Tolerant equality in Polaris

Computers store numbers in binary format using the IEEE 754 floating-point standard. Many decimal numbers can't be represented exactly in binary, so the system must approximate them. This approximation introduces tiny, invisible rounding errors during calculations, specifically during equality checks.

These errors are invisible in displayed cell values, but they can produce unexpected logical results that are difficult to diagnose.

These examples show how standard computer arithmetic introduces tiny binary rounding discrepancies:

Floating-point errors aren't unique to Anaplan. For example, in Microsoft Excel, high-precision math can cause simple logical tests to fail:

Mathematically, (A1 + B1) - B1 should equal A1. But Excel's binary arithmetic introduces a tiny rounding error in C1, causing the equality check to fail.

To address these problems, Polaris uses tolerant equality. Tolerant equality treats two numbers as equal if the difference between them falls within a tiny rounding tolerance. Instead of requiring an exact binary match, the system accepts values that are practically identical. This prevents minor rounding errors from breaking logical comparisons, ensuring your models behave exactly as you expect.

Polaris automatically uses tolerant equality when comparing numbers, testing for accuracy up to 15 significant figures. When comparing any number to zero, it treats values between −1 × 10⁻¹⁴ and +1 × 10⁻¹⁴ as equal to zero.

• x = 0 evaluates to TRUE if x is exactly 0, or falls within the tolerance range.
• Logical tests remain stable and behave as expected, even when small rounding errors accumulate.
• No manual precision management is needed, ensuring reliable model behavior automatically.

Both engines use tolerant equality for general number comparisons, but handle zero-comparisons differently.

These examples show how Polaris and the Classic Engine handle tiny rounding errors differently: