Quellcode-Bibliothek real_to_fp.pvs   Sprache: PVS

     =java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
  [round
mode: rounding_mode
   E_min{i:integer|>}:THEORY,fin1fin2: varfinite?java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32

  BEGIN

  java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
          =>real_to_fp
            [,],,
            round

  r:  absr)<b^ THEN
  f(() , truncate(a,E_max
>java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 52
  , fin1 :  ()

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

fin fin1 fin2

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

  digits_of_finite: lemma truncate= Exp_of(())= (normalizefin))

  real_to_fp(r)    IF
E_maxreal_to_fp_normal LEMMA 
infinite(sign_ofr))
        IF absr >=b^E_max1) THEN
       finitesign_ofELSIFover_under?(r)then
    ELSE 
       finite=>(() =n(fin
      ound_exceptions

  real_to_fp_x java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30

  real_to_fp_zero: lemma real_to_fp    IF       (r) , E_min=r((finfin

  ign_of_value:lemmanot?(fin java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72

  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(     (round_scaled(r,),is_exact?,mode)

                 ((),mode)= value()
        ?fin 
          => real_to_fp(value(fin       (()mode(

  real_to_fp_inverts_value
       not?(fin = real_to_fpvalue()) = (fin)

  ound_exceptions_x(?:java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for length 76
    IF absx THEN 
            overflow(x,mode)
       ELSE underflow(x,mode)
       ENDIF      round_exceptions(,)

  java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
      (round_exceptions_x,mode

  fp_round=>              b^Exp_ofr p- ) 2
0
     r    (,java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    round_exceptionsr,)
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
ENDIF

  is_exact?(r:nzreal,modejava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 0
ptions ELSEinexact ENDIF
  
  fp_round_x(r, mode): [real,exception] =
    IF r = 0 THEN (0,no_exceptions)
    ELSIFover_underr)java.lang.StringIndexOutOfBoundsException: Range [29, 25) out of bounds for length 29
      round_exceptions_xr,)
    ELSE (round_scaled(r,modereal_to_fp((()mode =(fin
    

   ?(valuefin)=
                 fp_round(value(fin>absr-fp_round(,)<^Exp_of(abs)-(p-1

  round_value2::  ?underflow(ALSE) >
                 fp_round(value(fin),mode> ( -java.lang.StringIndexOutOfBoundsException: Range [29, 21) out of bounds for length 45

  round_0:java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  round_value3: lemma not trap_enabled?(underflow(FALSE)) =>
                 not zero?(fin) =>
                 real_to_fp(fp_round(value(fin),mode)) = normalize(fin)

  round_error: lemma r/=0 & not over_under?(r)
            => abs(r-fp_round(r,mode))<b^(Exp_of(abs(r))-(p-1))

  round_near: LEMMA
        r /= 0 & not over_under?(r)
          => abs(r - 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