@@ -1133,10 +1133,114 @@ public static double min(double a, double b) { return Math.min(a, b); } /** + * 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. + * + * @apiNote This method corresponds to the fusedMultiplyAdd + * operation defined in IEEE 754-2008. + * + * @param a a value + * @param b a value + * @param c a value + * + * @return (<i>a</i> × <i>b</i> + <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) { + return Math.fma(a, b, 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 fma(a, 1.0f, c)} returns the same + * result as ({@code a + c}). However, + * {@code fma(a, b, +0.0f)} does <em>not</em> always return the + * same result as ({@code a * b}) since + * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while + * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is + * equivalent to ({@code a * b}) however. + * + * @apiNote This method corresponds to the fusedMultiplyAdd + * operation defined in IEEE 754-2008. + * + * @param a a value + * @param b a value + * @param c a value + * + * @return (<i>a</i> × <i>b</i> + <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) { + return Math.fma(a, b, c); + } + + /** * Returns the size of an ulp of the argument. An ulp, unit in * the last place, of a {@code double} value is the positive * distance between this floating-point value and the {@code * double} value next larger in magnitude. Note that for non-NaN * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.