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*
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* 2 along with this work; if not, write to the Free Software Foundation,
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/*
* @test
* @bug 4851638 4939441
* @summary Tests for {Math, StrictMath}.log1p
* @author Joseph D. Darcy
* @key randomness
*/
public class Log1pTests {
private Log1pTests(){}
static final double infinityD = Double.POSITIVE_INFINITY;
static final double NaNd = Double.NaN;
/**
* Formulation taken from HP-15C Advanced Functions Handbook, part
* number HP 0015-90011, p 181. This is accurate to a few ulps.
*/
static double hp15cLogp(double x) {
double u = 1.0 + x;
return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
}
/*
* The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
*
* x - x^2/2 + x^3/3 - ... -(-x^j)/j
*
* Therefore, for small values of x, log1p(x) ~= x. For large
* values of x, log1p(x) ~= log(x).
*
* Also x/(x+1) < ln(1+x) < x
*/
static int testLog1p() {
int failures = 0;
double [][] testCases = {
{Double.NaN, NaNd},
{Double.longBitsToDouble(0x7FF0000000000001L), NaNd},
{Double.longBitsToDouble(0xFFF0000000000001L), NaNd},
{Double.longBitsToDouble(0x7FF8555555555555L), NaNd},
{Double.longBitsToDouble(0xFFF8555555555555L), NaNd},
{Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd},
{Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
{Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
{Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
{Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
{Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
{Double.NEGATIVE_INFINITY, NaNd},
{-8.0, NaNd},
{-1.0, -infinityD},
{-0.0, -0.0},
{+0.0, +0.0},
{infinityD, infinityD},
};
// Test special cases
for(int i = 0; i < testCases.length; i++) {
failures += testLog1pCaseWithUlpDiff(testCases[i][0],
testCases[i][1], 0);
}
// For |x| < 2^-54 log1p(x) ~= x
for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
double d = Math.scalb(2, i);
failures += testLog1pCase(d, d);
failures += testLog1pCase(-d, -d);
}
// For x > 2^53 log1p(x) ~= log(x)
for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
double d = Math.scalb(2, i);
failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
}
// Construct random values with exponents ranging from -53 to
// 52 and compare against HP-15C formula.
java.util.Random rand = new java.util.Random();
for(int i = 0; i < 1000; i++) {
double d = rand.nextDouble();
d = Math.scalb(d, -53 - Tests.ilogb(d));
for(int j = -53; j <= 52; j++) {
failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
d *= 2.0; // increase exponent by 1
}
}
// Test for monotonicity failures near values y-1 where y ~=
// e^x. Test two numbers before and two numbers after each
// chosen value; i.e.
//
// pcNeighbors[] =
// {nextDown(nextDown(pc)),
// nextDown(pc),
// pc,
// nextUp(pc),
// nextUp(nextUp(pc))}
//
// and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
{
double pcNeighbors[] = new double[5];
double pcNeighborsLog1p[] = new double[5];
double pcNeighborsStrictLog1p[] = new double[5];
for(int i = -36; i <= 36; i++) {
double pc = StrictMath.pow(Math.E, i) - 1;
pcNeighbors[2] = pc;
pcNeighbors[1] = Math.nextDown(pc);
pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
pcNeighbors[3] = Math.nextUp(pc);
pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
for(int j = 0; j < pcNeighbors.length; j++) {
pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]);
pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
}
for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) {
failures++;
System.err.println("Monotonicity failure for Math.log1p on " +
pcNeighbors[j] + " and " +
pcNeighbors[j+1] + "\n\treturned " +
pcNeighborsLog1p[j] + " and " +
pcNeighborsLog1p[j+1] );
}
if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) {
failures++;
System.err.println("Monotonicity failure for StrictMath.log1p on " +
pcNeighbors[j] + " and " +
pcNeighbors[j+1] + "\n\treturned " +
pcNeighborsStrictLog1p[j] + " and " +
pcNeighborsStrictLog1p[j+1] );
}
}
}
}
return failures;
}
public static int testLog1pCase(double input,
double expected) {
return testLog1pCaseWithUlpDiff(input, expected, 1);
}
public static int testLog1pCaseWithUlpDiff(double input,
double expected,
double ulps) {
int failures = 0;
failures += Tests.testUlpDiff("Math.lop1p(double",
input, Math.log1p(input),
expected, ulps);
failures += Tests.testUlpDiff("StrictMath.log1p(double",
input, StrictMath.log1p(input),
expected, ulps);
return failures;
}
public static void main(String argv[]) {
int failures = 0;
failures += testLog1p();
if (failures > 0) {
System.err.println("Testing log1p incurred "
+ failures + " failures.");
throw new RuntimeException();
}
}
}