@Test
public void testBinomialCoefficient() {
long[] bcoef5 = {1, 5, 10, 10, 5, 1};
long[] bcoef6 = {1, 6, 15, 20, 15, 6, 1};
for (int i = 0; i < 6; i++) {
Assert.assertEquals("5 choose " + i, bcoef5[i], ArithmeticUtils.binomialCoefficient(5, i));
}
for (int i = 0; i < 7; i++) {
Assert.assertEquals("6 choose " + i, bcoef6[i], ArithmeticUtils.binomialCoefficient(6, i));
}
for (int n = 1; n < 10; n++) {
for (int k = 0; k <= n; k++) {
Assert.assertEquals(
n + " choose " + k,
binomialCoefficient(n, k),
ArithmeticUtils.binomialCoefficient(n, k));
Assert.assertEquals(
n + " choose " + k,
binomialCoefficient(n, k),
ArithmeticUtils.binomialCoefficientDouble(n, k),
Double.MIN_VALUE);
Assert.assertEquals(
n + " choose " + k,
FastMath.log(binomialCoefficient(n, k)),
ArithmeticUtils.binomialCoefficientLog(n, k),
10E-12);
}
}
int[] n = {34, 66, 100, 1500, 1500};
int[] k = {17, 33, 10, 1500 - 4, 4};
for (int i = 0; i < n.length; i++) {
long expected = binomialCoefficient(n[i], k[i]);
Assert.assertEquals(
n[i] + " choose " + k[i], expected, ArithmeticUtils.binomialCoefficient(n[i], k[i]));
Assert.assertEquals(
n[i] + " choose " + k[i],
expected,
ArithmeticUtils.binomialCoefficientDouble(n[i], k[i]),
0.0);
Assert.assertEquals(
"log(" + n[i] + " choose " + k[i] + ")",
FastMath.log(expected),
ArithmeticUtils.binomialCoefficientLog(n[i], k[i]),
0.0);
}
}
@Test
public void testFactorial() {
for (int i = 1; i < 21; i++) {
Assert.assertEquals(i + "! ", factorial(i), ArithmeticUtils.factorial(i));
Assert.assertEquals(
i + "! ", factorial(i), ArithmeticUtils.factorialDouble(i), Double.MIN_VALUE);
Assert.assertEquals(
i + "! ", FastMath.log(factorial(i)), ArithmeticUtils.factorialLog(i), 10E-12);
}
Assert.assertEquals("0", 1, ArithmeticUtils.factorial(0));
Assert.assertEquals("0", 1.0d, ArithmeticUtils.factorialDouble(0), 1E-14);
Assert.assertEquals("0", 0.0d, ArithmeticUtils.factorialLog(0), 1E-14);
}
/** Tests correctness for large n and sharpness of upper bound in API doc JIRA: MATH-241 */
@Test
public void testBinomialCoefficientLarge() throws Exception {
// This tests all legal and illegal values for n <= 200.
for (int n = 0; n <= 200; n++) {
for (int k = 0; k <= n; k++) {
long ourResult = -1;
long exactResult = -1;
boolean shouldThrow = false;
boolean didThrow = false;
try {
ourResult = ArithmeticUtils.binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
didThrow = true;
}
try {
exactResult = binomialCoefficient(n, k);
} catch (MathArithmeticException ex) {
shouldThrow = true;
}
Assert.assertEquals(n + " choose " + k, exactResult, ourResult);
Assert.assertEquals(n + " choose " + k, shouldThrow, didThrow);
Assert.assertTrue(n + " choose " + k, (n > 66 || !didThrow));
if (!shouldThrow && exactResult > 1) {
Assert.assertEquals(
n + " choose " + k,
1.,
ArithmeticUtils.binomialCoefficientDouble(n, k) / exactResult,
1e-10);
Assert.assertEquals(
n + " choose " + k,
1,
ArithmeticUtils.binomialCoefficientLog(n, k) / FastMath.log(exactResult),
1e-10);
}
}
}
long ourResult = ArithmeticUtils.binomialCoefficient(300, 3);
long exactResult = binomialCoefficient(300, 3);
Assert.assertEquals(exactResult, ourResult);
ourResult = ArithmeticUtils.binomialCoefficient(700, 697);
exactResult = binomialCoefficient(700, 697);
Assert.assertEquals(exactResult, ourResult);
// This one should throw
try {
ArithmeticUtils.binomialCoefficient(700, 300);
Assert.fail("Expecting MathArithmeticException");
} catch (MathArithmeticException ex) {
// Expected
}
int n = 10000;
ourResult = ArithmeticUtils.binomialCoefficient(n, 3);
exactResult = binomialCoefficient(n, 3);
Assert.assertEquals(exactResult, ourResult);
Assert.assertEquals(1, ArithmeticUtils.binomialCoefficientDouble(n, 3) / exactResult, 1e-10);
Assert.assertEquals(
1, ArithmeticUtils.binomialCoefficientLog(n, 3) / FastMath.log(exactResult), 1e-10);
}