1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                     A D A . N U M E R I C S . A U X                      --
6--                                                                          --
7--                                 S p e c                                  --
8--                          (Apple OS X Version)                            --
9--                                                                          --
10--          Copyright (C) 1992-2013, Free Software Foundation, Inc.         --
11--                                                                          --
12-- GNAT is free software;  you can  redistribute it  and/or modify it under --
13-- terms of the  GNU General Public License as published  by the Free Soft- --
14-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
15-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
16-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
17-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
18--                                                                          --
19-- As a special exception under Section 7 of GPL version 3, you are granted --
20-- additional permissions described in the GCC Runtime Library Exception,   --
21-- version 3.1, as published by the Free Software Foundation.               --
22--                                                                          --
23-- You should have received a copy of the GNU General Public License and    --
24-- a copy of the GCC Runtime Library Exception along with this program;     --
25-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
26-- <http://www.gnu.org/licenses/>.                                          --
27--                                                                          --
28-- GNAT was originally developed  by the GNAT team at  New York University. --
29-- Extensive contributions were provided by Ada Core Technologies Inc.      --
30--                                                                          --
31------------------------------------------------------------------------------
32
33--  This version is for use with normal Unix math functions, except for
34--  sine/cosine which have been implemented directly in Ada to get
35--  the required accuracy in OS X.  Alternative packages are used
36--  on OpenVMS (different import names), VxWorks (no need for the
37--  -lm Linker_Options), and on the x86 (where we have two
38--  versions one using inline ASM, and one importing from the C long
39--  routines that take 80-bit arguments).
40
41package Ada.Numerics.Aux is
42   pragma Pure;
43
44   pragma Linker_Options ("-lm");
45
46   type Double is digits 15;
47   --  Type Double is the type used to call the C routines
48
49   --  The following functions have been implemented in Ada, since
50   --  the OS X math library didn't meet accuracy requirements for
51   --  argument reduction. The implementation here has been tailored
52   --  to match Ada strict mode Numerics requirements while maintaining
53   --  maximum efficiency.
54   function Sin (X : Double) return Double;
55   pragma Inline (Sin);
56
57   function Cos (X : Double) return Double;
58   pragma Inline (Cos);
59
60   --  We import these functions directly from C. Note that we label them
61   --  all as pure functions, because indeed all of them are in fact pure.
62
63   function Tan (X : Double) return Double;
64   pragma Import (C, Tan, "tan");
65   pragma Pure_Function (Tan);
66
67   function Exp (X : Double) return Double;
68   pragma Import (C, Exp, "exp");
69   pragma Pure_Function (Exp);
70
71   function Sqrt (X : Double) return Double;
72   pragma Import (C, Sqrt, "sqrt");
73   pragma Pure_Function (Sqrt);
74
75   function Log (X : Double) return Double;
76   pragma Import (C, Log, "log");
77   pragma Pure_Function (Log);
78
79   function Acos (X : Double) return Double;
80   pragma Import (C, Acos, "acos");
81   pragma Pure_Function (Acos);
82
83   function Asin (X : Double) return Double;
84   pragma Import (C, Asin, "asin");
85   pragma Pure_Function (Asin);
86
87   function Atan (X : Double) return Double;
88   pragma Import (C, Atan, "atan");
89   pragma Pure_Function (Atan);
90
91   function Sinh (X : Double) return Double;
92   pragma Import (C, Sinh, "sinh");
93   pragma Pure_Function (Sinh);
94
95   function Cosh (X : Double) return Double;
96   pragma Import (C, Cosh, "cosh");
97   pragma Pure_Function (Cosh);
98
99   function Tanh (X : Double) return Double;
100   pragma Import (C, Tanh, "tanh");
101   pragma Pure_Function (Tanh);
102
103   function Pow (X, Y : Double) return Double;
104   pragma Import (C, Pow, "pow");
105   pragma Pure_Function (Pow);
106
107end Ada.Numerics.Aux;
108