[libre-riscv-dev] Last-bit accuracy

[Hendrik Boom]

On Wed, Aug 07, 2019 at 06:17:37PM -0700, MitchAlsup wrote:
> 
> My gut feeling tell me that the numericalists are perfectly willing to 
> accept an error of 0.51 ULP RMS on transcendental calculations.
> My gut feeling tell me that the numericalists are not willing to accept an 
> error of 0.75 ULP RMS on transcendental calculations.
> I have no feeling at all on where to draw the line.

Way back in the 70's, Morven Gentleman explained to me why last-bit 
accuracy was important, no matter by how much the avaiable precision 
may exceed the precision actually needed by the application.

The convergence of iterations often depends on the the monotonicity of 
the functions involved.  The eaasiest way of ensuring that the 
implemented functions are monotonic in the proper ranges is to have 
last-bit accuracy.  Failure of last-bit accuracy can create 
irregularities that can trap iterations forever.

This is probably irrelevant for a large class of applications, but 
crucial for others.

-- hendrik