8314489: Add javadoc index entries for java.lang.Math terms

Reviewed-by: alanb
This commit is contained in:
Joe Darcy 2023-08-17 17:32:49 +00:00
parent 2505cebc5d
commit 3bb8afba69

View file

@ -55,44 +55,46 @@ import jdk.internal.vm.annotation.IntrinsicCandidate;
* <p>The quality of implementation specifications concern two
* properties, accuracy of the returned result and monotonicity of the
* method. Accuracy of the floating-point {@code Math} methods is
* measured in terms of <i>ulps</i>, units in the last place. For a
* given floating-point format, an {@linkplain #ulp(double) ulp} of a
* specific real number value is the distance between the two
* floating-point values bracketing that numerical value. When
* discussing the accuracy of a method as a whole rather than at a
* specific argument, the number of ulps cited is for the worst-case
* error at any argument. If a method always has an error less than
* 0.5 ulps, the method always returns the floating-point number
* nearest the exact result; such a method is <i>correctly
* rounded</i>. A correctly rounded method is generally the best a
* floating-point approximation can be; however, it is impractical for
* many floating-point methods to be correctly rounded. Instead, for
* the {@code Math} class, a larger error bound of 1 or 2 ulps is
* allowed for certain methods. Informally, with a 1 ulp error bound,
* when the exact result is a representable number, the exact result
* should be returned as the computed result; otherwise, either of the
* two floating-point values which bracket the exact result may be
* returned. For exact results large in magnitude, one of the
* endpoints of the bracket may be infinite. Besides accuracy at
* individual arguments, maintaining proper relations between the
* method at different arguments is also important. Therefore, most
* methods with more than 0.5 ulp errors are required to be
* <i>semi-monotonic</i>: whenever the mathematical function is
* non-decreasing, so is the floating-point approximation, likewise,
* whenever the mathematical function is non-increasing, so is the
* floating-point approximation. Not all approximations that have 1
* ulp accuracy will automatically meet the monotonicity requirements.
* measured in terms of <dfn>{@index ulp}s</dfn>, {@index "units in
* the last place"}. For a given floating-point format, an
* {@linkplain #ulp(double) ulp} of a specific real number value is
* the distance between the two floating-point values bracketing that
* numerical value. When discussing the accuracy of a method as a
* whole rather than at a specific argument, the number of ulps cited
* is for the worst-case error at any argument. If a method always
* has an error less than 0.5 ulps, the method always returns the
* floating-point number nearest the exact result; such a method is
* <dfn>correctly rounded</dfn>. A {@index "correctly rounded"}
* method is generally the best a floating-point approximation can be;
* however, it is impractical for many floating-point methods to be
* correctly rounded. Instead, for the {@code Math} class, a larger
* error bound of 1 or 2 ulps is allowed for certain methods.
* Informally, with a 1 ulp error bound, when the exact result is a
* representable number, the exact result should be returned as the
* computed result; otherwise, either of the two floating-point values
* which bracket the exact result may be returned. For exact results
* large in magnitude, one of the endpoints of the bracket may be
* infinite. Besides accuracy at individual arguments, maintaining
* proper relations between the method at different arguments is also
* important. Therefore, most methods with more than 0.5 ulp errors
* are required to be <dfn>{@index "semi-monotonic"}</dfn>: whenever
* the mathematical function is non-decreasing, so is the
* floating-point approximation, likewise, whenever the mathematical
* function is non-increasing, so is the floating-point approximation.
* Not all approximations that have 1 ulp accuracy will automatically
* meet the monotonicity requirements.
*
* <p>
* The platform uses signed two's complement integer arithmetic with
* int and long primitive types. The developer should choose
* the primitive type to ensure that arithmetic operations consistently
* produce correct results, which in some cases means the operations
* will not overflow the range of values of the computation.
* The best practice is to choose the primitive type and algorithm to avoid
* overflow. In cases where the size is {@code int} or {@code long} and
* overflow errors need to be detected, the methods whose names end with
* {@code Exact} throw an {@code ArithmeticException} when the results overflow.
* {@code int} and {@code long} primitive types. The developer should
* choose the primitive type to ensure that arithmetic operations
* consistently produce correct results, which in some cases means the
* operations will not overflow the range of values of the
* computation. The best practice is to choose the primitive type and
* algorithm to avoid overflow. In cases where the size is {@code int}
* or {@code long} and overflow errors need to be detected, the
* methods whose names end with {@code Exact} throw an {@code
* ArithmeticException} when the results overflow.
*
* <h2><a id=Ieee754RecommendedOps>IEEE 754 Recommended
* Operations</a></h2>
@ -119,7 +121,6 @@ import jdk.internal.vm.annotation.IntrinsicCandidate;
* @see <a href="https://standards.ieee.org/ieee/754/6210/">
* <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
*
* @author Joseph D. Darcy
* @since 1.0
*/