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From: Jan Burse <janburse@fastmail.fm>
Newsgroups: comp.lang.java.programmer
Subject: Re: higher precision doubles
Date: Sun, 11 Sep 2011 13:50:53 +0200
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Jan Burse schrieb:
>     N[sin[3.14159265358979324],18] =
>
>      -1.53735661672049712×10^-18

Oops, just reading:
http://reference.wolfram.com/mathematica/tutorial/MachinePrecisionNumbers.html

So the second N[.,.] was not necessary. Could
simply do, but the output on Wolfram alfa looks
a little bit different:

	sin[3.14159265358979324] =
		
		-1.53736... ×10^-18


Or could try the following:

	N[sin[314159265358979324 / 100000000000000000],9] =

		-1.53735662×10^-18

	N[sin[314159265358979324 / 100000000000000000],18] =

		-1.53735661672049712×10^-18

	N[sin[314159265358979324 / 100000000000000000],36] =
		
		-1.53735661672049711580283060062489418×10^-18

Note how good the high precision computation is. The lower
precision number is always the rounding of the higher
precision number.

But mechanics for high precision numbers look a little bit
more complicated to me than BigDecimal. At least if
I look at:
http://reference.wolfram.com/mathematica/tutorial/ArbitraryPrecisionNumbers.html

There is a max extra precision, which is needed in the
evaluation function N[.,.]. BigDecimal does not know about
evaluation functions. And there is some special handling
of near zero values.

Bye