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------------------------------------------------------------------------------
-- --
-- GNAT RUN-TIME COMPONENTS --
-- --
-- S Y S T E M . E X N _ L L F --
-- --
-- B o d y --
-- --
-- Copyright (C) 1992-2016, 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 3, 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. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
-- --
-- GNAT was originally developed by the GNAT team at New York University. --
-- Extensive contributions were provided by Ada Core Technologies Inc. --
-- --
------------------------------------------------------------------------------
-- Note: the reason for treating exponents in the range 0 .. 4 specially is
-- to ensure identical results to the static inline expansion in the case of
-- a compile time known exponent in this range. The use of Float'Machine and
-- Long_Float'Machine is to avoid unwanted extra precision in the results.
-- Note that for a negative exponent in Left ** Right, we compute the result
-- as:
-- 1.0 / (Left ** (-Right))
-- Note that the case of Left being zero is not special, it will simply result
-- in a division by zero at the end, yielding a correctly signed infinity, or
-- possibly generating an overflow.
-- Note on overflow: This coding assumes that the target generates infinities
-- with standard IEEE semantics. If this is not the case, then the code
-- for negative exponent may raise Constraint_Error. This follows the
-- implementation permission given in RM 4.5.6(12).
package body System.Exn_LLF is
subtype Negative is Integer range Integer'First .. -1;
function Exp
(Left : Long_Long_Float;
Right : Natural) return Long_Long_Float;
-- Common routine used if Right is greater or equal to 5
---------------
-- Exn_Float --
---------------
function Exn_Float
(Left : Float;
Right : Integer) return Float
is
Temp : Float;
begin
case Right is
when 0 =>
return 1.0;
when 1 =>
return Left;
when 2 =>
return Float'Machine (Left * Left);
when 3 =>
return Float'Machine (Left * Left * Left);
when 4 =>
Temp := Float'Machine (Left * Left);
return Float'Machine (Temp * Temp);
when Negative =>
return Float'Machine (1.0 / Exn_Float (Left, -Right));
when others =>
return
Float'Machine
(Float (Exp (Long_Long_Float (Left), Right)));
end case;
end Exn_Float;
--------------------
-- Exn_Long_Float --
--------------------
function Exn_Long_Float
(Left : Long_Float;
Right : Integer) return Long_Float
is
Temp : Long_Float;
begin
case Right is
when 0 =>
return 1.0;
when 1 =>
return Left;
when 2 =>
return Long_Float'Machine (Left * Left);
when 3 =>
return Long_Float'Machine (Left * Left * Left);
when 4 =>
Temp := Long_Float'Machine (Left * Left);
return Long_Float'Machine (Temp * Temp);
when Negative =>
return Long_Float'Machine (1.0 / Exn_Long_Float (Left, -Right));
when others =>
return
Long_Float'Machine
(Long_Float (Exp (Long_Long_Float (Left), Right)));
end case;
end Exn_Long_Float;
-------------------------
-- Exn_Long_Long_Float --
-------------------------
function Exn_Long_Long_Float
(Left : Long_Long_Float;
Right : Integer) return Long_Long_Float
is
Temp : Long_Long_Float;
begin
case Right is
when 0 =>
return 1.0;
when 1 =>
return Left;
when 2 =>
return Left * Left;
when 3 =>
return Left * Left * Left;
when 4 =>
Temp := Left * Left;
return Temp * Temp;
when Negative =>
return 1.0 / Exn_Long_Long_Float (Left, -Right);
when others =>
return Exp (Left, Right);
end case;
end Exn_Long_Long_Float;
---------
-- Exp --
---------
function Exp
(Left : Long_Long_Float;
Right : Natural) return Long_Long_Float
is
Result : Long_Long_Float := 1.0;
Factor : Long_Long_Float := Left;
Exp : Natural := Right;
begin
-- We use the standard logarithmic approach, Exp gets shifted right
-- testing successive low order bits and Factor is the value of the
-- base raised to the next power of 2. If the low order bit or Exp is
-- set, multiply the result by this factor.
loop
if Exp rem 2 /= 0 then
Result := Result * Factor;
end if;
Exp := Exp / 2;
exit when Exp = 0;
Factor := Factor * Factor;
end loop;
return Result;
end Exp;
end System.Exn_LLF;
|
