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Fwd: Re: Binary128 - PI and E

-------- Original-Nachricht --------
Betreff: Re: Binary128 - PI and E
Datum: Wed, 11 May 2011 23:03:32 +0200
Von: Thorsten Siebenborn <7_born@xxxxxx>
An: William M Klein <wmklein@xxxxxxxxxxxxx>

Am 11.05.2011 21:27, schrieb William M Klein:
This may be a stupid question and I don't know if I am even expre4ssing it 
correct, BUT  Can anyone tell me or point me to some place that documents what 
the exact DECIMAL fixed-point value would be for the most accurate values of PI 
and E that can be stored in a binary128 data item? Would this just be (for PI) 
PI with 35 digits to the right of the decimal point?

The quad-precision format (binary128) has with the implicit hidden bit
113 bit stored which is for pi equivalent to


This is nearly 0,25 ulps lower than the correct value.

The correctly rounded value is

*Exact* conversion binary to decimal (with garbage
digits due to conversion)

Bit equivalent for e:


Nearly 0,49 ulps lower than the correct value.

Correctly rounded value:

*Exact* conversion binary to decimal (with garbage
digits due to conversion)


Best regards,

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