Re: [boost] Re: [Ann] Proposed Math library additions (complex numberinverse trig functions).

From: John Maddock (john_at_[hidden])
Date: 2005-04-06 05:07:57

>> log1p:
>> ~~~~
>>
>> This algorithm is part of C99, but by no means all compilers support it 
>> yet,
>> I used a Taylor series expansion for small x: I'm aware that there are 
>> much
>> more efficient methods, but optimizing compilers completely trash the 
>> logic
>> of these (Intel C++ proved to be particularly bad).
>
>      I had planed to work on it (and a few related such as expm1...)
> something liketwo years ago and had planed to add it to the same special
> functions library. They really are important.

Agreed: how were you planning to implement expm1?  The obvious series 
expansion:

expm1(z) = SUM[k=1, INF] (z^k / k!)

would converge in less than B steps for a B bit floating point type and  |z| 
< 0.5 (in other words reasonable but not astounding performance), in fact it 
would be trivial to plug that into my existing series summation code.

Alternatively there's a table based method 
(http://portal.acm.org/citation.cfm?doid=146847.146928) which claims to be 
particularly accurate.

Any others? You've got my curiosity roused...

John.