/* * @(#)StrictMath.java 1.18 06/10/10 * * Copyright 1990-2008 Sun Microsystems, Inc. All Rights Reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER * * This program 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. * * This program 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 at /legal/license.txt). * * 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 Sun Microsystems, Inc., 4150 Network Circle, Santa * Clara, CA 95054 or visit www.sun.com if you need additional * information or have any questions. * */ package java.lang; import java.util.Random; /** * The class <code>StrictMath</code> 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 * many 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</code> as the package "Freely Distributable * Math Library" (<code>fdlibm</code>). 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 network library may be found on the World Wide Web at: * <blockquote><pre> * <a href="http://metalab.unc.edu/">http://metalab.unc.edu/</a> * </pre></blockquote> * <p> * The Java math library is defined with respect to the version of * <code>fdlibm</code> dated January 4, 1995. Where * <code>fdlibm</code> provides more than one definition for a * function (such as <code>acos</code>), use the "IEEE 754 core * function" version (residing in a file whose name begins with * the letter <code>e</code>). * * @author unascribed * @version 1.9, 02/02/00 * @since 1.3 */ public final strictfp class StrictMath { /* Work-around for Symbian tool bug. No longer needed. */ private static native void init(); static { init(); } /** * Don't let anyone instantiate this class. */ private StrictMath() {} /** * The <code>double</code> 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</code> 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; /** * 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.</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 an angle, in the range of -<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 an angle, in the range of 0.0 through * <i>pi</i>. Special case: * <ul><li>If the argument is NaN or its absolute value is greater * than 1, then the result is NaN.</ul> * * @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 an angle, in the range of -<i>pi</i>/2 * through <i>pi</i>/2. Special cases: * <ul><li>If the argument is NaN, then the result is NaN. * <li>If the argument is zero, then the result is a zero with the * same sign as the argument.</ul> * * @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</code> * in radians. */ public static double toRadians(double angdeg) { 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 * <i>not</i> expect <code>cos(toRadians(90.0))</code> to exactly * equal <code>0.0</code>. * * @param angrad an angle, in radians * @return the measurement of the angle <code>angrad</code> * in degrees. */ public static double toDegrees(double angrad) { return angrad * 180.0 / PI; } /** * Returns Euler's number <i>e</i> raised to the power of a * <code>double</code> value. Special cases: * <ul><li>If the argument is NaN, the result is NaN. * <li>If the argument is positive infinity, then the result is * positive infinity. * <li>If the argument is negative infinity, then the result is * positive zero.</ul> * * @param a the exponent to raise <i>e</i> to. * @return the value <i>e</i><sup><code>a</code></sup>, * where <i>e</i> is the base of the natural logarithms. */ public static native double exp(double a); /** * Returns the natural logarithm (base <i>e</i>) of a <code>double</code> * value. Special cases: * <ul><li>If the argument is NaN or less than zero, then the result * is NaN. * <li>If the argument is positive infinity, then the result is * positive infinity. * <li>If the argument is positive zero or negative zero, then the * result is negative infinity.</ul> * * @param a a number greater than <code>0.0</code>. * @return the value ln <code>a</code>, the natural logarithm of * <code>a</code>. */ public static native double log(double a); /** * Returns the correctly rounded positive square root of a * <code>double</code> 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</code> value closest to * the true mathematical square root of the argument value. * * @param a a value. * <!--@return the value of √ <code>a</code>.--> * @return the positive square root of <code>a</code>. */ public static native double sqrt(double a); /** * Computes the remainder operation on two arguments as prescribed * by the IEEE 754 standard. * The remainder value is mathematically equal to * <code>f1 - f2</code> × <i>n</i>, * where <i>n</i> is the mathematical integer closest to the exact * mathematical value of the quotient <code>f1/f2</code>, and if two * mathematical integers are equally close to <code>f1/f2</code>, * 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</code> is divided by * <code>f2</code>. */ public static native double IEEEremainder(double f1, double f2); /** * Returns the smallest (closest to negative infinity) * <code>double</code> value that is not less than the argument and is * equal to a mathematical integer. Special cases: * <ul><li>If the argument value is already equal to a mathematical * integer, then the result is the same as the argument. * <li>If the argument is NaN or an infinity or positive zero or negative * zero, then the result is the same as the argument. * <li>If the argument value is less than zero but greater than -1.0, * then the result is negative zero.</ul> * Note that the value of <code>Math.ceil(x)</code> is exactly the * value of <code>-Math.floor(-x)</code>. * * @param a a value. * <!--@return the value ⌈ <code>a</code> ⌉.--> * @return the smallest (closest to negative infinity) * floating-point value that is not less than the argument * and is equal to a mathematical integer. */ public static native double ceil(double a); /** * Returns the largest (closest to positive infinity) * <code>double</code> value that is not greater than 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 <code>double</code> value. * <!--@return the value ⌊ <code>a</code> ⌋.--> * @return the largest (closest to positive infinity) * floating-point value that is not greater than the argument * and is equal to a mathematical integer. */ public static native double floor(double a); /** * Returns the <code>double</code> value that is closest in value * to the argument and is equal to a mathematical integer. If two * <code>double</code> 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</code> that is * equal to a mathematical integer. */ public static native double rint(double a); /** * Converts rectangular coordinates (<code>x</code>, <code>y</code>) * to polar (r, <i>theta</i>). * This method computes the phase <i>theta</i> by computing an arc tangent * of <code>y/x</code> 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</code> 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</code> 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</code> 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</code> value closest to -<i>pi</i>/2. * <li>If both arguments are positive infinity, then the result is the * <code>double</code> 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</code> * 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</code> value * closest to -<i>pi</i>/4. * <li>If both arguments are negative infinity, then the result is the * <code>double</code> value closest to -3*<i>pi</i>/4.</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</code> 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 <tt>ceil</tt>} or, * equivalently, a fixed point of the method {@link #floor * <tt>floor</tt>}. 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<sup>b</sup></code>. */ public static native double pow(double a, double b); /** * Returns the closest <code>int</code> to the argument. The * result is rounded to an integer by adding 1/2, taking the * floor of the result, and casting the result to type <code>int</code>. * In other words, the result is equal to the value of the expression: * <p><pre>(int)Math.floor(a + 0.5f)</pre> * <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</code>, the result is * equal to the value of <code>Integer.MIN_VALUE</code>. * <li>If the argument is positive infinity or any value greater than or * equal to the value of <code>Integer.MAX_VALUE</code>, the result is * equal to the value of <code>Integer.MAX_VALUE</code>.</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</code> value. * @see java.lang.Integer#MAX_VALUE * @see java.lang.Integer#MIN_VALUE */ public static int round(float a) { return (int)floor(a + 0.5f); } /** * Returns the closest <code>long</code> to the argument. The result * is rounded to an integer by adding 1/2, taking the floor of the * result, and casting the result to type <code>long</code>. In other * words, the result is equal to the value of the expression: * <p><pre>(long)Math.floor(a + 0.5d)</pre> * <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</code>, the result is * equal to the value of <code>Long.MIN_VALUE</code>. * <li>If the argument is positive infinity or any value greater than or * equal to the value of <code>Long.MAX_VALUE</code>, the result is * equal to the value of <code>Long.MAX_VALUE</code>.</ul> * * @param a a floating-point value to be rounded to a * <code>long</code>. * @return the value of the argument rounded to the nearest * <code>long</code> value. * @see java.lang.Long#MAX_VALUE * @see java.lang.Long#MIN_VALUE */ public static long round(double a) { return (long)floor(a + 0.5d); } private static Random randomNumberGenerator; private static synchronized void initRNG() { if (randomNumberGenerator == null) randomNumberGenerator = new Random(); } /** * Returns a <code>double</code> value with a positive sign, greater * than or equal to <code>0.0</code> and less than <code>1.0</code>. * 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><pre>new java.util.Random</pre></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</code> greater than or equal * to <code>0.0</code> and less than <code>1.0</code>. * @see java.util.Random#nextDouble() */ public static double random() { if (randomNumberGenerator == null) initRNG(); return randomNumberGenerator.nextDouble(); } /** * Returns the absolute value of an <code>int</code> 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 * <code>Integer.MIN_VALUE</code>, the most negative representable * <code>int</code> 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. * @see java.lang.Integer#MIN_VALUE */ public static int abs(int a) { return (a < 0) ? -a : a; } /** * Returns the absolute value of a <code>long</code> 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 * <code>Long.MIN_VALUE</code>, the most negative representable * <code>long</code> 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. * @see java.lang.Long#MIN_VALUE */ public static long abs(long a) { return (a < 0) ? -a : a; } /** * Returns the absolute value of a <code>float</code> value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * Special cases: * <ul><li>If the argument is positive zero or negative zero, the * result is positive zero. * <li>If the argument is infinite, the result is positive infinity. * <li>If the argument is NaN, the result is NaN.</ul> * In other words, the result is the same as the value of the expression: * <p><pre>Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))</pre> * * @param a the argument whose absolute value is to be determined * @return the absolute value of the argument. */ public static float abs(float a) { return (a <= 0.0F) ? 0.0F - a : a; } /** * Returns the absolute value of a <code>double</code> value. * If the argument is not negative, the argument is returned. * If the argument is negative, the negation of the argument is returned. * Special cases: * <ul><li>If the argument is positive zero or negative zero, the result * is positive zero. * <li>If the argument is infinite, the result is positive infinity. * <li>If the argument is NaN, the result is NaN.</ul> * In other words, the result is the same as the value of the expression: * <p><code>Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)</code> * * @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 (a <= 0.0D) ? 0.0D - a : a; } /** * Returns the greater of two <code>int</code> values. That is, the * result is the argument closer to the value of * <code>Integer.MAX_VALUE</code>. 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</code> and <code>b</code>. * @see java.lang.Long#MAX_VALUE */ public static int max(int a, int b) { return (a >= b) ? a : b; } /** * Returns the greater of two <code>long</code> values. That is, the * result is the argument closer to the value of * <code>Long.MAX_VALUE</code>. 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</code> and <code>b</code>. * @see java.lang.Long#MAX_VALUE */ public static long max(long a, long b) { return (a >= b) ? a : b; } private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f); private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d); /** * Returns the greater of two <code>float</code> 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 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</code> and <code>b</code>. */ public static float max(float a, float b) { if (a != a) return a; // a is NaN if ((a == 0.0f) && (b == 0.0f) && (Float.floatToIntBits(a) == negativeZeroFloatBits)) { return b; } return (a >= b) ? a : b; } /** * Returns the greater of two <code>double</code> 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 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</code> and <code>b</code>. */ public static double max(double a, double b) { if (a != a) return a; // a is NaN if ((a == 0.0d) && (b == 0.0d) && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) { return b; } return (a >= b) ? a : b; } /** * Returns the smaller of two <code>int</code> values. That is, * the result the argument closer to the value of * <code>Integer.MIN_VALUE</code>. 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</code> and <code>b</code>. * @see java.lang.Long#MIN_VALUE */ public static int min(int a, int b) { return (a <= b) ? a : b; } /** * Returns the smaller of two <code>long</code> values. That is, * the result is the argument closer to the value of * <code>Long.MIN_VALUE</code>. 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</code> and <code>b</code>. * @see java.lang.Long#MIN_VALUE */ public static long min(long a, long b) { return (a <= b) ? a : b; } /** * Returns the smaller of two <code>float</code> 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 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</code> and <code>b.</code> */ public static float min(float a, float b) { if (a != a) return a; // a is NaN if ((a == 0.0f) && (b == 0.0f) && (Float.floatToIntBits(b) == negativeZeroFloatBits)) { return b; } return (a <= b) ? a : b; } /** * Returns the smaller of two <code>double</code> 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 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</code> and <code>b</code>. */ public static double min(double a, double b) { if (a != a) return a; // a is NaN if ((a == 0.0d) && (b == 0.0d) && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) { return b; } return (a <= b) ? a : b; } }