HalfFloat.java

/*
 * Copyright 2010-2014 Ning, Inc.
 * Copyright 2014 The Billing Project, LLC
 *
 * Ning licenses this file to you under the Apache License, version 2.0
 * (the "License"); you may not use this file except in compliance with the
 * License.  You may obtain a copy of the License at:
 *
 *    http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.  See the
 * License for the specific language governing permissions and limitations
 * under the License.
 */

package org.killbill.billing.plugin.meter.timeline.samples;

public class HalfFloat {

    private final short halfFloat;

    public HalfFloat(final float input) {
        halfFloat = (short) fromFloat(input);
    }

    public float getFloat() {
        return toFloat((int) halfFloat);
    }

    // These two static methods were pinched from http://stackoverflow.com/questions/6162651/half-precision-floating-point-in-java/6162687#6162687
    // The last comments on that page is the author saying "I hereby commit these to the public domain"

    // Ignores the higher 16 bits
    public static float toFloat(final int hbits) {
        int mant = hbits & 0x03ff;                                   // 10 bits mantissa
        int exp = hbits & 0x7c00;                                   // 5 bits exponent
        if (exp == 0x7c00) {                                         // NaN/Inf
            exp = 0x3fc00;                                           // -> NaN/Inf
        } else if (exp != 0) {                                         // normalized value
            exp += 0x1c000;                                          // exp - 15 + 127
            if (mant == 0 && exp > 0x1c400) {                         // smooth transition
                return Float.intBitsToFloat((hbits & 0x8000) << 16 | exp << 13 | 0x3ff);
            }
        } else if (mant != 0) {                                        // && exp==0 -> subnormal
            exp = 0x1c400;                                           // make it normal
            do {
                mant <<= 1;                                          // mantissa * 2
                exp -= 0x400;                                        // decrease exp by 1
            } while ((mant & 0x400) == 0);                           // while not normal
            mant &= 0x3ff;                                           // discard subnormal bit
        }                                                            // else +/-0 -> +/-0
        return Float.intBitsToFloat(                                 // combine all parts
                                                                     (hbits & 0x8000) << 16                                   // sign  << (31 - 15)
                                                                     | (exp | mant) << 13
                                   );                                   // value << (23 - 10)
    }

    // returns all higher 16 bits as 0 for all results
    public static int fromFloat(final float fval) {
        final int fbits = Float.floatToIntBits(fval);
        final int sign = fbits >>> 16 & 0x8000;                      // sign only
        int val = (fbits & 0x7fffffff) + 0x1000;                     // rounded value

        if (val >= 0x47800000) {                                     // might be or become NaN/Inf
            if ((fbits & 0x7fffffff) >= 0x47800000) {                // is or must become NaN/Inf

                if (val < 0x7f800000) {                              // was value but too large
                    return sign | 0x7c00;                            // make it +/-Inf
                }
                return sign | 0x7c00 |                               // remains +/-Inf or NaN
                       (fbits & 0x007fffff) >>> 13;                     // keep NaN (and Inf) bits
            }
            return sign | 0x7bff;                                    // unrounded not quite Inf
        }
        if (val >= 0x38800000)                                        // remains normalized value
        {
            return sign | val - 0x38000000 >>> 13;                   // exp - 127 + 15
        }
        if (val < 0x33000000)                                         // too small for subnormal
        {
            return sign;                                             // becomes +/-0
        }
        val = (fbits & 0x7fffffff) >>> 23;                           // tmp exp for subnormal calc
        return sign | ((fbits & 0x7fffff | 0x800000)                 // add subnormal bit
                       + (0x800000 >>> val - 102) >>> 126 - val);              // round depending on cut off; div by 2^(1-(exp-127+15)) and >> 13 | exp=0
    }

    private static String describe(final int halfFloat) {
        final int sign = (halfFloat >> 15) & 1;
        final int exponent = (halfFloat >> 10) & 0x1f;
        final double fraction = (double) (0x400 + (halfFloat & 0x3ff)) / (1.0 * 0x400);
        final double product = fraction * Math.pow(2.0, exponent - 15) * (sign == 0 ? 1.0 : -1.0);
        return String.format("HalfFloat %f, representation %x, sign %d, exponent 0x%x == 2**%d, fraction %f, product %f",
                             toFloat(halfFloat),
                             halfFloat,
                             sign,
                             exponent,
                             exponent - 15,
                             fraction,
                             product);
    }

    public static void main(String[] args) {
        System.out.printf("%f double-converted = %f\n", 200.0, toFloat(fromFloat((float) 200.0)));
        System.out.printf("%s\n", describe(fromFloat(200.0f)));
    }
}