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Re: Why?

• To: mathgroup at smc.vnet.net
• Subject: [mg110459] Re: Why?
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sat, 19 Jun 2010 07:48:28 -0400 (EDT)
• References: <hto93n$kt8$1@smc.vnet.net>

Perhaps you wanted

SetPrecision [1.000000000000000000000001, 60] -1

which returns..


9.9999999999999863800355333982586279*10^-25

This takes the binary software-float number that
is closest to  1.000...1  accurate to the equivalent of about 24 decimal 
digits. Then extends it on the right by
appending additional binary zeros to it until it gets to the binary
precision which is the equivalent of about 60 decimal digits.
Then subtracts exactly 1, which happens to be an exact number
in binary float.

WRI claims their arithmetic is intuitive and easy to understand
and does the right thing almost all the time.

On the other hand, you are not the first person to be puzzled by it.

RJF