Hi All
Today's we notice one odd behavior of Round function.
Formula Round(4.975, 0.01) getting 4.97, is it should be 4.98? can't figure out why and also the behavior of select tool is same.
Hi there @Yongcan
You've stumbled across one of the deep problems with floating point representation. As I'm sure you know, integers are held in binary and can be exactly represented. 0101 = 5, 0110 = 6, etc. However, floats are stored in 3 parts
1 sign bit
8 exponent bits
23 Mantissa bits
The mantissa is the closest value of the series 1*(1/2) + 0*(1/4) + 1*(1/8) + 0*(1/16) +………+ 0*(1/2^23) = 0.625.
Some decimals are exactly represented
0.5=(1*(1/2) + 0*(1/4))
0.25(0*(1/2) + 1*(1/4))
0.75(1*(1/2) + 1*(1/4))
The problem arises because not all decimals can be exactly represented by this series. 0.1 is one particularly vexing example. As you can see in the table, the expansion of 0.1 is actually 0.10000000000000001
These results were generated using the following formulas
The Fixed17 column gives an approximation of how the number is represented internally
What's troubling about these results is that the round() function and the conversion to 19.2 don't give the same results suggesting that there are 2 different rounding mechanisms in place. I think you should open a ticket to have this addressed.
But how to solve your problem. If you add a small amount to each number before rounding you'll get consistent results. The small amount should be several orders of magnitude smaller than what your round to, but several orders larger than the internal representation. In my RoundPlusSmall formula I used
round([Number]+0.00000001,0.01)
Dan
notice once I change the number to string format then use select with fixedDecimal then i get the expect result. things getting interested now.
