What the name means

QF means quantifier-free. BVFP combines bit-vectors with floating-point arithmetic.

Quantifier-free formulas have no explicit "for every" or "there exists" binders. They can still contain unknown values that the solver must find.

A program may store a floating-point value as bits, inspect a sign bit, or convert a machine integer into a floating-point number. This division retains both kinds of values and the operations between them.

Reinterpreting bits and converting a number have different meanings. Reinterpretation reads a pattern as a floating-point representation. Numerical conversion attempts to preserve a numeric value, with rounding where the target format requires it.

Worked example

Read a negative-zero bit pattern

Take the 32-bit pattern 0x80000000 and reinterpret it as a binary32 floating-point value.

  1. Binary32 has a sign bit, eight exponent bits, and 23 stored fraction bits.
  2. The given pattern has sign bit one and all exponent and fraction bits zero.
  3. Reinterpretation therefore produces negative zero. Both the floating-point zero test and the negative-sign test hold.

Constraints requiring that pattern, reinterpretation, and both tests are sat.

This is an authored mathematical example, not captured Axeyum output. Here, sat means the constraints can all hold; unsat means they cannot.

A contrasting case

Numerically convert the same pattern as an unsigned integer. Its value is 2,147,483,648, so conversion to binary32 gives that positive value, not negative zero.

Use cases

  • Check serialization code that reads floating-point values from packet bits.
  • Analyze casts, sign tests, and mixed integer/floating-point branches in numeric software.

Modeling caution

State whether each conversion reinterprets a representation or converts a signed or unsigned number. A byte order must also be specified when assembling bytes into the bit-vector.

Axeyum coverage

The examples explain the logic's meaning. They do not establish complete Axeyum support for this division. Acceptance, solving, and evidence coverage depend on the input and the solver route.

This division appears in the site's retained regression scoreboard. Read the individual slices and their source records for the tested scope.

A solver may return unknown if it cannot settle a query. That result establishes neither sat nor unsat. Parsing a declared logic name alone does not prove support for every formula in it.

Engine support documentation at the site's recorded snapshot, 03ae4a3c9, 2026-10-05.

Definitions and references

Definitions consulted September 6, 2026. The worked examples and use-case explanations are authored for this guide.