diff -r 000000000000 -r cc0d42d2110a emul/src/main/java/java/lang/Math.java --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/emul/src/main/java/java/lang/Math.java Sat Sep 29 10:56:23 2012 +0200 @@ -0,0 +1,1526 @@ +/* + * Copyright (c) 1994, 2011, 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; + + +/** + * The class {@code Math} contains methods for performing basic + * numeric operations such as the elementary exponential, logarithm, + * square root, and trigonometric functions. + * + *
Unlike some of the numeric methods of class + * {@code StrictMath}, all implementations of the equivalent + * functions of class {@code Math} are not defined to return the + * bit-for-bit same results. This relaxation permits + * better-performing implementations where strict reproducibility is + * not required. + * + *
By default many of the {@code Math} methods simply call + * the equivalent method in {@code StrictMath} for their + * implementation. Code generators are encouraged to use + * platform-specific native libraries or microprocessor instructions, + * where available, to provide higher-performance implementations of + * {@code Math} methods. Such higher-performance + * implementations still must conform to the specification for + * {@code Math}. + * + *
The quality of implementation specifications concern two + * properties, accuracy of the returned result and monotonicity of the + * method. Accuracy of the floating-point {@code Math} methods + * is measured in terms of ulps, units in the last place. For + * a given floating-point format, an ulp of a specific real number + * value is the distance between the two floating-point values + * bracketing that numerical value. When discussing the accuracy of a + * method as a whole rather than at a specific argument, the number of + * ulps cited is for the worst-case error at any argument. If a + * method always has an error less than 0.5 ulps, the method always + * returns the floating-point number nearest the exact result; such a + * method is correctly rounded. A correctly rounded method is + * generally the best a floating-point approximation can be; however, + * it is impractical for many floating-point methods to be correctly + * rounded. Instead, for the {@code Math} class, a larger error + * bound of 1 or 2 ulps is allowed for certain methods. Informally, + * with a 1 ulp error bound, when the exact result is a representable + * number, the exact result should be returned as the computed result; + * otherwise, either of the two floating-point values which bracket + * the exact result may be returned. For exact results large in + * magnitude, one of the endpoints of the bracket may be infinite. + * Besides accuracy at individual arguments, maintaining proper + * relations between the method at different arguments is also + * important. Therefore, most methods with more than 0.5 ulp errors + * are required to be semi-monotonic: whenever the mathematical + * function is non-decreasing, so is the floating-point approximation, + * likewise, whenever the mathematical function is non-increasing, so + * is the floating-point approximation. Not all approximations that + * have 1 ulp accuracy will automatically meet the monotonicity + * requirements. + * + * @author unascribed + * @author Joseph D. Darcy + * @since JDK1.0 + */ + +public final class Math { + + /** + * Don't let anyone instantiate this class. + */ + private Math() {} + + /** + * The {@code double} value that is closer than any other to + * 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: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the sine of the argument. + */ + public static double sin(double a) { + return StrictMath.sin(a); // default impl. delegates to StrictMath + } + + /** + * Returns the trigonometric cosine of an angle. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the cosine of the argument. + */ + public static double cos(double a) { + return StrictMath.cos(a); // default impl. delegates to StrictMath + } + + /** + * Returns the trigonometric tangent of an angle. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the tangent of the argument. + */ + public static double tan(double a) { + return StrictMath.tan(a); // default impl. delegates to StrictMath + } + + /** + * Returns the arc sine of a value; the returned angle is in the + * range -pi/2 through pi/2. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc sine is to be returned. + * @return the arc sine of the argument. + */ + public static double asin(double a) { + return StrictMath.asin(a); // default impl. delegates to StrictMath + } + + /** + * Returns the arc cosine of a value; the returned angle is in the + * range 0.0 through pi. Special case: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc cosine is to be returned. + * @return the arc cosine of the argument. + */ + public static double acos(double a) { + return StrictMath.acos(a); // default impl. delegates to StrictMath + } + + /** + * Returns the arc tangent of a value; the returned angle is in the + * range -pi/2 through pi/2. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc tangent is to be returned. + * @return the arc tangent of the argument. + */ + public static double atan(double a) { + return StrictMath.atan(a); // default impl. delegates to StrictMath + } + + /** + * Converts an angle measured in degrees to an approximately + * equivalent angle measured in radians. The conversion from + * degrees to radians is generally inexact. + * + * @param angdeg an angle, in degrees + * @return the measurement of the angle {@code angdeg} + * in radians. + * @since 1.2 + */ + public static double toRadians(double angdeg) { + return angdeg / 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. + * @since 1.2 + */ + public static double toDegrees(double angrad) { + return angrad * 180.0 / PI; + } + + /** + * Returns Euler's number e raised to the power of a + * {@code double} value. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @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 double exp(double a) { + return StrictMath.exp(a); // default impl. delegates to StrictMath + } + + /** + * Returns the natural logarithm (base e) of a {@code double} + * value. Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a a value + * @return the value ln {@code a}, the natural logarithm of + * {@code a}. + */ + public static double log(double a) { + return StrictMath.log(a); // default impl. delegates to StrictMath + } + + /** + * Returns the base 10 logarithm of a {@code double} value. + * Special cases: + * + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a a value + * @return the base 10 logarithm of {@code a}. + * @since 1.5 + */ + public static double log10(double a) { + return StrictMath.log10(a); // default impl. delegates to StrictMath + } + + /** + * Returns the correctly rounded positive square root of a + * {@code double} value. + * Special cases: + *
The computed result must be within 1 ulp of the exact result.
+ *
+ * @param a a value.
+ * @return the cube root of {@code a}.
+ * @since 1.5
+ */
+ public static double cbrt(double a) {
+ return StrictMath.cbrt(a);
+ }
+
+ /**
+ * Computes the remainder operation on two arguments as prescribed
+ * by the IEEE 754 standard.
+ * The remainder value is mathematically equal to
+ * 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:
+ *
The computed result must be within 2 ulps of the exact result. + * Results must be semi-monotonic. + * + * @param y the ordinate coordinate + * @param x the abscissa coordinate + * @return the theta component of the point + * (r, theta) + * in polar coordinates that corresponds to the point + * (x, y) in Cartesian coordinates. + */ + public static double atan2(double y, double x) { + return StrictMath.atan2(y, x); // default impl. delegates to StrictMath + } + + /** + * Returns the value of the first argument raised to the power of the + * second argument. Special cases: + * + *
(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.) + * + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the base. + * @param b the exponent. + * @return the value {@code a}{@code b}. + */ + public static double pow(double a, double b) { + return StrictMath.pow(a, b); // default impl. delegates to StrictMath + } + + /** + * Returns the closest {@code int} to the argument, with ties + * rounding up. + * + *
+ * Special cases: + *
Special cases: + *
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 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 (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code long} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * + *
Note that if the argument is equal to the value of + * {@link Long#MIN_VALUE}, the most negative representable + * {@code long} value, the result is that same value, which + * is negative. + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static long abs(long a) { + return (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code float} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * Special cases: + *
{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static float abs(float a) { + return (a <= 0.0F) ? 0.0F - a : a; + } + + /** + * Returns the absolute value of a {@code double} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * Special cases: + *
{@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 (a <= 0.0D) ? 0.0D - a : a;
+ }
+
+ /**
+ * Returns the greater of two {@code int} values. That is, the
+ * result is the argument closer to the value of
+ * {@link Integer#MAX_VALUE}. If the arguments have the same value,
+ * the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static int max(int a, int b) {
+ return (a >= b) ? a : b;
+ }
+
+ /**
+ * Returns the greater of two {@code long} values. That is, the
+ * result is the argument closer to the value of
+ * {@link Long#MAX_VALUE}. If the arguments have the same value,
+ * the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static long max(long a, long b) {
+ return (a >= b) ? a : b;
+ }
+
+ private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
+ private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
+
+ /**
+ * Returns the greater of two {@code float} values. That is,
+ * the result is the argument closer to positive infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other negative zero, the
+ * result is positive zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static float max(float a, float b) {
+ if (a != a) return a; // a is NaN
+ if ((a == 0.0f) && (b == 0.0f)
+ && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
+ return b;
+ }
+ return (a >= b) ? a : b;
+ }
+
+ /**
+ * Returns the greater of two {@code double} values. That
+ * is, the result is the argument closer to positive infinity. If
+ * the arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other negative zero, the
+ * result is positive zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the larger of {@code a} and {@code b}.
+ */
+ public static double max(double a, double b) {
+ if (a != a) return a; // a is NaN
+ if ((a == 0.0d) && (b == 0.0d)
+ && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
+ return b;
+ }
+ return (a >= b) ? a : b;
+ }
+
+ /**
+ * Returns the smaller of two {@code int} values. That is,
+ * the result the argument closer to the value of
+ * {@link Integer#MIN_VALUE}. If the arguments have the same
+ * value, the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ public static int min(int a, int b) {
+ return (a <= b) ? a : b;
+ }
+
+ /**
+ * Returns the smaller of two {@code long} values. That is,
+ * the result is the argument closer to the value of
+ * {@link Long#MIN_VALUE}. If the arguments have the same
+ * value, the result is that same value.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ public static long min(long a, long b) {
+ return (a <= b) ? a : b;
+ }
+
+ /**
+ * Returns the smaller of two {@code float} values. That is,
+ * the result is the value closer to negative infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If
+ * one argument is positive zero and the other is negative zero,
+ * the result is negative zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ public static float min(float a, float b) {
+ if (a != a) return a; // a is NaN
+ if ((a == 0.0f) && (b == 0.0f)
+ && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
+ return b;
+ }
+ return (a <= b) ? a : b;
+ }
+
+ /**
+ * Returns the smaller of two {@code double} values. That
+ * is, the result is the value closer to negative infinity. If the
+ * arguments have the same value, the result is that same
+ * value. If either value is NaN, then the result is NaN. Unlike
+ * the numerical comparison operators, this method considers
+ * negative zero to be strictly smaller than positive zero. If one
+ * argument is positive zero and the other is negative zero, the
+ * result is negative zero.
+ *
+ * @param a an argument.
+ * @param b another argument.
+ * @return the smaller of {@code a} and {@code b}.
+ */
+ public static double min(double a, double b) {
+ if (a != a) return a; // a is NaN
+ if ((a == 0.0d) && (b == 0.0d)
+ && (Double.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} 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: + *
ulp(-x) == ulp(x)
.
+ *
+ * Special Cases: + *
Special Cases: + *
Special Cases: + *
Special cases: + *
The computed result must be within 2.5 ulps of the exact result. + * + * @param x The number whose hyperbolic sine is to be returned. + * @return The hyperbolic sine of {@code x}. + * @since 1.5 + */ + public static double sinh(double x) { + return StrictMath.sinh(x); + } + + /** + * Returns the hyperbolic cosine of a {@code double} value. + * The hyperbolic cosine of x is defined to be + * (ex + e-x)/2 + * where e is {@linkplain Math#E Euler's number}. + * + *
Special cases: + *
The computed result must be within 2.5 ulps of the exact result. + * + * @param x The number whose hyperbolic cosine is to be returned. + * @return The hyperbolic cosine of {@code x}. + * @since 1.5 + */ + public static double cosh(double x) { + return StrictMath.cosh(x); + } + + /** + * Returns the hyperbolic tangent of a {@code double} value. + * The hyperbolic tangent of 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: + *
The computed result must be within 2.5 ulps of the exact result. + * The result of {@code tanh} for any finite input must have + * an absolute value less than or equal to 1. Note that once the + * exact result of tanh is within 1/2 of an ulp of the limit value + * of ±1, correctly signed ±{@code 1.0} should + * be returned. + * + * @param x The number whose hyperbolic tangent is to be returned. + * @return The hyperbolic tangent of {@code x}. + * @since 1.5 + */ + public static double tanh(double x) { + return StrictMath.tanh(x); + } + + /** + * Returns sqrt(x2 +y2) + * without intermediate overflow or underflow. + * + *
Special cases: + *
The computed result must be within 1 ulp of the exact + * result. If one parameter is held constant, the results must be + * semi-monotonic in the other parameter. + * + * @param x a value + * @param y a value + * @return sqrt(x2 +y2) + * without intermediate overflow or underflow + * @since 1.5 + */ + public static double hypot(double x, double y) { + return StrictMath.hypot(x, 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)}. + * + *
Special cases: + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. The result of + * {@code expm1} for any finite input must be greater than or + * equal to {@code -1.0}. Note that once the exact result of + * e{@code x} - 1 is within 1/2 + * ulp of the limit value -1, {@code -1.0} should be + * returned. + * + * @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 double expm1(double x) { + return StrictMath.expm1(x); + } + + /** + * Returns the natural logarithm of the sum of the argument and 1. + * Note that for small values {@code x}, the result of + * {@code log1p(x)} is much closer to the true result of ln(1 + * + {@code x}) than the floating-point evaluation of + * {@code log(1.0+x)}. + * + *
Special cases: + * + *
The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param x a value + * @return the value ln({@code x} + 1), the natural + * log of {@code x} + 1 + * @since 1.5 + */ + public static double log1p(double x) { + return StrictMath.log1p(x); + } + + /** + * Returns the first floating-point argument with the sign of the + * second floating-point argument. Note that unlike the {@link + * StrictMath#copySign(double, double) StrictMath.copySign} + * method, this method does not require NaN {@code sign} + * arguments to be treated as positive values; implementations are + * permitted to treat some NaN arguments as positive and other NaN + * arguments as negative to allow greater performance. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} + * and the sign of {@code sign}. + * @since 1.6 + */ + public static double copySign(double magnitude, double sign) { + return sun.misc.FpUtils.rawCopySign(magnitude, sign); + } + + /** + * Returns the first floating-point argument with the sign of the + * second floating-point argument. Note that unlike the {@link + * StrictMath#copySign(float, float) StrictMath.copySign} + * method, this method does not require NaN {@code sign} + * arguments to be treated as positive values; implementations are + * permitted to treat some NaN arguments as positive and other NaN + * arguments as negative to allow greater performance. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} + * and the sign of {@code sign}. + * @since 1.6 + */ + public static float copySign(float magnitude, float sign) { + return sun.misc.FpUtils.rawCopySign(magnitude, sign); + } + + /** + * Returns the unbiased exponent used in the representation of a + * {@code float}. Special cases: + * + *
+ * Special cases: + *
+ * Special cases: + *
Special Cases: + *
Special Cases: + *
Special cases: + *
Special cases: + *