Quelle arithmetic_ops.pvs Sprache: PVS

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

  BEGIN

  IMPORTING IEEE_854_values[b,p,E_max,E_min],
            real_to_fp[b,p,alpha,E_max,E_min],
            enumerated_type_defs

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fp_op provides a template for defining a floating point operation
%  for the case when both arguments are finites.

  fin,fin1,fin2: var (finite?)
  op: var fp_ops
  mode: var rounding_mode

  apply(op,fin1,(fin2:{fin| div?(op) => not zero?(fin)})): real =
    cases op of
      add:  value(fin1) + value(fin2),
      sub:  value(fin1) - value(fin2),
      mult: value(fin1) * value(fin2),
      div:  value(fin1) / value(fin2)
    endcases

  signed_zero(op, fin1, fin2, mode): {fin | zero?(fin)} =
    CASES op OF
      add:
          IF zero?(fin1)
                & zero?(fin2) & sign(fin1) = sign(fin2) THEN fin1
          ELSIF to_neg?(mode) THEN neg_zero
          ELSE pos_zero
          ENDIF,
      sub:
          IF zero?(fin1)
                & zero?(fin2) & sign(fin1) /= sign(fin2) THEN fin1
          ELSIF to_neg?(mode) THEN neg_zero
          ELSE pos_zero
          ENDIF,
      mult:
          IF sign(fin1) = sign(fin2) THEN pos_zero
          ELSE neg_zero
          ENDIF,
      div:
          IF sign(fin1) = sign(fin2) THEN pos_zero
          ELSE neg_zero
          ENDIF
      ENDCASES

  fp_op(op, fin1, (fin2: {fin | div?(op) => NOT zero?(fin)}), mode): fp_num =
    LET r = fp_round(apply(op, fin1, fin2), mode)
      IN IF r = 0 THEN signed_zero(op, fin1, fin2, mode)
        ELSE real_to_fp(r)
        ENDIF

  fp_op_x(op,fin1,(fin2:{fin| div?(op) => not zero?(fin)}),mode):
    [fp_num, exception]
           =
    LET rp = fp_round_x(apply(op, fin1, fin2), mode)
      IN IF proj_1(rp) = 0 THEN (signed_zero(op, fin1, fin2, mode),proj_2(rp))
        ELSE real_to_fp_x(rp)
        ENDIF

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  END arithmetic_ops

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