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Fixed numeric problems reported in PR #29294 

Submitted by: C. Scott Ananian
Reviewed by: Phil Steitz


git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/lang/trunk@137879 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2004-07-11 23:20:17 +00:00
parent 02dde889ee
commit 13ae992c23
2 changed files with 609 additions and 126 deletions
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381
src/java/org/apache/commons/lang/math/Fraction.java
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@ -16,6 +16,7 @@
package org.apache.commons.lang.math; package org.apache.commons.lang.math;
import java.io.Serializable; import java.io.Serializable;
import java.math.BigInteger;
/** /**
* <p><code>Fraction</code> is a <code>Number</code> implementation that * <p><code>Fraction</code> is a <code>Number</code> implementation that
@ -28,8 +29,9 @@ import java.io.Serializable;
* @author Stephen Colebourne * @author Stephen Colebourne
* @author Tim O'Brien * @author Tim O'Brien
* @author Pete Gieser * @author Pete Gieser
* @author C. Scott Ananian
* @since 2.0 * @since 2.0
* @version $Id: Fraction.java,v 1.13 2004/02/18 22:56:13 ggregory Exp $ * @version $Id: Fraction.java,v 1.14 2004/07/11 23:20:17 psteitz Exp $
*/ */
public final class Fraction extends Number implements Serializable, Comparable { public final class Fraction extends Number implements Serializable, Comparable {
@ -137,6 +139,10 @@ public final class Fraction extends Number implements Serializable, Comparable {
throw new ArithmeticException("The denominator must not be zero"); throw new ArithmeticException("The denominator must not be zero");
} }
if (denominator < 0) { if (denominator < 0) {
if (numerator==Integer.MIN_VALUE ||
denominator==Integer.MIN_VALUE) {
throw new ArithmeticException("overflow: can't negate");
}
numerator = -numerator; numerator = -numerator;
denominator = -denominator; denominator = -denominator;
} }
@ -154,7 +160,7 @@ public final class Fraction extends Number implements Serializable, Comparable {
* @param denominator the denominator, for example the seven in 'one and three sevenths' * @param denominator the denominator, for example the seven in 'one and three sevenths'
* @return a new fraction instance * @return a new fraction instance
* @throws ArithmeticException if the denomiator is <code>zero</code> * @throws ArithmeticException if the denomiator is <code>zero</code>
* @throws ArithmeticException if the denomiator is negative * @throws ArithmeticException if the denominator is negative
* @throws ArithmeticException if the numerator is negative * @throws ArithmeticException if the numerator is negative
* @throws ArithmeticException if the resulting numerator exceeds * @throws ArithmeticException if the resulting numerator exceeds
* <code>Integer.MAX_VALUE</code> * <code>Integer.MAX_VALUE</code>
@ -169,13 +175,14 @@ public final class Fraction extends Number implements Serializable, Comparable {
if (numerator < 0) { if (numerator < 0) {
throw new ArithmeticException("The numerator must not be negative"); throw new ArithmeticException("The numerator must not be negative");
} }
double numeratorValue = 0; long numeratorValue;
if (whole < 0) { if (whole < 0) {
numeratorValue = (double) whole * denominator - numerator; numeratorValue = whole * (long)denominator - numerator;
} else { } else {
numeratorValue = (double) whole * denominator + numerator; numeratorValue = whole * (long)denominator + numerator;
} }
if (Math.abs(numeratorValue) > Integer.MAX_VALUE) { if (numeratorValue < Integer.MIN_VALUE ||
numeratorValue > Integer.MAX_VALUE) {
throw new ArithmeticException("Numerator too large to represent as an Integer."); throw new ArithmeticException("Numerator too large to represent as an Integer.");
} }
return new Fraction((int) numeratorValue, denominator); return new Fraction((int) numeratorValue, denominator);
@ -190,18 +197,32 @@ public final class Fraction extends Number implements Serializable, Comparable {
* @param numerator the numerator, for example the three in 'three sevenths' * @param numerator the numerator, for example the three in 'three sevenths'
* @param denominator the denominator, for example the seven in 'three sevenths' * @param denominator the denominator, for example the seven in 'three sevenths'
* @return a new fraction instance, with the numerator and denominator reduced * @return a new fraction instance, with the numerator and denominator reduced
* @throws ArithmeticException if the denomiator is <code>zero</code> * @throws ArithmeticException if the denominator is <code>zero</code>
*/ */
public static Fraction getReducedFraction(int numerator, int denominator) { public static Fraction getReducedFraction(int numerator, int denominator) {
if (denominator == 0) { if (denominator == 0) {
throw new ArithmeticException("The denominator must not be zero"); throw new ArithmeticException("The denominator must not be zero");
} }
if (numerator==0) {
return ZERO; // normalize zero.
}
// allow 2^k/-2^31 as a valid fraction (where k>0)
if (denominator==Integer.MIN_VALUE && (numerator&1)==0) {
numerator/=2; denominator/=2;
}
if (denominator < 0) { if (denominator < 0) {
if (numerator==Integer.MIN_VALUE ||
denominator==Integer.MIN_VALUE) {
throw new ArithmeticException("overflow: can't negate");
}
numerator = -numerator; numerator = -numerator;
denominator = -denominator; denominator = -denominator;
} }
int gcd = greatestCommonDivisor(Math.abs(numerator), denominator); // simplify fraction.
return new Fraction(numerator / gcd, denominator / gcd); int gcd = greatestCommonDivisor(numerator, denominator);
numerator /= gcd;
denominator /= gcd;
return new Fraction(numerator, denominator);
} }
/** /**
@ -215,7 +236,7 @@ public final class Fraction extends Number implements Serializable, Comparable {
* @return a new fraction instance that is close to the value * @return a new fraction instance that is close to the value
* @throws ArithmeticException if <code>|value| > Integer.MAX_VALUE</code> * @throws ArithmeticException if <code>|value| > Integer.MAX_VALUE</code>
* or <code>value = NaN</code> * or <code>value = NaN</code>
* @throws ArithmeticException if the calculated denomiator is <code>zero</code> * @throws ArithmeticException if the calculated denominator is <code>zero</code>
* @throws ArithmeticException if the the algorithm does not converge * @throws ArithmeticException if the the algorithm does not converge
*/ */
public static Fraction getFraction(double value) { public static Fraction getFraction(double value) {
@ -275,11 +296,11 @@ public final class Fraction extends Number implements Serializable, Comparable {
* *
* <p>The formats accepted are:</p> * <p>The formats accepted are:</p>
* *
* <p>
* <ol> * <ol>
* <li><code>double</code> String containing a dot</li> * <li><code>double</code> String containing a dot</li>
* <li>'X Y/Z'</li> * <li>'X Y/Z'</li>
* <li>'Y/Z'</li> * <li>'Y/Z'</li>
* <li>'X' (a simple whole number)</li>
* </ol> * </ol>
* and a .</p> * and a .</p>
* *
@ -307,11 +328,9 @@ public final class Fraction extends Number implements Serializable, Comparable {
if (pos < 0) { if (pos < 0) {
throw new NumberFormatException("The fraction could not be parsed as the format X Y/Z"); throw new NumberFormatException("The fraction could not be parsed as the format X Y/Z");
} else { } else {
int numer = Integer.parseInt(str.substring(0, pos));
int denom = Integer.parseInt(str.substring(pos + 1)); int denom = Integer.parseInt(str.substring(pos + 1));
return getFraction( return getFraction(whole, numer, denom);
Integer.parseInt(str.substring(0, pos)) + whole * denom,
denom
);
} }
} }
@ -321,10 +340,9 @@ public final class Fraction extends Number implements Serializable, Comparable {
// simple whole number // simple whole number
return getFraction(Integer.parseInt(str), 1); return getFraction(Integer.parseInt(str), 1);
} else { } else {
return getFraction( int numer = Integer.parseInt(str.substring(0, pos));
Integer.parseInt(str.substring(0, pos)), int denom = Integer.parseInt(str.substring(pos + 1));
Integer.parseInt(str.substring(pos + 1)) return getFraction(numer, denom);
);
} }
} }
@ -440,18 +458,26 @@ public final class Fraction extends Number implements Serializable, Comparable {
} }
/** /**
* <p>Gets a fraction that is the invert (1/fraction) of this one.</p> * <p>Gets a fraction that is the inverse (1/fraction) of this one.</p>
* *
* <p>The returned fraction is not reduced.</p> * <p>The returned fraction is not reduced.</p>
* *
* @return a new fraction instance with the numerator and denominator inverted * @return a new fraction instance with the numerator and denominator
* @throws ArithmeticException if the numerator is <code>zero</code> * inverted.
* @throws ArithmeticException if the fraction represents zero.
*/ */
public Fraction invert() { public Fraction invert() {
if (numerator == 0) { if (numerator == 0) {
throw new ArithmeticException("Unable to invert a fraction with a zero numerator"); throw new ArithmeticException("Unable to invert zero.");
}
if (numerator==Integer.MIN_VALUE) {
throw new ArithmeticException("overflow: can't negate numerator");
}
if (numerator<0) {
return new Fraction(-denominator, -numerator);
} else {
return new Fraction(denominator, numerator);
} }
return getFraction(denominator, numerator);
} }
/** /**
@ -462,12 +488,16 @@ public final class Fraction extends Number implements Serializable, Comparable {
* @return a new fraction instance with the opposite signed numerator * @return a new fraction instance with the opposite signed numerator
*/ */
public Fraction negate() { public Fraction negate() {
return getFraction(-numerator, denominator); // the positive range is one smaller than the negative range of an int.
if (numerator==Integer.MIN_VALUE) {
throw new ArithmeticException("overflow: too large to negate");
}
return new Fraction(-numerator, denominator);
} }
/** /**
* <p>Gets a fraction that is the positive equivalent of this one.</p> * <p>Gets a fraction that is the positive equivalent of this one.</p>
* <p>More precisely: <pre>(fraction >= 0 ? this : -fraction)</pre></p> * <p>More precisely: <code>(fraction >= 0 ? this : -fraction)</code></p>
* *
* <p>The returned fraction is not reduced.</p> * <p>The returned fraction is not reduced.</p>
* *
@ -478,13 +508,13 @@ public final class Fraction extends Number implements Serializable, Comparable {
if (numerator >= 0) { if (numerator >= 0) {
return this; return this;
} }
return getFraction(-numerator, denominator); return negate();
} }
/** /**
* <p>Gets a fraction that is raised to the passed in power.</p> * <p>Gets a fraction that is raised to the passed in power.</p>
* *
* <p>The returned fraction is not reduced.</p> * <p>The returned fraction is in reduced form.</p>
* *
* @param power the power to raise the fraction to * @param power the power to raise the fraction to
* @return <code>this</code> if the power is one, <code>ONE</code> if the power * @return <code>this</code> if the power is one, <code>ONE</code> if the power
@ -498,44 +528,150 @@ public final class Fraction extends Number implements Serializable, Comparable {
return this; return this;
} else if (power == 0) { } else if (power == 0) {
return ONE; return ONE;
} else if (power < 0) {
if (power==Integer.MIN_VALUE) { // MIN_VALUE can't be negated.
return this.invert().pow(2).pow(-(power/2));
}
return this.invert().pow(-power);
} else { } else {
double denominatorValue = Math.pow(denominator, power); Fraction f = this.multiplyBy(this);
double numeratorValue = Math.pow(numerator, power); if ((power % 2) == 0) { // if even...
if (numeratorValue > Integer.MAX_VALUE || denominatorValue > Integer.MAX_VALUE) { return f.pow(power/2);
throw new ArithmeticException("Integer overflow"); } else { // if odd...
return f.pow(power/2).multiplyBy(this);
} }
if (power < 0) {
return getFraction((int) Math.pow(denominator, -power),
(int) Math.pow(numerator, -power));
}
return getFraction((int) Math.pow(numerator, power),
(int) Math.pow(denominator, power));
} }
} }
/** /**
* <p>Gets the greatest common divisor of two numbers.</p> * <p>Gets the greatest common divisor of the absolute value of
* two numbers, using the "binary gcd" method which avoids
* division and modulo operations. See Knuth 4.5.2 algorithm B.
* This algorithm is due to Josef Stein (1961).</p>
* *
* @param number1 a positive number * @param u a non-zero number
* @param number2 a positive number * @param v a non-zero number
* @return the greatest common divisor, never zero * @return the greatest common divisor, never zero
*/ */
private static int greatestCommonDivisor(int number1, int number2) { private static int greatestCommonDivisor(int u, int v) {
int remainder = number1 % number2; // keep u and v negative, as negative integers range down to
while (remainder != 0) { // -2^31, while positive numbers can only be as large as 2^31-1
number1 = number2; // (i.e. we can't necessarily negate a negative number without
number2 = remainder; // overflow)
remainder = number1 % number2; /* assert u!=0 && v!=0; */
if (u>0) { u=-u; } // make u negative
if (v>0) { v=-v; } // make v negative
// B1. [Find power of 2]
int k=0;
while ((u&1)==0 && (v&1)==0 && k<31) { // while u and v are both even...
u/=2; v/=2; k++; // cast out twos.
} }
return number2; if (k==31) {
throw new ArithmeticException("overflow: gcd is 2^31");
}
// B2. Initialize: u and v have been divided by 2^k and at least
// one is odd.
int t = ((u&1)==1) ? v : -(u/2)/*B3*/;
// t negative: u was odd, v may be even (t replaces v)
// t positive: u was even, v is odd (t replaces u)
do {
/* assert u<0 && v<0; */
// B4/B3: cast out twos from t.
while ((t&1)==0) { // while t is even..
t/=2; // cast out twos
}
// B5 [reset max(u,v)]
if (t>0) {
u = -t;
} else {
v = t;
}
// B6/B3. at this point both u and v should be odd.
t = (v - u)/2;
// |u| larger: t positive (replace u)
// |v| larger: t negative (replace v)
} while (t!=0);
return -u*(1<<k); // gcd is u*2^k
} }
// Arithmetic // Arithmetic
//------------------------------------------------------------------- //-------------------------------------------------------------------
/**
* Multiply two integers, checking for overflow.
*
* @param x a factor
* @param y a factor
* @return the product <code>x*y</code>
* @throws ArithmeticException if the result can not be represented as
* an int
*/
private static int mulAndCheck(int x, int y) {
long m = ((long)x)*((long)y);
if (m < Integer.MIN_VALUE ||
m > Integer.MAX_VALUE) {
throw new ArithmeticException("overflow: mul");
}
return (int)m;
}
/** /**
* <p>Adds the value of this fraction to another, returning the result in * Multiply two non-negative integers, checking for overflow.
* reduced form.</p> *
* @param x a non-negative factor
* @param y a non-negative factor
* @return the product <code>x*y</code>
* @throws ArithmeticException if the result can not be represented as
* an int
*/
private static int mulPosAndCheck(int x, int y) {
/* assert x>=0 && y>=0; */
long m = ((long)x)*((long)y);
if (m > Integer.MAX_VALUE) {
throw new ArithmeticException("overflow: mulPos");
}
return (int)m;
}
/**
* Add two integers, checking for overflow.
*
* @param x an addend
* @param y an addend
* @return the sum <code>x+y</code>
* @throws ArithmeticException if the result can not be represented as
* an int
*/
private static int addAndCheck(int x, int y) {
long s = (long)x+(long)y;
if (s < Integer.MIN_VALUE ||
s > Integer.MAX_VALUE) {
throw new ArithmeticException("overflow: add");
}
return (int)s;
}
/**
* Subtract two integers, checking for overflow.
*
* @param x the minuend
* @param y the subtrahend
* @return the difference <code>x-y</code>
* @throws ArithmeticException if the result can not be represented as
* an int
*/
private static int subAndCheck(int x, int y) {
long s = (long)x-(long)y;
if (s < Integer.MIN_VALUE ||
s > Integer.MAX_VALUE) {
throw new ArithmeticException("overflow: add");
}
return (int)s;
}
/**
* <p>Adds the value of this fraction to another, returning the result in reduced form.
* The algorithm follows Knuth, 4.5.1.</p>
* *
* @param fraction the fraction to add, must not be <code>null</code> * @param fraction the fraction to add, must not be <code>null</code>
* @return a <code>Fraction</code> instance with the resulting values * @return a <code>Fraction</code> instance with the resulting values
@ -544,48 +680,82 @@ public final class Fraction extends Number implements Serializable, Comparable {
* <code>Integer.MAX_VALUE</code> * <code>Integer.MAX_VALUE</code>
*/ */
public Fraction add(Fraction fraction) { public Fraction add(Fraction fraction) {
if (fraction == null) { return addSub(fraction, true /* add */);
throw new IllegalArgumentException("The fraction must not be null");
}
if (numerator == 0) {
return fraction;
}
if (fraction.numerator == 0) {
return this;
}
// Compute lcd explicitly to limit overflow
int gcd = greatestCommonDivisor(Math.abs(fraction.denominator), Math.abs(denominator));
int thisResidue = denominator/gcd;
int thatResidue = fraction.denominator/gcd;
double denominatorValue = Math.abs((double) gcd * thisResidue * thatResidue);
double numeratorValue = (double) numerator * thatResidue + fraction.numerator * thisResidue;
if (Math.abs(numeratorValue) > Integer.MAX_VALUE ||
Math.abs(denominatorValue) > Integer.MAX_VALUE) {
throw new ArithmeticException("Integer overflow");
}
return Fraction.getReducedFraction((int) numeratorValue, (int) denominatorValue);
} }
/** /**
* <p>Subtracts the value of another fraction from the value of this one, * <p>Subtracts the value of another fraction from the value of this one,
* returning the result in reduced form.</p> * returning the result in reduced form.</p>
* *
* @param fraction the fraction to subtract, must not be <code>null</code> * @param fraction the fraction to subtract, must not be <code>null</code>
* @return a <code>Fraction</code> instance with the resulting values * @return a <code>Fraction</code> instance with the resulting values
* @throws IllegalArgumentException if the fraction is <code>null</code> * @throws IllegalArgumentException if the fraction is <code>null</code>
* @throws ArithmeticException if the resulting numerator or denominator exceeds * @throws ArithmeticException if the resulting numerator or denominator
* <code>Integer.MAX_VALUE</code> * cannot be represented in an <code>int</code>.
*/ */
public Fraction subtract(Fraction fraction) { public Fraction subtract(Fraction fraction) {
return addSub(fraction, false /* subtract */);
}
/**
* Implement add and subtract using algorithm described in Knuth 4.5.1.
*
* @param fraction the fraction to subtract, must not be <code>null</code>
* @param isAdd true to add, false to subtract
* @return a <code>Fraction</code> instance with the resulting values
* @throws IllegalArgumentException if the fraction is <code>null</code>
* @throws ArithmeticException if the resulting numerator or denominator
* cannot be represented in an <code>int</code>.
*/
private Fraction addSub(Fraction fraction, boolean isAdd) {
if (fraction == null) { if (fraction == null) {
throw new IllegalArgumentException("The fraction must not be null"); throw new IllegalArgumentException("The fraction must not be null");
} }
return add(fraction.negate()); // zero is identity for addition.
if (numerator == 0) {
return isAdd ? fraction : fraction.negate();
}
if (fraction.numerator == 0) {
return this;
}
// if denominators are randomly distributed, d1 will be 1 about 61%
// of the time.
int d1 = greatestCommonDivisor(denominator, fraction.denominator);
if (d1==1) {
// result is ( (u*v' +/- u'v) / u'v')
int uvp = mulAndCheck(numerator, fraction.denominator);
int upv = mulAndCheck(fraction.numerator, denominator);
return new Fraction
(isAdd ? addAndCheck(uvp, upv) : subAndCheck(uvp, upv),
mulPosAndCheck(denominator, fraction.denominator));
}
// the quantity 't' requires 65 bits of precision; see knuth 4.5.1
// exercise 7. we're going to use a BigInteger.
// t = u(v'/d1) +/- v(u'/d1)
BigInteger uvp = BigInteger.valueOf(numerator)
.multiply(BigInteger.valueOf(fraction.denominator/d1));
BigInteger upv = BigInteger.valueOf(fraction.numerator)
.multiply(BigInteger.valueOf(denominator/d1));
BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
// but d2 doesn't need extra precision because
// d2 = gcd(t,d1) = gcd(t mod d1, d1)
int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
int d2 = (tmodd1==0)?d1:greatestCommonDivisor(tmodd1, d1);
// result is (t/d2) / (u'/d1)(v'/d2)
BigInteger w = t.divide(BigInteger.valueOf(d2));
if (w.bitLength() > 31) {
throw new ArithmeticException
("overflow: numerator too large after multiply");
}
return new Fraction
(w.intValue(),
mulPosAndCheck(denominator/d1, fraction.denominator/d2));
} }
/** /**
* <p>Multiplies the value of this fraction by another, returning the result * <p>Multiplies the value of this fraction by another, returning the
* in reduced form.</p> * result in reduced form.</p>
* *
* @param fraction the fraction to multiply by, must not be <code>null</code> * @param fraction the fraction to multiply by, must not be <code>null</code>
* @return a <code>Fraction</code> instance with the resulting values * @return a <code>Fraction</code> instance with the resulting values
@ -600,18 +770,17 @@ public final class Fraction extends Number implements Serializable, Comparable {
if (numerator == 0 || fraction.numerator == 0) { if (numerator == 0 || fraction.numerator == 0) {
return ZERO; return ZERO;
} }
double numeratorValue = (double) numerator * fraction.numerator; // knuth 4.5.1
double denominatorValue = (double) denominator * fraction.denominator; // make sure we don't overflow unless the result *must* overflow.
if (Math.abs(numeratorValue) > Integer.MAX_VALUE || int d1 = greatestCommonDivisor(numerator, fraction.denominator);
Math.abs(denominatorValue) > Integer.MAX_VALUE) { int d2 = greatestCommonDivisor(fraction.numerator, denominator);
throw new ArithmeticException("Integer overflow"); return getReducedFraction
} (mulAndCheck(numerator/d1, fraction.numerator/d2),
return getReducedFraction((int) numeratorValue, (int) denominatorValue); mulPosAndCheck(denominator/d2, fraction.denominator/d1));
} }
/** /**
* <p>Divide the value of this fraction by another, returning the result * <p>Divide the value of this fraction by another.</p>
* in reduced form.</p>
* *
* @param fraction the fraction to divide by, must not be <code>null</code> * @param fraction the fraction to divide by, must not be <code>null</code>
* @return a <code>Fraction</code> instance with the resulting values * @return a <code>Fraction</code> instance with the resulting values
@ -627,16 +796,7 @@ public final class Fraction extends Number implements Serializable, Comparable {
if (fraction.numerator == 0) { if (fraction.numerator == 0) {
throw new ArithmeticException("The fraction to divide by must not be zero"); throw new ArithmeticException("The fraction to divide by must not be zero");
} }
if (numerator == 0) { return multiplyBy(fraction.invert());
return ZERO;
}
double numeratorValue = (double) numerator * fraction.denominator;
double denominatorValue = (double) denominator * fraction.numerator;
if (Math.abs(numeratorValue) > Integer.MAX_VALUE ||
Math.abs(denominatorValue) > Integer.MAX_VALUE) {
throw new ArithmeticException("Integer overflow");
}
return getReducedFraction((int) numeratorValue, (int) denominatorValue);
} }
// Basics // Basics
@ -658,8 +818,8 @@ public final class Fraction extends Number implements Serializable, Comparable {
return false; return false;
} }
Fraction other = (Fraction) obj; Fraction other = (Fraction) obj;
return (numerator == other.numerator && return (getNumerator() == other.getNumerator() &&
denominator == other.denominator); getDenominator() == other.getDenominator());
} }
/** /**
@ -669,9 +829,8 @@ public final class Fraction extends Number implements Serializable, Comparable {
*/ */
public int hashCode() { public int hashCode() {
if (hashCode == 0) { if (hashCode == 0) {
hashCode = 17; // hashcode update should be atomic.
hashCode = 37 * hashCode + numerator; hashCode = 37 * (37 * 17 + getNumerator()) + getDenominator();
hashCode = 37 * hashCode + denominator;
} }
return hashCode; return hashCode;
} }
@ -686,6 +845,9 @@ public final class Fraction extends Number implements Serializable, Comparable {
*/ */
public int compareTo(Object object) { public int compareTo(Object object) {
Fraction other = (Fraction) object; Fraction other = (Fraction) object;
if (this==other) {
return 0;
}
if (numerator == other.numerator && denominator == other.denominator) { if (numerator == other.numerator && denominator == other.denominator) {
return 0; return 0;
} }
@ -712,9 +874,9 @@ public final class Fraction extends Number implements Serializable, Comparable {
public String toString() { public String toString() {
if (toString == null) { if (toString == null) {
toString = new StringBuffer(32) toString = new StringBuffer(32)
.append(numerator) .append(getNumerator())
.append('/') .append('/')
.append(denominator).toString(); .append(getDenominator()).toString();
} }
return toString; return toString;
} }
@ -734,7 +896,11 @@ public final class Fraction extends Number implements Serializable, Comparable {
toProperString = "0"; toProperString = "0";
} else if (numerator == denominator) { } else if (numerator == denominator) {
toProperString = "1"; toProperString = "1";
} else if (Math.abs(numerator) > denominator) { } else if ((numerator>0?-numerator:numerator) < -denominator) {
// note that we do the magnitude comparison test above with
// NEGATIVE (not positive) numbers, since negative numbers
// have a larger range. otherwise numerator==Integer.MIN_VALUE
// is handled incorrectly.
int properNumerator = getProperNumerator(); int properNumerator = getProperNumerator();
if (properNumerator == 0) { if (properNumerator == 0) {
toProperString = Integer.toString(getProperWhole()); toProperString = Integer.toString(getProperWhole());
@ -742,15 +908,14 @@ public final class Fraction extends Number implements Serializable, Comparable {
toProperString = new StringBuffer(32) toProperString = new StringBuffer(32)
.append(getProperWhole()).append(' ') .append(getProperWhole()).append(' ')
.append(properNumerator).append('/') .append(properNumerator).append('/')
.append(denominator).toString(); .append(getDenominator()).toString();
} }
} else { } else {
toProperString = new StringBuffer(32) toProperString = new StringBuffer(32)
.append(numerator).append('/') .append(getNumerator()).append('/')
.append(denominator).toString(); .append(getDenominator()).toString();
} }
} }
return toProperString; return toProperString;
} }
} }

354
src/test/org/apache/commons/lang/math/FractionTest.java
View File

@ -18,15 +18,21 @@ package org.apache.commons.lang.math;
import junit.framework.Test; import junit.framework.Test;
import junit.framework.TestCase; import junit.framework.TestCase;
import junit.framework.TestSuite; import junit.framework.TestSuite;
import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
/** /**
* Test cases for the {@link Fraction} classes. * Test cases for the {@link Fraction} class
* *
* @author Stephen Colebourne * @author Stephen Colebourne
* @version $Id: FractionTest.java,v 1.6 2004/02/18 23:02:38 ggregory Exp $ * @author C. Scott Ananian
* @version $Id: FractionTest.java,v 1.7 2004/07/11 23:20:17 psteitz Exp $
*/ */
public class FractionTest extends TestCase { public class FractionTest extends TestCase {
private static final int SKIP = 53; private static final int SKIP = 500; //53
public FractionTest(String name) { public FractionTest(String name) {
super(name); super(name);
@ -80,7 +86,7 @@ public class FractionTest extends TestCase {
assertEquals(4, Fraction.FOUR_FIFTHS.getNumerator()); assertEquals(4, Fraction.FOUR_FIFTHS.getNumerator());
assertEquals(5, Fraction.FOUR_FIFTHS.getDenominator()); assertEquals(5, Fraction.FOUR_FIFTHS.getDenominator());
} }
public void testFactory_int_int() { public void testFactory_int_int() {
Fraction f = null; Fraction f = null;
@ -139,6 +145,16 @@ public class FractionTest extends TestCase {
f = Fraction.getFraction(-3, 0); f = Fraction.getFraction(-3, 0);
fail("expecting ArithmeticException"); fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
// very large: can't represent as unsimplified fraction, although
try {
f = Fraction.getFraction(4, Integer.MIN_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f = Fraction.getFraction(1, Integer.MIN_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
} }
public void testFactory_int_int_int() { public void testFactory_int_int_int() {
@ -223,8 +239,26 @@ public class FractionTest extends TestCase {
f = Fraction.getFraction(-Integer.MAX_VALUE, 1, 2); f = Fraction.getFraction(-Integer.MAX_VALUE, 1, 2);
fail("expecting ArithmeticException"); fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
}
// very large
f = Fraction.getFraction(-1, 0, Integer.MAX_VALUE);
assertEquals(-Integer.MAX_VALUE, f.getNumerator());
assertEquals(Integer.MAX_VALUE, f.getDenominator());
try {
// negative denominators not allowed in this constructor.
f = Fraction.getFraction(0, 4, Integer.MIN_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f = Fraction.getFraction(1, 1, Integer.MAX_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f = Fraction.getFraction(-1, 2, Integer.MAX_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
}
public void testReducedFactory_int_int() { public void testReducedFactory_int_int() {
Fraction f = null; Fraction f = null;
@ -296,6 +330,18 @@ public class FractionTest extends TestCase {
f = Fraction.getReducedFraction(121, 22); f = Fraction.getReducedFraction(121, 22);
assertEquals(11, f.getNumerator()); assertEquals(11, f.getNumerator());
assertEquals(2, f.getDenominator()); assertEquals(2, f.getDenominator());
// Extreme values
// OK, can reduce before negating
f = Fraction.getReducedFraction(-2, Integer.MIN_VALUE);
assertEquals(1, f.getNumerator());
assertEquals(-(Integer.MIN_VALUE / 2), f.getDenominator());
// Can't reduce, negation will throw
try {
f = Fraction.getReducedFraction(-7, Integer.MIN_VALUE);
fail("Expecting ArithmeticException");
} catch (ArithmeticException ex) {}
} }
public void testFactory_double() { public void testFactory_double() {
@ -391,7 +437,7 @@ public class FractionTest extends TestCase {
public void testFactory_String() { public void testFactory_String() {
try { try {
Fraction.getFraction(null); Fraction.getFraction(null);
fail("expecting ArithmeticException"); fail("expecting IllegalArgumentException");
} catch (IllegalArgumentException ex) {} } catch (IllegalArgumentException ex) {}
} }
@ -417,6 +463,7 @@ public class FractionTest extends TestCase {
try { try {
f = Fraction.getFraction("2.3R"); f = Fraction.getFraction("2.3R");
fail("Expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
@ -426,6 +473,7 @@ public class FractionTest extends TestCase {
try { try {
f = Fraction.getFraction("."); f = Fraction.getFraction(".");
fail("Expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
} }
@ -448,34 +496,42 @@ public class FractionTest extends TestCase {
assertEquals(6, f.getNumerator()); assertEquals(6, f.getNumerator());
assertEquals(4, f.getDenominator()); assertEquals(4, f.getDenominator());
f = Fraction.getFraction("-7 1/2");
assertEquals(-15, f.getNumerator());
assertEquals(2, f.getDenominator());
f = Fraction.getFraction("-1 2/4");
assertEquals(-6, f.getNumerator());
assertEquals(4, f.getDenominator());
try { try {
f = Fraction.getFraction("2 3"); f = Fraction.getFraction("2 3");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("a 3"); f = Fraction.getFraction("a 3");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("2 b/4"); f = Fraction.getFraction("2 b/4");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("2 "); f = Fraction.getFraction("2 ");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction(" 3"); f = Fraction.getFraction(" 3");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction(" "); f = Fraction.getFraction(" ");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
} }
@ -508,22 +564,22 @@ public class FractionTest extends TestCase {
try { try {
f = Fraction.getFraction("2/d"); f = Fraction.getFraction("2/d");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("2e/3"); f = Fraction.getFraction("2e/3");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("2/"); f = Fraction.getFraction("2/");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
try { try {
f = Fraction.getFraction("/"); f = Fraction.getFraction("/");
fail("expecting NumberFomatException"); fail("expecting NumberFormatException");
} catch (NumberFormatException ex) {} } catch (NumberFormatException ex) {}
} }
@ -541,6 +597,12 @@ public class FractionTest extends TestCase {
assertEquals(-3, f.getProperWhole()); assertEquals(-3, f.getProperWhole());
assertEquals(5, f.getProperNumerator()); assertEquals(5, f.getProperNumerator());
assertEquals(6, f.getDenominator()); assertEquals(6, f.getDenominator());
f = Fraction.getFraction(Integer.MIN_VALUE, 0, 1);
assertEquals(Integer.MIN_VALUE, f.getNumerator());
assertEquals(Integer.MIN_VALUE, f.getProperWhole());
assertEquals(0, f.getProperNumerator());
assertEquals(1, f.getDenominator());
} }
public void testConversions() { public void testConversions() {
@ -560,6 +622,11 @@ public class FractionTest extends TestCase {
f = f.reduce(); f = f.reduce();
assertEquals(2, f.getNumerator()); assertEquals(2, f.getNumerator());
assertEquals(3, f.getDenominator()); assertEquals(3, f.getDenominator());
f = Fraction.getFraction(2, 3);
f = f.reduce();
assertEquals(2, f.getNumerator());
assertEquals(3, f.getDenominator());
} }
public void testInvert() { public void testInvert() {
@ -575,10 +642,28 @@ public class FractionTest extends TestCase {
assertEquals(3, f.getNumerator()); assertEquals(3, f.getNumerator());
assertEquals(4, f.getDenominator()); assertEquals(4, f.getDenominator());
f = Fraction.getFraction(-15, 47);
f = f.invert();
assertEquals(-47, f.getNumerator());
assertEquals(15, f.getDenominator());
f = Fraction.getFraction(0, 3); f = Fraction.getFraction(0, 3);
try { try {
f = f.invert(); f = f.invert();
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
// large values
f = Fraction.getFraction(Integer.MIN_VALUE, 1);
try {
f = f.invert();
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f = Fraction.getFraction(Integer.MAX_VALUE, 1);
f = f.invert();
assertEquals(1, f.getNumerator());
assertEquals(Integer.MAX_VALUE, f.getDenominator());
} }
public void testNegate() { public void testNegate() {
@ -593,6 +678,18 @@ public class FractionTest extends TestCase {
f = f.negate(); f = f.negate();
assertEquals(50, f.getNumerator()); assertEquals(50, f.getNumerator());
assertEquals(75, f.getDenominator()); assertEquals(75, f.getDenominator());
// large values
f = Fraction.getFraction(Integer.MAX_VALUE-1, Integer.MAX_VALUE);
f = f.negate();
assertEquals(Integer.MIN_VALUE+2, f.getNumerator());
assertEquals(Integer.MAX_VALUE, f.getDenominator());
f = Fraction.getFraction(Integer.MIN_VALUE, 1);
try {
f = f.negate();
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
} }
public void testAbs() { public void testAbs() {
@ -607,6 +704,22 @@ public class FractionTest extends TestCase {
f = f.abs(); f = f.abs();
assertEquals(50, f.getNumerator()); assertEquals(50, f.getNumerator());
assertEquals(75, f.getDenominator()); assertEquals(75, f.getDenominator());
f = Fraction.getFraction(Integer.MAX_VALUE, 1);
f = f.abs();
assertEquals(Integer.MAX_VALUE, f.getNumerator());
assertEquals(1, f.getDenominator());
f = Fraction.getFraction(Integer.MAX_VALUE, -1);
f = f.abs();
assertEquals(Integer.MAX_VALUE, f.getNumerator());
assertEquals(1, f.getDenominator());
f = Fraction.getFraction(Integer.MIN_VALUE, 1);
try {
f = f.abs();
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
} }
public void testPow() { public void testPow() {
@ -617,6 +730,7 @@ public class FractionTest extends TestCase {
f = Fraction.getFraction(3, 5); f = Fraction.getFraction(3, 5);
assertSame(f, f.pow(1)); assertSame(f, f.pow(1));
assertEquals(f, f.pow(1));
f = Fraction.getFraction(3, 5); f = Fraction.getFraction(3, 5);
f = f.pow(2); f = f.pow(2);
@ -638,7 +752,82 @@ public class FractionTest extends TestCase {
assertEquals(25, f.getNumerator()); assertEquals(25, f.getNumerator());
assertEquals(9, f.getDenominator()); assertEquals(9, f.getDenominator());
f = Fraction.getFraction(Integer.MAX_VALUE); // check unreduced fractions stay that way.
f = Fraction.getFraction(6, 10);
assertEquals(Fraction.ONE, f.pow(0));
f = Fraction.getFraction(6, 10);
assertEquals(f, f.pow(1));
assertFalse(f.pow(1).equals(Fraction.getFraction(3,5)));
f = Fraction.getFraction(6, 10);
f = f.pow(2);
assertEquals(9, f.getNumerator());
assertEquals(25, f.getDenominator());
f = Fraction.getFraction(6, 10);
f = f.pow(3);
assertEquals(27, f.getNumerator());
assertEquals(125, f.getDenominator());
f = Fraction.getFraction(6, 10);
f = f.pow(-1);
assertEquals(10, f.getNumerator());
assertEquals(6, f.getDenominator());
f = Fraction.getFraction(6, 10);
f = f.pow(-2);
assertEquals(25, f.getNumerator());
assertEquals(9, f.getDenominator());
// zero to any positive power is still zero.
f = Fraction.getFraction(0, 1231);
f = f.pow(1);
assertTrue(0==f.compareTo(Fraction.ZERO));
assertEquals(0, f.getNumerator());
assertEquals(1231, f.getDenominator());
f = f.pow(2);
assertTrue(0==f.compareTo(Fraction.ZERO));
assertEquals(0, f.getNumerator());
assertEquals(1, f.getDenominator());
// zero to negative powers should throw an exception
try {
f = f.pow(-1);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f = f.pow(Integer.MIN_VALUE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
// one to any power is still one.
f = Fraction.getFraction(1, 1);
f = f.pow(0);
assertEquals(f, Fraction.ONE);
f = f.pow(1);
assertEquals(f, Fraction.ONE);
f = f.pow(-1);
assertEquals(f, Fraction.ONE);
f = f.pow(Integer.MAX_VALUE);
assertEquals(f, Fraction.ONE);
f = f.pow(Integer.MIN_VALUE);
assertEquals(f, Fraction.ONE);
f = Fraction.getFraction(Integer.MAX_VALUE, 1);
try {
f = f.pow(2);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
// Numerator growing too negative during the pow operation.
f = Fraction.getFraction(Integer.MIN_VALUE, 1);
try {
f = f.pow(3);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f = Fraction.getFraction(65536, 1);
try { try {
f = f.pow(2); f = f.pow(2);
fail("expecting ArithmeticException"); fail("expecting ArithmeticException");
@ -699,11 +888,31 @@ public class FractionTest extends TestCase {
f = f2.add(f1); f = f2.add(f1);
assertSame(f2, f); assertSame(f2, f);
f1 = Fraction.getFraction(-1, 13*13*2*2);
f2 = Fraction.getFraction(-2, 13*17*2);
f = f1.add(f2);
assertEquals(13*13*17*2*2, f.getDenominator());
assertEquals(-17 - 2*13*2, f.getNumerator());
try { try {
f.add(null); f.add(null);
fail("expecting IllegalArgumentException"); fail("expecting IllegalArgumentException");
} catch (IllegalArgumentException ex) {} } catch (IllegalArgumentException ex) {}
// if this fraction is added naively, it will overflow.
// check that it doesn't.
f1 = Fraction.getFraction(1,32768*3);
f2 = Fraction.getFraction(1,59049);
f = f1.add(f2);
assertEquals(52451, f.getNumerator());
assertEquals(1934917632, f.getDenominator());
f1 = Fraction.getFraction(Integer.MIN_VALUE, 3);
f2 = Fraction.ONE_THIRD;
f = f1.add(f2);
assertEquals(Integer.MIN_VALUE+1, f.getNumerator());
assertEquals(3, f.getDenominator());
f1 = Fraction.getFraction(Integer.MAX_VALUE - 1, 1); f1 = Fraction.getFraction(Integer.MAX_VALUE - 1, 1);
f2 = Fraction.ONE; f2 = Fraction.ONE;
f = f1.add(f2); f = f1.add(f2);
@ -715,12 +924,32 @@ public class FractionTest extends TestCase {
fail("expecting ArithmeticException but got: " + f.toString()); fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
// denominator should not be a multiple of 2 or 3 to trigger overflow
f1 = Fraction.getFraction(Integer.MIN_VALUE, 5);
f2 = Fraction.getFraction(-1,5);
try {
f = f1.add(f2); // should overflow
fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
try { try {
f= Fraction.getFraction(-Integer.MAX_VALUE, 1); f= Fraction.getFraction(-Integer.MAX_VALUE, 1);
f = f.add(f); f = f.add(f);
fail("expecting ArithmeticException"); fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
try {
f= Fraction.getFraction(-Integer.MAX_VALUE, 1);
f = f.add(f);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f1 = Fraction.getFraction(3,327680);
f2 = Fraction.getFraction(2,59049);
try {
f = f1.add(f2); // should overflow
fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
} }
public void testSubtract() { public void testSubtract() {
@ -780,6 +1009,26 @@ public class FractionTest extends TestCase {
fail("expecting IllegalArgumentException"); fail("expecting IllegalArgumentException");
} catch (IllegalArgumentException ex) {} } catch (IllegalArgumentException ex) {}
// if this fraction is subtracted naively, it will overflow.
// check that it doesn't.
f1 = Fraction.getFraction(1,32768*3);
f2 = Fraction.getFraction(1,59049);
f = f1.subtract(f2);
assertEquals(-13085, f.getNumerator());
assertEquals(1934917632, f.getDenominator());
f1 = Fraction.getFraction(Integer.MIN_VALUE, 3);
f2 = Fraction.ONE_THIRD.negate();
f = f1.subtract(f2);
assertEquals(Integer.MIN_VALUE+1, f.getNumerator());
assertEquals(3, f.getDenominator());
f1 = Fraction.getFraction(Integer.MAX_VALUE, 1);
f2 = Fraction.ONE;
f = f1.subtract(f2);
assertEquals(Integer.MAX_VALUE-1, f.getNumerator());
assertEquals(1, f.getDenominator());
try { try {
f1 = Fraction.getFraction(1, Integer.MAX_VALUE); f1 = Fraction.getFraction(1, Integer.MAX_VALUE);
f2 = Fraction.getFraction(1, Integer.MAX_VALUE - 1); f2 = Fraction.getFraction(1, Integer.MAX_VALUE - 1);
@ -787,6 +1036,32 @@ public class FractionTest extends TestCase {
fail("expecting ArithmeticException"); //should overflow fail("expecting ArithmeticException"); //should overflow
} catch (ArithmeticException ex) {} } catch (ArithmeticException ex) {}
// denominator should not be a multiple of 2 or 3 to trigger overflow
f1 = Fraction.getFraction(Integer.MIN_VALUE, 5);
f2 = Fraction.getFraction(1,5);
try {
f = f1.subtract(f2); // should overflow
fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
try {
f= Fraction.getFraction(Integer.MIN_VALUE, 1);
f = f.subtract(Fraction.ONE);
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
try {
f= Fraction.getFraction(Integer.MAX_VALUE, 1);
f = f.subtract(Fraction.ONE.negate());
fail("expecting ArithmeticException");
} catch (ArithmeticException ex) {}
f1 = Fraction.getFraction(3,327680);
f2 = Fraction.getFraction(2,59049);
try {
f = f1.subtract(f2); // should overflow
fail("expecting ArithmeticException but got: " + f.toString());
} catch (ArithmeticException ex) {}
} }
public void testMultiply() { public void testMultiply() {
@ -800,6 +1075,15 @@ public class FractionTest extends TestCase {
assertEquals(6, f.getNumerator()); assertEquals(6, f.getNumerator());
assertEquals(25, f.getDenominator()); assertEquals(25, f.getDenominator());
f1 = Fraction.getFraction(6, 10);
f2 = Fraction.getFraction(6, 10);
f = f1.multiplyBy(f2);
assertEquals(9, f.getNumerator());
assertEquals(25, f.getDenominator());
f = f.multiplyBy(f2);
assertEquals(27, f.getNumerator());
assertEquals(125, f.getDenominator());
f1 = Fraction.getFraction(3, 5); f1 = Fraction.getFraction(3, 5);
f2 = Fraction.getFraction(-2, 5); f2 = Fraction.getFraction(-2, 5);
f = f1.multiplyBy(f2); f = f1.multiplyBy(f2);
@ -812,6 +1096,7 @@ public class FractionTest extends TestCase {
assertEquals(6, f.getNumerator()); assertEquals(6, f.getNumerator());
assertEquals(25, f.getDenominator()); assertEquals(25, f.getDenominator());
f1 = Fraction.getFraction(0, 5); f1 = Fraction.getFraction(0, 5);
f2 = Fraction.getFraction(2, 7); f2 = Fraction.getFraction(2, 7);
f = f1.multiplyBy(f2); f = f1.multiplyBy(f2);
@ -823,6 +1108,12 @@ public class FractionTest extends TestCase {
assertEquals(2, f.getNumerator()); assertEquals(2, f.getNumerator());
assertEquals(7, f.getDenominator()); assertEquals(7, f.getDenominator());
f1 = Fraction.getFraction(Integer.MAX_VALUE, 1);
f2 = Fraction.getFraction(Integer.MIN_VALUE, Integer.MAX_VALUE);
f = f1.multiplyBy(f2);
assertEquals(Integer.MIN_VALUE, f.getNumerator());
assertEquals(1, f.getDenominator());
try { try {
f.multiplyBy(null); f.multiplyBy(null);
fail("expecting IllegalArgumentException"); fail("expecting IllegalArgumentException");
@ -875,6 +1166,12 @@ public class FractionTest extends TestCase {
assertEquals(1, f.getNumerator()); assertEquals(1, f.getNumerator());
assertEquals(1, f.getDenominator()); assertEquals(1, f.getDenominator());
f1 = Fraction.getFraction(Integer.MIN_VALUE, Integer.MAX_VALUE);
f2 = Fraction.getFraction(1, Integer.MAX_VALUE);
f = f1.divideBy(f2);
assertEquals(Integer.MIN_VALUE, f.getNumerator());
assertEquals(1, f.getDenominator());
try { try {
f.divideBy(null); f.divideBy(null);
fail("IllegalArgumentException"); fail("IllegalArgumentException");
@ -932,6 +1229,7 @@ public class FractionTest extends TestCase {
Fraction f2 = null; Fraction f2 = null;
f1 = Fraction.getFraction(3, 5); f1 = Fraction.getFraction(3, 5);
assertTrue(f1.compareTo(f1) == 0);
try { try {
f1.compareTo(null); f1.compareTo(null);
@ -945,15 +1243,24 @@ public class FractionTest extends TestCase {
f2 = Fraction.getFraction(2, 5); f2 = Fraction.getFraction(2, 5);
assertTrue(f1.compareTo(f2) > 0); assertTrue(f1.compareTo(f2) > 0);
assertTrue(f2.compareTo(f2) == 0);
f2 = Fraction.getFraction(4, 5); f2 = Fraction.getFraction(4, 5);
assertTrue(f1.compareTo(f2) < 0); assertTrue(f1.compareTo(f2) < 0);
assertTrue(f2.compareTo(f2) == 0);
f2 = Fraction.getFraction(3, 5); f2 = Fraction.getFraction(3, 5);
assertTrue(f1.compareTo(f2) == 0); assertTrue(f1.compareTo(f2) == 0);
assertTrue(f2.compareTo(f2) == 0);
f2 = Fraction.getFraction(6, 10); f2 = Fraction.getFraction(6, 10);
assertTrue(f1.compareTo(f2) == 0); assertTrue(f1.compareTo(f2) == 0);
assertTrue(f2.compareTo(f2) == 0);
f2 = Fraction.getFraction(-1, 1, Integer.MAX_VALUE);
assertTrue(f1.compareTo(f2) > 0);
assertTrue(f2.compareTo(f2) == 0);
} }
public void testToString() { public void testToString() {
@ -975,6 +1282,12 @@ public class FractionTest extends TestCase {
f = Fraction.getFraction(2, 2); f = Fraction.getFraction(2, 2);
assertEquals("2/2", f.toString()); assertEquals("2/2", f.toString());
f = Fraction.getFraction(Integer.MIN_VALUE, 0, 1);
assertEquals("-2147483648/1", f.toString());
f = Fraction.getFraction(-1, 1, Integer.MAX_VALUE);
assertEquals("-2147483648/2147483647", f.toString());
} }
public void testToProperString() { public void testToProperString() {
@ -1002,6 +1315,11 @@ public class FractionTest extends TestCase {
f = Fraction.getFraction(-7, 5); f = Fraction.getFraction(-7, 5);
assertEquals("-1 2/5", f.toProperString()); assertEquals("-1 2/5", f.toProperString());
f = Fraction.getFraction(Integer.MIN_VALUE, 0, 1);
assertEquals("-2147483648", f.toProperString());
f = Fraction.getFraction(-1, 1, Integer.MAX_VALUE);
assertEquals("-1 1/2147483647", f.toProperString());
} }
} }