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------------------------------------------------------------------------------
-- --
-- GNAT COMPILER COMPONENTS --
-- --
-- S Y S T E M . D O U B L E _ R E A L . P R O D U C T --
-- --
-- B o d y --
-- --
-- Copyright (C) 2021, 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. --
-- --
------------------------------------------------------------------------------
-- This is the default version of the separate package body
with Interfaces; use Interfaces;
separate (System.Double_Real)
package body Product is
procedure Split (N : Num; Hi : out Num; Lo : out Num);
-- Compute high part and low part of N
-----------
-- Split --
-----------
-- We use a bit manipulation algorithm instead of Veltkamp's splitting
-- because it is faster and has the property that the magnitude of the
-- high part is never larger than that of the input number, which will
-- avoid spurious overflows in the Two_Prod algorithm.
-- See the recent paper by Claude-Pierre Jeannerod, Jean-Michel Muller
-- and Paul Zimmermann: On various ways to split a floating-point number
-- ARITH 2018 - 25th IEEE Symposium on Computer Arithmetic, Jun 2018,
-- Amherst (MA), United States, pages 53-60.
procedure Split (N : Num; Hi : out Num; Lo : out Num) is
X : Num;
begin
-- Spill the input into the appropriate (maybe larger) bit container,
-- mask out the low bits and reload the modified value.
case Num'Machine_Mantissa is
when 24 =>
declare
Rep32 : aliased Interfaces.Unsigned_32;
Temp : Num := N with Address => Rep32'Address;
pragma Annotate (CodePeer, Modified, Rep32);
begin
-- Mask out the low 12 bits
Rep32 := Rep32 and 16#FFFFF000#;
X := Temp;
end;
when 53 =>
declare
Rep64 : aliased Interfaces.Unsigned_64;
Temp : Num := N with Address => Rep64'Address;
pragma Annotate (CodePeer, Modified, Rep64);
begin
-- Mask out the low 27 bits
Rep64 := Rep64 and 16#FFFFFFFFF8000000#;
X := Temp;
end;
when 64 =>
declare
Rep80 : aliased array (1 .. 2) of Interfaces.Unsigned_64;
Temp : Num := N with Address => Rep80'Address;
pragma Annotate (CodePeer, Modified, Rep80);
begin
-- Mask out the low 32 bits
if System.Default_Bit_Order = High_Order_First then
Rep80 (1) := Rep80 (1) and 16#FFFFFFFFFFFF0000#;
Rep80 (2) := Rep80 (2) and 16#0000FFFFFFFFFFFF#;
else
Rep80 (1) := Rep80 (1) and 16#FFFFFFFF00000000#;
end if;
X := Temp;
end;
when others =>
raise Program_Error;
end case;
-- Deal with denormalized numbers
if X = 0.0 then
Hi := N;
Lo := 0.0;
else
Hi := X;
Lo := N - X;
end if;
end Split;
--------------
-- Two_Prod --
--------------
function Two_Prod (A, B : Num) return Double_T is
P : constant Num := A * B;
Ahi, Alo, Bhi, Blo, E : Num;
begin
if Is_Infinity (P) or else Is_Zero (P) then
return (P, 0.0);
else
Split (A, Ahi, Alo);
Split (B, Bhi, Blo);
E := ((Ahi * Bhi - P) + Ahi * Blo + Alo * Bhi) + Alo * Blo;
return (P, E);
end if;
end Two_Prod;
-------------
-- Two_Sqr --
-------------
function Two_Sqr (A : Num) return Double_T is
Q : constant Num := A * A;
Hi, Lo, E : Num;
begin
if Is_Infinity (Q) or else Is_Zero (Q) then
return (Q, 0.0);
else
Split (A, Hi, Lo);
E := ((Hi * Hi - Q) + 2.0 * Hi * Lo) + Lo * Lo;
return (Q, E);
end if;
end Two_Sqr;
end Product;
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