8066842: java.math.BigDecimal.divide(BigDecimal, RoundingMode) produces incorrect result
Summary: Replace divWord() with non-truncating alternatives
Reviewed-by: psandoz, darcy
/*
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*
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* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
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* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
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* questions.
*/
/*
* @test
* @bug 4851776 4907265 6177836 6876282 8066842
* @summary Some tests for the divide methods.
* @author Joseph D. Darcy
*/
import java.math.*;
import static java.math.BigDecimal.*;
public class DivideTests {
// Preliminary exact divide method; could be used for comparison
// purposes.
BigDecimal anotherDivide(BigDecimal dividend, BigDecimal divisor) {
/*
* Handle zero cases first.
*/
if (divisor.signum() == 0) { // x/0
if (dividend.signum() == 0) // 0/0
throw new ArithmeticException("Division undefined"); // NaN
throw new ArithmeticException("Division by zero");
}
if (dividend.signum() == 0) // 0/y
return BigDecimal.ZERO;
else {
/*
* Determine if there is a result with a terminating
* decimal expansion. Putting aside overflow and
* underflow considerations, the existance of an exact
* result only depends on the ratio of the intVal's of the
* dividend (i.e. this) and and divisor since the scales
* of the argument just affect where the decimal point
* lies.
*
* For the ratio of (a = this.intVal) and (b =
* divisor.intVal) to have a finite decimal expansion,
* once a/b is put in lowest terms, b must be equal to
* (2^i)*(5^j) for some integer i,j >= 0. Therefore, we
* first compute to see if b_prime =(b/gcd(a,b)) is equal
* to (2^i)*(5^j).
*/
BigInteger TWO = BigInteger.valueOf(2);
BigInteger FIVE = BigInteger.valueOf(5);
BigInteger TEN = BigInteger.valueOf(10);
BigInteger divisorIntvalue = divisor.scaleByPowerOfTen(divisor.scale()).toBigInteger().abs();
BigInteger dividendIntvalue = dividend.scaleByPowerOfTen(dividend.scale()).toBigInteger().abs();
BigInteger b_prime = divisorIntvalue.divide(dividendIntvalue.gcd(divisorIntvalue));
boolean goodDivisor = false;
int i=0, j=0;
badDivisor: {
while(! b_prime.equals(BigInteger.ONE) ) {
int b_primeModTen = b_prime.mod(TEN).intValue() ;
switch(b_primeModTen) {
case 0:
// b_prime divisible by 10=2*5, increment i and j
i++;
j++;
b_prime = b_prime.divide(TEN);
break;
case 5:
// b_prime divisible by 5, increment j
j++;
b_prime = b_prime.divide(FIVE);
break;
case 2:
case 4:
case 6:
case 8:
// b_prime divisible by 2, increment i
i++;
b_prime = b_prime.divide(TWO);
break;
default: // hit something we shouldn't have
b_prime = BigInteger.ONE; // terminate loop
break badDivisor;
}
}
goodDivisor = true;
}
if( ! goodDivisor ) {
throw new ArithmeticException("Non terminating decimal expansion");
}
else {
// What is a rule for determining how many digits are
// needed? Once that is determined, cons up a new
// MathContext object and pass it on to the divide(bd,
// mc) method; precision == ?, roundingMode is unnecessary.
// Are we sure this is the right scale to use? Should
// also determine a precision-based method.
MathContext mc = new MathContext(dividend.precision() +
(int)Math.ceil(
10.0*divisor.precision()/3.0),
RoundingMode.UNNECESSARY);
// Should do some more work here to rescale, etc.
return dividend.divide(divisor, mc);
}
}
}
public static int powersOf2and5() {
int failures = 0;
for(int i = 0; i < 6; i++) {
int powerOf2 = (int)StrictMath.pow(2.0, i);
for(int j = 0; j < 6; j++) {
int powerOf5 = (int)StrictMath.pow(5.0, j);
int product;
BigDecimal bd;
try {
bd = BigDecimal.ONE.divide(new BigDecimal(product=powerOf2*powerOf5));
} catch (ArithmeticException e) {
failures++;
System.err.println((new BigDecimal(powerOf2)).toString() + " / " +
(new BigDecimal(powerOf5)).toString() + " threw an exception.");
e.printStackTrace();
}
try {
bd = new BigDecimal(powerOf2).divide(new BigDecimal(powerOf5));
} catch (ArithmeticException e) {
failures++;
System.err.println((new BigDecimal(powerOf2)).toString() + " / " +
(new BigDecimal(powerOf5)).toString() + " threw an exception.");
e.printStackTrace();
}
try {
bd = new BigDecimal(powerOf5).divide(new BigDecimal(powerOf2));
} catch (ArithmeticException e) {
failures++;
System.err.println((new BigDecimal(powerOf5)).toString() + " / " +
(new BigDecimal(powerOf2)).toString() + " threw an exception.");
e.printStackTrace();
}
}
}
return failures;
}
public static int nonTerminating() {
int failures = 0;
int[] primes = {1, 3, 7, 13, 17};
// For each pair of prime products, verify the ratio of
// non-equal products has a non-terminating expansion.
for(int i = 0; i < primes.length; i++) {
for(int j = i+1; j < primes.length; j++) {
for(int m = 0; m < primes.length; m++) {
for(int n = m+1; n < primes.length; n++) {
int dividend = primes[i] * primes[j];
int divisor = primes[m] * primes[n];
if ( ((dividend/divisor) * divisor) != dividend ) {
try {
BigDecimal quotient = (new BigDecimal(dividend).
divide(new BigDecimal(divisor)));
failures++;
System.err.println("Exact quotient " + quotient.toString() +
" returned for non-terminating fraction " +
dividend + " / " + divisor + ".");
}
catch (ArithmeticException e) {
; // Correct result
}
}
}
}
}
}
return failures;
}
public static int properScaleTests(){
int failures = 0;
BigDecimal[][] testCases = {
{new BigDecimal("1"), new BigDecimal("5"), new BigDecimal("2e-1")},
{new BigDecimal("1"), new BigDecimal("50e-1"), new BigDecimal("2e-1")},
{new BigDecimal("10e-1"), new BigDecimal("5"), new BigDecimal("2e-1")},
{new BigDecimal("1"), new BigDecimal("500e-2"), new BigDecimal("2e-1")},
{new BigDecimal("100e-2"), new BigDecimal("5"), new BigDecimal("20e-2")},
{new BigDecimal("1"), new BigDecimal("32"), new BigDecimal("3125e-5")},
{new BigDecimal("1"), new BigDecimal("64"), new BigDecimal("15625e-6")},
{new BigDecimal("1.0000000"), new BigDecimal("64"), new BigDecimal("156250e-7")},
};
for(BigDecimal[] tc : testCases) {
BigDecimal quotient;
if (! (quotient = tc[0].divide(tc[1])).equals(tc[2]) ) {
failures++;
System.err.println("Unexpected quotient from " + tc[0] + " / " + tc[1] +
"; expected " + tc[2] + " got " + quotient);
}
}
return failures;
}
public static int trailingZeroTests() {
int failures = 0;
MathContext mc = new MathContext(3, RoundingMode.FLOOR);
BigDecimal[][] testCases = {
{new BigDecimal("19"), new BigDecimal("100"), new BigDecimal("0.19")},
{new BigDecimal("21"), new BigDecimal("110"), new BigDecimal("0.190")},
};
for(BigDecimal[] tc : testCases) {
BigDecimal quotient;
if (! (quotient = tc[0].divide(tc[1], mc)).equals(tc[2]) ) {
failures++;
System.err.println("Unexpected quotient from " + tc[0] + " / " + tc[1] +
"; expected " + tc[2] + " got " + quotient);
}
}
return failures;
}
public static int scaledRoundedDivideTests() {
int failures = 0;
// Tests of the traditional scaled divide under different
// rounding modes.
// Encode rounding mode and scale for the divide in a
// BigDecimal with the significand equal to the rounding mode
// and the scale equal to the number's scale.
// {dividend, dividisor, rounding, quotient}
BigDecimal a = new BigDecimal("31415");
BigDecimal a_minus = a.negate();
BigDecimal b = new BigDecimal("10000");
BigDecimal c = new BigDecimal("31425");
BigDecimal c_minus = c.negate();
// Ad hoc tests
BigDecimal d = new BigDecimal(new BigInteger("-37361671119238118911893939591735"), 10);
BigDecimal e = new BigDecimal(new BigInteger("74723342238476237823787879183470"), 15);
BigDecimal[][] testCases = {
{a, b, BigDecimal.valueOf(ROUND_UP, 3), new BigDecimal("3.142")},
{a_minus, b, BigDecimal.valueOf(ROUND_UP, 3), new BigDecimal("-3.142")},
{a, b, BigDecimal.valueOf(ROUND_DOWN, 3), new BigDecimal("3.141")},
{a_minus, b, BigDecimal.valueOf(ROUND_DOWN, 3), new BigDecimal("-3.141")},
{a, b, BigDecimal.valueOf(ROUND_CEILING, 3), new BigDecimal("3.142")},
{a_minus, b, BigDecimal.valueOf(ROUND_CEILING, 3), new BigDecimal("-3.141")},
{a, b, BigDecimal.valueOf(ROUND_FLOOR, 3), new BigDecimal("3.141")},
{a_minus, b, BigDecimal.valueOf(ROUND_FLOOR, 3), new BigDecimal("-3.142")},
{a, b, BigDecimal.valueOf(ROUND_HALF_UP, 3), new BigDecimal("3.142")},
{a_minus, b, BigDecimal.valueOf(ROUND_HALF_UP, 3), new BigDecimal("-3.142")},
{a, b, BigDecimal.valueOf(ROUND_DOWN, 3), new BigDecimal("3.141")},
{a_minus, b, BigDecimal.valueOf(ROUND_DOWN, 3), new BigDecimal("-3.141")},
{a, b, BigDecimal.valueOf(ROUND_HALF_EVEN, 3), new BigDecimal("3.142")},
{a_minus, b, BigDecimal.valueOf(ROUND_HALF_EVEN, 3), new BigDecimal("-3.142")},
{c, b, BigDecimal.valueOf(ROUND_HALF_EVEN, 3), new BigDecimal("3.142")},
{c_minus, b, BigDecimal.valueOf(ROUND_HALF_EVEN, 3), new BigDecimal("-3.142")},
{d, e, BigDecimal.valueOf(ROUND_HALF_UP, -5), BigDecimal.valueOf(-1, -5)},
{d, e, BigDecimal.valueOf(ROUND_HALF_DOWN, -5), BigDecimal.valueOf(0, -5)},
{d, e, BigDecimal.valueOf(ROUND_HALF_EVEN, -5), BigDecimal.valueOf(0, -5)},
};
for(BigDecimal tc[] : testCases) {
int scale = tc[2].scale();
int rm = tc[2].unscaledValue().intValue();
BigDecimal quotient = tc[0].divide(tc[1], scale, rm);
if (!quotient.equals(tc[3])) {
failures++;
System.err.println("Unexpected quotient from " + tc[0] + " / " + tc[1] +
" scale " + scale + " rounding mode " + RoundingMode.valueOf(rm) +
"; expected " + tc[3] + " got " + quotient);
}
}
// 6876282
BigDecimal[][] testCases2 = {
// { dividend, divisor, expected quotient }
{ new BigDecimal(3090), new BigDecimal(7), new BigDecimal(441) },
{ new BigDecimal("309000000000000000000000"), new BigDecimal("700000000000000000000"),
new BigDecimal(441) },
{ new BigDecimal("962.430000000000"), new BigDecimal("8346463.460000000000"),
new BigDecimal("0.000115309916") },
{ new BigDecimal("18446744073709551631"), new BigDecimal("4611686018427387909"),
new BigDecimal(4) },
{ new BigDecimal("18446744073709551630"), new BigDecimal("4611686018427387909"),
new BigDecimal(4) },
{ new BigDecimal("23058430092136939523"), new BigDecimal("4611686018427387905"),
new BigDecimal(5) },
{ new BigDecimal("-18446744073709551661"), new BigDecimal("-4611686018427387919"),
new BigDecimal(4) },
{ new BigDecimal("-18446744073709551660"), new BigDecimal("-4611686018427387919"),
new BigDecimal(4) },
};
for (BigDecimal test[] : testCases2) {
BigDecimal quo = test[0].divide(test[1], RoundingMode.HALF_UP);
if (!quo.equals(test[2])) {
failures++;
System.err.println("Unexpected quotient from " + test[0] + " / " + test[1] +
" rounding mode HALF_UP" +
"; expected " + test[2] + " got " + quo);
}
}
return failures;
}
private static int divideByOneTests() {
int failures = 0;
//problematic divisor: one with scale 17
BigDecimal one = BigDecimal.ONE.setScale(17);
RoundingMode rounding = RoundingMode.UNNECESSARY;
long[][] unscaledAndScale = new long[][] {
{ Long.MAX_VALUE, 17},
{-Long.MAX_VALUE, 17},
{ Long.MAX_VALUE, 0},
{-Long.MAX_VALUE, 0},
{ Long.MAX_VALUE, 100},
{-Long.MAX_VALUE, 100}
};
for (long[] uas : unscaledAndScale) {
long unscaled = uas[0];
int scale = (int)uas[1];
BigDecimal noRound = null;
try {
noRound = BigDecimal.valueOf(unscaled, scale).
divide(one, RoundingMode.UNNECESSARY);
} catch (ArithmeticException e) {
failures++;
System.err.println("ArithmeticException for value " + unscaled
+ " and scale " + scale + " without rounding");
}
BigDecimal roundDown = null;
try {
roundDown = BigDecimal.valueOf(unscaled, scale).
divide(one, RoundingMode.DOWN);
} catch (ArithmeticException e) {
failures++;
System.err.println("ArithmeticException for value " + unscaled
+ " and scale " + scale + " with rounding down");
}
if (noRound != null && roundDown != null
&& noRound.compareTo(roundDown) != 0) {
failures++;
System.err.println("Equality failure for value " + unscaled
+ " and scale " + scale);
}
}
return failures;
}
public static void main(String argv[]) {
int failures = 0;
failures += powersOf2and5();
failures += nonTerminating();
failures += properScaleTests();
failures += trailingZeroTests();
failures += scaledRoundedDivideTests();
failures += divideByOneTests();
if (failures > 0) {
throw new RuntimeException("Incurred " + failures +
" failures while testing division.");
}
}
}