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Calculator for Determining the Signum (Algebraic Sign) of Values

Find the signum or sign of rational numbers. The signum function returns -1 for negative numbers, 1 for positive numbers, and 0 for zero. For input values, please enter one or more numbers separated by spaces, maximum 1000 numbers. Decimal separator can be , or .

Example: For the input 5 0 -8, the output is 1 0 -1.

The signum function is particularly important in computer science and control engineering. When the magnitude of a value is irrelevant and only its direction matters, the signum function is the simplest method to determine this.

Typical applications include:
Control engineering: Determining the direction of movement for motors or actuators, such as forward or backward, left or right.
Mathematical algorithms: Simplifying calculations where only the sign is needed for decision-making, such as in gradient methods or error correction.
Data analysis: Classifying deviations or trends in time series, such as whether a value is above or below a target value.
Physical simulations: Modeling forces or velocities where direction is the primary focus, such as attraction or repulsion.
Signal processing: Detecting phase changes or zero crossings in digital or analog signals.
Decision logic: Implementing threshold decisions where only the relative position to a reference value (positive or negative) is relevant.

Example: Positioning a robotic arm
Assume a robotic arm needs to move to a specific position. The control algorithm calculates the deviation between the target and actual position, known as the error. The signum function is used here to determine the motor's direction:
• If error > 0 (actual position is less than target position), the signum function returns +1: The motor moves forward to close the gap to the target position.
• If error < 0 (actual position is greater than target position), the signum function returns -1: The motor moves backward to reach the target position.
• If error = 0 (actual position matches target position), the signum function returns 0: The motor stops.
The check is performed cyclically in real time, so the size of the deviation is irrelevant for this algorithm.

Last updated on 01/31/2026. Author: Jürgen Kummer

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