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# Re: [Mingw-users] msvcrt printf bug

• Date: Sun, 05 Feb 2017 10:03:38 +0800
• From: KHMan <keinhong@xxxxxxxxx>
• Subject: Re: [Mingw-users] msvcrt printf bug

```On 2/5/2017 6:40 AM, tei.andu@xxxxxxxxxxxx wrote:
> [snip]
> According to Dr. Regan, the number of fractional bits is equal to
> the number of decimals in the corresponding decimal representation:
> http://www.exploringbinary.com/number-of-decimal-digits-in-a-binary-fraction
> <http://www.exploringbinary.com/number-of-decimal-digits-in-a-binary-fraction/>
> http://www.exploringbinary.com/maximum-number-of-decimal-digits-in-binary-floating-point-numbers

The phrasing in Rick Regan's articles may mislead some folks.

Much earlier, someone discussed the usual way to visualize floats
and doubles as unevenly spaced 'ticks' on a 'line'. Rick is doing
something in an artificial setting -- like the other writers, he
is discussing exact values of the tick marks.

Articles by R Regan, B Dawson, etc. discusses where are some exact
tick marks on a line of all floating point values. These tick
marks are the exact values of the binary formats of floating point
floats and doubles. This concept is only useful if your value is
precisely on a tick mark -- an artificial condition that can only
be meaningfully enforced in mathematical studies like what they
are doing.

I'd say, let us keep those mathematical studies and normal
floating point usage separate.

In normal use, values are almost always never on those tick marks.
Just do one multiplication* -- are we going to keep all 106 bits
from the 53 x 53 multiplier? (*Assume a real world calc where the
result requires more than 53 bits to fit in exactly.) Then round,
and stick it back into the double binary format. If you say that
the result is exactly on a tick mark, that is no longer the
calculation result, you have just decreed it to be exactly the
tick mark, accumulating error. So one accumulates error and insist
the calculation result is exactly on the tick mark, in the same
breath. Is that good?

In normal use, if the round trip conversion has no errors, the
processor is getting and calculating the same numbers in binary
format. Converting doubles beyond 17 significant digits is not
really useful. Even B Dawson of Google says so.

Well, it's fascinating there is so much support for exact tick
marks. We should keep on discussing.

> Yes, a float passed to printf will get converted to double because
> of stdarg, but this conversion is lossless (no rounding). If we
> convert this back to float we get the same input. (I had to use a
> macro to prevent this conversion on my microcontroller, as arm-gcc
> would use up a lot of code space for it.)
> All the best.
> [snipped all the rest]

--
Cheers,
Kein-Hong Man (esq.)
Selangor, Malaysia

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