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Date:	Thu, 25 Nov 2021 21:02:01 +0900
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Subject:	Re: possible snprintf() regression in 3.3.2
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From:	Takashi Yano via Cygwin <cygwin AT cygwin DOT com>
Reply-To:	Takashi Yano <takashi DOT yano AT nifty DOT ne DOT jp>
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On Wed, 24 Nov 2021 10:28:13 +0100
Corinna Vinschen wrote:
> On Nov 24 18:14, Takashi Yano via Cygwin wrote:
> > On Wed, 24 Nov 2021 17:52:04 +0900
> > Takashi Yano wrote:
> > > The printed value is still something wrong...
> > > sqrt(2)*1e70 should be an integer value.
> > 
> > I mean...
> > 
> > sqrt(2)*1e70 is actually not an integer, however, double has mantissa
> > of only 52 bit. So, (double value)*(5^70*2^70) should be an integer.
> 
> The conversion is a bit inexact, I guess, but that's another problem
> of this old ldto, right?

I looked into this problem and found that:

This problem is in principle unavoidable with current algorithms.
This is because the current algorithm uses a value of 10^n for
the conversion. When n>62, the value does not fit into the 144
bits of the mantissa part of the internal representation in ldtoa.
This degrades the precision.


-- 
Takashi Yano <takashi DOT yano AT nifty DOT ne DOT jp>

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