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/*
* Copyright (c) 2003, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
import java.util.function.DoubleBinaryOperator;
import java.util.function.DoubleUnaryOperator;
import java.util.function.DoubleToIntFunction;
/*
* Shared static test methods for numerical tests. Sharing these
* helper test methods avoids repeated functions in the various test
* programs. The test methods return 1 for a test failure and 0 for
* success. The order of arguments to the test methods is generally
* the test name, followed by the test arguments, the computed result,
* and finally the expected result.
*/
public class Tests {
private Tests(){}; // do not instantiate
public static String toHexString(float f) {
if (!Float.isNaN(f))
return Float.toHexString(f);
else
return "NaN(0x" + Integer.toHexString(Float.floatToRawIntBits(f)) + ")";
}
public static String toHexString(double d) {
if (!Double.isNaN(d))
return Double.toHexString(d);
else
return "NaN(0x" + Long.toHexString(Double.doubleToRawLongBits(d)) + ")";
}
/**
* Return the floating-point value next larger in magnitude.
*/
public static double nextOut(double d) {
if (d > 0.0)
return Math.nextUp(d);
else
return -Math.nextUp(-d);
}
/**
* Returns unbiased exponent of a {@code float}; for
* subnormal values, the number is treated as if it were
* normalized. That is for all finite, non-zero, positive numbers
* <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is
* always in the range [1, 2).
* <p>
* Special cases:
* <ul>
* <li> If the argument is NaN, then the result is 2<sup>30</sup>.
* <li> If the argument is infinite, then the result is 2<sup>28</sup>.
* <li> If the argument is zero, then the result is -(2<sup>28</sup>).
* </ul>
*
* @param f floating-point number whose exponent is to be extracted
* @return unbiased exponent of the argument.
*/
public static int ilogb(double d) {
int exponent = Math.getExponent(d);
switch (exponent) {
case Double.MAX_EXPONENT+1: // NaN or infinity
if( Double.isNaN(d) )
return (1<<30); // 2^30
else // infinite value
return (1<<28); // 2^28
case Double.MIN_EXPONENT-1: // zero or subnormal
if(d == 0.0) {
return -(1<<28); // -(2^28)
}
else {
long transducer = Double.doubleToRawLongBits(d);
/*
* To avoid causing slow arithmetic on subnormals,
* the scaling to determine when d's significand
* is normalized is done in integer arithmetic.
* (there must be at least one "1" bit in the
* significand since zero has been screened out.
*/
// isolate significand bits
transducer &= DoubleConsts.SIGNIF_BIT_MASK;
assert(transducer != 0L);
// This loop is simple and functional. We might be
// able to do something more clever that was faster;
// e.g. number of leading zero detection on
// (transducer << (# exponent and sign bits).
while (transducer <
(1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) {
transducer *= 2;
exponent--;
}
exponent++;
assert( exponent >=
Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) &&
exponent < Double.MIN_EXPONENT);
return exponent;
}
default:
assert( exponent >= Double.MIN_EXPONENT &&
exponent <= Double.MAX_EXPONENT);
return exponent;
}
}
/**
* Returns unbiased exponent of a {@code float}; for
* subnormal values, the number is treated as if it were
* normalized. That is for all finite, non-zero, positive numbers
* <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is
* always in the range [1, 2).
* <p>
* Special cases:
* <ul>
* <li> If the argument is NaN, then the result is 2<sup>30</sup>.
* <li> If the argument is infinite, then the result is 2<sup>28</sup>.
* <li> If the argument is zero, then the result is -(2<sup>28</sup>).
* </ul>
*
* @param f floating-point number whose exponent is to be extracted
* @return unbiased exponent of the argument.
*/
public static int ilogb(float f) {
int exponent = Math.getExponent(f);
switch (exponent) {
case Float.MAX_EXPONENT+1: // NaN or infinity
if( Float.isNaN(f) )
return (1<<30); // 2^30
else // infinite value
return (1<<28); // 2^28
case Float.MIN_EXPONENT-1: // zero or subnormal
if(f == 0.0f) {
return -(1<<28); // -(2^28)
}
else {
int transducer = Float.floatToRawIntBits(f);
/*
* To avoid causing slow arithmetic on subnormals,
* the scaling to determine when f's significand
* is normalized is done in integer arithmetic.
* (there must be at least one "1" bit in the
* significand since zero has been screened out.
*/
// isolate significand bits
transducer &= FloatConsts.SIGNIF_BIT_MASK;
assert(transducer != 0);
// This loop is simple and functional. We might be
// able to do something more clever that was faster;
// e.g. number of leading zero detection on
// (transducer << (# exponent and sign bits).
while (transducer <
(1 << (FloatConsts.SIGNIFICAND_WIDTH - 1))) {
transducer *= 2;
exponent--;
}
exponent++;
assert( exponent >=
Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1) &&
exponent < Float.MIN_EXPONENT);
return exponent;
}
default:
assert( exponent >= Float.MIN_EXPONENT &&
exponent <= Float.MAX_EXPONENT);
return exponent;
}
}
/**
* Returns {@code true} if the unordered relation holds
* between the two arguments. When two floating-point values are
* unordered, one value is neither less than, equal to, nor
* greater than the other. For the unordered relation to be true,
* at least one argument must be a {@code NaN}.
*
* @param arg1 the first argument
* @param arg2 the second argument
* @return {@code true} if at least one argument is a NaN,
* {@code false} otherwise.
*/
public static boolean isUnordered(float arg1, float arg2) {
return Float.isNaN(arg1) || Float.isNaN(arg2);
}
/**
* Returns {@code true} if the unordered relation holds
* between the two arguments. When two floating-point values are
* unordered, one value is neither less than, equal to, nor
* greater than the other. For the unordered relation to be true,
* at least one argument must be a {@code NaN}.
*
* @param arg1 the first argument
* @param arg2 the second argument
* @return {@code true} if at least one argument is a NaN,
* {@code false} otherwise.
*/
public static boolean isUnordered(double arg1, double arg2) {
return Double.isNaN(arg1) || Double.isNaN(arg2);
}
public static int test(String testName, float input,
boolean result, boolean expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName, double input,
boolean result, boolean expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName, float input1, float input2,
boolean result, boolean expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
}
return 0;
}
public static int test(String testName, double input1, double input2,
boolean result, boolean expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
}
return 0;
}
public static int test(String testName, float input,
int result, int expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
}
return 0;
}
public static int test(String testName,
double input,
DoubleToIntFunction func,
int expected) {
return test(testName, input, func.applyAsInt(input), expected);
}
public static int test(String testName, double input,
int result, int expected) {
if (expected != result) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\n" +
"\tgot " + result + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName, float input,
float result, float expected) {
if (Float.compare(expected, result) != 0 ) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
double input,
DoubleUnaryOperator func,
double expected) {
return test(testName, input, func.applyAsDouble(input), expected);
}
public static int test(String testName, double input,
double result, double expected) {
if (Double.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
float input1, double input2,
float result, float expected) {
if (Float.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
double input1, double input2,
DoubleBinaryOperator func,
double expected) {
return test(testName, input1, input2, func.applyAsDouble(input1, input2), expected);
}
public static int test(String testName,
double input1, double input2,
double result, double expected) {
if (Double.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
float input1, int input2,
float result, float expected) {
if (Float.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
double input1, int input2,
double result, double expected) {
if (Double.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
public static int test(String testName,
float input1, float input2, float input3,
float result, float expected) {
if (Float.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ") and"
+ input3 + "\t(" + toHexString(input3) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
@FunctionalInterface
public interface DoubleTernaryOperator {
double applyAsDouble(double input1, double input2, double input3);
}
public static int test(String testName,
double input1, double input2, double input3,
DoubleTernaryOperator func, double expected) {
return test(testName, input1, input2, input3, func.applyAsDouble(input1, input2, input3), expected);
}
public static int test(String testName,
double input1, double input2, double input3,
double result, double expected) {
if (Double.compare(expected, result ) != 0) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ") and"
+ input3 + "\t(" + toHexString(input3) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ").");
return 1;
} else {
return 0;
}
}
static int testUlpCore(double result, double expected, double ulps) {
// We assume we won't be unlucky and have an inexact expected
// be nextDown(2^i) when 2^i would be the correctly rounded
// answer. This would cause the ulp size to be half as large
// as it should be, doubling the measured error).
if (Double.compare(expected, result) == 0) {
return 0; // result and expected are equivalent
} else {
if( ulps == 0.0) {
// Equivalent results required but not found
return 1;
} else {
double difference = expected - result;
if (isUnordered(expected, result) ||
Double.isNaN(difference) ||
// fail if greater than or unordered
!(Math.abs( difference/Math.ulp(expected) ) <= Math.abs(ulps)) ) {
return 1;
} else {
return 0;
}
}
}
}
// One input argument.
public static int testUlpDiff(String testName, double input,
DoubleUnaryOperator func, double expected, double ulps) {
return testUlpDiff(testName, input, func.applyAsDouble(input), expected, ulps);
}
public static int testUlpDiff(String testName, double input,
double result, double expected, double ulps) {
int code = testUlpCore(result, expected, ulps);
if (code == 1) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ");\n" +
"\tdifference greater than ulp tolerance " + ulps);
}
return code;
}
// Two input arguments.
public static int testUlpDiff(String testName, double input1, double input2,
DoubleBinaryOperator func, double expected, double ulps) {
return testUlpDiff(testName, input1, input2, func.applyAsDouble(input1, input2), expected, ulps);
}
public static int testUlpDiff(String testName, double input1, double input2,
double result, double expected, double ulps) {
int code = testUlpCore(result, expected, ulps);
if (code == 1) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor inputs " + input1 + "\t(" + toHexString(input1) + ") and "
+ input2 + "\t(" + toHexString(input2) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ");\n" +
"\tdifference greater than ulp tolerance " + ulps);
}
return code;
}
// For a successful test, the result must be within the ulp bound of
// expected AND the result must have absolute value less than or
// equal to absBound.
public static int testUlpDiffWithAbsBound(String testName, double input,
DoubleUnaryOperator func, double expected,
double ulps, double absBound) {
return testUlpDiffWithAbsBound(testName, input,
func.applyAsDouble(input), expected,
ulps, absBound);
}
public static int testUlpDiffWithAbsBound(String testName, double input,
double result, double expected,
double ulps, double absBound) {
int code = 0; // return code value
if (!(StrictMath.abs(result) <= StrictMath.abs(absBound)) &&
!Double.isNaN(expected)) {
code = 1;
} else
code = testUlpCore(result, expected, ulps);
if (code == 1) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ");\n" +
"\tdifference greater than ulp tolerance " + ulps +
" or the result has larger magnitude than " + absBound);
}
return code;
}
// For a successful test, the result must be within the ulp bound of
// expected AND the result must have absolute value greater than
// or equal to the lowerBound.
public static int testUlpDiffWithLowerBound(String testName, double input,
DoubleUnaryOperator func, double expected,
double ulps, double lowerBound) {
return testUlpDiffWithLowerBound(testName, input,
func.applyAsDouble(input), expected,
ulps, lowerBound);
}
public static int testUlpDiffWithLowerBound(String testName, double input,
double result, double expected,
double ulps, double lowerBound) {
int code = 0; // return code value
if (!(result >= lowerBound) && !Double.isNaN(expected)) {
code = 1;
} else {
code = testUlpCore(result, expected, ulps);
}
if (code == 1) {
System.err.println("Failure for " + testName +
":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")" +
"\n\texpected " + expected + "\t(" + toHexString(expected) + ")" +
"\n\tgot " + result + "\t(" + toHexString(result) + ");" +
"\ndifference greater than ulp tolerance " + ulps +
" or result not greater than or equal to the bound " + lowerBound);
}
return code;
}
public static int testTolerance(String testName, double input,
DoubleUnaryOperator func, double expected, double tolerance) {
return testTolerance(testName, input, func.applyAsDouble(input), expected, tolerance);
}
public static int testTolerance(String testName, double input,
double result, double expected, double tolerance) {
if (Double.compare(expected, result ) != 0) {
double difference = expected - result;
if (isUnordered(expected, result) ||
Double.isNaN(difference) ||
// fail if greater than or unordered
!(Math.abs((difference)/expected) <= StrictMath.pow(10, -tolerance)) ) {
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\texpected " + expected + "\t(" + toHexString(expected) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ");\n" +
"\tdifference greater than tolerance 10^-" + tolerance);
return 1;
}
return 0;
} else {
return 0;
}
}
// For a successful test, the result must be within the upper and
// lower bounds.
public static int testBounds(String testName, double input, DoubleUnaryOperator func,
double bound1, double bound2) {
return testBounds(testName, input, func.applyAsDouble(input), bound1, bound2);
}
public static int testBounds(String testName, double input, double result,
double bound1, double bound2) {
if ((result >= bound1 && result <= bound2) ||
(result <= bound1 && result >= bound2))
return 0;
else {
double lowerBound = Math.min(bound1, bound2);
double upperBound = Math.max(bound1, bound2);
System.err.println("Failure for " + testName + ":\n" +
"\tFor input " + input + "\t(" + toHexString(input) + ")\n" +
"\tgot " + result + "\t(" + toHexString(result) + ");\n" +
"\toutside of range\n" +
"\t[" + lowerBound + "\t(" + toHexString(lowerBound) + "), " +
upperBound + "\t(" + toHexString(upperBound) + ")]");
return 1;
}
}
}
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