3648 lines
141 KiB
Java
3648 lines
141 KiB
Java
/*
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* Copyright (C) 2014 The Android Open Source Project
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* Copyright (c) 1994, 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 dalvik.annotation.optimization.CriticalNative;
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import java.math.BigDecimal;
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import java.util.Random;
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import jdk.internal.math.FloatConsts;
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import jdk.internal.math.DoubleConsts;
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import jdk.internal.vm.annotation.IntrinsicCandidate;
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// Android-note: Document that the results from Math are based on libm's behavior.
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// For performance, Android implements many of the methods in this class in terms of the underlying
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// OS's libm functions. libm has well-defined behavior for special cases. Where known these are
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// marked with the tag above and the documentation has been modified as needed.
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// Android-changed: Fixed method links in the last paragraph.
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/**
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* The class {@code Math} 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>Unlike some of the numeric methods of class
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* {@link java.lang.StrictMath StrictMath}, all implementations of the equivalent
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* functions of class {@code Math} are not defined to return the
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* bit-for-bit same results. This relaxation permits
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* better-performing implementations where strict reproducibility is
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* not required.
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*
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* <p>By default many of the {@code Math} methods simply call
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* the equivalent method in {@code StrictMath} for their
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* implementation. Code generators are encouraged to use
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* platform-specific native libraries or microprocessor instructions,
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* where available, to provide higher-performance implementations of
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* {@code Math} methods. Such higher-performance
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* implementations still must conform to the specification for
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* {@code Math}.
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*
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* <p>The quality of implementation specifications concern two
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* properties, accuracy of the returned result and monotonicity of the
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* method. Accuracy of the floating-point {@code Math} methods is
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* measured in terms of <i>ulps</i>, units in the last place. For a
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* given floating-point format, an {@linkplain #ulp(double) ulp} of a
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* specific real number value is the distance between the two
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* floating-point values bracketing that numerical value. When
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* discussing the accuracy of a method as a whole rather than at a
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* specific argument, the number of ulps cited is for the worst-case
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* error at any argument. If a method always has an error less than
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* 0.5 ulps, the method always returns the floating-point number
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* nearest the exact result; such a method is <i>correctly
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* rounded</i>. A correctly rounded method is generally the best a
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* floating-point approximation can be; however, it is impractical for
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* many floating-point methods to be correctly rounded. Instead, for
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* the {@code Math} class, a larger error bound of 1 or 2 ulps is
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* allowed for certain methods. Informally, with a 1 ulp error bound,
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* when the exact result is a representable number, the exact result
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* should be returned as the computed result; otherwise, either of the
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* two floating-point values which bracket the exact result may be
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* returned. For exact results large in magnitude, one of the
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* endpoints of the bracket may be infinite. Besides accuracy at
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* individual arguments, maintaining proper relations between the
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* method at different arguments is also important. Therefore, most
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* methods with more than 0.5 ulp errors are required to be
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* <i>semi-monotonic</i>: whenever the mathematical function is
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* non-decreasing, so is the floating-point approximation, likewise,
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* whenever the mathematical function is non-increasing, so is the
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* floating-point approximation. Not all approximations that have 1
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* ulp accuracy will automatically meet the monotonicity requirements.
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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 2019 revision of the IEEE 754 floating-point standard includes
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* a section of recommended operations and the semantics of those
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* operations if they are included in a programming environment. The
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* recommended operations present in this class include {@link #sin(double)
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* sin}, {@link #cos(double) cos}, {@link #tan(double) tan}, {@link #asin(double) asin}, {@link
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* #acos(double) acos}, {@link #atan(double) atan}, {@link #exp(double) exp}, {@link #expm1(double)
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* expm1}, {@link #log(double) log}, {@link #log10(double) log10}, {@link #log1p(double) log1p},
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* {@link #sinh(double) sinh}, {@link #cosh(double) cosh}, {@link #tanh(double) tanh}, {@link
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* #hypot(double, double) hypot}, and {@link #pow(double, double) pow}. (The {@link #sqrt(double) sqrt}
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* operation is a required part of IEEE 754 from a different section
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* of the standard.) The special case behavior of the recommended
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* operations generally follows the guidance of the IEEE 754
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* standard. However, the {@code pow} method defines different
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* behavior for some arguments, as noted in its {@linkplain #pow(double, double)
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* specification}. The IEEE 754 standard defines its operations to be
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* correctly rounded, which is a more stringent quality of
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* implementation condition than required for most of the methods in
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* question that are also included in this class.
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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 1.0
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*/
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public final class Math {
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// Android-changed: Numerous methods in this class are re-implemented in native for performance.
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// Those methods are also annotated @CriticalNative.
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/**
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* Don't let anyone instantiate this class.
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*/
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private Math() {}
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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
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* its 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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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@IntrinsicCandidate
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public static double sin(double a) {
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return StrictMath.sin(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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@IntrinsicCandidate
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public static double cos(double a) {
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return StrictMath.cos(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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@IntrinsicCandidate
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public static double tan(double a) {
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return StrictMath.tan(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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public static double asin(double a) {
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return StrictMath.asin(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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public static double acos(double a) {
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return StrictMath.acos(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
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/*
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public static double atan(double a) {
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return StrictMath.atan(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* @since 1.2
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*/
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public static double toRadians(double angdeg) {
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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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* @since 1.2
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*/
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public static double toDegrees(double angrad) {
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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@IntrinsicCandidate
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public static double exp(double a) {
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return StrictMath.exp(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
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@CriticalNative
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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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* <p>The computed result must be within 1 ulp of the exact result.
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* Results must be semi-monotonic.
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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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// BEGIN Android-changed: Reimplement in native
|
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/*
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@IntrinsicCandidate
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public static double log(double a) {
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return StrictMath.log(a); // default impl. delegates to StrictMath
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}
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*/
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// END Android-changed: Reimplement in native
|
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@CriticalNative
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public static native double log(double a);
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|
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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.
|
|
* </ul>
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact result.
|
|
* Results must be semi-monotonic.
|
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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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*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
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@IntrinsicCandidate
|
|
public static double log10(double a) {
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return StrictMath.log10(a); // default impl. delegates to StrictMath
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}
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*/
|
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// END Android-changed: Reimplement in native
|
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@CriticalNative
|
|
public static native double log10(double a);
|
|
|
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/**
|
|
* Returns the correctly rounded positive square root of a
|
|
* {@code double} value.
|
|
* Special cases:
|
|
* <ul><li>If the argument is NaN or less than zero, then the result
|
|
* is NaN.
|
|
* <li>If the argument is positive infinity, then the result is positive
|
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* infinity.
|
|
* <li>If the argument is positive zero or negative zero, then the
|
|
* result is the same as the argument.</ul>
|
|
* Otherwise, the result is the {@code double} value closest to
|
|
* the true mathematical square root of the argument value.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the squareRoot operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @param a a value.
|
|
* @return the positive square root of {@code a}.
|
|
* If the argument is NaN or less than zero, the result is NaN.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double sqrt(double a) {
|
|
return StrictMath.sqrt(a); // default impl. delegates to StrictMath
|
|
// Note that hardware sqrt instructions
|
|
// frequently can be directly used by JITs
|
|
// and should be much faster than doing
|
|
// Math.sqrt in software.
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double sqrt(double a);
|
|
|
|
|
|
/**
|
|
* Returns the cube root of a {@code double} value. For
|
|
* positive finite {@code x}, {@code cbrt(-x) ==
|
|
* -cbrt(x)}; that is, the cube root of a negative value is
|
|
* the negative of the cube root of that value's magnitude.
|
|
*
|
|
* Special cases:
|
|
*
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN, then the result is NaN.
|
|
*
|
|
* <li>If the argument is infinite, then the result is an infinity
|
|
* with the same sign as the argument.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact result.
|
|
*
|
|
* @param a a value.
|
|
* @return the cube root of {@code a}.
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double cbrt(double a) {
|
|
return StrictMath.cbrt(a);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double cbrt(double a);
|
|
|
|
/**
|
|
* Computes the remainder operation on two arguments as prescribed
|
|
* by the IEEE 754 standard.
|
|
* The remainder value is mathematically equal to
|
|
* <code>f1 - f2</code> × <i>n</i>,
|
|
* where <i>n</i> is the mathematical integer closest to the exact
|
|
* mathematical value of the quotient {@code f1/f2}, and if two
|
|
* mathematical integers are equally close to {@code f1/f2},
|
|
* then <i>n</i> is the integer that is even. If the remainder is
|
|
* zero, its sign is the same as the sign of the first argument.
|
|
* Special cases:
|
|
* <ul><li>If either argument is NaN, or the first argument is infinite,
|
|
* or the second argument is positive zero or negative zero, then the
|
|
* result is NaN.
|
|
* <li>If the first argument is finite and the second argument is
|
|
* infinite, then the result is the same as the first argument.</ul>
|
|
*
|
|
* @param f1 the dividend.
|
|
* @param f2 the divisor.
|
|
* @return the remainder when {@code f1} is divided by
|
|
* {@code f2}.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double IEEEremainder(double f1, double f2) {
|
|
return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double IEEEremainder(double f1, double f2);
|
|
|
|
/**
|
|
* Returns the smallest (closest to negative infinity)
|
|
* {@code double} value that is greater than or equal to the
|
|
* argument and is equal to a mathematical integer. Special cases:
|
|
* <ul><li>If the argument value is already equal to a
|
|
* mathematical integer, then the result is the same as the
|
|
* argument. <li>If the argument is NaN or an infinity or
|
|
* positive zero or negative zero, then the result is the same as
|
|
* the argument. <li>If the argument value is less than zero but
|
|
* greater than -1.0, then the result is negative zero.</ul> Note
|
|
* that the value of {@code Math.ceil(x)} is exactly the
|
|
* value of {@code -Math.floor(-x)}.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the roundToIntegralTowardPositive
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param a a value.
|
|
* @return the smallest (closest to negative infinity)
|
|
* floating-point value that is greater than or equal to
|
|
* the argument and is equal to a mathematical integer.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double ceil(double a) {
|
|
return StrictMath.ceil(a); // default impl. delegates to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double ceil(double a);
|
|
|
|
/**
|
|
* 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>
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the roundToIntegralTowardNegative
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @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.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double floor(double a) {
|
|
return StrictMath.floor(a); // default impl. delegates to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double floor(double a);
|
|
|
|
/**
|
|
* Returns the {@code double} value that is closest in value
|
|
* to the argument and is equal to a mathematical integer. If two
|
|
* {@code double} values that are mathematical integers are
|
|
* equally close, the result is the integer value that is
|
|
* even. Special cases:
|
|
* <ul><li>If the argument value is already equal to a mathematical
|
|
* integer, then the result is the same as the argument.
|
|
* <li>If the argument is NaN or an infinity or positive zero or negative
|
|
* zero, then the result is the same as the argument.</ul>
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the roundToIntegralTiesToEven
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param a a {@code double} value.
|
|
* @return the closest floating-point value to {@code a} that is
|
|
* equal to a mathematical integer.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double rint(double a) {
|
|
return StrictMath.rint(a); // default impl. delegates to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double rint(double a);
|
|
|
|
/**
|
|
* Returns the angle <i>theta</i> from the conversion of rectangular
|
|
* coordinates ({@code x}, {@code y}) to polar
|
|
* coordinates (r, <i>theta</i>).
|
|
* This method computes the phase <i>theta</i> by computing an arc tangent
|
|
* of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
|
|
* cases:
|
|
* <ul><li>If either argument is NaN, then the result is NaN.
|
|
* <li>If the first argument is positive zero and the second argument
|
|
* is positive, or the first argument is positive and finite and the
|
|
* second argument is positive infinity, then the result is positive
|
|
* zero.
|
|
* <li>If the first argument is negative zero and the second argument
|
|
* is positive, or the first argument is negative and finite and the
|
|
* second argument is positive infinity, then the result is negative zero.
|
|
* <li>If the first argument is positive zero and the second argument
|
|
* is negative, or the first argument is positive and finite and the
|
|
* second argument is negative infinity, then the result is the
|
|
* {@code double} value closest to <i>pi</i>.
|
|
* <li>If the first argument is negative zero and the second argument
|
|
* is negative, or the first argument is negative and finite and the
|
|
* second argument is negative infinity, then the result is the
|
|
* {@code double} value closest to -<i>pi</i>.
|
|
* <li>If the first argument is positive and the second argument is
|
|
* positive zero or negative zero, or the first argument is positive
|
|
* infinity and the second argument is finite, then the result is the
|
|
* {@code double} value closest to <i>pi</i>/2.
|
|
* <li>If the first argument is negative and the second argument is
|
|
* positive zero or negative zero, or the first argument is negative
|
|
* infinity and the second argument is finite, then the result is the
|
|
* {@code double} value closest to -<i>pi</i>/2.
|
|
* <li>If both arguments are positive infinity, then the result is the
|
|
* {@code double} value closest to <i>pi</i>/4.
|
|
* <li>If the first argument is positive infinity and the second argument
|
|
* is negative infinity, then the result is the {@code double}
|
|
* value closest to 3*<i>pi</i>/4.
|
|
* <li>If the first argument is negative infinity and the second argument
|
|
* is positive infinity, then the result is the {@code double} value
|
|
* closest to -<i>pi</i>/4.
|
|
* <li>If both arguments are negative infinity, then the result is the
|
|
* {@code double} value closest to -3*<i>pi</i>/4.</ul>
|
|
*
|
|
* <p>The computed result must be within 2 ulps of the exact result.
|
|
* Results must be semi-monotonic.
|
|
*
|
|
* @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.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double atan2(double y, double x) {
|
|
return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double atan2(double y, double x);
|
|
|
|
// Android-changed: Document that the results from Math are based on libm's behavior.
|
|
// The cases known to differ with libm's pow():
|
|
// If the first argument is 1.0 then result is always 1.0 (not NaN).
|
|
// If the first argument is -1.0 and the second argument is infinite, the result is 1.0 (not
|
|
// NaN).
|
|
/**
|
|
* 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 first argument is 1.0, then the result is 1.0.
|
|
* <li>If the second argument is NaN, then the result is NaN except where the first argument is
|
|
* 1.0.
|
|
* <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 1.0.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is positive zero and the second argument
|
|
* is greater than zero, or
|
|
* <li>the first argument is positive infinity and the second
|
|
* argument is less than zero,
|
|
* </ul>
|
|
* then the result is positive zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is positive zero and the second argument
|
|
* is less than zero, or
|
|
* <li>the first argument is positive infinity and the second
|
|
* argument is greater than zero,
|
|
* </ul>
|
|
* then the result is positive infinity.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is greater than zero but not a finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is less than zero but not a finite odd integer,
|
|
* </ul>
|
|
* then the result is positive zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is a positive finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is a negative finite odd integer,
|
|
* </ul>
|
|
* then the result is negative zero.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is less than zero but not a finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is greater than zero but not a finite odd integer,
|
|
* </ul>
|
|
* then the result is positive infinity.
|
|
*
|
|
* <li>If
|
|
* <ul>
|
|
* <li>the first argument is negative zero and the second argument
|
|
* is a negative finite odd integer, or
|
|
* <li>the first argument is negative infinity and the second
|
|
* argument is a positive finite odd integer,
|
|
* </ul>
|
|
* then the result is negative infinity.
|
|
*
|
|
* <li>If the first argument is finite and less than zero
|
|
* <ul>
|
|
* <li> if the second argument is a finite even integer, the
|
|
* result is equal to the result of raising the absolute value of
|
|
* the first argument to the power of the second argument
|
|
*
|
|
* <li>if the second argument is a finite odd integer, the result
|
|
* is equal to the negative of the result of raising the absolute
|
|
* value of the first argument to the power of the second
|
|
* argument
|
|
*
|
|
* <li>if the second argument is finite and not an integer, then
|
|
* the result is NaN.
|
|
* </ul>
|
|
*
|
|
* <li>If both arguments are integers, then the result is exactly equal
|
|
* to the mathematical result of raising the first argument to the power
|
|
* of the second argument if that result can in fact be represented
|
|
* exactly as a {@code double} value.</ul>
|
|
*
|
|
* <p>(In the foregoing descriptions, a floating-point value is
|
|
* considered to be an integer if and only if it is finite and a
|
|
* fixed point of the method {@link #ceil ceil} or,
|
|
* equivalently, a fixed point of the method {@link #floor
|
|
* floor}. A value is a fixed point of a one-argument
|
|
* method if and only if the result of applying the method to the
|
|
* value is equal to the value.)
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact result.
|
|
* Results must be semi-monotonic.
|
|
*
|
|
* @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 the base.
|
|
* @param b the exponent.
|
|
* @return the value {@code a}<sup>{@code b}</sup>.
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
@IntrinsicCandidate
|
|
public static double pow(double a, double b) {
|
|
return StrictMath.pow(a, b); // default impl. delegates to StrictMath
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int round(float a) {
|
|
int intBits = Float.floatToRawIntBits(a);
|
|
int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
|
|
>> (FloatConsts.SIGNIFICAND_WIDTH - 1);
|
|
int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
|
|
+ FloatConsts.EXP_BIAS) - biasedExp;
|
|
if ((shift & -32) == 0) { // shift >= 0 && shift < 32
|
|
// a is a finite number such that pow(2,-32) <= ulp(a) < 1
|
|
int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
|
|
| (FloatConsts.SIGNIF_BIT_MASK + 1));
|
|
if (intBits < 0) {
|
|
r = -r;
|
|
}
|
|
// In the comments below each Java expression evaluates to the value
|
|
// the corresponding mathematical expression:
|
|
// (r) evaluates to a / ulp(a)
|
|
// (r >> shift) evaluates to floor(a * 2)
|
|
// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
|
|
// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
|
|
return ((r >> shift) + 1) >> 1;
|
|
} else {
|
|
// a is either
|
|
// - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
|
|
// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
|
|
// - an infinity or NaN
|
|
return (int) a;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the closest {@code long} to the argument, with ties
|
|
* rounding to positive infinity.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul><li>If the argument is NaN, the result is 0.
|
|
* <li>If the argument is negative infinity or any value less than or
|
|
* equal to the value of {@code Long.MIN_VALUE}, the result is
|
|
* equal to the value of {@code Long.MIN_VALUE}.
|
|
* <li>If the argument is positive infinity or any value greater than or
|
|
* equal to the value of {@code Long.MAX_VALUE}, the result is
|
|
* equal to the value of {@code Long.MAX_VALUE}.</ul>
|
|
*
|
|
* @param a a floating-point value to be rounded to a
|
|
* {@code long}.
|
|
* @return the value of the argument rounded to the nearest
|
|
* {@code long} value.
|
|
* @see java.lang.Long#MAX_VALUE
|
|
* @see java.lang.Long#MIN_VALUE
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long round(double a) {
|
|
long longBits = Double.doubleToRawLongBits(a);
|
|
long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
|
|
>> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
|
|
long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
|
|
+ DoubleConsts.EXP_BIAS) - biasedExp;
|
|
if ((shift & -64) == 0) { // shift >= 0 && shift < 64
|
|
// a is a finite number such that pow(2,-64) <= ulp(a) < 1
|
|
long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
|
|
| (DoubleConsts.SIGNIF_BIT_MASK + 1));
|
|
if (longBits < 0) {
|
|
r = -r;
|
|
}
|
|
// In the comments below each Java expression evaluates to the value
|
|
// the corresponding mathematical expression:
|
|
// (r) evaluates to a / ulp(a)
|
|
// (r >> shift) evaluates to floor(a * 2)
|
|
// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
|
|
// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
|
|
return ((r >> shift) + 1) >> 1;
|
|
} else {
|
|
// a is either
|
|
// - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
|
|
// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
|
|
// - an infinity or NaN
|
|
return (long) a;
|
|
}
|
|
}
|
|
|
|
private static final class RandomNumberGeneratorHolder {
|
|
static final Random randomNumberGenerator = new Random();
|
|
}
|
|
|
|
/**
|
|
* Returns a {@code double} value with a positive sign, greater
|
|
* than or equal to {@code 0.0} and less than {@code 1.0}.
|
|
* Returned values are chosen pseudorandomly with (approximately)
|
|
* uniform distribution from that range.
|
|
*
|
|
* <p>When this method is first called, it creates a single new
|
|
* pseudorandom-number generator, exactly as if by the expression
|
|
*
|
|
* <blockquote>{@code new java.util.Random()}</blockquote>
|
|
*
|
|
* This new pseudorandom-number generator is used thereafter for
|
|
* all calls to this method and is used nowhere else.
|
|
*
|
|
* <p>This method is properly synchronized to allow correct use by
|
|
* more than one thread. However, if many threads need to generate
|
|
* pseudorandom numbers at a great rate, it may reduce contention
|
|
* for each thread to have its own pseudorandom-number generator.
|
|
*
|
|
* @apiNote
|
|
* As the largest {@code double} value less than {@code 1.0}
|
|
* is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range
|
|
* {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements
|
|
*
|
|
* <blockquote><pre>{@code
|
|
* double f = Math.random()/Math.nextDown(1.0);
|
|
* double x = x1*(1.0 - f) + x2*f;
|
|
* }</pre></blockquote>
|
|
*
|
|
* @return a pseudorandom {@code double} greater than or equal
|
|
* to {@code 0.0} and less than {@code 1.0}.
|
|
* @see #nextDown(double)
|
|
* @see Random#nextDouble()
|
|
*/
|
|
public static double random() {
|
|
return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
|
|
}
|
|
|
|
// Android-added: setRandomSeedInternal(long), called after zygote forks.
|
|
// This allows different processes to have different random seeds.
|
|
/**
|
|
* Set the seed for the pseudo random generator used by {@link #random()}
|
|
* and {@link #randomIntInternal()}.
|
|
*
|
|
* @hide for internal use only.
|
|
*/
|
|
public static void setRandomSeedInternal(long seed) {
|
|
RandomNumberGeneratorHolder.randomNumberGenerator.setSeed(seed);
|
|
}
|
|
|
|
// Android-added: randomIntInternal() method: like random() but for int.
|
|
/**
|
|
* @hide for internal use only.
|
|
*/
|
|
public static int randomIntInternal() {
|
|
return RandomNumberGeneratorHolder.randomNumberGenerator.nextInt();
|
|
}
|
|
|
|
// Android-added: randomLongInternal() method: like random() but for long.
|
|
/**
|
|
* @hide for internal use only.
|
|
*/
|
|
public static long randomLongInternal() {
|
|
return RandomNumberGeneratorHolder.randomNumberGenerator.nextLong();
|
|
}
|
|
|
|
/**
|
|
* Returns the sum of its arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int addExact(int x, int y) {
|
|
int r = x + y;
|
|
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
|
|
if (((x ^ r) & (y ^ r)) < 0) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Returns the sum of its arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long addExact(long x, long y) {
|
|
long r = x + y;
|
|
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
|
|
if (((x ^ r) & (y ^ r)) < 0) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Returns the difference of the arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value to subtract from the first
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int subtractExact(int x, int y) {
|
|
int r = x - y;
|
|
// HD 2-12 Overflow iff the arguments have different signs and
|
|
// the sign of the result is different from the sign of x
|
|
if (((x ^ y) & (x ^ r)) < 0) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Returns the difference of the arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value to subtract from the first
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long subtractExact(long x, long y) {
|
|
long r = x - y;
|
|
// HD 2-12 Overflow iff the arguments have different signs and
|
|
// the sign of the result is different from the sign of x
|
|
if (((x ^ y) & (x ^ r)) < 0) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments,
|
|
* throwing an exception if the result overflows an {@code int}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows an int
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int multiplyExact(int x, int y) {
|
|
long r = (long)x * (long)y;
|
|
if ((int)r != r) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
return (int)r;
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments, throwing an exception if the result
|
|
* overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @since 9
|
|
*/
|
|
public static long multiplyExact(long x, int y) {
|
|
return multiplyExact(x, (long)y);
|
|
}
|
|
|
|
/**
|
|
* Returns the product of the arguments,
|
|
* throwing an exception if the result overflows a {@code long}.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @throws ArithmeticException if the result overflows a long
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long multiplyExact(long x, long y) {
|
|
long r = x * y;
|
|
long ax = Math.abs(x);
|
|
long ay = Math.abs(y);
|
|
if (((ax | ay) >>> 31 != 0)) {
|
|
// Some bits greater than 2^31 that might cause overflow
|
|
// Check the result using the divide operator
|
|
// and check for the special case of Long.MIN_VALUE * -1
|
|
if (((y != 0) && (r / y != x)) ||
|
|
(x == Long.MIN_VALUE && y == -1)) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* Returns the 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 /
|
|
* @since 18
|
|
*/
|
|
public static int divideExact(int x, int y) {
|
|
int q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
/**
|
|
* 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 /
|
|
* @since 18
|
|
*/
|
|
public static long divideExact(long x, long y) {
|
|
long q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* For examples, see {@link #floorDiv(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero, or the
|
|
* dividend {@code x} is {@code Integer.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see #floorDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int floorDivExact(int x, int y) {
|
|
final int q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
// if the signs are different and modulo not zero, round down
|
|
if ((x ^ y) < 0 && (q * y != x)) {
|
|
return q - 1;
|
|
}
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
/**
|
|
* 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 #floorDiv(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero, or the
|
|
* dividend {@code x} is {@code Long.MIN_VALUE} and the divisor {@code y}
|
|
* is {@code -1}.
|
|
* @see #floorDiv(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long floorDivExact(long x, long y) {
|
|
final long q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
// if the signs are different and modulo not zero, round down
|
|
if ((x ^ y) < 0 && (q * y != x)) {
|
|
return q - 1;
|
|
}
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* For examples, see {@link #ceilDiv(int, int)}.
|
|
*
|
|
* @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 #ceilDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilDivExact(int x, int y) {
|
|
final int q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
// if the signs are the same and modulo not zero, round up
|
|
if ((x ^ y) >= 0 && (q * y != x)) {
|
|
return q + 1;
|
|
}
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
/**
|
|
* 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 #ceilDiv(int, int)}.
|
|
*
|
|
* @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 #ceilDiv(long,long)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDivExact(long x, long y) {
|
|
final long q = x / y;
|
|
if ((x & y & q) >= 0) {
|
|
// if the signs are the same and modulo not zero, round up
|
|
if ((x ^ y) >= 0 && (q * y != x)) {
|
|
return q + 1;
|
|
}
|
|
return q;
|
|
}
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
/**
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int incrementExact(int a) {
|
|
if (a == Integer.MAX_VALUE) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
return a + 1;
|
|
}
|
|
|
|
/**
|
|
* Returns the argument incremented by one, throwing an exception if the
|
|
* result overflows a {@code long}.
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long incrementExact(long a) {
|
|
if (a == Long.MAX_VALUE) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
return a + 1L;
|
|
}
|
|
|
|
/**
|
|
* Returns the argument decremented by one, throwing an exception if the
|
|
* result overflows an {@code int}.
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int decrementExact(int a) {
|
|
if (a == Integer.MIN_VALUE) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
return a - 1;
|
|
}
|
|
|
|
/**
|
|
* Returns the argument decremented by one, throwing an exception if the
|
|
* result overflows a {@code long}.
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long decrementExact(long a) {
|
|
if (a == Long.MIN_VALUE) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
return a - 1L;
|
|
}
|
|
|
|
/**
|
|
* Returns the negation of the argument, throwing an exception if the
|
|
* result overflows an {@code int}.
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int negateExact(int a) {
|
|
if (a == Integer.MIN_VALUE) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
|
|
return -a;
|
|
}
|
|
|
|
/**
|
|
* Returns the negation of the argument, throwing an exception if the
|
|
* result overflows a {@code long}.
|
|
* 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
|
|
* @since 1.8
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long negateExact(long a) {
|
|
if (a == Long.MIN_VALUE) {
|
|
throw new ArithmeticException("long overflow");
|
|
}
|
|
|
|
return -a;
|
|
}
|
|
|
|
/**
|
|
* Returns the value of the {@code long} argument,
|
|
* throwing an exception if the value overflows an {@code int}.
|
|
*
|
|
* @param value the long value
|
|
* @return the argument as an int
|
|
* @throws ArithmeticException if the {@code argument} overflows an int
|
|
* @since 1.8
|
|
*/
|
|
public static int toIntExact(long value) {
|
|
if ((int)value != value) {
|
|
throw new ArithmeticException("integer overflow");
|
|
}
|
|
return (int)value;
|
|
}
|
|
|
|
/**
|
|
* Returns the exact mathematical product of the arguments.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @since 9
|
|
*/
|
|
public static long multiplyFull(int x, int y) {
|
|
return (long)x * (long)y;
|
|
}
|
|
|
|
/**
|
|
* Returns as a {@code long} the most significant 64 bits of the 128-bit
|
|
* product of two 64-bit factors.
|
|
*
|
|
* @param x the first value
|
|
* @param y the second value
|
|
* @return the result
|
|
* @see #unsignedMultiplyHigh
|
|
* @since 9
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long multiplyHigh(long x, long y) {
|
|
// Use technique from section 8-2 of Henry S. Warren, Jr.,
|
|
// Hacker's Delight (2nd ed.) (Addison Wesley, 2013), 173-174.
|
|
long x1 = x >> 32;
|
|
long x2 = x & 0xFFFFFFFFL;
|
|
long y1 = y >> 32;
|
|
long y2 = y & 0xFFFFFFFFL;
|
|
|
|
long z2 = x2 * y2;
|
|
long t = x1 * y2 + (z2 >>> 32);
|
|
long z1 = t & 0xFFFFFFFFL;
|
|
long z0 = t >> 32;
|
|
z1 += x2 * y1;
|
|
|
|
return x1 * y1 + z0 + (z1 >> 32);
|
|
}
|
|
|
|
/**
|
|
* 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
|
|
* @since 18
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long unsignedMultiplyHigh(long x, long y) {
|
|
// Compute via multiplyHigh() to leverage the intrinsic
|
|
long result = Math.multiplyHigh(x, y);
|
|
result += (y & (x >> 63)); // equivalent to `if (x < 0) result += y;`
|
|
result += (x & (y >> 63)); // equivalent to `if (y < 0) result += x;`
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* negative infinity (floor) rounding mode.
|
|
* The floor rounding mode gives different results from truncation
|
|
* when the exact quotient is not an integer and is negative.
|
|
* <ul>
|
|
* <li>If the signs of the arguments are the same, the results of
|
|
* {@code floorDiv} and the {@code /} operator are the same. <br>
|
|
* For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
|
|
* <li>If the signs of the arguments are different, {@code floorDiv}
|
|
* returns the largest integer less than or equal to the quotient
|
|
* while the {@code /} operator returns the smallest integer greater
|
|
* than or equal to the quotient.
|
|
* They differ if and only if the quotient is not an integer.<br>
|
|
* For example, {@code floorDiv(-4, 3) == -2},
|
|
* whereas {@code (-4 / 3) == -1}.
|
|
* </li>
|
|
* </ul>
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code int} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorMod(int, int)
|
|
* @see #floor(double)
|
|
* @since 1.8
|
|
*/
|
|
public static int floorDiv(int x, int y) {
|
|
final int q = x / y;
|
|
// if the signs are different and modulo not zero, round down
|
|
if ((x ^ y) < 0 && (q * y != x)) {
|
|
return q - 1;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* negative infinity (floor) rounding mode.
|
|
* The floor rounding mode gives different results from truncation
|
|
* when the exact result is not an integer and is negative.
|
|
* <p>
|
|
* For examples, see {@link #floorDiv(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorMod(long, int)
|
|
* @see #floor(double)
|
|
* @since 9
|
|
*/
|
|
public static long floorDiv(long x, int y) {
|
|
return floorDiv(x, (long)y);
|
|
}
|
|
|
|
/**
|
|
* Returns the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* There is one special case: if the dividend is
|
|
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
|
|
* then integer overflow occurs and
|
|
* the result is equal to {@code Long.MIN_VALUE}.
|
|
* <p>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* negative infinity (floor) rounding mode.
|
|
* The floor rounding mode gives different results from truncation
|
|
* when the exact result is not an integer and is negative.
|
|
* <p>
|
|
* For examples, see {@link #floorDiv(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the largest (closest to positive infinity)
|
|
* {@code long} value that is less than or equal to the algebraic quotient.
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorMod(long, long)
|
|
* @see #floor(double)
|
|
* @since 1.8
|
|
*/
|
|
public static long floorDiv(long x, long y) {
|
|
final long q = x / y;
|
|
// if the signs are different and modulo not zero, round down
|
|
if ((x ^ y) < 0 && (q * y != x)) {
|
|
return q - 1;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* The difference in values between {@code floorMod} and the {@code %} operator
|
|
* is due to the difference between {@code floorDiv} and the {@code /}
|
|
* operator, as detailed in {@linkplain #floorDiv(int, int)}.
|
|
* <p>
|
|
* Examples:
|
|
* <ul>
|
|
* <li>Regardless of the signs of the arguments, {@code floorMod}(x, y)
|
|
* is zero exactly when {@code x % y} is zero as well.</li>
|
|
* <li>If neither {@code floorMod}(x, y) nor {@code x % y} is zero,
|
|
* they differ exactly when the signs of the arguments differ.<br>
|
|
* <ul>
|
|
* <li>{@code floorMod(+4, +3) == +1}; and {@code (+4 % +3) == +1}</li>
|
|
* <li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1}</li>
|
|
* <li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1}</li>
|
|
* <li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1}</li>
|
|
* </ul>
|
|
* </li>
|
|
* </ul>
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorDiv(int, int)
|
|
* @since 1.8
|
|
*/
|
|
public static int floorMod(int x, int y) {
|
|
final int r = x % y;
|
|
// if the signs are different and modulo not zero, adjust result
|
|
if ((x ^ y) < 0 && r != 0) {
|
|
return r + y;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* For examples, see {@link #floorMod(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorDiv(long, int)
|
|
* @since 9
|
|
*/
|
|
public static int floorMod(long x, int y) {
|
|
// Result cannot overflow the range of int.
|
|
return (int)floorMod(x, (long)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>
|
|
* For examples, see {@link #floorMod(int, int)}.
|
|
*
|
|
* @param x the dividend
|
|
* @param y the divisor
|
|
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
|
|
* @throws ArithmeticException if the divisor {@code y} is zero
|
|
* @see #floorDiv(long, long)
|
|
* @since 1.8
|
|
*/
|
|
public static long floorMod(long x, long y) {
|
|
final long r = x % y;
|
|
// if the signs are different and modulo not zero, adjust result
|
|
if ((x ^ y) < 0 && r != 0) {
|
|
return r + y;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* positive infinity (ceiling) rounding mode.
|
|
* The ceiling rounding mode gives different results from truncation
|
|
* when the exact quotient is not an integer and is positive.
|
|
* <ul>
|
|
* <li>If the signs of the arguments are different, the results of
|
|
* {@code ceilDiv} and the {@code /} operator are the same. <br>
|
|
* For example, {@code ceilDiv(-4, 3) == -1} and {@code (-4 / 3) == -1}.</li>
|
|
* <li>If the signs of the arguments are the same, {@code ceilDiv}
|
|
* returns the smallest integer greater than or equal to the quotient
|
|
* while the {@code /} operator returns the largest integer less
|
|
* than or equal to the quotient.
|
|
* They differ if and only if the quotient is not an integer.<br>
|
|
* For example, {@code ceilDiv(4, 3) == 2},
|
|
* whereas {@code (4 / 3) == 1}.
|
|
* </li>
|
|
* </ul>
|
|
*
|
|
* @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 #ceilMod(int, int)
|
|
* @see #ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static int ceilDiv(int x, int y) {
|
|
final int q = x / y;
|
|
// if the signs are the same and modulo not zero, round up
|
|
if ((x ^ y) >= 0 && (q * y != x)) {
|
|
return q + 1;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* positive infinity (ceiling) rounding mode.
|
|
* The ceiling rounding mode gives different results from truncation
|
|
* when the exact result is not an integer and is positive.
|
|
* <p>
|
|
* For examples, see {@link #ceilDiv(int, int)}.
|
|
*
|
|
* @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 #ceilMod(int, int)
|
|
* @see #ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDiv(long x, int y) {
|
|
return ceilDiv(x, (long)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>
|
|
* Normal integer division operates under the round to zero rounding mode
|
|
* (truncation). This operation instead acts under the round toward
|
|
* positive infinity (ceiling) rounding mode.
|
|
* The ceiling rounding mode gives different results from truncation
|
|
* when the exact result is not an integer and is positive.
|
|
* <p>
|
|
* For examples, see {@link #ceilDiv(int, int)}.
|
|
*
|
|
* @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 #ceilMod(int, int)
|
|
* @see #ceil(double)
|
|
* @since 18
|
|
*/
|
|
public static long ceilDiv(long x, long y) {
|
|
final long q = x / y;
|
|
// if the signs are the same and modulo not zero, round up
|
|
if ((x ^ y) >= 0 && (q * y != x)) {
|
|
return q + 1;
|
|
}
|
|
return q;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* The difference in values between {@code ceilMod} and the {@code %} operator
|
|
* is due to the difference between {@code ceilDiv} and the {@code /}
|
|
* operator, as detailed in {@linkplain #ceilDiv(int, int)}.
|
|
* <p>
|
|
* Examples:
|
|
* <ul>
|
|
* <li>Regardless of the signs of the arguments, {@code ceilMod}(x, y)
|
|
* is zero exactly when {@code x % y} is zero as well.</li>
|
|
* <li>If neither {@code ceilMod}(x, y) nor {@code x % y} is zero,
|
|
* they differ exactly when the signs of the arguments are the same.<br>
|
|
* <ul>
|
|
* <li>{@code ceilMod(+4, +3) == -2}; and {@code (+4 % +3) == +1}</li>
|
|
* <li>{@code ceilMod(-4, -3) == +2}; and {@code (-4 % -3) == -1}</li>
|
|
* <li>{@code ceilMod(+4, -3) == +1}; and {@code (+4 % -3) == +1}</li>
|
|
* <li>{@code ceilMod(-4, +3) == -1}; and {@code (-4 % +3) == -1}</li>
|
|
* </ul>
|
|
* </li>
|
|
* </ul>
|
|
*
|
|
* @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 #ceilDiv(int, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilMod(int x, int y) {
|
|
final int r = x % y;
|
|
// if the signs are the same and modulo not zero, adjust result
|
|
if ((x ^ y) >= 0 && r != 0) {
|
|
return r - y;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* 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>
|
|
* For examples, see {@link #ceilMod(int, int)}.
|
|
*
|
|
* @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 #ceilDiv(long, int)
|
|
* @since 18
|
|
*/
|
|
public static int ceilMod(long x, int y) {
|
|
// Result cannot overflow the range of int.
|
|
return (int)ceilMod(x, (long)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>
|
|
* For examples, see {@link #ceilMod(int, int)}.
|
|
*
|
|
* @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 #ceilDiv(long, long)
|
|
* @since 18
|
|
*/
|
|
public static long ceilMod(long x, long y) {
|
|
final long r = x % y;
|
|
// if the signs are the same and modulo not zero, adjust result
|
|
if ((x ^ y) >= 0 && r != 0) {
|
|
return r - y;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/**
|
|
* 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 Math#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)
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int abs(int a) {
|
|
return (a < 0) ? -a : 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)
|
|
* @since 15
|
|
*/
|
|
public static int absExact(int a) {
|
|
if (a == Integer.MIN_VALUE)
|
|
throw new ArithmeticException(
|
|
"Overflow to represent absolute value of Integer.MIN_VALUE");
|
|
else
|
|
return abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the absolute value of a {@code long} value.
|
|
* If the argument is not negative, the argument is returned.
|
|
* If the argument is negative, the negation of the argument is returned.
|
|
*
|
|
* <p>Note that if the argument is equal to the value of {@link
|
|
* Long#MIN_VALUE}, the most negative representable {@code long}
|
|
* value, the result is that same value, which is negative. In
|
|
* contrast, the {@link Math#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)
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static long abs(long a) {
|
|
return (a < 0) ? -a : 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)
|
|
* @since 15
|
|
*/
|
|
public static long absExact(long a) {
|
|
if (a == Long.MIN_VALUE)
|
|
throw new ArithmeticException(
|
|
"Overflow to represent absolute value of Long.MIN_VALUE");
|
|
else
|
|
return abs(a);
|
|
}
|
|
|
|
/**
|
|
* Returns the absolute value of a {@code float} value.
|
|
* If the argument is not negative, the argument is returned.
|
|
* If the argument is negative, the negation of the argument is returned.
|
|
* Special cases:
|
|
* <ul><li>If the argument is positive zero or negative zero, the
|
|
* result is positive zero.
|
|
* <li>If the argument is infinite, the result is positive infinity.
|
|
* <li>If the argument is NaN, the result is NaN.</ul>
|
|
*
|
|
* @apiNote As implied by the above, one valid implementation of
|
|
* this method is given by the expression below which computes a
|
|
* {@code float} with the same exponent and significand as the
|
|
* argument but with a guaranteed zero sign bit indicating a
|
|
* positive value:<br>
|
|
* {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
|
|
*
|
|
* @param a the argument whose absolute value is to be determined
|
|
* @return the absolute value of the argument.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float abs(float a) {
|
|
// Convert to bit field form, zero the sign bit, and convert back
|
|
return Float.intBitsToFloat(Float.floatToRawIntBits(a) & FloatConsts.MAG_BIT_MASK);
|
|
}
|
|
|
|
/**
|
|
* 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.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double abs(double a) {
|
|
// Convert to bit field form, zero the sign bit, and convert back
|
|
return Double.longBitsToDouble(Double.doubleToRawLongBits(a) & DoubleConsts.MAG_BIT_MASK);
|
|
}
|
|
|
|
/**
|
|
* 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 (a >= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code long} values. That is, the
|
|
* result is the argument closer to the value of
|
|
* {@link Long#MAX_VALUE}. If the arguments have the same value,
|
|
* the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the larger of {@code a} and {@code b}.
|
|
*/
|
|
public static long max(long a, long b) {
|
|
return (a >= b) ? a : b;
|
|
}
|
|
|
|
// Use raw bit-wise conversions on guaranteed non-NaN arguments.
|
|
private static final long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
|
|
private static final long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
|
|
|
|
/**
|
|
* Returns the greater of two {@code float} values. That is,
|
|
* the result is the argument closer to positive infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other negative zero, the
|
|
* result is positive zero.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the maximum operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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) {
|
|
if (a != a)
|
|
return a; // a is NaN
|
|
if ((a == 0.0f) &&
|
|
(b == 0.0f) &&
|
|
(Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
|
|
// Raw conversion ok since NaN can't map to -0.0.
|
|
return b;
|
|
}
|
|
return (a >= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the greater of two {@code double} values. That
|
|
* is, the result is the argument closer to positive infinity. If
|
|
* the arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other negative zero, the
|
|
* result is positive zero.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the maximum operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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) {
|
|
if (a != a)
|
|
return a; // a is NaN
|
|
if ((a == 0.0d) &&
|
|
(b == 0.0d) &&
|
|
(Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
|
|
// Raw conversion ok since NaN can't map to -0.0.
|
|
return b;
|
|
}
|
|
return (a >= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code int} values. That is,
|
|
* the result the argument closer to the value of
|
|
* {@link Integer#MIN_VALUE}. If the arguments have the same
|
|
* value, the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b}.
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static int min(int a, int b) {
|
|
return (a <= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code long} values. That is,
|
|
* the result is the argument closer to the value of
|
|
* {@link Long#MIN_VALUE}. If the arguments have the same
|
|
* value, the result is that same value.
|
|
*
|
|
* @param a an argument.
|
|
* @param b another argument.
|
|
* @return the smaller of {@code a} and {@code b}.
|
|
*/
|
|
public static long min(long a, long b) {
|
|
return (a <= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code float} values. That is,
|
|
* the result is the value closer to negative infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If
|
|
* one argument is positive zero and the other is negative zero,
|
|
* the result is negative zero.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the minimum operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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) {
|
|
if (a != a)
|
|
return a; // a is NaN
|
|
if ((a == 0.0f) &&
|
|
(b == 0.0f) &&
|
|
(Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
|
|
// Raw conversion ok since NaN can't map to -0.0.
|
|
return b;
|
|
}
|
|
return (a <= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* Returns the smaller of two {@code double} values. That
|
|
* is, the result is the value closer to negative infinity. If the
|
|
* arguments have the same value, the result is that same
|
|
* value. If either value is NaN, then the result is NaN. Unlike
|
|
* the numerical comparison operators, this method considers
|
|
* negative zero to be strictly smaller than positive zero. If one
|
|
* argument is positive zero and the other is negative zero, the
|
|
* result is negative zero.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the minimum operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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) {
|
|
if (a != a)
|
|
return a; // a is NaN
|
|
if ((a == 0.0d) &&
|
|
(b == 0.0d) &&
|
|
(Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
|
|
// Raw conversion ok since NaN can't map to -0.0.
|
|
return b;
|
|
}
|
|
return (a <= b) ? a : b;
|
|
}
|
|
|
|
/**
|
|
* 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) {
|
|
if (min > max) {
|
|
throw new IllegalArgumentException(min + " > " + max);
|
|
}
|
|
return (int) Math.min(max, Math.max(value, min));
|
|
}
|
|
|
|
/**
|
|
* 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) {
|
|
if (min > max) {
|
|
throw new IllegalArgumentException(min + " > " + max);
|
|
}
|
|
return Math.min(max, Math.max(value, min));
|
|
}
|
|
|
|
/**
|
|
* 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) {
|
|
// This unusual condition allows keeping only one branch
|
|
// on common path when min < max and neither of them is NaN.
|
|
// If min == max, we should additionally check for +0.0/-0.0 case,
|
|
// so we're still visiting the if statement.
|
|
if (!(min < max)) { // min greater than, equal to, or unordered with respect to max; NaN values are unordered
|
|
if (Double.isNaN(min)) {
|
|
throw new IllegalArgumentException("min is NaN");
|
|
}
|
|
if (Double.isNaN(max)) {
|
|
throw new IllegalArgumentException("max is NaN");
|
|
}
|
|
if (Double.compare(min, max) > 0) {
|
|
throw new IllegalArgumentException(min + " > " + max);
|
|
}
|
|
// Fall-through if min and max are exactly equal (or min = -0.0 and max = +0.0)
|
|
// and none of them is NaN
|
|
}
|
|
return Math.min(max, Math.max(value, min));
|
|
}
|
|
|
|
/**
|
|
* 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) {
|
|
// This unusual condition allows keeping only one branch
|
|
// on common path when min < max and neither of them is NaN.
|
|
// If min == max, we should additionally check for +0.0/-0.0 case,
|
|
// so we're still visiting the if statement.
|
|
if (!(min < max)) { // min greater than, equal to, or unordered with respect to max; NaN values are unordered
|
|
if (Float.isNaN(min)) {
|
|
throw new IllegalArgumentException("min is NaN");
|
|
}
|
|
if (Float.isNaN(max)) {
|
|
throw new IllegalArgumentException("max is NaN");
|
|
}
|
|
if (Float.compare(min, max) > 0) {
|
|
throw new IllegalArgumentException(min + " > " + max);
|
|
}
|
|
// Fall-through if min and max are exactly equal (or min = -0.0 and max = +0.0)
|
|
// and none of them is NaN
|
|
}
|
|
return Math.min(max, Math.max(value, min));
|
|
}
|
|
|
|
/**
|
|
* Returns the fused multiply add of the three arguments; that is,
|
|
* returns the exact product of the first two arguments summed
|
|
* with the third argument and then rounded once to the nearest
|
|
* {@code double}.
|
|
*
|
|
* The rounding is done using the {@linkplain
|
|
* java.math.RoundingMode#HALF_EVEN round to nearest even
|
|
* rounding mode}.
|
|
*
|
|
* In contrast, if {@code a * b + c} is evaluated as a regular
|
|
* floating-point expression, two rounding errors are involved,
|
|
* the first for the multiply operation, the second for the
|
|
* addition operation.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If any argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If one of the first two arguments is infinite and the
|
|
* other is zero, the result is NaN.
|
|
*
|
|
* <li> If the exact product of the first two arguments is infinite
|
|
* (in other words, at least one of the arguments is infinite and
|
|
* the other is neither zero nor NaN) and the third argument is an
|
|
* infinity of the opposite sign, the result is NaN.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>Note that {@code fma(a, 1.0, c)} returns the same
|
|
* result as ({@code a + c}). However,
|
|
* {@code fma(a, b, +0.0)} does <em>not</em> always return the
|
|
* same result as ({@code a * b}) since
|
|
* {@code fma(-0.0, +0.0, +0.0)} is {@code +0.0} while
|
|
* ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fma(a, b, -0.0)} is
|
|
* equivalent to ({@code a * b}) however.
|
|
*
|
|
* @apiNote This method corresponds to the fusedMultiplyAdd
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double fma(double a, double b, double c) {
|
|
/*
|
|
* Infinity and NaN arithmetic is not quite the same with two
|
|
* roundings as opposed to just one so the simple expression
|
|
* "a * b + c" cannot always be used to compute the correct
|
|
* result. With two roundings, the product can overflow and
|
|
* if the addend is infinite, a spurious NaN can be produced
|
|
* if the infinity from the overflow and the infinite addend
|
|
* have opposite signs.
|
|
*/
|
|
|
|
// First, screen for and handle non-finite input values whose
|
|
// arithmetic is not supported by BigDecimal.
|
|
if (Double.isNaN(a) || Double.isNaN(b) || Double.isNaN(c)) {
|
|
return Double.NaN;
|
|
} else { // All inputs non-NaN
|
|
boolean infiniteA = Double.isInfinite(a);
|
|
boolean infiniteB = Double.isInfinite(b);
|
|
boolean infiniteC = Double.isInfinite(c);
|
|
double result;
|
|
|
|
if (infiniteA || infiniteB || infiniteC) {
|
|
if (infiniteA && b == 0.0 ||
|
|
infiniteB && a == 0.0 ) {
|
|
return Double.NaN;
|
|
}
|
|
// Store product in a double field to cause an
|
|
// overflow even if non-strictfp evaluation is being
|
|
// used.
|
|
double product = a * b;
|
|
if (Double.isInfinite(product) && !infiniteA && !infiniteB) {
|
|
// Intermediate overflow; might cause a
|
|
// spurious NaN if added to infinite c.
|
|
assert Double.isInfinite(c);
|
|
return c;
|
|
} else {
|
|
result = product + c;
|
|
assert !Double.isFinite(result);
|
|
return result;
|
|
}
|
|
} else { // All inputs finite
|
|
BigDecimal product = (new BigDecimal(a)).multiply(new BigDecimal(b));
|
|
if (c == 0.0) { // Positive or negative zero
|
|
// If the product is an exact zero, use a
|
|
// floating-point expression to compute the sign
|
|
// of the zero final result. The product is an
|
|
// exact zero if and only if at least one of a and
|
|
// b is zero.
|
|
if (a == 0.0 || b == 0.0) {
|
|
return a * b + c;
|
|
} else {
|
|
// The sign of a zero addend doesn't matter if
|
|
// the product is nonzero. The sign of a zero
|
|
// addend is not factored in the result if the
|
|
// exact product is nonzero but underflows to
|
|
// zero; see IEEE-754 2008 section 6.3 "The
|
|
// sign bit".
|
|
return product.doubleValue();
|
|
}
|
|
} else {
|
|
return product.add(new BigDecimal(c)).doubleValue();
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the fused multiply add of the three arguments; that is,
|
|
* returns the exact product of the first two arguments summed
|
|
* with the third argument and then rounded once to the nearest
|
|
* {@code float}.
|
|
*
|
|
* The rounding is done using the {@linkplain
|
|
* java.math.RoundingMode#HALF_EVEN round to nearest even
|
|
* rounding mode}.
|
|
*
|
|
* In contrast, if {@code a * b + c} is evaluated as a regular
|
|
* floating-point expression, two rounding errors are involved,
|
|
* the first for the multiply operation, the second for the
|
|
* addition operation.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
* <li> If any argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If one of the first two arguments is infinite and the
|
|
* other is zero, the result is NaN.
|
|
*
|
|
* <li> If the exact product of the first two arguments is infinite
|
|
* (in other words, at least one of the arguments is infinite and
|
|
* the other is neither zero nor NaN) and the third argument is an
|
|
* infinity of the opposite sign, the result is NaN.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>Note that {@code fma(a, 1.0f, c)} returns the same
|
|
* result as ({@code a + c}). However,
|
|
* {@code fma(a, b, +0.0f)} does <em>not</em> always return the
|
|
* same result as ({@code a * b}) since
|
|
* {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
|
|
* ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
|
|
* equivalent to ({@code a * b}) however.
|
|
*
|
|
* @apiNote This method corresponds to the fusedMultiplyAdd
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float fma(float a, float b, float c) {
|
|
if (Float.isFinite(a) && Float.isFinite(b) && Float.isFinite(c)) {
|
|
if (a == 0.0 || b == 0.0) {
|
|
return a * b + c; // Handled signed zero cases
|
|
} else {
|
|
return (new BigDecimal((double)a * (double)b) // Exact multiply
|
|
.add(new BigDecimal((double)c))) // Exact sum
|
|
.floatValue(); // One rounding
|
|
// to a float value
|
|
}
|
|
} else {
|
|
// At least one of a,b, and c is non-finite. The result
|
|
// will be non-finite as well and will be the same
|
|
// non-finite value under double as float arithmetic.
|
|
return (float)fma((double)a, (double)b, (double)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) {
|
|
int exp = getExponent(d);
|
|
|
|
return switch(exp) {
|
|
case Double.MAX_EXPONENT + 1 -> Math.abs(d); // NaN or infinity
|
|
case Double.MIN_EXPONENT - 1 -> Double.MIN_VALUE; // zero or subnormal
|
|
default -> {
|
|
assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT;
|
|
|
|
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
|
|
exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH - 1);
|
|
if (exp >= Double.MIN_EXPONENT) {
|
|
yield powerOfTwoD(exp);
|
|
} else {
|
|
// return a subnormal result; left shift integer
|
|
// representation of Double.MIN_VALUE appropriate
|
|
// number of positions
|
|
yield Double.longBitsToDouble(1L <<
|
|
(exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH - 1))));
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
/**
|
|
* Returns the size of an ulp of the argument. An ulp, unit in
|
|
* the last place, of a {@code float} value is the positive
|
|
* distance between this floating-point value and the {@code
|
|
* float} value next larger in magnitude. Note that for non-NaN
|
|
* <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive or negative infinity, then the
|
|
* result is positive infinity.
|
|
* <li> If the argument is positive or negative zero, then the result is
|
|
* {@code Float.MIN_VALUE}.
|
|
* <li> If the argument is ±{@code Float.MAX_VALUE}, then
|
|
* the result is equal to 2<sup>104</sup>.
|
|
* </ul>
|
|
*
|
|
* @param f the floating-point value whose ulp is to be returned
|
|
* @return the size of an ulp of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
public static float ulp(float f) {
|
|
int exp = getExponent(f);
|
|
|
|
return switch(exp) {
|
|
case Float.MAX_EXPONENT + 1 -> Math.abs(f); // NaN or infinity
|
|
case Float.MIN_EXPONENT - 1 -> Float.MIN_VALUE; // zero or subnormal
|
|
default -> {
|
|
assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT;
|
|
|
|
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
|
|
exp = exp - (FloatConsts.SIGNIFICAND_WIDTH - 1);
|
|
if (exp >= Float.MIN_EXPONENT) {
|
|
yield powerOfTwoF(exp);
|
|
} else {
|
|
// return a subnormal result; left shift integer
|
|
// representation of FloatConsts.MIN_VALUE appropriate
|
|
// number of positions
|
|
yield Float.intBitsToFloat(1 <<
|
|
(exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH - 1))));
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
/**
|
|
* Returns the signum function of the argument; zero if the argument
|
|
* is zero, 1.0 if the argument is greater than zero, -1.0 if the
|
|
* argument is less than zero.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, then the result is NaN.
|
|
* <li> If the argument is positive zero or negative zero, then the
|
|
* result is the same as the argument.
|
|
* </ul>
|
|
*
|
|
* @param d the floating-point value whose signum is to be returned
|
|
* @return the signum function of the argument
|
|
* @author Joseph D. Darcy
|
|
* @since 1.5
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double signum(double d) {
|
|
// Android-changed: Optimize the compiled code by inlining 1.0d value. http://b/316160813
|
|
// return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d);
|
|
if (d == 0.0 || Double.isNaN(d)) {
|
|
return d;
|
|
} else {
|
|
return Double.longBitsToDouble((Double.doubleToRawLongBits(d) &
|
|
DoubleConsts.SIGN_BIT_MASK) |
|
|
0x3FF0000000000000L); // 1.0d
|
|
}
|
|
}
|
|
|
|
/**
|
|
* 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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float signum(float f) {
|
|
// Android-changed: Optimize the compiled code by inlining 1.0f value. http://b/316160813
|
|
// return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);
|
|
if (f == 0.0f || Float.isNaN(f)) {
|
|
return f;
|
|
} else {
|
|
return Float.intBitsToFloat((Float.floatToRawIntBits(f) & FloatConsts.SIGN_BIT_MASK) |
|
|
0x3F800000); // 1.0f
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the hyperbolic sine of a {@code double} value.
|
|
* The hyperbolic sine of <i>x</i> is defined to be
|
|
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
|
|
* where <i>e</i> is {@linkplain Math#E Euler's number}.
|
|
*
|
|
* <p>Special cases:
|
|
* <ul>
|
|
*
|
|
* <li>If the argument is NaN, then the result is NaN.
|
|
*
|
|
* <li>If the argument is infinite, then the result is an infinity
|
|
* with the same sign as the argument.
|
|
*
|
|
* <li>If the argument is zero, then the result is a zero with the
|
|
* same sign as the argument.
|
|
*
|
|
* </ul>
|
|
*
|
|
* <p>The computed result must be within 2.5 ulps of the exact result.
|
|
*
|
|
* @param x The number whose hyperbolic sine is to be returned.
|
|
* @return The hyperbolic sine of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double sinh(double x) {
|
|
return StrictMath.sinh(x);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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>
|
|
*
|
|
* <p>The computed result must be within 2.5 ulps of the exact result.
|
|
*
|
|
* @param x The number whose hyperbolic cosine is to be returned.
|
|
* @return The hyperbolic cosine of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double cosh(double x) {
|
|
return StrictMath.cosh(x);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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>
|
|
*
|
|
* <p>The computed result must be within 2.5 ulps of the exact result.
|
|
* The result of {@code tanh} for any finite input must have
|
|
* an absolute value less than or equal to 1. Note that once the
|
|
* exact result of tanh is within 1/2 of an ulp of the limit value
|
|
* of ±1, correctly signed ±{@code 1.0} should
|
|
* be returned.
|
|
*
|
|
* @param x The number whose hyperbolic tangent is to be returned.
|
|
* @return The hyperbolic tangent of {@code x}.
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double tanh(double x) {
|
|
return StrictMath.tanh(x);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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>
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact
|
|
* result. If one parameter is held constant, the results must be
|
|
* semi-monotonic in the other parameter.
|
|
*
|
|
* @param x a value
|
|
* @param y a value
|
|
* @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
|
|
* without intermediate overflow or underflow
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double hypot(double x, double y) {
|
|
return StrictMath.hypot(x, y);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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>
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact result.
|
|
* Results must be semi-monotonic. The result of
|
|
* {@code expm1} for any finite input must be greater than or
|
|
* equal to {@code -1.0}. Note that once the exact result of
|
|
* <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
|
|
* ulp of the limit value -1, {@code -1.0} should be
|
|
* returned.
|
|
*
|
|
* @param x the exponent to raise <i>e</i> to in the computation of
|
|
* <i>e</i><sup>{@code x}</sup> -1.
|
|
* @return the value <i>e</i><sup>{@code x}</sup> - 1.
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double expm1(double x) {
|
|
return StrictMath.expm1(x);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
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>
|
|
*
|
|
* <p>The computed result must be within 1 ulp of the exact result.
|
|
* Results must be semi-monotonic.
|
|
*
|
|
* @param x a value
|
|
* @return the value ln({@code x} + 1), the natural
|
|
* log of {@code x} + 1
|
|
* @since 1.5
|
|
*/
|
|
// BEGIN Android-changed: Reimplement in native
|
|
/*
|
|
public static double log1p(double x) {
|
|
return StrictMath.log1p(x);
|
|
}
|
|
*/
|
|
// END Android-changed: Reimplement in native
|
|
@CriticalNative
|
|
public static native double log1p(double x);
|
|
|
|
/**
|
|
* Returns the first floating-point argument with the sign of the
|
|
* second floating-point argument. Note that unlike the {@link
|
|
* StrictMath#copySign(double, double) StrictMath.copySign}
|
|
* method, this method does not require NaN {@code sign}
|
|
* arguments to be treated as positive values; implementations are
|
|
* permitted to treat some NaN arguments as positive and other NaN
|
|
* arguments as negative to allow greater performance.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the copySign operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static double copySign(double magnitude, double sign) {
|
|
return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
|
|
(DoubleConsts.SIGN_BIT_MASK)) |
|
|
(Double.doubleToRawLongBits(magnitude) &
|
|
(DoubleConsts.EXP_BIT_MASK |
|
|
DoubleConsts.SIGNIF_BIT_MASK)));
|
|
}
|
|
|
|
/**
|
|
* Returns the first floating-point argument with the sign of the
|
|
* second floating-point argument. Note that unlike the {@link
|
|
* StrictMath#copySign(float, float) StrictMath.copySign}
|
|
* method, this method does not require NaN {@code sign}
|
|
* arguments to be treated as positive values; implementations are
|
|
* permitted to treat some NaN arguments as positive and other NaN
|
|
* arguments as negative to allow greater performance.
|
|
*
|
|
* @apiNote
|
|
* This method corresponds to the copySign operation defined in
|
|
* IEEE 754.
|
|
*
|
|
* @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
|
|
*/
|
|
@IntrinsicCandidate
|
|
public static float copySign(float magnitude, float sign) {
|
|
return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
|
|
(FloatConsts.SIGN_BIT_MASK)) |
|
|
(Float.floatToRawIntBits(magnitude) &
|
|
(FloatConsts.EXP_BIT_MASK |
|
|
FloatConsts.SIGNIF_BIT_MASK)));
|
|
}
|
|
|
|
/**
|
|
* Returns the unbiased exponent used in the representation of a
|
|
* {@code float}. Special cases:
|
|
*
|
|
* <ul>
|
|
* <li>If the argument is NaN or infinite, then the result is
|
|
* {@link Float#MAX_EXPONENT} + 1.
|
|
* <li>If the argument is zero or subnormal, then the result is
|
|
* {@link Float#MIN_EXPONENT} - 1.
|
|
* </ul>
|
|
* @apiNote
|
|
* This method is analogous to the logB operation defined in IEEE
|
|
* 754, but returns a different value on subnormal arguments.
|
|
*
|
|
* @param f a {@code float} value
|
|
* @return the unbiased exponent of the argument
|
|
* @since 1.6
|
|
*/
|
|
public static int getExponent(float f) {
|
|
/*
|
|
* Bitwise convert f to integer, mask out exponent bits, shift
|
|
* to the right and then subtract out float's bias adjust to
|
|
* get true exponent value
|
|
*/
|
|
return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
|
|
(FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
|
|
}
|
|
|
|
/**
|
|
* Returns the unbiased exponent used in the representation of a
|
|
* {@code double}. Special cases:
|
|
*
|
|
* <ul>
|
|
* <li>If the argument is NaN or infinite, then the result is
|
|
* {@link Double#MAX_EXPONENT} + 1.
|
|
* <li>If the argument is zero or subnormal, then the result is
|
|
* {@link Double#MIN_EXPONENT} - 1.
|
|
* </ul>
|
|
* @apiNote
|
|
* This method is analogous to the logB operation defined in IEEE
|
|
* 754, but returns a different value on subnormal arguments.
|
|
*
|
|
* @param d a {@code double} value
|
|
* @return the unbiased exponent of the argument
|
|
* @since 1.6
|
|
*/
|
|
public static int getExponent(double d) {
|
|
/*
|
|
* Bitwise convert d to long, mask out exponent bits, shift
|
|
* to the right and then subtract out double's bias adjust to
|
|
* get true exponent value.
|
|
*/
|
|
return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
|
|
(DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point number adjacent to the first
|
|
* argument in the direction of the second argument. If both
|
|
* arguments compare as equal the second argument is returned.
|
|
*
|
|
* <p>
|
|
* Special cases:
|
|
* <ul>
|
|
* <li> If either argument is a NaN, then NaN is returned.
|
|
*
|
|
* <li> If both arguments are signed zeros, {@code direction}
|
|
* is returned unchanged (as implied by the requirement of
|
|
* returning the second argument if the arguments compare as
|
|
* equal).
|
|
*
|
|
* <li> If {@code start} is
|
|
* ±{@link Double#MIN_VALUE} and {@code direction}
|
|
* has a value such that the result should have a smaller
|
|
* magnitude, then a zero with the same sign as {@code start}
|
|
* is returned.
|
|
*
|
|
* <li> If {@code start} is infinite and
|
|
* {@code direction} has a value such that the result should
|
|
* have a smaller magnitude, {@link Double#MAX_VALUE} with the
|
|
* same sign as {@code start} is returned.
|
|
*
|
|
* <li> If {@code start} is equal to ±
|
|
* {@link Double#MAX_VALUE} and {@code direction} has a
|
|
* value such that the result should have a larger magnitude, an
|
|
* infinity with same sign as {@code start} is returned.
|
|
* </ul>
|
|
*
|
|
* @param start starting floating-point value
|
|
* @param direction value indicating which of
|
|
* {@code start}'s neighbors or {@code start} should
|
|
* be returned
|
|
* @return The floating-point number adjacent to {@code start} in the
|
|
* direction of {@code direction}.
|
|
* @since 1.6
|
|
*/
|
|
public static double nextAfter(double start, double direction) {
|
|
/*
|
|
* The cases:
|
|
*
|
|
* nextAfter(+infinity, 0) == MAX_VALUE
|
|
* nextAfter(+infinity, +infinity) == +infinity
|
|
* nextAfter(-infinity, 0) == -MAX_VALUE
|
|
* nextAfter(-infinity, -infinity) == -infinity
|
|
*
|
|
* are naturally handled without any additional testing
|
|
*/
|
|
|
|
/*
|
|
* IEEE 754 floating-point numbers are lexicographically
|
|
* ordered if treated as signed-magnitude integers.
|
|
* Since Java's integers are two's complement,
|
|
* incrementing the two's complement representation of a
|
|
* logically negative floating-point value *decrements*
|
|
* the signed-magnitude representation. Therefore, when
|
|
* the integer representation of a floating-point value
|
|
* is negative, the adjustment to the representation is in
|
|
* the opposite direction from what would initially be expected.
|
|
*/
|
|
|
|
// Branch to descending case first as it is more costly than ascending
|
|
// case due to start != 0.0d conditional.
|
|
if (start > direction) { // descending
|
|
if (start != 0.0d) {
|
|
final long transducer = Double.doubleToRawLongBits(start);
|
|
return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L));
|
|
} else { // start == 0.0d && direction < 0.0d
|
|
return -Double.MIN_VALUE;
|
|
}
|
|
} else if (start < direction) { // ascending
|
|
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
|
|
// then bitwise convert start to integer.
|
|
final long transducer = Double.doubleToRawLongBits(start + 0.0d);
|
|
return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
|
|
} else if (start == direction) {
|
|
return direction;
|
|
} else { // isNaN(start) || isNaN(direction)
|
|
return start + direction;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point number adjacent to the first
|
|
* argument in the direction of the second argument. If both
|
|
* arguments compare as equal a value equivalent to the second argument
|
|
* is returned.
|
|
*
|
|
* <p>
|
|
* Special cases:
|
|
* <ul>
|
|
* <li> If either argument is a NaN, then NaN is returned.
|
|
*
|
|
* <li> If both arguments are signed zeros, a value equivalent
|
|
* to {@code direction} is returned.
|
|
*
|
|
* <li> If {@code start} is
|
|
* ±{@link Float#MIN_VALUE} and {@code direction}
|
|
* has a value such that the result should have a smaller
|
|
* magnitude, then a zero with the same sign as {@code start}
|
|
* is returned.
|
|
*
|
|
* <li> If {@code start} is infinite and
|
|
* {@code direction} has a value such that the result should
|
|
* have a smaller magnitude, {@link Float#MAX_VALUE} with the
|
|
* same sign as {@code start} is returned.
|
|
*
|
|
* <li> If {@code start} is equal to ±
|
|
* {@link Float#MAX_VALUE} and {@code direction} has a
|
|
* value such that the result should have a larger magnitude, an
|
|
* infinity with same sign as {@code start} is returned.
|
|
* </ul>
|
|
*
|
|
* @param start starting floating-point value
|
|
* @param direction value indicating which of
|
|
* {@code start}'s neighbors or {@code start} should
|
|
* be returned
|
|
* @return The floating-point number adjacent to {@code start} in the
|
|
* direction of {@code direction}.
|
|
* @since 1.6
|
|
*/
|
|
public static float nextAfter(float start, double direction) {
|
|
/*
|
|
* The cases:
|
|
*
|
|
* nextAfter(+infinity, 0) == MAX_VALUE
|
|
* nextAfter(+infinity, +infinity) == +infinity
|
|
* nextAfter(-infinity, 0) == -MAX_VALUE
|
|
* nextAfter(-infinity, -infinity) == -infinity
|
|
*
|
|
* are naturally handled without any additional testing
|
|
*/
|
|
|
|
/*
|
|
* IEEE 754 floating-point numbers are lexicographically
|
|
* ordered if treated as signed-magnitude integers.
|
|
* Since Java's integers are two's complement,
|
|
* incrementing the two's complement representation of a
|
|
* logically negative floating-point value *decrements*
|
|
* the signed-magnitude representation. Therefore, when
|
|
* the integer representation of a floating-point value
|
|
* is negative, the adjustment to the representation is in
|
|
* the opposite direction from what would initially be expected.
|
|
*/
|
|
|
|
// Branch to descending case first as it is more costly than ascending
|
|
// case due to start != 0.0f conditional.
|
|
if (start > direction) { // descending
|
|
if (start != 0.0f) {
|
|
final int transducer = Float.floatToRawIntBits(start);
|
|
return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1));
|
|
} else { // start == 0.0f && direction < 0.0f
|
|
return -Float.MIN_VALUE;
|
|
}
|
|
} else if (start < direction) { // ascending
|
|
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
|
|
// then bitwise convert start to integer.
|
|
final int transducer = Float.floatToRawIntBits(start + 0.0f);
|
|
return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
|
|
} else if (start == direction) {
|
|
return (float)direction;
|
|
} else { // isNaN(start) || isNaN(direction)
|
|
return start + (float)direction;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code d} in
|
|
* the direction of positive infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(d,
|
|
* Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
|
|
* implementation may run faster than its equivalent
|
|
* {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is positive infinity, the result is
|
|
* positive infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@link Double#MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @apiNote This method corresponds to the nextUp
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param d starting floating-point value
|
|
* @return The adjacent floating-point value closer to positive
|
|
* infinity.
|
|
* @since 1.6
|
|
*/
|
|
public static double nextUp(double d) {
|
|
// Use a single conditional and handle the likely cases first.
|
|
if (d < Double.POSITIVE_INFINITY) {
|
|
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
|
|
final long transducer = Double.doubleToRawLongBits(d + 0.0D);
|
|
return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
|
|
} else { // d is NaN or +Infinity
|
|
return d;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code f} in
|
|
* the direction of positive infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(f,
|
|
* Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
|
|
* implementation may run faster than its equivalent
|
|
* {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is positive infinity, the result is
|
|
* positive infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@link Float#MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @apiNote This method corresponds to the nextUp
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param f starting floating-point value
|
|
* @return The adjacent floating-point value closer to positive
|
|
* infinity.
|
|
* @since 1.6
|
|
*/
|
|
public static float nextUp(float f) {
|
|
// Use a single conditional and handle the likely cases first.
|
|
if (f < Float.POSITIVE_INFINITY) {
|
|
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
|
|
final int transducer = Float.floatToRawIntBits(f + 0.0F);
|
|
return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
|
|
} else { // f is NaN or +Infinity
|
|
return f;
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code d} in
|
|
* the direction of negative infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(d,
|
|
* Double.NEGATIVE_INFINITY)}; however, a
|
|
* {@code nextDown} implementation may run faster than its
|
|
* equivalent {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is negative infinity, the result is
|
|
* negative infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@code -Double.MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @apiNote This method corresponds to the nextDown
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param d starting floating-point value
|
|
* @return The adjacent floating-point value closer to negative
|
|
* infinity.
|
|
* @since 1.8
|
|
*/
|
|
public static double nextDown(double d) {
|
|
if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
|
|
return d;
|
|
else {
|
|
if (d == 0.0)
|
|
return -Double.MIN_VALUE;
|
|
else
|
|
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
|
|
((d > 0.0d)?-1L:+1L));
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns the floating-point value adjacent to {@code f} in
|
|
* the direction of negative infinity. This method is
|
|
* semantically equivalent to {@code nextAfter(f,
|
|
* Float.NEGATIVE_INFINITY)}; however, a
|
|
* {@code nextDown} implementation may run faster than its
|
|
* equivalent {@code nextAfter} call.
|
|
*
|
|
* <p>Special Cases:
|
|
* <ul>
|
|
* <li> If the argument is NaN, the result is NaN.
|
|
*
|
|
* <li> If the argument is negative infinity, the result is
|
|
* negative infinity.
|
|
*
|
|
* <li> If the argument is zero, the result is
|
|
* {@code -Float.MIN_VALUE}
|
|
*
|
|
* </ul>
|
|
*
|
|
* @apiNote This method corresponds to the nextDown
|
|
* operation defined in IEEE 754.
|
|
*
|
|
* @param f starting floating-point value
|
|
* @return The adjacent floating-point value closer to negative
|
|
* infinity.
|
|
* @since 1.8
|
|
*/
|
|
public static float nextDown(float f) {
|
|
if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
|
|
return f;
|
|
else {
|
|
if (f == 0.0f)
|
|
return -Float.MIN_VALUE;
|
|
else
|
|
return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
|
|
((f > 0.0f)?-1:+1));
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns {@code d} × 2<sup>{@code scaleFactor}</sup>
|
|
* rounded as if performed by a single correctly rounded
|
|
* floating-point multiply. 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>
|
|
*
|
|
* @apiNote This method corresponds to the scaleB operation
|
|
* defined in IEEE 754.
|
|
*
|
|
* @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) {
|
|
/*
|
|
* When scaling up, it does not matter what order the
|
|
* multiply-store operations are done; the result will be
|
|
* finite or overflow regardless of the operation ordering.
|
|
* However, to get the correct result when scaling down, a
|
|
* particular ordering must be used.
|
|
*
|
|
* When scaling down, the multiply-store operations are
|
|
* sequenced so that it is not possible for two consecutive
|
|
* multiply-stores to return subnormal results. If one
|
|
* multiply-store result is subnormal, the next multiply will
|
|
* round it away to zero. This is done by first multiplying
|
|
* by 2 ^ (scaleFactor % n) and then multiplying several
|
|
* times by 2^n as needed where n is the exponent of number
|
|
* that is a convenient power of two. In this way, at most one
|
|
* real rounding error occurs.
|
|
*/
|
|
|
|
// magnitude of a power of two so large that scaling a finite
|
|
// nonzero value by it would be guaranteed to over or
|
|
// underflow; due to rounding, scaling down takes an
|
|
// additional power of two which is reflected here
|
|
final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT +
|
|
DoubleConsts.SIGNIFICAND_WIDTH + 1;
|
|
int exp_adjust = 0;
|
|
int scale_increment = 0;
|
|
double exp_delta = Double.NaN;
|
|
|
|
// Make sure scaling factor is in a reasonable range
|
|
|
|
if(scaleFactor < 0) {
|
|
scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
|
|
scale_increment = -512;
|
|
exp_delta = twoToTheDoubleScaleDown;
|
|
}
|
|
else {
|
|
scaleFactor = Math.min(scaleFactor, MAX_SCALE);
|
|
scale_increment = 512;
|
|
exp_delta = twoToTheDoubleScaleUp;
|
|
}
|
|
|
|
// Calculate (scaleFactor % +/-512), 512 = 2^9, using
|
|
// technique from "Hacker's Delight" section 10-2.
|
|
int t = (scaleFactor >> 9-1) >>> 32 - 9;
|
|
exp_adjust = ((scaleFactor + t) & (512 -1)) - t;
|
|
|
|
d *= powerOfTwoD(exp_adjust);
|
|
scaleFactor -= exp_adjust;
|
|
|
|
while(scaleFactor != 0) {
|
|
d *= exp_delta;
|
|
scaleFactor -= scale_increment;
|
|
}
|
|
return d;
|
|
}
|
|
|
|
/**
|
|
* Returns {@code f} × 2<sup>{@code scaleFactor}</sup>
|
|
* rounded as if performed by a single correctly rounded
|
|
* floating-point multiply. 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>
|
|
*
|
|
* @apiNote This method corresponds to the scaleB operation
|
|
* defined in IEEE 754.
|
|
*
|
|
* @param f number to be scaled by a power of two.
|
|
* @param scaleFactor power of 2 used to scale {@code f}
|
|
* @return {@code f} × 2<sup>{@code scaleFactor}</sup>
|
|
* @since 1.6
|
|
*/
|
|
public static float scalb(float f, int scaleFactor) {
|
|
// magnitude of a power of two so large that scaling a finite
|
|
// nonzero value by it would be guaranteed to over or
|
|
// underflow; due to rounding, scaling down takes an
|
|
// additional power of two which is reflected here
|
|
final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT +
|
|
FloatConsts.SIGNIFICAND_WIDTH + 1;
|
|
|
|
// Make sure scaling factor is in a reasonable range
|
|
scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);
|
|
|
|
/*
|
|
* Since + MAX_SCALE for float fits well within the double
|
|
* exponent range and + float -> double conversion is exact
|
|
* the multiplication below will be exact. Therefore, the
|
|
* rounding that occurs when the double product is cast to
|
|
* float will be the correctly rounded float result.
|
|
*/
|
|
return (float)((double)f*powerOfTwoD(scaleFactor));
|
|
}
|
|
|
|
// Constants used in scalb
|
|
static double twoToTheDoubleScaleUp = powerOfTwoD(512);
|
|
static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
|
|
|
|
/**
|
|
* Returns a floating-point power of two in the normal range.
|
|
*/
|
|
static double powerOfTwoD(int n) {
|
|
assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT);
|
|
return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
|
|
(DoubleConsts.SIGNIFICAND_WIDTH-1))
|
|
& DoubleConsts.EXP_BIT_MASK);
|
|
}
|
|
|
|
/**
|
|
* Returns a floating-point power of two in the normal range.
|
|
*/
|
|
static float powerOfTwoF(int n) {
|
|
assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT);
|
|
return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
|
|
(FloatConsts.SIGNIFICAND_WIDTH-1))
|
|
& FloatConsts.EXP_BIT_MASK);
|
|
}
|
|
}
|