Date: Sun, 7 Mar 1999 21:50:22 -0500 (EST)
From: Daniel Reed <djr AT narnia DOT n DOT ml DOT org>
To: Victor Senderov <victor DOT bg AT usa DOT net>
cc: djgpp AT delorie DOT com
Subject: Re: Problem with floats
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On Sun, 7 Mar 1999, Victor Senderov wrote:
)  cout << setprecision(25);
)  double test = 37000.95000;
)  cout << test;
 [...]
) Output : 37000.94999999999708961695
A similar concern was raised on a Visual C++ mailing list I'm on (I only
reply to questions relating to pure C problems). I think my reply adequately
explains the problem (see below). The poster had a question as to why
printf("%.2f")ing a variable containing the value 1.305 showed up as 1.30,
while printf("%.2f")ing the same variable reset to 1.605 showed up as 1.61.

-- 
Daniel Reed <n AT ml DOT org>
When you take stuff from one writer it's plagiarism; but when you take it from many writers, it's research. -- Wilson Mizner

---------------------------------------------------------------------------
Date: Wed, 10 Feb 1999 18:29:05 -0500 (EST)
From: Daniel Reed <djr AT narnia DOT n DOT ml DOT org>
To: vcpp AT earth DOT ml DOT org
Cc: windev AT rinolam DOT com DOT hk
Subject: Re: [VCPP-2953] Pls Help : Question about printf & precision rounding
    ..

On Wed, 10 Feb 1999 DavPatrick AT aol DOT com wrote:
) printf( " x = %.2f ", x );
Take a look at
	printf("%1.10f\n", x);
when x = 1.105 and when x = 1.305 and you can answer your own question.

)     1.105		1.11
)     1.205		1.21
)     1.305		1.30  << why did it round down here ?
)     1.405		1.41
)     1.505		1.50
)     1.605		1.61
)     1.705		1.71
)     1.805		1.80  << and here

(18:26)root AT narnia:~# cat davpatrick.c
int     main(void) {
        float   f = 0.0;

        f = 1.105;      printf("%1.10f\n", f);
        f = 1.205;      printf("%1.10f\n", f);
        f = 1.305;      printf("%1.10f\n", f);
        f = 1.405;      printf("%1.10f\n", f);
        f = 1.505;      printf("%1.10f\n", f);
        f = 1.605;      printf("%1.10f\n", f);
        f = 1.705;      printf("%1.10f\n", f);
        f = 1.805;      printf("%1.10f\n", f);
}
(18:26)root AT narnia:~# gcc davpatrick.c -o davpatrick
(18:26)root AT narnia:~# ./davpatrick
1.1050000191
1.2050000429
1.3049999475
1.4049999714
1.5049999952
1.6050000191
1.7050000429
1.8049999475
(18:26)root AT narnia:~#

Numbers are stored in binary form in computers, not as strings (which is how
humans store numbers). For fractional parts, there must be a set precision
used, which causes floating numbers to be stored in inexact forms.
1.3049999475 does, in truth, round to 1.30 when rounding to two decimal
places, while 1.6050000191 rounds to 1.61.

-- 
Daniel Reed <n AT ml DOT org>
Who controls the past controls the future. Who controls the present controls the past. -- George Orwell