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