author | darcy |
Wed, 21 Sep 2011 23:22:11 -0700 | |
changeset 10608 | 7cfca36fc79b |
parent 10598 | efd29b4b3e67 |
child 11510 | f52f50e63c9b |
permissions | -rw-r--r-- |
2 | 1 |
/* |
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* Copyright (c) 1994, 2011, Oracle and/or its affiliates. All rights reserved. |
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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* |
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* This code is free software; you can redistribute it and/or modify it |
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* under the terms of the GNU General Public License version 2 only, as |
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* published by the Free Software Foundation. Oracle designates this |
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* particular file as subject to the "Classpath" exception as provided |
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* by Oracle in the LICENSE file that accompanied this code. |
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* |
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* This code is distributed in the hope that it will be useful, but WITHOUT |
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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* version 2 for more details (a copy is included in the LICENSE file that |
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* accompanied this code). |
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* |
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* You should have received a copy of the GNU General Public License version |
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* 2 along with this work; if not, write to the Free Software Foundation, |
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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* |
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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* or visit www.oracle.com if you need additional information or have any |
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* questions. |
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*/ |
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package java.lang; |
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import java.util.Random; |
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||
10598
efd29b4b3e67
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changeset
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import sun.misc.FloatConsts; |
efd29b4b3e67
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diff
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import sun.misc.DoubleConsts; |
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/** |
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33 |
* The class {@code Math} contains methods for performing basic |
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* numeric operations such as the elementary exponential, logarithm, |
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* square root, and trigonometric functions. |
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* |
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* <p>Unlike some of the numeric methods of class |
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* {@code StrictMath}, all implementations of the equivalent |
|
39 |
* functions of class {@code Math} are not defined to return the |
|
40 |
* bit-for-bit same results. This relaxation permits |
|
41 |
* better-performing implementations where strict reproducibility is |
|
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* not required. |
|
43 |
* |
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44 |
* <p>By default many of the {@code Math} methods simply call |
|
45 |
* the equivalent method in {@code StrictMath} for their |
|
46 |
* implementation. Code generators are encouraged to use |
|
47 |
* platform-specific native libraries or microprocessor instructions, |
|
48 |
* where available, to provide higher-performance implementations of |
|
49 |
* {@code Math} methods. Such higher-performance |
|
50 |
* implementations still must conform to the specification for |
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* {@code Math}. |
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* |
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* <p>The quality of implementation specifications concern two |
|
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* properties, accuracy of the returned result and monotonicity of the |
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* method. Accuracy of the floating-point {@code Math} methods is |
56 |
* measured in terms of <i>ulps</i>, units in the last place. For a |
|
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* given floating-point format, an {@linkplain #ulp(double) ulp} of a |
|
58 |
* specific real number value is the distance between the two |
|
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* floating-point values bracketing that numerical value. When |
|
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* discussing the accuracy of a method as a whole rather than at a |
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* specific argument, the number of ulps cited is for the worst-case |
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* error at any argument. If a method always has an error less than |
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* 0.5 ulps, the method always returns the floating-point number |
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* nearest the exact result; such a method is <i>correctly |
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* rounded</i>. A correctly rounded method is generally the best a |
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* floating-point approximation can be; however, it is impractical for |
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* many floating-point methods to be correctly rounded. Instead, for |
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* the {@code Math} class, a larger error bound of 1 or 2 ulps is |
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* allowed for certain methods. Informally, with a 1 ulp error bound, |
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* when the exact result is a representable number, the exact result |
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* should be returned as the computed result; otherwise, either of the |
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* two floating-point values which bracket the exact result may be |
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* returned. For exact results large in magnitude, one of the |
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* endpoints of the bracket may be infinite. Besides accuracy at |
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* individual arguments, maintaining proper relations between the |
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* method at different arguments is also important. Therefore, most |
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* methods with more than 0.5 ulp errors are required to be |
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* <i>semi-monotonic</i>: whenever the mathematical function is |
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* non-decreasing, so is the floating-point approximation, likewise, |
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* whenever the mathematical function is non-increasing, so is the |
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* floating-point approximation. Not all approximations that have 1 |
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* ulp accuracy will automatically meet the monotonicity requirements. |
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* |
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* @author unascribed |
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* @author Joseph D. Darcy |
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* @since JDK1.0 |
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*/ |
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public final class Math { |
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||
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/** |
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* Don't let anyone instantiate this class. |
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*/ |
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private Math() {} |
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||
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/** |
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* The {@code double} value that is closer than any other to |
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* <i>e</i>, the base of the natural logarithms. |
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*/ |
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public static final double E = 2.7182818284590452354; |
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||
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/** |
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* The {@code double} value that is closer than any other to |
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* <i>pi</i>, the ratio of the circumference of a circle to its |
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* diameter. |
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*/ |
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public static final double PI = 3.14159265358979323846; |
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||
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/** |
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* Returns the trigonometric sine of an angle. Special cases: |
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* <ul><li>If the argument is NaN or an infinity, then the |
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* result is NaN. |
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* <li>If the argument is zero, then the result is a zero with the |
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* same sign as the argument.</ul> |
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* |
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* <p>The computed result must be within 1 ulp of the exact result. |
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* Results must be semi-monotonic. |
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118 |
* |
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119 |
* @param a an angle, in radians. |
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* @return the sine of the argument. |
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*/ |
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122 |
public static double sin(double a) { |
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return StrictMath.sin(a); // default impl. delegates to StrictMath |
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} |
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||
126 |
/** |
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127 |
* Returns the trigonometric cosine of an angle. Special cases: |
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* <ul><li>If the argument is NaN or an infinity, then the |
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* result is NaN.</ul> |
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* |
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* <p>The computed result must be within 1 ulp of the exact result. |
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* Results must be semi-monotonic. |
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133 |
* |
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* @param a an angle, in radians. |
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* @return the cosine of the argument. |
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*/ |
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137 |
public static double cos(double a) { |
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return StrictMath.cos(a); // default impl. delegates to StrictMath |
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} |
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||
141 |
/** |
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142 |
* Returns the trigonometric tangent of an angle. Special cases: |
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* <ul><li>If the argument is NaN or an infinity, then the result |
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144 |
* is NaN. |
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145 |
* <li>If the argument is zero, then the result is a zero with the |
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146 |
* same sign as the argument.</ul> |
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* |
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148 |
* <p>The computed result must be within 1 ulp of the exact result. |
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149 |
* Results must be semi-monotonic. |
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150 |
* |
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151 |
* @param a an angle, in radians. |
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* @return the tangent of the argument. |
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*/ |
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154 |
public static double tan(double a) { |
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return StrictMath.tan(a); // default impl. delegates to StrictMath |
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} |
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||
158 |
/** |
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159 |
* Returns the arc sine of a value; the returned angle is in the |
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* range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: |
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* <ul><li>If the argument is NaN or its absolute value is greater |
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* than 1, then the result is NaN. |
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* <li>If the argument is zero, then the result is a zero with the |
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* same sign as the argument.</ul> |
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* |
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* <p>The computed result must be within 1 ulp of the exact result. |
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* Results must be semi-monotonic. |
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168 |
* |
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* @param a the value whose arc sine is to be returned. |
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* @return the arc sine of the argument. |
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*/ |
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public static double asin(double a) { |
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return StrictMath.asin(a); // default impl. delegates to StrictMath |
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} |
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||
176 |
/** |
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* Returns the arc cosine of a value; the returned angle is in the |
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* range 0.0 through <i>pi</i>. Special case: |
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* <ul><li>If the argument is NaN or its absolute value is greater |
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* than 1, then the result is NaN.</ul> |
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181 |
* |
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* <p>The computed result must be within 1 ulp of the exact result. |
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183 |
* Results must be semi-monotonic. |
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184 |
* |
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185 |
* @param a the value whose arc cosine is to be returned. |
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* @return the arc cosine of the argument. |
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*/ |
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public static double acos(double a) { |
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return StrictMath.acos(a); // default impl. delegates to StrictMath |
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190 |
} |
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191 |
||
192 |
/** |
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193 |
* Returns the arc tangent of a value; the returned angle is in the |
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194 |
* range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: |
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195 |
* <ul><li>If the argument is NaN, then the result is NaN. |
|
196 |
* <li>If the argument is zero, then the result is a zero with the |
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197 |
* same sign as the argument.</ul> |
|
198 |
* |
|
199 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
200 |
* Results must be semi-monotonic. |
|
201 |
* |
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202 |
* @param a the value whose arc tangent is to be returned. |
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203 |
* @return the arc tangent of the argument. |
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204 |
*/ |
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205 |
public static double atan(double a) { |
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206 |
return StrictMath.atan(a); // default impl. delegates to StrictMath |
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207 |
} |
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208 |
||
209 |
/** |
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210 |
* Converts an angle measured in degrees to an approximately |
|
211 |
* equivalent angle measured in radians. The conversion from |
|
212 |
* degrees to radians is generally inexact. |
|
213 |
* |
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214 |
* @param angdeg an angle, in degrees |
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215 |
* @return the measurement of the angle {@code angdeg} |
|
216 |
* in radians. |
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217 |
* @since 1.2 |
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*/ |
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219 |
public static double toRadians(double angdeg) { |
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220 |
return angdeg / 180.0 * PI; |
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221 |
} |
|
222 |
||
223 |
/** |
|
224 |
* Converts an angle measured in radians to an approximately |
|
225 |
* equivalent angle measured in degrees. The conversion from |
|
226 |
* radians to degrees is generally inexact; users should |
|
227 |
* <i>not</i> expect {@code cos(toRadians(90.0))} to exactly |
|
228 |
* equal {@code 0.0}. |
|
229 |
* |
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230 |
* @param angrad an angle, in radians |
|
231 |
* @return the measurement of the angle {@code angrad} |
|
232 |
* in degrees. |
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233 |
* @since 1.2 |
|
234 |
*/ |
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235 |
public static double toDegrees(double angrad) { |
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236 |
return angrad * 180.0 / PI; |
|
237 |
} |
|
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||
239 |
/** |
|
240 |
* Returns Euler's number <i>e</i> raised to the power of a |
|
241 |
* {@code double} value. Special cases: |
|
242 |
* <ul><li>If the argument is NaN, the result is NaN. |
|
243 |
* <li>If the argument is positive infinity, then the result is |
|
244 |
* positive infinity. |
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245 |
* <li>If the argument is negative infinity, then the result is |
|
246 |
* positive zero.</ul> |
|
247 |
* |
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248 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
249 |
* Results must be semi-monotonic. |
|
250 |
* |
|
251 |
* @param a the exponent to raise <i>e</i> to. |
|
252 |
* @return the value <i>e</i><sup>{@code a}</sup>, |
|
253 |
* where <i>e</i> is the base of the natural logarithms. |
|
254 |
*/ |
|
255 |
public static double exp(double a) { |
|
256 |
return StrictMath.exp(a); // default impl. delegates to StrictMath |
|
257 |
} |
|
258 |
||
259 |
/** |
|
260 |
* Returns the natural logarithm (base <i>e</i>) of a {@code double} |
|
261 |
* value. Special cases: |
|
262 |
* <ul><li>If the argument is NaN or less than zero, then the result |
|
263 |
* is NaN. |
|
264 |
* <li>If the argument is positive infinity, then the result is |
|
265 |
* positive infinity. |
|
266 |
* <li>If the argument is positive zero or negative zero, then the |
|
267 |
* result is negative infinity.</ul> |
|
268 |
* |
|
269 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
270 |
* Results must be semi-monotonic. |
|
271 |
* |
|
272 |
* @param a a value |
|
273 |
* @return the value ln {@code a}, the natural logarithm of |
|
274 |
* {@code a}. |
|
275 |
*/ |
|
276 |
public static double log(double a) { |
|
277 |
return StrictMath.log(a); // default impl. delegates to StrictMath |
|
278 |
} |
|
279 |
||
280 |
/** |
|
281 |
* Returns the base 10 logarithm of a {@code double} value. |
|
282 |
* Special cases: |
|
283 |
* |
|
284 |
* <ul><li>If the argument is NaN or less than zero, then the result |
|
285 |
* is NaN. |
|
286 |
* <li>If the argument is positive infinity, then the result is |
|
287 |
* positive infinity. |
|
288 |
* <li>If the argument is positive zero or negative zero, then the |
|
289 |
* result is negative infinity. |
|
290 |
* <li> If the argument is equal to 10<sup><i>n</i></sup> for |
|
291 |
* integer <i>n</i>, then the result is <i>n</i>. |
|
292 |
* </ul> |
|
293 |
* |
|
294 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
295 |
* Results must be semi-monotonic. |
|
296 |
* |
|
297 |
* @param a a value |
|
298 |
* @return the base 10 logarithm of {@code a}. |
|
299 |
* @since 1.5 |
|
300 |
*/ |
|
301 |
public static double log10(double a) { |
|
302 |
return StrictMath.log10(a); // default impl. delegates to StrictMath |
|
303 |
} |
|
304 |
||
305 |
/** |
|
306 |
* Returns the correctly rounded positive square root of a |
|
307 |
* {@code double} value. |
|
308 |
* Special cases: |
|
309 |
* <ul><li>If the argument is NaN or less than zero, then the result |
|
310 |
* is NaN. |
|
311 |
* <li>If the argument is positive infinity, then the result is positive |
|
312 |
* infinity. |
|
313 |
* <li>If the argument is positive zero or negative zero, then the |
|
314 |
* result is the same as the argument.</ul> |
|
315 |
* Otherwise, the result is the {@code double} value closest to |
|
316 |
* the true mathematical square root of the argument value. |
|
317 |
* |
|
318 |
* @param a a value. |
|
319 |
* @return the positive square root of {@code a}. |
|
320 |
* If the argument is NaN or less than zero, the result is NaN. |
|
321 |
*/ |
|
322 |
public static double sqrt(double a) { |
|
323 |
return StrictMath.sqrt(a); // default impl. delegates to StrictMath |
|
324 |
// Note that hardware sqrt instructions |
|
325 |
// frequently can be directly used by JITs |
|
326 |
// and should be much faster than doing |
|
327 |
// Math.sqrt in software. |
|
328 |
} |
|
329 |
||
330 |
||
331 |
/** |
|
332 |
* Returns the cube root of a {@code double} value. For |
|
333 |
* positive finite {@code x}, {@code cbrt(-x) == |
|
334 |
* -cbrt(x)}; that is, the cube root of a negative value is |
|
335 |
* the negative of the cube root of that value's magnitude. |
|
336 |
* |
|
337 |
* Special cases: |
|
338 |
* |
|
339 |
* <ul> |
|
340 |
* |
|
341 |
* <li>If the argument is NaN, then the result is NaN. |
|
342 |
* |
|
343 |
* <li>If the argument is infinite, then the result is an infinity |
|
344 |
* with the same sign as the argument. |
|
345 |
* |
|
346 |
* <li>If the argument is zero, then the result is a zero with the |
|
347 |
* same sign as the argument. |
|
348 |
* |
|
349 |
* </ul> |
|
350 |
* |
|
351 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
352 |
* |
|
353 |
* @param a a value. |
|
354 |
* @return the cube root of {@code a}. |
|
355 |
* @since 1.5 |
|
356 |
*/ |
|
357 |
public static double cbrt(double a) { |
|
358 |
return StrictMath.cbrt(a); |
|
359 |
} |
|
360 |
||
361 |
/** |
|
362 |
* Computes the remainder operation on two arguments as prescribed |
|
363 |
* by the IEEE 754 standard. |
|
364 |
* The remainder value is mathematically equal to |
|
365 |
* <code>f1 - f2</code> × <i>n</i>, |
|
366 |
* where <i>n</i> is the mathematical integer closest to the exact |
|
367 |
* mathematical value of the quotient {@code f1/f2}, and if two |
|
368 |
* mathematical integers are equally close to {@code f1/f2}, |
|
369 |
* then <i>n</i> is the integer that is even. If the remainder is |
|
370 |
* zero, its sign is the same as the sign of the first argument. |
|
371 |
* Special cases: |
|
372 |
* <ul><li>If either argument is NaN, or the first argument is infinite, |
|
373 |
* or the second argument is positive zero or negative zero, then the |
|
374 |
* result is NaN. |
|
375 |
* <li>If the first argument is finite and the second argument is |
|
376 |
* infinite, then the result is the same as the first argument.</ul> |
|
377 |
* |
|
378 |
* @param f1 the dividend. |
|
379 |
* @param f2 the divisor. |
|
380 |
* @return the remainder when {@code f1} is divided by |
|
381 |
* {@code f2}. |
|
382 |
*/ |
|
383 |
public static double IEEEremainder(double f1, double f2) { |
|
384 |
return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath |
|
385 |
} |
|
386 |
||
387 |
/** |
|
388 |
* Returns the smallest (closest to negative infinity) |
|
389 |
* {@code double} value that is greater than or equal to the |
|
390 |
* argument and is equal to a mathematical integer. Special cases: |
|
391 |
* <ul><li>If the argument value is already equal to a |
|
392 |
* mathematical integer, then the result is the same as the |
|
393 |
* argument. <li>If the argument is NaN or an infinity or |
|
394 |
* positive zero or negative zero, then the result is the same as |
|
395 |
* the argument. <li>If the argument value is less than zero but |
|
396 |
* greater than -1.0, then the result is negative zero.</ul> Note |
|
397 |
* that the value of {@code Math.ceil(x)} is exactly the |
|
398 |
* value of {@code -Math.floor(-x)}. |
|
399 |
* |
|
400 |
* |
|
401 |
* @param a a value. |
|
402 |
* @return the smallest (closest to negative infinity) |
|
403 |
* floating-point value that is greater than or equal to |
|
404 |
* the argument and is equal to a mathematical integer. |
|
405 |
*/ |
|
406 |
public static double ceil(double a) { |
|
407 |
return StrictMath.ceil(a); // default impl. delegates to StrictMath |
|
408 |
} |
|
409 |
||
410 |
/** |
|
411 |
* Returns the largest (closest to positive infinity) |
|
412 |
* {@code double} value that is less than or equal to the |
|
413 |
* argument and is equal to a mathematical integer. Special cases: |
|
414 |
* <ul><li>If the argument value is already equal to a |
|
415 |
* mathematical integer, then the result is the same as the |
|
416 |
* argument. <li>If the argument is NaN or an infinity or |
|
417 |
* positive zero or negative zero, then the result is the same as |
|
418 |
* the argument.</ul> |
|
419 |
* |
|
420 |
* @param a a value. |
|
421 |
* @return the largest (closest to positive infinity) |
|
422 |
* floating-point value that less than or equal to the argument |
|
423 |
* and is equal to a mathematical integer. |
|
424 |
*/ |
|
425 |
public static double floor(double a) { |
|
426 |
return StrictMath.floor(a); // default impl. delegates to StrictMath |
|
427 |
} |
|
428 |
||
429 |
/** |
|
430 |
* Returns the {@code double} value that is closest in value |
|
431 |
* to the argument and is equal to a mathematical integer. If two |
|
432 |
* {@code double} values that are mathematical integers are |
|
433 |
* equally close, the result is the integer value that is |
|
434 |
* even. Special cases: |
|
435 |
* <ul><li>If the argument value is already equal to a mathematical |
|
436 |
* integer, then the result is the same as the argument. |
|
437 |
* <li>If the argument is NaN or an infinity or positive zero or negative |
|
438 |
* zero, then the result is the same as the argument.</ul> |
|
439 |
* |
|
440 |
* @param a a {@code double} value. |
|
441 |
* @return the closest floating-point value to {@code a} that is |
|
442 |
* equal to a mathematical integer. |
|
443 |
*/ |
|
444 |
public static double rint(double a) { |
|
445 |
return StrictMath.rint(a); // default impl. delegates to StrictMath |
|
446 |
} |
|
447 |
||
448 |
/** |
|
449 |
* Returns the angle <i>theta</i> from the conversion of rectangular |
|
450 |
* coordinates ({@code x}, {@code y}) to polar |
|
451 |
* coordinates (r, <i>theta</i>). |
|
452 |
* This method computes the phase <i>theta</i> by computing an arc tangent |
|
453 |
* of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special |
|
454 |
* cases: |
|
455 |
* <ul><li>If either argument is NaN, then the result is NaN. |
|
456 |
* <li>If the first argument is positive zero and the second argument |
|
457 |
* is positive, or the first argument is positive and finite and the |
|
458 |
* second argument is positive infinity, then the result is positive |
|
459 |
* zero. |
|
460 |
* <li>If the first argument is negative zero and the second argument |
|
461 |
* is positive, or the first argument is negative and finite and the |
|
462 |
* second argument is positive infinity, then the result is negative zero. |
|
463 |
* <li>If the first argument is positive zero and the second argument |
|
464 |
* is negative, or the first argument is positive and finite and the |
|
465 |
* second argument is negative infinity, then the result is the |
|
466 |
* {@code double} value closest to <i>pi</i>. |
|
467 |
* <li>If the first argument is negative zero and the second argument |
|
468 |
* is negative, or the first argument is negative and finite and the |
|
469 |
* second argument is negative infinity, then the result is the |
|
470 |
* {@code double} value closest to -<i>pi</i>. |
|
471 |
* <li>If the first argument is positive and the second argument is |
|
472 |
* positive zero or negative zero, or the first argument is positive |
|
473 |
* infinity and the second argument is finite, then the result is the |
|
474 |
* {@code double} value closest to <i>pi</i>/2. |
|
475 |
* <li>If the first argument is negative and the second argument is |
|
476 |
* positive zero or negative zero, or the first argument is negative |
|
477 |
* infinity and the second argument is finite, then the result is the |
|
478 |
* {@code double} value closest to -<i>pi</i>/2. |
|
479 |
* <li>If both arguments are positive infinity, then the result is the |
|
480 |
* {@code double} value closest to <i>pi</i>/4. |
|
481 |
* <li>If the first argument is positive infinity and the second argument |
|
482 |
* is negative infinity, then the result is the {@code double} |
|
483 |
* value closest to 3*<i>pi</i>/4. |
|
484 |
* <li>If the first argument is negative infinity and the second argument |
|
485 |
* is positive infinity, then the result is the {@code double} value |
|
486 |
* closest to -<i>pi</i>/4. |
|
487 |
* <li>If both arguments are negative infinity, then the result is the |
|
488 |
* {@code double} value closest to -3*<i>pi</i>/4.</ul> |
|
489 |
* |
|
490 |
* <p>The computed result must be within 2 ulps of the exact result. |
|
491 |
* Results must be semi-monotonic. |
|
492 |
* |
|
493 |
* @param y the ordinate coordinate |
|
494 |
* @param x the abscissa coordinate |
|
495 |
* @return the <i>theta</i> component of the point |
|
496 |
* (<i>r</i>, <i>theta</i>) |
|
497 |
* in polar coordinates that corresponds to the point |
|
498 |
* (<i>x</i>, <i>y</i>) in Cartesian coordinates. |
|
499 |
*/ |
|
500 |
public static double atan2(double y, double x) { |
|
501 |
return StrictMath.atan2(y, x); // default impl. delegates to StrictMath |
|
502 |
} |
|
503 |
||
504 |
/** |
|
505 |
* Returns the value of the first argument raised to the power of the |
|
506 |
* second argument. Special cases: |
|
507 |
* |
|
508 |
* <ul><li>If the second argument is positive or negative zero, then the |
|
509 |
* result is 1.0. |
|
510 |
* <li>If the second argument is 1.0, then the result is the same as the |
|
511 |
* first argument. |
|
512 |
* <li>If the second argument is NaN, then the result is NaN. |
|
513 |
* <li>If the first argument is NaN and the second argument is nonzero, |
|
514 |
* then the result is NaN. |
|
515 |
* |
|
516 |
* <li>If |
|
517 |
* <ul> |
|
518 |
* <li>the absolute value of the first argument is greater than 1 |
|
519 |
* and the second argument is positive infinity, or |
|
520 |
* <li>the absolute value of the first argument is less than 1 and |
|
521 |
* the second argument is negative infinity, |
|
522 |
* </ul> |
|
523 |
* then the result is positive infinity. |
|
524 |
* |
|
525 |
* <li>If |
|
526 |
* <ul> |
|
527 |
* <li>the absolute value of the first argument is greater than 1 and |
|
528 |
* the second argument is negative infinity, or |
|
529 |
* <li>the absolute value of the |
|
530 |
* first argument is less than 1 and the second argument is positive |
|
531 |
* infinity, |
|
532 |
* </ul> |
|
533 |
* then the result is positive zero. |
|
534 |
* |
|
535 |
* <li>If the absolute value of the first argument equals 1 and the |
|
536 |
* second argument is infinite, then the result is NaN. |
|
537 |
* |
|
538 |
* <li>If |
|
539 |
* <ul> |
|
540 |
* <li>the first argument is positive zero and the second argument |
|
541 |
* is greater than zero, or |
|
542 |
* <li>the first argument is positive infinity and the second |
|
543 |
* argument is less than zero, |
|
544 |
* </ul> |
|
545 |
* then the result is positive zero. |
|
546 |
* |
|
547 |
* <li>If |
|
548 |
* <ul> |
|
549 |
* <li>the first argument is positive zero and the second argument |
|
550 |
* is less than zero, or |
|
551 |
* <li>the first argument is positive infinity and the second |
|
552 |
* argument is greater than zero, |
|
553 |
* </ul> |
|
554 |
* then the result is positive infinity. |
|
555 |
* |
|
556 |
* <li>If |
|
557 |
* <ul> |
|
558 |
* <li>the first argument is negative zero and the second argument |
|
559 |
* is greater than zero but not a finite odd integer, or |
|
560 |
* <li>the first argument is negative infinity and the second |
|
561 |
* argument is less than zero but not a finite odd integer, |
|
562 |
* </ul> |
|
563 |
* then the result is positive zero. |
|
564 |
* |
|
565 |
* <li>If |
|
566 |
* <ul> |
|
567 |
* <li>the first argument is negative zero and the second argument |
|
568 |
* is a positive finite odd integer, or |
|
569 |
* <li>the first argument is negative infinity and the second |
|
570 |
* argument is a negative finite odd integer, |
|
571 |
* </ul> |
|
572 |
* then the result is negative zero. |
|
573 |
* |
|
574 |
* <li>If |
|
575 |
* <ul> |
|
576 |
* <li>the first argument is negative zero and the second argument |
|
577 |
* is less than zero but not a finite odd integer, or |
|
578 |
* <li>the first argument is negative infinity and the second |
|
579 |
* argument is greater than zero but not a finite odd integer, |
|
580 |
* </ul> |
|
581 |
* then the result is positive infinity. |
|
582 |
* |
|
583 |
* <li>If |
|
584 |
* <ul> |
|
585 |
* <li>the first argument is negative zero and the second argument |
|
586 |
* is a negative finite odd integer, or |
|
587 |
* <li>the first argument is negative infinity and the second |
|
588 |
* argument is a positive finite odd integer, |
|
589 |
* </ul> |
|
590 |
* then the result is negative infinity. |
|
591 |
* |
|
592 |
* <li>If the first argument is finite and less than zero |
|
593 |
* <ul> |
|
594 |
* <li> if the second argument is a finite even integer, the |
|
595 |
* result is equal to the result of raising the absolute value of |
|
596 |
* the first argument to the power of the second argument |
|
597 |
* |
|
598 |
* <li>if the second argument is a finite odd integer, the result |
|
599 |
* is equal to the negative of the result of raising the absolute |
|
600 |
* value of the first argument to the power of the second |
|
601 |
* argument |
|
602 |
* |
|
603 |
* <li>if the second argument is finite and not an integer, then |
|
604 |
* the result is NaN. |
|
605 |
* </ul> |
|
606 |
* |
|
607 |
* <li>If both arguments are integers, then the result is exactly equal |
|
608 |
* to the mathematical result of raising the first argument to the power |
|
609 |
* of the second argument if that result can in fact be represented |
|
610 |
* exactly as a {@code double} value.</ul> |
|
611 |
* |
|
612 |
* <p>(In the foregoing descriptions, a floating-point value is |
|
613 |
* considered to be an integer if and only if it is finite and a |
|
614 |
* fixed point of the method {@link #ceil ceil} or, |
|
615 |
* equivalently, a fixed point of the method {@link #floor |
|
616 |
* floor}. A value is a fixed point of a one-argument |
|
617 |
* method if and only if the result of applying the method to the |
|
618 |
* value is equal to the value.) |
|
619 |
* |
|
620 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
621 |
* Results must be semi-monotonic. |
|
622 |
* |
|
623 |
* @param a the base. |
|
624 |
* @param b the exponent. |
|
625 |
* @return the value {@code a}<sup>{@code b}</sup>. |
|
626 |
*/ |
|
627 |
public static double pow(double a, double b) { |
|
628 |
return StrictMath.pow(a, b); // default impl. delegates to StrictMath |
|
629 |
} |
|
630 |
||
631 |
/** |
|
9269
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
632 |
* Returns the closest {@code int} to the argument, with ties |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
633 |
* rounding up. |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
634 |
* |
2 | 635 |
* <p> |
636 |
* Special cases: |
|
637 |
* <ul><li>If the argument is NaN, the result is 0. |
|
638 |
* <li>If the argument is negative infinity or any value less than or |
|
639 |
* equal to the value of {@code Integer.MIN_VALUE}, the result is |
|
640 |
* equal to the value of {@code Integer.MIN_VALUE}. |
|
641 |
* <li>If the argument is positive infinity or any value greater than or |
|
642 |
* equal to the value of {@code Integer.MAX_VALUE}, the result is |
|
643 |
* equal to the value of {@code Integer.MAX_VALUE}.</ul> |
|
644 |
* |
|
645 |
* @param a a floating-point value to be rounded to an integer. |
|
646 |
* @return the value of the argument rounded to the nearest |
|
647 |
* {@code int} value. |
|
648 |
* @see java.lang.Integer#MAX_VALUE |
|
649 |
* @see java.lang.Integer#MIN_VALUE |
|
650 |
*/ |
|
651 |
public static int round(float a) { |
|
9269
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
652 |
if (a != 0x1.fffffep-2f) // greatest float value less than 0.5 |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
653 |
return (int)floor(a + 0.5f); |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
654 |
else |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
655 |
return 0; |
2 | 656 |
} |
657 |
||
658 |
/** |
|
9269
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
659 |
* Returns the closest {@code long} to the argument, with ties |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
660 |
* rounding up. |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
661 |
* |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
662 |
* <p>Special cases: |
2 | 663 |
* <ul><li>If the argument is NaN, the result is 0. |
664 |
* <li>If the argument is negative infinity or any value less than or |
|
665 |
* equal to the value of {@code Long.MIN_VALUE}, the result is |
|
666 |
* equal to the value of {@code Long.MIN_VALUE}. |
|
667 |
* <li>If the argument is positive infinity or any value greater than or |
|
668 |
* equal to the value of {@code Long.MAX_VALUE}, the result is |
|
669 |
* equal to the value of {@code Long.MAX_VALUE}.</ul> |
|
670 |
* |
|
671 |
* @param a a floating-point value to be rounded to a |
|
672 |
* {@code long}. |
|
673 |
* @return the value of the argument rounded to the nearest |
|
674 |
* {@code long} value. |
|
675 |
* @see java.lang.Long#MAX_VALUE |
|
676 |
* @see java.lang.Long#MIN_VALUE |
|
677 |
*/ |
|
678 |
public static long round(double a) { |
|
9269
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
679 |
if (a != 0x1.fffffffffffffp-2) // greatest double value less than 0.5 |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
680 |
return (long)floor(a + 0.5d); |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
681 |
else |
f66626469aa8
6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2
darcy
parents:
7668
diff
changeset
|
682 |
return 0; |
2 | 683 |
} |
684 |
||
685 |
private static Random randomNumberGenerator; |
|
686 |
||
5781
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
687 |
private static synchronized Random initRNG() { |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
688 |
Random rnd = randomNumberGenerator; |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
689 |
return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd; |
2 | 690 |
} |
691 |
||
692 |
/** |
|
693 |
* Returns a {@code double} value with a positive sign, greater |
|
694 |
* than or equal to {@code 0.0} and less than {@code 1.0}. |
|
695 |
* Returned values are chosen pseudorandomly with (approximately) |
|
696 |
* uniform distribution from that range. |
|
697 |
* |
|
698 |
* <p>When this method is first called, it creates a single new |
|
699 |
* pseudorandom-number generator, exactly as if by the expression |
|
5781
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
700 |
* |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
701 |
* <blockquote>{@code new java.util.Random()}</blockquote> |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
702 |
* |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
703 |
* This new pseudorandom-number generator is used thereafter for |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
704 |
* all calls to this method and is used nowhere else. |
2 | 705 |
* |
706 |
* <p>This method is properly synchronized to allow correct use by |
|
707 |
* more than one thread. However, if many threads need to generate |
|
708 |
* pseudorandom numbers at a great rate, it may reduce contention |
|
709 |
* for each thread to have its own pseudorandom-number generator. |
|
710 |
* |
|
711 |
* @return a pseudorandom {@code double} greater than or equal |
|
712 |
* to {@code 0.0} and less than {@code 1.0}. |
|
5781
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
713 |
* @see Random#nextDouble() |
2 | 714 |
*/ |
715 |
public static double random() { |
|
5781
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
716 |
Random rnd = randomNumberGenerator; |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
717 |
if (rnd == null) rnd = initRNG(); |
11a42d91eb56
6959259: Minor improvements to static Random field caching
martin
parents:
5506
diff
changeset
|
718 |
return rnd.nextDouble(); |
2 | 719 |
} |
720 |
||
721 |
/** |
|
722 |
* Returns the absolute value of an {@code int} value. |
|
723 |
* If the argument is not negative, the argument is returned. |
|
724 |
* If the argument is negative, the negation of the argument is returned. |
|
725 |
* |
|
726 |
* <p>Note that if the argument is equal to the value of |
|
727 |
* {@link Integer#MIN_VALUE}, the most negative representable |
|
728 |
* {@code int} value, the result is that same value, which is |
|
729 |
* negative. |
|
730 |
* |
|
731 |
* @param a the argument whose absolute value is to be determined |
|
732 |
* @return the absolute value of the argument. |
|
733 |
*/ |
|
734 |
public static int abs(int a) { |
|
735 |
return (a < 0) ? -a : a; |
|
736 |
} |
|
737 |
||
738 |
/** |
|
739 |
* Returns the absolute value of a {@code long} value. |
|
740 |
* If the argument is not negative, the argument is returned. |
|
741 |
* If the argument is negative, the negation of the argument is returned. |
|
742 |
* |
|
743 |
* <p>Note that if the argument is equal to the value of |
|
744 |
* {@link Long#MIN_VALUE}, the most negative representable |
|
745 |
* {@code long} value, the result is that same value, which |
|
746 |
* is negative. |
|
747 |
* |
|
748 |
* @param a the argument whose absolute value is to be determined |
|
749 |
* @return the absolute value of the argument. |
|
750 |
*/ |
|
751 |
public static long abs(long a) { |
|
752 |
return (a < 0) ? -a : a; |
|
753 |
} |
|
754 |
||
755 |
/** |
|
756 |
* Returns the absolute value of a {@code float} value. |
|
757 |
* If the argument is not negative, the argument is returned. |
|
758 |
* If the argument is negative, the negation of the argument is returned. |
|
759 |
* Special cases: |
|
760 |
* <ul><li>If the argument is positive zero or negative zero, the |
|
761 |
* result is positive zero. |
|
762 |
* <li>If the argument is infinite, the result is positive infinity. |
|
763 |
* <li>If the argument is NaN, the result is NaN.</ul> |
|
764 |
* In other words, the result is the same as the value of the expression: |
|
765 |
* <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} |
|
766 |
* |
|
767 |
* @param a the argument whose absolute value is to be determined |
|
768 |
* @return the absolute value of the argument. |
|
769 |
*/ |
|
770 |
public static float abs(float a) { |
|
771 |
return (a <= 0.0F) ? 0.0F - a : a; |
|
772 |
} |
|
773 |
||
774 |
/** |
|
775 |
* Returns the absolute value of a {@code double} value. |
|
776 |
* If the argument is not negative, the argument is returned. |
|
777 |
* If the argument is negative, the negation of the argument is returned. |
|
778 |
* Special cases: |
|
779 |
* <ul><li>If the argument is positive zero or negative zero, the result |
|
780 |
* is positive zero. |
|
781 |
* <li>If the argument is infinite, the result is positive infinity. |
|
782 |
* <li>If the argument is NaN, the result is NaN.</ul> |
|
783 |
* In other words, the result is the same as the value of the expression: |
|
784 |
* <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} |
|
785 |
* |
|
786 |
* @param a the argument whose absolute value is to be determined |
|
787 |
* @return the absolute value of the argument. |
|
788 |
*/ |
|
789 |
public static double abs(double a) { |
|
790 |
return (a <= 0.0D) ? 0.0D - a : a; |
|
791 |
} |
|
792 |
||
793 |
/** |
|
794 |
* Returns the greater of two {@code int} values. That is, the |
|
795 |
* result is the argument closer to the value of |
|
796 |
* {@link Integer#MAX_VALUE}. If the arguments have the same value, |
|
797 |
* the result is that same value. |
|
798 |
* |
|
799 |
* @param a an argument. |
|
800 |
* @param b another argument. |
|
801 |
* @return the larger of {@code a} and {@code b}. |
|
802 |
*/ |
|
803 |
public static int max(int a, int b) { |
|
804 |
return (a >= b) ? a : b; |
|
805 |
} |
|
806 |
||
807 |
/** |
|
808 |
* Returns the greater of two {@code long} values. That is, the |
|
809 |
* result is the argument closer to the value of |
|
810 |
* {@link Long#MAX_VALUE}. If the arguments have the same value, |
|
811 |
* the result is that same value. |
|
812 |
* |
|
813 |
* @param a an argument. |
|
814 |
* @param b another argument. |
|
815 |
* @return the larger of {@code a} and {@code b}. |
|
816 |
*/ |
|
817 |
public static long max(long a, long b) { |
|
818 |
return (a >= b) ? a : b; |
|
819 |
} |
|
820 |
||
821 |
private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f); |
|
822 |
private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d); |
|
823 |
||
824 |
/** |
|
825 |
* Returns the greater of two {@code float} values. That is, |
|
826 |
* the result is the argument closer to positive infinity. If the |
|
827 |
* arguments have the same value, the result is that same |
|
828 |
* value. If either value is NaN, then the result is NaN. Unlike |
|
829 |
* the numerical comparison operators, this method considers |
|
830 |
* negative zero to be strictly smaller than positive zero. If one |
|
831 |
* argument is positive zero and the other negative zero, the |
|
832 |
* result is positive zero. |
|
833 |
* |
|
834 |
* @param a an argument. |
|
835 |
* @param b another argument. |
|
836 |
* @return the larger of {@code a} and {@code b}. |
|
837 |
*/ |
|
838 |
public static float max(float a, float b) { |
|
839 |
if (a != a) return a; // a is NaN |
|
840 |
if ((a == 0.0f) && (b == 0.0f) |
|
841 |
&& (Float.floatToIntBits(a) == negativeZeroFloatBits)) { |
|
842 |
return b; |
|
843 |
} |
|
844 |
return (a >= b) ? a : b; |
|
845 |
} |
|
846 |
||
847 |
/** |
|
848 |
* Returns the greater of two {@code double} values. That |
|
849 |
* is, the result is the argument closer to positive infinity. If |
|
850 |
* the arguments have the same value, the result is that same |
|
851 |
* value. If either value is NaN, then the result is NaN. Unlike |
|
852 |
* the numerical comparison operators, this method considers |
|
853 |
* negative zero to be strictly smaller than positive zero. If one |
|
854 |
* argument is positive zero and the other negative zero, the |
|
855 |
* result is positive zero. |
|
856 |
* |
|
857 |
* @param a an argument. |
|
858 |
* @param b another argument. |
|
859 |
* @return the larger of {@code a} and {@code b}. |
|
860 |
*/ |
|
861 |
public static double max(double a, double b) { |
|
862 |
if (a != a) return a; // a is NaN |
|
863 |
if ((a == 0.0d) && (b == 0.0d) |
|
864 |
&& (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) { |
|
865 |
return b; |
|
866 |
} |
|
867 |
return (a >= b) ? a : b; |
|
868 |
} |
|
869 |
||
870 |
/** |
|
871 |
* Returns the smaller of two {@code int} values. That is, |
|
872 |
* the result the argument closer to the value of |
|
873 |
* {@link Integer#MIN_VALUE}. If the arguments have the same |
|
874 |
* value, the result is that same value. |
|
875 |
* |
|
876 |
* @param a an argument. |
|
877 |
* @param b another argument. |
|
878 |
* @return the smaller of {@code a} and {@code b}. |
|
879 |
*/ |
|
880 |
public static int min(int a, int b) { |
|
881 |
return (a <= b) ? a : b; |
|
882 |
} |
|
883 |
||
884 |
/** |
|
885 |
* Returns the smaller of two {@code long} values. That is, |
|
886 |
* the result is the argument closer to the value of |
|
887 |
* {@link Long#MIN_VALUE}. If the arguments have the same |
|
888 |
* value, the result is that same value. |
|
889 |
* |
|
890 |
* @param a an argument. |
|
891 |
* @param b another argument. |
|
892 |
* @return the smaller of {@code a} and {@code b}. |
|
893 |
*/ |
|
894 |
public static long min(long a, long b) { |
|
895 |
return (a <= b) ? a : b; |
|
896 |
} |
|
897 |
||
898 |
/** |
|
899 |
* Returns the smaller of two {@code float} values. That is, |
|
900 |
* the result is the value closer to negative infinity. If the |
|
901 |
* arguments have the same value, the result is that same |
|
902 |
* value. If either value is NaN, then the result is NaN. Unlike |
|
903 |
* the numerical comparison operators, this method considers |
|
904 |
* negative zero to be strictly smaller than positive zero. If |
|
905 |
* one argument is positive zero and the other is negative zero, |
|
906 |
* the result is negative zero. |
|
907 |
* |
|
908 |
* @param a an argument. |
|
909 |
* @param b another argument. |
|
910 |
* @return the smaller of {@code a} and {@code b}. |
|
911 |
*/ |
|
912 |
public static float min(float a, float b) { |
|
913 |
if (a != a) return a; // a is NaN |
|
914 |
if ((a == 0.0f) && (b == 0.0f) |
|
915 |
&& (Float.floatToIntBits(b) == negativeZeroFloatBits)) { |
|
916 |
return b; |
|
917 |
} |
|
918 |
return (a <= b) ? a : b; |
|
919 |
} |
|
920 |
||
921 |
/** |
|
922 |
* Returns the smaller of two {@code double} values. That |
|
923 |
* is, the result is the value closer to negative infinity. If the |
|
924 |
* arguments have the same value, the result is that same |
|
925 |
* value. If either value is NaN, then the result is NaN. Unlike |
|
926 |
* the numerical comparison operators, this method considers |
|
927 |
* negative zero to be strictly smaller than positive zero. If one |
|
928 |
* argument is positive zero and the other is negative zero, the |
|
929 |
* result is negative zero. |
|
930 |
* |
|
931 |
* @param a an argument. |
|
932 |
* @param b another argument. |
|
933 |
* @return the smaller of {@code a} and {@code b}. |
|
934 |
*/ |
|
935 |
public static double min(double a, double b) { |
|
936 |
if (a != a) return a; // a is NaN |
|
937 |
if ((a == 0.0d) && (b == 0.0d) |
|
938 |
&& (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) { |
|
939 |
return b; |
|
940 |
} |
|
941 |
return (a <= b) ? a : b; |
|
942 |
} |
|
943 |
||
944 |
/** |
|
10122 | 945 |
* Returns the size of an ulp of the argument. An ulp, unit in |
946 |
* the last place, of a {@code double} value is the positive |
|
947 |
* distance between this floating-point value and the {@code |
|
948 |
* double} value next larger in magnitude. Note that for non-NaN |
|
949 |
* <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. |
|
2 | 950 |
* |
951 |
* <p>Special Cases: |
|
952 |
* <ul> |
|
953 |
* <li> If the argument is NaN, then the result is NaN. |
|
954 |
* <li> If the argument is positive or negative infinity, then the |
|
955 |
* result is positive infinity. |
|
956 |
* <li> If the argument is positive or negative zero, then the result is |
|
957 |
* {@code Double.MIN_VALUE}. |
|
958 |
* <li> If the argument is ±{@code Double.MAX_VALUE}, then |
|
959 |
* the result is equal to 2<sup>971</sup>. |
|
960 |
* </ul> |
|
961 |
* |
|
962 |
* @param d the floating-point value whose ulp is to be returned |
|
963 |
* @return the size of an ulp of the argument |
|
964 |
* @author Joseph D. Darcy |
|
965 |
* @since 1.5 |
|
966 |
*/ |
|
967 |
public static double ulp(double d) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
968 |
int exp = getExponent(d); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
969 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
970 |
switch(exp) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
971 |
case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
972 |
return Math.abs(d); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
973 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
974 |
case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
975 |
return Double.MIN_VALUE; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
976 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
977 |
default: |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
978 |
assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
979 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
980 |
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
981 |
exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
982 |
if (exp >= DoubleConsts.MIN_EXPONENT) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
983 |
return powerOfTwoD(exp); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
984 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
985 |
else { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
986 |
// return a subnormal result; left shift integer |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
987 |
// representation of Double.MIN_VALUE appropriate |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
988 |
// number of positions |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
989 |
return Double.longBitsToDouble(1L << |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
990 |
(exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) )); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
991 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
992 |
} |
2 | 993 |
} |
994 |
||
995 |
/** |
|
10122 | 996 |
* Returns the size of an ulp of the argument. An ulp, unit in |
997 |
* the last place, of a {@code float} value is the positive |
|
998 |
* distance between this floating-point value and the {@code |
|
999 |
* float} value next larger in magnitude. Note that for non-NaN |
|
1000 |
* <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. |
|
2 | 1001 |
* |
1002 |
* <p>Special Cases: |
|
1003 |
* <ul> |
|
1004 |
* <li> If the argument is NaN, then the result is NaN. |
|
1005 |
* <li> If the argument is positive or negative infinity, then the |
|
1006 |
* result is positive infinity. |
|
1007 |
* <li> If the argument is positive or negative zero, then the result is |
|
1008 |
* {@code Float.MIN_VALUE}. |
|
1009 |
* <li> If the argument is ±{@code Float.MAX_VALUE}, then |
|
1010 |
* the result is equal to 2<sup>104</sup>. |
|
1011 |
* </ul> |
|
1012 |
* |
|
1013 |
* @param f the floating-point value whose ulp is to be returned |
|
1014 |
* @return the size of an ulp of the argument |
|
1015 |
* @author Joseph D. Darcy |
|
1016 |
* @since 1.5 |
|
1017 |
*/ |
|
1018 |
public static float ulp(float f) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1019 |
int exp = getExponent(f); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1020 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1021 |
switch(exp) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1022 |
case FloatConsts.MAX_EXPONENT+1: // NaN or infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1023 |
return Math.abs(f); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1024 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1025 |
case FloatConsts.MIN_EXPONENT-1: // zero or subnormal |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1026 |
return FloatConsts.MIN_VALUE; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1027 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1028 |
default: |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1029 |
assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1030 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1031 |
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1032 |
exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1033 |
if (exp >= FloatConsts.MIN_EXPONENT) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1034 |
return powerOfTwoF(exp); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1035 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1036 |
else { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1037 |
// return a subnormal result; left shift integer |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1038 |
// representation of FloatConsts.MIN_VALUE appropriate |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1039 |
// number of positions |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1040 |
return Float.intBitsToFloat(1 << |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1041 |
(exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) )); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1042 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1043 |
} |
2 | 1044 |
} |
1045 |
||
1046 |
/** |
|
1047 |
* Returns the signum function of the argument; zero if the argument |
|
1048 |
* is zero, 1.0 if the argument is greater than zero, -1.0 if the |
|
1049 |
* argument is less than zero. |
|
1050 |
* |
|
1051 |
* <p>Special Cases: |
|
1052 |
* <ul> |
|
1053 |
* <li> If the argument is NaN, then the result is NaN. |
|
1054 |
* <li> If the argument is positive zero or negative zero, then the |
|
1055 |
* result is the same as the argument. |
|
1056 |
* </ul> |
|
1057 |
* |
|
1058 |
* @param d the floating-point value whose signum is to be returned |
|
1059 |
* @return the signum function of the argument |
|
1060 |
* @author Joseph D. Darcy |
|
1061 |
* @since 1.5 |
|
1062 |
*/ |
|
1063 |
public static double signum(double d) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1064 |
return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d); |
2 | 1065 |
} |
1066 |
||
1067 |
/** |
|
1068 |
* Returns the signum function of the argument; zero if the argument |
|
1069 |
* is zero, 1.0f if the argument is greater than zero, -1.0f if the |
|
1070 |
* argument is less than zero. |
|
1071 |
* |
|
1072 |
* <p>Special Cases: |
|
1073 |
* <ul> |
|
1074 |
* <li> If the argument is NaN, then the result is NaN. |
|
1075 |
* <li> If the argument is positive zero or negative zero, then the |
|
1076 |
* result is the same as the argument. |
|
1077 |
* </ul> |
|
1078 |
* |
|
1079 |
* @param f the floating-point value whose signum is to be returned |
|
1080 |
* @return the signum function of the argument |
|
1081 |
* @author Joseph D. Darcy |
|
1082 |
* @since 1.5 |
|
1083 |
*/ |
|
1084 |
public static float signum(float f) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1085 |
return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f); |
2 | 1086 |
} |
1087 |
||
1088 |
/** |
|
1089 |
* Returns the hyperbolic sine of a {@code double} value. |
|
1090 |
* The hyperbolic sine of <i>x</i> is defined to be |
|
1091 |
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 |
|
1092 |
* where <i>e</i> is {@linkplain Math#E Euler's number}. |
|
1093 |
* |
|
1094 |
* <p>Special cases: |
|
1095 |
* <ul> |
|
1096 |
* |
|
1097 |
* <li>If the argument is NaN, then the result is NaN. |
|
1098 |
* |
|
1099 |
* <li>If the argument is infinite, then the result is an infinity |
|
1100 |
* with the same sign as the argument. |
|
1101 |
* |
|
1102 |
* <li>If the argument is zero, then the result is a zero with the |
|
1103 |
* same sign as the argument. |
|
1104 |
* |
|
1105 |
* </ul> |
|
1106 |
* |
|
1107 |
* <p>The computed result must be within 2.5 ulps of the exact result. |
|
1108 |
* |
|
1109 |
* @param x The number whose hyperbolic sine is to be returned. |
|
1110 |
* @return The hyperbolic sine of {@code x}. |
|
1111 |
* @since 1.5 |
|
1112 |
*/ |
|
1113 |
public static double sinh(double x) { |
|
1114 |
return StrictMath.sinh(x); |
|
1115 |
} |
|
1116 |
||
1117 |
/** |
|
1118 |
* Returns the hyperbolic cosine of a {@code double} value. |
|
1119 |
* The hyperbolic cosine of <i>x</i> is defined to be |
|
1120 |
* (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 |
|
1121 |
* where <i>e</i> is {@linkplain Math#E Euler's number}. |
|
1122 |
* |
|
1123 |
* <p>Special cases: |
|
1124 |
* <ul> |
|
1125 |
* |
|
1126 |
* <li>If the argument is NaN, then the result is NaN. |
|
1127 |
* |
|
1128 |
* <li>If the argument is infinite, then the result is positive |
|
1129 |
* infinity. |
|
1130 |
* |
|
1131 |
* <li>If the argument is zero, then the result is {@code 1.0}. |
|
1132 |
* |
|
1133 |
* </ul> |
|
1134 |
* |
|
1135 |
* <p>The computed result must be within 2.5 ulps of the exact result. |
|
1136 |
* |
|
1137 |
* @param x The number whose hyperbolic cosine is to be returned. |
|
1138 |
* @return The hyperbolic cosine of {@code x}. |
|
1139 |
* @since 1.5 |
|
1140 |
*/ |
|
1141 |
public static double cosh(double x) { |
|
1142 |
return StrictMath.cosh(x); |
|
1143 |
} |
|
1144 |
||
1145 |
/** |
|
1146 |
* Returns the hyperbolic tangent of a {@code double} value. |
|
1147 |
* The hyperbolic tangent of <i>x</i> is defined to be |
|
1148 |
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), |
|
1149 |
* in other words, {@linkplain Math#sinh |
|
1150 |
* sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note |
|
1151 |
* that the absolute value of the exact tanh is always less than |
|
1152 |
* 1. |
|
1153 |
* |
|
1154 |
* <p>Special cases: |
|
1155 |
* <ul> |
|
1156 |
* |
|
1157 |
* <li>If the argument is NaN, then the result is NaN. |
|
1158 |
* |
|
1159 |
* <li>If the argument is zero, then the result is a zero with the |
|
1160 |
* same sign as the argument. |
|
1161 |
* |
|
1162 |
* <li>If the argument is positive infinity, then the result is |
|
1163 |
* {@code +1.0}. |
|
1164 |
* |
|
1165 |
* <li>If the argument is negative infinity, then the result is |
|
1166 |
* {@code -1.0}. |
|
1167 |
* |
|
1168 |
* </ul> |
|
1169 |
* |
|
1170 |
* <p>The computed result must be within 2.5 ulps of the exact result. |
|
1171 |
* The result of {@code tanh} for any finite input must have |
|
1172 |
* an absolute value less than or equal to 1. Note that once the |
|
1173 |
* exact result of tanh is within 1/2 of an ulp of the limit value |
|
1174 |
* of ±1, correctly signed ±{@code 1.0} should |
|
1175 |
* be returned. |
|
1176 |
* |
|
1177 |
* @param x The number whose hyperbolic tangent is to be returned. |
|
1178 |
* @return The hyperbolic tangent of {@code x}. |
|
1179 |
* @since 1.5 |
|
1180 |
*/ |
|
1181 |
public static double tanh(double x) { |
|
1182 |
return StrictMath.tanh(x); |
|
1183 |
} |
|
1184 |
||
1185 |
/** |
|
1186 |
* Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) |
|
1187 |
* without intermediate overflow or underflow. |
|
1188 |
* |
|
1189 |
* <p>Special cases: |
|
1190 |
* <ul> |
|
1191 |
* |
|
1192 |
* <li> If either argument is infinite, then the result |
|
1193 |
* is positive infinity. |
|
1194 |
* |
|
1195 |
* <li> If either argument is NaN and neither argument is infinite, |
|
1196 |
* then the result is NaN. |
|
1197 |
* |
|
1198 |
* </ul> |
|
1199 |
* |
|
1200 |
* <p>The computed result must be within 1 ulp of the exact |
|
1201 |
* result. If one parameter is held constant, the results must be |
|
1202 |
* semi-monotonic in the other parameter. |
|
1203 |
* |
|
1204 |
* @param x a value |
|
1205 |
* @param y a value |
|
1206 |
* @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) |
|
1207 |
* without intermediate overflow or underflow |
|
1208 |
* @since 1.5 |
|
1209 |
*/ |
|
1210 |
public static double hypot(double x, double y) { |
|
1211 |
return StrictMath.hypot(x, y); |
|
1212 |
} |
|
1213 |
||
1214 |
/** |
|
1215 |
* Returns <i>e</i><sup>x</sup> -1. Note that for values of |
|
1216 |
* <i>x</i> near 0, the exact sum of |
|
1217 |
* {@code expm1(x)} + 1 is much closer to the true |
|
1218 |
* result of <i>e</i><sup>x</sup> than {@code exp(x)}. |
|
1219 |
* |
|
1220 |
* <p>Special cases: |
|
1221 |
* <ul> |
|
1222 |
* <li>If the argument is NaN, the result is NaN. |
|
1223 |
* |
|
1224 |
* <li>If the argument is positive infinity, then the result is |
|
1225 |
* positive infinity. |
|
1226 |
* |
|
1227 |
* <li>If the argument is negative infinity, then the result is |
|
1228 |
* -1.0. |
|
1229 |
* |
|
1230 |
* <li>If the argument is zero, then the result is a zero with the |
|
1231 |
* same sign as the argument. |
|
1232 |
* |
|
1233 |
* </ul> |
|
1234 |
* |
|
1235 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
1236 |
* Results must be semi-monotonic. The result of |
|
1237 |
* {@code expm1} for any finite input must be greater than or |
|
1238 |
* equal to {@code -1.0}. Note that once the exact result of |
|
1239 |
* <i>e</i><sup>{@code x}</sup> - 1 is within 1/2 |
|
1240 |
* ulp of the limit value -1, {@code -1.0} should be |
|
1241 |
* returned. |
|
1242 |
* |
|
1243 |
* @param x the exponent to raise <i>e</i> to in the computation of |
|
1244 |
* <i>e</i><sup>{@code x}</sup> -1. |
|
1245 |
* @return the value <i>e</i><sup>{@code x}</sup> - 1. |
|
1246 |
* @since 1.5 |
|
1247 |
*/ |
|
1248 |
public static double expm1(double x) { |
|
1249 |
return StrictMath.expm1(x); |
|
1250 |
} |
|
1251 |
||
1252 |
/** |
|
1253 |
* Returns the natural logarithm of the sum of the argument and 1. |
|
1254 |
* Note that for small values {@code x}, the result of |
|
1255 |
* {@code log1p(x)} is much closer to the true result of ln(1 |
|
1256 |
* + {@code x}) than the floating-point evaluation of |
|
1257 |
* {@code log(1.0+x)}. |
|
1258 |
* |
|
1259 |
* <p>Special cases: |
|
1260 |
* |
|
1261 |
* <ul> |
|
1262 |
* |
|
1263 |
* <li>If the argument is NaN or less than -1, then the result is |
|
1264 |
* NaN. |
|
1265 |
* |
|
1266 |
* <li>If the argument is positive infinity, then the result is |
|
1267 |
* positive infinity. |
|
1268 |
* |
|
1269 |
* <li>If the argument is negative one, then the result is |
|
1270 |
* negative infinity. |
|
1271 |
* |
|
1272 |
* <li>If the argument is zero, then the result is a zero with the |
|
1273 |
* same sign as the argument. |
|
1274 |
* |
|
1275 |
* </ul> |
|
1276 |
* |
|
1277 |
* <p>The computed result must be within 1 ulp of the exact result. |
|
1278 |
* Results must be semi-monotonic. |
|
1279 |
* |
|
1280 |
* @param x a value |
|
1281 |
* @return the value ln({@code x} + 1), the natural |
|
1282 |
* log of {@code x} + 1 |
|
1283 |
* @since 1.5 |
|
1284 |
*/ |
|
1285 |
public static double log1p(double x) { |
|
1286 |
return StrictMath.log1p(x); |
|
1287 |
} |
|
1288 |
||
1289 |
/** |
|
1290 |
* Returns the first floating-point argument with the sign of the |
|
1291 |
* second floating-point argument. Note that unlike the {@link |
|
1292 |
* StrictMath#copySign(double, double) StrictMath.copySign} |
|
1293 |
* method, this method does not require NaN {@code sign} |
|
1294 |
* arguments to be treated as positive values; implementations are |
|
1295 |
* permitted to treat some NaN arguments as positive and other NaN |
|
1296 |
* arguments as negative to allow greater performance. |
|
1297 |
* |
|
1298 |
* @param magnitude the parameter providing the magnitude of the result |
|
1299 |
* @param sign the parameter providing the sign of the result |
|
1300 |
* @return a value with the magnitude of {@code magnitude} |
|
1301 |
* and the sign of {@code sign}. |
|
1302 |
* @since 1.6 |
|
1303 |
*/ |
|
1304 |
public static double copySign(double magnitude, double sign) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1305 |
return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) & |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1306 |
(DoubleConsts.SIGN_BIT_MASK)) | |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1307 |
(Double.doubleToRawLongBits(magnitude) & |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1308 |
(DoubleConsts.EXP_BIT_MASK | |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1309 |
DoubleConsts.SIGNIF_BIT_MASK))); |
2 | 1310 |
} |
1311 |
||
1312 |
/** |
|
1313 |
* Returns the first floating-point argument with the sign of the |
|
1314 |
* second floating-point argument. Note that unlike the {@link |
|
1315 |
* StrictMath#copySign(float, float) StrictMath.copySign} |
|
1316 |
* method, this method does not require NaN {@code sign} |
|
1317 |
* arguments to be treated as positive values; implementations are |
|
1318 |
* permitted to treat some NaN arguments as positive and other NaN |
|
1319 |
* arguments as negative to allow greater performance. |
|
1320 |
* |
|
1321 |
* @param magnitude the parameter providing the magnitude of the result |
|
1322 |
* @param sign the parameter providing the sign of the result |
|
1323 |
* @return a value with the magnitude of {@code magnitude} |
|
1324 |
* and the sign of {@code sign}. |
|
1325 |
* @since 1.6 |
|
1326 |
*/ |
|
1327 |
public static float copySign(float magnitude, float sign) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1328 |
return Float.intBitsToFloat((Float.floatToRawIntBits(sign) & |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1329 |
(FloatConsts.SIGN_BIT_MASK)) | |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1330 |
(Float.floatToRawIntBits(magnitude) & |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1331 |
(FloatConsts.EXP_BIT_MASK | |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1332 |
FloatConsts.SIGNIF_BIT_MASK))); |
2 | 1333 |
} |
1334 |
||
1335 |
/** |
|
1336 |
* Returns the unbiased exponent used in the representation of a |
|
1337 |
* {@code float}. Special cases: |
|
1338 |
* |
|
1339 |
* <ul> |
|
1340 |
* <li>If the argument is NaN or infinite, then the result is |
|
1341 |
* {@link Float#MAX_EXPONENT} + 1. |
|
1342 |
* <li>If the argument is zero or subnormal, then the result is |
|
1343 |
* {@link Float#MIN_EXPONENT} -1. |
|
1344 |
* </ul> |
|
1345 |
* @param f a {@code float} value |
|
1346 |
* @return the unbiased exponent of the argument |
|
1347 |
* @since 1.6 |
|
1348 |
*/ |
|
1349 |
public static int getExponent(float f) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1350 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1351 |
* Bitwise convert f to integer, mask out exponent bits, shift |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1352 |
* to the right and then subtract out float's bias adjust to |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1353 |
* get true exponent value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1354 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1355 |
return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >> |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1356 |
(FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS; |
2 | 1357 |
} |
1358 |
||
1359 |
/** |
|
1360 |
* Returns the unbiased exponent used in the representation of a |
|
1361 |
* {@code double}. Special cases: |
|
1362 |
* |
|
1363 |
* <ul> |
|
1364 |
* <li>If the argument is NaN or infinite, then the result is |
|
1365 |
* {@link Double#MAX_EXPONENT} + 1. |
|
1366 |
* <li>If the argument is zero or subnormal, then the result is |
|
1367 |
* {@link Double#MIN_EXPONENT} -1. |
|
1368 |
* </ul> |
|
1369 |
* @param d a {@code double} value |
|
1370 |
* @return the unbiased exponent of the argument |
|
1371 |
* @since 1.6 |
|
1372 |
*/ |
|
1373 |
public static int getExponent(double d) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1374 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1375 |
* Bitwise convert d to long, mask out exponent bits, shift |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1376 |
* to the right and then subtract out double's bias adjust to |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1377 |
* get true exponent value. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1378 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1379 |
return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >> |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1380 |
(DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS); |
2 | 1381 |
} |
1382 |
||
1383 |
/** |
|
1384 |
* Returns the floating-point number adjacent to the first |
|
1385 |
* argument in the direction of the second argument. If both |
|
1386 |
* arguments compare as equal the second argument is returned. |
|
1387 |
* |
|
1388 |
* <p> |
|
1389 |
* Special cases: |
|
1390 |
* <ul> |
|
1391 |
* <li> If either argument is a NaN, then NaN is returned. |
|
1392 |
* |
|
1393 |
* <li> If both arguments are signed zeros, {@code direction} |
|
1394 |
* is returned unchanged (as implied by the requirement of |
|
1395 |
* returning the second argument if the arguments compare as |
|
1396 |
* equal). |
|
1397 |
* |
|
1398 |
* <li> If {@code start} is |
|
1399 |
* ±{@link Double#MIN_VALUE} and {@code direction} |
|
1400 |
* has a value such that the result should have a smaller |
|
1401 |
* magnitude, then a zero with the same sign as {@code start} |
|
1402 |
* is returned. |
|
1403 |
* |
|
1404 |
* <li> If {@code start} is infinite and |
|
1405 |
* {@code direction} has a value such that the result should |
|
1406 |
* have a smaller magnitude, {@link Double#MAX_VALUE} with the |
|
1407 |
* same sign as {@code start} is returned. |
|
1408 |
* |
|
1409 |
* <li> If {@code start} is equal to ± |
|
1410 |
* {@link Double#MAX_VALUE} and {@code direction} has a |
|
1411 |
* value such that the result should have a larger magnitude, an |
|
1412 |
* infinity with same sign as {@code start} is returned. |
|
1413 |
* </ul> |
|
1414 |
* |
|
1415 |
* @param start starting floating-point value |
|
1416 |
* @param direction value indicating which of |
|
1417 |
* {@code start}'s neighbors or {@code start} should |
|
1418 |
* be returned |
|
1419 |
* @return The floating-point number adjacent to {@code start} in the |
|
1420 |
* direction of {@code direction}. |
|
1421 |
* @since 1.6 |
|
1422 |
*/ |
|
1423 |
public static double nextAfter(double start, double direction) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1424 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1425 |
* The cases: |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1426 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1427 |
* nextAfter(+infinity, 0) == MAX_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1428 |
* nextAfter(+infinity, +infinity) == +infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1429 |
* nextAfter(-infinity, 0) == -MAX_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1430 |
* nextAfter(-infinity, -infinity) == -infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1431 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1432 |
* are naturally handled without any additional testing |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1433 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1434 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1435 |
// First check for NaN values |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1436 |
if (Double.isNaN(start) || Double.isNaN(direction)) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1437 |
// return a NaN derived from the input NaN(s) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1438 |
return start + direction; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1439 |
} else if (start == direction) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1440 |
return direction; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1441 |
} else { // start > direction or start < direction |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1442 |
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1443 |
// then bitwise convert start to integer. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1444 |
long transducer = Double.doubleToRawLongBits(start + 0.0d); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1445 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1446 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1447 |
* IEEE 754 floating-point numbers are lexicographically |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1448 |
* ordered if treated as signed- magnitude integers . |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1449 |
* Since Java's integers are two's complement, |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1450 |
* incrementing" the two's complement representation of a |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1451 |
* logically negative floating-point value *decrements* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1452 |
* the signed-magnitude representation. Therefore, when |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1453 |
* the integer representation of a floating-point values |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1454 |
* is less than zero, the adjustment to the representation |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1455 |
* is in the opposite direction than would be expected at |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1456 |
* first . |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1457 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1458 |
if (direction > start) { // Calculate next greater value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1459 |
transducer = transducer + (transducer >= 0L ? 1L:-1L); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1460 |
} else { // Calculate next lesser value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1461 |
assert direction < start; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1462 |
if (transducer > 0L) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1463 |
--transducer; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1464 |
else |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1465 |
if (transducer < 0L ) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1466 |
++transducer; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1467 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1468 |
* transducer==0, the result is -MIN_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1469 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1470 |
* The transition from zero (implicitly |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1471 |
* positive) to the smallest negative |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1472 |
* signed magnitude value must be done |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1473 |
* explicitly. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1474 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1475 |
else |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1476 |
transducer = DoubleConsts.SIGN_BIT_MASK | 1L; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1477 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1478 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1479 |
return Double.longBitsToDouble(transducer); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1480 |
} |
2 | 1481 |
} |
1482 |
||
1483 |
/** |
|
1484 |
* Returns the floating-point number adjacent to the first |
|
1485 |
* argument in the direction of the second argument. If both |
|
1486 |
* arguments compare as equal a value equivalent to the second argument |
|
1487 |
* is returned. |
|
1488 |
* |
|
1489 |
* <p> |
|
1490 |
* Special cases: |
|
1491 |
* <ul> |
|
1492 |
* <li> If either argument is a NaN, then NaN is returned. |
|
1493 |
* |
|
1494 |
* <li> If both arguments are signed zeros, a value equivalent |
|
1495 |
* to {@code direction} is returned. |
|
1496 |
* |
|
1497 |
* <li> If {@code start} is |
|
1498 |
* ±{@link Float#MIN_VALUE} and {@code direction} |
|
1499 |
* has a value such that the result should have a smaller |
|
1500 |
* magnitude, then a zero with the same sign as {@code start} |
|
1501 |
* is returned. |
|
1502 |
* |
|
1503 |
* <li> If {@code start} is infinite and |
|
1504 |
* {@code direction} has a value such that the result should |
|
1505 |
* have a smaller magnitude, {@link Float#MAX_VALUE} with the |
|
1506 |
* same sign as {@code start} is returned. |
|
1507 |
* |
|
1508 |
* <li> If {@code start} is equal to ± |
|
1509 |
* {@link Float#MAX_VALUE} and {@code direction} has a |
|
1510 |
* value such that the result should have a larger magnitude, an |
|
1511 |
* infinity with same sign as {@code start} is returned. |
|
1512 |
* </ul> |
|
1513 |
* |
|
1514 |
* @param start starting floating-point value |
|
1515 |
* @param direction value indicating which of |
|
1516 |
* {@code start}'s neighbors or {@code start} should |
|
1517 |
* be returned |
|
1518 |
* @return The floating-point number adjacent to {@code start} in the |
|
1519 |
* direction of {@code direction}. |
|
1520 |
* @since 1.6 |
|
1521 |
*/ |
|
1522 |
public static float nextAfter(float start, double direction) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1523 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1524 |
* The cases: |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1525 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1526 |
* nextAfter(+infinity, 0) == MAX_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1527 |
* nextAfter(+infinity, +infinity) == +infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1528 |
* nextAfter(-infinity, 0) == -MAX_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1529 |
* nextAfter(-infinity, -infinity) == -infinity |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1530 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1531 |
* are naturally handled without any additional testing |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1532 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1533 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1534 |
// First check for NaN values |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1535 |
if (Float.isNaN(start) || Double.isNaN(direction)) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1536 |
// return a NaN derived from the input NaN(s) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1537 |
return start + (float)direction; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1538 |
} else if (start == direction) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1539 |
return (float)direction; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1540 |
} else { // start > direction or start < direction |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1541 |
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1542 |
// then bitwise convert start to integer. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1543 |
int transducer = Float.floatToRawIntBits(start + 0.0f); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1544 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1545 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1546 |
* IEEE 754 floating-point numbers are lexicographically |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1547 |
* ordered if treated as signed- magnitude integers . |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1548 |
* Since Java's integers are two's complement, |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1549 |
* incrementing" the two's complement representation of a |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1550 |
* logically negative floating-point value *decrements* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1551 |
* the signed-magnitude representation. Therefore, when |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1552 |
* the integer representation of a floating-point values |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1553 |
* is less than zero, the adjustment to the representation |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1554 |
* is in the opposite direction than would be expected at |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1555 |
* first. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1556 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1557 |
if (direction > start) {// Calculate next greater value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1558 |
transducer = transducer + (transducer >= 0 ? 1:-1); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1559 |
} else { // Calculate next lesser value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1560 |
assert direction < start; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1561 |
if (transducer > 0) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1562 |
--transducer; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1563 |
else |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1564 |
if (transducer < 0 ) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1565 |
++transducer; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1566 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1567 |
* transducer==0, the result is -MIN_VALUE |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1568 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1569 |
* The transition from zero (implicitly |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1570 |
* positive) to the smallest negative |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1571 |
* signed magnitude value must be done |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1572 |
* explicitly. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1573 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1574 |
else |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1575 |
transducer = FloatConsts.SIGN_BIT_MASK | 1; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1576 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1577 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1578 |
return Float.intBitsToFloat(transducer); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1579 |
} |
2 | 1580 |
} |
1581 |
||
1582 |
/** |
|
1583 |
* Returns the floating-point value adjacent to {@code d} in |
|
1584 |
* the direction of positive infinity. This method is |
|
1585 |
* semantically equivalent to {@code nextAfter(d, |
|
1586 |
* Double.POSITIVE_INFINITY)}; however, a {@code nextUp} |
|
1587 |
* implementation may run faster than its equivalent |
|
1588 |
* {@code nextAfter} call. |
|
1589 |
* |
|
1590 |
* <p>Special Cases: |
|
1591 |
* <ul> |
|
1592 |
* <li> If the argument is NaN, the result is NaN. |
|
1593 |
* |
|
1594 |
* <li> If the argument is positive infinity, the result is |
|
1595 |
* positive infinity. |
|
1596 |
* |
|
1597 |
* <li> If the argument is zero, the result is |
|
1598 |
* {@link Double#MIN_VALUE} |
|
1599 |
* |
|
1600 |
* </ul> |
|
1601 |
* |
|
1602 |
* @param d starting floating-point value |
|
1603 |
* @return The adjacent floating-point value closer to positive |
|
1604 |
* infinity. |
|
1605 |
* @since 1.6 |
|
1606 |
*/ |
|
1607 |
public static double nextUp(double d) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1608 |
if( Double.isNaN(d) || d == Double.POSITIVE_INFINITY) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1609 |
return d; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1610 |
else { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1611 |
d += 0.0d; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1612 |
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1613 |
((d >= 0.0d)?+1L:-1L)); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1614 |
} |
2 | 1615 |
} |
1616 |
||
1617 |
/** |
|
1618 |
* Returns the floating-point value adjacent to {@code f} in |
|
1619 |
* the direction of positive infinity. This method is |
|
1620 |
* semantically equivalent to {@code nextAfter(f, |
|
1621 |
* Float.POSITIVE_INFINITY)}; however, a {@code nextUp} |
|
1622 |
* implementation may run faster than its equivalent |
|
1623 |
* {@code nextAfter} call. |
|
1624 |
* |
|
1625 |
* <p>Special Cases: |
|
1626 |
* <ul> |
|
1627 |
* <li> If the argument is NaN, the result is NaN. |
|
1628 |
* |
|
1629 |
* <li> If the argument is positive infinity, the result is |
|
1630 |
* positive infinity. |
|
1631 |
* |
|
1632 |
* <li> If the argument is zero, the result is |
|
1633 |
* {@link Float#MIN_VALUE} |
|
1634 |
* |
|
1635 |
* </ul> |
|
1636 |
* |
|
1637 |
* @param f starting floating-point value |
|
1638 |
* @return The adjacent floating-point value closer to positive |
|
1639 |
* infinity. |
|
1640 |
* @since 1.6 |
|
1641 |
*/ |
|
1642 |
public static float nextUp(float f) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1643 |
if( Float.isNaN(f) || f == FloatConsts.POSITIVE_INFINITY) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1644 |
return f; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1645 |
else { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1646 |
f += 0.0f; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1647 |
return Float.intBitsToFloat(Float.floatToRawIntBits(f) + |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1648 |
((f >= 0.0f)?+1:-1)); |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1649 |
} |
2 | 1650 |
} |
1651 |
||
10608 | 1652 |
/** |
1653 |
* Returns the floating-point value adjacent to {@code d} in |
|
1654 |
* the direction of negative infinity. This method is |
|
1655 |
* semantically equivalent to {@code nextAfter(d, |
|
1656 |
* Double.NEGATIVE_INFINITY)}; however, a |
|
1657 |
* {@code nextDown} implementation may run faster than its |
|
1658 |
* equivalent {@code nextAfter} call. |
|
1659 |
* |
|
1660 |
* <p>Special Cases: |
|
1661 |
* <ul> |
|
1662 |
* <li> If the argument is NaN, the result is NaN. |
|
1663 |
* |
|
1664 |
* <li> If the argument is negative infinity, the result is |
|
1665 |
* negative infinity. |
|
1666 |
* |
|
1667 |
* <li> If the argument is zero, the result is |
|
1668 |
* {@code -Double.MIN_VALUE} |
|
1669 |
* |
|
1670 |
* </ul> |
|
1671 |
* |
|
1672 |
* @param d starting floating-point value |
|
1673 |
* @return The adjacent floating-point value closer to negative |
|
1674 |
* infinity. |
|
1675 |
* @since 1.8 |
|
1676 |
*/ |
|
1677 |
public static double nextDown(double d) { |
|
1678 |
if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY) |
|
1679 |
return d; |
|
1680 |
else { |
|
1681 |
if (d == 0.0) |
|
1682 |
return -Double.MIN_VALUE; |
|
1683 |
else |
|
1684 |
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + |
|
1685 |
((d > 0.0d)?-1L:+1L)); |
|
1686 |
} |
|
1687 |
} |
|
1688 |
||
1689 |
/** |
|
1690 |
* Returns the floating-point value adjacent to {@code f} in |
|
1691 |
* the direction of negative infinity. This method is |
|
1692 |
* semantically equivalent to {@code nextAfter(f, |
|
1693 |
* Float.NEGATIVE_INFINITY)}; however, a |
|
1694 |
* {@code nextDown} implementation may run faster than its |
|
1695 |
* equivalent {@code nextAfter} call. |
|
1696 |
* |
|
1697 |
* <p>Special Cases: |
|
1698 |
* <ul> |
|
1699 |
* <li> If the argument is NaN, the result is NaN. |
|
1700 |
* |
|
1701 |
* <li> If the argument is negative infinity, the result is |
|
1702 |
* negative infinity. |
|
1703 |
* |
|
1704 |
* <li> If the argument is zero, the result is |
|
1705 |
* {@code -Float.MIN_VALUE} |
|
1706 |
* |
|
1707 |
* </ul> |
|
1708 |
* |
|
1709 |
* @param f starting floating-point value |
|
1710 |
* @return The adjacent floating-point value closer to negative |
|
1711 |
* infinity. |
|
1712 |
* @since 1.8 |
|
1713 |
*/ |
|
1714 |
public static float nextDown(float f) { |
|
1715 |
if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY) |
|
1716 |
return f; |
|
1717 |
else { |
|
1718 |
if (f == 0.0f) |
|
1719 |
return -Float.MIN_VALUE; |
|
1720 |
else |
|
1721 |
return Float.intBitsToFloat(Float.floatToRawIntBits(f) + |
|
1722 |
((f > 0.0f)?-1:+1)); |
|
1723 |
} |
|
1724 |
} |
|
2 | 1725 |
|
1726 |
/** |
|
1727 |
* Return {@code d} × |
|
1728 |
* 2<sup>{@code scaleFactor}</sup> rounded as if performed |
|
1729 |
* by a single correctly rounded floating-point multiply to a |
|
1730 |
* member of the double value set. See the Java |
|
1731 |
* Language Specification for a discussion of floating-point |
|
1732 |
* value sets. If the exponent of the result is between {@link |
|
1733 |
* Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the |
|
1734 |
* answer is calculated exactly. If the exponent of the result |
|
1735 |
* would be larger than {@code Double.MAX_EXPONENT}, an |
|
1736 |
* infinity is returned. Note that if the result is subnormal, |
|
1737 |
* precision may be lost; that is, when {@code scalb(x, n)} |
|
1738 |
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal |
|
1739 |
* <i>x</i>. When the result is non-NaN, the result has the same |
|
1740 |
* sign as {@code d}. |
|
1741 |
* |
|
1742 |
* <p>Special cases: |
|
1743 |
* <ul> |
|
1744 |
* <li> If the first argument is NaN, NaN is returned. |
|
1745 |
* <li> If the first argument is infinite, then an infinity of the |
|
1746 |
* same sign is returned. |
|
1747 |
* <li> If the first argument is zero, then a zero of the same |
|
1748 |
* sign is returned. |
|
1749 |
* </ul> |
|
1750 |
* |
|
1751 |
* @param d number to be scaled by a power of two. |
|
1752 |
* @param scaleFactor power of 2 used to scale {@code d} |
|
1753 |
* @return {@code d} × 2<sup>{@code scaleFactor}</sup> |
|
1754 |
* @since 1.6 |
|
1755 |
*/ |
|
1756 |
public static double scalb(double d, int scaleFactor) { |
|
10598
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1757 |
/* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1758 |
* This method does not need to be declared strictfp to |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1759 |
* compute the same correct result on all platforms. When |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1760 |
* scaling up, it does not matter what order the |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1761 |
* multiply-store operations are done; the result will be |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1762 |
* finite or overflow regardless of the operation ordering. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1763 |
* However, to get the correct result when scaling down, a |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1764 |
* particular ordering must be used. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1765 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1766 |
* When scaling down, the multiply-store operations are |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1767 |
* sequenced so that it is not possible for two consecutive |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1768 |
* multiply-stores to return subnormal results. If one |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1769 |
* multiply-store result is subnormal, the next multiply will |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1770 |
* round it away to zero. This is done by first multiplying |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1771 |
* by 2 ^ (scaleFactor % n) and then multiplying several |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1772 |
* times by by 2^n as needed where n is the exponent of number |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1773 |
* that is a covenient power of two. In this way, at most one |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1774 |
* real rounding error occurs. If the double value set is |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1775 |
* being used exclusively, the rounding will occur on a |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1776 |
* multiply. If the double-extended-exponent value set is |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1777 |
* being used, the products will (perhaps) be exact but the |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1778 |
* stores to d are guaranteed to round to the double value |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1779 |
* set. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1780 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1781 |
* It is _not_ a valid implementation to first multiply d by |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1782 |
* 2^MIN_EXPONENT and then by 2 ^ (scaleFactor % |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1783 |
* MIN_EXPONENT) since even in a strictfp program double |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1784 |
* rounding on underflow could occur; e.g. if the scaleFactor |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1785 |
* argument was (MIN_EXPONENT - n) and the exponent of d was a |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1786 |
* little less than -(MIN_EXPONENT - n), meaning the final |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1787 |
* result would be subnormal. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1788 |
* |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1789 |
* Since exact reproducibility of this method can be achieved |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1790 |
* without any undue performance burden, there is no |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1791 |
* compelling reason to allow double rounding on underflow in |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1792 |
* scalb. |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1793 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1794 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1795 |
// magnitude of a power of two so large that scaling a finite |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1796 |
// nonzero value by it would be guaranteed to over or |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1797 |
// underflow; due to rounding, scaling down takes takes an |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1798 |
// additional power of two which is reflected here |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1799 |
final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT + |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1800 |
DoubleConsts.SIGNIFICAND_WIDTH + 1; |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1801 |
int exp_adjust = 0; |
efd29b4b3e67
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|
1802 |
int scale_increment = 0; |
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|
1803 |
double exp_delta = Double.NaN; |
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|
1804 |
|
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|
1805 |
// Make sure scaling factor is in a reasonable range |
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|
1806 |
|
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|
1807 |
if(scaleFactor < 0) { |
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|
1808 |
scaleFactor = Math.max(scaleFactor, -MAX_SCALE); |
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|
1809 |
scale_increment = -512; |
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|
1810 |
exp_delta = twoToTheDoubleScaleDown; |
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|
1811 |
} |
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|
1812 |
else { |
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|
1813 |
scaleFactor = Math.min(scaleFactor, MAX_SCALE); |
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|
1814 |
scale_increment = 512; |
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|
1815 |
exp_delta = twoToTheDoubleScaleUp; |
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|
1816 |
} |
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|
1817 |
|
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changeset
|
1818 |
// Calculate (scaleFactor % +/-512), 512 = 2^9, using |
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|
1819 |
// technique from "Hacker's Delight" section 10-2. |
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|
1820 |
int t = (scaleFactor >> 9-1) >>> 32 - 9; |
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|
1821 |
exp_adjust = ((scaleFactor + t) & (512 -1)) - t; |
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|
1822 |
|
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changeset
|
1823 |
d *= powerOfTwoD(exp_adjust); |
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|
1824 |
scaleFactor -= exp_adjust; |
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|
1825 |
|
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|
1826 |
while(scaleFactor != 0) { |
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|
1827 |
d *= exp_delta; |
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|
1828 |
scaleFactor -= scale_increment; |
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|
1829 |
} |
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|
1830 |
return d; |
2 | 1831 |
} |
1832 |
||
1833 |
/** |
|
1834 |
* Return {@code f} × |
|
1835 |
* 2<sup>{@code scaleFactor}</sup> rounded as if performed |
|
1836 |
* by a single correctly rounded floating-point multiply to a |
|
1837 |
* member of the float value set. See the Java |
|
1838 |
* Language Specification for a discussion of floating-point |
|
1839 |
* value sets. If the exponent of the result is between {@link |
|
1840 |
* Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the |
|
1841 |
* answer is calculated exactly. If the exponent of the result |
|
1842 |
* would be larger than {@code Float.MAX_EXPONENT}, an |
|
1843 |
* infinity is returned. Note that if the result is subnormal, |
|
1844 |
* precision may be lost; that is, when {@code scalb(x, n)} |
|
1845 |
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal |
|
1846 |
* <i>x</i>. When the result is non-NaN, the result has the same |
|
1847 |
* sign as {@code f}. |
|
1848 |
* |
|
1849 |
* <p>Special cases: |
|
1850 |
* <ul> |
|
1851 |
* <li> If the first argument is NaN, NaN is returned. |
|
1852 |
* <li> If the first argument is infinite, then an infinity of the |
|
1853 |
* same sign is returned. |
|
1854 |
* <li> If the first argument is zero, then a zero of the same |
|
1855 |
* sign is returned. |
|
1856 |
* </ul> |
|
1857 |
* |
|
1858 |
* @param f number to be scaled by a power of two. |
|
1859 |
* @param scaleFactor power of 2 used to scale {@code f} |
|
1860 |
* @return {@code f} × 2<sup>{@code scaleFactor}</sup> |
|
1861 |
* @since 1.6 |
|
1862 |
*/ |
|
1863 |
public static float scalb(float f, int scaleFactor) { |
|
10598
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changeset
|
1864 |
// magnitude of a power of two so large that scaling a finite |
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|
1865 |
// nonzero value by it would be guaranteed to over or |
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changeset
|
1866 |
// underflow; due to rounding, scaling down takes takes an |
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changeset
|
1867 |
// additional power of two which is reflected here |
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|
1868 |
final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT + |
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changeset
|
1869 |
FloatConsts.SIGNIFICAND_WIDTH + 1; |
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changeset
|
1870 |
|
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changeset
|
1871 |
// Make sure scaling factor is in a reasonable range |
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|
1872 |
scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE); |
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changeset
|
1873 |
|
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changeset
|
1874 |
/* |
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changeset
|
1875 |
* Since + MAX_SCALE for float fits well within the double |
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changeset
|
1876 |
* exponent range and + float -> double conversion is exact |
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changeset
|
1877 |
* the multiplication below will be exact. Therefore, the |
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changeset
|
1878 |
* rounding that occurs when the double product is cast to |
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changeset
|
1879 |
* float will be the correctly rounded float result. Since |
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changeset
|
1880 |
* all operations other than the final multiply will be exact, |
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changeset
|
1881 |
* it is not necessary to declare this method strictfp. |
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changeset
|
1882 |
*/ |
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changeset
|
1883 |
return (float)((double)f*powerOfTwoD(scaleFactor)); |
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changeset
|
1884 |
} |
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changeset
|
1885 |
|
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changeset
|
1886 |
// Constants used in scalb |
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diff
changeset
|
1887 |
static double twoToTheDoubleScaleUp = powerOfTwoD(512); |
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changeset
|
1888 |
static double twoToTheDoubleScaleDown = powerOfTwoD(-512); |
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changeset
|
1889 |
|
efd29b4b3e67
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parents:
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diff
changeset
|
1890 |
/** |
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diff
changeset
|
1891 |
* Returns a floating-point power of two in the normal range. |
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diff
changeset
|
1892 |
*/ |
efd29b4b3e67
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diff
changeset
|
1893 |
static double powerOfTwoD(int n) { |
efd29b4b3e67
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diff
changeset
|
1894 |
assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT); |
efd29b4b3e67
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darcy
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diff
changeset
|
1895 |
return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) << |
efd29b4b3e67
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darcy
parents:
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diff
changeset
|
1896 |
(DoubleConsts.SIGNIFICAND_WIDTH-1)) |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
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diff
changeset
|
1897 |
& DoubleConsts.EXP_BIT_MASK); |
efd29b4b3e67
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parents:
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diff
changeset
|
1898 |
} |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
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parents:
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diff
changeset
|
1899 |
|
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
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parents:
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diff
changeset
|
1900 |
/** |
efd29b4b3e67
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parents:
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diff
changeset
|
1901 |
* Returns a floating-point power of two in the normal range. |
efd29b4b3e67
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parents:
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diff
changeset
|
1902 |
*/ |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
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parents:
10122
diff
changeset
|
1903 |
public static float powerOfTwoF(int n) { |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
10122
diff
changeset
|
1904 |
assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT); |
efd29b4b3e67
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darcy
parents:
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diff
changeset
|
1905 |
return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) << |
efd29b4b3e67
7091682: Move sun.misc.FpUtils code into java.lang.Math
darcy
parents:
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diff
changeset
|
1906 |
(FloatConsts.SIGNIFICAND_WIDTH-1)) |
efd29b4b3e67
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darcy
parents:
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diff
changeset
|
1907 |
& FloatConsts.EXP_BIT_MASK); |
2 | 1908 |
} |
1909 |
} |