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8289551: Conversions between bit representations of half precision values and floats
Reviewed-by: psandoz, jrose
This commit is contained in:
Joe Darcy
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2ae8e31183
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7318b22209
3 changed files with 703 additions and 0 deletions
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@ -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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