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------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                     A D A . N U M E R I C S . A U X                      --
--                                                                          --
--                                 S p e c                                  --
--                          (Apple OS X Version)                            --
--                                                                          --
--          Copyright (C) 1992-2009, 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 version is for use with normal Unix math functions, except for
--  sine/cosine which have been implemented directly in Ada to get
--  the required accuracy in OS X.  Alternative packages are used
--  on OpenVMS (different import names), VxWorks (no need for the
--  -lm Linker_Options), and on the x86 (where we have two
--  versions one using inline ASM, and one importing from the C long
--  routines that take 80-bit arguments).
 
package Ada.Numerics.Aux is
   pragma Pure;
 
   pragma Linker_Options ("-lm");
 
   type Double is digits 15;
   --  Type Double is the type used to call the C routines
 
   --  The following functions have been implemented in Ada, since
   --  the OS X math library didn't meet accuracy requirements for
   --  argument reduction. The implementation here has been tailored
   --  to match Ada strict mode Numerics requirements while maintaining
   --  maximum efficiency.
   function Sin (X : Double) return Double;
   pragma Inline (Sin);
 
   function Cos (X : Double) return Double;
   pragma Inline (Cos);
 
   --  We import these functions directly from C. Note that we label them
   --  all as pure functions, because indeed all of them are in fact pure!
 
   function Tan (X : Double) return Double;
   pragma Import (C, Tan, "tan");
   pragma Pure_Function (Tan);
 
   function Exp (X : Double) return Double;
   pragma Import (C, Exp, "exp");
   pragma Pure_Function (Exp);
 
   function Sqrt (X : Double) return Double;
   pragma Import (C, Sqrt, "sqrt");
   pragma Pure_Function (Sqrt);
 
   function Log (X : Double) return Double;
   pragma Import (C, Log, "log");
   pragma Pure_Function (Log);
 
   function Acos (X : Double) return Double;
   pragma Import (C, Acos, "acos");
   pragma Pure_Function (Acos);
 
   function Asin (X : Double) return Double;
   pragma Import (C, Asin, "asin");
   pragma Pure_Function (Asin);
 
   function Atan (X : Double) return Double;
   pragma Import (C, Atan, "atan");
   pragma Pure_Function (Atan);
 
   function Sinh (X : Double) return Double;
   pragma Import (C, Sinh, "sinh");
   pragma Pure_Function (Sinh);
 
   function Cosh (X : Double) return Double;
   pragma Import (C, Cosh, "cosh");
   pragma Pure_Function (Cosh);
 
   function Tanh (X : Double) return Double;
   pragma Import (C, Tanh, "tanh");
   pragma Pure_Function (Tanh);
 
   function Pow (X, Y : Double) return Double;
   pragma Import (C, Pow, "pow");
   pragma Pure_Function (Pow);
 
end Ada.Numerics.Aux;