8289551: Conversions between bit representations of half precision values and floats
Reviewed-by: psandoz, jrose
This commit is contained in:
Joe Darcy
parent
2ae8e31183
commit
7318b22209
@ -30,6 +30,7 @@ import java.lang.constant.Constable;
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import java.lang.constant.ConstantDesc;
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import java.util.Optional;
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import jdk.internal.math.FloatConsts;
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import jdk.internal.math.FloatingDecimal;
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import jdk.internal.math.FloatToDecimal;
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import jdk.internal.vm.annotation.IntrinsicCandidate;
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@ -975,6 +976,198 @@ public final class Float extends Number
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@IntrinsicCandidate
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public static native float intBitsToFloat(int bits);
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/**
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* {@return the {@code float} value closest to the numerical value
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* of the argument, a floating-point binary16 value encoded in a
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* {@code short}} The conversion is exact; all binary16 values can
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* be exactly represented in {@code float}.
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*
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* Special cases:
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* <ul>
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* <li> If the argument is zero, the result is a zero with the
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* same sign as the argument.
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* <li> If the argument is infinite, the result is an infinity
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* with the same sign as the argument.
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* <li> If the argument is a NaN, the result is a NaN.
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* </ul>
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*
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* <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4>
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* The IEEE 754 standard defines binary16 as a 16-bit format, along
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* with the 32-bit binary32 format (corresponding to the {@code
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* float} type) and the 64-bit binary64 format (corresponding to
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* the {@code double} type). The binary16 format is similar to the
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* other IEEE 754 formats, except smaller, having all the usual
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* IEEE 754 values such as NaN, signed infinities, signed zeros,
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* and subnormals. The parameters (JLS {@jls 4.2.3}) for the
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* binary16 format are N = 11 precision bits, K = 5 exponent bits,
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* <i>E</i><sub><i>max</i></sub> = 15, and
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* <i>E</i><sub><i>min</i></sub> = -14.
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*
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* @apiNote
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* This method corresponds to the convertFormat operation defined
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* in IEEE 754 from the binary16 format to the binary32 format.
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* The operation of this method is analogous to a primitive
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* widening conversion (JLS {@jls 5.1.2}).
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*
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* @param floatBinary16 the binary16 value to convert to {@code float}
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* @since 20
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*/
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// @IntrinsicCandidate
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public static float float16ToFloat(short floatBinary16) {
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/*
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* The binary16 format has 1 sign bit, 5 exponent bits, and 10
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* significand bits. The exponent bias is 15.
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*/
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int bin16arg = (int)floatBinary16;
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int bin16SignBit = 0x8000 & bin16arg;
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int bin16ExpBits = 0x7c00 & bin16arg;
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int bin16SignifBits = 0x03FF & bin16arg;
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// Shift left difference in the number of significand bits in
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// the float and binary16 formats
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final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11);
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float sign = (bin16SignBit != 0) ? -1.0f : 1.0f;
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// Extract binary16 exponent, remove its bias, add in the bias
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// of a float exponent and shift to correct bit location
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// (significand width includes the implicit bit so shift one
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// less).
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int bin16Exp = (bin16ExpBits >> 10) - 15;
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if (bin16Exp == -15) {
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// For subnormal binary16 values and 0, the numerical
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// value is 2^24 * the significand as an integer (no
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// implicit bit).
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return sign * (0x1p-24f * bin16SignifBits);
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} else if (bin16Exp == 16) {
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return (bin16SignifBits == 0) ?
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sign * Float.POSITIVE_INFINITY :
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Float.intBitsToFloat((bin16SignBit << 16) |
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0x7f80_0000 |
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// Preserve NaN signif bits
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( bin16SignifBits << SIGNIF_SHIFT ));
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}
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assert -15 < bin16Exp && bin16Exp < 16;
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int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS)
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<< (FloatConsts.SIGNIFICAND_WIDTH - 1);
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// Compute and combine result sign, exponent, and significand bits.
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return Float.intBitsToFloat((bin16SignBit << 16) |
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floatExpBits |
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(bin16SignifBits << SIGNIF_SHIFT));
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}
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/**
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* {@return the floating-point binary16 value, encoded in a {@code
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* short}, closest in value to the argument}
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* The conversion is computed under the {@linkplain
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* java.math.RoundingMode#HALF_EVEN round to nearest even rounding
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* mode}.
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*
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* Special cases:
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* <ul>
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* <li> If the argument is zero, the result is a zero with the
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* same sign as the argument.
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* <li> If the argument is infinite, the result is an infinity
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* with the same sign as the argument.
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* <li> If the argument is a NaN, the result is a NaN.
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* </ul>
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*
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* The <a href="#binary16Format">binary16 format</a> is discussed in
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* more detail in the {@link #float16ToFloat} method.
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*
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* @apiNote
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* This method corresponds to the convertFormat operation defined
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* in IEEE 754 from the binary32 format to the binary16 format.
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* The operation of this method is analogous to a primitive
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* narrowing conversion (JLS {@jls 5.1.3}).
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*
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* @param f the {@code float} value to convert to binary16
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* @since 20
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*/
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// @IntrinsicCandidate
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public static short floatToFloat16(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 >= (0x1.ffcp15f + 0x0.002p15f) ) {
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return (short)(sign_bit | 0x7c00); // Positive or negative infinity
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}
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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-24f * 0.5f) { // 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 binary16
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// (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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// For binary16 subnormals, beside forcing exp to -15, retain
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// the difference expdelta = E_min - exp. This is the excess
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// shift value, in addition to 13, to be used in the
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// computations below. Further the (hidden) msb with value 1
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// in f must be involved as well.
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int expdelta = 0;
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int msb = 0x0000_0000;
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if (exp < -14) {
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expdelta = -14 - exp;
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exp = -15;
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msb = 0x0080_0000;
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}
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int f_signif_bits = doppel & 0x007f_ffff | msb;
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// Significand bits as if using rounding to zero (truncation).
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short signif_bits = (short)(f_signif_bits >> (13 + expdelta));
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// For round to nearest even, determining whether or not to
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// round up (in magnitude) is a function of the least
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// significant bit (LSB), the next bit position (the round
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// position), and the sticky bit (whether there are any
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// nonzero bits in the exact result to the right of the round
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// digit). An increment occurs in three cases:
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//
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// LSB Round Sticky
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// 0 1 1
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// 1 1 0
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// 1 1 1
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// See "Computer Arithmetic Algorithms," Koren, Table 4.9
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int lsb = f_signif_bits & (1 << 13 + expdelta);
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int round = f_signif_bits & (1 << 12 + expdelta);
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int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1);
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if (round != 0 && ((lsb | sticky) != 0 )) {
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signif_bits++;
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}
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// No bits set in significand beyond the *first* exponent bit,
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// not just the sigificand; quantity is added to the exponent
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// to implement a carry out from rounding the significand.
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assert (0xf800 & signif_bits) == 0x0;
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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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* Compares two {@code Float} objects numerically.
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*
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422
test/jdk/java/lang/Float/Binary16Conversion.java
Normal file
422
test/jdk/java/lang/Float/Binary16Conversion.java
Normal file
@ -0,0 +1,422 @@
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/*
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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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*/
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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)) {
|
||||
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);
|
||||
}
|
||||
}
|
||||
}
|
||||
88
test/jdk/java/lang/Float/Binary16ConversionNaN.java
Normal file
88
test/jdk/java/lang/Float/Binary16ConversionNaN.java
Normal file
@ -0,0 +1,88 @@
|
||||
/*
|
||||
* 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 NaN sign and significand bits are preserved across conversions
|
||||
*/
|
||||
|
||||
/*
|
||||
* The behavior tested below is an implementation property not
|
||||
* required by the specification. It would be acceptable for this
|
||||
* information to not be preserved (as long as a NaN is returned) if,
|
||||
* say, a intrinsified version using native hardware instructions
|
||||
* behaved differently.
|
||||
*
|
||||
* If that is the case, this test should be modified to disable
|
||||
* intrinsics or to otherwise not run on platforms with an differently
|
||||
* behaving intrinsic.
|
||||
*/
|
||||
public class Binary16ConversionNaN {
|
||||
public static void main(String... argv) {
|
||||
int errors = 0;
|
||||
errors += binary16NaNRoundTrip();
|
||||
|
||||
if (errors > 0)
|
||||
throw new RuntimeException(errors + " errors");
|
||||
}
|
||||
|
||||
/*
|
||||
* Put all 16-bit NaN values through a conversion loop and make
|
||||
* sure the significand, sign, and exponent are all preserved.
|
||||
*/
|
||||
private static int binary16NaNRoundTrip() {
|
||||
int errors = 0;
|
||||
final int NAN_EXPONENT = 0x7c00;
|
||||
final int SIGN_BIT = 0x8000;
|
||||
|
||||
// A NaN has a nonzero significand
|
||||
for (int i = 1; i <= 0x3ff; i++) {
|
||||
short binary16NaN = (short)(NAN_EXPONENT | i);
|
||||
assert isNaN(binary16NaN);
|
||||
errors += testRoundTrip( binary16NaN);
|
||||
errors += testRoundTrip((short)(SIGN_BIT | binary16NaN));
|
||||
}
|
||||
return errors;
|
||||
}
|
||||
|
||||
private static boolean isNaN(short binary16) {
|
||||
return ((binary16 & 0x7c00) == 0x7c00) // Max exponent and...
|
||||
&& ((binary16 & 0x03ff) != 0 ); // significand nonzero.
|
||||
}
|
||||
|
||||
private static int testRoundTrip(int i) {
|
||||
int errors = 0;
|
||||
short s = (short)i;
|
||||
float f = Float.float16ToFloat(s);
|
||||
short s2 = Float.floatToFloat16(f);
|
||||
|
||||
if (s != s2) {
|
||||
errors++;
|
||||
System.out.println("Roundtrip failure on NaN value " +
|
||||
Integer.toHexString(0xFFFF & (int)s) +
|
||||
"\t got back " + Integer.toHexString(0xFFFF & (int)s2));
|
||||
}
|
||||
return errors;
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user