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JDK 17 java.base.jmod - Base Module

JDK 17 java.base.jmod is the JMOD file for JDK 17 Base module.

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JDK 17 Base module source code files are stored in \fyicenter\jdk-17.0.5\lib\src.zip\java.base.

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**⏎ java/lang/StrictMath.java**

/* * Copyright (c) 1999, 2021, Oracle and/or its affiliates. All rights reserved. * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms. * * * * * * * * * * * * * * * * * * * * */ package java.lang; import java.util.Random; import jdk.internal.math.DoubleConsts; import jdk.internal.vm.annotation.IntrinsicCandidate; /** * The class {@code StrictMath} contains methods for performing basic * numeric operations such as the elementary exponential, logarithm, * square root, and trigonometric functions. * * <p>To help ensure portability of Java programs, the definitions of * some of the numeric functions in this package require that they * produce the same results as certain published algorithms. These * algorithms are available from the well-known network library * {@code netlib} as the package "Freely Distributable Math * Library," <a * href="https://www.netlib.org/fdlibm/">{@code fdlibm}</a>. These * algorithms, which are written in the C programming language, are * then to be understood as executed with all floating-point * operations following the rules of Java floating-point arithmetic. * * <p>The Java math library is defined with respect to * {@code fdlibm} version 5.3. Where {@code fdlibm} provides * more than one definition for a function (such as * {@code acos}), use the "IEEE 754 core function" version * (residing in a file whose name begins with the letter * {@code e}). The methods which require {@code fdlibm} * semantics are {@code sin}, {@code cos}, {@code tan}, * {@code asin}, {@code acos}, {@code atan}, * {@code exp}, {@code log}, {@code log10}, * {@code cbrt}, {@code atan2}, {@code pow}, * {@code sinh}, {@code cosh}, {@code tanh}, * {@code hypot}, {@code expm1}, and {@code log1p}. * * <p> * The platform uses signed two's complement integer arithmetic with * int and long primitive types. The developer should choose * the primitive type to ensure that arithmetic operations consistently * produce correct results, which in some cases means the operations * will not overflow the range of values of the computation. * The best practice is to choose the primitive type and algorithm to avoid * overflow. In cases where the size is {@code int} or {@code long} and * overflow errors need to be detected, the methods {@code addExact}, * {@code subtractExact}, {@code multiplyExact}, {@code toIntExact}, * {@code incrementExact}, {@code decrementExact} and {@code negateExact} * throw an {@code ArithmeticException} when the results overflow. * For the arithmetic operations divide and absolute value, overflow * occurs only with a specific minimum or maximum value and * should be checked against the minimum or maximum as appropriate. * * <h2><a id=Ieee754RecommendedOps>IEEE 754 Recommended * Operations</a></h2> * * The {@link java.lang.Math Math} class discusses how the shared * quality of implementation criteria for selected {@code Math} and * {@code StrictMath} methods <a * href="Math.html#Ieee754RecommendedOps">relate to the IEEE 754 * recommended operations</a>. * * @author Joseph D. Darcy * @since 1.3 */ public final class StrictMath { /** * Don't let anyone instantiate this class. */ private StrictMath() {} /** * The {@code double} value that is closer than any other to * <i>e</i>, the base of the natural logarithms. */ public static final double E = 2.7182818284590452354; /** * The {@code double} value that is closer than any other to * <i>pi</i>, the ratio of the circumference of a circle to its * diameter. */ public static final double PI = 3.14159265358979323846; /** * Constant by which to multiply an angular value in degrees to obtain an * angular value in radians. */ private static final double DEGREES_TO_RADIANS = 0.017453292519943295; /** * Constant by which to multiply an angular value in radians to obtain an * angular value in degrees. */ private static final double RADIANS_TO_DEGREES = 57.29577951308232; /** * Returns the trigonometric sine of an angle. Special cases: * <ul><li>If the argument is NaN or an infinity, then the * result is NaN. * <li>If the argument is zero, then the result is a zero with the * same sign as the argument.</ul> * * @param a an angle, in radians. * @return the sine of the argument. */ public static native double sin(double a); /** * Returns the trigonometric cosine of an angle. Special cases: * <ul><li>If the argument is NaN or an infinity, then the * result is NaN. * <li>If the argument is zero, then the result is {@code 1.0}. * </ul> * * @param a an angle, in radians. * @return the cosine of the argument. */ public static native double cos(double a); /** * Returns the trigonometric tangent of an angle. Special cases: * <ul><li>If the argument is NaN or an infinity, then the result * is NaN. * <li>If the argument is zero, then the result is a zero with the * same sign as the argument.</ul> * * @param a an angle, in radians. * @return the tangent of the argument. */ public static native double tan(double a); /** * Returns the arc sine of a value; the returned angle is in the * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: * <ul><li>If the argument is NaN or its absolute value is greater * than 1, then the result is NaN. * <li>If the argument is zero, then the result is a zero with the * same sign as the argument.</ul> * * @param a the value whose arc sine is to be returned. * @return the arc sine of the argument. */ public static native double asin(double a); /** * Returns the arc cosine of a value; the returned angle is in the * range 0.0 through <i>pi</i>. Special case: * <ul><li>If the argument is NaN or its absolute value is greater * than 1, then the result is NaN. * <li>If the argument is {@code 1.0}, the result is positive zero. * </ul> * * @param a the value whose arc cosine is to be returned. * @return the arc cosine of the argument. */ public static native double acos(double a); /** * Returns the arc tangent of a value; the returned angle is in the * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: * <ul><li>If the argument is NaN, then the result is NaN. * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * <li>If the argument is {@linkplain Double#isInfinite infinite}, * then the result is the closest value to <i>pi</i>/2 with the * same sign as the input. * </ul> * * @param a the value whose arc tangent is to be returned. * @return the arc tangent of the argument. */ public static native double atan(double a); /** * Converts an angle measured in degrees to an approximately * equivalent angle measured in radians. The conversion from * degrees to radians is generally inexact. * * @param angdeg an angle, in degrees * @return the measurement of the angle {@code angdeg} * in radians. */ public static double toRadians(double angdeg) { return Math.toRadians(angdeg); } /** * Converts an angle measured in radians to an approximately * equivalent angle measured in degrees. The conversion from * radians to degrees is generally inexact; users should * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly * equal {@code 0.0}. * * @param angrad an angle, in radians * @return the measurement of the angle {@code angrad} * in degrees. */ public static double toDegrees(double angrad) { return Math.toDegrees(angrad); } /** * 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. * <li>If the argument is zero, then the result is {@code 1.0}. * </ul> * * @param a the exponent to raise <i>e</i> to. * @return the value <i>e</i><sup>{@code a}</sup>, * where <i>e</i> is the base of the natural logarithms. */ public static double exp(double a) { return FdLibm.Exp.compute(a); } /** * Returns the natural logarithm (base <i>e</i>) of a {@code double} * value. Special cases: * <ul><li>If the argument is NaN or less than zero, then the result * is NaN. * <li>If the argument is positive infinity, then the result is * positive infinity. * <li>If the argument is positive zero or negative zero, then the * result is negative infinity. * <li>If the argument is {@code 1.0}, then the result is positive * zero. * </ul> * * @param a a value * @return the value ln {@code a}, the natural logarithm of * {@code a}. */ public static native double log(double a); /** * Returns the base 10 logarithm of a {@code double} value. * Special cases: * * <ul><li>If the argument is NaN or less than zero, then the result * is NaN. * <li>If the argument is positive infinity, then the result is * positive infinity. * <li>If the argument is positive zero or negative zero, then the * result is negative infinity. * <li>If the argument is equal to 10<sup><i>n</i></sup> for * integer <i>n</i>, then the result is <i>n</i>. In particular, * if the argument is {@code 1.0} (10<sup>0</sup>), then the * result is positive zero. * </ul> * * @param a a value * @return the base 10 logarithm of {@code a}. * @since 1.5 */ public static native double log10(double a); /** * Returns the correctly rounded positive square root of a * {@code double} value. * Special cases: * <ul><li>If the argument is NaN or less than zero, then the result * is NaN. * <li>If the argument is positive infinity, then the result is positive * infinity. * <li>If the argument is positive zero or negative zero, then the * result is the same as the argument.</ul> * Otherwise, the result is the {@code double} value closest to * the true mathematical square root of the argument value. * * @param a a value. * @return the positive square root of {@code a}. */ @IntrinsicCandidate public static native double sqrt(double a); /** * Returns the cube root of a {@code double} value. For * positive finite {@code x}, {@code cbrt(-x) == * -cbrt(x)}; that is, the cube root of a negative value is * the negative of the cube root of that value's magnitude. * Special cases: * * <ul> * * <li>If the argument is NaN, then the result is NaN. * * <li>If the argument is infinite, then the result is an infinity * with the same sign as the argument. * * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * * </ul> * * @param a a value. * @return the cube root of {@code a}. * @since 1.5 */ public static double cbrt(double a) { return FdLibm.Cbrt.compute(a); } /** * Computes the remainder operation on two arguments as prescribed * by the IEEE 754 standard. * The remainder value is mathematically equal to * <code>f1 - f2</code> × <i>n</i>, * where <i>n</i> is the mathematical integer closest to the exact * mathematical value of the quotient {@code f1/f2}, and if two * mathematical integers are equally close to {@code f1/f2}, * then <i>n</i> is the integer that is even. If the remainder is * zero, its sign is the same as the sign of the first argument. * Special cases: * <ul><li>If either argument is NaN, or the first argument is infinite, * or the second argument is positive zero or negative zero, then the * result is NaN. * <li>If the first argument is finite and the second argument is * infinite, then the result is the same as the first argument.</ul> * * @param f1 the dividend. * @param f2 the divisor. * @return the remainder when {@code f1} is divided by * {@code f2}. */ public static native double IEEEremainder(double f1, double f2); /** * Returns the smallest (closest to negative infinity) * {@code double} value that is greater than or equal to the * argument and is equal to a mathematical integer. Special cases: * <ul><li>If the argument value is already equal to a * mathematical integer, then the result is the same as the * argument. <li>If the argument is NaN or an infinity or * positive zero or negative zero, then the result is the same as * the argument. <li>If the argument value is less than zero but * greater than -1.0, then the result is negative zero.</ul> Note * that the value of {@code StrictMath.ceil(x)} is exactly the * value of {@code -StrictMath.floor(-x)}. * * @param a a value. * @return the smallest (closest to negative infinity) * floating-point value that is greater than or equal to * the argument and is equal to a mathematical integer. */ public static double ceil(double a) { return floorOrCeil(a, -0.0, 1.0, 1.0); } /** * Returns the largest (closest to positive infinity) * {@code double} value that is less than or equal to the * argument and is equal to a mathematical integer. Special cases: * <ul><li>If the argument value is already equal to a * mathematical integer, then the result is the same as the * argument. <li>If the argument is NaN or an infinity or * positive zero or negative zero, then the result is the same as * the argument.</ul> * * @param a a value. * @return the largest (closest to positive infinity) * floating-point value that less than or equal to the argument * and is equal to a mathematical integer. */ public static double floor(double a) { return floorOrCeil(a, -1.0, 0.0, -1.0); } /** * Internal method to share logic between floor and ceil. * * @param a the value to be floored or ceiled * @param negativeBoundary result for values in (-1, 0) * @param positiveBoundary result for values in (0, 1) * @param increment value to add when the argument is non-integral */ private static double floorOrCeil(double a, double negativeBoundary, double positiveBoundary, double sign) { int exponent = Math.getExponent(a); if (exponent < 0) { /* * Absolute value of argument is less than 1. * floorOrceil(-0.0) => -0.0 * floorOrceil(+0.0) => +0.0 */ return ((a == 0.0) ? a : ( (a < 0.0) ? negativeBoundary : positiveBoundary) ); } else if (exponent >= 52) { /* * Infinity, NaN, or a value so large it must be integral. */ return a; } // Else the argument is either an integral value already XOR it // has to be rounded to one. assert exponent >= 0 && exponent <= 51; long doppel = Double.doubleToRawLongBits(a); long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent; if ( (mask & doppel) == 0L ) return a; // integral value else { double result = Double.longBitsToDouble(doppel & (~mask)); if (sign*a > 0.0) result = result + sign; return result; } } /** * Returns the {@code double} value that is closest in value * to the argument and is equal to a mathematical integer. If two * {@code double} values that are mathematical integers are * equally close to the value of the argument, the result is the * integer value that is even. Special cases: * <ul><li>If the argument value is already equal to a mathematical * integer, then the result is the same as the argument. * <li>If the argument is NaN or an infinity or positive zero or negative * zero, then the result is the same as the argument.</ul> * * @param a a value. * @return the closest floating-point value to {@code a} that is * equal to a mathematical integer. * @author Joseph D. Darcy */ public static double rint(double a) { /* * If the absolute value of a is not less than 2^52, it * is either a finite integer (the double format does not have * enough significand bits for a number that large to have any * fractional portion), an infinity, or a NaN. In any of * these cases, rint of the argument is the argument. * * Otherwise, the sum (twoToThe52 + a ) will properly round * away any fractional portion of a since ulp(twoToThe52) == * 1.0; subtracting out twoToThe52 from this sum will then be * exact and leave the rounded integer portion of a. */ double twoToThe52 = (double)(1L << 52); // 2^52 double sign = Math.copySign(1.0, a); // preserve sign info a = Math.abs(a); if (a < twoToThe52) { // E_min <= ilogb(a) <= 51 a = ((twoToThe52 + a ) - twoToThe52); } return sign * a; // restore original sign } /** * Returns the angle <i>theta</i> from the conversion of rectangular * coordinates ({@code x}, {@code y}) to polar * coordinates (r, <i>theta</i>). * This method computes the phase <i>theta</i> by computing an arc tangent * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special * cases: * <ul><li>If either argument is NaN, then the result is NaN. * <li>If the first argument is positive zero and the second argument * is positive, or the first argument is positive and finite and the * second argument is positive infinity, then the result is positive * zero. * <li>If the first argument is negative zero and the second argument * is positive, or the first argument is negative and finite and the * second argument is positive infinity, then the result is negative zero. * <li>If the first argument is positive zero and the second argument * is negative, or the first argument is positive and finite and the * second argument is negative infinity, then the result is the * {@code double} value closest to <i>pi</i>. * <li>If the first argument is negative zero and the second argument * is negative, or the first argument is negative and finite and the * second argument is negative infinity, then the result is the * {@code double} value closest to -<i>pi</i>. * <li>If the first argument is positive and the second argument is * positive zero or negative zero, or the first argument is positive * infinity and the second argument is finite, then the result is the * {@code double} value closest to <i>pi</i>/2. * <li>If the first argument is negative and the second argument is * positive zero or negative zero, or the first argument is negative * infinity and the second argument is finite, then the result is the * {@code double} value closest to -<i>pi</i>/2. * <li>If both arguments are positive infinity, then the result is the * {@code double} value closest to <i>pi</i>/4. * <li>If the first argument is positive infinity and the second argument * is negative infinity, then the result is the {@code double} * value closest to 3*<i>pi</i>/4. * <li>If the first argument is negative infinity and the second argument * is positive infinity, then the result is the {@code double} value * closest to -<i>pi</i>/4. * <li>If both arguments are negative infinity, then the result is the * {@code double} value closest to -3*<i>pi</i>/4.</ul> * * @apiNote * For <i>y</i> with a positive sign and finite nonzero * <i>x</i>, the exact mathematical value of {@code atan2} is * equal to: * <ul> * <li>If <i>x</i> {@literal >} 0, atan(abs(<i>y</i>/<i>x</i>)) * <li>If <i>x</i> {@literal <} 0, π - atan(abs(<i>y</i>/<i>x</i>)) * </ul> * * @param y the ordinate coordinate * @param x the abscissa coordinate * @return the <i>theta</i> component of the point * (<i>r</i>, <i>theta</i>) * in polar coordinates that corresponds to the point * (<i>x</i>, <i>y</i>) in Cartesian coordinates. */ public static native double atan2(double y, double x); /** * Returns the value of the first argument raised to the power of the * second argument. Special cases: * * <ul><li>If the second argument is positive or negative zero, then the * result is 1.0. * <li>If the second argument is 1.0, then the result is the same as the * first argument. * <li>If the second argument is NaN, then the result is NaN. * <li>If the first argument is NaN and the second argument is nonzero, * then the result is NaN. * * <li>If * <ul> * <li>the absolute value of the first argument is greater than 1 * and the second argument is positive infinity, or * <li>the absolute value of the first argument is less than 1 and * the second argument is negative infinity, * </ul> * then the result is positive infinity. * * <li>If * <ul> * <li>the absolute value of the first argument is greater than 1 and * the second argument is negative infinity, or * <li>the absolute value of the * first argument is less than 1 and the second argument is positive * infinity, * </ul> * then the result is positive zero. * * <li>If the absolute value of the first argument equals 1 and the * second argument is infinite, then the result is NaN. * * <li>If * <ul> * <li>the first argument is positive zero and the second argument * is greater than zero, or * <li>the first argument is positive infinity and the second * argument is less than zero, * </ul> * then the result is positive zero. * * <li>If * <ul> * <li>the first argument is positive zero and the second argument * is less than zero, or * <li>the first argument is positive infinity and the second * argument is greater than zero, * </ul> * then the result is positive infinity. * * <li>If * <ul> * <li>the first argument is negative zero and the second argument * is greater than zero but not a finite odd integer, or * <li>the first argument is negative infinity and the second * argument is less than zero but not a finite odd integer, * </ul> * then the result is positive zero. * * <li>If * <ul> * <li>the first argument is negative zero and the second argument * is a positive finite odd integer, or * <li>the first argument is negative infinity and the second * argument is a negative finite odd integer, * </ul> * then the result is negative zero. * * <li>If * <ul> * <li>the first argument is negative zero and the second argument * is less than zero but not a finite odd integer, or * <li>the first argument is negative infinity and the second * argument is greater than zero but not a finite odd integer, * </ul> * then the result is positive infinity. * * <li>If * <ul> * <li>the first argument is negative zero and the second argument * is a negative finite odd integer, or * <li>the first argument is negative infinity and the second * argument is a positive finite odd integer, * </ul> * then the result is negative infinity. * * <li>If the first argument is finite and less than zero * <ul> * <li> if the second argument is a finite even integer, the * result is equal to the result of raising the absolute value of * the first argument to the power of the second argument * * <li>if the second argument is a finite odd integer, the result * is equal to the negative of the result of raising the absolute * value of the first argument to the power of the second * argument * * <li>if the second argument is finite and not an integer, then * the result is NaN. * </ul> * * <li>If both arguments are integers, then the result is exactly equal * to the mathematical result of raising the first argument to the power * of the second argument if that result can in fact be represented * exactly as a {@code double} value.</ul> * * <p>(In the foregoing descriptions, a floating-point value is * considered to be an integer if and only if it is finite and a * fixed point of the method {@link #ceil ceil} or, * equivalently, a fixed point of the method {@link #floor * floor}. A value is a fixed point of a one-argument * method if and only if the result of applying the method to the * value is equal to the value.) * * @apiNote * The special cases definitions of this method differ from the * special case definitions of the IEEE 754 recommended {@code * pow} operation for ±{@code 1.0} raised to an infinite * power. This method treats such cases as indeterminate and * specifies a NaN is returned. The IEEE 754 specification treats * the infinite power as a large integer (large-magnitude * floating-point numbers are numerically integers, specifically * even integers) and therefore specifies {@code 1.0} be returned. * * @param a base. * @param b the exponent. * @return the value {@code a}<sup>{@code b}</sup>. */ public static double pow(double a, double b) { return FdLibm.Pow.compute(a, b); } /** * Returns the closest {@code int} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Integer.MIN_VALUE}, the result is * equal to the value of {@code Integer.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Integer.MAX_VALUE}, the result is * equal to the value of {@code Integer.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to an integer. * @return the value of the argument rounded to the nearest * {@code int} value. * @see java.lang.Integer#MAX_VALUE * @see java.lang.Integer#MIN_VALUE */ public static int round(float a) { return Math.round(a); } /** * Returns the closest {@code long} to the argument, with ties * rounding to positive infinity. * * <p>Special cases: * <ul><li>If the argument is NaN, the result is 0. * <li>If the argument is negative infinity or any value less than or * equal to the value of {@code Long.MIN_VALUE}, the result is * equal to the value of {@code Long.MIN_VALUE}. * <li>If the argument is positive infinity or any value greater than or * equal to the value of {@code Long.MAX_VALUE}, the result is * equal to the value of {@code Long.MAX_VALUE}.</ul> * * @param a a floating-point value to be rounded to a * {@code long}. * @return the value of the argument rounded to the nearest * {@code long} value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { return Math.round(a); } private static final class RandomNumberGeneratorHolder { static final Random randomNumberGenerator = new Random(); } /** * Returns a {@code double} value with a positive sign, greater * than or equal to {@code 0.0} and less than {@code 1.0}. * Returned values are chosen pseudorandomly with (approximately) * uniform distribution from that range. * * <p>When this method is first called, it creates a single new * pseudorandom-number generator, exactly as if by the expression * * <blockquote>{@code new java.util.Random()}</blockquote> * * This new pseudorandom-number generator is used thereafter for * all calls to this method and is used nowhere else. * * <p>This method is properly synchronized to allow correct use by * more than one thread. However, if many threads need to generate * pseudorandom numbers at a great rate, it may reduce contention * for each thread to have its own pseudorandom-number generator. * * @return a pseudorandom {@code double} greater than or equal * to {@code 0.0} and less than {@code 1.0}. * @see Random#nextDouble() */ public static double random() { return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble(); } /** * Returns the sum of its arguments, * throwing an exception if the result overflows an {@code int}. * * @param x the first value * @param y the second value * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#addExact(int,int) * @since 1.8 */ public static int addExact(int x, int y) { return Math.addExact(x, y); } /** * Returns the sum of its arguments, * throwing an exception if the result overflows a {@code long}. * * @param x the first value * @param y the second value * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#addExact(long,long) * @since 1.8 */ public static long addExact(long x, long y) { return Math.addExact(x, y); } /** * Returns the difference of the arguments, * throwing an exception if the result overflows an {@code int}. * * @param x the first value * @param y the second value to subtract from the first * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#subtractExact(int,int) * @since 1.8 */ public static int subtractExact(int x, int y) { return Math.subtractExact(x, y); } /** * Returns the difference of the arguments, * throwing an exception if the result overflows a {@code long}. * * @param x the first value * @param y the second value to subtract from the first * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#subtractExact(long,long) * @since 1.8 */ public static long subtractExact(long x, long y) { return Math.subtractExact(x, y); } /** * Returns the product of the arguments, * throwing an exception if the result overflows an {@code int}. * * @param x the first value * @param y the second value * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#multiplyExact(int,int) * @since 1.8 */ public static int multiplyExact(int x, int y) { return Math.multiplyExact(x, y); } /** * Returns the product of the arguments, throwing an exception if the result * overflows a {@code long}. * * @param x the first value * @param y the second value * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#multiplyExact(long,int) * @since 9 */ public static long multiplyExact(long x, int y) { return Math.multiplyExact(x, y); } /** * Returns the product of the arguments, * throwing an exception if the result overflows a {@code long}. * * @param x the first value * @param y the second value * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#multiplyExact(long,long) * @since 1.8 */ public static long multiplyExact(long x, long y) { return Math.multiplyExact(x, y); } /** * Returns the argument incremented by one, * throwing an exception if the result overflows an {@code int}. * The overflow only occurs for {@linkplain Integer#MAX_VALUE the maximum value}. * * @param a the value to increment * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#incrementExact(int) * @since 14 */ public static int incrementExact(int a) { return Math.incrementExact(a); } /** * Returns the argument incremented by one, * throwing an exception if the result overflows a {@code long}. * The overflow only occurs for {@linkplain Long#MAX_VALUE the maximum value}. * * @param a the value to increment * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#incrementExact(long) * @since 14 */ public static long incrementExact(long a) { return Math.incrementExact(a); } /** * Returns the argument decremented by one, * throwing an exception if the result overflows an {@code int}. * The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}. * * @param a the value to decrement * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#decrementExact(int) * @since 14 */ public static int decrementExact(int a) { return Math.decrementExact(a); } /** * Returns the argument decremented by one, * throwing an exception if the result overflows a {@code long}. * The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}. * * @param a the value to decrement * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#decrementExact(long) * @since 14 */ public static long decrementExact(long a) { return Math.decrementExact(a); } /** * Returns the negation of the argument, * throwing an exception if the result overflows an {@code int}. * The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}. * * @param a the value to negate * @return the result * @throws ArithmeticException if the result overflows an int * @see Math#negateExact(int) * @since 14 */ public static int negateExact(int a) { return Math.negateExact(a); } /** * Returns the negation of the argument, * throwing an exception if the result overflows a {@code long}. * The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}. * * @param a the value to negate * @return the result * @throws ArithmeticException if the result overflows a long * @see Math#negateExact(long) * @since 14 */ public static long negateExact(long a) { return Math.negateExact(a); } /** * Returns the value of the {@code long} argument, throwing an exception * if the value overflows an {@code int}. * * @param value the long value * @return the argument as an int * @throws ArithmeticException if the {@code argument} overflows an int * @see Math#toIntExact(long) * @since 1.8 */ public static int toIntExact(long value) { return Math.toIntExact(value); } /** * Returns the exact mathematical product of the arguments. * * @param x the first value * @param y the second value * @return the result * @see Math#multiplyFull(int,int) * @since 9 */ public static long multiplyFull(int x, int y) { return Math.multiplyFull(x, y); } /** * Returns as a {@code long} the most significant 64 bits of the 128-bit * product of two 64-bit factors. * * @param x the first value * @param y the second value * @return the result * @see Math#multiplyHigh(long,long) * @since 9 */ public static long multiplyHigh(long x, long y) { return Math.multiplyHigh(x, y); } /** * Returns the largest (closest to positive infinity) * {@code int} value that is less than or equal to the algebraic quotient. * There is one special case, if the dividend is the * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1}, * then integer overflow occurs and * the result is equal to the {@code Integer.MIN_VALUE}. * <p> * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and * a comparison to the integer division {@code /} operator. * * @param x the dividend * @param y the divisor * @return the largest (closest to positive infinity) * {@code int} value that is less than or equal to the algebraic quotient. * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorDiv(int, int) * @see Math#floor(double) * @since 1.8 */ public static int floorDiv(int x, int y) { return Math.floorDiv(x, y); } /** * Returns the largest (closest to positive infinity) * {@code long} value that is less than or equal to the algebraic quotient. * There is one special case, if the dividend is the * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, * then integer overflow occurs and * the result is equal to {@code Long.MIN_VALUE}. * <p> * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and * a comparison to the integer division {@code /} operator. * * @param x the dividend * @param y the divisor * @return the largest (closest to positive infinity) * {@code int} value that is less than or equal to the algebraic quotient. * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorDiv(long, int) * @see Math#floor(double) * @since 9 */ public static long floorDiv(long x, int y) { return Math.floorDiv(x, y); } /** * Returns the largest (closest to positive infinity) * {@code long} value that is less than or equal to the algebraic quotient. * There is one special case, if the dividend is the * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, * then integer overflow occurs and * the result is equal to the {@code Long.MIN_VALUE}. * <p> * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and * a comparison to the integer division {@code /} operator. * * @param x the dividend * @param y the divisor * @return the largest (closest to positive infinity) * {@code long} value that is less than or equal to the algebraic quotient. * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorDiv(long, long) * @see Math#floor(double) * @since 1.8 */ public static long floorDiv(long x, long y) { return Math.floorDiv(x, y); } /** * Returns the floor modulus of the {@code int} arguments. * <p> * The floor modulus is {@code x - (floorDiv(x, y) * y)}, * has the same sign as the divisor {@code y}, and * is in the range of {@code -abs(y) < r < +abs(y)}. * <p> * The relationship between {@code floorDiv} and {@code floorMod} is such that: * <ul> * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} * </ul> * <p> * See {@link Math#floorMod(int, int) Math.floorMod} for examples and * a comparison to the {@code %} operator. * * @param x the dividend * @param y the divisor * @return the floor modulus {@code x - (floorDiv(x, y) * y)} * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorMod(int, int) * @see StrictMath#floorDiv(int, int) * @since 1.8 */ public static int floorMod(int x, int y) { return Math.floorMod(x , y); } /** * Returns the floor modulus of the {@code long} and {@code int} arguments. * <p> * The floor modulus is {@code x - (floorDiv(x, y) * y)}, * has the same sign as the divisor {@code y}, and * is in the range of {@code -abs(y) < r < +abs(y)}. * * <p> * The relationship between {@code floorDiv} and {@code floorMod} is such that: * <ul> * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} * </ul> * <p> * See {@link Math#floorMod(int, int) Math.floorMod} for examples and * a comparison to the {@code %} operator. * * @param x the dividend * @param y the divisor * @return the floor modulus {@code x - (floorDiv(x, y) * y)} * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorMod(long, int) * @see StrictMath#floorDiv(long, int) * @since 9 */ public static int floorMod(long x, int y) { return Math.floorMod(x , y); } /** * Returns the floor modulus of the {@code long} arguments. * <p> * The floor modulus is {@code x - (floorDiv(x, y) * y)}, * has the same sign as the divisor {@code y}, and * is in the range of {@code -abs(y) < r < +abs(y)}. * <p> * The relationship between {@code floorDiv} and {@code floorMod} is such that: * <ul> * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} * </ul> * <p> * See {@link Math#floorMod(int, int) Math.floorMod} for examples and * a comparison to the {@code %} operator. * * @param x the dividend * @param y the divisor * @return the floor modulus {@code x - (floorDiv(x, y) * y)} * @throws ArithmeticException if the divisor {@code y} is zero * @see Math#floorMod(long, long) * @see StrictMath#floorDiv(long, long) * @since 1.8 */ public static long floorMod(long x, long y) { return Math.floorMod(x, y); } /** * Returns the absolute value of an {@code int} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * * <p>Note that if the argument is equal to the value of {@link * Integer#MIN_VALUE}, the most negative representable {@code int} * value, the result is that same value, which is negative. In * contrast, the {@link StrictMath#absExact(int)} method throws an * {@code ArithmeticException} for this value. * * @param a the argument whose absolute value is to be determined. * @return the absolute value of the argument. * @see Math#absExact(int) */ public static int abs(int a) { return Math.abs(a); } /** * Returns the mathematical absolute value of an {@code int} value * if it is exactly representable as an {@code int}, throwing * {@code ArithmeticException} if the result overflows the * positive {@code int} range. * * <p>Since the range of two's complement integers is asymmetric * with one additional negative value (JLS {@jls 4.2.1}), the * mathematical absolute value of {@link Integer#MIN_VALUE} * overflows the positive {@code int} range, so an exception is * thrown for that argument. * * @param a the argument whose absolute value is to be determined * @return the absolute value of the argument, unless overflow occurs * @throws ArithmeticException if the argument is {@link Integer#MIN_VALUE} * @see Math#abs(int) * @see Math#absExact(int) * @since 15 */ public static int absExact(int a) { return Math.absExact(a); } /** * Returns the absolute value of a {@code long} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * * <p>Note that if the argument is equal to the value of {@link * Long#MIN_VALUE}, the most negative representable {@code long} * value, the result is that same value, which is negative. In * contrast, the {@link StrictMath#absExact(long)} method throws * an {@code ArithmeticException} for this value. * * @param a the argument whose absolute value is to be determined. * @return the absolute value of the argument. * @see Math#absExact(long) */ public static long abs(long a) { return Math.abs(a); } /** * Returns the mathematical absolute value of an {@code long} value * if it is exactly representable as an {@code long}, throwing * {@code ArithmeticException} if the result overflows the * positive {@code long} range. * * <p>Since the range of two's complement integers is asymmetric * with one additional negative value (JLS {@jls 4.2.1}), the * mathematical absolute value of {@link Long#MIN_VALUE} overflows * the positive {@code long} range, so an exception is thrown for * that argument. * * @param a the argument whose absolute value is to be determined * @return the absolute value of the argument, unless overflow occurs * @throws ArithmeticException if the argument is {@link Long#MIN_VALUE} * @see Math#abs(long) * @see Math#absExact(long) * @since 15 */ public static long absExact(long a) { return Math.absExact(a); } /** * Returns the absolute value of a {@code float} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * Special cases: * <ul><li>If the argument is positive zero or negative zero, the * result is positive zero. * <li>If the argument is infinite, the result is positive infinity. * <li>If the argument is NaN, the result is NaN.</ul> * * @apiNote As implied by the above, one valid implementation of * this method is given by the expression below which computes a * {@code float} with the same exponent and significand as the * argument but with a guaranteed zero sign bit indicating a * positive value: <br> * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))} * * @param a the argument whose absolute value is to be determined * @return the absolute value of the argument. */ public static float abs(float a) { return Math.abs(a); } /** * Returns the absolute value of a {@code double} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * Special cases: * <ul><li>If the argument is positive zero or negative zero, the result * is positive zero. * <li>If the argument is infinite, the result is positive infinity. * <li>If the argument is NaN, the result is NaN.</ul> * * @apiNote As implied by the above, one valid implementation of * this method is given by the expression below which computes a * {@code double} with the same exponent and significand as the * argument but with a guaranteed zero sign bit indicating a * positive value: <br> * {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)} * * @param a the argument whose absolute value is to be determined * @return the absolute value of the argument. */ public static double abs(double a) { return Math.abs(a); } /** * Returns the greater of two {@code int} values. That is, the * result is the argument closer to the value of * {@link Integer#MAX_VALUE}. If the arguments have the same value, * the result is that same value. * * @param a an argument. * @param b another argument. * @return the larger of {@code a} and {@code b}. */ @IntrinsicCandidate public static int max(int a, int b) { return Math.max(a, b); } /** * Returns the greater of two {@code long} values. That is, the * result is the argument closer to the value of * {@link Long#MAX_VALUE}. If the arguments have the same value, * the result is that same value. * * @param a an argument. * @param b another argument. * @return the larger of {@code a} and {@code b}. */ public static long max(long a, long b) { return Math.max(a, b); } /** * Returns the greater of two {@code float} values. That is, * the result is the argument closer to positive infinity. If the * arguments have the same value, the result is that same * value. If either value is NaN, then the result is NaN. Unlike * the numerical comparison operators, this method considers * negative zero to be strictly smaller than positive zero. If one * argument is positive zero and the other negative zero, the * result is positive zero. * * @param a an argument. * @param b another argument. * @return the larger of {@code a} and {@code b}. */ @IntrinsicCandidate public static float max(float a, float b) { return Math.max(a, b); } /** * Returns the greater of two {@code double} values. That * is, the result is the argument closer to positive infinity. If * the arguments have the same value, the result is that same * value. If either value is NaN, then the result is NaN. Unlike * the numerical comparison operators, this method considers * negative zero to be strictly smaller than positive zero. If one * argument is positive zero and the other negative zero, the * result is positive zero. * * @param a an argument. * @param b another argument. * @return the larger of {@code a} and {@code b}. */ @IntrinsicCandidate public static double max(double a, double b) { return Math.max(a, b); } /** * Returns the smaller of two {@code int} values. That is, * the result the argument closer to the value of * {@link Integer#MIN_VALUE}. If the arguments have the same * value, the result is that same value. * * @param a an argument. * @param b another argument. * @return the smaller of {@code a} and {@code b}. */ @IntrinsicCandidate public static int min(int a, int b) { return Math.min(a, b); } /** * Returns the smaller of two {@code long} values. That is, * the result is the argument closer to the value of * {@link Long#MIN_VALUE}. If the arguments have the same * value, the result is that same value. * * @param a an argument. * @param b another argument. * @return the smaller of {@code a} and {@code b}. */ public static long min(long a, long b) { return Math.min(a, b); } /** * Returns the smaller of two {@code float} values. That is, * the result is the value closer to negative infinity. If the * arguments have the same value, the result is that same * value. If either value is NaN, then the result is NaN. Unlike * the numerical comparison operators, this method considers * negative zero to be strictly smaller than positive zero. If * one argument is positive zero and the other is negative zero, * the result is negative zero. * * @param a an argument. * @param b another argument. * @return the smaller of {@code a} and {@code b.} */ @IntrinsicCandidate public static float min(float a, float b) { return Math.min(a, b); } /** * Returns the smaller of two {@code double} values. That * is, the result is the value closer to negative infinity. If the * arguments have the same value, the result is that same * value. If either value is NaN, then the result is NaN. Unlike * the numerical comparison operators, this method considers * negative zero to be strictly smaller than positive zero. If one * argument is positive zero and the other is negative zero, the * result is negative zero. * * @param a an argument. * @param b another argument. * @return the smaller of {@code a} and {@code b}. */ @IntrinsicCandidate public static double min(double a, double b) { return Math.min(a, b); } /** * Returns the fused multiply add of the three arguments; that is, * returns the exact product of the first two arguments summed * with the third argument and then rounded once to the nearest * {@code double}. * * The rounding is done using the {@linkplain * java.math.RoundingMode#HALF_EVEN round to nearest even * rounding mode}. * * In contrast, if {@code a * b + c} is evaluated as a regular * floating-point expression, two rounding errors are involved, * the first for the multiply operation, the second for the * addition operation. * * <p>Special cases: * <ul> * <li> If any argument is NaN, the result is NaN. * * <li> If one of the first two arguments is infinite and the * other is zero, the result is NaN. * * <li> If the exact product of the first two arguments is infinite * (in other words, at least one of the arguments is infinite and * the other is neither zero nor NaN) and the third argument is an * infinity of the opposite sign, the result is NaN. * * </ul> * * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same * result as ({@code a + c}). However, * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the * same result as ({@code a * b}) since * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is * equivalent to ({@code a * b}) however. * * @apiNote This method corresponds to the fusedMultiplyAdd * operation defined in IEEE 754-2008. * * @param a a value * @param b a value * @param c a value * * @return (<i>a</i> × <i>b</i> + <i>c</i>) * computed, as if with unlimited range and precision, and rounded * once to the nearest {@code double} value * * @since 9 */ public static double fma(double a, double b, double c) { return Math.fma(a, b, c); } /** * Returns the fused multiply add of the three arguments; that is, * returns the exact product of the first two arguments summed * with the third argument and then rounded once to the nearest * {@code float}. * * The rounding is done using the {@linkplain * java.math.RoundingMode#HALF_EVEN round to nearest even * rounding mode}. * * In contrast, if {@code a * b + c} is evaluated as a regular * floating-point expression, two rounding errors are involved, * the first for the multiply operation, the second for the * addition operation. * * <p>Special cases: * <ul> * <li> If any argument is NaN, the result is NaN. * * <li> If one of the first two arguments is infinite and the * other is zero, the result is NaN. * * <li> If the exact product of the first two arguments is infinite * (in other words, at least one of the arguments is infinite and * the other is neither zero nor NaN) and the third argument is an * infinity of the opposite sign, the result is NaN. * * </ul> * * <p>Note that {@code fma(a, 1.0f, c)} returns the same * result as ({@code a + c}). However, * {@code fma(a, b, +0.0f)} does <em>not</em> always return the * same result as ({@code a * b}) since * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is * equivalent to ({@code a * b}) however. * * @apiNote This method corresponds to the fusedMultiplyAdd * operation defined in IEEE 754-2008. * * @param a a value * @param b a value * @param c a value * * @return (<i>a</i> × <i>b</i> + <i>c</i>) * computed, as if with unlimited range and precision, and rounded * once to the nearest {@code float} value * * @since 9 */ public static float fma(float a, float b, float c) { return Math.fma(a, b, c); } /** * Returns the size of an ulp of the argument. An ulp, unit in * the last place, of a {@code double} value is the positive * distance between this floating-point value and the {@code * double} value next larger in magnitude. Note that for non-NaN * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, then the result is NaN. * <li> If the argument is positive or negative infinity, then the * result is positive infinity. * <li> If the argument is positive or negative zero, then the result is * {@code Double.MIN_VALUE}. * <li> If the argument is ±{@code Double.MAX_VALUE}, then * the result is equal to 2<sup>971</sup>. * </ul> * * @param d the floating-point value whose ulp is to be returned * @return the size of an ulp of the argument * @author Joseph D. Darcy * @since 1.5 */ public static double ulp(double d) { return Math.ulp(d); } /** * Returns the size of an ulp of the argument. An ulp, unit in * the last place, of a {@code float} value is the positive * distance between this floating-point value and the {@code * float} value next larger in magnitude. Note that for non-NaN * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, then the result is NaN. * <li> If the argument is positive or negative infinity, then the * result is positive infinity. * <li> If the argument is positive or negative zero, then the result is * {@code Float.MIN_VALUE}. * <li> If the argument is ±{@code Float.MAX_VALUE}, then * the result is equal to 2<sup>104</sup>. * </ul> * * @param f the floating-point value whose ulp is to be returned * @return the size of an ulp of the argument * @author Joseph D. Darcy * @since 1.5 */ public static float ulp(float f) { return Math.ulp(f); } /** * Returns the signum function of the argument; zero if the argument * is zero, 1.0 if the argument is greater than zero, -1.0 if the * argument is less than zero. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, then the result is NaN. * <li> If the argument is positive zero or negative zero, then the * result is the same as the argument. * </ul> * * @param d the floating-point value whose signum is to be returned * @return the signum function of the argument * @author Joseph D. Darcy * @since 1.5 */ public static double signum(double d) { return Math.signum(d); } /** * Returns the signum function of the argument; zero if the argument * is zero, 1.0f if the argument is greater than zero, -1.0f if the * argument is less than zero. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, then the result is NaN. * <li> If the argument is positive zero or negative zero, then the * result is the same as the argument. * </ul> * * @param f the floating-point value whose signum is to be returned * @return the signum function of the argument * @author Joseph D. Darcy * @since 1.5 */ public static float signum(float f) { return Math.signum(f); } /** * Returns the hyperbolic sine of a {@code double} value. * The hyperbolic sine of <i>x</i> is defined to be * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 * where <i>e</i> is {@linkplain Math#E Euler's number}. * * <p>Special cases: * <ul> * * <li>If the argument is NaN, then the result is NaN. * * <li>If the argument is infinite, then the result is an infinity * with the same sign as the argument. * * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * * </ul> * * @param x The number whose hyperbolic sine is to be returned. * @return The hyperbolic sine of {@code x}. * @since 1.5 */ public static native double sinh(double x); /** * Returns the hyperbolic cosine of a {@code double} value. * The hyperbolic cosine of <i>x</i> is defined to be * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 * where <i>e</i> is {@linkplain Math#E Euler's number}. * * <p>Special cases: * <ul> * * <li>If the argument is NaN, then the result is NaN. * * <li>If the argument is infinite, then the result is positive * infinity. * * <li>If the argument is zero, then the result is {@code 1.0}. * * </ul> * * @param x The number whose hyperbolic cosine is to be returned. * @return The hyperbolic cosine of {@code x}. * @since 1.5 */ public static native double cosh(double x); /** * Returns the hyperbolic tangent of a {@code double} value. * The hyperbolic tangent of <i>x</i> is defined to be * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), * in other words, {@linkplain Math#sinh * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note * that the absolute value of the exact tanh is always less than * 1. * * <p>Special cases: * <ul> * * <li>If the argument is NaN, then the result is NaN. * * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * * <li>If the argument is positive infinity, then the result is * {@code +1.0}. * * <li>If the argument is negative infinity, then the result is * {@code -1.0}. * * </ul> * * @param x The number whose hyperbolic tangent is to be returned. * @return The hyperbolic tangent of {@code x}. * @since 1.5 */ public static native double tanh(double x); /** * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) * without intermediate overflow or underflow. * * <p>Special cases: * <ul> * * <li> If either argument is infinite, then the result * is positive infinity. * * <li> If either argument is NaN and neither argument is infinite, * then the result is NaN. * * <li> If both arguments are zero, the result is positive zero. * </ul> * * @param x a value * @param y a value * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) * without intermediate overflow or underflow * @since 1.5 */ public static double hypot(double x, double y) { return FdLibm.Hypot.compute(x, y); } /** * Returns <i>e</i><sup>x</sup> -1. Note that for values of * <i>x</i> near 0, the exact sum of * {@code expm1(x)} + 1 is much closer to the true * result of <i>e</i><sup>x</sup> than {@code exp(x)}. * * <p>Special cases: * <ul> * <li>If the argument is NaN, the result is NaN. * * <li>If the argument is positive infinity, then the result is * positive infinity. * * <li>If the argument is negative infinity, then the result is * -1.0. * * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * * </ul> * * @param x the exponent to raise <i>e</i> to in the computation of * <i>e</i><sup>{@code x}</sup> -1. * @return the value <i>e</i><sup>{@code x}</sup> - 1. * @since 1.5 */ public static native double expm1(double x); /** * Returns the natural logarithm of the sum of the argument and 1. * Note that for small values {@code x}, the result of * {@code log1p(x)} is much closer to the true result of ln(1 * + {@code x}) than the floating-point evaluation of * {@code log(1.0+x)}. * * <p>Special cases: * <ul> * * <li>If the argument is NaN or less than -1, then the result is * NaN. * * <li>If the argument is positive infinity, then the result is * positive infinity. * * <li>If the argument is negative one, then the result is * negative infinity. * * <li>If the argument is zero, then the result is a zero with the * same sign as the argument. * * </ul> * * @param x a value * @return the value ln({@code x} + 1), the natural * log of {@code x} + 1 * @since 1.5 */ public static native double log1p(double x); /** * Returns the first floating-point argument with the sign of the * second floating-point argument. For this method, a NaN * {@code sign} argument is always treated as if it were * positive. * * @param magnitude the parameter providing the magnitude of the result * @param sign the parameter providing the sign of the result * @return a value with the magnitude of {@code magnitude} * and the sign of {@code sign}. * @since 1.6 */ public static double copySign(double magnitude, double sign) { return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign)); } /** * Returns the first floating-point argument with the sign of the * second floating-point argument. For this method, a NaN * {@code sign} argument is always treated as if it were * positive. * * @param magnitude the parameter providing the magnitude of the result * @param sign the parameter providing the sign of the result * @return a value with the magnitude of {@code magnitude} * and the sign of {@code sign}. * @since 1.6 */ public static float copySign(float magnitude, float sign) { return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign)); } /** * Returns the unbiased exponent used in the representation of a * {@code float}. Special cases: * * <ul> * <li>If the argument is NaN or infinite, then the result is * {@link Float#MAX_EXPONENT} + 1. * <li>If the argument is zero or subnormal, then the result is * {@link Float#MIN_EXPONENT} -1. * </ul> * @param f a {@code float} value * @return the unbiased exponent of the argument * @since 1.6 */ public static int getExponent(float f) { return Math.getExponent(f); } /** * Returns the unbiased exponent used in the representation of a * {@code double}. Special cases: * * <ul> * <li>If the argument is NaN or infinite, then the result is * {@link Double#MAX_EXPONENT} + 1. * <li>If the argument is zero or subnormal, then the result is * {@link Double#MIN_EXPONENT} -1. * </ul> * @param d a {@code double} value * @return the unbiased exponent of the argument * @since 1.6 */ public static int getExponent(double d) { return Math.getExponent(d); } /** * Returns the floating-point number adjacent to the first * argument in the direction of the second argument. If both * arguments compare as equal the second argument is returned. * * <p>Special cases: * <ul> * <li> If either argument is a NaN, then NaN is returned. * * <li> If both arguments are signed zeros, {@code direction} * is returned unchanged (as implied by the requirement of * returning the second argument if the arguments compare as * equal). * * <li> If {@code start} is * ±{@link Double#MIN_VALUE} and {@code direction} * has a value such that the result should have a smaller * magnitude, then a zero with the same sign as {@code start} * is returned. * * <li> If {@code start} is infinite and * {@code direction} has a value such that the result should * have a smaller magnitude, {@link Double#MAX_VALUE} with the * same sign as {@code start} is returned. * * <li> If {@code start} is equal to ± * {@link Double#MAX_VALUE} and {@code direction} has a * value such that the result should have a larger magnitude, an * infinity with same sign as {@code start} is returned. * </ul> * * @param start starting floating-point value * @param direction value indicating which of * {@code start}'s neighbors or {@code start} should * be returned * @return The floating-point number adjacent to {@code start} in the * direction of {@code direction}. * @since 1.6 */ public static double nextAfter(double start, double direction) { return Math.nextAfter(start, direction); } /** * Returns the floating-point number adjacent to the first * argument in the direction of the second argument. If both * arguments compare as equal a value equivalent to the second argument * is returned. * * <p>Special cases: * <ul> * <li> If either argument is a NaN, then NaN is returned. * * <li> If both arguments are signed zeros, a value equivalent * to {@code direction} is returned. * * <li> If {@code start} is * ±{@link Float#MIN_VALUE} and {@code direction} * has a value such that the result should have a smaller * magnitude, then a zero with the same sign as {@code start} * is returned. * * <li> If {@code start} is infinite and * {@code direction} has a value such that the result should * have a smaller magnitude, {@link Float#MAX_VALUE} with the * same sign as {@code start} is returned. * * <li> If {@code start} is equal to ± * {@link Float#MAX_VALUE} and {@code direction} has a * value such that the result should have a larger magnitude, an * infinity with same sign as {@code start} is returned. * </ul> * * @param start starting floating-point value * @param direction value indicating which of * {@code start}'s neighbors or {@code start} should * be returned * @return The floating-point number adjacent to {@code start} in the * direction of {@code direction}. * @since 1.6 */ public static float nextAfter(float start, double direction) { return Math.nextAfter(start, direction); } /** * Returns the floating-point value adjacent to {@code d} in * the direction of positive infinity. This method is * semantically equivalent to {@code nextAfter(d, * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} * implementation may run faster than its equivalent * {@code nextAfter} call. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, the result is NaN. * * <li> If the argument is positive infinity, the result is * positive infinity. * * <li> If the argument is zero, the result is * {@link Double#MIN_VALUE} * * </ul> * * @param d starting floating-point value * @return The adjacent floating-point value closer to positive * infinity. * @since 1.6 */ public static double nextUp(double d) { return Math.nextUp(d); } /** * Returns the floating-point value adjacent to {@code f} in * the direction of positive infinity. This method is * semantically equivalent to {@code nextAfter(f, * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} * implementation may run faster than its equivalent * {@code nextAfter} call. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, the result is NaN. * * <li> If the argument is positive infinity, the result is * positive infinity. * * <li> If the argument is zero, the result is * {@link Float#MIN_VALUE} * * </ul> * * @param f starting floating-point value * @return The adjacent floating-point value closer to positive * infinity. * @since 1.6 */ public static float nextUp(float f) { return Math.nextUp(f); } /** * Returns the floating-point value adjacent to {@code d} in * the direction of negative infinity. This method is * semantically equivalent to {@code nextAfter(d, * Double.NEGATIVE_INFINITY)}; however, a * {@code nextDown} implementation may run faster than its * equivalent {@code nextAfter} call. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, the result is NaN. * * <li> If the argument is negative infinity, the result is * negative infinity. * * <li> If the argument is zero, the result is * {@code -Double.MIN_VALUE} * * </ul> * * @param d starting floating-point value * @return The adjacent floating-point value closer to negative * infinity. * @since 1.8 */ public static double nextDown(double d) { return Math.nextDown(d); } /** * Returns the floating-point value adjacent to {@code f} in * the direction of negative infinity. This method is * semantically equivalent to {@code nextAfter(f, * Float.NEGATIVE_INFINITY)}; however, a * {@code nextDown} implementation may run faster than its * equivalent {@code nextAfter} call. * * <p>Special Cases: * <ul> * <li> If the argument is NaN, the result is NaN. * * <li> If the argument is negative infinity, the result is * negative infinity. * * <li> If the argument is zero, the result is * {@code -Float.MIN_VALUE} * * </ul> * * @param f starting floating-point value * @return The adjacent floating-point value closer to negative * infinity. * @since 1.8 */ public static float nextDown(float f) { return Math.nextDown(f); } /** * Returns {@code d} × 2<sup>{@code scaleFactor}</sup> * rounded as if performed by a single correctly rounded * floating-point multiply. If the exponent of the result is * between {@link Double#MIN_EXPONENT} and {@link * Double#MAX_EXPONENT}, the answer is calculated exactly. If the * exponent of the result would be larger than {@code * Double.MAX_EXPONENT}, an infinity is returned. Note that if * the result is subnormal, precision may be lost; that is, when * {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n), * -n)} may not equal <i>x</i>. When the result is non-NaN, the * result has the same sign as {@code d}. * * <p>Special cases: * <ul> * <li> If the first argument is NaN, NaN is returned. * <li> If the first argument is infinite, then an infinity of the * same sign is returned. * <li> If the first argument is zero, then a zero of the same * sign is returned. * </ul> * * @param d number to be scaled by a power of two. * @param scaleFactor power of 2 used to scale {@code d} * @return {@code d} × 2<sup>{@code scaleFactor}</sup> * @since 1.6 */ public static double scalb(double d, int scaleFactor) { return Math.scalb(d, scaleFactor); } /** * Returns {@code f} × 2<sup>{@code scaleFactor}</sup> * rounded as if performed by a single correctly rounded * floating-point multiply. If the exponent of the result is * between {@link Float#MIN_EXPONENT} and {@link * Float#MAX_EXPONENT}, the answer is calculated exactly. If the * exponent of the result would be larger than {@code * Float.MAX_EXPONENT}, an infinity is returned. Note that if the * result is subnormal, precision may be lost; that is, when * {@code scalb(x, n)} is subnormal, {@code scalb(scalb(x, n), * -n)} may not equal <i>x</i>. When the result is non-NaN, the * result has the same sign as {@code f}. * * <p>Special cases: * <ul> * <li> If the first argument is NaN, NaN is returned. * <li> If the first argument is infinite, then an infinity of the * same sign is returned. * <li> If the first argument is zero, then a zero of the same * sign is returned. * </ul> * * @param f number to be scaled by a power of two. * @param scaleFactor power of 2 used to scale {@code f} * @return {@code f} × 2<sup>{@code scaleFactor}</sup> * @since 1.6 */ public static float scalb(float f, int scaleFactor) { return Math.scalb(f, scaleFactor); } }

**⏎ java/lang/StrictMath.java**

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