425 lines
19 KiB
Java
425 lines
19 KiB
Java
/*
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* Copyright (c) 2022, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/*
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* @test
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* @bug 8289551
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* @summary Verify conversion between float and the binary16 format
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* @library ../Math
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* @build FloatConsts
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* @run main Binary16Conversion
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* @run main/othervm -XX:+UnlockDiagnosticVMOptions
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* -XX:DisableIntrinsic=_float16ToFloat,_floatToFloat16 Binary16Conversion
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*/
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public class Binary16Conversion {
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public static void main(String... argv) {
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int errors = 0;
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errors += binary16RoundTrip();
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// Note that helper methods do sign-symmetric testing
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errors += binary16CardinalValues();
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errors += roundFloatToBinary16();
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errors += roundFloatToBinary16HalfWayCases();
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errors += roundFloatToBinary16FullBinade();
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errors += alternativeImplementation();
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if (errors > 0)
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throw new RuntimeException(errors + " errors");
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}
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/*
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* Put all 16-bit values through a conversion loop and make sure
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* the values are preserved (NaN bit patterns notwithstanding).
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*/
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private static int binary16RoundTrip() {
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int errors = 0;
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for (int i = Short.MIN_VALUE; i < Short.MAX_VALUE; i++) {
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short s = (short)i;
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float f = Float.float16ToFloat(s);
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short s2 = Float.floatToFloat16(f);
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if (!Binary16.equivalent(s, s2)) {
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errors++;
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System.out.println("Roundtrip failure on " +
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Integer.toHexString(0xFFFF & (int)s) +
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"\t got back " + Integer.toHexString(0xFFFF & (int)s2));
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}
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}
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return errors;
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}
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private static int binary16CardinalValues() {
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int errors = 0;
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// Encode short value for different binary16 cardinal values as an
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// integer-valued float.
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float[][] testCases = {
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{Binary16.POSITIVE_ZERO, +0.0f},
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{Binary16.MIN_VALUE, 0x1.0p-24f},
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{Binary16.MAX_SUBNORMAL, 0x1.ff8p-15f},
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{Binary16.MIN_NORMAL, 0x1.0p-14f},
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{Binary16.ONE, 1.0f},
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{Binary16.MAX_VALUE, 65504.0f},
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{Binary16.POSITIVE_INFINITY, Float.POSITIVE_INFINITY},
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};
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// Check conversions in both directions
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// short -> float
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for (var testCase : testCases) {
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errors += compareAndReportError((short)testCase[0],
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testCase[1]);
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}
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// float -> short
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for (var testCase : testCases) {
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errors += compareAndReportError(testCase[1],
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(short)testCase[0]);
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}
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return errors;
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}
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private static int roundFloatToBinary16() {
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int errors = 0;
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float[][] testCases = {
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// Test all combinations of LSB, round, and sticky bit
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// LSB = 0, test combination of round and sticky
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{0x1.ff8000p-1f, (short)0x3bfe}, // round = 0, sticky = 0
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{0x1.ff8010p-1f, (short)0x3bfe}, // round = 0, sticky = 1
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{0x1.ffa000p-1f, (short)0x3bfe}, // round = 1, sticky = 0
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{0x1.ffa010p-1f, (short)0x3bff}, // round = 1, sticky = 1 => ++
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// LSB = 1, test combination of round and sticky
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{0x1.ffc000p-1f, Binary16.ONE-1}, // round = 0, sticky = 0
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{0x1.ffc010p-1f, Binary16.ONE-1}, // round = 0, sticky = 1
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{0x1.ffe000p-1f, Binary16.ONE}, // round = 1, sticky = 0 => ++
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{0x1.ffe010p-1f, Binary16.ONE}, // round = 1, sticky = 1 => ++
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// Test subnormal rounding
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// Largest subnormal binary16 0x03ff => 0x1.ff8p-15f; LSB = 1
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{0x1.ff8000p-15f, Binary16.MAX_SUBNORMAL}, // round = 0, sticky = 0
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{0x1.ff8010p-15f, Binary16.MAX_SUBNORMAL}, // round = 0, sticky = 1
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{0x1.ffc000p-15f, Binary16.MIN_NORMAL}, // round = 1, sticky = 0 => ++
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{0x1.ffc010p-15f, Binary16.MIN_NORMAL}, // round = 1, sticky = 1 => ++
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// Test rounding near binary16 MIN_VALUE
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// Smallest in magnitude subnormal binary16 value 0x0001 => 0x1.0p-24f
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// Half-way case,0x1.0p-25f, and smaller should round down to zero
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{0x1.fffffep-26f, Binary16.POSITIVE_ZERO}, // nextDown in float
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{0x1.000000p-25f, Binary16.POSITIVE_ZERO},
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{0x1.000002p-25f, Binary16.MIN_VALUE}, // nextUp in float
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{0x1.100000p-25f, Binary16.MIN_VALUE},
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// Test rounding near overflow threshold
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// Largest normal binary16 number 0x7bff => 0x1.ffcp15f; LSB = 1
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{0x1.ffc000p15f, Binary16.MAX_VALUE}, // round = 0, sticky = 0
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{0x1.ffc010p15f, Binary16.MAX_VALUE}, // round = 0, sticky = 1
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{0x1.ffe000p15f, Binary16.POSITIVE_INFINITY}, // round = 1, sticky = 0 => ++
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{0x1.ffe010p15f, Binary16.POSITIVE_INFINITY}, // round = 1, sticky = 1 => ++
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};
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for (var testCase : testCases) {
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errors += compareAndReportError(testCase[0],
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(short)testCase[1]);
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}
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return errors;
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}
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private static int roundFloatToBinary16HalfWayCases() {
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int errors = 0;
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// Test rounding of exact half-way cases between each pair of
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// finite exactly-representable binary16 numbers. Also test
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// rounding of half-way +/- ulp of the *float* value.
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// Additionally, test +/- float ulp of the endpoints. (Other
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// tests in this file make sure all short values round-trip so
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// that doesn't need to be tested here.)
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for (int i = Binary16.POSITIVE_ZERO; // 0x0000
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i <= Binary16.MAX_VALUE; // 0x7bff
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i += 2) { // Check every even/odd pair once
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short lower = (short) i;
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short upper = (short)(i+1);
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float lowerFloat = Float.float16ToFloat(lower);
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float upperFloat = Float.float16ToFloat(upper);
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assert lowerFloat < upperFloat;
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float midway = (lowerFloat + upperFloat) * 0.5f; // Exact midpoint
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errors += compareAndReportError(Math.nextUp(lowerFloat), lower);
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errors += compareAndReportError(Math.nextDown(midway), lower);
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// Under round to nearest even, the midway point will
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// round *down* to the (even) lower endpoint.
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errors += compareAndReportError( midway, lower);
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errors += compareAndReportError(Math.nextUp( midway), upper);
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errors += compareAndReportError(Math.nextDown(upperFloat), upper);
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}
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// More testing around the overflow threshold
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// Binary16.ulp(Binary16.MAX_VALUE) == 32.0f; test around Binary16.MAX_VALUE + 1/2 ulp
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float binary16_MAX_VALUE = Float.float16ToFloat(Binary16.MAX_VALUE);
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float binary16_MAX_VALUE_halfUlp = binary16_MAX_VALUE + 16.0f;
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errors += compareAndReportError(Math.nextDown(binary16_MAX_VALUE), Binary16.MAX_VALUE);
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errors += compareAndReportError( binary16_MAX_VALUE, Binary16.MAX_VALUE);
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errors += compareAndReportError(Math.nextUp( binary16_MAX_VALUE), Binary16.MAX_VALUE);
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// Binary16.MAX_VALUE is an "odd" value since its LSB = 1 so
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// the half-way value greater than Binary16.MAX_VALUE should
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// round up to the next even value, in this case Binary16.POSITIVE_INFINITY.
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errors += compareAndReportError(Math.nextDown(binary16_MAX_VALUE_halfUlp), Binary16.MAX_VALUE);
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errors += compareAndReportError( binary16_MAX_VALUE_halfUlp, Binary16.POSITIVE_INFINITY);
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errors += compareAndReportError(Math.nextUp( binary16_MAX_VALUE_halfUlp), Binary16.POSITIVE_INFINITY);
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return errors;
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}
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private static int compareAndReportError(float input,
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short expected) {
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// Round to nearest even is sign symmetric
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return compareAndReportError0( input, expected) +
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compareAndReportError0(-input, Binary16.negate(expected));
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}
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private static int compareAndReportError0(float input,
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short expected) {
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short actual = Float.floatToFloat16(input);
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if (!Binary16.equivalent(actual, expected)) {
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System.out.println("Unexpected result of converting " +
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Float.toHexString(input) +
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" to short. Expected 0x" + Integer.toHexString(0xFFFF & expected) +
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" got 0x" + Integer.toHexString(0xFFFF & actual));
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return 1;
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}
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return 0;
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}
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private static int compareAndReportError0(short input,
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float expected) {
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float actual = Float.float16ToFloat(input);
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if (Float.compare(actual, expected) != 0) {
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System.out.println("Unexpected result of converting " +
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Integer.toHexString(input & 0xFFFF) +
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" to float. Expected " + Float.toHexString(expected) +
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" got " + Float.toHexString(actual));
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return 1;
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}
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return 0;
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}
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private static int compareAndReportError(short input,
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float expected) {
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// Round to nearest even is sign symmetric
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return compareAndReportError0( input, expected) +
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compareAndReportError0(Binary16.negate(input), -expected);
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}
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private static int roundFloatToBinary16FullBinade() {
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int errors = 0;
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// For each float value between 1.0 and less than 2.0
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// (i.e. set of float values with an exponent of 0), convert
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// each value to binary16 and then convert that binary16 value
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// back to float.
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//
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// Any exponent could be used; the maximum exponent for normal
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// values would not exercise the full set of code paths since
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// there is an up-front check on values that would overflow,
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// which correspond to a ripple-carry of the significand that
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// bumps the exponent.
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short previous = (short)0;
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for (int i = Float.floatToIntBits(1.0f);
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i <= Float.floatToIntBits(Math.nextDown(2.0f));
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i++) {
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// (Could also express the loop control directly in terms
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// of floating-point operations, incrementing by ulp(1.0),
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// etc.)
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float f = Float.intBitsToFloat(i);
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short f_as_bin16 = Float.floatToFloat16(f);
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short f_as_bin16_down = (short)(f_as_bin16 - 1);
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short f_as_bin16_up = (short)(f_as_bin16 + 1);
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// Across successive float values to convert to binary16,
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// the binary16 results should be semi-monotonic,
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// non-decreasing in this case.
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// Only positive binary16 values so can compare using integer operations
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if (f_as_bin16 < previous) {
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errors++;
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System.out.println("Semi-monotonicity violation observed on " +
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Integer.toHexString(0xfff & f_as_bin16));
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}
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previous = f_as_bin16;
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// If round-to-nearest was correctly done, when exactly
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// mapped back to float, f_as_bin16 should be at least as
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// close as either of its neighbors to the original value
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// of f.
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float f_prime_down = Float.float16ToFloat(f_as_bin16_down);
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float f_prime = Float.float16ToFloat(f_as_bin16);
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float f_prime_up = Float.float16ToFloat(f_as_bin16_up);
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float f_prime_diff = Math.abs(f - f_prime);
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if (f_prime_diff == 0.0) {
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continue;
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}
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float f_prime_down_diff = Math.abs(f - f_prime_down);
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float f_prime_up_diff = Math.abs(f - f_prime_up);
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if (f_prime_diff > f_prime_down_diff ||
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f_prime_diff > f_prime_up_diff) {
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errors++;
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System.out.println("Round-to-nearest violation on converting " +
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Float.toHexString(f) + " to binary16 and back.");
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}
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}
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return errors;
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}
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private static int alternativeImplementation() {
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int errors = 0;
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// For exhaustive test of all float values use
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// for (long ell = Integer.MIN_VALUE; ell <= Integer.MAX_VALUE; ell++) {
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for (long ell = Float.floatToIntBits(2.0f);
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ell <= Float.floatToIntBits(4.0f);
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ell++) {
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float f = Float.intBitsToFloat((int)ell);
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short s1 = Float.floatToFloat16(f);
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short s2 = altFloatToFloat16(f);
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if (s1 != s2) {
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errors++;
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System.out.println("Different conversion of float value " + Float.toHexString(f));
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}
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}
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return errors;
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}
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/*
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* Rely on float operations to do rounding in both normal and
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* subnormal binary16 cases.
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*/
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public static short altFloatToFloat16(float f) {
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int doppel = Float.floatToRawIntBits(f);
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short sign_bit = (short)((doppel & 0x8000_0000) >> 16);
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if (Float.isNaN(f)) {
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// Preserve sign and attempt to preserve significand bits
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return (short)(sign_bit
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| 0x7c00 // max exponent + 1
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// Preserve high order bit of float NaN in the
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// binary16 result NaN (tenth bit); OR in remaining
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// bits into lower 9 bits of binary 16 significand.
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| (doppel & 0x007f_e000) >> 13 // 10 bits
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| (doppel & 0x0000_1ff0) >> 4 // 9 bits
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| (doppel & 0x0000_000f)); // 4 bits
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}
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float abs_f = Math.abs(f);
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// The overflow threshold is binary16 MAX_VALUE + 1/2 ulp
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if (abs_f >= (65504.0f + 16.0f) ) {
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return (short)(sign_bit | 0x7c00); // Positive or negative infinity
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} else {
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// Smallest magnitude nonzero representable binary16 value
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// is equal to 0x1.0p-24; half-way and smaller rounds to zero.
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if (abs_f <= 0x1.0p-25f) { // Covers float zeros and subnormals.
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return sign_bit; // Positive or negative zero
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}
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// Dealing with finite values in exponent range of
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// binary16 (when rounding is done, could still round up)
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int exp = Math.getExponent(f);
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assert -25 <= exp && exp <= 15;
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short signif_bits;
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if (exp <= -15) { // scale down to float subnormal range to do rounding
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// Use a float multiply to compute the correct
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// trailing significand bits for a binary16 subnormal.
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//
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// The exponent range of normalized binary16 subnormal
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// values is [-24, -15]. The exponent range of float
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// subnormals is [-149, -140]. Multiply abs_f down by
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// 2^(-125) -- since (-125 = -149 - (-24)) -- so that
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// the trailing bits of a subnormal float represent
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// the correct trailing bits of a binary16 subnormal.
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exp = -15; // Subnormal encoding using -E_max.
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float f_adjust = abs_f * 0x1.0p-125f;
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// In case the significand rounds up and has a carry
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// propagate all the way up, take the bottom 11 bits
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// rather than bottom 10 bits. Adding this value,
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// rather than OR'ing htis value, will cause the right
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// exponent adjustment.
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signif_bits = (short)(Float.floatToRawIntBits(f_adjust) & 0x07ff);
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return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) );
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} else {
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// Scale down to subnormal range to round off excess bits
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int scalingExp = -139 - exp;
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float scaled = Math.scalb(Math.scalb(f, scalingExp),
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-scalingExp);
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exp = Math.getExponent(scaled);
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doppel = Float.floatToRawIntBits(scaled);
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signif_bits = (short)((doppel & 0x007f_e000) >>
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(FloatConsts.SIGNIFICAND_WIDTH - 11));
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return (short)(sign_bit | ( ((exp + 15) << 10) | signif_bits ) );
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}
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}
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}
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public static class Binary16 {
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public static final short POSITIVE_INFINITY = (short)0x7c00;
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public static final short MAX_VALUE = 0x7bff;
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public static final short ONE = 0x3c00;
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public static final short MIN_NORMAL = 0x0400;
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public static final short MAX_SUBNORMAL = 0x03ff;
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public static final short MIN_VALUE = 0x0001;
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public static final short POSITIVE_ZERO = 0x0000;
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public static boolean isNaN(short binary16) {
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return ((binary16 & 0x7c00) == 0x7c00) // Max exponent and...
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&& ((binary16 & 0x03ff) != 0 ); // significand nonzero.
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}
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public static short negate(short binary16) {
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return (short)(binary16 ^ 0x8000 ); // Flip only sign bit.
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}
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public static boolean equivalent(short bin16_1, short bin16_2) {
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return (bin16_1 == bin16_2) ||
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isNaN(bin16_1) && isNaN(bin16_2);
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}
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}
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}
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