SymFPU : The Symbolic Floating Point Unit

SymFPU is an implementation of the SMT-LIB / IEEE-754 operations in terms of bit-vector operations. It is templated in terms of the bit-vectors, propositions, floating-point formats and rounding mode types used. This allow the same code to be executed as an arbitrary precision "SoftFloat" library (although it's performance would not be good) or to be used to build symbolic representation of floating-point operations suitable for use in "bit-blasting" SMT solvers (you could also generate circuits from them but again, performance will likely not be good).

A considerable amount of effort has gone in to checking that these encodings are correct and so please do report any discrepancies you see.

The library is Free Software licensed under the GPL V3. If this poses a particular challenge for your application, please contact the author.

A Quick Start

Create a "back-end", a class with the following members:

class traits {
  public :
  // The base types to use.
  // Must implement the SMT-LIB-like interfaces used by other back-ends
  typedef YourBitWidthType bwt;
  typedef YourRoundingMode rm;
  typedef YourFloatingPointTypeInfo fpt;
  typedef YourProposition prop;
  typedef YourSignedBitVector sbv;
  typedef YourUnsignedBitVector ubv;

  // Return an instance of each rounding mode.
  static rm RNE(void);
  static rm RNA(void);
  static rm RTP(void);
  static rm RTN(void);
  static rm RTZ(void);

  // Handle various invariants.
  // These can be empty to start with.
  static void precondition(const bool b) { assert(b); }
  static void postcondition(const bool b) { assert(b); }
  static void invariant(const bool b) { assert(b); }
  static void precondition(const prop &p) {}
  static void postcondition(const prop &p) {}
  static void invariant(const prop &p) {}
};

If you are stuck; start from one of the existing (symbolic or literal) ones. baseTypes/shared.h gives suitable implementations of fpt and bwt, plus if it is executable, you can use bool for prop.

Make sure symfpu is on your path and include the following headers:

#include "symfpu/core/unpackedFloat.h"
#include "symfpu/core/packing.h"
#include "symfpu/core/add.h"

To generate a (32-bit) unsigned bit-vector containing the single precision addition of two other 32-bit bit-vectors, use the following code:

fpt format(8,24);
ubv packed1 = ...  // Must be 32-bit.
ubv packed2 = ...  // Must be 32-bit.

uf unpacked1(symfpu::unpack<traits>(format, packed1));
uf unpacked2(symfpu::unpack<traits>(format, packed2));
    
uf added(symfpu::add<traits>(format, traits::RNE(), unpacked1, unpacked2, prop(true)));
    
ubv repacked(symfpu::pack<traits>(format, added));

See applications/implementation.h for examples of other operations (although, really, it is pretty similar).

martin-cs/symfpu

SymFPU : The Symbolic Floating Point Unit

A Quick Start