| /* |
| * Copyright (c) 1994, 2016, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| package java.lang; |
| |
| import java.util.Random; |
| import jdk.internal.math.FloatConsts; |
| import jdk.internal.math.DoubleConsts; |
| import jdk.internal.HotSpotIntrinsicCandidate; |
| |
| /** |
| * The class {@code Math} contains methods for performing basic |
| * numeric operations such as the elementary exponential, logarithm, |
| * square root, and trigonometric functions. |
| * |
| * <p>Unlike some of the numeric methods of class |
| * {@code StrictMath}, all implementations of the equivalent |
| * functions of class {@code Math} are not defined to return the |
| * bit-for-bit same results. This relaxation permits |
| * better-performing implementations where strict reproducibility is |
| * not required. |
| * |
| * <p>By default many of the {@code Math} methods simply call |
| * the equivalent method in {@code StrictMath} for their |
| * implementation. Code generators are encouraged to use |
| * platform-specific native libraries or microprocessor instructions, |
| * where available, to provide higher-performance implementations of |
| * {@code Math} methods. Such higher-performance |
| * implementations still must conform to the specification for |
| * {@code Math}. |
| * |
| * <p>The quality of implementation specifications concern two |
| * properties, accuracy of the returned result and monotonicity of the |
| * method. Accuracy of the floating-point {@code Math} methods is |
| * measured in terms of <i>ulps</i>, units in the last place. For a |
| * given floating-point format, an {@linkplain #ulp(double) ulp} of a |
| * specific real number value is the distance between the two |
| * floating-point values bracketing that numerical value. When |
| * discussing the accuracy of a method as a whole rather than at a |
| * specific argument, the number of ulps cited is for the worst-case |
| * error at any argument. If a method always has an error less than |
| * 0.5 ulps, the method always returns the floating-point number |
| * nearest the exact result; such a method is <i>correctly |
| * rounded</i>. A correctly rounded method is generally the best a |
| * floating-point approximation can be; however, it is impractical for |
| * many floating-point methods to be correctly rounded. Instead, for |
| * the {@code Math} class, a larger error bound of 1 or 2 ulps is |
| * allowed for certain methods. Informally, with a 1 ulp error bound, |
| * when the exact result is a representable number, the exact result |
| * should be returned as the computed result; otherwise, either of the |
| * two floating-point values which bracket the exact result may be |
| * returned. For exact results large in magnitude, one of the |
| * endpoints of the bracket may be infinite. Besides accuracy at |
| * individual arguments, maintaining proper relations between the |
| * method at different arguments is also important. Therefore, most |
| * methods with more than 0.5 ulp errors are required to be |
| * <i>semi-monotonic</i>: whenever the mathematical function is |
| * non-decreasing, so is the floating-point approximation, likewise, |
| * whenever the mathematical function is non-increasing, so is the |
| * floating-point approximation. Not all approximations that have 1 |
| * ulp accuracy will automatically meet the monotonicity requirements. |
| * |
| * <p> |
| * The platform uses signed two's complement integer arithmetic with |
| * int and long primitive types. The developer should choose |
| * the primitive type to ensure that arithmetic operations consistently |
| * produce correct results, which in some cases means the operations |
| * will not overflow the range of values of the computation. |
| * The best practice is to choose the primitive type and algorithm to avoid |
| * overflow. In cases where the size is {@code int} or {@code long} and |
| * overflow errors need to be detected, the methods {@code addExact}, |
| * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact} |
| * throw an {@code ArithmeticException} when the results overflow. |
| * For other arithmetic operations such as divide, absolute value, |
| * increment, decrement, and negation overflow occurs only with |
| * a specific minimum or maximum value and should be checked against |
| * the minimum or maximum as appropriate. |
| * |
| * @author unascribed |
| * @author Joseph D. Darcy |
| * @since 1.0 |
| */ |
| |
| public final class Math { |
| |
| /** |
| * Don't let anyone instantiate this class. |
| */ |
| private Math() {} |
| |
| /** |
| * The {@code double} value that is closer than any other to |
| * <i>e</i>, the base of the natural logarithms. |
| */ |
| public static final double E = 2.7182818284590452354; |
| |
| /** |
| * The {@code double} value that is closer than any other to |
| * <i>pi</i>, the ratio of the circumference of a circle to its |
| * diameter. |
| */ |
| public static final double PI = 3.14159265358979323846; |
| |
| /** |
| * Constant by which to multiply an angular value in degrees to obtain an |
| * angular value in radians. |
| */ |
| private static final double DEGREES_TO_RADIANS = 0.017453292519943295; |
| |
| /** |
| * Constant by which to multiply an angular value in radians to obtain an |
| * angular value in degrees. |
| */ |
| private static final double RADIANS_TO_DEGREES = 57.29577951308232; |
| |
| /** |
| * Returns the trigonometric sine of an angle. Special cases: |
| * <ul><li>If the argument is NaN or an infinity, then the |
| * result is NaN. |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a an angle, in radians. |
| * @return the sine of the argument. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double sin(double a) { |
| return StrictMath.sin(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the trigonometric cosine of an angle. Special cases: |
| * <ul><li>If the argument is NaN or an infinity, then the |
| * result is NaN.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a an angle, in radians. |
| * @return the cosine of the argument. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double cos(double a) { |
| return StrictMath.cos(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the trigonometric tangent of an angle. Special cases: |
| * <ul><li>If the argument is NaN or an infinity, then the result |
| * is NaN. |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a an angle, in radians. |
| * @return the tangent of the argument. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double tan(double a) { |
| return StrictMath.tan(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the arc sine of a value; the returned angle is in the |
| * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: |
| * <ul><li>If the argument is NaN or its absolute value is greater |
| * than 1, then the result is NaN. |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a the value whose arc sine is to be returned. |
| * @return the arc sine of the argument. |
| */ |
| public static double asin(double a) { |
| return StrictMath.asin(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the arc cosine of a value; the returned angle is in the |
| * range 0.0 through <i>pi</i>. Special case: |
| * <ul><li>If the argument is NaN or its absolute value is greater |
| * than 1, then the result is NaN.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a the value whose arc cosine is to be returned. |
| * @return the arc cosine of the argument. |
| */ |
| public static double acos(double a) { |
| return StrictMath.acos(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the arc tangent of a value; the returned angle is in the |
| * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: |
| * <ul><li>If the argument is NaN, then the result is NaN. |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a the value whose arc tangent is to be returned. |
| * @return the arc tangent of the argument. |
| */ |
| public static double atan(double a) { |
| return StrictMath.atan(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Converts an angle measured in degrees to an approximately |
| * equivalent angle measured in radians. The conversion from |
| * degrees to radians is generally inexact. |
| * |
| * @param angdeg an angle, in degrees |
| * @return the measurement of the angle {@code angdeg} |
| * in radians. |
| * @since 1.2 |
| */ |
| public static double toRadians(double angdeg) { |
| return angdeg * DEGREES_TO_RADIANS; |
| } |
| |
| /** |
| * Converts an angle measured in radians to an approximately |
| * equivalent angle measured in degrees. The conversion from |
| * radians to degrees is generally inexact; users should |
| * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly |
| * equal {@code 0.0}. |
| * |
| * @param angrad an angle, in radians |
| * @return the measurement of the angle {@code angrad} |
| * in degrees. |
| * @since 1.2 |
| */ |
| public static double toDegrees(double angrad) { |
| return angrad * RADIANS_TO_DEGREES; |
| } |
| |
| /** |
| * Returns Euler's number <i>e</i> raised to the power of a |
| * {@code double} value. Special cases: |
| * <ul><li>If the argument is NaN, the result is NaN. |
| * <li>If the argument is positive infinity, then the result is |
| * positive infinity. |
| * <li>If the argument is negative infinity, then the result is |
| * positive zero.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a the exponent to raise <i>e</i> to. |
| * @return the value <i>e</i><sup>{@code a}</sup>, |
| * where <i>e</i> is the base of the natural logarithms. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double exp(double a) { |
| return StrictMath.exp(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the natural logarithm (base <i>e</i>) of a {@code double} |
| * value. Special cases: |
| * <ul><li>If the argument is NaN or less than zero, then the result |
| * is NaN. |
| * <li>If the argument is positive infinity, then the result is |
| * positive infinity. |
| * <li>If the argument is positive zero or negative zero, then the |
| * result is negative infinity.</ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a a value |
| * @return the value ln {@code a}, the natural logarithm of |
| * {@code a}. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double log(double a) { |
| return StrictMath.log(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the base 10 logarithm of a {@code double} value. |
| * Special cases: |
| * |
| * <ul><li>If the argument is NaN or less than zero, then the result |
| * is NaN. |
| * <li>If the argument is positive infinity, then the result is |
| * positive infinity. |
| * <li>If the argument is positive zero or negative zero, then the |
| * result is negative infinity. |
| * <li> If the argument is equal to 10<sup><i>n</i></sup> for |
| * integer <i>n</i>, then the result is <i>n</i>. |
| * </ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a a value |
| * @return the base 10 logarithm of {@code a}. |
| * @since 1.5 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double log10(double a) { |
| return StrictMath.log10(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the correctly rounded positive square root of a |
| * {@code double} value. |
| * Special cases: |
| * <ul><li>If the argument is NaN or less than zero, then the result |
| * is NaN. |
| * <li>If the argument is positive infinity, then the result is positive |
| * infinity. |
| * <li>If the argument is positive zero or negative zero, then the |
| * result is the same as the argument.</ul> |
| * Otherwise, the result is the {@code double} value closest to |
| * the true mathematical square root of the argument value. |
| * |
| * @param a a value. |
| * @return the positive square root of {@code a}. |
| * If the argument is NaN or less than zero, the result is NaN. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double sqrt(double a) { |
| return StrictMath.sqrt(a); // default impl. delegates to StrictMath |
| // Note that hardware sqrt instructions |
| // frequently can be directly used by JITs |
| // and should be much faster than doing |
| // Math.sqrt in software. |
| } |
| |
| |
| /** |
| * Returns the cube root of a {@code double} value. For |
| * positive finite {@code x}, {@code cbrt(-x) == |
| * -cbrt(x)}; that is, the cube root of a negative value is |
| * the negative of the cube root of that value's magnitude. |
| * |
| * Special cases: |
| * |
| * <ul> |
| * |
| * <li>If the argument is NaN, then the result is NaN. |
| * |
| * <li>If the argument is infinite, then the result is an infinity |
| * with the same sign as the argument. |
| * |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * |
| * @param a a value. |
| * @return the cube root of {@code a}. |
| * @since 1.5 |
| */ |
| public static double cbrt(double a) { |
| return StrictMath.cbrt(a); |
| } |
| |
| /** |
| * Computes the remainder operation on two arguments as prescribed |
| * by the IEEE 754 standard. |
| * The remainder value is mathematically equal to |
| * <code>f1 - f2</code> × <i>n</i>, |
| * where <i>n</i> is the mathematical integer closest to the exact |
| * mathematical value of the quotient {@code f1/f2}, and if two |
| * mathematical integers are equally close to {@code f1/f2}, |
| * then <i>n</i> is the integer that is even. If the remainder is |
| * zero, its sign is the same as the sign of the first argument. |
| * Special cases: |
| * <ul><li>If either argument is NaN, or the first argument is infinite, |
| * or the second argument is positive zero or negative zero, then the |
| * result is NaN. |
| * <li>If the first argument is finite and the second argument is |
| * infinite, then the result is the same as the first argument.</ul> |
| * |
| * @param f1 the dividend. |
| * @param f2 the divisor. |
| * @return the remainder when {@code f1} is divided by |
| * {@code f2}. |
| */ |
| public static double IEEEremainder(double f1, double f2) { |
| return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath |
| } |
| |
| /** |
| * Returns the smallest (closest to negative infinity) |
| * {@code double} value that is greater than or equal to the |
| * argument and is equal to a mathematical integer. Special cases: |
| * <ul><li>If the argument value is already equal to a |
| * mathematical integer, then the result is the same as the |
| * argument. <li>If the argument is NaN or an infinity or |
| * positive zero or negative zero, then the result is the same as |
| * the argument. <li>If the argument value is less than zero but |
| * greater than -1.0, then the result is negative zero.</ul> Note |
| * that the value of {@code Math.ceil(x)} is exactly the |
| * value of {@code -Math.floor(-x)}. |
| * |
| * |
| * @param a a value. |
| * @return the smallest (closest to negative infinity) |
| * floating-point value that is greater than or equal to |
| * the argument and is equal to a mathematical integer. |
| */ |
| public static double ceil(double a) { |
| return StrictMath.ceil(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the largest (closest to positive infinity) |
| * {@code double} value that is less than or equal to the |
| * argument and is equal to a mathematical integer. Special cases: |
| * <ul><li>If the argument value is already equal to a |
| * mathematical integer, then the result is the same as the |
| * argument. <li>If the argument is NaN or an infinity or |
| * positive zero or negative zero, then the result is the same as |
| * the argument.</ul> |
| * |
| * @param a a value. |
| * @return the largest (closest to positive infinity) |
| * floating-point value that less than or equal to the argument |
| * and is equal to a mathematical integer. |
| */ |
| public static double floor(double a) { |
| return StrictMath.floor(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the {@code double} value that is closest in value |
| * to the argument and is equal to a mathematical integer. If two |
| * {@code double} values that are mathematical integers are |
| * equally close, the result is the integer value that is |
| * even. Special cases: |
| * <ul><li>If the argument value is already equal to a mathematical |
| * integer, then the result is the same as the argument. |
| * <li>If the argument is NaN or an infinity or positive zero or negative |
| * zero, then the result is the same as the argument.</ul> |
| * |
| * @param a a {@code double} value. |
| * @return the closest floating-point value to {@code a} that is |
| * equal to a mathematical integer. |
| */ |
| public static double rint(double a) { |
| return StrictMath.rint(a); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the angle <i>theta</i> from the conversion of rectangular |
| * coordinates ({@code x}, {@code y}) to polar |
| * coordinates (r, <i>theta</i>). |
| * This method computes the phase <i>theta</i> by computing an arc tangent |
| * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special |
| * cases: |
| * <ul><li>If either argument is NaN, then the result is NaN. |
| * <li>If the first argument is positive zero and the second argument |
| * is positive, or the first argument is positive and finite and the |
| * second argument is positive infinity, then the result is positive |
| * zero. |
| * <li>If the first argument is negative zero and the second argument |
| * is positive, or the first argument is negative and finite and the |
| * second argument is positive infinity, then the result is negative zero. |
| * <li>If the first argument is positive zero and the second argument |
| * is negative, or the first argument is positive and finite and the |
| * second argument is negative infinity, then the result is the |
| * {@code double} value closest to <i>pi</i>. |
| * <li>If the first argument is negative zero and the second argument |
| * is negative, or the first argument is negative and finite and the |
| * second argument is negative infinity, then the result is the |
| * {@code double} value closest to -<i>pi</i>. |
| * <li>If the first argument is positive and the second argument is |
| * positive zero or negative zero, or the first argument is positive |
| * infinity and the second argument is finite, then the result is the |
| * {@code double} value closest to <i>pi</i>/2. |
| * <li>If the first argument is negative and the second argument is |
| * positive zero or negative zero, or the first argument is negative |
| * infinity and the second argument is finite, then the result is the |
| * {@code double} value closest to -<i>pi</i>/2. |
| * <li>If both arguments are positive infinity, then the result is the |
| * {@code double} value closest to <i>pi</i>/4. |
| * <li>If the first argument is positive infinity and the second argument |
| * is negative infinity, then the result is the {@code double} |
| * value closest to 3*<i>pi</i>/4. |
| * <li>If the first argument is negative infinity and the second argument |
| * is positive infinity, then the result is the {@code double} value |
| * closest to -<i>pi</i>/4. |
| * <li>If both arguments are negative infinity, then the result is the |
| * {@code double} value closest to -3*<i>pi</i>/4.</ul> |
| * |
| * <p>The computed result must be within 2 ulps of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param y the ordinate coordinate |
| * @param x the abscissa coordinate |
| * @return the <i>theta</i> component of the point |
| * (<i>r</i>, <i>theta</i>) |
| * in polar coordinates that corresponds to the point |
| * (<i>x</i>, <i>y</i>) in Cartesian coordinates. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double atan2(double y, double x) { |
| return StrictMath.atan2(y, x); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the value of the first argument raised to the power of the |
| * second argument. Special cases: |
| * |
| * <ul><li>If the second argument is positive or negative zero, then the |
| * result is 1.0. |
| * <li>If the second argument is 1.0, then the result is the same as the |
| * first argument. |
| * <li>If the second argument is NaN, then the result is NaN. |
| * <li>If the first argument is NaN and the second argument is nonzero, |
| * then the result is NaN. |
| * |
| * <li>If |
| * <ul> |
| * <li>the absolute value of the first argument is greater than 1 |
| * and the second argument is positive infinity, or |
| * <li>the absolute value of the first argument is less than 1 and |
| * the second argument is negative infinity, |
| * </ul> |
| * then the result is positive infinity. |
| * |
| * <li>If |
| * <ul> |
| * <li>the absolute value of the first argument is greater than 1 and |
| * the second argument is negative infinity, or |
| * <li>the absolute value of the |
| * first argument is less than 1 and the second argument is positive |
| * infinity, |
| * </ul> |
| * then the result is positive zero. |
| * |
| * <li>If the absolute value of the first argument equals 1 and the |
| * second argument is infinite, then the result is NaN. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is positive zero and the second argument |
| * is greater than zero, or |
| * <li>the first argument is positive infinity and the second |
| * argument is less than zero, |
| * </ul> |
| * then the result is positive zero. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is positive zero and the second argument |
| * is less than zero, or |
| * <li>the first argument is positive infinity and the second |
| * argument is greater than zero, |
| * </ul> |
| * then the result is positive infinity. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is negative zero and the second argument |
| * is greater than zero but not a finite odd integer, or |
| * <li>the first argument is negative infinity and the second |
| * argument is less than zero but not a finite odd integer, |
| * </ul> |
| * then the result is positive zero. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is negative zero and the second argument |
| * is a positive finite odd integer, or |
| * <li>the first argument is negative infinity and the second |
| * argument is a negative finite odd integer, |
| * </ul> |
| * then the result is negative zero. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is negative zero and the second argument |
| * is less than zero but not a finite odd integer, or |
| * <li>the first argument is negative infinity and the second |
| * argument is greater than zero but not a finite odd integer, |
| * </ul> |
| * then the result is positive infinity. |
| * |
| * <li>If |
| * <ul> |
| * <li>the first argument is negative zero and the second argument |
| * is a negative finite odd integer, or |
| * <li>the first argument is negative infinity and the second |
| * argument is a positive finite odd integer, |
| * </ul> |
| * then the result is negative infinity. |
| * |
| * <li>If the first argument is finite and less than zero |
| * <ul> |
| * <li> if the second argument is a finite even integer, the |
| * result is equal to the result of raising the absolute value of |
| * the first argument to the power of the second argument |
| * |
| * <li>if the second argument is a finite odd integer, the result |
| * is equal to the negative of the result of raising the absolute |
| * value of the first argument to the power of the second |
| * argument |
| * |
| * <li>if the second argument is finite and not an integer, then |
| * the result is NaN. |
| * </ul> |
| * |
| * <li>If both arguments are integers, then the result is exactly equal |
| * to the mathematical result of raising the first argument to the power |
| * of the second argument if that result can in fact be represented |
| * exactly as a {@code double} value.</ul> |
| * |
| * <p>(In the foregoing descriptions, a floating-point value is |
| * considered to be an integer if and only if it is finite and a |
| * fixed point of the method {@link #ceil ceil} or, |
| * equivalently, a fixed point of the method {@link #floor |
| * floor}. A value is a fixed point of a one-argument |
| * method if and only if the result of applying the method to the |
| * value is equal to the value.) |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param a the base. |
| * @param b the exponent. |
| * @return the value {@code a}<sup>{@code b}</sup>. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double pow(double a, double b) { |
| return StrictMath.pow(a, b); // default impl. delegates to StrictMath |
| } |
| |
| /** |
| * Returns the closest {@code int} to the argument, with ties |
| * rounding to positive infinity. |
| * |
| * <p> |
| * Special cases: |
| * <ul><li>If the argument is NaN, the result is 0. |
| * <li>If the argument is negative infinity or any value less than or |
| * equal to the value of {@code Integer.MIN_VALUE}, the result is |
| * equal to the value of {@code Integer.MIN_VALUE}. |
| * <li>If the argument is positive infinity or any value greater than or |
| * equal to the value of {@code Integer.MAX_VALUE}, the result is |
| * equal to the value of {@code Integer.MAX_VALUE}.</ul> |
| * |
| * @param a a floating-point value to be rounded to an integer. |
| * @return the value of the argument rounded to the nearest |
| * {@code int} value. |
| * @see java.lang.Integer#MAX_VALUE |
| * @see java.lang.Integer#MIN_VALUE |
| */ |
| public static int round(float a) { |
| int intBits = Float.floatToRawIntBits(a); |
| int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK) |
| >> (FloatConsts.SIGNIFICAND_WIDTH - 1); |
| int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2 |
| + FloatConsts.EXP_BIAS) - biasedExp; |
| if ((shift & -32) == 0) { // shift >= 0 && shift < 32 |
| // a is a finite number such that pow(2,-32) <= ulp(a) < 1 |
| int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK) |
| | (FloatConsts.SIGNIF_BIT_MASK + 1)); |
| if (intBits < 0) { |
| r = -r; |
| } |
| // In the comments below each Java expression evaluates to the value |
| // the corresponding mathematical expression: |
| // (r) evaluates to a / ulp(a) |
| // (r >> shift) evaluates to floor(a * 2) |
| // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) |
| // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) |
| return ((r >> shift) + 1) >> 1; |
| } else { |
| // a is either |
| // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2 |
| // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer |
| // - an infinity or NaN |
| return (int) a; |
| } |
| } |
| |
| /** |
| * Returns the closest {@code long} to the argument, with ties |
| * rounding to positive infinity. |
| * |
| * <p>Special cases: |
| * <ul><li>If the argument is NaN, the result is 0. |
| * <li>If the argument is negative infinity or any value less than or |
| * equal to the value of {@code Long.MIN_VALUE}, the result is |
| * equal to the value of {@code Long.MIN_VALUE}. |
| * <li>If the argument is positive infinity or any value greater than or |
| * equal to the value of {@code Long.MAX_VALUE}, the result is |
| * equal to the value of {@code Long.MAX_VALUE}.</ul> |
| * |
| * @param a a floating-point value to be rounded to a |
| * {@code long}. |
| * @return the value of the argument rounded to the nearest |
| * {@code long} value. |
| * @see java.lang.Long#MAX_VALUE |
| * @see java.lang.Long#MIN_VALUE |
| */ |
| public static long round(double a) { |
| long longBits = Double.doubleToRawLongBits(a); |
| long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) |
| >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); |
| long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 |
| + DoubleConsts.EXP_BIAS) - biasedExp; |
| if ((shift & -64) == 0) { // shift >= 0 && shift < 64 |
| // a is a finite number such that pow(2,-64) <= ulp(a) < 1 |
| long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) |
| | (DoubleConsts.SIGNIF_BIT_MASK + 1)); |
| if (longBits < 0) { |
| r = -r; |
| } |
| // In the comments below each Java expression evaluates to the value |
| // the corresponding mathematical expression: |
| // (r) evaluates to a / ulp(a) |
| // (r >> shift) evaluates to floor(a * 2) |
| // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) |
| // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) |
| return ((r >> shift) + 1) >> 1; |
| } else { |
| // a is either |
| // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 |
| // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer |
| // - an infinity or NaN |
| return (long) a; |
| } |
| } |
| |
| private static final class RandomNumberGeneratorHolder { |
| static final Random randomNumberGenerator = new Random(); |
| } |
| |
| /** |
| * Returns a {@code double} value with a positive sign, greater |
| * than or equal to {@code 0.0} and less than {@code 1.0}. |
| * Returned values are chosen pseudorandomly with (approximately) |
| * uniform distribution from that range. |
| * |
| * <p>When this method is first called, it creates a single new |
| * pseudorandom-number generator, exactly as if by the expression |
| * |
| * <blockquote>{@code new java.util.Random()}</blockquote> |
| * |
| * This new pseudorandom-number generator is used thereafter for |
| * all calls to this method and is used nowhere else. |
| * |
| * <p>This method is properly synchronized to allow correct use by |
| * more than one thread. However, if many threads need to generate |
| * pseudorandom numbers at a great rate, it may reduce contention |
| * for each thread to have its own pseudorandom-number generator. |
| * |
| * @apiNote |
| * As the largest {@code double} value less than {@code 1.0} |
| * is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range |
| * {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements |
| * |
| * <blockquote><pre>{@code |
| * double f = Math.random()/Math.nextDown(1.0); |
| * double x = x1*(1.0 - f) + x2*f; |
| * }</pre></blockquote> |
| * |
| * @return a pseudorandom {@code double} greater than or equal |
| * to {@code 0.0} and less than {@code 1.0}. |
| * @see #nextDown(double) |
| * @see Random#nextDouble() |
| */ |
| public static double random() { |
| return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble(); |
| } |
| |
| /** |
| * Returns the sum of its arguments, |
| * throwing an exception if the result overflows an {@code int}. |
| * |
| * @param x the first value |
| * @param y the second value |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int addExact(int x, int y) { |
| int r = x + y; |
| // HD 2-12 Overflow iff both arguments have the opposite sign of the result |
| if (((x ^ r) & (y ^ r)) < 0) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the sum of its arguments, |
| * throwing an exception if the result overflows a {@code long}. |
| * |
| * @param x the first value |
| * @param y the second value |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long addExact(long x, long y) { |
| long r = x + y; |
| // HD 2-12 Overflow iff both arguments have the opposite sign of the result |
| if (((x ^ r) & (y ^ r)) < 0) { |
| throw new ArithmeticException("long overflow"); |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the difference of the arguments, |
| * throwing an exception if the result overflows an {@code int}. |
| * |
| * @param x the first value |
| * @param y the second value to subtract from the first |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int subtractExact(int x, int y) { |
| int r = x - y; |
| // HD 2-12 Overflow iff the arguments have different signs and |
| // the sign of the result is different than the sign of x |
| if (((x ^ y) & (x ^ r)) < 0) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the difference of the arguments, |
| * throwing an exception if the result overflows a {@code long}. |
| * |
| * @param x the first value |
| * @param y the second value to subtract from the first |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long subtractExact(long x, long y) { |
| long r = x - y; |
| // HD 2-12 Overflow iff the arguments have different signs and |
| // the sign of the result is different than the sign of x |
| if (((x ^ y) & (x ^ r)) < 0) { |
| throw new ArithmeticException("long overflow"); |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the product of the arguments, |
| * throwing an exception if the result overflows an {@code int}. |
| * |
| * @param x the first value |
| * @param y the second value |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int multiplyExact(int x, int y) { |
| long r = (long)x * (long)y; |
| if ((int)r != r) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| return (int)r; |
| } |
| |
| /** |
| * Returns the product of the arguments, |
| * throwing an exception if the result overflows a {@code long}. |
| * |
| * @param x the first value |
| * @param y the second value |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long multiplyExact(long x, long y) { |
| long r = x * y; |
| long ax = Math.abs(x); |
| long ay = Math.abs(y); |
| if (((ax | ay) >>> 31 != 0)) { |
| // Some bits greater than 2^31 that might cause overflow |
| // Check the result using the divide operator |
| // and check for the special case of Long.MIN_VALUE * -1 |
| if (((y != 0) && (r / y != x)) || |
| (x == Long.MIN_VALUE && y == -1)) { |
| throw new ArithmeticException("long overflow"); |
| } |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the argument incremented by one, throwing an exception if the |
| * result overflows an {@code int}. |
| * |
| * @param a the value to increment |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int incrementExact(int a) { |
| if (a == Integer.MAX_VALUE) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| |
| return a + 1; |
| } |
| |
| /** |
| * Returns the argument incremented by one, throwing an exception if the |
| * result overflows a {@code long}. |
| * |
| * @param a the value to increment |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long incrementExact(long a) { |
| if (a == Long.MAX_VALUE) { |
| throw new ArithmeticException("long overflow"); |
| } |
| |
| return a + 1L; |
| } |
| |
| /** |
| * Returns the argument decremented by one, throwing an exception if the |
| * result overflows an {@code int}. |
| * |
| * @param a the value to decrement |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int decrementExact(int a) { |
| if (a == Integer.MIN_VALUE) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| |
| return a - 1; |
| } |
| |
| /** |
| * Returns the argument decremented by one, throwing an exception if the |
| * result overflows a {@code long}. |
| * |
| * @param a the value to decrement |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long decrementExact(long a) { |
| if (a == Long.MIN_VALUE) { |
| throw new ArithmeticException("long overflow"); |
| } |
| |
| return a - 1L; |
| } |
| |
| /** |
| * Returns the negation of the argument, throwing an exception if the |
| * result overflows an {@code int}. |
| * |
| * @param a the value to negate |
| * @return the result |
| * @throws ArithmeticException if the result overflows an int |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int negateExact(int a) { |
| if (a == Integer.MIN_VALUE) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| |
| return -a; |
| } |
| |
| /** |
| * Returns the negation of the argument, throwing an exception if the |
| * result overflows a {@code long}. |
| * |
| * @param a the value to negate |
| * @return the result |
| * @throws ArithmeticException if the result overflows a long |
| * @since 1.8 |
| */ |
| @HotSpotIntrinsicCandidate |
| public static long negateExact(long a) { |
| if (a == Long.MIN_VALUE) { |
| throw new ArithmeticException("long overflow"); |
| } |
| |
| return -a; |
| } |
| |
| /** |
| * Returns the value of the {@code long} argument; |
| * throwing an exception if the value overflows an {@code int}. |
| * |
| * @param value the long value |
| * @return the argument as an int |
| * @throws ArithmeticException if the {@code argument} overflows an int |
| * @since 1.8 |
| */ |
| public static int toIntExact(long value) { |
| if ((int)value != value) { |
| throw new ArithmeticException("integer overflow"); |
| } |
| return (int)value; |
| } |
| |
| /** |
| * Returns the largest (closest to positive infinity) |
| * {@code int} value that is less than or equal to the algebraic quotient. |
| * There is one special case, if the dividend is the |
| * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1}, |
| * then integer overflow occurs and |
| * the result is equal to the {@code Integer.MIN_VALUE}. |
| * <p> |
| * 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 than truncation |
| * when the exact result is negative. |
| * <ul> |
| * <li>If the signs of the arguments are the same, the results of |
| * {@code floorDiv} and the {@code /} operator are the same. <br> |
| * For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li> |
| * <li>If the signs of the arguments are different, the quotient is negative and |
| * {@code floorDiv} returns the integer less than or equal to the quotient |
| * and the {@code /} operator returns the integer closest to zero.<br> |
| * For example, {@code floorDiv(-4, 3) == -2}, |
| * whereas {@code (-4 / 3) == -1}. |
| * </li> |
| * </ul> |
| * |
| * @param x the dividend |
| * @param y the divisor |
| * @return the largest (closest to positive infinity) |
| * {@code int} value that is less than or equal to the algebraic quotient. |
| * @throws ArithmeticException if the divisor {@code y} is zero |
| * @see #floorMod(int, int) |
| * @see #floor(double) |
| * @since 1.8 |
| */ |
| public static int floorDiv(int x, int y) { |
| int r = x / y; |
| // if the signs are different and modulo not zero, round down |
| if ((x ^ y) < 0 && (r * y != x)) { |
| r--; |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the largest (closest to positive infinity) |
| * {@code long} value that is less than or equal to the algebraic quotient. |
| * There is one special case, if the dividend is the |
| * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, |
| * then integer overflow occurs and |
| * the result is equal to the {@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 than truncation |
| * when the exact result is negative. |
| * <p> |
| * For examples, see {@link #floorDiv(int, int)}. |
| * |
| * @param x the dividend |
| * @param y the divisor |
| * @return the largest (closest to positive infinity) |
| * {@code long} value that is less than or equal to the algebraic quotient. |
| * @throws ArithmeticException if the divisor {@code y} is zero |
| * @see #floorMod(long, long) |
| * @see #floor(double) |
| * @since 1.8 |
| */ |
| public static long floorDiv(long x, long y) { |
| long r = x / y; |
| // if the signs are different and modulo not zero, round down |
| if ((x ^ y) < 0 && (r * y != x)) { |
| r--; |
| } |
| return r; |
| } |
| |
| /** |
| * Returns the floor modulus of the {@code int} arguments. |
| * <p> |
| * The floor modulus is {@code x - (floorDiv(x, y) * y)}, |
| * has the same sign as the divisor {@code y}, and |
| * is in the range of {@code -abs(y) < r < +abs(y)}. |
| * |
| * <p> |
| * The relationship between {@code floorDiv} and {@code floorMod} is such that: |
| * <ul> |
| * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} |
| * </ul> |
| * <p> |
| * The difference in values between {@code floorMod} and |
| * the {@code %} operator is due to the difference between |
| * {@code floorDiv} that returns the integer less than or equal to the quotient |
| * and the {@code /} operator that returns the integer closest to zero. |
| * <p> |
| * Examples: |
| * <ul> |
| * <li>If the signs of the arguments are the same, the results |
| * of {@code floorMod} and the {@code %} operator are the same. <br> |
| * <ul> |
| * <li>{@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}</li> |
| * </ul> |
| * <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br> |
| * <ul> |
| * <li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1} </li> |
| * <li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1} </li> |
| * <li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 } </li> |
| * </ul> |
| * </li> |
| * </ul> |
| * <p> |
| * If the signs of arguments are unknown and a positive modulus |
| * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}. |
| * |
| * @param x the dividend |
| * @param y the divisor |
| * @return the floor modulus {@code x - (floorDiv(x, y) * y)} |
| * @throws ArithmeticException if the divisor {@code y} is zero |
| * @see #floorDiv(int, int) |
| * @since 1.8 |
| */ |
| public static int floorMod(int x, int y) { |
| int r = x - floorDiv(x, y) * y; |
| return r; |
| } |
| |
| /** |
| * Returns the floor modulus of the {@code long} arguments. |
| * <p> |
| * The floor modulus is {@code x - (floorDiv(x, y) * y)}, |
| * has the same sign as the divisor {@code y}, and |
| * is in the range of {@code -abs(y) < r < +abs(y)}. |
| * |
| * <p> |
| * The relationship between {@code floorDiv} and {@code floorMod} is such that: |
| * <ul> |
| * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} |
| * </ul> |
| * <p> |
| * For examples, see {@link #floorMod(int, int)}. |
| * |
| * @param x the dividend |
| * @param y the divisor |
| * @return the floor modulus {@code x - (floorDiv(x, y) * y)} |
| * @throws ArithmeticException if the divisor {@code y} is zero |
| * @see #floorDiv(long, long) |
| * @since 1.8 |
| */ |
| public static long floorMod(long x, long y) { |
| return x - floorDiv(x, y) * y; |
| } |
| |
| /** |
| * Returns the absolute value of an {@code int} value. |
| * If the argument is not negative, the argument is returned. |
| * If the argument is negative, the negation of the argument is returned. |
| * |
| * <p>Note that if the argument is equal to the value of |
| * {@link Integer#MIN_VALUE}, the most negative representable |
| * {@code int} value, the result is that same value, which is |
| * negative. |
| * |
| * @param a the argument whose absolute value is to be determined |
| * @return the absolute value of the argument. |
| */ |
| public static int abs(int a) { |
| return (a < 0) ? -a : a; |
| } |
| |
| /** |
| * Returns the absolute value of a {@code long} value. |
| * If the argument is not negative, the argument is returned. |
| * If the argument is negative, the negation of the argument is returned. |
| * |
| * <p>Note that if the argument is equal to the value of |
| * {@link Long#MIN_VALUE}, the most negative representable |
| * {@code long} value, the result is that same value, which |
| * is negative. |
| * |
| * @param a the argument whose absolute value is to be determined |
| * @return the absolute value of the argument. |
| */ |
| public static long abs(long a) { |
| return (a < 0) ? -a : a; |
| } |
| |
| /** |
| * Returns the absolute value of a {@code float} value. |
| * If the argument is not negative, the argument is returned. |
| * If the argument is negative, the negation of the argument is returned. |
| * Special cases: |
| * <ul><li>If the argument is positive zero or negative zero, the |
| * result is positive zero. |
| * <li>If the argument is infinite, the result is positive infinity. |
| * <li>If the argument is NaN, the result is NaN.</ul> |
| * In other words, the result is the same as the value of the expression: |
| * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} |
| * |
| * @param a the argument whose absolute value is to be determined |
| * @return the absolute value of the argument. |
| */ |
| public static float abs(float a) { |
| return (a <= 0.0F) ? 0.0F - a : a; |
| } |
| |
| /** |
| * Returns the absolute value of a {@code double} value. |
| * If the argument is not negative, the argument is returned. |
| * If the argument is negative, the negation of the argument is returned. |
| * Special cases: |
| * <ul><li>If the argument is positive zero or negative zero, the result |
| * is positive zero. |
| * <li>If the argument is infinite, the result is positive infinity. |
| * <li>If the argument is NaN, the result is NaN.</ul> |
| * In other words, the result is the same as the value of the expression: |
| * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} |
| * |
| * @param a the argument whose absolute value is to be determined |
| * @return the absolute value of the argument. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static double abs(double a) { |
| return (a <= 0.0D) ? 0.0D - a : a; |
| } |
| |
| /** |
| * Returns the greater of two {@code int} values. That is, the |
| * result is the argument closer to the value of |
| * {@link Integer#MAX_VALUE}. If the arguments have the same value, |
| * the result is that same value. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the larger of {@code a} and {@code b}. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int max(int a, int b) { |
| return (a >= b) ? a : b; |
| } |
| |
| /** |
| * Returns the greater of two {@code long} values. That is, the |
| * result is the argument closer to the value of |
| * {@link Long#MAX_VALUE}. If the arguments have the same value, |
| * the result is that same value. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the larger of {@code a} and {@code b}. |
| */ |
| public static long max(long a, long b) { |
| return (a >= b) ? a : b; |
| } |
| |
| // Use raw bit-wise conversions on guaranteed non-NaN arguments. |
| private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f); |
| private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d); |
| |
| /** |
| * Returns the greater of two {@code float} values. That is, |
| * the result is the argument closer to positive infinity. If the |
| * arguments have the same value, the result is that same |
| * value. If either value is NaN, then the result is NaN. Unlike |
| * the numerical comparison operators, this method considers |
| * negative zero to be strictly smaller than positive zero. If one |
| * argument is positive zero and the other negative zero, the |
| * result is positive zero. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the larger of {@code a} and {@code b}. |
| */ |
| public static float max(float a, float b) { |
| if (a != a) |
| return a; // a is NaN |
| if ((a == 0.0f) && |
| (b == 0.0f) && |
| (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) { |
| // Raw conversion ok since NaN can't map to -0.0. |
| return b; |
| } |
| return (a >= b) ? a : b; |
| } |
| |
| /** |
| * Returns the greater of two {@code double} values. That |
| * is, the result is the argument closer to positive infinity. If |
| * the arguments have the same value, the result is that same |
| * value. If either value is NaN, then the result is NaN. Unlike |
| * the numerical comparison operators, this method considers |
| * negative zero to be strictly smaller than positive zero. If one |
| * argument is positive zero and the other negative zero, the |
| * result is positive zero. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the larger of {@code a} and {@code b}. |
| */ |
| public static double max(double a, double b) { |
| if (a != a) |
| return a; // a is NaN |
| if ((a == 0.0d) && |
| (b == 0.0d) && |
| (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) { |
| // Raw conversion ok since NaN can't map to -0.0. |
| return b; |
| } |
| return (a >= b) ? a : b; |
| } |
| |
| /** |
| * Returns the smaller of two {@code int} values. That is, |
| * the result the argument closer to the value of |
| * {@link Integer#MIN_VALUE}. If the arguments have the same |
| * value, the result is that same value. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the smaller of {@code a} and {@code b}. |
| */ |
| @HotSpotIntrinsicCandidate |
| public static int min(int a, int b) { |
| return (a <= b) ? a : b; |
| } |
| |
| /** |
| * Returns the smaller of two {@code long} values. That is, |
| * the result is the argument closer to the value of |
| * {@link Long#MIN_VALUE}. If the arguments have the same |
| * value, the result is that same value. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the smaller of {@code a} and {@code b}. |
| */ |
| public static long min(long a, long b) { |
| return (a <= b) ? a : b; |
| } |
| |
| /** |
| * Returns the smaller of two {@code float} values. That is, |
| * the result is the value closer to negative infinity. If the |
| * arguments have the same value, the result is that same |
| * value. If either value is NaN, then the result is NaN. Unlike |
| * the numerical comparison operators, this method considers |
| * negative zero to be strictly smaller than positive zero. If |
| * one argument is positive zero and the other is negative zero, |
| * the result is negative zero. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the smaller of {@code a} and {@code b}. |
| */ |
| public static float min(float a, float b) { |
| if (a != a) |
| return a; // a is NaN |
| if ((a == 0.0f) && |
| (b == 0.0f) && |
| (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) { |
| // Raw conversion ok since NaN can't map to -0.0. |
| return b; |
| } |
| return (a <= b) ? a : b; |
| } |
| |
| /** |
| * Returns the smaller of two {@code double} values. That |
| * is, the result is the value closer to negative infinity. If the |
| * arguments have the same value, the result is that same |
| * value. If either value is NaN, then the result is NaN. Unlike |
| * the numerical comparison operators, this method considers |
| * negative zero to be strictly smaller than positive zero. If one |
| * argument is positive zero and the other is negative zero, the |
| * result is negative zero. |
| * |
| * @param a an argument. |
| * @param b another argument. |
| * @return the smaller of {@code a} and {@code b}. |
| */ |
| public static double min(double a, double b) { |
| if (a != a) |
| return a; // a is NaN |
| if ((a == 0.0d) && |
| (b == 0.0d) && |
| (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) { |
| // Raw conversion ok since NaN can't map to -0.0. |
| return b; |
| } |
| return (a <= b) ? a : b; |
| } |
| |
| /** |
| * Returns the size of an ulp of the argument. An ulp, unit in |
| * the last place, of a {@code double} value is the positive |
| * distance between this floating-point value and the {@code |
| * double} value next larger in magnitude. Note that for non-NaN |
| * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, then the result is NaN. |
| * <li> If the argument is positive or negative infinity, then the |
| * result is positive infinity. |
| * <li> If the argument is positive or negative zero, then the result is |
| * {@code Double.MIN_VALUE}. |
| * <li> If the argument is ±{@code Double.MAX_VALUE}, then |
| * the result is equal to 2<sup>971</sup>. |
| * </ul> |
| * |
| * @param d the floating-point value whose ulp is to be returned |
| * @return the size of an ulp of the argument |
| * @author Joseph D. Darcy |
| * @since 1.5 |
| */ |
| public static double ulp(double d) { |
| int exp = getExponent(d); |
| |
| switch(exp) { |
| case Double.MAX_EXPONENT + 1: // NaN or infinity |
| return Math.abs(d); |
| |
| case Double.MIN_EXPONENT - 1: // zero or subnormal |
| return Double.MIN_VALUE; |
| |
| default: |
| assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT; |
| |
| // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) |
| exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1); |
| if (exp >= Double.MIN_EXPONENT) { |
| return powerOfTwoD(exp); |
| } |
| else { |
| // return a subnormal result; left shift integer |
| // representation of Double.MIN_VALUE appropriate |
| // number of positions |
| return Double.longBitsToDouble(1L << |
| (exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) )); |
| } |
| } |
| } |
| |
| /** |
| * Returns the size of an ulp of the argument. An ulp, unit in |
| * the last place, of a {@code float} value is the positive |
| * distance between this floating-point value and the {@code |
| * float} value next larger in magnitude. Note that for non-NaN |
| * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, then the result is NaN. |
| * <li> If the argument is positive or negative infinity, then the |
| * result is positive infinity. |
| * <li> If the argument is positive or negative zero, then the result is |
| * {@code Float.MIN_VALUE}. |
| * <li> If the argument is ±{@code Float.MAX_VALUE}, then |
| * the result is equal to 2<sup>104</sup>. |
| * </ul> |
| * |
| * @param f the floating-point value whose ulp is to be returned |
| * @return the size of an ulp of the argument |
| * @author Joseph D. Darcy |
| * @since 1.5 |
| */ |
| public static float ulp(float f) { |
| int exp = getExponent(f); |
| |
| switch(exp) { |
| case Float.MAX_EXPONENT+1: // NaN or infinity |
| return Math.abs(f); |
| |
| case Float.MIN_EXPONENT-1: // zero or subnormal |
| return Float.MIN_VALUE; |
| |
| default: |
| assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT; |
| |
| // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) |
| exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1); |
| if (exp >= Float.MIN_EXPONENT) { |
| return powerOfTwoF(exp); |
| } else { |
| // return a subnormal result; left shift integer |
| // representation of FloatConsts.MIN_VALUE appropriate |
| // number of positions |
| return Float.intBitsToFloat(1 << |
| (exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) )); |
| } |
| } |
| } |
| |
| /** |
| * Returns the signum function of the argument; zero if the argument |
| * is zero, 1.0 if the argument is greater than zero, -1.0 if the |
| * argument is less than zero. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, then the result is NaN. |
| * <li> If the argument is positive zero or negative zero, then the |
| * result is the same as the argument. |
| * </ul> |
| * |
| * @param d the floating-point value whose signum is to be returned |
| * @return the signum function of the argument |
| * @author Joseph D. Darcy |
| * @since 1.5 |
| */ |
| public static double signum(double d) { |
| return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d); |
| } |
| |
| /** |
| * Returns the signum function of the argument; zero if the argument |
| * is zero, 1.0f if the argument is greater than zero, -1.0f if the |
| * argument is less than zero. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, then the result is NaN. |
| * <li> If the argument is positive zero or negative zero, then the |
| * result is the same as the argument. |
| * </ul> |
| * |
| * @param f the floating-point value whose signum is to be returned |
| * @return the signum function of the argument |
| * @author Joseph D. Darcy |
| * @since 1.5 |
| */ |
| public static float signum(float f) { |
| return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f); |
| } |
| |
| /** |
| * Returns the hyperbolic sine of a {@code double} value. |
| * The hyperbolic sine of <i>x</i> is defined to be |
| * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 |
| * where <i>e</i> is {@linkplain Math#E Euler's number}. |
| * |
| * <p>Special cases: |
| * <ul> |
| * |
| * <li>If the argument is NaN, then the result is NaN. |
| * |
| * <li>If the argument is infinite, then the result is an infinity |
| * with the same sign as the argument. |
| * |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 2.5 ulps of the exact result. |
| * |
| * @param x The number whose hyperbolic sine is to be returned. |
| * @return The hyperbolic sine of {@code x}. |
| * @since 1.5 |
| */ |
| public static double sinh(double x) { |
| return StrictMath.sinh(x); |
| } |
| |
| /** |
| * Returns the hyperbolic cosine of a {@code double} value. |
| * The hyperbolic cosine of <i>x</i> is defined to be |
| * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 |
| * where <i>e</i> is {@linkplain Math#E Euler's number}. |
| * |
| * <p>Special cases: |
| * <ul> |
| * |
| * <li>If the argument is NaN, then the result is NaN. |
| * |
| * <li>If the argument is infinite, then the result is positive |
| * infinity. |
| * |
| * <li>If the argument is zero, then the result is {@code 1.0}. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 2.5 ulps of the exact result. |
| * |
| * @param x The number whose hyperbolic cosine is to be returned. |
| * @return The hyperbolic cosine of {@code x}. |
| * @since 1.5 |
| */ |
| public static double cosh(double x) { |
| return StrictMath.cosh(x); |
| } |
| |
| /** |
| * Returns the hyperbolic tangent of a {@code double} value. |
| * The hyperbolic tangent of <i>x</i> is defined to be |
| * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), |
| * in other words, {@linkplain Math#sinh |
| * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note |
| * that the absolute value of the exact tanh is always less than |
| * 1. |
| * |
| * <p>Special cases: |
| * <ul> |
| * |
| * <li>If the argument is NaN, then the result is NaN. |
| * |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument. |
| * |
| * <li>If the argument is positive infinity, then the result is |
| * {@code +1.0}. |
| * |
| * <li>If the argument is negative infinity, then the result is |
| * {@code -1.0}. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 2.5 ulps of the exact result. |
| * The result of {@code tanh} for any finite input must have |
| * an absolute value less than or equal to 1. Note that once the |
| * exact result of tanh is within 1/2 of an ulp of the limit value |
| * of ±1, correctly signed ±{@code 1.0} should |
| * be returned. |
| * |
| * @param x The number whose hyperbolic tangent is to be returned. |
| * @return The hyperbolic tangent of {@code x}. |
| * @since 1.5 |
| */ |
| public static double tanh(double x) { |
| return StrictMath.tanh(x); |
| } |
| |
| /** |
| * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) |
| * without intermediate overflow or underflow. |
| * |
| * <p>Special cases: |
| * <ul> |
| * |
| * <li> If either argument is infinite, then the result |
| * is positive infinity. |
| * |
| * <li> If either argument is NaN and neither argument is infinite, |
| * then the result is NaN. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact |
| * result. If one parameter is held constant, the results must be |
| * semi-monotonic in the other parameter. |
| * |
| * @param x a value |
| * @param y a value |
| * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) |
| * without intermediate overflow or underflow |
| * @since 1.5 |
| */ |
| public static double hypot(double x, double y) { |
| return StrictMath.hypot(x, y); |
| } |
| |
| /** |
| * Returns <i>e</i><sup>x</sup> -1. Note that for values of |
| * <i>x</i> near 0, the exact sum of |
| * {@code expm1(x)} + 1 is much closer to the true |
| * result of <i>e</i><sup>x</sup> than {@code exp(x)}. |
| * |
| * <p>Special cases: |
| * <ul> |
| * <li>If the argument is NaN, the result is NaN. |
| * |
| * <li>If the argument is positive infinity, then the result is |
| * positive infinity. |
| * |
| * <li>If the argument is negative infinity, then the result is |
| * -1.0. |
| * |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. The result of |
| * {@code expm1} for any finite input must be greater than or |
| * equal to {@code -1.0}. Note that once the exact result of |
| * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2 |
| * ulp of the limit value -1, {@code -1.0} should be |
| * returned. |
| * |
| * @param x the exponent to raise <i>e</i> to in the computation of |
| * <i>e</i><sup>{@code x}</sup> -1. |
| * @return the value <i>e</i><sup>{@code x}</sup> - 1. |
| * @since 1.5 |
| */ |
| public static double expm1(double x) { |
| return StrictMath.expm1(x); |
| } |
| |
| /** |
| * Returns the natural logarithm of the sum of the argument and 1. |
| * Note that for small values {@code x}, the result of |
| * {@code log1p(x)} is much closer to the true result of ln(1 |
| * + {@code x}) than the floating-point evaluation of |
| * {@code log(1.0+x)}. |
| * |
| * <p>Special cases: |
| * |
| * <ul> |
| * |
| * <li>If the argument is NaN or less than -1, then the result is |
| * NaN. |
| * |
| * <li>If the argument is positive infinity, then the result is |
| * positive infinity. |
| * |
| * <li>If the argument is negative one, then the result is |
| * negative infinity. |
| * |
| * <li>If the argument is zero, then the result is a zero with the |
| * same sign as the argument. |
| * |
| * </ul> |
| * |
| * <p>The computed result must be within 1 ulp of the exact result. |
| * Results must be semi-monotonic. |
| * |
| * @param x a value |
| * @return the value ln({@code x} + 1), the natural |
| * log of {@code x} + 1 |
| * @since 1.5 |
| */ |
| public static double log1p(double x) { |
| return StrictMath.log1p(x); |
| } |
| |
| /** |
| * Returns the first floating-point argument with the sign of the |
| * second floating-point argument. Note that unlike the {@link |
| * StrictMath#copySign(double, double) StrictMath.copySign} |
| * method, this method does not require NaN {@code sign} |
| * arguments to be treated as positive values; implementations are |
| * permitted to treat some NaN arguments as positive and other NaN |
| * arguments as negative to allow greater performance. |
| * |
| * @param magnitude the parameter providing the magnitude of the result |
| * @param sign the parameter providing the sign of the result |
| * @return a value with the magnitude of {@code magnitude} |
| * and the sign of {@code sign}. |
| * @since 1.6 |
| */ |
| public static double copySign(double magnitude, double sign) { |
| return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) & |
| (DoubleConsts.SIGN_BIT_MASK)) | |
| (Double.doubleToRawLongBits(magnitude) & |
| (DoubleConsts.EXP_BIT_MASK | |
| DoubleConsts.SIGNIF_BIT_MASK))); |
| } |
| |
| /** |
| * Returns the first floating-point argument with the sign of the |
| * second floating-point argument. Note that unlike the {@link |
| * StrictMath#copySign(float, float) StrictMath.copySign} |
| * method, this method does not require NaN {@code sign} |
| * arguments to be treated as positive values; implementations are |
| * permitted to treat some NaN arguments as positive and other NaN |
| * arguments as negative to allow greater performance. |
| * |
| * @param magnitude the parameter providing the magnitude of the result |
| * @param sign the parameter providing the sign of the result |
| * @return a value with the magnitude of {@code magnitude} |
| * and the sign of {@code sign}. |
| * @since 1.6 |
| */ |
| public static float copySign(float magnitude, float sign) { |
| return Float.intBitsToFloat((Float.floatToRawIntBits(sign) & |
| (FloatConsts.SIGN_BIT_MASK)) | |
| (Float.floatToRawIntBits(magnitude) & |
| (FloatConsts.EXP_BIT_MASK | |
| FloatConsts.SIGNIF_BIT_MASK))); |
| } |
| |
| /** |
| * Returns the unbiased exponent used in the representation of a |
| * {@code float}. Special cases: |
| * |
| * <ul> |
| * <li>If the argument is NaN or infinite, then the result is |
| * {@link Float#MAX_EXPONENT} + 1. |
| * <li>If the argument is zero or subnormal, then the result is |
| * {@link Float#MIN_EXPONENT} -1. |
| * </ul> |
| * @param f a {@code float} value |
| * @return the unbiased exponent of the argument |
| * @since 1.6 |
| */ |
| public static int getExponent(float f) { |
| /* |
| * Bitwise convert f to integer, mask out exponent bits, shift |
| * to the right and then subtract out float's bias adjust to |
| * get true exponent value |
| */ |
| return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >> |
| (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS; |
| } |
| |
| /** |
| * Returns the unbiased exponent used in the representation of a |
| * {@code double}. Special cases: |
| * |
| * <ul> |
| * <li>If the argument is NaN or infinite, then the result is |
| * {@link Double#MAX_EXPONENT} + 1. |
| * <li>If the argument is zero or subnormal, then the result is |
| * {@link Double#MIN_EXPONENT} -1. |
| * </ul> |
| * @param d a {@code double} value |
| * @return the unbiased exponent of the argument |
| * @since 1.6 |
| */ |
| public static int getExponent(double d) { |
| /* |
| * Bitwise convert d to long, mask out exponent bits, shift |
| * to the right and then subtract out double's bias adjust to |
| * get true exponent value. |
| */ |
| return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >> |
| (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS); |
| } |
| |
| /** |
| * Returns the floating-point number adjacent to the first |
| * argument in the direction of the second argument. If both |
| * arguments compare as equal the second argument is returned. |
| * |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li> If either argument is a NaN, then NaN is returned. |
| * |
| * <li> If both arguments are signed zeros, {@code direction} |
| * is returned unchanged (as implied by the requirement of |
| * returning the second argument if the arguments compare as |
| * equal). |
| * |
| * <li> If {@code start} is |
| * ±{@link Double#MIN_VALUE} and {@code direction} |
| * has a value such that the result should have a smaller |
| * magnitude, then a zero with the same sign as {@code start} |
| * is returned. |
| * |
| * <li> If {@code start} is infinite and |
| * {@code direction} has a value such that the result should |
| * have a smaller magnitude, {@link Double#MAX_VALUE} with the |
| * same sign as {@code start} is returned. |
| * |
| * <li> If {@code start} is equal to ± |
| * {@link Double#MAX_VALUE} and {@code direction} has a |
| * value such that the result should have a larger magnitude, an |
| * infinity with same sign as {@code start} is returned. |
| * </ul> |
| * |
| * @param start starting floating-point value |
| * @param direction value indicating which of |
| * {@code start}'s neighbors or {@code start} should |
| * be returned |
| * @return The floating-point number adjacent to {@code start} in the |
| * direction of {@code direction}. |
| * @since 1.6 |
| */ |
| public static double nextAfter(double start, double direction) { |
| /* |
| * The cases: |
| * |
| * nextAfter(+infinity, 0) == MAX_VALUE |
| * nextAfter(+infinity, +infinity) == +infinity |
| * nextAfter(-infinity, 0) == -MAX_VALUE |
| * nextAfter(-infinity, -infinity) == -infinity |
| * |
| * are naturally handled without any additional testing |
| */ |
| |
| /* |
| * IEEE 754 floating-point numbers are lexicographically |
| * ordered if treated as signed-magnitude integers. |
| * Since Java's integers are two's complement, |
| * incrementing the two's complement representation of a |
| * logically negative floating-point value *decrements* |
| * the signed-magnitude representation. Therefore, when |
| * the integer representation of a floating-point value |
| * is negative, the adjustment to the representation is in |
| * the opposite direction from what would initially be expected. |
| */ |
| |
| // Branch to descending case first as it is more costly than ascending |
| // case due to start != 0.0d conditional. |
| if (start > direction) { // descending |
| if (start != 0.0d) { |
| final long transducer = Double.doubleToRawLongBits(start); |
| return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L)); |
| } else { // start == 0.0d && direction < 0.0d |
| return -Double.MIN_VALUE; |
| } |
| } else if (start < direction) { // ascending |
| // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) |
| // then bitwise convert start to integer. |
| final long transducer = Double.doubleToRawLongBits(start + 0.0d); |
| return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L)); |
| } else if (start == direction) { |
| return direction; |
| } else { // isNaN(start) || isNaN(direction) |
| return start + direction; |
| } |
| } |
| |
| /** |
| * Returns the floating-point number adjacent to the first |
| * argument in the direction of the second argument. If both |
| * arguments compare as equal a value equivalent to the second argument |
| * is returned. |
| * |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li> If either argument is a NaN, then NaN is returned. |
| * |
| * <li> If both arguments are signed zeros, a value equivalent |
| * to {@code direction} is returned. |
| * |
| * <li> If {@code start} is |
| * ±{@link Float#MIN_VALUE} and {@code direction} |
| * has a value such that the result should have a smaller |
| * magnitude, then a zero with the same sign as {@code start} |
| * is returned. |
| * |
| * <li> If {@code start} is infinite and |
| * {@code direction} has a value such that the result should |
| * have a smaller magnitude, {@link Float#MAX_VALUE} with the |
| * same sign as {@code start} is returned. |
| * |
| * <li> If {@code start} is equal to ± |
| * {@link Float#MAX_VALUE} and {@code direction} has a |
| * value such that the result should have a larger magnitude, an |
| * infinity with same sign as {@code start} is returned. |
| * </ul> |
| * |
| * @param start starting floating-point value |
| * @param direction value indicating which of |
| * {@code start}'s neighbors or {@code start} should |
| * be returned |
| * @return The floating-point number adjacent to {@code start} in the |
| * direction of {@code direction}. |
| * @since 1.6 |
| */ |
| public static float nextAfter(float start, double direction) { |
| /* |
| * The cases: |
| * |
| * nextAfter(+infinity, 0) == MAX_VALUE |
| * nextAfter(+infinity, +infinity) == +infinity |
| * nextAfter(-infinity, 0) == -MAX_VALUE |
| * nextAfter(-infinity, -infinity) == -infinity |
| * |
| * are naturally handled without any additional testing |
| */ |
| |
| /* |
| * IEEE 754 floating-point numbers are lexicographically |
| * ordered if treated as signed-magnitude integers. |
| * Since Java's integers are two's complement, |
| * incrementing the two's complement representation of a |
| * logically negative floating-point value *decrements* |
| * the signed-magnitude representation. Therefore, when |
| * the integer representation of a floating-point value |
| * is negative, the adjustment to the representation is in |
| * the opposite direction from what would initially be expected. |
| */ |
| |
| // Branch to descending case first as it is more costly than ascending |
| // case due to start != 0.0f conditional. |
| if (start > direction) { // descending |
| if (start != 0.0f) { |
| final int transducer = Float.floatToRawIntBits(start); |
| return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1)); |
| } else { // start == 0.0f && direction < 0.0f |
| return -Float.MIN_VALUE; |
| } |
| } else if (start < direction) { // ascending |
| // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) |
| // then bitwise convert start to integer. |
| final int transducer = Float.floatToRawIntBits(start + 0.0f); |
| return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1)); |
| } else if (start == direction) { |
| return (float)direction; |
| } else { // isNaN(start) || isNaN(direction) |
| return start + (float)direction; |
| } |
| } |
| |
| /** |
| * Returns the floating-point value adjacent to {@code d} in |
| * the direction of positive infinity. This method is |
| * semantically equivalent to {@code nextAfter(d, |
| * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} |
| * implementation may run faster than its equivalent |
| * {@code nextAfter} call. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, the result is NaN. |
| * |
| * <li> If the argument is positive infinity, the result is |
| * positive infinity. |
| * |
| * <li> If the argument is zero, the result is |
| * {@link Double#MIN_VALUE} |
| * |
| * </ul> |
| * |
| * @param d starting floating-point value |
| * @return The adjacent floating-point value closer to positive |
| * infinity. |
| * @since 1.6 |
| */ |
| public static double nextUp(double d) { |
| // Use a single conditional and handle the likely cases first. |
| if (d < Double.POSITIVE_INFINITY) { |
| // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0). |
| final long transducer = Double.doubleToRawLongBits(d + 0.0D); |
| return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L)); |
| } else { // d is NaN or +Infinity |
| return d; |
| } |
| } |
| |
| /** |
| * Returns the floating-point value adjacent to {@code f} in |
| * the direction of positive infinity. This method is |
| * semantically equivalent to {@code nextAfter(f, |
| * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} |
| * implementation may run faster than its equivalent |
| * {@code nextAfter} call. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, the result is NaN. |
| * |
| * <li> If the argument is positive infinity, the result is |
| * positive infinity. |
| * |
| * <li> If the argument is zero, the result is |
| * {@link Float#MIN_VALUE} |
| * |
| * </ul> |
| * |
| * @param f starting floating-point value |
| * @return The adjacent floating-point value closer to positive |
| * infinity. |
| * @since 1.6 |
| */ |
| public static float nextUp(float f) { |
| // Use a single conditional and handle the likely cases first. |
| if (f < Float.POSITIVE_INFINITY) { |
| // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0). |
| final int transducer = Float.floatToRawIntBits(f + 0.0F); |
| return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1)); |
| } else { // f is NaN or +Infinity |
| return f; |
| } |
| } |
| |
| /** |
| * Returns the floating-point value adjacent to {@code d} in |
| * the direction of negative infinity. This method is |
| * semantically equivalent to {@code nextAfter(d, |
| * Double.NEGATIVE_INFINITY)}; however, a |
| * {@code nextDown} implementation may run faster than its |
| * equivalent {@code nextAfter} call. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, the result is NaN. |
| * |
| * <li> If the argument is negative infinity, the result is |
| * negative infinity. |
| * |
| * <li> If the argument is zero, the result is |
| * {@code -Double.MIN_VALUE} |
| * |
| * </ul> |
| * |
| * @param d starting floating-point value |
| * @return The adjacent floating-point value closer to negative |
| * infinity. |
| * @since 1.8 |
| */ |
| public static double nextDown(double d) { |
| if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY) |
| return d; |
| else { |
| if (d == 0.0) |
| return -Double.MIN_VALUE; |
| else |
| return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + |
| ((d > 0.0d)?-1L:+1L)); |
| } |
| } |
| |
| /** |
| * Returns the floating-point value adjacent to {@code f} in |
| * the direction of negative infinity. This method is |
| * semantically equivalent to {@code nextAfter(f, |
| * Float.NEGATIVE_INFINITY)}; however, a |
| * {@code nextDown} implementation may run faster than its |
| * equivalent {@code nextAfter} call. |
| * |
| * <p>Special Cases: |
| * <ul> |
| * <li> If the argument is NaN, the result is NaN. |
| * |
| * <li> If the argument is negative infinity, the result is |
| * negative infinity. |
| * |
| * <li> If the argument is zero, the result is |
| * {@code -Float.MIN_VALUE} |
| * |
| * </ul> |
| * |
| * @param f starting floating-point value |
| * @return The adjacent floating-point value closer to negative |
| * infinity. |
| * @since 1.8 |
| */ |
| public static float nextDown(float f) { |
| if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY) |
| return f; |
| else { |
| if (f == 0.0f) |
| return -Float.MIN_VALUE; |
| else |
| return Float.intBitsToFloat(Float.floatToRawIntBits(f) + |
| ((f > 0.0f)?-1:+1)); |
| } |
| } |
| |
| /** |
| * Returns {@code d} × |
| * 2<sup>{@code scaleFactor}</sup> rounded as if performed |
| * by a single correctly rounded floating-point multiply to a |
| * member of the double value set. See the Java |
| * Language Specification for a discussion of floating-point |
| * value sets. If the exponent of the result is between {@link |
| * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the |
| * answer is calculated exactly. If the exponent of the result |
| * would be larger than {@code Double.MAX_EXPONENT}, an |
| * infinity is returned. Note that if the result is subnormal, |
| * precision may be lost; that is, when {@code scalb(x, n)} |
| * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal |
| * <i>x</i>. When the result is non-NaN, the result has the same |
| * sign as {@code d}. |
| * |
| * <p>Special cases: |
| * <ul> |
| * <li> If the first argument is NaN, NaN is returned. |
| * <li> If the first argument is infinite, then an infinity of the |
| * same sign is returned. |
| * <li> If the first argument is zero, then a zero of the same |
| * sign is returned. |
| * </ul> |
| * |
| * @param d number to be scaled by a power of two. |
| * @param scaleFactor power of 2 used to scale {@code d} |
| * @return {@code d} × 2<sup>{@code scaleFactor}</sup> |
| * @since 1.6 |
| */ |
| public static double scalb(double d, int scaleFactor) { |
| /* |
| * This method does not need to be declared strictfp to |
| * compute the same correct result on all platforms. When |
| * scaling up, it does not matter what order the |
| * multiply-store operations are done; the result will be |
| * finite or overflow regardless of the operation ordering. |
| * However, to get the correct result when scaling down, a |
| * particular ordering must be used. |
| * |
| * When scaling down, the multiply-store operations are |
| * sequenced so that it is not possible for two consecutive |
| * multiply-stores to return subnormal results. If one |
| * multiply-store result is subnormal, the next multiply will |
| * round it away to zero. This is done by first multiplying |
| * by 2 ^ (scaleFactor % n) and then multiplying several |
| * times by 2^n as needed where n is the exponent of number |
| * that is a covenient power of two. In this way, at most one |
| * real rounding error occurs. If the double value set is |
| * being used exclusively, the rounding will occur on a |
| * multiply. If the double-extended-exponent value set is |
| * being used, the products will (perhaps) be exact but the |
| * stores to d are guaranteed to round to the double value |
| * set. |
| * |
| * It is _not_ a valid implementation to first multiply d by |
| * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor % |
| * MIN_EXPONENT) since even in a strictfp program double |
| * rounding on underflow could occur; e.g. if the scaleFactor |
| * argument was (MIN_EXPONENT - n) and the exponent of d was a |
| * little less than -(MIN_EXPONENT - n), meaning the final |
| * result would be subnormal. |
| * |
| * Since exact reproducibility of this method can be achieved |
| * without any undue performance burden, there is no |
| * compelling reason to allow double rounding on underflow in |
| * scalb. |
| */ |
| |
| // magnitude of a power of two so large that scaling a finite |
| // nonzero value by it would be guaranteed to over or |
| // underflow; due to rounding, scaling down takes an |
| // additional power of two which is reflected here |
| final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT + |
| DoubleConsts.SIGNIFICAND_WIDTH + 1; |
| int exp_adjust = 0; |
| int scale_increment = 0; |
| double exp_delta = Double.NaN; |
| |
| // Make sure scaling factor is in a reasonable range |
| |
| if(scaleFactor < 0) { |
| scaleFactor = Math.max(scaleFactor, -MAX_SCALE); |
| scale_increment = -512; |
| exp_delta = twoToTheDoubleScaleDown; |
| } |
| else { |
| scaleFactor = Math.min(scaleFactor, MAX_SCALE); |
| scale_increment = 512; |
| exp_delta = twoToTheDoubleScaleUp; |
| } |
| |
| // Calculate (scaleFactor % +/-512), 512 = 2^9, using |
| // technique from "Hacker's Delight" section 10-2. |
| int t = (scaleFactor >> 9-1) >>> 32 - 9; |
| exp_adjust = ((scaleFactor + t) & (512 -1)) - t; |
| |
| d *= powerOfTwoD(exp_adjust); |
| scaleFactor -= exp_adjust; |
| |
| while(scaleFactor != 0) { |
| d *= exp_delta; |
| scaleFactor -= scale_increment; |
| } |
| return d; |
| } |
| |
| /** |
| * Returns {@code f} × |
| * 2<sup>{@code scaleFactor}</sup> rounded as if performed |
| * by a single correctly rounded floating-point multiply to a |
| * member of the float value set. See the Java |
| * Language Specification for a discussion of floating-point |
| * value sets. If the exponent of the result is between {@link |
| * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the |
| * answer is calculated exactly. If the exponent of the result |
| * would be larger than {@code Float.MAX_EXPONENT}, an |
| * infinity is returned. Note that if the result is subnormal, |
| * precision may be lost; that is, when {@code scalb(x, n)} |
| * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal |
| * <i>x</i>. When the result is non-NaN, the result has the same |
| * sign as {@code f}. |
| * |
| * <p>Special cases: |
| * <ul> |
| * <li> If the first argument is NaN, NaN is returned. |
| * <li> If the first argument is infinite, then an infinity of the |
| * same sign is returned. |
| * <li> If the first argument is zero, then a zero of the same |
| * sign is returned. |
| * </ul> |
| * |
| * @param f number to be scaled by a power of two. |
| * @param scaleFactor power of 2 used to scale {@code f} |
| * @return {@code f} × 2<sup>{@code scaleFactor}</sup> |
| * @since 1.6 |
| */ |
| public static float scalb(float f, int scaleFactor) { |
| // magnitude of a power of two so large that scaling a finite |
| // nonzero value by it would be guaranteed to over or |
| // underflow; due to rounding, scaling down takes an |
| // additional power of two which is reflected here |
| final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT + |
| FloatConsts.SIGNIFICAND_WIDTH + 1; |
| |
| // Make sure scaling factor is in a reasonable range |
| scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE); |
| |
| /* |
| * Since + MAX_SCALE for float fits well within the double |
| * exponent range and + float -> double conversion is exact |
| * the multiplication below will be exact. Therefore, the |
| * rounding that occurs when the double product is cast to |
| * float will be the correctly rounded float result. Since |
| * all operations other than the final multiply will be exact, |
| * it is not necessary to declare this method strictfp. |
| */ |
| return (float)((double)f*powerOfTwoD(scaleFactor)); |
| } |
| |
| // Constants used in scalb |
| static double twoToTheDoubleScaleUp = powerOfTwoD(512); |
| static double twoToTheDoubleScaleDown = powerOfTwoD(-512); |
| |
| /** |
| * Returns a floating-point power of two in the normal range. |
| */ |
| static double powerOfTwoD(int n) { |
| assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT); |
| return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) << |
| (DoubleConsts.SIGNIFICAND_WIDTH-1)) |
| & DoubleConsts.EXP_BIT_MASK); |
| } |
| |
| /** |
| * Returns a floating-point power of two in the normal range. |
| */ |
| static float powerOfTwoF(int n) { |
| assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT); |
| return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) << |
| (FloatConsts.SIGNIFICAND_WIDTH-1)) |
| & FloatConsts.EXP_BIT_MASK); |
| } |
| } |