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Datei: NaN_ops.pvs Sprache: PVS

Original von: PVS^©

NaN_ops
  [b,p:above(1),
   E_max:integer,
   E_min:{i:integer|E_max>i}]: THEORY

  BEGIN

  IMPORTING IEEE_854_values[b,p,E_max,E_min],
            enumerated_type_defs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Placeholders for defining results of operations on NaNs

  fp,fp1,fp2: var fp_num
  nan,nan1,nan2: var (NaN?)

  op: var fp_ops

  signal?(fp):bool = if NaN?(fp) then signal?(status(fp)) else false endif

% mk_quiet takes an fp_num and coerces all NaNs into quiet NaNs.
%  all numeric floating-point arguments are left unchanged
  mk_quiet(fp): fp_num = if NaN?(fp) then NaN(quiet,data(fp)) else fp endif

  mk_quiet_correct: lemma not signal?(fp) => mk_quiet(fp) = fp

  fp_quiet(op,fp1,(fp2| NaN?(fp1) OR NaN?(fp2))):{nan| nan=fp1 or nan=fp2}

  fp_signal(op, fp1,(fp2| NaN?(fp1) OR NaN?(fp2))): fp_num =
    IF trap_enabled?(invalid_operation) THEN invalid
    ELSE fp_quiet(op, mk_quiet(fp1), mk_quiet(fp2))
    ENDIF

  fp_nan(op, fp1, (fp2| NaN?(fp1) OR NaN?(fp2))): fp_num =
    IF signal?(fp1) OR signal?(fp2) THEN fp_signal(op, fp1, fp2)
    ELSE fp_quiet(op, fp1, fp2)
    ENDIF

  NaN_ops_correct: LEMMA
        NOT trap_enabled?(invalid_operation) & (NaN?(fp1) OR NaN?(fp2))
          => quiet?(status(fp_nan(op, fp1, fp2)))

  fp_nan_x(op, fp1, (fp2| NaN?(fp1) OR NaN?(fp2))): [fp_num,exception] =
    IF signal?(fp1) OR signal?(fp2) THEN
       (fp_signal(op, fp1, fp2),invalid_operation)
    ELSE
       (fp_quiet(op, fp1, fp2), no_exceptions)
    ENDIF
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  NaN_sqrt(nan): fp_num =
    if signal?(status(nan))
        & trap_enabled?(invalid_operation) then
       invalid
    else NaN(quiet,data(nan))
    endif


  END NaN_ops

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