There are situations where more precision is required for mathematical comparisons. Take for the example comparing 1 against 0.9999999. The expected result should be that 1 is greater than 0.9999999 and the "Greater" alert will appear.

C_REAL($exactly_r;$almost_r) $exactly_r:=1 $almost_r:=0.9999999 Case of    : ($exactly_r=$almost_r)    ALERT("Equal")       : ($exactly_r>$almost_r)    ALERT("Greater")       : ($exactly_r<$almost_r)    ALERT("Less")    End case

However, the actual result is the "Equal" alert. Why is that?



4D takes the difference of two real numbers and compares it to this default epsilon value of 10^-6. If the difference is greater than 10^-6, the comparison returns not equal. Otherwise the comparison returns equal.

In the case above, the difference is 0.0000001 (or 10^-7). Since 10^-7 is less than the default epsilon value 10^-6, 1 and 0.9999999 are considered equal. To resolve this issue, the epsilon value must to be set to a value that is less than the difference. In this case, the command SET REAL COMPARISON LEVEL(10^-8) can be used for a more accurate comparison which now returns the correct alert "Greater".



Just be aware of this SET REAL COMPARISON LEVEL command when working with precise calculations.