REXX NUMERIC DIGITS and NUMERIC FUZZ precision and comparison behavior across implementations

Default Precision and Tolerance

In most standard REXX implementations—including ooRexx and Regina—the default value for NUMERIC DIGITS is 9, and the default for NUMERIC FUZZ is 0. While these defaults are generally consistent, the maximum allowable value for NUMERIC DIGITS varies significantly between interpreters. For example, mainframe z/OS REXX typically enforces a lower maximum limit than ooRexx or Regina, which can cause scripts relying on extreme precision to fail during migration.

How NUMERIC FUZZ Defines Equality

NUMERIC FUZZ does not affect arithmetic calculations; it only modifies the behavior of numeric comparisons (e.g., =, <>, >, <). When FUZZ is set to a value n, the interpreter rounds both operands of a comparison to (DIGITS - n) significant digits before evaluating the expression.

If two numbers are identical after this rounding, they are treated as equal. This allows developers to ignore insignificant trailing digits caused by precision limits without manually rounding every variable.

Comparison Example

/* Assume NUMERIC DIGITS 9 */
NUMERIC FUZZ 2
SAY (100.4 = 100.3) /* Returns 1 (True) because both round to 100 */

NUMERIC FUZZ 0
SAY (100.4 = 100.3) /* Returns 0 (False) */

Portability Considerations

To ensure numeric consistency across different REXX implementations, consider the following:

• Explicit Initialization: Do not rely on defaults. Explicitly set NUMERIC DIGITS and NUMERIC FUZZ at the start of your script to ensure identical behavior across environments.
• Avoid High Precision Limits: Avoid setting NUMERIC DIGITS to extremely high values (e.g., 100+) if the code must run on z/OS REXX.
• Global State Risks: NUMERIC FUZZ is a global setting. If a called subroutine changes the fuzz value, it affects all subsequent comparisons in the calling program.
• Non-Transitivity: Be aware that "fuzzed" equality is not strictly transitive. If A equals B and B equals C under a specific fuzz setting, A may not necessarily equal C.

Verification Commands

You can verify your current environment using the following commands:

SAY "Digits:" DIGITS()
SAY "Fuzz:" FUZZ()
SAY "Form:" FORM()