Re: Q: how to compute modulo Pi for large arguments?

From: Russell Wallace (wallacethinmintr_at_eircom.net)
Date: 06/01/04 

Date: Tue, 01 Jun 2004 14:56:53 GMT

On Sun, 30 May 2004 19:37:57 +0200, Axel Vogt <nonail@axelvogt.de>
wrote:

>May be that is a naive question in numerics ...
>
>Given a positive real or natural number x <= 1E308 i want the
>the remainder of x/Pi with precision of ~ 15 - 18 digits. And
>want to use it for periodics of large arguments in a C pgm.

Is that going to be possible?

Suppose x ~= 1E300. Now, given that you mentioned 1E308 and C, I
assume you're talking about 64-bit floating point.

But that's only got ~16 digits of precision at the best of times. So
the error in the input is going to be on the order of 1E284, isn't it?
Someone with more expertise in numerical analysis please correct me if
I'm missing something, but as far as I can see you'd need a format
that can represent 1E300 with an error << pi, i.e. one that has more
than 300 digits of precision? 

-- 
"Sore wa himitsu desu."
To reply by email, remove
the small snack from address.

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