Summary

Add fused multiply-add methods to Math and StrictMath.

Problem

A fused multiply-add method is not included in Java's math libraries.

More and more processors are including this operation as an instruction.

Solution

Add float and double fma methods to the Java math libraries.

Specification

// The following specifications are duplicated in Math and StrictMath.

    /**
     * Returns the fused multiply add of the three arguments;
     * that is, returns the exact product of the first two arguments
     * summed with the third argument and then rounded once to the
     * nearest {@code double}.
     *
     * The rounding is done using the {@linkplain
     * java.math.RoundingMode#HALF_EVEN round to nearest even
     * rounding mode}.
     *
     * In contrast, if {@code a * b + c} is evaluated as a regular
     * floating-point expression, two rounding errors are involved,
     * the first for the multiply operation, the second for the
     * addition operation.
     *
     * <p>Special cases:
     * <ul>
     * <li> If any argument is NaN, the result is NaN.
     *
     * <li> If one of the first two arguments is infinite and the
     * other is zero, the result is NaN.
     *
     * <li> If the exact product of the first two arguments is infinite
     * (in other words, at least one of the arguments is infinite and
     * the other is neither zero nor NaN) and the third argument is an
     * infinity of the opposite sign, the result is NaN.
     *
     * </ul>
     *
     * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
     * result as ({@code a + c}).  However,
     * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
     * same result as ({@code a * b}) since
     * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
     * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
     * equivalent to ({@code a * b}) however.
     *
     * @param a a value
     * @param b a value
     * @param c a value
     *
     * @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
     * computed, as if with unlimited range and precision, and rounded
     * once to the nearest {@code double} value
     */
    public static double fma(double a, double b, double c)

    /**
     * Returns the fused multiply add of the three arguments;
     * that is, returns the exact product of the first two arguments
     * summed with the third argument and then rounded once to the
     * nearest {@code float}.
     *
     * The rounding is done using the {@linkplain
     * java.math.RoundingMode#HALF_EVEN round to nearest even
     * rounding mode}.
     *
     * In contrast, if {@code a * b + c} is evaluated as a regular
     * floating-point expression, two rounding errors are involved,
     * the first for the multiply operation, the second for the
     * addition operation.
     *
     * <p>Special cases:
     * <ul>
     * <li> If any argument is NaN, the result is NaN.
     *
     * <li> If one of the first two arguments is infinite and the
     * other is zero, the result is NaN.
     *
     * <li> If the exact product of the first two arguments is infinite
     * (in other words, at least one of the arguments is infinite and
     * the other is neither zero nor NaN) and the third argument is an
     * infinity of the opposite sign, the result is NaN.
     *
     * </ul>
     *
     * <p>Note that {@code fusedMac(a, 1.0f, c)} returns the same
     * result as ({@code a + c}).  However,
     * {@code fusedMac(a, b, +0.0f)} does <em>not</em> always return the
     * same result as ({@code a * b}) since
     * {@code fusedMac(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
     * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fusedMac(a, b, -0.0f)} is
     * equivalent to ({@code a * b}) however.
     *
     * @param a a value
     * @param b a value
     * @param c a value
     *
     * @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
     * computed, as if with unlimited range and precision, and rounded
     * once to the nearest {@code float} value
     */
    public static float fma(float a, float b, float c)