Posito: Experimental Posit Validation Variant

Why

When developing and validating a new number system, it is essential to have independent implementations that can be cross-checked against each other. The posito type is an alternative implementation of posit arithmetic used for experimental validation and research. It shares the same mathematical specification as posit and posit1 but follows a separate implementation path, making it useful for detecting implementation bugs through differential testing.

What

posito<nbits, es> implements the same posit encoding as posit1:

Parameter	Type	Description
nbits	unsigned	Total bits
es	unsigned	Maximum exponent bits

Key Properties

• Same encoding as posit/posit1: sign, regime, exponent, fraction
• Same value semantics: tapered precision, NaR, reciprocal symmetry
• Independent implementation path for validation
• Uses posit1 internal classes (positRegime, positExponent, positFraction)
• Two-parameter template (like posit1, no BlockType parameter)

How to Use It

Include

#include <universal/number/posito/posito.hpp>
using namespace sw::universal;

Differential Testing

// Cross-check posit implementations
posit<32, 2> p(3.14159);
posito<32, 2> po(3.14159);

// Both should produce identical results
auto p_result = p * posit<32, 2>(2.71828);
auto po_result = po * posito<32, 2>(2.71828);

assert(double(p_result) == double(po_result));

When to Use

• Research: validating posit arithmetic properties
• Testing: differential testing against posit/posit1
• Legacy: compatibility with code that depends on posito
• For new code: prefer posit<nbits, es, bt> (the current v2 implementation)