--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.base/share/classes/java/lang/StrictMath.java Tue Sep 12 19:03:39 2017 +0200
@@ -0,0 +1,1947 @@
+/*
+ * Copyright (c) 1999, 2016, 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. Oracle designates this
+ * particular file as subject to the "Classpath" exception as provided
+ * by Oracle in the LICENSE file that accompanied this code.
+ *
+ * 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.
+ */
+
+package java.lang;
+
+import java.util.Random;
+import jdk.internal.math.DoubleConsts;
+import jdk.internal.HotSpotIntrinsicCandidate;
+
+/**
+ * The class {@code StrictMath} contains methods for performing basic
+ * numeric operations such as the elementary exponential, logarithm,
+ * square root, and trigonometric functions.
+ *
+ * <p>To help ensure portability of Java programs, the definitions of
+ * some of the numeric functions in this package require that they
+ * produce the same results as certain published algorithms. These
+ * algorithms are available from the well-known network library
+ * {@code netlib} as the package "Freely Distributable Math
+ * Library," <a
+ * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
+ * algorithms, which are written in the C programming language, are
+ * then to be understood as executed with all floating-point
+ * operations following the rules of Java floating-point arithmetic.
+ *
+ * <p>The Java math library is defined with respect to
+ * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
+ * more than one definition for a function (such as
+ * {@code acos}), use the "IEEE 754 core function" version
+ * (residing in a file whose name begins with the letter
+ * {@code e}). The methods which require {@code fdlibm}
+ * semantics are {@code sin}, {@code cos}, {@code tan},
+ * {@code asin}, {@code acos}, {@code atan},
+ * {@code exp}, {@code log}, {@code log10},
+ * {@code cbrt}, {@code atan2}, {@code pow},
+ * {@code sinh}, {@code cosh}, {@code tanh},
+ * {@code hypot}, {@code expm1}, and {@code log1p}.
+ *
+ * <p>
+ * The platform uses signed two's complement integer arithmetic with
+ * int and long primitive types. The developer should choose
+ * the primitive type to ensure that arithmetic operations consistently
+ * produce correct results, which in some cases means the operations
+ * will not overflow the range of values of the computation.
+ * The best practice is to choose the primitive type and algorithm to avoid
+ * overflow. In cases where the size is {@code int} or {@code long} and
+ * overflow errors need to be detected, the methods {@code addExact},
+ * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
+ * throw an {@code ArithmeticException} when the results overflow.
+ * For other arithmetic operations such as divide, absolute value,
+ * increment by one, decrement by one, and negation overflow occurs only with
+ * a specific minimum or maximum value and should be checked against
+ * the minimum or maximum as appropriate.
+ *
+ * @author unascribed
+ * @author Joseph D. Darcy
+ * @since 1.3
+ */
+
+public final class StrictMath {
+
+ /**
+ * Don't let anyone instantiate this class.
+ */
+ private StrictMath() {}
+
+ /**
+ * The {@code double} value that is closer than any other to
+ * <i>e</i>, the base of the natural logarithms.
+ */
+ public static final double E = 2.7182818284590452354;
+
+ /**
+ * The {@code double} value that is closer than any other to
+ * <i>pi</i>, the ratio of the circumference of a circle to its
+ * diameter.
+ */
+ public static final double PI = 3.14159265358979323846;
+
+ /**
+ * Constant by which to multiply an angular value in degrees to obtain an
+ * angular value in radians.
+ */
+ private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
+
+ /**
+ * Constant by which to multiply an angular value in radians to obtain an
+ * angular value in degrees.
+ */
+
+ private static final double RADIANS_TO_DEGREES = 57.29577951308232;
+
+ /**
+ * Returns the trigonometric sine of an angle. Special cases:
+ * <ul><li>If the argument is NaN or an infinity, then the
+ * result is NaN.
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.</ul>
+ *
+ * @param a an angle, in radians.
+ * @return the sine of the argument.
+ */
+ public static native double sin(double a);
+
+ /**
+ * Returns the trigonometric cosine of an angle. Special cases:
+ * <ul><li>If the argument is NaN or an infinity, then the
+ * result is NaN.</ul>
+ *
+ * @param a an angle, in radians.
+ * @return the cosine of the argument.
+ */
+ public static native double cos(double a);
+
+ /**
+ * Returns the trigonometric tangent of an angle. Special cases:
+ * <ul><li>If the argument is NaN or an infinity, then the result
+ * is NaN.
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.</ul>
+ *
+ * @param a an angle, in radians.
+ * @return the tangent of the argument.
+ */
+ public static native double tan(double a);
+
+ /**
+ * Returns the arc sine of a value; the returned angle is in the
+ * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
+ * <ul><li>If the argument is NaN or its absolute value is greater
+ * than 1, then the result is NaN.
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.</ul>
+ *
+ * @param a the value whose arc sine is to be returned.
+ * @return the arc sine of the argument.
+ */
+ public static native double asin(double a);
+
+ /**
+ * Returns the arc cosine of a value; the returned angle is in the
+ * range 0.0 through <i>pi</i>. Special case:
+ * <ul><li>If the argument is NaN or its absolute value is greater
+ * than 1, then the result is NaN.</ul>
+ *
+ * @param a the value whose arc cosine is to be returned.
+ * @return the arc cosine of the argument.
+ */
+ public static native double acos(double a);
+
+ /**
+ * Returns the arc tangent of a value; the returned angle is in the
+ * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
+ * <ul><li>If the argument is NaN, then the result is NaN.
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.</ul>
+ *
+ * @param a the value whose arc tangent is to be returned.
+ * @return the arc tangent of the argument.
+ */
+ public static native double atan(double a);
+
+ /**
+ * Converts an angle measured in degrees to an approximately
+ * equivalent angle measured in radians. The conversion from
+ * degrees to radians is generally inexact.
+ *
+ * @param angdeg an angle, in degrees
+ * @return the measurement of the angle {@code angdeg}
+ * in radians.
+ */
+ public static strictfp double toRadians(double angdeg) {
+ // Do not delegate to Math.toRadians(angdeg) because
+ // this method has the strictfp modifier.
+ return angdeg * DEGREES_TO_RADIANS;
+ }
+
+ /**
+ * Converts an angle measured in radians to an approximately
+ * equivalent angle measured in degrees. The conversion from
+ * radians to degrees is generally inexact; users should
+ * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
+ * equal {@code 0.0}.
+ *
+ * @param angrad an angle, in radians
+ * @return the measurement of the angle {@code angrad}
+ * in degrees.
+ */
+ public static strictfp double toDegrees(double angrad) {
+ // Do not delegate to Math.toDegrees(angrad) because
+ // this method has the strictfp modifier.
+ return angrad * RADIANS_TO_DEGREES;
+ }
+
+ /**
+ * Returns Euler's number <i>e</i> raised to the power of a
+ * {@code double} value. Special cases:
+ * <ul><li>If the argument is NaN, the result is NaN.
+ * <li>If the argument is positive infinity, then the result is
+ * positive infinity.
+ * <li>If the argument is negative infinity, then the result is
+ * positive zero.</ul>
+ *
+ * @param a the exponent to raise <i>e</i> to.
+ * @return the value <i>e</i><sup>{@code a}</sup>,
+ * where <i>e</i> is the base of the natural logarithms.
+ */
+ public static double exp(double a) {
+ return FdLibm.Exp.compute(a);
+ }
+
+ /**
+ * Returns the natural logarithm (base <i>e</i>) of a {@code double}
+ * value. Special cases:
+ * <ul><li>If the argument is NaN or less than zero, then the result
+ * is NaN.
+ * <li>If the argument is positive infinity, then the result is
+ * positive infinity.
+ * <li>If the argument is positive zero or negative zero, then the
+ * result is negative infinity.</ul>
+ *
+ * @param a a value
+ * @return the value ln {@code a}, the natural logarithm of
+ * {@code a}.
+ */
+ public static native double log(double a);
+
+ /**
+ * Returns the base 10 logarithm of a {@code double} value.
+ * Special cases:
+ *
+ * <ul><li>If the argument is NaN or less than zero, then the result
+ * is NaN.
+ * <li>If the argument is positive infinity, then the result is
+ * positive infinity.
+ * <li>If the argument is positive zero or negative zero, then the
+ * result is negative infinity.
+ * <li> If the argument is equal to 10<sup><i>n</i></sup> for
+ * integer <i>n</i>, then the result is <i>n</i>.
+ * </ul>
+ *
+ * @param a a value
+ * @return the base 10 logarithm of {@code a}.
+ * @since 1.5
+ */
+ public static native double log10(double a);
+
+ /**
+ * Returns the correctly rounded positive square root of a
+ * {@code double} value.
+ * Special cases:
+ * <ul><li>If the argument is NaN or less than zero, then the result
+ * is NaN.
+ * <li>If the argument is positive infinity, then the result is positive
+ * infinity.
+ * <li>If the argument is positive zero or negative zero, then the
+ * result is the same as the argument.</ul>
+ * Otherwise, the result is the {@code double} value closest to
+ * the true mathematical square root of the argument value.
+ *
+ * @param a a value.
+ * @return the positive square root of {@code a}.
+ */
+ @HotSpotIntrinsicCandidate
+ public static native double sqrt(double a);
+
+ /**
+ * Returns the cube root of a {@code double} value. For
+ * positive finite {@code x}, {@code cbrt(-x) ==
+ * -cbrt(x)}; that is, the cube root of a negative value is
+ * the negative of the cube root of that value's magnitude.
+ * Special cases:
+ *
+ * <ul>
+ *
+ * <li>If the argument is NaN, then the result is NaN.
+ *
+ * <li>If the argument is infinite, then the result is an infinity
+ * with the same sign as the argument.
+ *
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.
+ *
+ * </ul>
+ *
+ * @param a a value.
+ * @return the cube root of {@code a}.
+ * @since 1.5
+ */
+ public static double cbrt(double a) {
+ return FdLibm.Cbrt.compute(a);
+ }
+
+ /**
+ * Computes the remainder operation on two arguments as prescribed
+ * by the IEEE 754 standard.
+ * The remainder value is mathematically equal to
+ * <code>f1 - f2</code> × <i>n</i>,
+ * where <i>n</i> is the mathematical integer closest to the exact
+ * mathematical value of the quotient {@code f1/f2}, and if two
+ * mathematical integers are equally close to {@code f1/f2},
+ * then <i>n</i> is the integer that is even. If the remainder is
+ * zero, its sign is the same as the sign of the first argument.
+ * Special cases:
+ * <ul><li>If either argument is NaN, or the first argument is infinite,
+ * or the second argument is positive zero or negative zero, then the
+ * result is NaN.
+ * <li>If the first argument is finite and the second argument is
+ * infinite, then the result is the same as the first argument.</ul>
+ *
+ * @param f1 the dividend.
+ * @param f2 the divisor.
+ * @return the remainder when {@code f1} is divided by
+ * {@code f2}.
+ */
+ public static native double IEEEremainder(double f1, double f2);
+
+ /**
+ * Returns the smallest (closest to negative infinity)
+ * {@code double} value that is greater than or equal to the
+ * argument and is equal to a mathematical integer. Special cases:
+ * <ul><li>If the argument value is already equal to a
+ * mathematical integer, then the result is the same as the
+ * argument. <li>If the argument is NaN or an infinity or
+ * positive zero or negative zero, then the result is the same as
+ * the argument. <li>If the argument value is less than zero but
+ * greater than -1.0, then the result is negative zero.</ul> Note
+ * that the value of {@code StrictMath.ceil(x)} is exactly the
+ * value of {@code -StrictMath.floor(-x)}.
+ *
+ * @param a a value.
+ * @return the smallest (closest to negative infinity)
+ * floating-point value that is greater than or equal to
+ * the argument and is equal to a mathematical integer.
+ */
+ public static double ceil(double a) {
+ return floorOrCeil(a, -0.0, 1.0, 1.0);
+ }
+
+ /**
+ * Returns the largest (closest to positive infinity)
+ * {@code double} value that is less than or equal to the
+ * argument and is equal to a mathematical integer. Special cases:
+ * <ul><li>If the argument value is already equal to a
+ * mathematical integer, then the result is the same as the
+ * argument. <li>If the argument is NaN or an infinity or
+ * positive zero or negative zero, then the result is the same as
+ * the argument.</ul>
+ *
+ * @param a a value.
+ * @return the largest (closest to positive infinity)
+ * floating-point value that less than or equal to the argument
+ * and is equal to a mathematical integer.
+ */
+ public static double floor(double a) {
+ return floorOrCeil(a, -1.0, 0.0, -1.0);
+ }
+
+ /**
+ * Internal method to share logic between floor and ceil.
+ *
+ * @param a the value to be floored or ceiled
+ * @param negativeBoundary result for values in (-1, 0)
+ * @param positiveBoundary result for values in (0, 1)
+ * @param increment value to add when the argument is non-integral
+ */
+ private static double floorOrCeil(double a,
+ double negativeBoundary,
+ double positiveBoundary,
+ double sign) {
+ int exponent = Math.getExponent(a);
+
+ if (exponent < 0) {
+ /*
+ * Absolute value of argument is less than 1.
+ * floorOrceil(-0.0) => -0.0
+ * floorOrceil(+0.0) => +0.0
+ */
+ return ((a == 0.0) ? a :
+ ( (a < 0.0) ? negativeBoundary : positiveBoundary) );
+ } else if (exponent >= 52) {
+ /*
+ * Infinity, NaN, or a value so large it must be integral.
+ */
+ return a;
+ }
+ // Else the argument is either an integral value already XOR it
+ // has to be rounded to one.
+ assert exponent >= 0 && exponent <= 51;
+
+ long doppel = Double.doubleToRawLongBits(a);
+ long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
+
+ if ( (mask & doppel) == 0L )
+ return a; // integral value
+ else {
+ double result = Double.longBitsToDouble(doppel & (~mask));
+ if (sign*a > 0.0)
+ result = result + sign;
+ return result;
+ }
+ }
+
+ /**
+ * Returns the {@code double} value that is closest in value
+ * to the argument and is equal to a mathematical integer. If two
+ * {@code double} values that are mathematical integers are
+ * equally close to the value of the argument, the result is the
+ * integer value that is even. Special cases:
+ * <ul><li>If the argument value is already equal to a mathematical
+ * integer, then the result is the same as the argument.
+ * <li>If the argument is NaN or an infinity or positive zero or negative
+ * zero, then the result is the same as the argument.</ul>
+ *
+ * @param a a value.
+ * @return the closest floating-point value to {@code a} that is
+ * equal to a mathematical integer.
+ * @author Joseph D. Darcy
+ */
+ public static double rint(double a) {
+ /*
+ * If the absolute value of a is not less than 2^52, it
+ * is either a finite integer (the double format does not have
+ * enough significand bits for a number that large to have any
+ * fractional portion), an infinity, or a NaN. In any of
+ * these cases, rint of the argument is the argument.
+ *
+ * Otherwise, the sum (twoToThe52 + a ) will properly round
+ * away any fractional portion of a since ulp(twoToThe52) ==
+ * 1.0; subtracting out twoToThe52 from this sum will then be
+ * exact and leave the rounded integer portion of a.
+ *
+ * This method does *not* need to be declared strictfp to get
+ * fully reproducible results. Whether or not a method is
+ * declared strictfp can only make a difference in the
+ * returned result if some operation would overflow or
+ * underflow with strictfp semantics. The operation
+ * (twoToThe52 + a ) cannot overflow since large values of a
+ * are screened out; the add cannot underflow since twoToThe52
+ * is too large. The subtraction ((twoToThe52 + a ) -
+ * twoToThe52) will be exact as discussed above and thus
+ * cannot overflow or meaningfully underflow. Finally, the
+ * last multiply in the return statement is by plus or minus
+ * 1.0, which is exact too.
+ */
+ double twoToThe52 = (double)(1L << 52); // 2^52
+ double sign = Math.copySign(1.0, a); // preserve sign info
+ a = Math.abs(a);
+
+ if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
+ a = ((twoToThe52 + a ) - twoToThe52);
+ }
+
+ return sign * a; // restore original sign
+ }
+
+ /**
+ * Returns the angle <i>theta</i> from the conversion of rectangular
+ * coordinates ({@code x}, {@code y}) to polar
+ * coordinates (r, <i>theta</i>).
+ * This method computes the phase <i>theta</i> by computing an arc tangent
+ * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
+ * cases:
+ * <ul><li>If either argument is NaN, then the result is NaN.
+ * <li>If the first argument is positive zero and the second argument
+ * is positive, or the first argument is positive and finite and the
+ * second argument is positive infinity, then the result is positive
+ * zero.
+ * <li>If the first argument is negative zero and the second argument
+ * is positive, or the first argument is negative and finite and the
+ * second argument is positive infinity, then the result is negative zero.
+ * <li>If the first argument is positive zero and the second argument
+ * is negative, or the first argument is positive and finite and the
+ * second argument is negative infinity, then the result is the
+ * {@code double} value closest to <i>pi</i>.
+ * <li>If the first argument is negative zero and the second argument
+ * is negative, or the first argument is negative and finite and the
+ * second argument is negative infinity, then the result is the
+ * {@code double} value closest to -<i>pi</i>.
+ * <li>If the first argument is positive and the second argument is
+ * positive zero or negative zero, or the first argument is positive
+ * infinity and the second argument is finite, then the result is the
+ * {@code double} value closest to <i>pi</i>/2.
+ * <li>If the first argument is negative and the second argument is
+ * positive zero or negative zero, or the first argument is negative
+ * infinity and the second argument is finite, then the result is the
+ * {@code double} value closest to -<i>pi</i>/2.
+ * <li>If both arguments are positive infinity, then the result is the
+ * {@code double} value closest to <i>pi</i>/4.
+ * <li>If the first argument is positive infinity and the second argument
+ * is negative infinity, then the result is the {@code double}
+ * value closest to 3*<i>pi</i>/4.
+ * <li>If the first argument is negative infinity and the second argument
+ * is positive infinity, then the result is the {@code double} value
+ * closest to -<i>pi</i>/4.
+ * <li>If both arguments are negative infinity, then the result is the
+ * {@code double} value closest to -3*<i>pi</i>/4.</ul>
+ *
+ * @param y the ordinate coordinate
+ * @param x the abscissa coordinate
+ * @return the <i>theta</i> component of the point
+ * (<i>r</i>, <i>theta</i>)
+ * in polar coordinates that corresponds to the point
+ * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
+ */
+ public static native double atan2(double y, double x);
+
+ /**
+ * Returns the value of the first argument raised to the power of the
+ * second argument. Special cases:
+ *
+ * <ul><li>If the second argument is positive or negative zero, then the
+ * result is 1.0.
+ * <li>If the second argument is 1.0, then the result is the same as the
+ * first argument.
+ * <li>If the second argument is NaN, then the result is NaN.
+ * <li>If the first argument is NaN and the second argument is nonzero,
+ * then the result is NaN.
+ *
+ * <li>If
+ * <ul>
+ * <li>the absolute value of the first argument is greater than 1
+ * and the second argument is positive infinity, or
+ * <li>the absolute value of the first argument is less than 1 and
+ * the second argument is negative infinity,
+ * </ul>
+ * then the result is positive infinity.
+ *
+ * <li>If
+ * <ul>
+ * <li>the absolute value of the first argument is greater than 1 and
+ * the second argument is negative infinity, or
+ * <li>the absolute value of the
+ * first argument is less than 1 and the second argument is positive
+ * infinity,
+ * </ul>
+ * then the result is positive zero.
+ *
+ * <li>If the absolute value of the first argument equals 1 and the
+ * second argument is infinite, then the result is NaN.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is positive zero and the second argument
+ * is greater than zero, or
+ * <li>the first argument is positive infinity and the second
+ * argument is less than zero,
+ * </ul>
+ * then the result is positive zero.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is positive zero and the second argument
+ * is less than zero, or
+ * <li>the first argument is positive infinity and the second
+ * argument is greater than zero,
+ * </ul>
+ * then the result is positive infinity.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is negative zero and the second argument
+ * is greater than zero but not a finite odd integer, or
+ * <li>the first argument is negative infinity and the second
+ * argument is less than zero but not a finite odd integer,
+ * </ul>
+ * then the result is positive zero.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is negative zero and the second argument
+ * is a positive finite odd integer, or
+ * <li>the first argument is negative infinity and the second
+ * argument is a negative finite odd integer,
+ * </ul>
+ * then the result is negative zero.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is negative zero and the second argument
+ * is less than zero but not a finite odd integer, or
+ * <li>the first argument is negative infinity and the second
+ * argument is greater than zero but not a finite odd integer,
+ * </ul>
+ * then the result is positive infinity.
+ *
+ * <li>If
+ * <ul>
+ * <li>the first argument is negative zero and the second argument
+ * is a negative finite odd integer, or
+ * <li>the first argument is negative infinity and the second
+ * argument is a positive finite odd integer,
+ * </ul>
+ * then the result is negative infinity.
+ *
+ * <li>If the first argument is finite and less than zero
+ * <ul>
+ * <li> if the second argument is a finite even integer, the
+ * result is equal to the result of raising the absolute value of
+ * the first argument to the power of the second argument
+ *
+ * <li>if the second argument is a finite odd integer, the result
+ * is equal to the negative of the result of raising the absolute
+ * value of the first argument to the power of the second
+ * argument
+ *
+ * <li>if the second argument is finite and not an integer, then
+ * the result is NaN.
+ * </ul>
+ *
+ * <li>If both arguments are integers, then the result is exactly equal
+ * to the mathematical result of raising the first argument to the power
+ * of the second argument if that result can in fact be represented
+ * exactly as a {@code double} value.</ul>
+ *
+ * <p>(In the foregoing descriptions, a floating-point value is
+ * considered to be an integer if and only if it is finite and a
+ * fixed point of the method {@link #ceil ceil} or,
+ * equivalently, a fixed point of the method {@link #floor
+ * floor}. A value is a fixed point of a one-argument
+ * method if and only if the result of applying the method to the
+ * value is equal to the value.)
+ *
+ * @param a base.
+ * @param b the exponent.
+ * @return the value {@code a}<sup>{@code b}</sup>.
+ */
+ public static double pow(double a, double b) {
+ return FdLibm.Pow.compute(a, b);
+ }
+
+ /**
+ * Returns the closest {@code int} to the argument, with ties
+ * rounding to positive infinity.
+ *
+ * <p>Special cases:
+ * <ul><li>If the argument is NaN, the result is 0.
+ * <li>If the argument is negative infinity or any value less than or
+ * equal to the value of {@code Integer.MIN_VALUE}, the result is
+ * equal to the value of {@code Integer.MIN_VALUE}.
+ * <li>If the argument is positive infinity or any value greater than or
+ * equal to the value of {@code Integer.MAX_VALUE}, the result is
+ * equal to the value of {@code Integer.MAX_VALUE}.</ul>
+ *
+ * @param a a floating-point value to be rounded to an integer.
+ * @return the value of the argument rounded to the nearest
+ * {@code int} value.
+ * @see java.lang.Integer#MAX_VALUE
+ * @see java.lang.Integer#MIN_VALUE
+ */
+ public static int round(float a) {
+ return Math.round(a);
+ }
+
+ /**
+ * Returns the closest {@code long} to the argument, with ties
+ * rounding to positive infinity.
+ *
+ * <p>Special cases:
+ * <ul><li>If the argument is NaN, the result is 0.
+ * <li>If the argument is negative infinity or any value less than or
+ * equal to the value of {@code Long.MIN_VALUE}, the result is
+ * equal to the value of {@code Long.MIN_VALUE}.
+ * <li>If the argument is positive infinity or any value greater than or
+ * equal to the value of {@code Long.MAX_VALUE}, the result is
+ * equal to the value of {@code Long.MAX_VALUE}.</ul>
+ *
+ * @param a a floating-point value to be rounded to a
+ * {@code long}.
+ * @return the value of the argument rounded to the nearest
+ * {@code long} value.
+ * @see java.lang.Long#MAX_VALUE
+ * @see java.lang.Long#MIN_VALUE
+ */
+ public static long round(double a) {
+ return Math.round(a);
+ }
+
+ private static final class RandomNumberGeneratorHolder {
+ static final Random randomNumberGenerator = new Random();
+ }
+
+ /**
+ * Returns a {@code double} value with a positive sign, greater
+ * than or equal to {@code 0.0} and less than {@code 1.0}.
+ * Returned values are chosen pseudorandomly with (approximately)
+ * uniform distribution from that range.
+ *
+ * <p>When this method is first called, it creates a single new
+ * pseudorandom-number generator, exactly as if by the expression
+ *
+ * <blockquote>{@code new java.util.Random()}</blockquote>
+ *
+ * This new pseudorandom-number generator is used thereafter for
+ * all calls to this method and is used nowhere else.
+ *
+ * <p>This method is properly synchronized to allow correct use by
+ * more than one thread. However, if many threads need to generate
+ * pseudorandom numbers at a great rate, it may reduce contention
+ * for each thread to have its own pseudorandom-number generator.
+ *
+ * @return a pseudorandom {@code double} greater than or equal
+ * to {@code 0.0} and less than {@code 1.0}.
+ * @see Random#nextDouble()
+ */
+ public static double random() {
+ return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
+ }
+
+ /**
+ * Returns the sum of its arguments,
+ * throwing an exception if the result overflows an {@code int}.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @see Math#addExact(int,int)
+ * @since 1.8
+ */
+ public static int addExact(int x, int y) {
+ return Math.addExact(x, y);
+ }
+
+ /**
+ * Returns the sum of its arguments,
+ * throwing an exception if the result overflows a {@code long}.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @see Math#addExact(long,long)
+ * @since 1.8
+ */
+ public static long addExact(long x, long y) {
+ return Math.addExact(x, y);
+ }
+
+ /**
+ * Returns the difference of the arguments,
+ * throwing an exception if the result overflows an {@code int}.
+ *
+ * @param x the first value
+ * @param y the second value to subtract from the first
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @see Math#subtractExact(int,int)
+ * @since 1.8
+ */
+ public static int subtractExact(int x, int y) {
+ return Math.subtractExact(x, y);
+ }
+
+ /**
+ * Returns the difference of the arguments,
+ * throwing an exception if the result overflows a {@code long}.
+ *
+ * @param x the first value
+ * @param y the second value to subtract from the first
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @see Math#subtractExact(long,long)
+ * @since 1.8
+ */
+ public static long subtractExact(long x, long y) {
+ return Math.subtractExact(x, y);
+ }
+
+ /**
+ * Returns the product of the arguments,
+ * throwing an exception if the result overflows an {@code int}.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @see Math#multiplyExact(int,int)
+ * @since 1.8
+ */
+ public static int multiplyExact(int x, int y) {
+ return Math.multiplyExact(x, y);
+ }
+
+ /**
+ * Returns the product of the arguments, throwing an exception if the result
+ * overflows a {@code long}.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @see Math#multiplyExact(long,int)
+ * @since 9
+ */
+ public static long multiplyExact(long x, int y) {
+ return Math.multiplyExact(x, y);
+ }
+
+ /**
+ * Returns the product of the arguments,
+ * throwing an exception if the result overflows a {@code long}.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @see Math#multiplyExact(long,long)
+ * @since 1.8
+ */
+ public static long multiplyExact(long x, long y) {
+ return Math.multiplyExact(x, y);
+ }
+
+ /**
+ * Returns the value of the {@code long} argument;
+ * throwing an exception if the value overflows an {@code int}.
+ *
+ * @param value the long value
+ * @return the argument as an int
+ * @throws ArithmeticException if the {@code argument} overflows an int
+ * @see Math#toIntExact(long)
+ * @since 1.8
+ */
+ public static int toIntExact(long value) {
+ return Math.toIntExact(value);
+ }
+
+ /**
+ * Returns the exact mathematical product of the arguments.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @see Math#multiplyFull(int,int)
+ * @since 9
+ */
+ public static long multiplyFull(int x, int y) {
+ return Math.multiplyFull(x, y);
+ }
+
+ /**
+ * Returns as a {@code long} the most significant 64 bits of the 128-bit
+ * product of two 64-bit factors.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @see Math#multiplyHigh(long,long)
+ * @since 9
+ */
+ public static long multiplyHigh(long x, long y) {
+ return Math.multiplyHigh(x, y);
+ }
+
+ /**
+ * Returns the largest (closest to positive infinity)
+ * {@code int} value that is less than or equal to the algebraic quotient.
+ * There is one special case, if the dividend is the
+ * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
+ * then integer overflow occurs and
+ * the result is equal to the {@code Integer.MIN_VALUE}.
+ * <p>
+ * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
+ * a comparison to the integer division {@code /} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the largest (closest to positive infinity)
+ * {@code int} value that is less than or equal to the algebraic quotient.
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorDiv(int, int)
+ * @see Math#floor(double)
+ * @since 1.8
+ */
+ public static int floorDiv(int x, int y) {
+ return Math.floorDiv(x, y);
+ }
+
+ /**
+ * Returns the largest (closest to positive infinity)
+ * {@code long} value that is less than or equal to the algebraic quotient.
+ * There is one special case, if the dividend is the
+ * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
+ * then integer overflow occurs and
+ * the result is equal to {@code Long.MIN_VALUE}.
+ * <p>
+ * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
+ * a comparison to the integer division {@code /} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the largest (closest to positive infinity)
+ * {@code int} value that is less than or equal to the algebraic quotient.
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorDiv(long, int)
+ * @see Math#floor(double)
+ * @since 9
+ */
+ public static long floorDiv(long x, int y) {
+ return Math.floorDiv(x, y);
+ }
+
+ /**
+ * Returns the largest (closest to positive infinity)
+ * {@code long} value that is less than or equal to the algebraic quotient.
+ * There is one special case, if the dividend is the
+ * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
+ * then integer overflow occurs and
+ * the result is equal to the {@code Long.MIN_VALUE}.
+ * <p>
+ * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
+ * a comparison to the integer division {@code /} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the largest (closest to positive infinity)
+ * {@code long} value that is less than or equal to the algebraic quotient.
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorDiv(long, long)
+ * @see Math#floor(double)
+ * @since 1.8
+ */
+ public static long floorDiv(long x, long y) {
+ return Math.floorDiv(x, y);
+ }
+
+ /**
+ * Returns the floor modulus of the {@code int} arguments.
+ * <p>
+ * The floor modulus is {@code x - (floorDiv(x, y) * y)},
+ * has the same sign as the divisor {@code y}, and
+ * is in the range of {@code -abs(y) < r < +abs(y)}.
+ * <p>
+ * The relationship between {@code floorDiv} and {@code floorMod} is such that:
+ * <ul>
+ * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
+ * </ul>
+ * <p>
+ * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
+ * a comparison to the {@code %} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorMod(int, int)
+ * @see StrictMath#floorDiv(int, int)
+ * @since 1.8
+ */
+ public static int floorMod(int x, int y) {
+ return Math.floorMod(x , y);
+ }
+
+ /**
+ * Returns the floor modulus of the {@code long} and {@code int} arguments.
+ * <p>
+ * The floor modulus is {@code x - (floorDiv(x, y) * y)},
+ * has the same sign as the divisor {@code y}, and
+ * is in the range of {@code -abs(y) < r < +abs(y)}.
+ *
+ * <p>
+ * The relationship between {@code floorDiv} and {@code floorMod} is such that:
+ * <ul>
+ * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
+ * </ul>
+ * <p>
+ * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
+ * a comparison to the {@code %} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorMod(long, int)
+ * @see StrictMath#floorDiv(long, int)
+ * @since 9
+ */
+ public static int floorMod(long x, int y) {
+ return Math.floorMod(x , y);
+ }
+
+ /**
+ * Returns the floor modulus of the {@code long} arguments.
+ * <p>
+ * The floor modulus is {@code x - (floorDiv(x, y) * y)},
+ * has the same sign as the divisor {@code y}, and
+ * is in the range of {@code -abs(y) < r < +abs(y)}.
+ * <p>
+ * The relationship between {@code floorDiv} and {@code floorMod} is such that:
+ * <ul>
+ * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
+ * </ul>
+ * <p>
+ * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
+ * a comparison to the {@code %} operator.
+ *
+ * @param x the dividend
+ * @param y the divisor
+ * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
+ * @throws ArithmeticException if the divisor {@code y} is zero
+ * @see Math#floorMod(long, long)
+ * @see StrictMath#floorDiv(long, long)
+ * @since 1.8
+ */
+ public static long floorMod(long x, long y) {
+ return Math.floorMod(x, y);
+ }
+
+ /**
+ * Returns the absolute value of an {@code int} value.
+ * If the argument is not negative, the argument is returned.
+ * If the argument is negative, the negation of the argument is returned.
+ *
+ * <p>Note that if the argument is equal to the value of
+ * {@link Integer#MIN_VALUE}, the most negative representable
+ * {@code int} value, the result is that same value, which is
+ * negative.
+ *
+ * @param a the argument whose absolute value is to be determined.
+ * @return the absolute value of the argument.
+ */
+ public static int abs(int a) {
+ return Math.abs(a);
+ }
+
+ /**
+ * Returns the absolute value of a {@code long} value.
+ * If the argument is not negative, the argument is returned.
+ * If the argument is negative, the negation of the argument is returned.
+ *
+ * <p>Note that if the argument is equal to the value of
+ * {@link Long#MIN_VALUE}, the most negative representable
+ * {@code long} value, the result is that same value, which
+ * is negative.
+ *
+ * @param a the argument whose absolute value is to be determined.
+ * @return the absolute value of the argument.
+ */
+ public static long abs(long a) {
+ return Math.abs(a);
+ }
+
+ /**
+ * Returns the absolute value of a {@code float} value.
+ * If the argument is not negative, the argument is returned.
+ * If the argument is negative, the negation of the argument is returned.
+ * Special cases:
+ * <ul><li>If the argument is positive zero or negative zero, the
+ * result is positive zero.
+ * <li>If the argument is infinite, the result is positive infinity.
+ * <li>If the argument is NaN, the result is NaN.</ul>
+ *
+ * @apiNote As implied by the above, one valid implementation of
+ * this method is given by the expression below which computes a
+ * {@code float} with the same exponent and significand as the
+ * argument but with a guaranteed zero sign bit indicating a
+ * positive value: <br>
+ * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
+ *
+ * @param a the argument whose absolute value is to be determined
+ * @return the absolute value of the argument.
+ */
+ public static float abs(float a) {
+ return Math.abs(a);
+ }
+
+ /**
+ * Returns the absolute value of a {@code double} value.
+ * If the argument is not negative, the argument is returned.
+ * If the argument is negative, the negation of the argument is returned.
+ * Special cases:
+ * <ul><li>If the argument is positive zero or negative zero, the result
+ * is positive zero.
+ * <li>If the argument is infinite, the result is positive infinity.
+ * <li>If the argument is NaN, the result is NaN.</ul>
+ *
+ * @apiNote As implied by the above, one valid implementation of
+ * this method is given by the expression below which computes a
+ * {@code double} with the same exponent and significand as the
+ * argument but with a guaranteed zero sign bit indicating a
+ * positive value: <br>
+ * {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
+ *
+ * @param a the argument whose absolute value is to be determined
+ * @return the absolute value of the argument.
+ */
+ public static double abs(double a) {
+ return Math.abs(a);
+ }
+
+ /**
+ * Returns the greater of two {@code int} values. That is, the
+ * result is the argument closer to the value of
+ * {@link Integer#MAX_VALUE}. If the arguments have the same value,
+ * the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ @HotSpotIntrinsicCandidate
+ public static int max(int a, int b) {
+ return Math.max(a, b);
+ }
+
+ /**
+ * Returns the greater of two {@code long} values. That is, the
+ * result is the argument closer to the value of
+ * {@link Long#MAX_VALUE}. If the arguments have the same value,
+ * the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static long max(long a, long b) {
+ return Math.max(a, b);
+ }
+
+ /**
+ * Returns the greater of two {@code float} values. That is,
+ * the result is the argument closer to positive infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other negative zero, the
+ * result is positive zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static float max(float a, float b) {
+ return Math.max(a, b);
+ }
+
+ /**
+ * Returns the greater of two {@code double} values. That
+ * is, the result is the argument closer to positive infinity. If
+ * the arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other negative zero, the
+ * result is positive zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static double max(double a, double b) {
+ return Math.max(a, b);
+ }
+
+ /**
+ * Returns the smaller of two {@code int} values. That is,
+ * the result the argument closer to the value of
+ * {@link Integer#MIN_VALUE}. If the arguments have the same
+ * value, the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ @HotSpotIntrinsicCandidate
+ public static int min(int a, int b) {
+ return Math.min(a, b);
+ }
+
+ /**
+ * Returns the smaller of two {@code long} values. That is,
+ * the result is the argument closer to the value of
+ * {@link Long#MIN_VALUE}. If the arguments have the same
+ * value, the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ public static long min(long a, long b) {
+ return Math.min(a, b);
+ }
+
+ /**
+ * Returns the smaller of two {@code float} values. That is,
+ * the result is the value closer to negative infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If
+ * one argument is positive zero and the other is negative zero,
+ * the result is negative zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b.}
+ */
+ public static float min(float a, float b) {
+ return Math.min(a, b);
+ }
+
+ /**
+ * Returns the smaller of two {@code double} values. That
+ * is, the result is the value closer to negative infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other is negative zero, the
+ * result is negative zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ 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
+ *
+ * @since 9
+ */
+ 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
+ *
+ * @since 9
+ */
+ 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>.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, then the result is NaN.
+ * <li> If the argument is positive or negative infinity, then the
+ * result is positive infinity.
+ * <li> If the argument is positive or negative zero, then the result is
+ * {@code Double.MIN_VALUE}.
+ * <li> If the argument is ±{@code Double.MAX_VALUE}, then
+ * the result is equal to 2<sup>971</sup>.
+ * </ul>
+ *
+ * @param d the floating-point value whose ulp is to be returned
+ * @return the size of an ulp of the argument
+ * @author Joseph D. Darcy
+ * @since 1.5
+ */
+ public static double ulp(double d) {
+ return Math.ulp(d);
+ }
+
+ /**
+ * Returns the size of an ulp of the argument. An ulp, unit in
+ * the last place, of a {@code float} value is the positive
+ * distance between this floating-point value and the {@code
+ * float} value next larger in magnitude. Note that for non-NaN
+ * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, then the result is NaN.
+ * <li> If the argument is positive or negative infinity, then the
+ * result is positive infinity.
+ * <li> If the argument is positive or negative zero, then the result is
+ * {@code Float.MIN_VALUE}.
+ * <li> If the argument is ±{@code Float.MAX_VALUE}, then
+ * the result is equal to 2<sup>104</sup>.
+ * </ul>
+ *
+ * @param f the floating-point value whose ulp is to be returned
+ * @return the size of an ulp of the argument
+ * @author Joseph D. Darcy
+ * @since 1.5
+ */
+ public static float ulp(float f) {
+ return Math.ulp(f);
+ }
+
+ /**
+ * Returns the signum function of the argument; zero if the argument
+ * is zero, 1.0 if the argument is greater than zero, -1.0 if the
+ * argument is less than zero.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, then the result is NaN.
+ * <li> If the argument is positive zero or negative zero, then the
+ * result is the same as the argument.
+ * </ul>
+ *
+ * @param d the floating-point value whose signum is to be returned
+ * @return the signum function of the argument
+ * @author Joseph D. Darcy
+ * @since 1.5
+ */
+ public static double signum(double d) {
+ return Math.signum(d);
+ }
+
+ /**
+ * Returns the signum function of the argument; zero if the argument
+ * is zero, 1.0f if the argument is greater than zero, -1.0f if the
+ * argument is less than zero.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, then the result is NaN.
+ * <li> If the argument is positive zero or negative zero, then the
+ * result is the same as the argument.
+ * </ul>
+ *
+ * @param f the floating-point value whose signum is to be returned
+ * @return the signum function of the argument
+ * @author Joseph D. Darcy
+ * @since 1.5
+ */
+ public static float signum(float f) {
+ return Math.signum(f);
+ }
+
+ /**
+ * Returns the hyperbolic sine of a {@code double} value.
+ * The hyperbolic sine of <i>x</i> is defined to be
+ * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
+ * where <i>e</i> is {@linkplain Math#E Euler's number}.
+ *
+ * <p>Special cases:
+ * <ul>
+ *
+ * <li>If the argument is NaN, then the result is NaN.
+ *
+ * <li>If the argument is infinite, then the result is an infinity
+ * with the same sign as the argument.
+ *
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.
+ *
+ * </ul>
+ *
+ * @param x The number whose hyperbolic sine is to be returned.
+ * @return The hyperbolic sine of {@code x}.
+ * @since 1.5
+ */
+ public static native double sinh(double x);
+
+ /**
+ * Returns the hyperbolic cosine of a {@code double} value.
+ * The hyperbolic cosine of <i>x</i> is defined to be
+ * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
+ * where <i>e</i> is {@linkplain Math#E Euler's number}.
+ *
+ * <p>Special cases:
+ * <ul>
+ *
+ * <li>If the argument is NaN, then the result is NaN.
+ *
+ * <li>If the argument is infinite, then the result is positive
+ * infinity.
+ *
+ * <li>If the argument is zero, then the result is {@code 1.0}.
+ *
+ * </ul>
+ *
+ * @param x The number whose hyperbolic cosine is to be returned.
+ * @return The hyperbolic cosine of {@code x}.
+ * @since 1.5
+ */
+ public static native double cosh(double x);
+
+ /**
+ * Returns the hyperbolic tangent of a {@code double} value.
+ * The hyperbolic tangent of <i>x</i> is defined to be
+ * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
+ * in other words, {@linkplain Math#sinh
+ * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
+ * that the absolute value of the exact tanh is always less than
+ * 1.
+ *
+ * <p>Special cases:
+ * <ul>
+ *
+ * <li>If the argument is NaN, then the result is NaN.
+ *
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.
+ *
+ * <li>If the argument is positive infinity, then the result is
+ * {@code +1.0}.
+ *
+ * <li>If the argument is negative infinity, then the result is
+ * {@code -1.0}.
+ *
+ * </ul>
+ *
+ * @param x The number whose hyperbolic tangent is to be returned.
+ * @return The hyperbolic tangent of {@code x}.
+ * @since 1.5
+ */
+ public static native double tanh(double x);
+
+ /**
+ * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * without intermediate overflow or underflow.
+ *
+ * <p>Special cases:
+ * <ul>
+ *
+ * <li> If either argument is infinite, then the result
+ * is positive infinity.
+ *
+ * <li> If either argument is NaN and neither argument is infinite,
+ * then the result is NaN.
+ *
+ * </ul>
+ *
+ * @param x a value
+ * @param y a value
+ * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * without intermediate overflow or underflow
+ * @since 1.5
+ */
+ public static double hypot(double x, double y) {
+ return FdLibm.Hypot.compute(x, y);
+ }
+
+ /**
+ * Returns <i>e</i><sup>x</sup> -1. Note that for values of
+ * <i>x</i> near 0, the exact sum of
+ * {@code expm1(x)} + 1 is much closer to the true
+ * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li>If the argument is NaN, the result is NaN.
+ *
+ * <li>If the argument is positive infinity, then the result is
+ * positive infinity.
+ *
+ * <li>If the argument is negative infinity, then the result is
+ * -1.0.
+ *
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.
+ *
+ * </ul>
+ *
+ * @param x the exponent to raise <i>e</i> to in the computation of
+ * <i>e</i><sup>{@code x}</sup> -1.
+ * @return the value <i>e</i><sup>{@code x}</sup> - 1.
+ * @since 1.5
+ */
+ public static native double expm1(double x);
+
+ /**
+ * Returns the natural logarithm of the sum of the argument and 1.
+ * Note that for small values {@code x}, the result of
+ * {@code log1p(x)} is much closer to the true result of ln(1
+ * + {@code x}) than the floating-point evaluation of
+ * {@code log(1.0+x)}.
+ *
+ * <p>Special cases:
+ * <ul>
+ *
+ * <li>If the argument is NaN or less than -1, then the result is
+ * NaN.
+ *
+ * <li>If the argument is positive infinity, then the result is
+ * positive infinity.
+ *
+ * <li>If the argument is negative one, then the result is
+ * negative infinity.
+ *
+ * <li>If the argument is zero, then the result is a zero with the
+ * same sign as the argument.
+ *
+ * </ul>
+ *
+ * @param x a value
+ * @return the value ln({@code x} + 1), the natural
+ * log of {@code x} + 1
+ * @since 1.5
+ */
+ public static native double log1p(double x);
+
+ /**
+ * Returns the first floating-point argument with the sign of the
+ * second floating-point argument. For this method, a NaN
+ * {@code sign} argument is always treated as if it were
+ * positive.
+ *
+ * @param magnitude the parameter providing the magnitude of the result
+ * @param sign the parameter providing the sign of the result
+ * @return a value with the magnitude of {@code magnitude}
+ * and the sign of {@code sign}.
+ * @since 1.6
+ */
+ public static double copySign(double magnitude, double sign) {
+ return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
+ }
+
+ /**
+ * Returns the first floating-point argument with the sign of the
+ * second floating-point argument. For this method, a NaN
+ * {@code sign} argument is always treated as if it were
+ * positive.
+ *
+ * @param magnitude the parameter providing the magnitude of the result
+ * @param sign the parameter providing the sign of the result
+ * @return a value with the magnitude of {@code magnitude}
+ * and the sign of {@code sign}.
+ * @since 1.6
+ */
+ public static float copySign(float magnitude, float sign) {
+ return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
+ }
+ /**
+ * Returns the unbiased exponent used in the representation of a
+ * {@code float}. Special cases:
+ *
+ * <ul>
+ * <li>If the argument is NaN or infinite, then the result is
+ * {@link Float#MAX_EXPONENT} + 1.
+ * <li>If the argument is zero or subnormal, then the result is
+ * {@link Float#MIN_EXPONENT} -1.
+ * </ul>
+ * @param f a {@code float} value
+ * @return the unbiased exponent of the argument
+ * @since 1.6
+ */
+ public static int getExponent(float f) {
+ return Math.getExponent(f);
+ }
+
+ /**
+ * Returns the unbiased exponent used in the representation of a
+ * {@code double}. Special cases:
+ *
+ * <ul>
+ * <li>If the argument is NaN or infinite, then the result is
+ * {@link Double#MAX_EXPONENT} + 1.
+ * <li>If the argument is zero or subnormal, then the result is
+ * {@link Double#MIN_EXPONENT} -1.
+ * </ul>
+ * @param d a {@code double} value
+ * @return the unbiased exponent of the argument
+ * @since 1.6
+ */
+ public static int getExponent(double d) {
+ return Math.getExponent(d);
+ }
+
+ /**
+ * Returns the floating-point number adjacent to the first
+ * argument in the direction of the second argument. If both
+ * arguments compare as equal the second argument is returned.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li> If either argument is a NaN, then NaN is returned.
+ *
+ * <li> If both arguments are signed zeros, {@code direction}
+ * is returned unchanged (as implied by the requirement of
+ * returning the second argument if the arguments compare as
+ * equal).
+ *
+ * <li> If {@code start} is
+ * ±{@link Double#MIN_VALUE} and {@code direction}
+ * has a value such that the result should have a smaller
+ * magnitude, then a zero with the same sign as {@code start}
+ * is returned.
+ *
+ * <li> If {@code start} is infinite and
+ * {@code direction} has a value such that the result should
+ * have a smaller magnitude, {@link Double#MAX_VALUE} with the
+ * same sign as {@code start} is returned.
+ *
+ * <li> If {@code start} is equal to ±
+ * {@link Double#MAX_VALUE} and {@code direction} has a
+ * value such that the result should have a larger magnitude, an
+ * infinity with same sign as {@code start} is returned.
+ * </ul>
+ *
+ * @param start starting floating-point value
+ * @param direction value indicating which of
+ * {@code start}'s neighbors or {@code start} should
+ * be returned
+ * @return The floating-point number adjacent to {@code start} in the
+ * direction of {@code direction}.
+ * @since 1.6
+ */
+ public static double nextAfter(double start, double direction) {
+ return Math.nextAfter(start, direction);
+ }
+
+ /**
+ * Returns the floating-point number adjacent to the first
+ * argument in the direction of the second argument. If both
+ * arguments compare as equal a value equivalent to the second argument
+ * is returned.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li> If either argument is a NaN, then NaN is returned.
+ *
+ * <li> If both arguments are signed zeros, a value equivalent
+ * to {@code direction} is returned.
+ *
+ * <li> If {@code start} is
+ * ±{@link Float#MIN_VALUE} and {@code direction}
+ * has a value such that the result should have a smaller
+ * magnitude, then a zero with the same sign as {@code start}
+ * is returned.
+ *
+ * <li> If {@code start} is infinite and
+ * {@code direction} has a value such that the result should
+ * have a smaller magnitude, {@link Float#MAX_VALUE} with the
+ * same sign as {@code start} is returned.
+ *
+ * <li> If {@code start} is equal to ±
+ * {@link Float#MAX_VALUE} and {@code direction} has a
+ * value such that the result should have a larger magnitude, an
+ * infinity with same sign as {@code start} is returned.
+ * </ul>
+ *
+ * @param start starting floating-point value
+ * @param direction value indicating which of
+ * {@code start}'s neighbors or {@code start} should
+ * be returned
+ * @return The floating-point number adjacent to {@code start} in the
+ * direction of {@code direction}.
+ * @since 1.6
+ */
+ public static float nextAfter(float start, double direction) {
+ return Math.nextAfter(start, direction);
+ }
+
+ /**
+ * Returns the floating-point value adjacent to {@code d} in
+ * the direction of positive infinity. This method is
+ * semantically equivalent to {@code nextAfter(d,
+ * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
+ * implementation may run faster than its equivalent
+ * {@code nextAfter} call.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, the result is NaN.
+ *
+ * <li> If the argument is positive infinity, the result is
+ * positive infinity.
+ *
+ * <li> If the argument is zero, the result is
+ * {@link Double#MIN_VALUE}
+ *
+ * </ul>
+ *
+ * @param d starting floating-point value
+ * @return The adjacent floating-point value closer to positive
+ * infinity.
+ * @since 1.6
+ */
+ public static double nextUp(double d) {
+ return Math.nextUp(d);
+ }
+
+ /**
+ * Returns the floating-point value adjacent to {@code f} in
+ * the direction of positive infinity. This method is
+ * semantically equivalent to {@code nextAfter(f,
+ * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
+ * implementation may run faster than its equivalent
+ * {@code nextAfter} call.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, the result is NaN.
+ *
+ * <li> If the argument is positive infinity, the result is
+ * positive infinity.
+ *
+ * <li> If the argument is zero, the result is
+ * {@link Float#MIN_VALUE}
+ *
+ * </ul>
+ *
+ * @param f starting floating-point value
+ * @return The adjacent floating-point value closer to positive
+ * infinity.
+ * @since 1.6
+ */
+ public static float nextUp(float f) {
+ return Math.nextUp(f);
+ }
+
+ /**
+ * Returns the floating-point value adjacent to {@code d} in
+ * the direction of negative infinity. This method is
+ * semantically equivalent to {@code nextAfter(d,
+ * Double.NEGATIVE_INFINITY)}; however, a
+ * {@code nextDown} implementation may run faster than its
+ * equivalent {@code nextAfter} call.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, the result is NaN.
+ *
+ * <li> If the argument is negative infinity, the result is
+ * negative infinity.
+ *
+ * <li> If the argument is zero, the result is
+ * {@code -Double.MIN_VALUE}
+ *
+ * </ul>
+ *
+ * @param d starting floating-point value
+ * @return The adjacent floating-point value closer to negative
+ * infinity.
+ * @since 1.8
+ */
+ public static double nextDown(double d) {
+ return Math.nextDown(d);
+ }
+
+ /**
+ * Returns the floating-point value adjacent to {@code f} in
+ * the direction of negative infinity. This method is
+ * semantically equivalent to {@code nextAfter(f,
+ * Float.NEGATIVE_INFINITY)}; however, a
+ * {@code nextDown} implementation may run faster than its
+ * equivalent {@code nextAfter} call.
+ *
+ * <p>Special Cases:
+ * <ul>
+ * <li> If the argument is NaN, the result is NaN.
+ *
+ * <li> If the argument is negative infinity, the result is
+ * negative infinity.
+ *
+ * <li> If the argument is zero, the result is
+ * {@code -Float.MIN_VALUE}
+ *
+ * </ul>
+ *
+ * @param f starting floating-point value
+ * @return The adjacent floating-point value closer to negative
+ * infinity.
+ * @since 1.8
+ */
+ public static float nextDown(float f) {
+ return Math.nextDown(f);
+ }
+
+ /**
+ * Returns {@code d} ×
+ * 2<sup>{@code scaleFactor}</sup> rounded as if performed
+ * by a single correctly rounded floating-point multiply to a
+ * member of the double value set. See the Java
+ * Language Specification for a discussion of floating-point
+ * value sets. If the exponent of the result is between {@link
+ * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
+ * answer is calculated exactly. If the exponent of the result
+ * would be larger than {@code Double.MAX_EXPONENT}, an
+ * infinity is returned. Note that if the result is subnormal,
+ * precision may be lost; that is, when {@code scalb(x, n)}
+ * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
+ * <i>x</i>. When the result is non-NaN, the result has the same
+ * sign as {@code d}.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li> If the first argument is NaN, NaN is returned.
+ * <li> If the first argument is infinite, then an infinity of the
+ * same sign is returned.
+ * <li> If the first argument is zero, then a zero of the same
+ * sign is returned.
+ * </ul>
+ *
+ * @param d number to be scaled by a power of two.
+ * @param scaleFactor power of 2 used to scale {@code d}
+ * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
+ * @since 1.6
+ */
+ public static double scalb(double d, int scaleFactor) {
+ return Math.scalb(d, scaleFactor);
+ }
+
+ /**
+ * Returns {@code f} ×
+ * 2<sup>{@code scaleFactor}</sup> rounded as if performed
+ * by a single correctly rounded floating-point multiply to a
+ * member of the float value set. See the Java
+ * Language Specification for a discussion of floating-point
+ * value sets. If the exponent of the result is between {@link
+ * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
+ * answer is calculated exactly. If the exponent of the result
+ * would be larger than {@code Float.MAX_EXPONENT}, an
+ * infinity is returned. Note that if the result is subnormal,
+ * precision may be lost; that is, when {@code scalb(x, n)}
+ * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
+ * <i>x</i>. When the result is non-NaN, the result has the same
+ * sign as {@code f}.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li> If the first argument is NaN, NaN is returned.
+ * <li> If the first argument is infinite, then an infinity of the
+ * same sign is returned.
+ * <li> If the first argument is zero, then a zero of the same
+ * sign is returned.
+ * </ul>
+ *
+ * @param f number to be scaled by a power of two.
+ * @param scaleFactor power of 2 used to scale {@code f}
+ * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
+ * @since 1.6
+ */
+ public static float scalb(float f, int scaleFactor) {
+ return Math.scalb(f, scaleFactor);
+ }
+}