| /* |
| * Copyright (c) 2003, 2016, 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. |
| */ |
| |
| /* |
| * 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, |
| 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, |
| 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, |
| 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; |
| } |
| |
| 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, |
| 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, |
| 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, |
| 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, |
| 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, |
| 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, 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; |
| } |
| } |
| } |
