[libre-riscv-dev] Last-bit accuracy
hendrik at topoi.pooq.com
Thu Aug 8 19:27:51 BST 2019
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.
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