Approximations (was Re: Microcode, which is a no-go for modern designs)

[Eric Korpela]

On Sun, Jan 6, 2019 at 1:00 PM Fred Cisin via cctalk <cctalk at classiccmp.org>
wrote:

> Few people (but most are right here) can recite PI to enough digits to
> reach the level of inaccuracy.   And those who believe that PI is exactly
> 22/7 are unaffected by FDIV.   (YES, some schools do still teach that!)
>

Really?  I find it hard to believe any schools taught that as anything
other than
an approximation.   And as an approximation it's not good for much unless
you are
multiplying PI in your head by a factors of 7 a lot (i.e 21*PI ~ 66).
Personally, I use the
PI^2 ~ 10 approximation far more often when doing math in my head.  But
since I'm
almost always sitting at a screen, approximations are less useful than they
used to be.
If I need PI to 600 places, "scale=600;a(1)*4" is always there for the
asking.

The exception is the approximations that provide physical scale.  For
example, 1 km/s ~
1 parsec/million years, or v=4.74 PM/parallax, which provides the
conversion from proper
motion to parallax, 5 magnitudes is a factor of 100.  And of course, "c" in
whatever units
you need.  They are just easier to remember than to look up.

-- 
Eric Korpela
korpela at ssl.berkeley.edu
AST:7731^29u18e3