Posit v1 (Legacy): Original Reference Implementation

Why

The posit v1 implementation (posit1) is the original reference implementation of John Gustafson’s posit arithmetic, dating to ~2017. It is maintained for backward compatibility and is the only posit implementation that provides full quire (super-accumulator) support with fused dot product (FDP) operations.

If you are starting a new project, use posit<nbits, es, bt> (the current v2 implementation). Use posit1 only if you need:

• Compatibility with code written against the original posit API
• The original quire implementation with full FDP support
• Specialized posit configurations (posit_2_0, posit_3_0, etc.)

What

posit<nbits, es> (in the posit1 namespace) is the original two-parameter posit:

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

Note: unlike the current posit (v2), posit1 does not have a BlockType template parameter. It uses bitblock<> internally with uint64_t storage.

Key Differences from Posit v2

Feature	Posit v1 (posit1)	Posit v2 (posit)
Template params	2: nbits, es	3: nbits, es, bt
Internal storage	bitblock<> (legacy)	blockbinary<> (modern)
Arithmetic engine	internal::value<>	blocktriple<>
Block type	Fixed uint64_t	Configurable (uint8_t-uint64_t)
Quire	Full support	Bridge header available
Status	Legacy/maintenance	Active development

Quire (Super-Accumulator)

The quire is the distinguishing feature of posit1:

template<unsigned nbits, unsigned es, unsigned capacity = 2>
class quire;

The quire is a fixed-point accumulator wide enough to hold the exact sum of any number of posit products without intermediate rounding. For posit<32, 2>, the quire is approximately 512 bits wide.

How to Use It

Include

#include <universal/number/posit1/posit1.hpp>
using namespace sw::universal;

Exact Dot Product with Quire

using Posit = posit<32, 2>;
using Quire = quire<32, 2>;

std::vector<Posit> a = { Posit(1.0), Posit(2.0), Posit(3.0) };
std::vector<Posit> b = { Posit(4.0), Posit(5.0), Posit(6.0) };

Quire q;
q.clear();
for (size_t i = 0; i < a.size(); ++i) {
    q += quire_mul(a[i], b[i]);  // Exact: no intermediate rounding
}

Posit result;
convert(q.to_value(), result);
// result = 32.0 exactly (1*4 + 2*5 + 3*6)

Fused Dot Product (FDP)

// fdp: fused dot product -- accumulate in quire, round once at the end
Posit fdp_result = fdp(a, b);  // Equivalent to quire-based accumulation

When to Use Posit v1 vs Posit v2

Use Case	Recommendation
New project, general posit arithmetic	Use posit (v2)
Need configurable block type for hardware	Use posit (v2)
Need full quire/FDP support	Use posit1
Backward compatibility with existing code	Use posit1
Reproducible linear algebra (BLAS)	Use posit1 with quire
Mixed-precision algorithm exploration	Use posit (v2)