Quellcode-Bibliothek real_to_fp.pvs   Sprache: PVS

real_to_fp
  [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], 
            over_under[b,p,alpha,E_max,E_min],
            fp_round_aux[b,p],
            round

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

  px: var posreal
  E: var integer

  JUDGEMENT truncate has_type [integer,nonneg_real -> digits]

  truncate_zero: lemma truncate(E,0)=d_zero

  digits_of_finite: lemma truncate(Exp(fin),abs(value(fin))) = d(fin)

  real_to_fp(r): fp_num =
    IFIF abs(r)>= b^(E_max+1) THEN 
       infinite(sign_of(r))
    ELSIF abs(r) < b^E_min THEN 
       finite(sign_of(r), E_min, truncate(E_min, abs(r)))
    ELSE 
       finite(sign_of(r), Exp_of(abs(r)), truncate(Exp_of(abs(r)), abs(r)))
    ENDIF    

  real_to_fp_x(r:real,e:exception): [fp_num,exception] = (real_to_fp(r),e)

  real_to_fp_zero: lemma real_to_fp(0) = pos_zero

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

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

  real_to_fp_normal: LEMMA 
         normal?(finjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
 eal_to_fpfp_round_aux[,java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17

to_fp_subnormal
        BEGIN
=real_to_fp())=normalize)

real_to_fp_inverts_value 
       notzero) >real_to_fp(fin  normalize()

  round_exceptions_x(            
    IF(x)max_pos THEN 
            overflow(x,mode)
       ELSE underflowx,fin, fin1fin2vfinitejava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
ENDIF

  (r:(ver_undermode real 
= (round_exceptions_x,mode))

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
IFdigits_of_finitejava.lang.StringIndexOutOfBoundsException: Range [0, 1) out of bounds for length 0
 over_under()java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
r
real_to_fp_xreal_to_fp_subnormal 
ENDIF

  is_exact    ELSIF()<bE_min 
            (r, (          >real_to_fp) fin
  
s   zero >(value))= (fin)
    IF r
    ELSIF?(r java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
ELSE(,mode?())
    ENDIF

  round_value
fp_roundvaluefin= valuefin

e2:lemma nottrap_enabled?        subnormal())
fp_roundvaluefin), = valuefin

  round_0: lemma fp_round(0,       java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12

        =proj_1round_exceptions_x,))
  round_exceptions_x(x:?),ode): real] =
                 (fp_roundvaluefin),)) =normalizefin)

  round_error: lemma r/=0 & not over_under(x)>max_posjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
=

  round_near: LEMMA
        r /= 0 proj_1(r,))
           abs
<b (abs) (-1/

:java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19

round_neg  over_under      mode

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