Floating Point Values¶
A calculation with floating points can lead to the following values:
0 (zero)
If a calculation results in an underrun, the value is set to 0 (result near 0, but not presentable). Depending on the sign bit, it can be a positive zero or a negative zero. The operator “=” of -0 and 0 returns TRUE.
Infinity
If a calculation results in an overrun, the value is set to Infinity (the result is not presentable). Depending on the sign bit, it can be a positive infinity (Infinity) or negative infinity (-Infinity).
If Infinity is converted into another data type it results in the maximum value of the other data type (e.g.. conversion into DWORD with REAL_TO_DWORD: 16#FFFFFFFF, into DINT with REAL_TO_DINT: 16#7FFFFFFF).
If -Infinity is converted into another data type it results in the maximum value of the other data type (e.g.. conversion into DWORD with REAL_TO_DWORD: 16#00000000, into DINT with REAL_TO_DINT: 16#80000000).
Except for:
TRUE := REAL_TO_BOOL(Infinity);
'#Inf' := REAL_TO_STRING(Infinity);
'-#Inf' := REAL_TO_STRING(-Infinity);
Examples:
| Infinity | -Infinity |
|---|---|
| Infinity := 1.0 / 0.0 | -Infinity := -1.0 / 0.0 |
| Infinity := Infinity + Infinity | -Infinity := -Infinity -Infinity |
| Infinity := Infinity + 1.0 | -Infinity := -Infinity + 1.0 |
| Infinity := LREAL_TO_REAL(Infinity) | -Infinity := LREAL_TO_REAL(-Infinity) |
NaN
If a calculation results in an undefined value the result is set to NaN (Not a Number). The result of each calculation with NaN is NaN. The operators “<”, “<=”, “>” and “>=” return FALSE if either or both operands are NaN.
Operator “=” returns FALSE if one operand is NaN.
Operator “<>” returns TRUE if one operand is NaN.
If NaN is converted into another data type the result is 0.
Except for:
TRUE := REAL_TO_BOOL(NaN);
'#NaN' := REAL_TO_STRING(NaN);
Examples:
NaN := SQRT(-2.0)
NaN := 0.0 / 0.0
NaN := Infinity -Infinity
NaN := 0.0 * Infinity
NaN := Inifnity / Infinity
The result of an operation can be checked with the following program parts:
| Check for NaN (REAL): | Check for NaN (LREAL): |
|---|---|
(* rX is a NaN *)
|
(* lrX is a NaN *)
|
| Check for Infinity (REAL): | Check for Infinity (LREAL): |
|---|---|
Infinity is represented with sign bit 0, exponent of all 1s and a fraction of all 0s. -Infinity is represented with sign bit 1, exponent of all 1s and a fraction of all 0s. |
|
(* rX is Infinity *)
(* rX is -Infinity *)
|
(* lrX is Infinity *)
(* lrX is -Infinity *)
|