printf rounding behavior for doubles

Question

Can someone explain this behavior? I am well aware of machine-level representation of floating point numbers. This seems to be related to printf and its formats. Both numbers are represented exactly by floating-point notation (check: multiplying by 64 gives an integer).

#include <stdio.h>
#include <iostream>
using namespace std;

int main() {
  double x1=108.765625;
  printf("%34.30f\n", x1);
  printf("%9.5f\n", x1);
  printf("%34.30f\n", x1*64);

  double x2=108.046875;
  printf("%34.30lf\n", x2);
  printf("%9.5f\n", x2);
  printf("%34.30f\n", x2*64);
}

Output:

> 108.765625000000000000000000000000
> 108.76562
> 6961.000000000000000000000000000000
> 108.046875000000000000000000000000
> 108.04688
> 6915.000000000000000000000000000000

Note, the first number gets rounded down, and the second one gets rounded up.

You might be interested in my article http://www.exploringbinary.com/inconsistent-rounding-of-printed-floating-point-numbers/ . Some implementations use "round-half-away-from-zero" instead of "round-half-to-even". — Rick Regan, Apr 28 '12 at 17:19
It appears that Microsoft changed their default rounding behaviour some time between VS 2010 and VS2015. I just upgraded from one to the other and got some very annoying and subtle bugs. [This blog](https://blogs.msdn.microsoft.com/vcblog/2014/06/18/c-runtime-crt-features-fixes-and-breaking-changes-in-visual-studio-14-ctp1/) is probably meant to highlight the change, but you'd be forgiven for missing it entirely. — omatai, Oct 10 '16 at 04:52
it depends on implementation [Rounding differences on Windows vs Unix based system in sprintf](http://stackoverflow.com/q/4649554/995714), [C++ Rounding behavior consistency for ties with sprintf](http://stackoverflow.com/q/31142600/995714) — phuclv, Nov 02 '16 at 04:29

score 20 · Accepted Answer · edited Apr 27 '12 at 20:20

20

It's "round half to even" or "Banker's rounding". The last digit of the rounded representation is chosen to be even if the number is exactly half way between the two.

http://linuxgazette.net/144/misc/lg/a_question_of_rounding_in_issue_143.html:
"For the GNU C library, the rounding rule used by printf() is "bankers rounding" or "round to even". This is more correct than some other C libraries, as the C99 specification says that conversion to decimal should use the currently selected IEEE rounding mode (default bankers rounding)."

edited Apr 27 '12 at 20:20

Mooing Duck

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answered Apr 27 '12 at 20:15

Daniel Fischer

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The author of the linked article is incompetent. "Binary and decimal radix do not share the same set of irrational numbers" - that's nonsense. Rationality/irrationality is independent of base. – R.. GitHub STOP HELPING ICE Apr 27 '12 at 21:47
1

@R.. Indeed. But the quoted passage of the article is correct, as the author painfully learned in his [bug report](http://sourceware.org/bugzilla/show_bug.cgi?id=4943). – Daniel Fischer Apr 28 '12 at 01:53
"not all finite decimal expansions have finite binary expansions" – Antti Haapala -- Слава Україні Oct 12 '20 at 18:27

score 0 · Answer 2 · answered Apr 27 '12 at 20:15

0

The %9.5f output gives the number with 5 digits after the decimal dot which is the nearest of the source number.

answered Apr 27 '12 at 20:15

Basile Starynkevitch

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The point of the question, I believe, is: what if the source number is exactly halfway between two possible outputs? – Spike0xff Dec 11 '19 at 21:09

printf rounding behavior for doubles

2 Answers2

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