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From: anton@mips.complang.tuwien.ac.at (Anton Ertl)
Newsgroups: comp.arch
Subject: binary128 implementation (was: Making Lemonade (Floating-point format changes)
Date: Mon, 20 May 2024 10:56:48 GMT
Organization: Institut fuer Computersprachen, Technische Universitaet Wien
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Message-ID: <2024May20.125648@mips.complang.tuwien.ac.at>
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Michael S <already5chosen@yahoo.com> writes:
>On Sun, 19 May 2024 18:37:51 +0200
>Terje Mathisen <terje.mathisen@tmsw.no> wrote:
>> The FMA normalizer has to handle a maximally bad cancellation, so it 
>> needs to be around 350 bits wide. Mitch knows of course but I'm
>> guessing that this could at least be close to needing an extra cycle
>> on its own and/or heroic hardware?
>> 
>> Terje
>> 
>
>Why so wide?
>Assuming that subnormal multiplier inputs are normalized before
>multiplication, the product of multiplication is 226 bits

The product of the mantissa multiplication is at most 226 bits even if
you don't normalize subnormal numbers.  For cancellation to play a
role the addend has to be close in absolute value and have the
opposite sign as the product, so at most one additional bit comes into
play for that case (for something like the product being
0111111... and the addend being -10000000...).

- anton
-- 
'Anyone trying for "industrial quality" ISA should avoid undefined behavior.'
  Mitch Alsup, <c17fcd89-f024-40e7-a594-88a85ac10d20o@googlegroups.com>