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/* * @(#)StrictMath.java 1.29 05/11/17 * * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms. */ package java.lang; import java.util.Random; import sun.misc.FpUtils; /** * 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 * 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</code> as the package "Freely Distributable Math * Library," <a * href="ftp://ftp.netlib.org/fdlibm.tar"><code>fdlibm</code></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</code> version 5.3. 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>). The methods which require <code>fdlibm</code> * semantics are <code>sin</code>, <code>cos</code>, <code>tan</code>, * <code>asin</code>, <code>acos</code>, <code>atan</code>, * <code>exp</code>, <code>log</code>, <code>log10</code>, * <code>cbrt</code>, <code>atan2</code>, <code>pow</code>, * <code>sinh</code>, <code>cosh</code>, <code>tanh</code>, * <code>hypot</code>, <code>expm1</code>, and <code>log1p</code>. * * @author unascribed * @author Joseph D. Darcy * @version 1.29, 11/17/05 * @since 1.3 */ public final class StrictMath { /** * 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 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.</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.</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 strictfp 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 strictfp 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 value * @return the value ln <code>a</code>, the natural logarithm of * <code>a</code>. */ public static native double log(double a); /** * Returns the base 10 logarithm 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. * <li> If the argument is equal to 10<sup><i>n</i></sup> for * integer <i>n</i>, then the result is <i>n</i>. * </ul> * * @param a a value * @return the base 10 logarithm of <code>a</code>. * @since 1.5 */ public static native double log10(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 positive square root of <code>a</code>. */ public static native double sqrt(double a); /** * Returns the cube root of a <code>double</code> value. For * positive finite <code>x</code>, <code>cbrt(-x) == * -cbrt(x)</code>; 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</code>. * @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 * <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 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)</code> is exactly the * value of <code>-StrictMath.floor(-x)</code>. * * @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 native double ceil(double a); /** * Returns the largest (closest to positive infinity) * <code>double</code> 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 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. * @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 = FpUtils.rawCopySign(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>, <code>y</code>) to polar * coordinates (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 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 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 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 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; } /** * Returns the size of an ulp of the argument. An ulp of a * <code>double</code> value is the positive distance between this * floating-point value and the <code>double</code> 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</code>. * <li> If the argument is ±<code>Double.MAX_VALUE</code>, 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 sun.misc.FpUtils.ulp(d); } /** * Returns the size of an ulp of the argument. An ulp of a * <code>float</code> value is the positive distance between this * floating-point value and the <code>float</code> 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</code>. * <li> If the argument is ±<code>Float.MAX_VALUE</code>, 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 sun.misc.FpUtils.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 sun.misc.FpUtils.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 sun.misc.FpUtils.signum(f); } /** * Returns the hyperbolic sine of a <code>double</code> 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</code>. * @since 1.5 */ public static native double sinh(double x); /** * Returns the hyperbolic cosine of a <code>double</code> 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</code>. * * </ul> * * @param x The number whose hyperbolic cosine is to be returned. * @return The hyperbolic cosine of <code>x</code>. * @since 1.5 */ public static native double cosh(double x); /** * Returns the hyperbolic tangent of a <code>double</code> 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</code>. * * <li>If the argument is negative infinity, then the result is * <code>-1.0</code>. * * </ul> * * @param x The number whose hyperbolic tangent is to be returned. * @return The hyperbolic tangent of <code>x</code>. * @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. * * </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 native double hypot(double x, double y); /** * Returns <i>e</i><sup>x</sup> -1. Note that for values of * <i>x</i> near 0, the exact sum of * <code>expm1(x)</code> + 1 is much closer to the true * result of <i>e</i><sup>x</sup> than <code>exp(x)</code>. * * <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</code></sup> -1. * @return the value <i>e</i><sup><code>x</code></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</code>, the result of * <code>log1p(x)</code> is much closer to the true result of ln(1 * + <code>x</code>) than the floating-point evaluation of * <code>log(1.0+x)</code>. * * <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</code> + 1), the natural * log of <code>x</code> + 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 sun.misc.FpUtils.copySign(magnitude, 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 sun.misc.FpUtils.copySign(magnitude, 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 * @since 1.6 */ public static int getExponent(float f) { return sun.misc.FpUtils.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 * @since 1.6 */ public static int getExponent(double d) { return sun.misc.FpUtils.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 sun.misc.FpUtils.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 sun.misc.FpUtils.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 sun.misc.FpUtils.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 sun.misc.FpUtils.nextUp(f); } /** * Return {@code d} × * 2<sup>{@code scaleFactor}</sup> rounded as if performed * by a single correctly rounded floating-point multiply to a * member of the double value set. See the Java * Language Specification for a discussion of floating-point * value sets. If the exponent of the result is between {@link * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the * answer is calculated exactly. If the exponent of the result * would be larger than {@code Double.MAX_EXPONENT}, an * infinity is returned. Note that if the result is subnormal, * precision may be lost; that is, when {@code scalb(x, n)} * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal * <i>x</i>. When the result is non-NaN, the result has the same * sign as {@code d}. * *<p> * Special cases: * <ul> * <li> If the first argument is NaN, NaN is returned. * <li> If the first argument is infinite, then an infinity of the * same sign is returned. * <li> If the first argument is zero, then a zero of the same * sign is returned. * </ul> * * @param d number to be scaled by a power of two. * @param scaleFactor power of 2 used to scale {@code d} * @return {@code d} × 2<sup>{@code scaleFactor}</sup> * @since 1.6 */ public static double scalb(double d, int scaleFactor) { return sun.misc.FpUtils.scalb(d, scaleFactor); } /** * Return {@code f} × * 2<sup>{@code scaleFactor}</sup> rounded as if performed * by a single correctly rounded floating-point multiply to a * member of the float value set. See the Java * Language Specification for a discussion of floating-point * value sets. If the exponent of the result is between {@link * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the * answer is calculated exactly. If the exponent of the result * would be larger than {@code Float.MAX_EXPONENT}, an * infinity is returned. Note that if the result is subnormal, * precision may be lost; that is, when {@code scalb(x, n)} * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal * <i>x</i>. When the result is non-NaN, the result has the same * sign as {@code f}. * *<p> * Special cases: * <ul> * <li> If the first argument is NaN, NaN is returned. * <li> If the first argument is infinite, then an infinity of the * same sign is returned. * <li> If the first argument is zero, then a zero of the same * sign is returned. * </ul> * * @param f number to be scaled by a power of two. * @param scaleFactor power of 2 used to scale {@code f} * @return {@code f} × 2<sup>{@code scaleFactor}</sup> * @since 1.6 */ public static float scalb(float f, int scaleFactor) { return sun.misc.FpUtils.scalb(f, scaleFactor); } }
