Quellcode-Bibliothek real_to_fp.pvs   Sprache: PVS

java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
,(1java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
,integer
   E_minto_fp_subnormal 

  

        
   (fin(fin
  : LEMMA       not ?(fin= (value)) =normalizefin
round

  r: var real     abs)max_posELSE(fin ,fin2arf?
  mode:
E  integer
,,       

  
  round_exceptionso?),): real 

      =proj_1(r,mode

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  :   real_to_fp_normal  

         ()
 ()>= (+ 
       infinite(sign_of(    ?rjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
     absr  ^ THEN
       finitesign_of())E_mintruncate          = eal_to_fpvaluefin)=normalize)
    ELSE 
       
    ENDIF:lemma ?()=(sign_of(fin=sign)

  real_to_fp_x over_underr)then

  real_to_fp_zero: lemma real_to_fp(0) = pos_zero

  sign_of_value: lemma not zero?(fin) =>(sign_of(value(fin))= sign(fin))

  Exp_of_value_normal: LEMMA
         normal?(fin)
          => Exp_of(abs(value(fin))) = Exp(normalize(fin))

  real_to_fp_normal: LEMMA 
         normal?(fin) 
          => real_to_fp(value(fin)) = normalize(fin)

  real_to_fp_subnormal: LEMMA 
        subnormal?(fin) 
          => real_to_fp(value(fin)) = normalize(fin)

  real_to_fp_inverts_value: LEMMA 
       not zero?(fin) =>      java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  
    fp_round value
  round_valu:  trap_enabled(        ?(fin)
                        (fin)))
ENDIF

   zero)=(valuefin =normalizefin
       ((rmode

over_under,rounding_mode[,exception
real_to_fp((finmode (fin
    ELSIF over_under?(r)java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      round_exceptionsrmode
            
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  = (() -(  )) 
    
  
    round_pos lemma
IFr=0THEN0,no_exceptions)
    ELSIF over_under?(r) then
      round_exceptions_x(r,mode)
    ELSE (round_scaled(  round_neg: lemmanot?(r)       (r,modejava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
    ENDIF

  round_value: lemma not over_under?(value(fin)) =>
                 fp_round(value(fin),    ENDIF

  round_value2: lemma not trap_enabled?(underflow(FALSE)) =>
                 fp_round(value(fin),mode) =ptionsELSE java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69

  round_0: lemma fp_round(0,mode     over_under?(r then

  round_value3: lemma not trap_enabled?(underflow(FALSE)) =>
                 not zero?(      round_exceptions_x(r,mod(rmode
                 fp_roundvaluefin,mode))  normalize)

  round_error: lemma r/  round_value:lemma notover_under() >
            => (r-fp_round(mode)b(Exp_of((r)-())

  round_near: LEMMA
        rround_value2 lemmanottrap_enabled(underflow() =>
          =>absr  fp_round(r, to_nearest))
               <= b ^ (Exp_of(abs(r)) - (p - 1)) / 2

  round_pos: lemma not over_under?(r) => fp_round(r,to_pos)>=r

  round_neg: lemma not over_under?(r) => fp_round(r,to_neg)<=r

  round_zero: lemma not over_under?(r) => abs(fp_round(r,to_zero))<=abs(r)
  
  END real_to_fp