[libre-riscv-dev] [isa-dev] Re: FP transcendentals (trigonometry, root/exp/log) proposal

[Mitchalsup]

Mitch AlsupMitchAlsup at aol.com

-----Original Message-----
From: Luke Kenneth Casson Leighton <lkcl at lkcl.net>
To: Mitchalsup <mitchalsup at aol.com>
Cc: Libre-RISCV General Development <libre-riscv-dev at lists.libre-riscv.org>
Sent: Thu, Jan 16, 2020 2:57 pm
Subject: Re: [libre-riscv-dev] [isa-dev] Re: FP transcendentals (trigonometry, root/exp/log) proposal



On Thu, Jan 16, 2020 at 5:59 PM Mitchalsup <mitchalsup at aol.com> wrote:
 
ah HA!  ok now it makes sense.  the error analysis is also a mathematical function, which can be implemented *in hardware* and the error-quantity computed along-side the actual output.
You could do this, but it is easier to simply recognize that with a given number of bits of "Known accuracy" (which HAS to be at least 3-bits larger than the fraction) you need to look for 3-patterns that have the potential of spanning a rounding-decision-break-point.

because only those patterns will round up or down, all others will not, no matter what happens.niice.
Because only those 3 patterns could round either way--all other patterns round directionallyand without uncertainty.
Also note: the patterns for Round Nearest and Round Magnitude are different from the patterns that round directionally (towards zero, towards +Infinity, and towards -Infinity.)But the difference in the patterns is a single bit at the point of most significance!
l.