implementing LOG1P

zp3 · ‎08-19-2017

Hi,

As everyone knows, log(1+dx) suffers heavily on cancellation errors when dx gets sufficient small. The solution is, as in most other programming languages already implemented, the use of the log1p() function. One common way to implement a workaround DIY is the rewriting of log(1+dx) as:

log1p=log(1+dx)*dx/((1-dx)-1)

The problem with this now is, that most compilers probably optimize it simply back to log(1+dx). Therefore I'd like to ask if there is a safe way to tell the compiler to just not touch this line of code?

Thanks for any advice!

mecej4 · ‎08-19-2017

The formula that you listed has a sign error. Rather than use a trick, why not use the C-library function log1p(), or write code such as

if(abs(dx) < 1d-8)then
   log1p = dx*(1d0 - 0.5d0*dx)
else
   log1p = log(1d0 + dx)
endif

See also https://www.johndcook.com/blog/2010/06/07/math-library-functions-that-seem-unnecessary/ .

TimP · ‎08-19-2017

Most compilers have options to respect parentheses, such as ifort -standard-semantics .