Limitations of 32-bit Numbers

When performing mathematical calculations in the RMC, keep in mind that the numbers are 32-bit numbers. 32-bit numbers do not provide infinite resolution or range. This topic describes some of these limitations and how to work around them.

DINT Numbers

DINT numbers are 32-bit integers. DINTs range from -2,147,483,648 to +2,147,483,647. If a result exceeds these limits, the number will wrap.

REAL Numbers

The RMC's REAL data type conforms to the IEEE-754 Floating-Point specification. Real numbers do not have infinite accuracy. They are limited to a certain number of significant digits. The primary effect is that adding a small number to a large number does not result in great accuracy.

In the RMC75E, RMC75S, RMC75P, RMC150, and RMC200, the 32-bit REAL numbers range is -340.28235E+36 to 340.28235E+36. The smallest number that can be represented is 1.4013E-45.

The RMC75E, RMC150E, and RMC200 support Inf, -Inf, and NaN as described below.

Incrementing a Value

Continually incrementing a value by some small amount in a loop can cause problems. For example, incrementing a variable i by 0.001 will eventually cause resolution problems. After reaching a large value, such as 1000, adding 0.001 will not result in exactly 1000.001 due to the resolution limitation.

To avoid this problem, it is possible to increment an integer by 1, then multiply by 1000. Or, if possible, use algorithms that restart the counter periodically, wrap integers, or employ modulo arithmetic.

Not a Number (NaN)

NaN is a symbol that is produced as the result of an operation on invalid input operands.

The RMCs will fault the task if an invalid input to the following functions and operands is detected: SQRT, LN, LOG, ASIN, ACOS, /, and MOD.

Otherwise, the RMC75E, RMC150E, and RMC200 will generate NaN when the result is truly unknown or undefined, which includes the following:

Any operation where NaN is in at least one operand.
The divisions ∞/∞, -∞/∞, ∞/-∞, and -∞/-∞.
The multiplications 0x∞ and 0x-∞.
The additions ∞+(-∞) and (-∞)+∞ and equivalent subtractions.
Applying a function arguments outside of its domain, including taking the tangent of an odd multiple of 90 degrees.

The RMC75S and RMC75P do not have NaN. These controllers will return a saturated value (such as -340.28235E+36 for log10(-50)) or 0 when they have an invalid result.

Infinity (Inf)

The RMC75E, RMC150E, and RMC200 will generate Inf or -Inf when the result is infinity or negative infinity or the result overflows the 32-bit limits. Examples: division by zero, multiplication by infinity

The RMC75S and RMC75P do not have Inf or -Inf. These controllers will return a saturated value, either 340.28235E+36 or -340.28235E+36 when the result is infinity or negative infinity.