--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/java.base/share/classes/java/lang/Math.java Tue Sep 12 19:03:39 2017 +0200
@@ -0,0 +1,2714 @@
+/*
+ * Copyright (c) 1994, 2017, 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.math.BigDecimal;
+import java.util.Random;
+import jdk.internal.math.FloatConsts;
+import jdk.internal.math.DoubleConsts;
+import jdk.internal.HotSpotIntrinsicCandidate;
+
+/**
+ * The class {@code Math} contains methods for performing basic
+ * numeric operations such as the elementary exponential, logarithm,
+ * square root, and trigonometric functions.
+ *
+ * <p>Unlike some of the numeric methods of class
+ * {@code StrictMath}, all implementations of the equivalent
+ * functions of class {@code Math} are not defined to return the
+ * bit-for-bit same results. This relaxation permits
+ * better-performing implementations where strict reproducibility is
+ * not required.
+ *
+ * <p>By default many of the {@code Math} methods simply call
+ * the equivalent method in {@code StrictMath} for their
+ * implementation. Code generators are encouraged to use
+ * platform-specific native libraries or microprocessor instructions,
+ * where available, to provide higher-performance implementations of
+ * {@code Math} methods. Such higher-performance
+ * implementations still must conform to the specification for
+ * {@code Math}.
+ *
+ * <p>The quality of implementation specifications concern two
+ * properties, accuracy of the returned result and monotonicity of the
+ * method. Accuracy of the floating-point {@code Math} methods is
+ * measured in terms of <i>ulps</i>, units in the last place. For a
+ * given floating-point format, an {@linkplain #ulp(double) ulp} of a
+ * specific real number value is the distance between the two
+ * floating-point values bracketing that numerical value. When
+ * discussing the accuracy of a method as a whole rather than at a
+ * specific argument, the number of ulps cited is for the worst-case
+ * error at any argument. If a method always has an error less than
+ * 0.5 ulps, the method always returns the floating-point number
+ * nearest the exact result; such a method is <i>correctly
+ * rounded</i>. A correctly rounded method is generally the best a
+ * floating-point approximation can be; however, it is impractical for
+ * many floating-point methods to be correctly rounded. Instead, for
+ * the {@code Math} class, a larger error bound of 1 or 2 ulps is
+ * allowed for certain methods. Informally, with a 1 ulp error bound,
+ * when the exact result is a representable number, the exact result
+ * should be returned as the computed result; otherwise, either of the
+ * two floating-point values which bracket the exact result may be
+ * returned. For exact results large in magnitude, one of the
+ * endpoints of the bracket may be infinite. Besides accuracy at
+ * individual arguments, maintaining proper relations between the
+ * method at different arguments is also important. Therefore, most
+ * methods with more than 0.5 ulp errors are required to be
+ * <i>semi-monotonic</i>: whenever the mathematical function is
+ * non-decreasing, so is the floating-point approximation, likewise,
+ * whenever the mathematical function is non-increasing, so is the
+ * floating-point approximation. Not all approximations that have 1
+ * ulp accuracy will automatically meet the monotonicity requirements.
+ *
+ * <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 1.0
+ */
+
+public final class Math {
+
+ /**
+ * Don't let anyone instantiate this class.
+ */
+ private Math() {}
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a an angle, in radians.
+ * @return the sine of the argument.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double sin(double a) {
+ return StrictMath.sin(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a an angle, in radians.
+ * @return the cosine of the argument.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double cos(double a) {
+ return StrictMath.cos(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a an angle, in radians.
+ * @return the tangent of the argument.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double tan(double a) {
+ return StrictMath.tan(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a the value whose arc sine is to be returned.
+ * @return the arc sine of the argument.
+ */
+ public static double asin(double a) {
+ return StrictMath.asin(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a the value whose arc cosine is to be returned.
+ * @return the arc cosine of the argument.
+ */
+ public static double acos(double a) {
+ return StrictMath.acos(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a the value whose arc tangent is to be returned.
+ * @return the arc tangent of the argument.
+ */
+ public static double atan(double a) {
+ return StrictMath.atan(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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.
+ * @since 1.2
+ */
+ public static double toRadians(double angdeg) {
+ 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.
+ * @since 1.2
+ */
+ public static double toDegrees(double angrad) {
+ 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @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.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double exp(double a) {
+ return StrictMath.exp(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a a value
+ * @return the value ln {@code a}, the natural logarithm of
+ * {@code a}.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double log(double a) {
+ return StrictMath.log(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a a value
+ * @return the base 10 logarithm of {@code a}.
+ * @since 1.5
+ */
+ @HotSpotIntrinsicCandidate
+ public static double log10(double a) {
+ return StrictMath.log10(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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}.
+ * If the argument is NaN or less than zero, the result is NaN.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double sqrt(double a) {
+ return StrictMath.sqrt(a); // default impl. delegates to StrictMath
+ // Note that hardware sqrt instructions
+ // frequently can be directly used by JITs
+ // and should be much faster than doing
+ // Math.sqrt in software.
+ }
+
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ *
+ * @param a a value.
+ * @return the cube root of {@code a}.
+ * @since 1.5
+ */
+ public static double cbrt(double a) {
+ return StrictMath.cbrt(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 double IEEEremainder(double f1, double f2) {
+ return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
+ }
+
+ /**
+ * 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 Math.ceil(x)} is exactly the
+ * value of {@code -Math.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 StrictMath.ceil(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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 StrictMath.floor(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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, 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 {@code double} value.
+ * @return the closest floating-point value to {@code a} that is
+ * equal to a mathematical integer.
+ */
+ public static double rint(double a) {
+ return StrictMath.rint(a); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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>
+ *
+ * <p>The computed result must be within 2 ulps of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @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.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double atan2(double y, double x) {
+ return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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.)
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param a the base.
+ * @param b the exponent.
+ * @return the value {@code a}<sup>{@code b}</sup>.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double pow(double a, double b) {
+ return StrictMath.pow(a, b); // default impl. delegates to StrictMath
+ }
+
+ /**
+ * 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) {
+ int intBits = Float.floatToRawIntBits(a);
+ int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
+ >> (FloatConsts.SIGNIFICAND_WIDTH - 1);
+ int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
+ + FloatConsts.EXP_BIAS) - biasedExp;
+ if ((shift & -32) == 0) { // shift >= 0 && shift < 32
+ // a is a finite number such that pow(2,-32) <= ulp(a) < 1
+ int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
+ | (FloatConsts.SIGNIF_BIT_MASK + 1));
+ if (intBits < 0) {
+ r = -r;
+ }
+ // In the comments below each Java expression evaluates to the value
+ // the corresponding mathematical expression:
+ // (r) evaluates to a / ulp(a)
+ // (r >> shift) evaluates to floor(a * 2)
+ // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
+ // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
+ return ((r >> shift) + 1) >> 1;
+ } else {
+ // a is either
+ // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
+ // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
+ // - an infinity or NaN
+ return (int) 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) {
+ long longBits = Double.doubleToRawLongBits(a);
+ long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
+ >> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
+ long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
+ + DoubleConsts.EXP_BIAS) - biasedExp;
+ if ((shift & -64) == 0) { // shift >= 0 && shift < 64
+ // a is a finite number such that pow(2,-64) <= ulp(a) < 1
+ long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
+ | (DoubleConsts.SIGNIF_BIT_MASK + 1));
+ if (longBits < 0) {
+ r = -r;
+ }
+ // In the comments below each Java expression evaluates to the value
+ // the corresponding mathematical expression:
+ // (r) evaluates to a / ulp(a)
+ // (r >> shift) evaluates to floor(a * 2)
+ // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
+ // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
+ return ((r >> shift) + 1) >> 1;
+ } else {
+ // a is either
+ // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
+ // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
+ // - an infinity or NaN
+ return (long) 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.
+ *
+ * @apiNote
+ * As the largest {@code double} value less than {@code 1.0}
+ * is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range
+ * {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements
+ *
+ * <blockquote><pre>{@code
+ * double f = Math.random()/Math.nextDown(1.0);
+ * double x = x1*(1.0 - f) + x2*f;
+ * }</pre></blockquote>
+ *
+ * @return a pseudorandom {@code double} greater than or equal
+ * to {@code 0.0} and less than {@code 1.0}.
+ * @see #nextDown(double)
+ * @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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int addExact(int x, int y) {
+ int r = x + y;
+ // HD 2-12 Overflow iff both arguments have the opposite sign of the result
+ if (((x ^ r) & (y ^ r)) < 0) {
+ throw new ArithmeticException("integer overflow");
+ }
+ return r;
+ }
+
+ /**
+ * 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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long addExact(long x, long y) {
+ long r = x + y;
+ // HD 2-12 Overflow iff both arguments have the opposite sign of the result
+ if (((x ^ r) & (y ^ r)) < 0) {
+ throw new ArithmeticException("long overflow");
+ }
+ return r;
+ }
+
+ /**
+ * 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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int subtractExact(int x, int y) {
+ int r = x - y;
+ // HD 2-12 Overflow iff the arguments have different signs and
+ // the sign of the result is different from the sign of x
+ if (((x ^ y) & (x ^ r)) < 0) {
+ throw new ArithmeticException("integer overflow");
+ }
+ return r;
+ }
+
+ /**
+ * 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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long subtractExact(long x, long y) {
+ long r = x - y;
+ // HD 2-12 Overflow iff the arguments have different signs and
+ // the sign of the result is different from the sign of x
+ if (((x ^ y) & (x ^ r)) < 0) {
+ throw new ArithmeticException("long overflow");
+ }
+ return r;
+ }
+
+ /**
+ * 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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int multiplyExact(int x, int y) {
+ long r = (long)x * (long)y;
+ if ((int)r != r) {
+ throw new ArithmeticException("integer overflow");
+ }
+ return (int)r;
+ }
+
+ /**
+ * 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
+ * @since 9
+ */
+ public static long multiplyExact(long x, int y) {
+ return multiplyExact(x, (long)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
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long multiplyExact(long x, long y) {
+ long r = x * y;
+ long ax = Math.abs(x);
+ long ay = Math.abs(y);
+ if (((ax | ay) >>> 31 != 0)) {
+ // Some bits greater than 2^31 that might cause overflow
+ // Check the result using the divide operator
+ // and check for the special case of Long.MIN_VALUE * -1
+ if (((y != 0) && (r / y != x)) ||
+ (x == Long.MIN_VALUE && y == -1)) {
+ throw new ArithmeticException("long overflow");
+ }
+ }
+ return r;
+ }
+
+ /**
+ * Returns the argument incremented by one, throwing an exception if the
+ * result overflows an {@code int}.
+ *
+ * @param a the value to increment
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int incrementExact(int a) {
+ if (a == Integer.MAX_VALUE) {
+ throw new ArithmeticException("integer overflow");
+ }
+
+ return a + 1;
+ }
+
+ /**
+ * Returns the argument incremented by one, throwing an exception if the
+ * result overflows a {@code long}.
+ *
+ * @param a the value to increment
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long incrementExact(long a) {
+ if (a == Long.MAX_VALUE) {
+ throw new ArithmeticException("long overflow");
+ }
+
+ return a + 1L;
+ }
+
+ /**
+ * Returns the argument decremented by one, throwing an exception if the
+ * result overflows an {@code int}.
+ *
+ * @param a the value to decrement
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int decrementExact(int a) {
+ if (a == Integer.MIN_VALUE) {
+ throw new ArithmeticException("integer overflow");
+ }
+
+ return a - 1;
+ }
+
+ /**
+ * Returns the argument decremented by one, throwing an exception if the
+ * result overflows a {@code long}.
+ *
+ * @param a the value to decrement
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long decrementExact(long a) {
+ if (a == Long.MIN_VALUE) {
+ throw new ArithmeticException("long overflow");
+ }
+
+ return a - 1L;
+ }
+
+ /**
+ * Returns the negation of the argument, throwing an exception if the
+ * result overflows an {@code int}.
+ *
+ * @param a the value to negate
+ * @return the result
+ * @throws ArithmeticException if the result overflows an int
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static int negateExact(int a) {
+ if (a == Integer.MIN_VALUE) {
+ throw new ArithmeticException("integer overflow");
+ }
+
+ return -a;
+ }
+
+ /**
+ * Returns the negation of the argument, throwing an exception if the
+ * result overflows a {@code long}.
+ *
+ * @param a the value to negate
+ * @return the result
+ * @throws ArithmeticException if the result overflows a long
+ * @since 1.8
+ */
+ @HotSpotIntrinsicCandidate
+ public static long negateExact(long a) {
+ if (a == Long.MIN_VALUE) {
+ throw new ArithmeticException("long overflow");
+ }
+
+ return -a;
+ }
+
+ /**
+ * 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
+ * @since 1.8
+ */
+ public static int toIntExact(long value) {
+ if ((int)value != value) {
+ throw new ArithmeticException("integer overflow");
+ }
+ return (int)value;
+ }
+
+ /**
+ * Returns the exact mathematical product of the arguments.
+ *
+ * @param x the first value
+ * @param y the second value
+ * @return the result
+ * @since 9
+ */
+ public static long multiplyFull(int x, int y) {
+ return (long)x * (long)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
+ * @since 9
+ */
+ public static long multiplyHigh(long x, long y) {
+ if (x < 0 || y < 0) {
+ // Use technique from section 8-2 of Henry S. Warren, Jr.,
+ // Hacker's Delight (2nd ed.) (Addison Wesley, 2013), 173-174.
+ long x1 = x >> 32;
+ long x2 = x & 0xFFFFFFFFL;
+ long y1 = y >> 32;
+ long y2 = y & 0xFFFFFFFFL;
+ long z2 = x2 * y2;
+ long t = x1 * y2 + (z2 >>> 32);
+ long z1 = t & 0xFFFFFFFFL;
+ long z0 = t >> 32;
+ z1 += x2 * y1;
+ return x1 * y1 + z0 + (z1 >> 32);
+ } else {
+ // Use Karatsuba technique with two base 2^32 digits.
+ long x1 = x >>> 32;
+ long y1 = y >>> 32;
+ long x2 = x & 0xFFFFFFFFL;
+ long y2 = y & 0xFFFFFFFFL;
+ long A = x1 * y1;
+ long B = x2 * y2;
+ long C = (x1 + x2) * (y1 + y2);
+ long K = C - A - B;
+ return (((B >>> 32) + K) >>> 32) + A;
+ }
+ }
+
+ /**
+ * 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 {@code Integer.MIN_VALUE}.
+ * <p>
+ * Normal integer division operates under the round to zero rounding mode
+ * (truncation). This operation instead acts under the round toward
+ * negative infinity (floor) rounding mode.
+ * The floor rounding mode gives different results from truncation
+ * when the exact result is negative.
+ * <ul>
+ * <li>If the signs of the arguments are the same, the results of
+ * {@code floorDiv} and the {@code /} operator are the same. <br>
+ * For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
+ * <li>If the signs of the arguments are different, the quotient is negative and
+ * {@code floorDiv} returns the integer less than or equal to the quotient
+ * and the {@code /} operator returns the integer closest to zero.<br>
+ * For example, {@code floorDiv(-4, 3) == -2},
+ * whereas {@code (-4 / 3) == -1}.
+ * </li>
+ * </ul>
+ *
+ * @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 #floorMod(int, int)
+ * @see #floor(double)
+ * @since 1.8
+ */
+ public static int floorDiv(int x, int y) {
+ int r = x / y;
+ // if the signs are different and modulo not zero, round down
+ if ((x ^ y) < 0 && (r * y != x)) {
+ r--;
+ }
+ return r;
+ }
+
+ /**
+ * 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>
+ * Normal integer division operates under the round to zero rounding mode
+ * (truncation). This operation instead acts under the round toward
+ * negative infinity (floor) rounding mode.
+ * The floor rounding mode gives different results from truncation
+ * when the exact result is negative.
+ * <p>
+ * For examples, see {@link #floorDiv(int, int)}.
+ *
+ * @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 #floorMod(long, int)
+ * @see #floor(double)
+ * @since 9
+ */
+ public static long floorDiv(long x, int y) {
+ return floorDiv(x, (long)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>
+ * Normal integer division operates under the round to zero rounding mode
+ * (truncation). This operation instead acts under the round toward
+ * negative infinity (floor) rounding mode.
+ * The floor rounding mode gives different results from truncation
+ * when the exact result is negative.
+ * <p>
+ * For examples, see {@link #floorDiv(int, int)}.
+ *
+ * @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 #floorMod(long, long)
+ * @see #floor(double)
+ * @since 1.8
+ */
+ public static long floorDiv(long x, long y) {
+ long r = x / y;
+ // if the signs are different and modulo not zero, round down
+ if ((x ^ y) < 0 && (r * y != x)) {
+ r--;
+ }
+ return r;
+ }
+
+ /**
+ * 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>
+ * The difference in values between {@code floorMod} and
+ * the {@code %} operator is due to the difference between
+ * {@code floorDiv} that returns the integer less than or equal to the quotient
+ * and the {@code /} operator that returns the integer closest to zero.
+ * <p>
+ * Examples:
+ * <ul>
+ * <li>If the signs of the arguments are the same, the results
+ * of {@code floorMod} and the {@code %} operator are the same. <br>
+ * <ul>
+ * <li>{@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}</li>
+ * </ul>
+ * <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br>
+ * <ul>
+ * <li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1} </li>
+ * <li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1} </li>
+ * <li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 } </li>
+ * </ul>
+ * </li>
+ * </ul>
+ * <p>
+ * If the signs of arguments are unknown and a positive modulus
+ * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
+ *
+ * @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 #floorDiv(int, int)
+ * @since 1.8
+ */
+ public static int floorMod(int x, int y) {
+ return x - floorDiv(x, y) * 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>
+ * For examples, see {@link #floorMod(int, int)}.
+ *
+ * @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 #floorDiv(long, int)
+ * @since 9
+ */
+ public static int floorMod(long x, int y) {
+ // Result cannot overflow the range of int.
+ return (int)(x - floorDiv(x, y) * 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>
+ * For examples, see {@link #floorMod(int, int)}.
+ *
+ * @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 #floorDiv(long, long)
+ * @since 1.8
+ */
+ public static long floorMod(long x, long y) {
+ return x - floorDiv(x, y) * 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 (a < 0) ? -a : 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 (a < 0) ? -a : 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 (a <= 0.0F) ? 0.0F - a : 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.
+ */
+ @HotSpotIntrinsicCandidate
+ public static double abs(double a) {
+ return (a <= 0.0D) ? 0.0D - a : 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 (a >= b) ? 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 (a >= b) ? a : b;
+ }
+
+ // Use raw bit-wise conversions on guaranteed non-NaN arguments.
+ private static final long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
+ private static final long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
+
+ /**
+ * 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) {
+ if (a != a)
+ return a; // a is NaN
+ if ((a == 0.0f) &&
+ (b == 0.0f) &&
+ (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
+ // Raw conversion ok since NaN can't map to -0.0.
+ return b;
+ }
+ return (a >= b) ? 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) {
+ if (a != a)
+ return a; // a is NaN
+ if ((a == 0.0d) &&
+ (b == 0.0d) &&
+ (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
+ // Raw conversion ok since NaN can't map to -0.0.
+ return b;
+ }
+ return (a >= b) ? 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 (a <= b) ? 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 (a <= b) ? 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) {
+ if (a != a)
+ return a; // a is NaN
+ if ((a == 0.0f) &&
+ (b == 0.0f) &&
+ (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
+ // Raw conversion ok since NaN can't map to -0.0.
+ return b;
+ }
+ return (a <= b) ? 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) {
+ if (a != a)
+ return a; // a is NaN
+ if ((a == 0.0d) &&
+ (b == 0.0d) &&
+ (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
+ // Raw conversion ok since NaN can't map to -0.0.
+ return b;
+ }
+ return (a <= b) ? 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 fma(a, 1.0, c)} returns the same
+ * result as ({@code a + c}). However,
+ * {@code fma(a, b, +0.0)} does <em>not</em> always return the
+ * same result as ({@code a * b}) since
+ * {@code fma(-0.0, +0.0, +0.0)} is {@code +0.0} while
+ * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fma(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
+ */
+ @HotSpotIntrinsicCandidate
+ public static double fma(double a, double b, double c) {
+ /*
+ * Infinity and NaN arithmetic is not quite the same with two
+ * roundings as opposed to just one so the simple expression
+ * "a * b + c" cannot always be used to compute the correct
+ * result. With two roundings, the product can overflow and
+ * if the addend is infinite, a spurious NaN can be produced
+ * if the infinity from the overflow and the infinite addend
+ * have opposite signs.
+ */
+
+ // First, screen for and handle non-finite input values whose
+ // arithmetic is not supported by BigDecimal.
+ if (Double.isNaN(a) || Double.isNaN(b) || Double.isNaN(c)) {
+ return Double.NaN;
+ } else { // All inputs non-NaN
+ boolean infiniteA = Double.isInfinite(a);
+ boolean infiniteB = Double.isInfinite(b);
+ boolean infiniteC = Double.isInfinite(c);
+ double result;
+
+ if (infiniteA || infiniteB || infiniteC) {
+ if (infiniteA && b == 0.0 ||
+ infiniteB && a == 0.0 ) {
+ return Double.NaN;
+ }
+ // Store product in a double field to cause an
+ // overflow even if non-strictfp evaluation is being
+ // used.
+ double product = a * b;
+ if (Double.isInfinite(product) && !infiniteA && !infiniteB) {
+ // Intermediate overflow; might cause a
+ // spurious NaN if added to infinite c.
+ assert Double.isInfinite(c);
+ return c;
+ } else {
+ result = product + c;
+ assert !Double.isFinite(result);
+ return result;
+ }
+ } else { // All inputs finite
+ BigDecimal product = (new BigDecimal(a)).multiply(new BigDecimal(b));
+ if (c == 0.0) { // Positive or negative zero
+ // If the product is an exact zero, use a
+ // floating-point expression to compute the sign
+ // of the zero final result. The product is an
+ // exact zero if and only if at least one of a and
+ // b is zero.
+ if (a == 0.0 || b == 0.0) {
+ return a * b + c;
+ } else {
+ // The sign of a zero addend doesn't matter if
+ // the product is nonzero. The sign of a zero
+ // addend is not factored in the result if the
+ // exact product is nonzero but underflows to
+ // zero; see IEEE-754 2008 section 6.3 "The
+ // sign bit".
+ return product.doubleValue();
+ }
+ } else {
+ return product.add(new BigDecimal(c)).doubleValue();
+ }
+ }
+ }
+ }
+
+ /**
+ * 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
+ */
+ @HotSpotIntrinsicCandidate
+ public static float fma(float a, float b, float c) {
+ /*
+ * Since the double format has more than twice the precision
+ * of the float format, the multiply of a * b is exact in
+ * double. The add of c to the product then incurs one
+ * rounding error. Since the double format moreover has more
+ * than (2p + 2) precision bits compared to the p bits of the
+ * float format, the two roundings of (a * b + c), first to
+ * the double format and then secondarily to the float format,
+ * are equivalent to rounding the intermediate result directly
+ * to the float format.
+ *
+ * In terms of strictfp vs default-fp concerns related to
+ * overflow and underflow, since
+ *
+ * (Float.MAX_VALUE * Float.MAX_VALUE) << Double.MAX_VALUE
+ * (Float.MIN_VALUE * Float.MIN_VALUE) >> Double.MIN_VALUE
+ *
+ * neither the multiply nor add will overflow or underflow in
+ * double. Therefore, it is not necessary for this method to
+ * be declared strictfp to have reproducible
+ * behavior. However, it is necessary to explicitly store down
+ * to a float variable to avoid returning a value in the float
+ * extended value set.
+ */
+ float result = (float)(((double) a * (double) b ) + (double) c);
+ return result;
+ }
+
+ /**
+ * 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) {
+ int exp = getExponent(d);
+
+ switch(exp) {
+ case Double.MAX_EXPONENT + 1: // NaN or infinity
+ return Math.abs(d);
+
+ case Double.MIN_EXPONENT - 1: // zero or subnormal
+ return Double.MIN_VALUE;
+
+ default:
+ assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT;
+
+ // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
+ exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
+ if (exp >= Double.MIN_EXPONENT) {
+ return powerOfTwoD(exp);
+ }
+ else {
+ // return a subnormal result; left shift integer
+ // representation of Double.MIN_VALUE appropriate
+ // number of positions
+ return Double.longBitsToDouble(1L <<
+ (exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
+ }
+ }
+ }
+
+ /**
+ * 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) {
+ int exp = getExponent(f);
+
+ switch(exp) {
+ case Float.MAX_EXPONENT+1: // NaN or infinity
+ return Math.abs(f);
+
+ case Float.MIN_EXPONENT-1: // zero or subnormal
+ return Float.MIN_VALUE;
+
+ default:
+ assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT;
+
+ // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
+ exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
+ if (exp >= Float.MIN_EXPONENT) {
+ return powerOfTwoF(exp);
+ } else {
+ // return a subnormal result; left shift integer
+ // representation of FloatConsts.MIN_VALUE appropriate
+ // number of positions
+ return Float.intBitsToFloat(1 <<
+ (exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
+ }
+ }
+ }
+
+ /**
+ * 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 (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, 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 (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, 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>
+ *
+ * <p>The computed result must be within 2.5 ulps of the exact result.
+ *
+ * @param x The number whose hyperbolic sine is to be returned.
+ * @return The hyperbolic sine of {@code x}.
+ * @since 1.5
+ */
+ public static double sinh(double x) {
+ return StrictMath.sinh(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>
+ *
+ * <p>The computed result must be within 2.5 ulps of the exact result.
+ *
+ * @param x The number whose hyperbolic cosine is to be returned.
+ * @return The hyperbolic cosine of {@code x}.
+ * @since 1.5
+ */
+ public static double cosh(double x) {
+ return StrictMath.cosh(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>
+ *
+ * <p>The computed result must be within 2.5 ulps of the exact result.
+ * The result of {@code tanh} for any finite input must have
+ * an absolute value less than or equal to 1. Note that once the
+ * exact result of tanh is within 1/2 of an ulp of the limit value
+ * of ±1, correctly signed ±{@code 1.0} should
+ * be returned.
+ *
+ * @param x The number whose hyperbolic tangent is to be returned.
+ * @return The hyperbolic tangent of {@code x}.
+ * @since 1.5
+ */
+ public static double tanh(double x) {
+ return StrictMath.tanh(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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact
+ * result. If one parameter is held constant, the results must be
+ * semi-monotonic in the other parameter.
+ *
+ * @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 StrictMath.hypot(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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic. The result of
+ * {@code expm1} for any finite input must be greater than or
+ * equal to {@code -1.0}. Note that once the exact result of
+ * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
+ * ulp of the limit value -1, {@code -1.0} should be
+ * returned.
+ *
+ * @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 double expm1(double x) {
+ return StrictMath.expm1(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>
+ *
+ * <p>The computed result must be within 1 ulp of the exact result.
+ * Results must be semi-monotonic.
+ *
+ * @param x a value
+ * @return the value ln({@code x} + 1), the natural
+ * log of {@code x} + 1
+ * @since 1.5
+ */
+ public static double log1p(double x) {
+ return StrictMath.log1p(x);
+ }
+
+ /**
+ * Returns the first floating-point argument with the sign of the
+ * second floating-point argument. Note that unlike the {@link
+ * StrictMath#copySign(double, double) StrictMath.copySign}
+ * method, this method does not require NaN {@code sign}
+ * arguments to be treated as positive values; implementations are
+ * permitted to treat some NaN arguments as positive and other NaN
+ * arguments as negative to allow greater performance.
+ *
+ * @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 Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
+ (DoubleConsts.SIGN_BIT_MASK)) |
+ (Double.doubleToRawLongBits(magnitude) &
+ (DoubleConsts.EXP_BIT_MASK |
+ DoubleConsts.SIGNIF_BIT_MASK)));
+ }
+
+ /**
+ * Returns the first floating-point argument with the sign of the
+ * second floating-point argument. Note that unlike the {@link
+ * StrictMath#copySign(float, float) StrictMath.copySign}
+ * method, this method does not require NaN {@code sign}
+ * arguments to be treated as positive values; implementations are
+ * permitted to treat some NaN arguments as positive and other NaN
+ * arguments as negative to allow greater performance.
+ *
+ * @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 Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
+ (FloatConsts.SIGN_BIT_MASK)) |
+ (Float.floatToRawIntBits(magnitude) &
+ (FloatConsts.EXP_BIT_MASK |
+ FloatConsts.SIGNIF_BIT_MASK)));
+ }
+
+ /**
+ * 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) {
+ /*
+ * Bitwise convert f to integer, mask out exponent bits, shift
+ * to the right and then subtract out float's bias adjust to
+ * get true exponent value
+ */
+ return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
+ (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
+ }
+
+ /**
+ * 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) {
+ /*
+ * Bitwise convert d to long, mask out exponent bits, shift
+ * to the right and then subtract out double's bias adjust to
+ * get true exponent value.
+ */
+ return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
+ (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
+ }
+
+ /**
+ * 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) {
+ /*
+ * The cases:
+ *
+ * nextAfter(+infinity, 0) == MAX_VALUE
+ * nextAfter(+infinity, +infinity) == +infinity
+ * nextAfter(-infinity, 0) == -MAX_VALUE
+ * nextAfter(-infinity, -infinity) == -infinity
+ *
+ * are naturally handled without any additional testing
+ */
+
+ /*
+ * IEEE 754 floating-point numbers are lexicographically
+ * ordered if treated as signed-magnitude integers.
+ * Since Java's integers are two's complement,
+ * incrementing the two's complement representation of a
+ * logically negative floating-point value *decrements*
+ * the signed-magnitude representation. Therefore, when
+ * the integer representation of a floating-point value
+ * is negative, the adjustment to the representation is in
+ * the opposite direction from what would initially be expected.
+ */
+
+ // Branch to descending case first as it is more costly than ascending
+ // case due to start != 0.0d conditional.
+ if (start > direction) { // descending
+ if (start != 0.0d) {
+ final long transducer = Double.doubleToRawLongBits(start);
+ return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L));
+ } else { // start == 0.0d && direction < 0.0d
+ return -Double.MIN_VALUE;
+ }
+ } else if (start < direction) { // ascending
+ // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
+ // then bitwise convert start to integer.
+ final long transducer = Double.doubleToRawLongBits(start + 0.0d);
+ return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
+ } else if (start == direction) {
+ return direction;
+ } else { // isNaN(start) || isNaN(direction)
+ return 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) {
+ /*
+ * The cases:
+ *
+ * nextAfter(+infinity, 0) == MAX_VALUE
+ * nextAfter(+infinity, +infinity) == +infinity
+ * nextAfter(-infinity, 0) == -MAX_VALUE
+ * nextAfter(-infinity, -infinity) == -infinity
+ *
+ * are naturally handled without any additional testing
+ */
+
+ /*
+ * IEEE 754 floating-point numbers are lexicographically
+ * ordered if treated as signed-magnitude integers.
+ * Since Java's integers are two's complement,
+ * incrementing the two's complement representation of a
+ * logically negative floating-point value *decrements*
+ * the signed-magnitude representation. Therefore, when
+ * the integer representation of a floating-point value
+ * is negative, the adjustment to the representation is in
+ * the opposite direction from what would initially be expected.
+ */
+
+ // Branch to descending case first as it is more costly than ascending
+ // case due to start != 0.0f conditional.
+ if (start > direction) { // descending
+ if (start != 0.0f) {
+ final int transducer = Float.floatToRawIntBits(start);
+ return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1));
+ } else { // start == 0.0f && direction < 0.0f
+ return -Float.MIN_VALUE;
+ }
+ } else if (start < direction) { // ascending
+ // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
+ // then bitwise convert start to integer.
+ final int transducer = Float.floatToRawIntBits(start + 0.0f);
+ return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
+ } else if (start == direction) {
+ return (float)direction;
+ } else { // isNaN(start) || isNaN(direction)
+ return start + (float)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) {
+ // Use a single conditional and handle the likely cases first.
+ if (d < Double.POSITIVE_INFINITY) {
+ // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
+ final long transducer = Double.doubleToRawLongBits(d + 0.0D);
+ return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
+ } else { // d is NaN or +Infinity
+ return 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) {
+ // Use a single conditional and handle the likely cases first.
+ if (f < Float.POSITIVE_INFINITY) {
+ // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
+ final int transducer = Float.floatToRawIntBits(f + 0.0F);
+ return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
+ } else { // f is NaN or +Infinity
+ return 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) {
+ if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
+ return d;
+ else {
+ if (d == 0.0)
+ return -Double.MIN_VALUE;
+ else
+ return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
+ ((d > 0.0d)?-1L:+1L));
+ }
+ }
+
+ /**
+ * 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) {
+ if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
+ return f;
+ else {
+ if (f == 0.0f)
+ return -Float.MIN_VALUE;
+ else
+ return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
+ ((f > 0.0f)?-1:+1));
+ }
+ }
+
+ /**
+ * 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) {
+ /*
+ * This method does not need to be declared strictfp to
+ * compute the same correct result on all platforms. When
+ * scaling up, it does not matter what order the
+ * multiply-store operations are done; the result will be
+ * finite or overflow regardless of the operation ordering.
+ * However, to get the correct result when scaling down, a
+ * particular ordering must be used.
+ *
+ * When scaling down, the multiply-store operations are
+ * sequenced so that it is not possible for two consecutive
+ * multiply-stores to return subnormal results. If one
+ * multiply-store result is subnormal, the next multiply will
+ * round it away to zero. This is done by first multiplying
+ * by 2 ^ (scaleFactor % n) and then multiplying several
+ * times by 2^n as needed where n is the exponent of number
+ * that is a covenient power of two. In this way, at most one
+ * real rounding error occurs. If the double value set is
+ * being used exclusively, the rounding will occur on a
+ * multiply. If the double-extended-exponent value set is
+ * being used, the products will (perhaps) be exact but the
+ * stores to d are guaranteed to round to the double value
+ * set.
+ *
+ * It is _not_ a valid implementation to first multiply d by
+ * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %
+ * MIN_EXPONENT) since even in a strictfp program double
+ * rounding on underflow could occur; e.g. if the scaleFactor
+ * argument was (MIN_EXPONENT - n) and the exponent of d was a
+ * little less than -(MIN_EXPONENT - n), meaning the final
+ * result would be subnormal.
+ *
+ * Since exact reproducibility of this method can be achieved
+ * without any undue performance burden, there is no
+ * compelling reason to allow double rounding on underflow in
+ * scalb.
+ */
+
+ // magnitude of a power of two so large that scaling a finite
+ // nonzero value by it would be guaranteed to over or
+ // underflow; due to rounding, scaling down takes an
+ // additional power of two which is reflected here
+ final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT +
+ DoubleConsts.SIGNIFICAND_WIDTH + 1;
+ int exp_adjust = 0;
+ int scale_increment = 0;
+ double exp_delta = Double.NaN;
+
+ // Make sure scaling factor is in a reasonable range
+
+ if(scaleFactor < 0) {
+ scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
+ scale_increment = -512;
+ exp_delta = twoToTheDoubleScaleDown;
+ }
+ else {
+ scaleFactor = Math.min(scaleFactor, MAX_SCALE);
+ scale_increment = 512;
+ exp_delta = twoToTheDoubleScaleUp;
+ }
+
+ // Calculate (scaleFactor % +/-512), 512 = 2^9, using
+ // technique from "Hacker's Delight" section 10-2.
+ int t = (scaleFactor >> 9-1) >>> 32 - 9;
+ exp_adjust = ((scaleFactor + t) & (512 -1)) - t;
+
+ d *= powerOfTwoD(exp_adjust);
+ scaleFactor -= exp_adjust;
+
+ while(scaleFactor != 0) {
+ d *= exp_delta;
+ scaleFactor -= scale_increment;
+ }
+ return d;
+ }
+
+ /**
+ * 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) {
+ // magnitude of a power of two so large that scaling a finite
+ // nonzero value by it would be guaranteed to over or
+ // underflow; due to rounding, scaling down takes an
+ // additional power of two which is reflected here
+ final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT +
+ FloatConsts.SIGNIFICAND_WIDTH + 1;
+
+ // Make sure scaling factor is in a reasonable range
+ scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);
+
+ /*
+ * Since + MAX_SCALE for float fits well within the double
+ * exponent range and + float -> double conversion is exact
+ * the multiplication below will be exact. Therefore, the
+ * rounding that occurs when the double product is cast to
+ * float will be the correctly rounded float result. Since
+ * all operations other than the final multiply will be exact,
+ * it is not necessary to declare this method strictfp.
+ */
+ return (float)((double)f*powerOfTwoD(scaleFactor));
+ }
+
+ // Constants used in scalb
+ static double twoToTheDoubleScaleUp = powerOfTwoD(512);
+ static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
+
+ /**
+ * Returns a floating-point power of two in the normal range.
+ */
+ static double powerOfTwoD(int n) {
+ assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT);
+ return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
+ (DoubleConsts.SIGNIFICAND_WIDTH-1))
+ & DoubleConsts.EXP_BIT_MASK);
+ }
+
+ /**
+ * Returns a floating-point power of two in the normal range.
+ */
+ static float powerOfTwoF(int n) {
+ assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT);
+ return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
+ (FloatConsts.SIGNIFICAND_WIDTH-1))
+ & FloatConsts.EXP_BIT_MASK);
+ }
+}