Summary

Widen allowable error bound of Math.tan to accommodate a demonstrated worst-case error bound slightly outside of the currently allowable range.

Problem

Recent work (https://members.loria.fr/PZimmermann/papers/accuracy.pdf) has found a worst-case error bound for an FDLIBM-derived math library that is slightly outside of the analytically understood worst-case.

Solution

Widen the stated error bound from less than 1 ulp to less than 1.25 ulps, which would allow the 1.02 ulps worst-case observed bound.

Specification

diff --git a/src/java.base/share/classes/java/lang/Math.java b/src/java.base/share/classes/java/lang/Math.java
index 11c636c8434..fa45b6436c7 100644
--- a/src/java.base/share/classes/java/lang/Math.java
+++ b/src/java.base/share/classes/java/lang/Math.java
@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 1994, 2023, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 1994, 2024, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * This code is free software; you can redistribute it and/or modify it
@@ -212,7 +212,7 @@ public static double cos(double a) {
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.</ul>
      *
-     * <p>The computed result must be within 1 ulp of the exact result.
+     * <p>The computed result must be within 1.25 ulps of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   an angle, in radians.