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------------------------------------------------------------------------------
-- --
-- GNAT COMPILER COMPONENTS --
-- --
-- E V A L _ F A T --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2003 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 Errout; use Errout;
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).
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_Emin (RT : R) return Int;
-- Return value of the Machine_Emin attribute
function Machine_Mantissa (RT : R) return Nat;
-- Return value of the Machine_Mantissa attribute
--------------
-- 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
pragma Warnings (Off, RT);
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.
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;
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
begin
return Float_Radix ** UI_From_Int
(Machine_Emin (RT) - Machine_Mantissa (RT));
end Eps_Denorm;
---------------
-- Eps_Model --
---------------
function Eps_Model (RT : R) return T is
begin
return Float_Radix ** UI_From_Int (Machine_Emin (RT));
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;
Enode : Node_Id)
return T
is
pragma Warnings (Off, Enode); -- not yet referenced
X_Frac : T;
X_Exp : UI;
Emin : constant UI := UI_From_Int (Machine_Emin (RT));
begin
if UR_Is_Zero (X) then
return X;
else
Decompose (RT, X, X_Frac, X_Exp, Mode);
-- Case of denormalized number or (gradual) underflow
-- A denormalized number is one with the minimum exponent Emin, but
-- that breaks the assumption that the first digit of the mantissa
-- is a one. This allows the first non-zero digit to be in any
-- of the remaining Mant - 1 spots. The gap between subsequent
-- denormalized numbers is the same as for the smallest normalized
-- numbers. However, the number of significant digits left decreases
-- as a result of the mantissa now having leading seros.
if X_Exp < Emin then
declare
Emin_Den : constant UI :=
UI_From_Int
(Machine_Emin (RT) - Machine_Mantissa (RT) + 1);
begin
if X_Exp < Emin_Den or not Denorm_On_Target then
if UR_Is_Negative (X) then
Error_Msg_N
("floating-point value underflows to -0.0?", Enode);
return Ureal_M_0;
else
Error_Msg_N
("floating-point value underflows to 0.0?", Enode);
return Ureal_0;
end if;
elsif Denorm_On_Target then
-- Emin - Mant <= X_Exp < Emin, so result is denormal.
-- Handle gradual underflow by first computing the
-- number of significant bits still available for the
-- mantissa and then truncating the fraction to this
-- number of bits.
-- If this value is different from the original
-- fraction, precision is lost due to gradual underflow.
-- We probably should round here and prevent double
-- rounding as a result of first rounding to a model
-- number and then to a machine number. However, this
-- is an extremely rare case that is not worth the extra
-- complexity. In any case, a warning is issued in cases
-- where gradual underflow occurs.
declare
Denorm_Sig_Bits : constant UI := X_Exp - Emin_Den + 1;
X_Frac_Denorm : constant T := UR_From_Components
(UR_Trunc (Scaling (RT, abs X_Frac, Denorm_Sig_Bits)),
Denorm_Sig_Bits,
Radix,
UR_Is_Negative (X));
begin
if X_Frac_Denorm /= X_Frac then
Error_Msg_N
("gradual underflow causes loss of precision?",
Enode);
X_Frac := X_Frac_Denorm;
end if;
end;
end if;
end;
end if;
return Scaling (RT, X_Frac, X_Exp);
end if;
end Machine;
------------------
-- Machine_Emin --
------------------
function Machine_Emin (RT : R) return Int 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 Emin;
end Machine_Emin;
----------------------
-- 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
pragma Warnings (Off, RT);
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
pragma Warnings (Off, RT);
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;