/* * Copyright (c) 1999, 2012, 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 sun.misc.DoubleConsts; /** * The class {@code StrictMath} contains methods for performing basic * numeric operations such as the elementary exponential, logarithm, * square root, and trigonometric functions. * *

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," {@code fdlibm}. 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. * *

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}. * *

* 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 1.3 */ public final class StrictMath { /** * Don't let anyone instantiate this class. */ private StrictMath() {} /** * The {@code double} value that is closer than any other to * e, the base of the natural logarithms. */ public static final double E = 2.7182818284590452354; /** * The {@code double} value that is closer than any other to * pi, the ratio of the circumference of a circle to its * diameter. */ public static final double PI = 3.14159265358979323846; /** * Returns the trigonometric sine of an angle. Special cases: *

* * @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: * * * @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: * * * @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 -pi/2 through pi/2. Special cases: * * * @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 pi. Special case: * * * @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 -pi/2 through pi/2. Special cases: * * * @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 strictfp double toRadians(double angdeg) { // Do not delegate to Math.toRadians(angdeg) because // this method has the strictfp modifier. return angdeg / 180.0 * PI; } /** * 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 * not 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 strictfp double toDegrees(double angrad) { // Do not delegate to Math.toDegrees(angrad) because // this method has the strictfp modifier. return angrad * 180.0 / PI; } /** * Returns Euler's number e raised to the power of a * {@code double} value. Special cases: * * * @param a the exponent to raise e to. * @return the value e{@code a}, * where e is the base of the natural logarithms. */ public static native double exp(double a); /** * Returns the natural logarithm (base e) of a {@code double} * value. Special cases: * * * @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: * * * * @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: * * 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}. */ 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: * * * * @param a a value. * @return the cube root of {@code a}. * @since 1.5 */ public static native double cbrt(double a); /** * Computes the remainder operation on two arguments as prescribed * by the IEEE 754 standard. * The remainder value is mathematically equal to * f1 - f2 × n, * where n 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 n 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: * * * @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: * 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: * * * @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: * * * @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. * * This method does *not* need to be declared strictfp to get * fully reproducible results. Whether or not a method is * declared strictfp can only make a difference in the * returned result if some operation would overflow or * underflow with strictfp semantics. The operation * (twoToThe52 + a ) cannot overflow since large values of a * are screened out; the add cannot underflow since twoToThe52 * is too large. The subtraction ((twoToThe52 + a ) - * twoToThe52) will be exact as discussed above and thus * cannot overflow or meaningfully underflow. Finally, the * last multiply in the return statement is by plus or minus * 1.0, which is exact too. */ 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 theta from the conversion of rectangular * coordinates ({@code x}, {@code y}) to polar * coordinates (r, theta). * This method computes the phase theta by computing an arc tangent * of {@code y/x} in the range of -pi to pi. Special * cases: * * * @param y the ordinate coordinate * @param x the abscissa coordinate * @return the theta component of the point * (r, theta) * in polar coordinates that corresponds to the point * (x, y) 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: * * * *

(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.) * * @param a base. * @param b the exponent. * @return the value {@code a}{@code b}. */ public static native double pow(double a, double b); /** * Returns the closest {@code int} to the argument, with ties * rounding up. * *

Special cases: *

* * @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 up. * *

Special cases: *

* * @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 Random randomNumberGenerator; private static synchronized Random initRNG() { Random rnd = randomNumberGenerator; return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd; } /** * 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. * *

When this method is first called, it creates a single new * pseudorandom-number generator, exactly as if by the expression * *

{@code new java.util.Random()}
* * This new pseudorandom-number generator is used thereafter for * all calls to this method and is used nowhere else. * *

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() { Random rnd = randomNumberGenerator; if (rnd == null) rnd = initRNG(); return rnd.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,long) * @since 1.8 */ public static long multiplyExact(long x, long y) { return Math.multiplyExact(x, y); } /** * 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 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}. *

* 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 the {@code Long.MIN_VALUE}. *

* 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. *

* 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)}. *

* The relationship between {@code floorDiv} and {@code floorMod} is such that: *

*

* 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} arguments. *

* 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)}. *

* The relationship between {@code floorDiv} and {@code floorMod} is such that: *

*

* 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. * *

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 Math.abs(a); } /** * Returns the absolute value of a {@code long} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * *

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 Math.abs(a); } /** * Returns the absolute value of a {@code float} value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * Special cases: *

* In other words, the result is the same as the value of the expression: *

{@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 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: *

* In other words, the result is the same as the value of the expression: *

{@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. */ 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}. */ 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}. */ 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}. */ 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}. */ 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.} */ 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}. */ public static double min(double a, double b) { return Math.min(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 * x, ulp(-x) == ulp(x). * *

Special Cases: *

* * @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 * x, ulp(-x) == ulp(x). * *

Special Cases: *

* * @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. * *

Special Cases: *

* * @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. * *

Special Cases: *

* * @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 x is defined to be * (ex - e-x)/2 * where e is {@linkplain Math#E Euler's number}. * *

Special cases: *

* * @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 x is defined to be * (ex + e-x)/2 * where e is {@linkplain Math#E Euler's number}. * *

Special cases: *

* * @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 x is defined to be * (ex - e-x)/(ex + e-x), * in other words, {@linkplain Math#sinh * sinh(x)}/{@linkplain Math#cosh cosh(x)}. Note * that the absolute value of the exact tanh is always less than * 1. * *

Special cases: *

* * @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(x2 +y2) * without intermediate overflow or underflow. * *

Special cases: *

* * @param x a value * @param y a value * @return sqrt(x2 +y2) * without intermediate overflow or underflow * @since 1.5 */ public static native double hypot(double x, double y); /** * Returns ex -1. Note that for values of * x near 0, the exact sum of * {@code expm1(x)} + 1 is much closer to the true * result of ex than {@code exp(x)}. * *

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* * @param x the exponent to raise e to in the computation of * e{@code x} -1. * @return the value e{@code x} - 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)}. * *

Special cases: *

* * @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: * * * @param f a {@code float} value * @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: * * * @param d a {@code double} value * @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. * *

Special cases: *

* * @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. * *

Special cases: *

* * @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. * *

Special Cases: *

* * @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. * *

Special Cases: *

* * @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. * *

Special Cases: *

* * @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. * *

Special Cases: *

* * @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{@code scaleFactor} 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 * x. When the result is non-NaN, the result has the same * sign as {@code d}. * *

Special cases: *

* * @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{@code scaleFactor} * @since 1.6 */ public static double scalb(double d, int scaleFactor) { return Math.scalb(d, scaleFactor); } /** * Returns {@code f} × * 2{@code scaleFactor} 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 * x. When the result is non-NaN, the result has the same * sign as {@code f}. * *

Special cases: *

* * @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{@code scaleFactor} * @since 1.6 */ public static float scalb(float f, int scaleFactor) { return Math.scalb(f, scaleFactor); } }