+++ /dev/null
-------------------------------------------------------------------------------
--- --
--- GNAT COMPILER COMPONENTS --
--- --
--- E V A L _ F A T --
--- --
--- B o d y --
--- --
--- $Revision: 1.1.16.1 $
--- --
--- Copyright (C) 1992-2001 Free Software Foundation, Inc. --
--- --
--- GNAT is free software; you can redistribute it and/or modify it under --
--- terms of the GNU General Public License as published by the Free Soft- --
--- ware Foundation; either version 2, or (at your option) any later ver- --
--- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
--- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
--- or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License --
--- for more details. You should have received a copy of the GNU General --
--- Public License distributed with GNAT; see file COPYING. If not, write --
--- to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, --
--- MA 02111-1307, USA. --
--- --
--- GNAT was originally developed by the GNAT team at New York University. --
--- Extensive contributions were provided by Ada Core Technologies Inc. --
--- --
-------------------------------------------------------------------------------
-
-with Einfo; use Einfo;
-with Sem_Util; use Sem_Util;
-with Ttypef; use Ttypef;
-with Targparm; use Targparm;
-
-package body Eval_Fat is
-
- Radix : constant Int := 2;
- -- This code is currently only correct for the radix 2 case. We use
- -- the symbolic value Radix where possible to help in the unlikely
- -- case of anyone ever having to adjust this code for another value,
- -- and for documentation purposes.
-
- type Radix_Power_Table is array (Int range 1 .. 4) of Int;
-
- Radix_Powers : constant Radix_Power_Table
- := (Radix**1, Radix**2, Radix**3, Radix**4);
-
- function Float_Radix return T renames Ureal_2;
- -- Radix expressed in real form
-
- -----------------------
- -- Local Subprograms --
- -----------------------
-
- procedure Decompose
- (RT : R;
- X : in T;
- Fraction : out T;
- Exponent : out UI;
- Mode : Rounding_Mode := Round);
- -- Decomposes a non-zero floating-point number into fraction and
- -- exponent parts. The fraction is in the interval 1.0 / Radix ..
- -- T'Pred (1.0) and uses Rbase = Radix.
- -- The result is rounded to a nearest machine number.
-
- procedure Decompose_Int
- (RT : R;
- X : in T;
- Fraction : out UI;
- Exponent : out UI;
- Mode : Rounding_Mode);
- -- This is similar to Decompose, except that the Fraction value returned
- -- is an integer representing the value Fraction * Scale, where Scale is
- -- the value (Radix ** Machine_Mantissa (RT)). The value is obtained by
- -- using biased rounding (halfway cases round away from zero), round to
- -- even, a floor operation or a ceiling operation depending on the setting
- -- of Mode (see corresponding descriptions in Urealp).
- -- In case rounding was specified, Rounding_Was_Biased is set True
- -- if the input was indeed halfway between to machine numbers and
- -- got rounded away from zero to an odd number.
-
- function Eps_Model (RT : R) return T;
- -- Return the smallest model number of R.
-
- function Eps_Denorm (RT : R) return T;
- -- Return the smallest denormal of type R.
-
- function Machine_Mantissa (RT : R) return Nat;
- -- Get value of machine mantissa
-
- --------------
- -- Adjacent --
- --------------
-
- function Adjacent (RT : R; X, Towards : T) return T is
- begin
- if Towards = X then
- return X;
-
- elsif Towards > X then
- return Succ (RT, X);
-
- else
- return Pred (RT, X);
- end if;
- end Adjacent;
-
- -------------
- -- Ceiling --
- -------------
-
- function Ceiling (RT : R; X : T) return T is
- XT : constant T := Truncation (RT, X);
-
- begin
- if UR_Is_Negative (X) then
- return XT;
-
- elsif X = XT then
- return X;
-
- else
- return XT + Ureal_1;
- end if;
- end Ceiling;
-
- -------------
- -- Compose --
- -------------
-
- function Compose (RT : R; Fraction : T; Exponent : UI) return T is
- Arg_Frac : T;
- Arg_Exp : UI;
-
- begin
- if UR_Is_Zero (Fraction) then
- return Fraction;
- else
- Decompose (RT, Fraction, Arg_Frac, Arg_Exp);
- return Scaling (RT, Arg_Frac, Exponent);
- end if;
- end Compose;
-
- ---------------
- -- Copy_Sign --
- ---------------
-
- function Copy_Sign (RT : R; Value, Sign : T) return T is
- Result : T;
-
- begin
- Result := abs Value;
-
- if UR_Is_Negative (Sign) then
- return -Result;
- else
- return Result;
- end if;
- end Copy_Sign;
-
- ---------------
- -- Decompose --
- ---------------
-
- procedure Decompose
- (RT : R;
- X : in T;
- Fraction : out T;
- Exponent : out UI;
- Mode : Rounding_Mode := Round)
- is
- Int_F : UI;
-
- begin
- Decompose_Int (RT, abs X, Int_F, Exponent, Mode);
-
- Fraction := UR_From_Components
- (Num => Int_F,
- Den => UI_From_Int (Machine_Mantissa (RT)),
- Rbase => Radix,
- Negative => False);
-
- if UR_Is_Negative (X) then
- Fraction := -Fraction;
- end if;
-
- return;
- end Decompose;
-
- -------------------
- -- Decompose_Int --
- -------------------
-
- -- This procedure should be modified with care, as there
- -- are many non-obvious details that may cause problems
- -- that are hard to detect. The cases of positive and
- -- negative zeroes are also special and should be
- -- verified separately.
-
- procedure Decompose_Int
- (RT : R;
- X : in T;
- Fraction : out UI;
- Exponent : out UI;
- Mode : Rounding_Mode)
- is
- Base : Int := Rbase (X);
- N : UI := abs Numerator (X);
- D : UI := Denominator (X);
-
- N_Times_Radix : UI;
-
- Even : Boolean;
- -- True iff Fraction is even
-
- Most_Significant_Digit : constant UI :=
- Radix ** (Machine_Mantissa (RT) - 1);
-
- Uintp_Mark : Uintp.Save_Mark;
- -- The code is divided into blocks that systematically release
- -- intermediate values (this routine generates lots of junk!)
-
- begin
- Calculate_D_And_Exponent_1 : begin
- Uintp_Mark := Mark;
- Exponent := Uint_0;
-
- -- In cases where Base > 1, the actual denominator is
- -- Base**D. For cases where Base is a power of Radix, use
- -- the value 1 for the Denominator and adjust the exponent.
-
- -- Note: Exponent has different sign from D, because D is a divisor
-
- for Power in 1 .. Radix_Powers'Last loop
- if Base = Radix_Powers (Power) then
- Exponent := -D * Power;
- Base := 0;
- D := Uint_1;
- exit;
- end if;
- end loop;
-
- Release_And_Save (Uintp_Mark, D, Exponent);
- end Calculate_D_And_Exponent_1;
-
- if Base > 0 then
- Calculate_Exponent : begin
- Uintp_Mark := Mark;
-
- -- For bases that are a multiple of the Radix, divide
- -- the base by Radix and adjust the Exponent. This will
- -- help because D will be much smaller and faster to process.
-
- -- This occurs for decimal bases on a machine with binary
- -- floating-point for example. When calculating 1E40,
- -- with Radix = 2, N will be 93 bits instead of 133.
-
- -- N E
- -- ------ * Radix
- -- D
- -- Base
-
- -- N E
- -- = -------------------------- * Radix
- -- D D
- -- (Base/Radix) * Radix
-
- -- N E-D
- -- = --------------- * Radix
- -- D
- -- (Base/Radix)
-
- -- This code is commented out, because it causes numerous
- -- failures in the regression suite. To be studied ???
-
- while False and then Base > 0 and then Base mod Radix = 0 loop
- Base := Base / Radix;
- Exponent := Exponent + D;
- end loop;
-
- Release_And_Save (Uintp_Mark, Exponent);
- end Calculate_Exponent;
-
- -- For remaining bases we must actually compute
- -- the exponentiation.
-
- -- Because the exponentiation can be negative, and D must
- -- be integer, the numerator is corrected instead.
-
- Calculate_N_And_D : begin
- Uintp_Mark := Mark;
-
- if D < 0 then
- N := N * Base ** (-D);
- D := Uint_1;
- else
- D := Base ** D;
- end if;
-
- Release_And_Save (Uintp_Mark, N, D);
- end Calculate_N_And_D;
-
- Base := 0;
- end if;
-
- -- Now scale N and D so that N / D is a value in the
- -- interval [1.0 / Radix, 1.0) and adjust Exponent accordingly,
- -- so the value N / D * Radix ** Exponent remains unchanged.
-
- -- Step 1 - Adjust N so N / D >= 1 / Radix, or N = 0
-
- -- N and D are positive, so N / D >= 1 / Radix implies N * Radix >= D.
- -- This scaling is not possible for N is Uint_0 as there
- -- is no way to scale Uint_0 so the first digit is non-zero.
-
- Calculate_N_And_Exponent : begin
- Uintp_Mark := Mark;
-
- N_Times_Radix := N * Radix;
-
- if N /= Uint_0 then
- while not (N_Times_Radix >= D) loop
- N := N_Times_Radix;
- Exponent := Exponent - 1;
-
- N_Times_Radix := N * Radix;
- end loop;
- end if;
-
- Release_And_Save (Uintp_Mark, N, Exponent);
- end Calculate_N_And_Exponent;
-
- -- Step 2 - Adjust D so N / D < 1
-
- -- Scale up D so N / D < 1, so N < D
-
- Calculate_D_And_Exponent_2 : begin
- Uintp_Mark := Mark;
-
- while not (N < D) loop
-
- -- As N / D >= 1, N / (D * Radix) will be at least 1 / Radix,
- -- so the result of Step 1 stays valid
-
- D := D * Radix;
- Exponent := Exponent + 1;
- end loop;
-
- Release_And_Save (Uintp_Mark, D, Exponent);
- end Calculate_D_And_Exponent_2;
-
- -- Here the value N / D is in the range [1.0 / Radix .. 1.0)
-
- -- Now find the fraction by doing a very simple-minded
- -- division until enough digits have been computed.
-
- -- This division works for all radices, but is only efficient for
- -- a binary radix. It is just like a manual division algorithm,
- -- but instead of moving the denominator one digit right, we move
- -- the numerator one digit left so the numerator and denominator
- -- remain integral.
-
- Fraction := Uint_0;
- Even := True;
-
- Calculate_Fraction_And_N : begin
- Uintp_Mark := Mark;
-
- loop
- while N >= D loop
- N := N - D;
- Fraction := Fraction + 1;
- Even := not Even;
- end loop;
-
- -- Stop when the result is in [1.0 / Radix, 1.0)
-
- exit when Fraction >= Most_Significant_Digit;
-
- N := N * Radix;
- Fraction := Fraction * Radix;
- Even := True;
- end loop;
-
- Release_And_Save (Uintp_Mark, Fraction, N);
- end Calculate_Fraction_And_N;
-
- Calculate_Fraction_And_Exponent : begin
- Uintp_Mark := Mark;
-
- -- Put back sign before applying the rounding.
-
- if UR_Is_Negative (X) then
- Fraction := -Fraction;
- end if;
-
- -- Determine correct rounding based on the remainder
- -- which is in N and the divisor D.
-
- Rounding_Was_Biased := False; -- Until proven otherwise
-
- case Mode is
- when Round_Even =>
-
- -- This rounding mode should not be used for static
- -- expressions, but only for compile-time evaluation
- -- of non-static expressions.
-
- if (Even and then N * 2 > D)
- or else
- (not Even and then N * 2 >= D)
- then
- Fraction := Fraction + 1;
- end if;
-
- when Round =>
-
- -- Do not round to even as is done with IEEE arithmetic,
- -- but instead round away from zero when the result is
- -- exactly between two machine numbers. See RM 4.9(38).
-
- if N * 2 >= D then
- Fraction := Fraction + 1;
-
- Rounding_Was_Biased := Even and then N * 2 = D;
- -- Check for the case where the result is actually
- -- different from Round_Even.
- end if;
-
- when Ceiling =>
- if N > Uint_0 then
- Fraction := Fraction + 1;
- end if;
-
- when Floor => null;
- end case;
-
- -- The result must be normalized to [1.0/Radix, 1.0),
- -- so adjust if the result is 1.0 because of rounding.
-
- if Fraction = Most_Significant_Digit * Radix then
- Fraction := Most_Significant_Digit;
- Exponent := Exponent + 1;
- end if;
-
- Release_And_Save (Uintp_Mark, Fraction, Exponent);
- end Calculate_Fraction_And_Exponent;
-
- end Decompose_Int;
-
- ----------------
- -- Eps_Denorm --
- ----------------
-
- function Eps_Denorm (RT : R) return T is
- Digs : constant UI := Digits_Value (RT);
- Emin : Int;
- Mant : Int;
-
- begin
- if Vax_Float (RT) then
- if Digs = VAXFF_Digits then
- Emin := VAXFF_Machine_Emin;
- Mant := VAXFF_Machine_Mantissa;
-
- elsif Digs = VAXDF_Digits then
- Emin := VAXDF_Machine_Emin;
- Mant := VAXDF_Machine_Mantissa;
-
- else
- pragma Assert (Digs = VAXGF_Digits);
- Emin := VAXGF_Machine_Emin;
- Mant := VAXGF_Machine_Mantissa;
- end if;
-
- elsif Is_AAMP_Float (RT) then
- if Digs = AAMPS_Digits then
- Emin := AAMPS_Machine_Emin;
- Mant := AAMPS_Machine_Mantissa;
-
- else
- pragma Assert (Digs = AAMPL_Digits);
- Emin := AAMPL_Machine_Emin;
- Mant := AAMPL_Machine_Mantissa;
- end if;
-
- else
- if Digs = IEEES_Digits then
- Emin := IEEES_Machine_Emin;
- Mant := IEEES_Machine_Mantissa;
-
- elsif Digs = IEEEL_Digits then
- Emin := IEEEL_Machine_Emin;
- Mant := IEEEL_Machine_Mantissa;
-
- else
- pragma Assert (Digs = IEEEX_Digits);
- Emin := IEEEX_Machine_Emin;
- Mant := IEEEX_Machine_Mantissa;
- end if;
- end if;
-
- return Float_Radix ** UI_From_Int (Emin - Mant);
- end Eps_Denorm;
-
- ---------------
- -- Eps_Model --
- ---------------
-
- function Eps_Model (RT : R) return T is
- Digs : constant UI := Digits_Value (RT);
- Emin : Int;
-
- begin
- if Vax_Float (RT) then
- if Digs = VAXFF_Digits then
- Emin := VAXFF_Machine_Emin;
-
- elsif Digs = VAXDF_Digits then
- Emin := VAXDF_Machine_Emin;
-
- else
- pragma Assert (Digs = VAXGF_Digits);
- Emin := VAXGF_Machine_Emin;
- end if;
-
- elsif Is_AAMP_Float (RT) then
- if Digs = AAMPS_Digits then
- Emin := AAMPS_Machine_Emin;
-
- else
- pragma Assert (Digs = AAMPL_Digits);
- Emin := AAMPL_Machine_Emin;
- end if;
-
- else
- if Digs = IEEES_Digits then
- Emin := IEEES_Machine_Emin;
-
- elsif Digs = IEEEL_Digits then
- Emin := IEEEL_Machine_Emin;
-
- else
- pragma Assert (Digs = IEEEX_Digits);
- Emin := IEEEX_Machine_Emin;
- end if;
- end if;
-
- return Float_Radix ** UI_From_Int (Emin);
- end Eps_Model;
-
- --------------
- -- Exponent --
- --------------
-
- function Exponent (RT : R; X : T) return UI is
- X_Frac : UI;
- X_Exp : UI;
-
- begin
- if UR_Is_Zero (X) then
- return Uint_0;
- else
- Decompose_Int (RT, X, X_Frac, X_Exp, Round_Even);
- return X_Exp;
- end if;
- end Exponent;
-
- -----------
- -- Floor --
- -----------
-
- function Floor (RT : R; X : T) return T is
- XT : constant T := Truncation (RT, X);
-
- begin
- if UR_Is_Positive (X) then
- return XT;
-
- elsif XT = X then
- return X;
-
- else
- return XT - Ureal_1;
- end if;
- end Floor;
-
- --------------
- -- Fraction --
- --------------
-
- function Fraction (RT : R; X : T) return T is
- X_Frac : T;
- X_Exp : UI;
-
- begin
- if UR_Is_Zero (X) then
- return X;
- else
- Decompose (RT, X, X_Frac, X_Exp);
- return X_Frac;
- end if;
- end Fraction;
-
- ------------------
- -- Leading_Part --
- ------------------
-
- function Leading_Part (RT : R; X : T; Radix_Digits : UI) return T is
- L : UI;
- Y, Z : T;
-
- begin
- if Radix_Digits >= Machine_Mantissa (RT) then
- return X;
-
- else
- L := Exponent (RT, X) - Radix_Digits;
- Y := Truncation (RT, Scaling (RT, X, -L));
- Z := Scaling (RT, Y, L);
- return Z;
- end if;
-
- end Leading_Part;
-
- -------------
- -- Machine --
- -------------
-
- function Machine (RT : R; X : T; Mode : Rounding_Mode) return T is
- X_Frac : T;
- X_Exp : UI;
-
- begin
- if UR_Is_Zero (X) then
- return X;
- else
- Decompose (RT, X, X_Frac, X_Exp, Mode);
- return Scaling (RT, X_Frac, X_Exp);
- end if;
- end Machine;
-
- ----------------------
- -- Machine_Mantissa --
- ----------------------
-
- function Machine_Mantissa (RT : R) return Nat is
- Digs : constant UI := Digits_Value (RT);
- Mant : Nat;
-
- begin
- if Vax_Float (RT) then
- if Digs = VAXFF_Digits then
- Mant := VAXFF_Machine_Mantissa;
-
- elsif Digs = VAXDF_Digits then
- Mant := VAXDF_Machine_Mantissa;
-
- else
- pragma Assert (Digs = VAXGF_Digits);
- Mant := VAXGF_Machine_Mantissa;
- end if;
-
- elsif Is_AAMP_Float (RT) then
- if Digs = AAMPS_Digits then
- Mant := AAMPS_Machine_Mantissa;
-
- else
- pragma Assert (Digs = AAMPL_Digits);
- Mant := AAMPL_Machine_Mantissa;
- end if;
-
- else
- if Digs = IEEES_Digits then
- Mant := IEEES_Machine_Mantissa;
-
- elsif Digs = IEEEL_Digits then
- Mant := IEEEL_Machine_Mantissa;
-
- else
- pragma Assert (Digs = IEEEX_Digits);
- Mant := IEEEX_Machine_Mantissa;
- end if;
- end if;
-
- return Mant;
- end Machine_Mantissa;
-
- -----------
- -- Model --
- -----------
-
- function Model (RT : R; X : T) return T is
- X_Frac : T;
- X_Exp : UI;
-
- begin
- Decompose (RT, X, X_Frac, X_Exp);
- return Compose (RT, X_Frac, X_Exp);
- end Model;
-
- ----------
- -- Pred --
- ----------
-
- function Pred (RT : R; X : T) return T is
- Result_F : UI;
- Result_X : UI;
-
- begin
- if abs X < Eps_Model (RT) then
- if Denorm_On_Target then
- return X - Eps_Denorm (RT);
-
- elsif X > Ureal_0 then
- -- Target does not support denorms, so predecessor is 0.0
- return Ureal_0;
-
- else
- -- Target does not support denorms, and X is 0.0
- -- or at least bigger than -Eps_Model (RT)
-
- return -Eps_Model (RT);
- end if;
-
- else
- Decompose_Int (RT, X, Result_F, Result_X, Ceiling);
- return UR_From_Components
- (Num => Result_F - 1,
- Den => Machine_Mantissa (RT) - Result_X,
- Rbase => Radix,
- Negative => False);
- -- Result_F may be false, but this is OK as UR_From_Components
- -- handles that situation.
- end if;
- end Pred;
-
- ---------------
- -- Remainder --
- ---------------
-
- function Remainder (RT : R; X, Y : T) return T is
- A : T;
- B : T;
- Arg : T;
- P : T;
- Arg_Frac : T;
- P_Frac : T;
- Sign_X : T;
- IEEE_Rem : T;
- Arg_Exp : UI;
- P_Exp : UI;
- K : UI;
- P_Even : Boolean;
-
- begin
- if UR_Is_Positive (X) then
- Sign_X := Ureal_1;
- else
- Sign_X := -Ureal_1;
- end if;
-
- Arg := abs X;
- P := abs Y;
-
- if Arg < P then
- P_Even := True;
- IEEE_Rem := Arg;
- P_Exp := Exponent (RT, P);
-
- else
- -- ??? what about zero cases?
- Decompose (RT, Arg, Arg_Frac, Arg_Exp);
- Decompose (RT, P, P_Frac, P_Exp);
-
- P := Compose (RT, P_Frac, Arg_Exp);
- K := Arg_Exp - P_Exp;
- P_Even := True;
- IEEE_Rem := Arg;
-
- for Cnt in reverse 0 .. UI_To_Int (K) loop
- if IEEE_Rem >= P then
- P_Even := False;
- IEEE_Rem := IEEE_Rem - P;
- else
- P_Even := True;
- end if;
-
- P := P * Ureal_Half;
- end loop;
- end if;
-
- -- That completes the calculation of modulus remainder. The final step
- -- is get the IEEE remainder. Here we compare Rem with (abs Y) / 2.
-
- if P_Exp >= 0 then
- A := IEEE_Rem;
- B := abs Y * Ureal_Half;
-
- else
- A := IEEE_Rem * Ureal_2;
- B := abs Y;
- end if;
-
- if A > B or else (A = B and then not P_Even) then
- IEEE_Rem := IEEE_Rem - abs Y;
- end if;
-
- return Sign_X * IEEE_Rem;
-
- end Remainder;
-
- --------------
- -- Rounding --
- --------------
-
- function Rounding (RT : R; X : T) return T is
- Result : T;
- Tail : T;
-
- begin
- Result := Truncation (RT, abs X);
- Tail := abs X - Result;
-
- if Tail >= Ureal_Half then
- Result := Result + Ureal_1;
- end if;
-
- if UR_Is_Negative (X) then
- return -Result;
- else
- return Result;
- end if;
-
- end Rounding;
-
- -------------
- -- Scaling --
- -------------
-
- function Scaling (RT : R; X : T; Adjustment : UI) return T is
- begin
- if Rbase (X) = Radix then
- return UR_From_Components
- (Num => Numerator (X),
- Den => Denominator (X) - Adjustment,
- Rbase => Radix,
- Negative => UR_Is_Negative (X));
-
- elsif Adjustment >= 0 then
- return X * Radix ** Adjustment;
- else
- return X / Radix ** (-Adjustment);
- end if;
- end Scaling;
-
- ----------
- -- Succ --
- ----------
-
- function Succ (RT : R; X : T) return T is
- Result_F : UI;
- Result_X : UI;
-
- begin
- if abs X < Eps_Model (RT) then
- if Denorm_On_Target then
- return X + Eps_Denorm (RT);
-
- elsif X < Ureal_0 then
- -- Target does not support denorms, so successor is 0.0
- return Ureal_0;
-
- else
- -- Target does not support denorms, and X is 0.0
- -- or at least smaller than Eps_Model (RT)
-
- return Eps_Model (RT);
- end if;
-
- else
- Decompose_Int (RT, X, Result_F, Result_X, Floor);
- return UR_From_Components
- (Num => Result_F + 1,
- Den => Machine_Mantissa (RT) - Result_X,
- Rbase => Radix,
- Negative => False);
- -- Result_F may be false, but this is OK as UR_From_Components
- -- handles that situation.
- end if;
- end Succ;
-
- ----------------
- -- Truncation --
- ----------------
-
- function Truncation (RT : R; X : T) return T is
- begin
- return UR_From_Uint (UR_Trunc (X));
- end Truncation;
-
- -----------------------
- -- Unbiased_Rounding --
- -----------------------
-
- function Unbiased_Rounding (RT : R; X : T) return T is
- Abs_X : constant T := abs X;
- Result : T;
- Tail : T;
-
- begin
- Result := Truncation (RT, Abs_X);
- Tail := Abs_X - Result;
-
- if Tail > Ureal_Half then
- Result := Result + Ureal_1;
-
- elsif Tail = Ureal_Half then
- Result := Ureal_2 *
- Truncation (RT, (Result / Ureal_2) + Ureal_Half);
- end if;
-
- if UR_Is_Negative (X) then
- return -Result;
- elsif UR_Is_Positive (X) then
- return Result;
-
- -- For zero case, make sure sign of zero is preserved
-
- else
- return X;
- end if;
-
- end Unbiased_Rounding;
-
-end Eval_Fat;