At 7:10 AM -0500 12/1/07, Christoph Boget wrote:
Why does
sprintf( '%.03f', 0.15250000 )
return 0.152 while
sprintf( '%.03f', 0.15750000 )
return 0.158?
The 4th significant digit in both cases is '5' but in the first case, it's
rounded down but in the second case it is rounded up. Is sprintf() basing
it's decision on the value of the 3rd significant digit? If so, why?
Shouldn't rounding decisions be based on subsequent digits and not preceding
ones?
I am using PHP 4.3.11
thnx,
Christoph
Actually, it's more accurate to use the preceding digit to determine
rounding. What you describe is "if even then round down else round
up". That's more accurate than always rounding up or always rounding
down.
Please follow:
When the digit is zero, no rounding takes place.
When the digit is 1 - 4, round down.
When the digit is 6 - 9, round up.
Fine up to there -- but, if you always round up or down for 5, then
you are introducing bias.
So, if you use the even/odd value of the preceding digit to determine
which way to round for 5, then it's more accurate.
However, no rounding is accurate -- it's just that some methods are
less error prone.
Here's a demo:
http://www.webbytedd.com/bbb/rounding/
My rounding method doesn't always win against php's round(), but it
wins more times than not. Plus, it takes a lot of rounding to
introduce the bias I found and thus for most applications using the
round() function (always round down) will suffice.
Cheers,
tedd
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