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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;