From 554fd8c5195424bdbcabf5de30fdc183aba391bd Mon Sep 17 00:00:00 2001 From: upstream source tree Date: Sun, 15 Mar 2015 20:14:05 -0400 Subject: obtained gcc-4.6.4.tar.bz2 from upstream website; verified gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream tarball. downloading a git-generated archive based on the 'upstream' tag should provide you with a source tree that is binary identical to the one extracted from the above tarball. if you have obtained the source via the command 'git clone', however, do note that line-endings of files in your working directory might differ from line-endings of the respective files in the upstream repository. --- libjava/classpath/java/lang/Math.java | 1052 +++++++++++++++++++++++++++++++++ 1 file changed, 1052 insertions(+) create mode 100644 libjava/classpath/java/lang/Math.java (limited to 'libjava/classpath/java/lang/Math.java') diff --git a/libjava/classpath/java/lang/Math.java b/libjava/classpath/java/lang/Math.java new file mode 100644 index 000000000..6cf29b4a0 --- /dev/null +++ b/libjava/classpath/java/lang/Math.java @@ -0,0 +1,1052 @@ +/* java.lang.Math -- common mathematical functions, native allowed (VMMath) + Copyright (C) 1998, 2001, 2002, 2003, 2006 Free Software Foundation, Inc. + +This file is part of GNU Classpath. + +GNU Classpath is free software; you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation; either version 2, or (at your option) +any later version. + +GNU Classpath 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 for more details. + +You should have received a copy of the GNU General Public License +along with GNU Classpath; see the file COPYING. If not, write to the +Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA +02110-1301 USA. + +Linking this library statically or dynamically with other modules is +making a combined work based on this library. Thus, the terms and +conditions of the GNU General Public License cover the whole +combination. + +As a special exception, the copyright holders of this library give you +permission to link this library with independent modules to produce an +executable, regardless of the license terms of these independent +modules, and to copy and distribute the resulting executable under +terms of your choice, provided that you also meet, for each linked +independent module, the terms and conditions of the license of that +module. An independent module is a module which is not derived from +or based on this library. If you modify this library, you may extend +this exception to your version of the library, but you are not +obligated to do so. If you do not wish to do so, delete this +exception statement from your version. */ + + +package java.lang; + +import gnu.classpath.Configuration; + +import java.util.Random; + +/** + * Helper class containing useful mathematical functions and constants. + *

+ * + * Note that angles are specified in radians. Conversion functions are + * provided for your convenience. + * + * @author Paul Fisher + * @author John Keiser + * @author Eric Blake (ebb9@email.byu.edu) + * @author Andrew John Hughes (gnu_andrew@member.fsf.org) + * @since 1.0 + */ +public final class Math +{ + + // FIXME - This is here because we need to load the "javalang" system + // library somewhere late in the bootstrap cycle. We cannot do this + // from VMSystem or VMRuntime since those are used to actually load + // the library. This is mainly here because historically Math was + // late enough in the bootstrap cycle to start using System after it + // was initialized (called from the java.util classes). + static + { + if (Configuration.INIT_LOAD_LIBRARY) + { + System.loadLibrary("javalang"); + } + } + + /** + * Math is non-instantiable + */ + private Math() + { + } + + /** + * A random number generator, initialized on first use. + */ + private static Random rand; + + /** + * The most accurate approximation to the mathematical constant e: + * 2.718281828459045. Used in natural log and exp. + * + * @see #log(double) + * @see #exp(double) + */ + public static final double E = 2.718281828459045; + + /** + * The most accurate approximation to the mathematical constant pi: + * 3.141592653589793. This is the ratio of a circle's diameter + * to its circumference. + */ + public static final double PI = 3.141592653589793; + + /** + * Take the absolute value of the argument. + * (Absolute value means make it positive.) + *

+ * + * Note that the the largest negative value (Integer.MIN_VALUE) cannot + * be made positive. In this case, because of the rules of negation in + * a computer, MIN_VALUE is what will be returned. + * This is a negative value. You have been warned. + * + * @param i the number to take the absolute value of + * @return the absolute value + * @see Integer#MIN_VALUE + */ + public static int abs(int i) + { + return (i < 0) ? -i : i; + } + + /** + * Take the absolute value of the argument. + * (Absolute value means make it positive.) + *

+ * + * Note that the the largest negative value (Long.MIN_VALUE) cannot + * be made positive. In this case, because of the rules of negation in + * a computer, MIN_VALUE is what will be returned. + * This is a negative value. You have been warned. + * + * @param l the number to take the absolute value of + * @return the absolute value + * @see Long#MIN_VALUE + */ + public static long abs(long l) + { + return (l < 0) ? -l : l; + } + + /** + * Take the absolute value of the argument. + * (Absolute value means make it positive.) + *

+ * + * This is equivalent, but faster than, calling + * Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a)). + * + * @param f the number to take the absolute value of + * @return the absolute value + */ + public static float abs(float f) + { + return (f <= 0) ? 0 - f : f; + } + + /** + * Take the absolute value of the argument. + * (Absolute value means make it positive.) + * + * This is equivalent, but faster than, calling + * Double.longBitsToDouble(Double.doubleToLongBits(a) + * << 1) >>> 1);. + * + * @param d the number to take the absolute value of + * @return the absolute value + */ + public static double abs(double d) + { + return (d <= 0) ? 0 - d : d; + } + + /** + * Return whichever argument is smaller. + * + * @param a the first number + * @param b a second number + * @return the smaller of the two numbers + */ + public static int min(int a, int b) + { + return (a < b) ? a : b; + } + + /** + * Return whichever argument is smaller. + * + * @param a the first number + * @param b a second number + * @return the smaller of the two numbers + */ + public static long min(long a, long b) + { + return (a < b) ? a : b; + } + + /** + * Return whichever argument is smaller. If either argument is NaN, the + * result is NaN, and when comparing 0 and -0, -0 is always smaller. + * + * @param a the first number + * @param b a second number + * @return the smaller of the two numbers + */ + public static float min(float a, float b) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return a; + // no need to check if b is NaN; < will work correctly + // recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special + if (a == 0 && b == 0) + return -(-a - b); + return (a < b) ? a : b; + } + + /** + * Return whichever argument is smaller. If either argument is NaN, the + * result is NaN, and when comparing 0 and -0, -0 is always smaller. + * + * @param a the first number + * @param b a second number + * @return the smaller of the two numbers + */ + public static double min(double a, double b) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return a; + // no need to check if b is NaN; < will work correctly + // recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special + if (a == 0 && b == 0) + return -(-a - b); + return (a < b) ? a : b; + } + + /** + * Return whichever argument is larger. + * + * @param a the first number + * @param b a second number + * @return the larger of the two numbers + */ + public static int max(int a, int b) + { + return (a > b) ? a : b; + } + + /** + * Return whichever argument is larger. + * + * @param a the first number + * @param b a second number + * @return the larger of the two numbers + */ + public static long max(long a, long b) + { + return (a > b) ? a : b; + } + + /** + * Return whichever argument is larger. If either argument is NaN, the + * result is NaN, and when comparing 0 and -0, 0 is always larger. + * + * @param a the first number + * @param b a second number + * @return the larger of the two numbers + */ + public static float max(float a, float b) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return a; + // no need to check if b is NaN; > will work correctly + // recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special + if (a == 0 && b == 0) + return a - -b; + return (a > b) ? a : b; + } + + /** + * Return whichever argument is larger. If either argument is NaN, the + * result is NaN, and when comparing 0 and -0, 0 is always larger. + * + * @param a the first number + * @param b a second number + * @return the larger of the two numbers + */ + public static double max(double a, double b) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return a; + // no need to check if b is NaN; > will work correctly + // recall that -0.0 == 0.0, but [+-]0.0 - [+-]0.0 behaves special + if (a == 0 && b == 0) + return a - -b; + return (a > b) ? a : b; + } + + /** + * The trigonometric function sin. The sine of NaN or infinity is + * NaN, and the sine of 0 retains its sign. This is accurate within 1 ulp, + * and is semi-monotonic. + * + * @param a the angle (in radians) + * @return sin(a) + */ + public static double sin(double a) + { + return VMMath.sin(a); + } + + /** + * The trigonometric function cos. The cosine of NaN or infinity is + * NaN. This is accurate within 1 ulp, and is semi-monotonic. + * + * @param a the angle (in radians) + * @return cos(a) + */ + public static double cos(double a) + { + return VMMath.cos(a); + } + + /** + * The trigonometric function tan. The tangent of NaN or infinity + * is NaN, and the tangent of 0 retains its sign. This is accurate within 1 + * ulp, and is semi-monotonic. + * + * @param a the angle (in radians) + * @return tan(a) + */ + public static double tan(double a) + { + return VMMath.tan(a); + } + + /** + * The trigonometric function arcsin. The range of angles returned + * is -pi/2 to pi/2 radians (-90 to 90 degrees). If the argument is NaN or + * its absolute value is beyond 1, the result is NaN; and the arcsine of + * 0 retains its sign. This is accurate within 1 ulp, and is semi-monotonic. + * + * @param a the sin to turn back into an angle + * @return arcsin(a) + */ + public static double asin(double a) + { + return VMMath.asin(a); + } + + /** + * The trigonometric function arccos. The range of angles returned + * is 0 to pi radians (0 to 180 degrees). If the argument is NaN or + * its absolute value is beyond 1, the result is NaN. This is accurate + * within 1 ulp, and is semi-monotonic. + * + * @param a the cos to turn back into an angle + * @return arccos(a) + */ + public static double acos(double a) + { + return VMMath.acos(a); + } + + /** + * The trigonometric function arcsin. The range of angles returned + * is -pi/2 to pi/2 radians (-90 to 90 degrees). If the argument is NaN, the + * result is NaN; and the arctangent of 0 retains its sign. This is accurate + * within 1 ulp, and is semi-monotonic. + * + * @param a the tan to turn back into an angle + * @return arcsin(a) + * @see #atan2(double, double) + */ + public static double atan(double a) + { + return VMMath.atan(a); + } + + /** + * A special version of the trigonometric function arctan, for + * converting rectangular coordinates (x, y) to polar + * (r, theta). This computes the arctangent of x/y in the range + * of -pi to pi radians (-180 to 180 degrees). Special cases:

This is accurate within 2 ulps, and is semi-monotonic. To get r, + * use sqrt(x*x+y*y). + * + * @param y the y position + * @param x the x position + * @return theta in the conversion of (x, y) to (r, theta) + * @see #atan(double) + */ + public static double atan2(double y, double x) + { + return VMMath.atan2(y,x); + } + + /** + * Take ea. The opposite of log(). If the + * argument is NaN, the result is NaN; if the argument is positive infinity, + * the result is positive infinity; and if the argument is negative + * infinity, the result is positive zero. This is accurate within 1 ulp, + * and is semi-monotonic. + * + * @param a the number to raise to the power + * @return the number raised to the power of e + * @see #log(double) + * @see #pow(double, double) + */ + public static double exp(double a) + { + return VMMath.exp(a); + } + + /** + * Take ln(a) (the natural log). The opposite of exp(). If the + * argument is NaN or negative, the result is NaN; if the argument is + * positive infinity, the result is positive infinity; and if the argument + * is either zero, the result is negative infinity. This is accurate within + * 1 ulp, and is semi-monotonic. + * + *

Note that the way to get logb(a) is to do this: + * ln(a) / ln(b). + * + * @param a the number to take the natural log of + * @return the natural log of a + * @see #exp(double) + */ + public static double log(double a) + { + return VMMath.log(a); + } + + /** + * Take a square root. If the argument is NaN or negative, the result is + * NaN; if the argument is positive infinity, the result is positive + * infinity; and if the result is either zero, the result is the same. + * This is accurate within the limits of doubles. + * + *

For a cube root, use cbrt. For other roots, use + * pow(a, 1 / rootNumber).

+ * + * @param a the numeric argument + * @return the square root of the argument + * @see #cbrt(double) + * @see #pow(double, double) + */ + public static double sqrt(double a) + { + return VMMath.sqrt(a); + } + + /** + * Raise a number to a power. Special cases:

(In the foregoing descriptions, a floating-point value is + * considered to be an integer if and only if it is a fixed point of the + * method {@link #ceil(double)} or, equivalently, a fixed point of the + * method {@link #floor(double)}. 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.) This is accurate within 1 ulp, and is semi-monotonic. + * + * @param a the number to raise + * @param b the power to raise it to + * @return ab + */ + public static double pow(double a, double b) + { + return VMMath.pow(a,b); + } + + /** + * Get the IEEE 754 floating point remainder on two numbers. This is the + * value of x - y * n, where n is the closest + * double to x / y (ties go to the even n); for a zero + * remainder, the sign is that of x. If either argument is NaN, + * the first argument is infinite, or the second argument is zero, the result + * is NaN; if x is finite but y is infinite, the result is x. This is + * accurate within the limits of doubles. + * + * @param x the dividend (the top half) + * @param y the divisor (the bottom half) + * @return the IEEE 754-defined floating point remainder of x/y + * @see #rint(double) + */ + public static double IEEEremainder(double x, double y) + { + return VMMath.IEEEremainder(x,y); + } + + /** + * Take the nearest integer that is that is greater than or equal to the + * argument. If the argument is NaN, infinite, or zero, the result is the + * same; if the argument is between -1 and 0, the result is negative zero. + * Note that Math.ceil(x) == -Math.floor(-x). + * + * @param a the value to act upon + * @return the nearest integer >= a + */ + public static double ceil(double a) + { + return VMMath.ceil(a); + } + + /** + * Take the nearest integer that is that is less than or equal to the + * argument. If the argument is NaN, infinite, or zero, the result is the + * same. Note that Math.ceil(x) == -Math.floor(-x). + * + * @param a the value to act upon + * @return the nearest integer <= a + */ + public static double floor(double a) + { + return VMMath.floor(a); + } + + /** + * Take the nearest integer to the argument. If it is exactly between + * two integers, the even integer is taken. If the argument is NaN, + * infinite, or zero, the result is the same. + * + * @param a the value to act upon + * @return the nearest integer to a + */ + public static double rint(double a) + { + return VMMath.rint(a); + } + + /** + * Take the nearest integer to the argument. This is equivalent to + * (int) Math.floor(a + 0.5f). If the argument is NaN, the result + * is 0; otherwise if the argument is outside the range of int, the result + * will be Integer.MIN_VALUE or Integer.MAX_VALUE, as appropriate. + * + * @param a the argument to round + * @return the nearest integer to the argument + * @see Integer#MIN_VALUE + * @see Integer#MAX_VALUE + */ + public static int round(float a) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return 0; + return (int) floor(a + 0.5f); + } + + /** + * Take the nearest long to the argument. This is equivalent to + * (long) Math.floor(a + 0.5). If the argument is NaN, the + * result is 0; otherwise if the argument is outside the range of long, the + * result will be Long.MIN_VALUE or Long.MAX_VALUE, as appropriate. + * + * @param a the argument to round + * @return the nearest long to the argument + * @see Long#MIN_VALUE + * @see Long#MAX_VALUE + */ + public static long round(double a) + { + // this check for NaN, from JLS 15.21.1, saves a method call + if (a != a) + return 0; + return (long) floor(a + 0.5d); + } + + /** + * Get a random number. This behaves like Random.nextDouble(), seeded by + * System.currentTimeMillis() when first called. In other words, the number + * is from a pseudorandom sequence, and lies in the range [+0.0, 1.0). + * This random sequence is only used by this method, and is threadsafe, + * although you may want your own random number generator if it is shared + * among threads. + * + * @return a random number + * @see Random#nextDouble() + * @see System#currentTimeMillis() + */ + public static synchronized double random() + { + if (rand == null) + rand = new Random(); + return rand.nextDouble(); + } + + /** + * Convert from degrees to radians. The formula for this is + * radians = degrees * (pi/180); however it is not always exact given the + * limitations of floating point numbers. + * + * @param degrees an angle in degrees + * @return the angle in radians + * @since 1.2 + */ + public static double toRadians(double degrees) + { + return (degrees * PI) / 180; + } + + /** + * Convert from radians to degrees. The formula for this is + * degrees = radians * (180/pi); however it is not always exact given the + * limitations of floating point numbers. + * + * @param rads an angle in radians + * @return the angle in degrees + * @since 1.2 + */ + public static double toDegrees(double rads) + { + return (rads * 180) / PI; + } + + /** + *

+ * Take a cube root. If the argument is NaN, an infinity or + * zero, then the original value is returned. The returned result is + * within 1 ulp of the exact result. For a finite value, x, + * the cube root of -x is equal to the negation of the cube root + * of x. + *

+ *

+ * For a square root, use sqrt. For other roots, use + * pow(a, 1 / rootNumber). + *

+ * + * @param a the numeric argument + * @return the cube root of the argument + * @see #sqrt(double) + * @see #pow(double, double) + * @since 1.5 + */ + public static double cbrt(double a) + { + return VMMath.cbrt(a); + } + + /** + *

+ * Returns the hyperbolic cosine of the given value. For a value, + * x, the hyperbolic cosine is (ex + + * e-x)/2 + * with e being Euler's number. The returned + * result is within 2.5 ulps of the exact result. + *

+ *

+ * If the supplied value is NaN, then the original value is + * returned. For either infinity, positive infinity is returned. + * The hyperbolic cosine of zero is 1.0. + *

+ * + * @param a the numeric argument + * @return the hyperbolic cosine of a. + * @since 1.5 + */ + public static double cosh(double a) + { + return VMMath.cosh(a); + } + + /** + *

+ * Returns ea - 1. For values close to 0, the + * result of expm1(a) + 1 tend to be much closer to the + * exact result than simply exp(x). The result is within + * 1 ulp of the exact result, and results are semi-monotonic. For finite + * inputs, the returned value is greater than or equal to -1.0. Once + * a result enters within half a ulp of this limit, the limit is returned. + *

+ *

+ * For NaN, positive infinity and zero, the original value + * is returned. Negative infinity returns a result of -1.0 (the limit). + *

+ * + * @param a the numeric argument + * @return ea - 1 + * @since 1.5 + */ + public static double expm1(double a) + { + return VMMath.expm1(a); + } + + /** + *

+ * Returns the hypotenuse, a2 + b2, + * without intermediate overflow or underflow. The returned result is + * within 1 ulp of the exact result. If one parameter is held constant, + * then the result in the other parameter is semi-monotonic. + *

+ *

+ * If either of the arguments is an infinity, then the returned result + * is positive infinity. Otherwise, if either argument is NaN, + * then NaN is returned. + *

+ * + * @param a the first parameter. + * @param b the second parameter. + * @return the hypotenuse matching the supplied parameters. + * @since 1.5 + */ + public static double hypot(double a, double b) + { + return VMMath.hypot(a,b); + } + + /** + *

+ * Returns the base 10 logarithm of the supplied value. The returned + * result is within 1 ulp of the exact result, and the results are + * semi-monotonic. + *

+ *

+ * Arguments of either NaN or less than zero return + * NaN. An argument of positive infinity returns positive + * infinity. Negative infinity is returned if either positive or negative + * zero is supplied. Where the argument is the result of + * 10n, then n is returned. + *

+ * + * @param a the numeric argument. + * @return the base 10 logarithm of a. + * @since 1.5 + */ + public static double log10(double a) + { + return VMMath.log10(a); + } + + /** + *

+ * Returns the natural logarithm resulting from the sum of the argument, + * a and 1. For values close to 0, the + * result of log1p(a) tend to be much closer to the + * exact result than simply log(1.0+a). The returned + * result is within 1 ulp of the exact result, and the results are + * semi-monotonic. + *

+ *

+ * Arguments of either NaN or less than -1 return + * NaN. An argument of positive infinity or zero + * returns the original argument. Negative infinity is returned from an + * argument of -1. + *

+ * + * @param a the numeric argument. + * @return the natural logarithm of a + 1. + * @since 1.5 + */ + public static double log1p(double a) + { + return VMMath.log1p(a); + } + + /** + *

+ * Returns the sign of the argument as follows: + *

+ *
    + *
  • If a is greater than zero, the result is 1.0.
    • + *
  • If a is less than zero, the result is -1.0.
    • + *
  • If a is NaN, the result is NaN. + *
  • If a is positive or negative zero, the result is the + * same.
    • + *
+ * + * @param a the numeric argument. + * @return the sign of the argument. + * @since 1.5. + */ + public static double signum(double a) + { + if (Double.isNaN(a)) + return Double.NaN; + if (a > 0) + return 1.0; + if (a < 0) + return -1.0; + return a; + } + + /** + *

+ * Returns the sign of the argument as follows: + *

+ *
    + *
  • If a is greater than zero, the result is 1.0f.
    • + *
  • If a is less than zero, the result is -1.0f.
    • + *
  • If a is NaN, the result is NaN. + *
  • If a is positive or negative zero, the result is the + * same.
    • + *
+ * + * @param a the numeric argument. + * @return the sign of the argument. + * @since 1.5. + */ + public static float signum(float a) + { + if (Float.isNaN(a)) + return Float.NaN; + if (a > 0) + return 1.0f; + if (a < 0) + return -1.0f; + return a; + } + + /** + *

+ * Returns the hyperbolic sine of the given value. For a value, + * x, the hyperbolic sine is (ex - + * e-x)/2 + * with e being Euler's number. The returned + * result is within 2.5 ulps of the exact result. + *

+ *

+ * If the supplied value is NaN, an infinity or a zero, then the + * original value is returned. + *

+ * + * @param a the numeric argument + * @return the hyperbolic sine of a. + * @since 1.5 + */ + public static double sinh(double a) + { + return VMMath.sinh(a); + } + + /** + *

+ * Returns the hyperbolic tangent of the given value. For a value, + * x, the hyperbolic tangent is (ex - + * e-x)/(ex + e-x) + * (i.e. sinh(a)/cosh(a)) + * with e being Euler's number. The returned + * result is within 2.5 ulps of the exact result. The absolute value + * of the exact result is always less than 1. Computed results are thus + * less than or equal to 1 for finite arguments, with results within + * half a ulp of either positive or negative 1 returning the appropriate + * limit value (i.e. as if the argument was an infinity). + *

+ *

+ * If the supplied value is NaN or zero, then the original + * value is returned. Positive infinity returns +1.0 and negative infinity + * returns -1.0. + *

+ * + * @param a the numeric argument + * @return the hyperbolic tangent of a. + * @since 1.5 + */ + public static double tanh(double a) + { + return VMMath.tanh(a); + } + + /** + * Return the ulp for the given double argument. The ulp is the + * difference between the argument and the next larger double. Note + * that the sign of the double argument is ignored, that is, + * ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned. + * If the argument is an infinity, then +Inf is returned. If the + * argument is zero (either positive or negative), then + * {@link Double#MIN_VALUE} is returned. + * @param d the double whose ulp should be returned + * @return the difference between the argument and the next larger double + * @since 1.5 + */ + public static double ulp(double d) + { + if (Double.isNaN(d)) + return d; + if (Double.isInfinite(d)) + return Double.POSITIVE_INFINITY; + // This handles both +0.0 and -0.0. + if (d == 0.0) + return Double.MIN_VALUE; + long bits = Double.doubleToLongBits(d); + final int mantissaBits = 52; + final int exponentBits = 11; + final long mantMask = (1L << mantissaBits) - 1; + long mantissa = bits & mantMask; + final long expMask = (1L << exponentBits) - 1; + long exponent = (bits >>> mantissaBits) & expMask; + + // Denormal number, so the answer is easy. + if (exponent == 0) + { + long result = (exponent << mantissaBits) | 1L; + return Double.longBitsToDouble(result); + } + + // Conceptually we want to have '1' as the mantissa. Then we would + // shift the mantissa over to make a normal number. If this underflows + // the exponent, we will make a denormal result. + long newExponent = exponent - mantissaBits; + long newMantissa; + if (newExponent > 0) + newMantissa = 0; + else + { + newMantissa = 1L << -(newExponent - 1); + newExponent = 0; + } + return Double.longBitsToDouble((newExponent << mantissaBits) | newMantissa); + } + + /** + * Return the ulp for the given float argument. The ulp is the + * difference between the argument and the next larger float. Note + * that the sign of the float argument is ignored, that is, + * ulp(x) == ulp(-x). If the argument is a NaN, then NaN is returned. + * If the argument is an infinity, then +Inf is returned. If the + * argument is zero (either positive or negative), then + * {@link Float#MIN_VALUE} is returned. + * @param f the float whose ulp should be returned + * @return the difference between the argument and the next larger float + * @since 1.5 + */ + public static float ulp(float f) + { + if (Float.isNaN(f)) + return f; + if (Float.isInfinite(f)) + return Float.POSITIVE_INFINITY; + // This handles both +0.0 and -0.0. + if (f == 0.0) + return Float.MIN_VALUE; + int bits = Float.floatToIntBits(f); + final int mantissaBits = 23; + final int exponentBits = 8; + final int mantMask = (1 << mantissaBits) - 1; + int mantissa = bits & mantMask; + final int expMask = (1 << exponentBits) - 1; + int exponent = (bits >>> mantissaBits) & expMask; + + // Denormal number, so the answer is easy. + if (exponent == 0) + { + int result = (exponent << mantissaBits) | 1; + return Float.intBitsToFloat(result); + } + + // Conceptually we want to have '1' as the mantissa. Then we would + // shift the mantissa over to make a normal number. If this underflows + // the exponent, we will make a denormal result. + int newExponent = exponent - mantissaBits; + int newMantissa; + if (newExponent > 0) + newMantissa = 0; + else + { + newMantissa = 1 << -(newExponent - 1); + newExponent = 0; + } + return Float.intBitsToFloat((newExponent << mantissaBits) | newMantissa); + } +} -- cgit v1.2.3