Code review request for 6908131 Pure Java implementations of StrictMath.floor(double) &StrictMath.ceil(double)

[Dmitry Nadezhin]

 > The current specification of the "interesting" methods in StrictMath, 
such as sin/cos, log, > etc. are to use the FDLIBM algorithms.

Thank you. I forgot about these lines in java.lang.StrictMath .

* <p>To help ensure portability of Java programs, the definitions of
* some of the numeric functions in this package require that they
* produce the same results as certain published algorithms. These
* algorithms are available from the well-known network library
* {@code netlib} as the package "Freely Distributable Math
* Library," <a
* href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
* algorithms, which are written in the C programming language, are
* then to be understood as executed with all floating-point
* operations following the rules of Java floating-point arithmetic.
*
* <p>The Java math library is defined with respect to
* {@code fdlibm} version 5.3.

As specification of java.lang.StrictMath is in terms of reference fdlibm 
C library
and algorithms in new java.lang.StrictMath are expected similar to 
fdlibm algorithms,
the task of formal verification becomes easier.

The comment 3 in fdlibm's readme file warns about
---
   3. Compiler failure on non-standard code
   Statements like
               *(1+(int*)&t1) = 0;
   are not standard C and cause some optimizing compilers (e.g. GCC)
   to generate bad code under optimization.    These cases
   are to be addressed in the next release.
---
Nevertheless, I hope that for some additional assumptions about C 
pointers, the meaning
of fdlibm C code can be used as the specification.

However, there is a question. Many methods of java.lang.StrictMath are
used in a reference implementation of java.lang.Math methods.
java.lang.Math specifies methods in terms of accuracy of the returned 
result
and monotonicity of the methods.
Suppose that there is still a bug in fdlibm 5.3 and some fdlibm function 
fails to
satisfy one ulp accuracy or monotonicity. What will be the specification of
corresponding java.lang.StrictMath method in such a case ?

Joseph D. Darcy wrote:
> Dmitry Nadezhin wrote:
>> Joseph D. Darcy wrote:
>>> Yes, porting FDLIBM to Java has been an oft-delayed "nice to have" 
>>> project of mine.  It is not obvious from looking at my ceil/floor 
>>> code, but it started with the FDLIBM versions of those algorithms.  
>>> The tests are new and greatly outnumber the code changes, as it 
>>> typical in this line of work :-)  I think getting an all-java 
>>> StrictMath library would be best done as a series of small batches 
>>> so floor/ceil could be a start.
>> Floating-point algorithms are difficult to test.
>> Maybe, the new StrictMath.java can be verified by formal methods (in 
>> addition to tests) ?
>> We would be more confident, if we obtain machine-checked proof that 
>> the result of method execution by JVM differs from exact mathematical 
>> result no more than 1 ulp in for all Float/Double inputs.
>>
>> I googled some papers on verification of floating-point:
>> http://www-lipn.univ-paris13.fr/CerPAN/files/ARITH.pdf
>> http://shemesh.larc.nasa.gov/fm/papers/Boldo-CR-2006-214298-Floating-Point.pdf 
>>
>> http://www.cl.cam.ac.uk/~jrh13/papers/fparith.pdf
>>
>> What do you think about such perspective ?
>>
>>
>
> The current specification of the "interesting" methods in StrictMath, 
> such as sin/cos, log, etc. are to use the FDLIBM algorithms.  Another 
> approach would be to specify that "correctly rounded" algorithms be 
> used.  Such a specification would constrain the result according to 
> the method's behavior (i.e. define a mathematically "correct" result) 
> rather than defining the correct result based on matching a particular 
> implementation.  Developing and testing correctly rounded algorithms 
> remains a research area with Jean-Michel Muller and associates doing 
> good work.
>
> That said, while there is certainly value in formal methods, I think 
> they would be overkill for the regression testing needs of the JDK.
>
> -Joe