  if (s == 0)
    error("Zero denominator.");
  else if (s < 0)
  {
    den.negate();
    num.negate();
  }

  Integer g = gcd(num, den);
  if (ucompare(g, _Int_One) != 0)
  {
    num /= g;
    den /= g;
  }
}

RatTmp Rational::operator + (Rational& y)
{
  return RatTmp(num * y.den + den * y.num, den * y.den);
}

RatTmp Rational::operator - (Rational& y)
{
  return RatTmp(num * y.den - den * y.num, den * y.den);
}

RatTmp Rational::operator * (Rational& y)
{
  return RatTmp(num * y.num, den * y.den);
}

RatTmp Rational::operator / (Rational& y)
{
  return RatTmp(num * y.den, den * y.num);
}

RatTmp Rational::operator - ()
{
  Integer d = den;
  return RatTmp(-num, d);
}

RatTmp RatTmp::operator - ()
{
  num.negate();
  return *this;
}

RatTmp abs(Rational& x)
{
  Integer d = x.den;
  return RatTmp(abs(x.num), d);
}

RatTmp abs(RatTmp& x)
{
  x.num.abs();
  return x;
}

RatTmp sqr(Rational& x)
{
  return RatTmp(x.num * x.num, x.den * x.den);
}

RatTmp sqr(RatTmp& x)
{
  x.num *= x.num;
  x.den *= x.den;
  return x;
}

void Rational::operator +=(Rational& y)
{
  num = num * y.den + den * y.num;
  den *= y.den;
  normalize();
}

void Rational::operator -=(Rational& y)
{
  num = num * y.den - den * y.num;
  den *= y.den;
  normalize();
}

void Rational::operator *=(Rational& y)
{
  num *= y.num;
  den *= y.den;
  normalize();
}

void Rational::operator /=(Rational& y)
{
  if (&y == this)
  {
    Integer n = num * y.den;
    den *= y.num;
    num = n;
  }
  else
  {
    num *= y.den;
    den *= y.num;
  }
  normalize();
}

RatTmp RatTmp::operator + (Rational& y)
{
  num = num * y.den + den * y.num;
  den *= y.den;
  normalize();
  return *this;
}

RatTmp RatTmp::operator - (Rational& y)
{
  num = num * y.den - den * y.num;
  den *= y.den;
  normalize();
  return *this;
}

RatTmp RatTmp::operator * (Rational& y)
{
  num *= y.num;
  den *= y.den;
  normalize();
  return *this;
}

RatTmp RatTmp::operator / (Rational& y)
{
  if (&y == this)
  {
    Integer n = num * y.den;
    den *= y.num;
    num = n;
  }
  else
  {
    num *= y.den;
    den *= y.num;
  }
  normalize();
  return *this;
}

void Rational::invert()
{
  Integer tmp = num;
  num = den;
  den = tmp;
  int s = sign(den);
  if (s == 0)
    error("Zero denominator.");
  else if (s < 0)
  {
    den.negate();
    num.negate();
  }
}

int compare(Rational& x, Rational& y)
{
  int xsgn = sign(x.num);
  int ysgn = sign(y.num);
  int d = xsgn - ysgn;
  if (d == 0 && xsgn != 0) d = compare(x.num * y.den, x.den * y.num);
  return d;
}

Rational::Rational(double x)
{
  num = 0;
  den = 1;
  if (x != 0.0)
  {
    int neg = x < 0;
    if (neg)
      x = -x;

    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;
    if (neg)
      num.negate();
  }
  normalize();
}

IntTmp floor(Rational& x)
{
  Integer q, r;
  divide(x.num, x.den, q, r);
  if (sign(x.num) < 0 && sign(r) != 0) q--;
  return q;
}

IntTmp ceil(Rational& x)
{
  Integer q, r;
  divide(x.num, x.den, q, r);
  if (sign(x.num) >= 0 && sign(r) != 0) q++;
  return q;
}

IntTmp round(Rational& x)
{
  Integer q, r;
  divide(x.num, x.den, q, r);
  r <<= 1;
  if (ucompare(r, x.den) >= 0)
  {
    if (sign(x.num) >= 0)
      q++;
    else
      q--;
  }
  return q;
}

IntTmp trunc(Rational& x)
{
  return x.num / x.den ;
}

IntTmp Rational::numerator()
{
  Integer n = num;
  return n;
}

IntTmp Rational::denominator()
{
  Integer d = den;
  return d;
}

RatTmp pow(Rational& x, Integer& y)
{
  long yy = long(y);
  return pow(x, yy);
}

double Rational::operator double()
{
  return ratio(num, den);
}


// power: no need to normalize since num & den already relatively prime

RatTmp pow(Rational& x, long y)
{
  Rational r;
  if (y >= 0)
  {
    r.num = pow(x.num, y);
    r.den = pow(x.den, y);
  }
  else
  {
    y = -y;
    r.den = pow(x.num, y);
    r.num = pow(x.den, y);
    if (sign(r.den) < 0)
    {
      r.num.negate();
      r.den.negate();
    }
  }
  return r;
}


ostream& operator << (ostream& s, Rational& y)
{
  if (y.den == 1)
    s << Itoa(y.num);
  else
  {
    s << Itoa(y.num);
    s << "/";
    s << Itoa(y.den);
  }
  return s;
}

istream& operator >> (istream& s, Rational& y)
{
  s >> y.num;
  if (s)
  {
    char ch = 0;
    s.get(ch);
    if (ch == '/')
    {
      s >> y.den;
      y.normalize();
    }
    else
    {
      s.unget(ch);
      y.den = 1;
    }
  }
  return s;
}

int Rational::OK()
{
  int v = num.OK() && den.OK(); // have valid num and denom
  v &= sign(den) > 0;           // denominator positive;
  v &=  ucompare(gcd(num, den), _Int_One) == 0; // relatively prime
  if (!v) error("invariant failure");
  return v;
}