2667 lines
99 KiB
Java
2667 lines
99 KiB
Java
/*
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* Copyright (c) 1999, 2023, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package java.lang;
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import java.util.Random;
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import jdk.internal.math.DoubleConsts;
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import jdk.internal.vm.annotation.IntrinsicCandidate;
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/**
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* The class {@code StrictMath} contains methods for performing basic
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* numeric operations such as the elementary exponential, logarithm,
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* square root, and trigonometric functions.
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*
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* <p>To help ensure portability of Java programs, the definitions of
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* some of the numeric functions in this package require that they
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* produce the same results as certain published algorithms. These
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* algorithms are available from the well-known network library
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* {@code netlib} as the package "Freely Distributable Math
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* Library," <a
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* href="https://www.netlib.org/fdlibm/">{@code fdlibm}</a>. These
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* algorithms, which are written in the C programming language, are
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* then to be understood to be transliterated into Java and executed
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* with all floating-point and integer operations following the rules
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* of Java arithmetic. The following transformations are used in the
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* transliteration:
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*
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* <ul>
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* <li>Extraction and setting of the high and low halves of a 64-bit
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* {@code double} in C is expressed using Java platform methods that
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* perform bit-wise conversions {@linkplain
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* Double#doubleToRawLongBits(double) from {@code double} to {@code
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* long}} and {@linkplain Double#longBitsToDouble(long) {@code long}
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* to {@code double}}.
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*
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* <li>Unsigned {@code int} values in C are mapped to signed {@code
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* int} values in Java with updates to operations to replicate
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* unsigned semantics where the results on the same textual operation
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* would differ. For example, {@code >>} shifts on unsigned C values
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* are replaced with {@code >>>} shifts on signed Java values. Sized
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* comparisons on unsigned C values ({@code <}, {@code <=}, {@code >},
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* {@code >=}) are replaced with semantically equivalent calls to
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* {@link Integer#compareUnsigned(int, int) compareUnsigned}.
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* </ul>
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*
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* <p>The Java math library is defined with respect to
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* {@code fdlibm} version 5.3. Where {@code fdlibm} provides
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* more than one definition for a function (such as
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* {@code acos}), use the "IEEE 754 core function" version
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* (residing in a file whose name begins with the letter
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* {@code e}). The methods which require {@code fdlibm}
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* semantics are {@code sin}, {@code cos}, {@code tan},
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* {@code asin}, {@code acos}, {@code atan},
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* {@code exp}, {@code log}, {@code log10},
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* {@code cbrt}, {@code atan2}, {@code pow},
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* {@code sinh}, {@code cosh}, {@code tanh},
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* {@code hypot}, {@code expm1}, and {@code log1p}.
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*
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* <p>
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* The platform uses signed two's complement integer arithmetic with
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* int and long primitive types. The developer should choose
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* the primitive type to ensure that arithmetic operations consistently
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* produce correct results, which in some cases means the operations
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* will not overflow the range of values of the computation.
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* The best practice is to choose the primitive type and algorithm to avoid
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* overflow. In cases where the size is {@code int} or {@code long} and
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* overflow errors need to be detected, the methods whose names end with
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* {@code Exact} throw an {@code ArithmeticException} when the results overflow.
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*
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* <h2><a id=Ieee754RecommendedOps>IEEE 754 Recommended
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* Operations</a></h2>
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*
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* The {@link java.lang.Math Math} class discusses how the shared
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* quality of implementation criteria for selected {@code Math} and
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* {@code StrictMath} methods <a
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* href="Math.html#Ieee754RecommendedOps">relate to the IEEE 754
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* recommended operations</a>.
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*
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* @see <a href="https://standards.ieee.org/ieee/754/6210/">
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* <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
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*
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* @author Joseph D. Darcy
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* @since 1.3
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*/
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public final class StrictMath {
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/**
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* Don't let anyone instantiate this class.
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*/
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private StrictMath() {}
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/**
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* The {@code double} value that is closer than any other to
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* <i>e</i>, the base of the natural logarithms.
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*/
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public static final double E = 2.718281828459045;
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/**
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* The {@code double} value that is closer than any other to
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* <i>pi</i> (π), the ratio of the circumference of a circle to its
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* diameter.
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*/
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public static final double PI = 3.141592653589793;
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/**
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* The {@code double} value that is closer than any other to
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* <i>tau</i> (τ), the ratio of the circumference of a circle
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* to its radius.
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*
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* @apiNote
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* The value of <i>pi</i> is one half that of <i>tau</i>; in other
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* words, <i>tau</i> is double <i>pi</i> .
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*
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* @since 19
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*/
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public static final double TAU = 2.0 * PI;
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/**
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* Constant by which to multiply an angular value in degrees to obtain an
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* angular value in radians.
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*/
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private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
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/**
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* Constant by which to multiply an angular value in radians to obtain an
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* angular value in degrees.
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*/
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private static final double RADIANS_TO_DEGREES = 57.29577951308232;
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/**
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* Returns the trigonometric sine of an angle. Special cases:
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* <ul><li>If the argument is NaN or an infinity, then the
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* result is NaN.
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* <li>If the argument is zero, then the result is a zero with the
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* same sign as the argument.</ul>
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*
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* @param a an angle, in radians.
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* @return the sine of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double sin(double a) {
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// return FdLibm.Sin.compute(a);
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// }
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public static native double sin(double a);
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/**
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* Returns the trigonometric cosine of an angle. Special cases:
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* <ul><li>If the argument is NaN or an infinity, then the
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* result is NaN.
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* <li>If the argument is zero, then the result is {@code 1.0}.
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* </ul>
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*
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* @param a an angle, in radians.
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* @return the cosine of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double cos(double a) {
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// return FdLibm.Cos.compute(a);
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// }
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public static native double cos(double a);
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/**
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* Returns the trigonometric tangent of an angle. Special cases:
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* <ul><li>If the argument is NaN or an infinity, then the result
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* is NaN.
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* <li>If the argument is zero, then the result is a zero with the
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* same sign as the argument.</ul>
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*
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* @param a an angle, in radians.
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* @return the tangent of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double tan(double a) {
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// return FdLibm.Tan.compute(a);
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// }
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public static native double tan(double a);
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/**
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* Returns the arc sine of a value; the returned angle is in the
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* range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
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* <ul><li>If the argument is NaN or its absolute value is greater
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* than 1, then the result is NaN.
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* <li>If the argument is zero, then the result is a zero with the
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* same sign as the argument.</ul>
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*
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* @param a the value whose arc sine is to be returned.
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* @return the arc sine of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double asin(double a) {
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// return FdLibm.Asin.compute(a);
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// }
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public static native double asin(double a);
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/**
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* Returns the arc cosine of a value; the returned angle is in the
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* range 0.0 through <i>pi</i>. Special case:
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* <ul><li>If the argument is NaN or its absolute value is greater
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* than 1, then the result is NaN.
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* <li>If the argument is {@code 1.0}, the result is positive zero.
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* </ul>
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*
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* @param a the value whose arc cosine is to be returned.
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* @return the arc cosine of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double acos(double a) {
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// return FdLibm.Acos.compute(a);
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// }
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public static native double acos(double a);
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/**
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* Returns the arc tangent of a value; the returned angle is in the
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* range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
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* <ul><li>If the argument is NaN, then the result is NaN.
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* <li>If the argument is zero, then the result is a zero with the
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* same sign as the argument.
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* <li>If the argument is {@linkplain Double#isInfinite infinite},
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* then the result is the closest value to <i>pi</i>/2 with the
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* same sign as the input.
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* </ul>
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*
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* @param a the value whose arc tangent is to be returned.
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* @return the arc tangent of the argument.
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*/
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// Android-changed: Reimplement in native
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// public static double atan(double a) {
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// return FdLibm.Atan.compute(a);
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// }
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public static native double atan(double a);
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/**
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* Converts an angle measured in degrees to an approximately
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* equivalent angle measured in radians. The conversion from
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* degrees to radians is generally inexact.
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*
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* @param angdeg an angle, in degrees
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* @return the measurement of the angle {@code angdeg}
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* in radians.
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*/
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public static strictfp double toRadians(double angdeg) {
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// Do not delegate to Math.toRadians(angdeg) because
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// this method has the strictfp modifier.
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return angdeg * DEGREES_TO_RADIANS;
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}
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/**
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* Converts an angle measured in radians to an approximately
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* equivalent angle measured in degrees. The conversion from
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* radians to degrees is generally inexact; users should
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* <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
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* equal {@code 0.0}.
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*
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* @param angrad an angle, in radians
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* @return the measurement of the angle {@code angrad}
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* in degrees.
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*/
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public static strictfp double toDegrees(double angrad) {
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// Do not delegate to Math.toDegrees(angrad) because
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// this method has the strictfp modifier.
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return angrad * RADIANS_TO_DEGREES;
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}
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/**
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* Returns Euler's number <i>e</i> raised to the power of a
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* {@code double} value. Special cases:
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* <ul><li>If the argument is NaN, the result is NaN.
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* <li>If the argument is positive infinity, then the result is
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* positive infinity.
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* <li>If the argument is negative infinity, then the result is
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* positive zero.
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* <li>If the argument is zero, then the result is {@code 1.0}.
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* </ul>
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*
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* @param a the exponent to raise <i>e</i> to.
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* @return the value <i>e</i><sup>{@code a}</sup>,
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* where <i>e</i> is the base of the natural logarithms.
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*/
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// BEGIN Android-changed: Reimplement in native
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/*
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public static double exp(double a) {
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return FdLibm.Exp.compute(a);
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}
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*/
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// END Android-changed: Reimplement in native
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public static native double exp(double a);
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/**
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* Returns the natural logarithm (base <i>e</i>) of a {@code double}
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* value. Special cases:
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* <ul><li>If the argument is NaN or less than zero, then the result
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* is NaN.
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* <li>If the argument is positive infinity, then the result is
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* positive infinity.
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* <li>If the argument is positive zero or negative zero, then the
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* result is negative infinity.
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* <li>If the argument is {@code 1.0}, then the result is positive
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* zero.
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* </ul>
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*
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* @param a a value
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* @return the value ln {@code a}, the natural logarithm of
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* {@code a}.
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*/
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// Android-changed: Reimplement in native
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// public static double log(double a) {
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// return FdLibm.Log.compute(a);
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// }
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public static native double log(double a);
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/**
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* Returns the base 10 logarithm of a {@code double} value.
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* Special cases:
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*
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* <ul><li>If the argument is NaN or less than zero, then the result
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* is NaN.
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* <li>If the argument is positive infinity, then the result is
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* positive infinity.
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* <li>If the argument is positive zero or negative zero, then the
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* result is negative infinity.
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* <li>If the argument is equal to 10<sup><i>n</i></sup> for
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* integer <i>n</i>, then the result is <i>n</i>. In particular,
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* if the argument is {@code 1.0} (10<sup>0</sup>), then the
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* result is positive zero.
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* </ul>
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*
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* @param a a value
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* @return the base 10 logarithm of {@code a}.
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* @since 1.5
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*/
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// Android-changed: Reimplement in native
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// public static double log10(double a) {
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// return FdLibm.Log10.compute(a);
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// }
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public static native double log10(double a);
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/**
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* Returns the correctly rounded positive square root of a
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* {@code double} value.
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* Special cases:
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* <ul><li>If the argument is NaN or less than zero, then the result
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* is NaN.
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* <li>If the argument is positive infinity, then the result is positive
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* infinity.
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* <li>If the argument is positive zero or negative zero, then the
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* result is the same as the argument.</ul>
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* Otherwise, the result is the {@code double} value closest to
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* the true mathematical square root of the argument value.
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*
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* @param a a value.
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* @return the positive square root of {@code a}.
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*/
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@IntrinsicCandidate
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// Android-changed: Reimplement in native
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// public static double sqrt(double a) {
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// return FdLibm.Sqrt.compute(a);
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// }
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public static native double sqrt(double a);
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/**
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* Returns the cube root of a {@code double} value. For
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* positive finite {@code x}, {@code cbrt(-x) ==
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* -cbrt(x)}; that is, the cube root of a negative value is
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* the negative of the cube root of that value's magnitude.
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* Special cases:
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*
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* <ul>
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*
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* <li>If the argument is NaN, then the result is NaN.
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*
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* <li>If the argument is infinite, then the result is an infinity
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* with the same sign as the argument.
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*
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* <li>If the argument is zero, then the result is a zero with the
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* same sign as the argument.
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*
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* </ul>
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*
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* @param a a value.
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* @return the cube root of {@code a}.
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* @since 1.5
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*/
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// BEGIN Android-changed: Reimplement in native
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/*
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public static double cbrt(double a) {
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return FdLibm.Cbrt.compute(a);
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}
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*/
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// END Android-changed: Reimplement in native
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public static native double cbrt(double a);
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/**
|
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* Computes the remainder operation on two arguments as prescribed
|
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* by the IEEE 754 standard.
|
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* The remainder value is mathematically equal to
|
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* <code>f1 - f2</code> × <i>n</i>,
|
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* where <i>n</i> is the mathematical integer closest to the exact
|
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* 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.
|
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* @param f2 the divisor.
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* @return the remainder when {@code f1} is divided by
|
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* {@code f2}.
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*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double IEEEremainder(double f1, double f2) {
|
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// return FdLibm.IEEEremainder.compute(f1, f2);
|
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// }
|
|
public static native double IEEEremainder(double f1, double f2);
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code double} value that is greater than or equal to the
|
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* 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
|
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* argument. <li>If the argument is NaN or an infinity or
|
|
* positive zero or negative zero, then the result is the same as
|
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* the argument. <li>If the argument value is less than zero but
|
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* greater than -1.0, then the result is negative zero.</ul> Note
|
|
* that the value of {@code StrictMath.ceil(x)} is exactly the
|
|
* value of {@code -StrictMath.floor(-x)}.
|
|
*
|
|
* @param a a value.
|
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* @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.
|
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*/
|
|
public static double ceil(double a) {
|
|
return floorOrCeil(a, -0.0, 1.0, 1.0);
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|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code double} value that is less than or equal to the
|
|
* argument and is equal to a mathematical integer. Special cases:
|
|
* <ul><li>If the argument value is already equal to a
|
|
* mathematical integer, then the result is the same as the
|
|
* argument. <li>If the argument is NaN or an infinity or
|
|
* positive zero or negative zero, then the result is the same as
|
|
* the argument.</ul>
|
|
*
|
|
* @param a a value.
|
|
* @return the largest (closest to positive infinity)
|
|
* floating-point value that less than or equal to the argument
|
|
* and is equal to a mathematical integer.
|
|
*/
|
|
public static double floor(double a) {
|
|
return floorOrCeil(a, -1.0, 0.0, -1.0);
|
|
}
|
|
|
|
/**
|
|
* Internal method to share logic between floor and ceil.
|
|
*
|
|
* @param a the value to be floored or ceiled
|
|
* @param negativeBoundary result for values in (-1, 0)
|
|
* @param positiveBoundary result for values in (0, 1)
|
|
* @param sign the sign of the result
|
|
*/
|
|
private static double floorOrCeil(double a,
|
|
double negativeBoundary,
|
|
double positiveBoundary,
|
|
double sign) {
|
|
int exponent = Math.getExponent(a);
|
|
|
|
if (exponent < 0) {
|
|
/*
|
|
* Absolute value of argument is less than 1.
|
|
* floorOrCeil(-0.0) => -0.0
|
|
* floorOrCeil(+0.0) => +0.0
|
|
*/
|
|
return ((a == 0.0) ? a :
|
|
( (a < 0.0) ? negativeBoundary : positiveBoundary) );
|
|
} else if (exponent >= 52) {
|
|
/*
|
|
* Infinity, NaN, or a value so large it must be integral.
|
|
*/
|
|
return a;
|
|
}
|
|
// Else the argument is either an integral value already XOR it
|
|
// has to be rounded to one.
|
|
assert exponent >= 0 && exponent <= 51;
|
|
|
|
long doppel = Double.doubleToRawLongBits(a);
|
|
long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
|
|
|
|
if ( (mask & doppel) == 0L )
|
|
return a; // integral value
|
|
else {
|
|
double result = Double.longBitsToDouble(doppel & (~mask));
|
|
if (sign*a > 0.0)
|
|
result = result + sign;
|
|
return result;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the {@code double} value that is closest in value
|
|
* to the argument and is equal to a mathematical integer. If two
|
|
* {@code double} values that are mathematical integers are
|
|
* equally close to the value of the argument, the result is the
|
|
* integer value that is even. Special cases:
|
|
* <ul><li>If the argument value is already equal to a mathematical
|
|
* integer, then the result is the same as the argument.
|
|
* <li>If the argument is NaN or an infinity or positive zero or negative
|
|
* zero, then the result is the same as the argument.</ul>
|
|
*
|
|
* @param a a value.
|
|
* @return the closest floating-point value to {@code a} that is
|
|
* equal to a mathematical integer.
|
|
* @author Joseph D. Darcy
|
|
*/
|
|
public static double rint(double a) {
|
|
/*
|
|
* If the absolute value of a is not less than 2^52, it
|
|
* is either a finite integer (the double format does not have
|
|
* enough significand bits for a number that large to have any
|
|
* fractional portion), an infinity, or a NaN. In any of
|
|
* these cases, rint of the argument is the argument.
|
|
*
|
|
* Otherwise, the sum (twoToThe52 + a ) will properly round
|
|
* away any fractional portion of a since ulp(twoToThe52) ==
|
|
* 1.0; subtracting out twoToThe52 from this sum will then be
|
|
* exact and leave the rounded integer portion of a.
|
|
*/
|
|
double twoToThe52 = (double)(1L << 52); // 2^52
|
|
double sign = Math.copySign(1.0, a); // preserve sign info
|
|
a = Math.abs(a);
|
|
|
|
if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
|
|
a = ((twoToThe52 + a ) - twoToThe52);
|
|
}
|
|
|
|
return sign * a; // restore original sign
|
|
}
|
|
|
|
/**
|
|
* Returns the angle <i>theta</i> from the conversion of rectangular
|
|
* coordinates ({@code x}, {@code y}) to polar
|
|
* coordinates (r, <i>theta</i>).
|
|
* This method computes the phase <i>theta</i> by computing an arc tangent
|
|
* of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
|
|
* cases:
|
|
* <ul><li>If either argument is NaN, then the result is NaN.
|
|
* <li>If the first argument is positive zero and the second argument
|
|
* is positive, or the first argument is positive and finite and the
|
|
* second argument is positive infinity, then the result is positive
|
|
* zero.
|
|
* <li>If the first argument is negative zero and the second argument
|
|
* is positive, or the first argument is negative and finite and the
|
|
* second argument is positive infinity, then the result is negative zero.
|
|
* <li>If the first argument is positive zero and the second argument
|
|
* is negative, or the first argument is positive and finite and the
|
|
* second argument is negative infinity, then the result is the
|
|
* {@code double} value closest to <i>pi</i>.
|
|
* <li>If the first argument is negative zero and the second argument
|
|
* is negative, or the first argument is negative and finite and the
|
|
* second argument is negative infinity, then the result is the
|
|
* {@code double} value closest to -<i>pi</i>.
|
|
* <li>If the first argument is positive and the second argument is
|
|
* positive zero or negative zero, or the first argument is positive
|
|
* infinity and the second argument is finite, then the result is the
|
|
* {@code double} value closest to <i>pi</i>/2.
|
|
* <li>If the first argument is negative and the second argument is
|
|
* positive zero or negative zero, or the first argument is negative
|
|
* infinity and the second argument is finite, then the result is the
|
|
* {@code double} value closest to -<i>pi</i>/2.
|
|
* <li>If both arguments are positive infinity, then the result is the
|
|
* {@code double} value closest to <i>pi</i>/4.
|
|
* <li>If the first argument is positive infinity and the second argument
|
|
* is negative infinity, then the result is the {@code double}
|
|
* value closest to 3*<i>pi</i>/4.
|
|
* <li>If the first argument is negative infinity and the second argument
|
|
* is positive infinity, then the result is the {@code double} value
|
|
* closest to -<i>pi</i>/4.
|
|
* <li>If both arguments are negative infinity, then the result is the
|
|
* {@code double} value closest to -3*<i>pi</i>/4.</ul>
|
|
*
|
|
* @apiNote
|
|
* For <i>y</i> with a positive sign and finite nonzero
|
|
* <i>x</i>, the exact mathematical value of {@code atan2} is
|
|
* equal to:
|
|
* <ul>
|
|
* <li>If <i>x</i> {@literal >} 0, atan(abs(<i>y</i>/<i>x</i>))
|
|
* <li>If <i>x</i> {@literal <} 0, π - atan(abs(<i>y</i>/<i>x</i>))
|
|
* </ul>
|
|
*
|
|
* @param y the ordinate coordinate
|
|
* @param x the abscissa coordinate
|
|
* @return the <i>theta</i> component of the point
|
|
* (<i>r</i>, <i>theta</i>)
|
|
* in polar coordinates that corresponds to the point
|
|
* (<i>x</i>, <i>y</i>) in Cartesian coordinates.
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double atan2(double y, double x) {
|
|
// return FdLibm.Atan2.compute(y, x);
|
|
// }
|
|
public static native double atan2(double y, double x);
|
|
|
|
/**
|
|
* Returns the value of the first argument raised to the power of the
|
|
* second argument. Special cases:
|
|
*
|
|
* <ul><li>If the second argument is positive or negative zero, then the
|
|
* result is 1.0.
|
|
* <li>If the second argument is 1.0, then the result is the same as the
|
|
* first argument.
|
|
* <li>If the second argument is NaN, then the result is NaN.
|
|
* <li>If the first argument is NaN and the second argument is nonzero,
|
|
* then the result is NaN.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the absolute value of the first argument is greater than 1
|
|
* and the second argument is positive infinity, or
|
|
* <li>the absolute value of the first argument is less than 1 and
|
|
* the second argument is negative infinity,
|
|
* </ul>
|
|
* then the result is positive infinity.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the absolute value of the first argument is greater than 1 and
|
|
* the second argument is negative infinity, or
|
|
* <li>the absolute value of the
|
|
* first argument is less than 1 and the second argument is positive
|
|
* infinity,
|
|
* </ul>
|
|
* then the result is positive zero.
|
|
*
|
|
* <li>If the absolute value of the first argument equals 1 and the
|
|
* second argument is infinite, then the result is NaN.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is positive zero and the second argument
|
|
* is greater than zero, or
|
|
* <li>the first argument is positive infinity and the second
|
|
* argument is less than zero,
|
|
* </ul>
|
|
* then the result is positive zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is positive zero and the second argument
|
|
* is less than zero, or
|
|
* <li>the first argument is positive infinity and the second
|
|
* argument is greater than zero,
|
|
* </ul>
|
|
* then the result is positive infinity.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is greater than zero but not a finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is less than zero but not a finite odd integer,
|
|
* </ul>
|
|
* then the result is positive zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is a positive finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is a negative finite odd integer,
|
|
* </ul>
|
|
* then the result is negative zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is less than zero but not a finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is greater than zero but not a finite odd integer,
|
|
* </ul>
|
|
* then the result is positive infinity.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is a negative finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is a positive finite odd integer,
|
|
* </ul>
|
|
* then the result is negative infinity.
|
|
*
|
|
* <li>If the first argument is finite and less than zero
|
|
* <ul>
|
|
* <li> if the second argument is a finite even integer, the
|
|
* result is equal to the result of raising the absolute value of
|
|
* the first argument to the power of the second argument
|
|
*
|
|
* <li>if the second argument is a finite odd integer, the result
|
|
* is equal to the negative of the result of raising the absolute
|
|
* value of the first argument to the power of the second
|
|
* argument
|
|
*
|
|
* <li>if the second argument is finite and not an integer, then
|
|
* the result is NaN.
|
|
* </ul>
|
|
*
|
|
* <li>If both arguments are integers, then the result is exactly equal
|
|
* to the mathematical result of raising the first argument to the power
|
|
* of the second argument if that result can in fact be represented
|
|
* exactly as a {@code double} value.</ul>
|
|
*
|
|
* <p>(In the foregoing descriptions, a floating-point value is
|
|
* considered to be an integer if and only if it is finite and a
|
|
* fixed point of the method {@link #ceil ceil} or,
|
|
* equivalently, a fixed point of the method {@link #floor
|
|
* floor}. A value is a fixed point of a one-argument
|
|
* method if and only if the result of applying the method to the
|
|
* value is equal to the value.)
|
|
*
|
|
* @apiNote
|
|
* The special cases definitions of this method differ from the
|
|
* special case definitions of the IEEE 754 recommended {@code
|
|
* pow} operation for ±{@code 1.0} raised to an infinite
|
|
* power. This method treats such cases as indeterminate and
|
|
* specifies a NaN is returned. The IEEE 754 specification treats
|
|
* the infinite power as a large integer (large-magnitude
|
|
* floating-point numbers are numerically integers, specifically
|
|
* even integers) and therefore specifies {@code 1.0} be returned.
|
|
*
|
|
* @param a base.
|
|
* @param b the exponent.
|
|
* @return the value {@code a}<sup>{@code b}</sup>.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double pow(double a, double b) {
|
|
return FdLibm.Pow.compute(a, b);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
public static native double pow(double a, double b);
|
|
|
|
/**
|
|
* Returns the closest {@code int} to the argument, with ties
|
|
* rounding to positive infinity.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul><li>If the argument is NaN, the result is 0.
|
|
* <li>If the argument is negative infinity or any value less than or
|
|
* equal to the value of {@code Integer.MIN_VALUE}, the result is
|
|
* equal to the value of {@code Integer.MIN_VALUE}.
|
|
* <li>If the argument is positive infinity or any value greater than or
|
|
* equal to the value of {@code Integer.MAX_VALUE}, the result is
|
|
* equal to the value of {@code Integer.MAX_VALUE}.</ul>
|
|
*
|
|
* @param a a floating-point value to be rounded to an integer.
|
|
* @return the value of the argument rounded to the nearest
|
|
* {@code int} value.
|
|
* @see java.lang.Integer#MAX_VALUE
|
|
* @see java.lang.Integer#MIN_VALUE
|
|
*/
|
|
public static int round(float a) {
|
|
return Math.round(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the closest {@code long} to the argument, with ties
|
|
* rounding to positive infinity.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul><li>If the argument is NaN, the result is 0.
|
|
* <li>If the argument is negative infinity or any value less than or
|
|
* equal to the value of {@code Long.MIN_VALUE}, the result is
|
|
* equal to the value of {@code Long.MIN_VALUE}.
|
|
* <li>If the argument is positive infinity or any value greater than or
|
|
* equal to the value of {@code Long.MAX_VALUE}, the result is
|
|
* equal to the value of {@code Long.MAX_VALUE}.</ul>
|
|
*
|
|
* @param a a floating-point value to be rounded to a
|
|
* {@code long}.
|
|
* @return the value of the argument rounded to the nearest
|
|
* {@code long} value.
|
|
* @see java.lang.Long#MAX_VALUE
|
|
* @see java.lang.Long#MIN_VALUE
|
|
*/
|
|
public static long round(double a) {
|
|
return Math.round(a);
|
|
}
|
|
|
|
private static final class RandomNumberGeneratorHolder {
|
|
static final Random randomNumberGenerator = new Random();
|
|
}
|
|
|
|
/**
|
|
* Returns a {@code double} value with a positive sign, greater
|
|
* than or equal to {@code 0.0} and less than {@code 1.0}.
|
|
* Returned values are chosen pseudorandomly with (approximately)
|
|
* uniform distribution from that range.
|
|
*
|
|
* <p>When this method is first called, it creates a single new
|
|
* pseudorandom-number generator, exactly as if by the expression
|
|
*
|
|
* <blockquote>{@code new java.util.Random()}</blockquote>
|
|
*
|
|
* This new pseudorandom-number generator is used thereafter for
|
|
* all calls to this method and is used nowhere else.
|
|
*
|
|
* <p>This method is properly synchronized to allow correct use by
|
|
* more than one thread. However, if many threads need to generate
|
|
* pseudorandom numbers at a great rate, it may reduce contention
|
|
* for each thread to have its own pseudorandom-number generator.
|
|
*
|
|
* @return a pseudorandom {@code double} greater than or equal
|
|
* to {@code 0.0} and less than {@code 1.0}.
|
|
* @see Random#nextDouble()
|
|
*/
|
|
public static double random() {
|
|
return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
|
|
}
|
|
|
|
/**
|
|
* Returns the sum of its arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#addExact(int,int)
|
|
* @since 1.8
|
|
*/
|
|
public static int addExact(int x, int y) {
|
|
return Math.addExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the sum of its arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#addExact(long,long)
|
|
* @since 1.8
|
|
*/
|
|
public static long addExact(long x, long y) {
|
|
return Math.addExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the difference of the arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value to subtract from the first
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#subtractExact(int,int)
|
|
* @since 1.8
|
|
*/
|
|
public static int subtractExact(int x, int y) {
|
|
return Math.subtractExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the difference of the arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value to subtract from the first
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#subtractExact(long,long)
|
|
* @since 1.8
|
|
*/
|
|
public static long subtractExact(long x, long y) {
|
|
return Math.subtractExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#multiplyExact(int,int)
|
|
* @since 1.8
|
|
*/
|
|
public static int multiplyExact(int x, int y) {
|
|
return Math.multiplyExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments, throwing an exception if the result
|
|
* overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#multiplyExact(long,int)
|
|
* @since 9
|
|
*/
|
|
public static long multiplyExact(long x, int y) {
|
|
return Math.multiplyExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#multiplyExact(long,long)
|
|
* @since 1.8
|
|
*/
|
|
public static long multiplyExact(long x, long y) {
|
|
return Math.multiplyExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the quotient of the arguments, throwing an exception if the
|
|
* result overflows an {@code int}. Such overflow occurs in this method if
|
|
* {@code x} is {@link Integer#MIN_VALUE} and {@code y} is {@code -1}.
|
|
* In contrast, if {@code Integer.MIN_VALUE / -1} were evaluated directly,
|
|
* the result would be {@code Integer.MIN_VALUE} and no exception would be
|
|
* thrown.
|
|
* <p>
|
|
* If {@code y} is zero, an {@code ArithmeticException} is thrown
|
|
* (JLS {@jls 15.17.2}).
|
|
* <p>
|
|
* The built-in remainder operator "{@code %}" is a suitable counterpart
|
|
* both for this method and for the built-in division operator "{@code /}".
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the quotient {@code x / y}
|
|
* @throws ArithmeticException if {@code y} is zero or the quotient
|
|
* overflows an int
|
|
* @jls 15.17.2 Division Operator /
|
|
* @see Math#divideExact(int,int)
|
|
* @since 18
|
|
*/
|
|
public static int divideExact(int x, int y) {
|
|
return Math.divideExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the quotient of the arguments, throwing an exception if the
|
|
* result overflows a {@code long}. Such overflow occurs in this method if
|
|
* {@code x} is {@link Long#MIN_VALUE} and {@code y} is {@code -1}.
|
|
* In contrast, if {@code Long.MIN_VALUE / -1} were evaluated directly,
|
|
* the result would be {@code Long.MIN_VALUE} and no exception would be
|
|
* thrown.
|
|
* <p>
|
|
* If {@code y} is zero, an {@code ArithmeticException} is thrown
|
|
* (JLS {@jls 15.17.2}).
|
|
* <p>
|
|
* The built-in remainder operator "{@code %}" is a suitable counterpart
|
|
* both for this method and for the built-in division operator "{@code /}".
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the quotient {@code x / y}
|
|
* @throws ArithmeticException if {@code y} is zero or the quotient
|
|
* overflows a long
|
|
* @jls 15.17.2 Division Operator /
|
|
* @see Math#divideExact(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long divideExact(long x, long y) {
|
|
return Math.divideExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* This method is identical to {@link #floorDiv(int,int)} except that it
|
|
* throws an {@code ArithmeticException} when the dividend is
|
|
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is
|
|
* {@code -1} instead of ignoring the integer overflow and returning
|
|
* {@code Integer.MIN_VALUE}.
|
|
* <p>
|
|
* The floor modulus method {@link #floorMod(int,int)} is a suitable
|
|
* counterpart both for this method and for the {@link #floorDiv(int,int)}
|
|
* method.
|
|
* <p>
|
|
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero, or the
|
|
* dividend {@code x} is {@code Integer.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see Math#floorDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int floorDivExact(int x, int y) {
|
|
return Math.floorDivExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* This method is identical to {@link #floorDiv(long,long)} except that it
|
|
* throws an {@code ArithmeticException} when the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is
|
|
* {@code -1} instead of ignoring the integer overflow and returning
|
|
* {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* The floor modulus method {@link #floorMod(long,long)} is a suitable
|
|
* counterpart both for this method and for the {@link #floorDiv(long,long)}
|
|
* method.
|
|
* <p>
|
|
* For examples, see {@link Math#floorDiv(int, int) Math.floorDiv}.
|
|
*
|
|
* @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, or the
|
|
* dividend {@code x} is {@code Long.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see Math#floorDiv(int, int)
|
|
* @see Math#floorDiv(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long floorDivExact(long x, long y) {
|
|
return Math.floorDivExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code int} value that is greater than or equal to the algebraic quotient.
|
|
* This method is identical to {@link #ceilDiv(int,int)} except that it
|
|
* throws an {@code ArithmeticException} when the dividend is
|
|
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is
|
|
* {@code -1} instead of ignoring the integer overflow and returning
|
|
* {@code Integer.MIN_VALUE}.
|
|
* <p>
|
|
* The ceil modulus method {@link #ceilMod(int,int)} is a suitable
|
|
* counterpart both for this method and for the {@link #ceilDiv(int,int)}
|
|
* method.
|
|
* <p>
|
|
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the smallest (closest to negative infinity)
|
|
* {@code int} value that is greater than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero, or the
|
|
* dividend {@code x} is {@code Integer.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see Math#ceilDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilDivExact(int x, int y) {
|
|
return Math.ceilDivExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* This method is identical to {@link #ceilDiv(long,long)} except that it
|
|
* throws an {@code ArithmeticException} when the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is
|
|
* {@code -1} instead of ignoring the integer overflow and returning
|
|
* {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* The ceil modulus method {@link #ceilMod(long,long)} is a suitable
|
|
* counterpart both for this method and for the {@link #ceilDiv(long,long)}
|
|
* method.
|
|
* <p>
|
|
* For examples, see {@link Math#ceilDiv(int, int) Math.ceilDiv}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero, or the
|
|
* dividend {@code x} is {@code Long.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see Math#ceilDiv(int, int)
|
|
* @see Math#ceilDiv(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDivExact(long x, long y) {
|
|
return Math.ceilDivExact(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the argument incremented by one,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
* The overflow only occurs for {@linkplain Integer#MAX_VALUE the maximum value}.
|
|
*
|
|
* @param a the value to increment
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#incrementExact(int)
|
|
* @since 14
|
|
*/
|
|
public static int incrementExact(int a) {
|
|
return Math.incrementExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the argument incremented by one,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
* The overflow only occurs for {@linkplain Long#MAX_VALUE the maximum value}.
|
|
*
|
|
* @param a the value to increment
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#incrementExact(long)
|
|
* @since 14
|
|
*/
|
|
public static long incrementExact(long a) {
|
|
return Math.incrementExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the argument decremented by one,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
* The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
|
|
*
|
|
* @param a the value to decrement
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#decrementExact(int)
|
|
* @since 14
|
|
*/
|
|
public static int decrementExact(int a) {
|
|
return Math.decrementExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the argument decremented by one,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
* The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
|
|
*
|
|
* @param a the value to decrement
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#decrementExact(long)
|
|
* @since 14
|
|
*/
|
|
public static long decrementExact(long a) {
|
|
return Math.decrementExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the negation of the argument,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
* The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
|
|
*
|
|
* @param a the value to negate
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @see Math#negateExact(int)
|
|
* @since 14
|
|
*/
|
|
public static int negateExact(int a) {
|
|
return Math.negateExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the negation of the argument,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
* The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
|
|
*
|
|
* @param a the value to negate
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @see Math#negateExact(long)
|
|
* @since 14
|
|
*/
|
|
public static long negateExact(long a) {
|
|
return Math.negateExact(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
|
|
* @see Math#toIntExact(long)
|
|
* @since 1.8
|
|
*/
|
|
public static int toIntExact(long value) {
|
|
return Math.toIntExact(value);
|
|
}
|
|
|
|
/**
|
|
* Returns the exact mathematical product of the arguments.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @see Math#multiplyFull(int,int)
|
|
* @since 9
|
|
*/
|
|
public static long multiplyFull(int x, int y) {
|
|
return Math.multiplyFull(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns as a {@code long} the most significant 64 bits of the 128-bit
|
|
* product of two 64-bit factors.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @see #unsignedMultiplyHigh
|
|
* @see Math#multiplyHigh(long,long)
|
|
* @since 9
|
|
*/
|
|
public static long multiplyHigh(long x, long y) {
|
|
return Math.multiplyHigh(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns as a {@code long} the most significant 64 bits of the unsigned
|
|
* 128-bit product of two unsigned 64-bit factors.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @see #multiplyHigh
|
|
* @see Math#unsignedMultiplyHigh(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long unsignedMultiplyHigh(long x, long y) {
|
|
return Math.unsignedMultiplyHigh(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@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>
|
|
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorDiv(int, int)
|
|
* @see Math#floor(double)
|
|
* @since 1.8
|
|
*/
|
|
public static int floorDiv(int x, int y) {
|
|
return Math.floorDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
|
|
* then integer overflow occurs and
|
|
* the result is equal to {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorDiv(long, int)
|
|
* @see Math#floor(double)
|
|
* @since 9
|
|
*/
|
|
public static long floorDiv(long x, int y) {
|
|
return Math.floorDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
|
|
* then integer overflow occurs and
|
|
* the result is equal to {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorDiv(long, long)
|
|
* @see Math#floor(double)
|
|
* @since 1.8
|
|
*/
|
|
public static long floorDiv(long x, long y) {
|
|
return Math.floorDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the floor modulus of the {@code int} arguments.
|
|
* <p>
|
|
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
|
|
* has the same sign as the divisor {@code y} or is zero, 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}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorMod(int, int)
|
|
* @see StrictMath#floorDiv(int, int)
|
|
* @since 1.8
|
|
*/
|
|
public static int floorMod(int x, int y) {
|
|
return Math.floorMod(x , y);
|
|
}
|
|
|
|
/**
|
|
* Returns the floor modulus of the {@code long} and {@code int} arguments.
|
|
* <p>
|
|
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
|
|
* has the same sign as the divisor {@code y} or is zero, 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}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorMod(long, int)
|
|
* @see StrictMath#floorDiv(long, int)
|
|
* @since 9
|
|
*/
|
|
public static int floorMod(long x, int y) {
|
|
return Math.floorMod(x , y);
|
|
}
|
|
|
|
/**
|
|
* Returns the floor modulus of the {@code long} arguments.
|
|
* <p>
|
|
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
|
|
* has the same sign as the divisor {@code y} or is zero, 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}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#floorMod(long, long)
|
|
* @see StrictMath#floorDiv(long, long)
|
|
* @since 1.8
|
|
*/
|
|
public static long floorMod(long x, long y) {
|
|
return Math.floorMod(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code int} value that is greater than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@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>
|
|
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the smallest (closest to negative infinity)
|
|
* {@code int} value that is greater than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilDiv(int, int)
|
|
* @see Math#ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static int ceilDiv(int x, int y) {
|
|
return Math.ceilDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
|
|
* then integer overflow occurs and
|
|
* the result is equal to {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilDiv(long, int)
|
|
* @see Math#ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDiv(long x, int y) {
|
|
return Math.ceilDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
|
|
* then integer overflow occurs and
|
|
* the result is equal to {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
|
|
* a comparison to the integer division {@code /} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the smallest (closest to negative infinity)
|
|
* {@code long} value that is greater than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilDiv(long, long)
|
|
* @see Math#ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDiv(long x, long y) {
|
|
return Math.ceilDiv(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the ceiling modulus of the {@code int} arguments.
|
|
* <p>
|
|
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
|
|
* has the opposite sign as the divisor {@code y} or is zero, and
|
|
* is in the range of {@code -abs(y) < r < +abs(y)}.
|
|
*
|
|
* <p>
|
|
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
|
|
* <ul>
|
|
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilMod(int, int)
|
|
* @see StrictMath#ceilDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilMod(int x, int y) {
|
|
return Math.ceilMod(x , y);
|
|
}
|
|
|
|
/**
|
|
* Returns the ceiling modulus of the {@code long} and {@code int} arguments.
|
|
* <p>
|
|
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
|
|
* has the opposite sign as the divisor {@code y} or is zero, and
|
|
* is in the range of {@code -abs(y) < r < +abs(y)}.
|
|
*
|
|
* <p>
|
|
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
|
|
* <ul>
|
|
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilMod(long, int)
|
|
* @see StrictMath#ceilDiv(long, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilMod(long x, int y) {
|
|
return Math.ceilMod(x , y);
|
|
}
|
|
|
|
/**
|
|
* Returns the ceiling modulus of the {@code long} arguments.
|
|
* <p>
|
|
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
|
|
* has the opposite sign as the divisor {@code y} or is zero, and
|
|
* is in the range of {@code -abs(y) < r < +abs(y)}.
|
|
*
|
|
* <p>
|
|
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
|
|
* <ul>
|
|
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
|
|
* </ul>
|
|
* <p>
|
|
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
|
|
* a comparison to the {@code %} operator.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see Math#ceilMod(long, long)
|
|
* @see StrictMath#ceilDiv(long, long)
|
|
* @since 18
|
|
*/
|
|
public static long ceilMod(long x, long y) {
|
|
return Math.ceilMod(x, y);
|
|
}
|
|
|
|
/**
|
|
* Returns the absolute value of an {@code int} value.
|
|
* If the argument is not negative, the argument is returned.
|
|
* If the argument is negative, the negation of the argument is returned.
|
|
*
|
|
* <p>Note that if the argument is equal to the value of {@link
|
|
* Integer#MIN_VALUE}, the most negative representable {@code int}
|
|
* value, the result is that same value, which is negative. In
|
|
* contrast, the {@link StrictMath#absExact(int)} method throws an
|
|
* {@code ArithmeticException} for this value.
|
|
*
|
|
* @param a the argument whose absolute value is to be determined.
|
|
* @return the absolute value of the argument.
|
|
* @see Math#absExact(int)
|
|
*/
|
|
public static int abs(int a) {
|
|
return Math.abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the mathematical absolute value of an {@code int} value
|
|
* if it is exactly representable as an {@code int}, throwing
|
|
* {@code ArithmeticException} if the result overflows the
|
|
* positive {@code int} range.
|
|
*
|
|
* <p>Since the range of two's complement integers is asymmetric
|
|
* with one additional negative value (JLS {@jls 4.2.1}), the
|
|
* mathematical absolute value of {@link Integer#MIN_VALUE}
|
|
* overflows the positive {@code int} range, so an exception is
|
|
* thrown for that argument.
|
|
*
|
|
* @param a the argument whose absolute value is to be determined
|
|
* @return the absolute value of the argument, unless overflow occurs
|
|
* @throws ArithmeticException if the argument is {@link Integer#MIN_VALUE}
|
|
* @see Math#abs(int)
|
|
* @see Math#absExact(int)
|
|
* @since 15
|
|
*/
|
|
public static int absExact(int a) {
|
|
return Math.absExact(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. In
|
|
* contrast, the {@link StrictMath#absExact(long)} method throws
|
|
* an {@code ArithmeticException} for this value.
|
|
*
|
|
* @param a the argument whose absolute value is to be determined.
|
|
* @return the absolute value of the argument.
|
|
* @see Math#absExact(long)
|
|
*/
|
|
public static long abs(long a) {
|
|
return Math.abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the mathematical absolute value of an {@code long} value
|
|
* if it is exactly representable as an {@code long}, throwing
|
|
* {@code ArithmeticException} if the result overflows the
|
|
* positive {@code long} range.
|
|
*
|
|
* <p>Since the range of two's complement integers is asymmetric
|
|
* with one additional negative value (JLS {@jls 4.2.1}), the
|
|
* mathematical absolute value of {@link Long#MIN_VALUE} overflows
|
|
* the positive {@code long} range, so an exception is thrown for
|
|
* that argument.
|
|
*
|
|
* @param a the argument whose absolute value is to be determined
|
|
* @return the absolute value of the argument, unless overflow occurs
|
|
* @throws ArithmeticException if the argument is {@link Long#MIN_VALUE}
|
|
* @see Math#abs(long)
|
|
* @see Math#absExact(long)
|
|
* @since 15
|
|
*/
|
|
public static long absExact(long a) {
|
|
return Math.absExact(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the absolute value of a {@code float} value.
|
|
* If the argument is not negative, the argument is returned.
|
|
* If the argument is negative, the negation of the argument is returned.
|
|
* Special cases:
|
|
* <ul><li>If the argument is positive zero or negative zero, the
|
|
* result is positive zero.
|
|
* <li>If the argument is infinite, the result is positive infinity.
|
|
* <li>If the argument is NaN, the result is NaN.</ul>
|
|
*
|
|
* @apiNote As implied by the above, one valid implementation of
|
|
* this method is given by the expression below which computes a
|
|
* {@code float} with the same exponent and significand as the
|
|
* argument but with a guaranteed zero sign bit indicating a
|
|
* positive value: <br>
|
|
* {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
|
|
*
|
|
* @param a the argument whose absolute value is to be determined
|
|
* @return the absolute value of the argument.
|
|
*/
|
|
public static float abs(float a) {
|
|
return Math.abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the absolute value of a {@code double} value.
|
|
* If the argument is not negative, the argument is returned.
|
|
* If the argument is negative, the negation of the argument is returned.
|
|
* Special cases:
|
|
* <ul><li>If the argument is positive zero or negative zero, the result
|
|
* is positive zero.
|
|
* <li>If the argument is infinite, the result is positive infinity.
|
|
* <li>If the argument is NaN, the result is NaN.</ul>
|
|
*
|
|
* @apiNote As implied by the above, one valid implementation of
|
|
* this method is given by the expression below which computes a
|
|
* {@code double} with the same exponent and significand as the
|
|
* argument but with a guaranteed zero sign bit indicating a
|
|
* positive value: <br>
|
|
* {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
|
|
*
|
|
* @param a the argument whose absolute value is to be determined
|
|
* @return the absolute value of the argument.
|
|
*/
|
|
public static double abs(double a) {
|
|
return Math.abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code int} values. That is, the
|
|
* result is the argument closer to the value of
|
|
* {@link Integer#MAX_VALUE}. If the arguments have the same value,
|
|
* the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the larger of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int max(int a, int b) {
|
|
return Math.max(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code long} values. That is, the
|
|
* result is the argument closer to the value of
|
|
* {@link Long#MAX_VALUE}. If the arguments have the same value,
|
|
* the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the larger of {@code a} and {@code b}.
|
|
*/
|
|
public static long max(long a, long b) {
|
|
return Math.max(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code float} values. That is,
|
|
* the result is the argument closer to positive infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other negative zero, the
|
|
* result is positive zero.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the larger of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float max(float a, float b) {
|
|
return Math.max(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code double} values. That
|
|
* is, the result is the argument closer to positive infinity. If
|
|
* the arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other negative zero, the
|
|
* result is positive zero.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the larger of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double max(double a, double b) {
|
|
return Math.max(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code int} values. That is,
|
|
* the result the argument closer to the value of
|
|
* {@link Integer#MIN_VALUE}. If the arguments have the same
|
|
* value, the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int min(int a, int b) {
|
|
return Math.min(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code long} values. That is,
|
|
* the result is the argument closer to the value of
|
|
* {@link Long#MIN_VALUE}. If the arguments have the same
|
|
* value, the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b}.
|
|
*/
|
|
public static long min(long a, long b) {
|
|
return Math.min(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code float} values. That is,
|
|
* the result is the value closer to negative infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If
|
|
* one argument is positive zero and the other is negative zero,
|
|
* the result is negative zero.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b.}
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float min(float a, float b) {
|
|
return Math.min(a, b);
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code double} values. That
|
|
* is, the result is the value closer to negative infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other is negative zero, the
|
|
* result is negative zero.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double min(double a, double b) {
|
|
return Math.min(a, b);
|
|
}
|
|
|
|
/**
|
|
* Clamps the value to fit between min and max. If the value is less
|
|
* than {@code min}, then {@code min} is returned. If the value is greater
|
|
* than {@code max}, then {@code max} is returned. Otherwise, the original
|
|
* value is returned.
|
|
* <p>
|
|
* While the original value of type long may not fit into the int type,
|
|
* the bounds have the int type, so the result always fits the int type.
|
|
* This allows to use method to safely cast long value to int with
|
|
* saturation.
|
|
*
|
|
* @param value value to clamp
|
|
* @param min minimal allowed value
|
|
* @param max maximal allowed value
|
|
* @return a clamped value that fits into {@code min..max} interval
|
|
* @throws IllegalArgumentException if {@code min > max}
|
|
*
|
|
* @since 21
|
|
*/
|
|
public static int clamp(long value, int min, int max) {
|
|
return Math.clamp(value, min, max);
|
|
}
|
|
|
|
/**
|
|
* Clamps the value to fit between min and max. If the value is less
|
|
* than {@code min}, then {@code min} is returned. If the value is greater
|
|
* than {@code max}, then {@code max} is returned. Otherwise, the original
|
|
* value is returned.
|
|
*
|
|
* @param value value to clamp
|
|
* @param min minimal allowed value
|
|
* @param max maximal allowed value
|
|
* @return a clamped value that fits into {@code min..max} interval
|
|
* @throws IllegalArgumentException if {@code min > max}
|
|
*
|
|
* @since 21
|
|
*/
|
|
public static long clamp(long value, long min, long max) {
|
|
return Math.clamp(value, min, max);
|
|
}
|
|
|
|
/**
|
|
* Clamps the value to fit between min and max. If the value is less
|
|
* than {@code min}, then {@code min} is returned. If the value is greater
|
|
* than {@code max}, then {@code max} is returned. Otherwise, the original
|
|
* value is returned. If value is NaN, the result is also NaN.
|
|
* <p>
|
|
* Unlike the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero.
|
|
* E.g., {@code clamp(-0.0, 0.0, 1.0)} returns 0.0.
|
|
*
|
|
* @param value value to clamp
|
|
* @param min minimal allowed value
|
|
* @param max maximal allowed value
|
|
* @return a clamped value that fits into {@code min..max} interval
|
|
* @throws IllegalArgumentException if either of {@code min} and {@code max}
|
|
* arguments is NaN, or {@code min > max}, or {@code min} is +0.0, and
|
|
* {@code max} is -0.0.
|
|
*
|
|
* @since 21
|
|
*/
|
|
public static double clamp(double value, double min, double max) {
|
|
return Math.clamp(value, min, max);
|
|
}
|
|
|
|
/**
|
|
* Clamps the value to fit between min and max. If the value is less
|
|
* than {@code min}, then {@code min} is returned. If the value is greater
|
|
* than {@code max}, then {@code max} is returned. Otherwise, the original
|
|
* value is returned. If value is NaN, the result is also NaN.
|
|
* <p>
|
|
* Unlike the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero.
|
|
* E.g., {@code clamp(-0.0f, 0.0f, 1.0f)} returns 0.0f.
|
|
*
|
|
* @param value value to clamp
|
|
* @param min minimal allowed value
|
|
* @param max maximal allowed value
|
|
* @return a clamped value that fits into {@code min..max} interval
|
|
* @throws IllegalArgumentException if either of {@code min} and {@code max}
|
|
* arguments is NaN, or {@code min > max}, or {@code min} is +0.0f, and
|
|
* {@code max} is -0.0f.
|
|
*
|
|
* @since 21
|
|
*/
|
|
public static float clamp(float value, float min, float max) {
|
|
return Math.clamp(value, min, max);
|
|
}
|
|
|
|
/**
|
|
* Returns the fused multiply add of the three arguments; that is,
|
|
* returns the exact product of the first two arguments summed
|
|
* with the third argument and then rounded once to the nearest
|
|
* {@code double}.
|
|
*
|
|
* The rounding is done using the {@linkplain
|
|
* java.math.RoundingMode#HALF_EVEN round to nearest even
|
|
* rounding mode}.
|
|
*
|
|
* In contrast, if {@code a * b + c} is evaluated as a regular
|
|
* floating-point expression, two rounding errors are involved,
|
|
* the first for the multiply operation, the second for the
|
|
* addition operation.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If any argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If one of the first two arguments is infinite and the
|
|
* other is zero, the result is NaN.
|
|
*
|
|
* <li> If the exact product of the first two arguments is infinite
|
|
* (in other words, at least one of the arguments is infinite and
|
|
* the other is neither zero nor NaN) and the third argument is an
|
|
* infinity of the opposite sign, the result is NaN.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
|
|
* result as ({@code a + c}). However,
|
|
* {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
|
|
* same result as ({@code a * b}) since
|
|
* {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
|
|
* ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
|
|
* equivalent to ({@code a * b}) however.
|
|
*
|
|
* @apiNote This method corresponds to the fusedMultiplyAdd
|
|
* operation defined in IEEE 754-2008.
|
|
*
|
|
* @param a a value
|
|
* @param b a value
|
|
* @param c a value
|
|
*
|
|
* @return (<i>a</i> × <i>b</i> + <i>c</i>)
|
|
* computed, as if with unlimited range and precision, and rounded
|
|
* once to the nearest {@code double} value
|
|
*
|
|
* @since 9
|
|
*/
|
|
public static double fma(double a, double b, double c) {
|
|
return Math.fma(a, b, c);
|
|
}
|
|
|
|
/**
|
|
* Returns the fused multiply add of the three arguments; that is,
|
|
* returns the exact product of the first two arguments summed
|
|
* with the third argument and then rounded once to the nearest
|
|
* {@code float}.
|
|
*
|
|
* The rounding is done using the {@linkplain
|
|
* java.math.RoundingMode#HALF_EVEN round to nearest even
|
|
* rounding mode}.
|
|
*
|
|
* In contrast, if {@code a * b + c} is evaluated as a regular
|
|
* floating-point expression, two rounding errors are involved,
|
|
* the first for the multiply operation, the second for the
|
|
* addition operation.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If any argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If one of the first two arguments is infinite and the
|
|
* other is zero, the result is NaN.
|
|
*
|
|
* <li> If the exact product of the first two arguments is infinite
|
|
* (in other words, at least one of the arguments is infinite and
|
|
* the other is neither zero nor NaN) and the third argument is an
|
|
* infinity of the opposite sign, the result is NaN.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>Note that {@code fma(a, 1.0f, c)} returns the same
|
|
* result as ({@code a + c}). However,
|
|
* {@code fma(a, b, +0.0f)} does <em>not</em> always return the
|
|
* same result as ({@code a * b}) since
|
|
* {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
|
|
* ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
|
|
* equivalent to ({@code a * b}) however.
|
|
*
|
|
* @apiNote This method corresponds to the fusedMultiplyAdd
|
|
* operation defined in IEEE 754-2008.
|
|
*
|
|
* @param a a value
|
|
* @param b a value
|
|
* @param c a value
|
|
*
|
|
* @return (<i>a</i> × <i>b</i> + <i>c</i>)
|
|
* computed, as if with unlimited range and precision, and rounded
|
|
* once to the nearest {@code float} value
|
|
*
|
|
* @since 9
|
|
*/
|
|
public static float fma(float a, float b, float c) {
|
|
return Math.fma(a, b, c);
|
|
}
|
|
|
|
/**
|
|
* Returns the size of an ulp of the argument. An ulp, unit in
|
|
* the last place, of a {@code double} value is the positive
|
|
* distance between this floating-point value and the {@code
|
|
* double} value next larger in magnitude. Note that for non-NaN
|
|
* <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive or negative infinity, then the
|
|
* result is positive infinity.
|
|
* <li> If the argument is positive or negative zero, then the result is
|
|
* {@code Double.MIN_VALUE}.
|
|
* <li> If the argument is ±{@code Double.MAX_VALUE}, then
|
|
* the result is equal to 2<sup>971</sup>.
|
|
* </ul>
|
|
*
|
|
* @param d the floating-point value whose ulp is to be returned
|
|
* @return the size of an ulp of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
public static double ulp(double d) {
|
|
return Math.ulp(d);
|
|
}
|
|
|
|
/**
|
|
* Returns the size of an ulp of the argument. An ulp, unit in
|
|
* the last place, of a {@code float} value is the positive
|
|
* distance between this floating-point value and the {@code
|
|
* float} value next larger in magnitude. Note that for non-NaN
|
|
* <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive or negative infinity, then the
|
|
* result is positive infinity.
|
|
* <li> If the argument is positive or negative zero, then the result is
|
|
* {@code Float.MIN_VALUE}.
|
|
* <li> If the argument is ±{@code Float.MAX_VALUE}, then
|
|
* the result is equal to 2<sup>104</sup>.
|
|
* </ul>
|
|
*
|
|
* @param f the floating-point value whose ulp is to be returned
|
|
* @return the size of an ulp of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
public static float ulp(float f) {
|
|
return Math.ulp(f);
|
|
}
|
|
|
|
/**
|
|
* Returns the signum function of the argument; zero if the argument
|
|
* is zero, 1.0 if the argument is greater than zero, -1.0 if the
|
|
* argument is less than zero.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive zero or negative zero, then the
|
|
* result is the same as the argument.
|
|
* </ul>
|
|
*
|
|
* @param d the floating-point value whose signum is to be returned
|
|
* @return the signum function of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
public static double signum(double d) {
|
|
return Math.signum(d);
|
|
}
|
|
|
|
/**
|
|
* Returns the signum function of the argument; zero if the argument
|
|
* is zero, 1.0f if the argument is greater than zero, -1.0f if the
|
|
* argument is less than zero.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive zero or negative zero, then the
|
|
* result is the same as the argument.
|
|
* </ul>
|
|
*
|
|
* @param f the floating-point value whose signum is to be returned
|
|
* @return the signum function of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
public static float signum(float f) {
|
|
return Math.signum(f);
|
|
}
|
|
|
|
/**
|
|
* Returns the hyperbolic sine of a {@code double} value.
|
|
* The hyperbolic sine of <i>x</i> is defined to be
|
|
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
|
|
* where <i>e</i> is {@linkplain Math#E Euler's number}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN, then the result is NaN.
|
|
*
|
|
* <li>If the argument is infinite, then the result is an infinity
|
|
* with the same sign as the argument.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param x The number whose hyperbolic sine is to be returned.
|
|
* @return The hyperbolic sine of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double sinh(double x) {
|
|
// return FdLibm.Sinh.compute(x);
|
|
// }
|
|
public static native double sinh(double x);
|
|
|
|
/**
|
|
* Returns the hyperbolic cosine of a {@code double} value.
|
|
* The hyperbolic cosine of <i>x</i> is defined to be
|
|
* (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
|
|
* where <i>e</i> is {@linkplain Math#E Euler's number}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN, then the result is NaN.
|
|
*
|
|
* <li>If the argument is infinite, then the result is positive
|
|
* infinity.
|
|
*
|
|
* <li>If the argument is zero, then the result is {@code 1.0}.
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param x The number whose hyperbolic cosine is to be returned.
|
|
* @return The hyperbolic cosine of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double cosh(double x) {
|
|
// return FdLibm.Cosh.compute(x);
|
|
// }
|
|
public static native double cosh(double x);
|
|
|
|
/**
|
|
* Returns the hyperbolic tangent of a {@code double} value.
|
|
* The hyperbolic tangent of <i>x</i> is defined to be
|
|
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
|
|
* in other words, {@linkplain Math#sinh
|
|
* sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
|
|
* that the absolute value of the exact tanh is always less than
|
|
* 1.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN, then the result is NaN.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* <li>If the argument is positive infinity, then the result is
|
|
* {@code +1.0}.
|
|
*
|
|
* <li>If the argument is negative infinity, then the result is
|
|
* {@code -1.0}.
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param x The number whose hyperbolic tangent is to be returned.
|
|
* @return The hyperbolic tangent of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double tanh(double x) {
|
|
// return FdLibm.Tanh.compute(x);
|
|
// }
|
|
public static native double tanh(double x);
|
|
|
|
/**
|
|
* Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
|
|
* without intermediate overflow or underflow.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li> If either argument is infinite, then the result
|
|
* is positive infinity.
|
|
*
|
|
* <li> If either argument is NaN and neither argument is infinite,
|
|
* then the result is NaN.
|
|
*
|
|
* <li> If both arguments are zero, the result is positive zero.
|
|
* </ul>
|
|
*
|
|
* @param x a value
|
|
* @param y a value
|
|
* @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
|
|
* without intermediate overflow or underflow
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double hypot(double x, double y) {
|
|
return FdLibm.Hypot.compute(x, y);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
public static native double hypot(double x, double y);
|
|
|
|
/**
|
|
* Returns <i>e</i><sup>x</sup> -1. Note that for values of
|
|
* <i>x</i> near 0, the exact sum of
|
|
* {@code expm1(x)} + 1 is much closer to the true
|
|
* result of <i>e</i><sup>x</sup> than {@code exp(x)}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li>If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li>If the argument is positive infinity, then the result is
|
|
* positive infinity.
|
|
*
|
|
* <li>If the argument is negative infinity, then the result is
|
|
* -1.0.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param x the exponent to raise <i>e</i> to in the computation of
|
|
* <i>e</i><sup>{@code x}</sup> -1.
|
|
* @return the value <i>e</i><sup>{@code x}</sup> - 1.
|
|
* @since 1.5
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double expm1(double x) {
|
|
// return FdLibm.Expm1.compute(x);
|
|
// }
|
|
public static native double expm1(double x);
|
|
|
|
/**
|
|
* Returns the natural logarithm of the sum of the argument and 1.
|
|
* Note that for small values {@code x}, the result of
|
|
* {@code log1p(x)} is much closer to the true result of ln(1
|
|
* + {@code x}) than the floating-point evaluation of
|
|
* {@code log(1.0+x)}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN or less than -1, then the result is
|
|
* NaN.
|
|
*
|
|
* <li>If the argument is positive infinity, then the result is
|
|
* positive infinity.
|
|
*
|
|
* <li>If the argument is negative one, then the result is
|
|
* negative infinity.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param x a value
|
|
* @return the value ln({@code x} + 1), the natural
|
|
* log of {@code x} + 1
|
|
* @since 1.5
|
|
*/
|
|
// Android-changed: Reimplement in native
|
|
// public static double log1p(double x) {
|
|
// return FdLibm.Log1p.compute(x);
|
|
// }
|
|
public static native double log1p(double x);
|
|
|
|
/**
|
|
* Returns the first floating-point argument with the sign of the
|
|
* second floating-point argument. For this method, a NaN
|
|
* {@code sign} argument is always treated as if it were
|
|
* positive.
|
|
*
|
|
* @param magnitude the parameter providing the magnitude of the result
|
|
* @param sign the parameter providing the sign of the result
|
|
* @return a value with the magnitude of {@code magnitude}
|
|
* and the sign of {@code sign}.
|
|
* @since 1.6
|
|
*/
|
|
public static double copySign(double magnitude, double sign) {
|
|
return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
|
|
}
|
|
|
|
/**
|
|
* Returns the first floating-point argument with the sign of the
|
|
* second floating-point argument. For this method, a NaN
|
|
* {@code sign} argument is always treated as if it were
|
|
* positive.
|
|
*
|
|
* @param magnitude the parameter providing the magnitude of the result
|
|
* @param sign the parameter providing the sign of the result
|
|
* @return a value with the magnitude of {@code magnitude}
|
|
* and the sign of {@code sign}.
|
|
* @since 1.6
|
|
*/
|
|
public static float copySign(float magnitude, float sign) {
|
|
return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
|
|
}
|
|
/**
|
|
* Returns the unbiased exponent used in the representation of a
|
|
* {@code float}. Special cases:
|
|
*
|
|
* <ul>
|
|
* <li>If the argument is NaN or infinite, then the result is
|
|
* {@link Float#MAX_EXPONENT} + 1.
|
|
* <li>If the argument is zero or subnormal, then the result is
|
|
* {@link Float#MIN_EXPONENT} -1.
|
|
* </ul>
|
|
* @param f a {@code float} value
|
|
* @return the unbiased exponent of the argument
|
|
* @since 1.6
|
|
*/
|
|
public static int getExponent(float f) {
|
|
return Math.getExponent(f);
|
|
}
|
|
|
|
/**
|
|
* Returns the unbiased exponent used in the representation of a
|
|
* {@code double}. Special cases:
|
|
*
|
|
* <ul>
|
|
* <li>If the argument is NaN or infinite, then the result is
|
|
* {@link Double#MAX_EXPONENT} + 1.
|
|
* <li>If the argument is zero or subnormal, then the result is
|
|
* {@link Double#MIN_EXPONENT} -1.
|
|
* </ul>
|
|
* @param d a {@code double} value
|
|
* @return the unbiased exponent of the argument
|
|
* @since 1.6
|
|
*/
|
|
public static int getExponent(double d) {
|
|
return Math.getExponent(d);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point number adjacent to the first
|
|
* argument in the direction of the second argument. If both
|
|
* arguments compare as equal the second argument is returned.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If either argument is a NaN, then NaN is returned.
|
|
*
|
|
* <li> If both arguments are signed zeros, {@code direction}
|
|
* is returned unchanged (as implied by the requirement of
|
|
* returning the second argument if the arguments compare as
|
|
* equal).
|
|
*
|
|
* <li> If {@code start} is
|
|
* ±{@link Double#MIN_VALUE} and {@code direction}
|
|
* has a value such that the result should have a smaller
|
|
* magnitude, then a zero with the same sign as {@code start}
|
|
* is returned.
|
|
*
|
|
* <li> If {@code start} is infinite and
|
|
* {@code direction} has a value such that the result should
|
|
* have a smaller magnitude, {@link Double#MAX_VALUE} with the
|
|
* same sign as {@code start} is returned.
|
|
*
|
|
* <li> If {@code start} is equal to ±
|
|
* {@link Double#MAX_VALUE} and {@code direction} has a
|
|
* value such that the result should have a larger magnitude, an
|
|
* infinity with same sign as {@code start} is returned.
|
|
* </ul>
|
|
*
|
|
* @param start starting floating-point value
|
|
* @param direction value indicating which of
|
|
* {@code start}'s neighbors or {@code start} should
|
|
* be returned
|
|
* @return The floating-point number adjacent to {@code start} in the
|
|
* direction of {@code direction}.
|
|
* @since 1.6
|
|
*/
|
|
public static double nextAfter(double start, double direction) {
|
|
return Math.nextAfter(start, direction);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point number adjacent to the first
|
|
* argument in the direction of the second argument. If both
|
|
* arguments compare as equal a value equivalent to the second argument
|
|
* is returned.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If either argument is a NaN, then NaN is returned.
|
|
*
|
|
* <li> If both arguments are signed zeros, a value equivalent
|
|
* to {@code direction} is returned.
|
|
*
|
|
* <li> If {@code start} is
|
|
* ±{@link Float#MIN_VALUE} and {@code direction}
|
|
* has a value such that the result should have a smaller
|
|
* magnitude, then a zero with the same sign as {@code start}
|
|
* is returned.
|
|
*
|
|
* <li> If {@code start} is infinite and
|
|
* {@code direction} has a value such that the result should
|
|
* have a smaller magnitude, {@link Float#MAX_VALUE} with the
|
|
* same sign as {@code start} is returned.
|
|
*
|
|
* <li> If {@code start} is equal to ±
|
|
* {@link Float#MAX_VALUE} and {@code direction} has a
|
|
* value such that the result should have a larger magnitude, an
|
|
* infinity with same sign as {@code start} is returned.
|
|
* </ul>
|
|
*
|
|
* @param start starting floating-point value
|
|
* @param direction value indicating which of
|
|
* {@code start}'s neighbors or {@code start} should
|
|
* be returned
|
|
* @return The floating-point number adjacent to {@code start} in the
|
|
* direction of {@code direction}.
|
|
* @since 1.6
|
|
*/
|
|
public static float nextAfter(float start, double direction) {
|
|
return Math.nextAfter(start, direction);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code d} in
|
|
* the direction of positive infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(d,
|
|
* Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
|
|
* implementation may run faster than its equivalent
|
|
* {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is positive infinity, the result is
|
|
* positive infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@link Double#MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param d starting floating-point value
|
|
* @return The adjacent floating-point value closer to positive
|
|
* infinity.
|
|
* @since 1.6
|
|
*/
|
|
public static double nextUp(double d) {
|
|
return Math.nextUp(d);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code f} in
|
|
* the direction of positive infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(f,
|
|
* Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
|
|
* implementation may run faster than its equivalent
|
|
* {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is positive infinity, the result is
|
|
* positive infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@link Float#MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param f starting floating-point value
|
|
* @return The adjacent floating-point value closer to positive
|
|
* infinity.
|
|
* @since 1.6
|
|
*/
|
|
public static float nextUp(float f) {
|
|
return Math.nextUp(f);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code d} in
|
|
* the direction of negative infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(d,
|
|
* Double.NEGATIVE_INFINITY)}; however, a
|
|
* {@code nextDown} implementation may run faster than its
|
|
* equivalent {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is negative infinity, the result is
|
|
* negative infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@code -Double.MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param d starting floating-point value
|
|
* @return The adjacent floating-point value closer to negative
|
|
* infinity.
|
|
* @since 1.8
|
|
*/
|
|
public static double nextDown(double d) {
|
|
return Math.nextDown(d);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code f} in
|
|
* the direction of negative infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(f,
|
|
* Float.NEGATIVE_INFINITY)}; however, a
|
|
* {@code nextDown} implementation may run faster than its
|
|
* equivalent {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is negative infinity, the result is
|
|
* negative infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@code -Float.MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @param f starting floating-point value
|
|
* @return The adjacent floating-point value closer to negative
|
|
* infinity.
|
|
* @since 1.8
|
|
*/
|
|
public static float nextDown(float f) {
|
|
return Math.nextDown(f);
|
|
}
|
|
|
|
/**
|
|
* Returns {@code d} × 2<sup>{@code scaleFactor}</sup>
|
|
* rounded as if performed by a single correctly rounded
|
|
* floating-point multiply. If the exponent of the result is
|
|
* between {@link Double#MIN_EXPONENT} and {@link
|
|
* Double#MAX_EXPONENT}, the answer is calculated exactly. If the
|
|
* exponent of the result would be larger than {@code
|
|
* Double.MAX_EXPONENT}, an infinity is returned. Note that if
|
|
* the result is subnormal, precision may be lost; that is, when
|
|
* {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n),
|
|
* -n)} may not equal <i>x</i>. When the result is non-NaN, the
|
|
* result has the same sign as {@code d}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If the first argument is NaN, NaN is returned.
|
|
* <li> If the first argument is infinite, then an infinity of the
|
|
* same sign is returned.
|
|
* <li> If the first argument is zero, then a zero of the same
|
|
* sign is returned.
|
|
* </ul>
|
|
*
|
|
* @param d number to be scaled by a power of two.
|
|
* @param scaleFactor power of 2 used to scale {@code d}
|
|
* @return {@code d} × 2<sup>{@code scaleFactor}</sup>
|
|
* @since 1.6
|
|
*/
|
|
public static double scalb(double d, int scaleFactor) {
|
|
return Math.scalb(d, scaleFactor);
|
|
}
|
|
|
|
/**
|
|
* Returns {@code f} × 2<sup>{@code scaleFactor}</sup>
|
|
* rounded as if performed by a single correctly rounded
|
|
* floating-point multiply. If the exponent of the result is
|
|
* between {@link Float#MIN_EXPONENT} and {@link
|
|
* Float#MAX_EXPONENT}, the answer is calculated exactly. If the
|
|
* exponent of the result would be larger than {@code
|
|
* Float.MAX_EXPONENT}, an infinity is returned. Note that if the
|
|
* result is subnormal, precision may be lost; that is, when
|
|
* {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n),
|
|
* -n)} may not equal <i>x</i>. When the result is non-NaN, the
|
|
* result has the same sign as {@code f}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If the first argument is NaN, NaN is returned.
|
|
* <li> If the first argument is infinite, then an infinity of the
|
|
* same sign is returned.
|
|
* <li> If the first argument is zero, then a zero of the same
|
|
* sign is returned.
|
|
* </ul>
|
|
*
|
|
* @param f number to be scaled by a power of two.
|
|
* @param scaleFactor power of 2 used to scale {@code f}
|
|
* @return {@code f} × 2<sup>{@code scaleFactor}</sup>
|
|
* @since 1.6
|
|
*/
|
|
public static float scalb(float f, int scaleFactor) {
|
|
return Math.scalb(f, scaleFactor);
|
|
}
|
|
}
|