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From: Szabolcs Nagy <nsz@port70.net>
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Subject: Re: printf issues
Date: Mon, 7 Apr 2014 17:36:11 +0200
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* Morten Welinder <mwelinder@gmail.com> [2014-04-07 10:13:26 -0400]:
> The frequency of this problem is something like 1 in 5e6.
> Observations:
> 
> *  I only seem to be able to trigger it for %g even though all my
>    samples print in "e" form.
> 
> * The numbers are all roughly the same size: 1e15
> 
> * The numbers are all integers ending in 05.  (Except two cases
>    where the 05 is followed by zeros.)
> 
> * The precision is always just below the value that would have
>   make an exact representation.

printf("%.12g\n", 1000000000005.0);
printf("%.11g\n", 500000000045.0);
printf("%.11g\n", 275000000025.0);

prints

1.00000000001e+12
5.0000000005e+11
2.7500000003e+11

in fmt_fp
	if (x || d+1!=z) {
		long double round = CONCAT(0x1p,LDBL_MANT_DIG);
		long double small;
		if (*d/i & 1) round += 2;
		if (x<i/2) small=0x0.8p0;
		else if (x==i/2 && d+1==z) small=0x1.0p0;
		else small=0x1.8p0;
		...

here
	i == 10
	x == *d%i == 5 == i/2
but the half-way case does not trigger because z-d == 2 instead of 1
and z[-1] == 0 which should not happen here