1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUN-TIME COMPONENTS                         --
4--                                                                          --
5--                ADA.NUMERICS.GENERIC_ELEMENTARY_FUNCTIONS                 --
6--                                                                          --
7--                                 S p e c                                  --
8--                                                                          --
9--          Copyright (C) 2012-2013, Free Software Foundation, Inc.         --
10--                                                                          --
11-- This specification is derived from the Ada Reference Manual for use with --
12-- GNAT. The copyright notice above, and the license provisions that follow --
13-- apply solely to the Post aspects that have been added to the spec.       --
14--                                                                          --
15-- GNAT is free software;  you can  redistribute it  and/or modify it under --
16-- terms of the  GNU General Public License as published  by the Free Soft- --
17-- ware  Foundation;  either version 3,  or (at your option) any later ver- --
18-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
19-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
20-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
21--                                                                          --
22-- As a special exception under Section 7 of GPL version 3, you are granted --
23-- additional permissions described in the GCC Runtime Library Exception,   --
24-- version 3.1, as published by the Free Software Foundation.               --
25--                                                                          --
26-- You should have received a copy of the GNU General Public License and    --
27-- a copy of the GCC Runtime Library Exception along with this program;     --
28-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
29-- <http://www.gnu.org/licenses/>.                                          --
30--                                                                          --
31-- GNAT was originally developed  by the GNAT team at  New York University. --
32-- Extensive contributions were provided by Ada Core Technologies Inc.      --
33--                                                                          --
34------------------------------------------------------------------------------
35
36generic
37   type Float_Type is digits <>;
38
39package Ada.Numerics.Generic_Elementary_Functions is
40   pragma Pure;
41
42   function Sqrt (X : Float_Type'Base) return Float_Type'Base with
43     Post => Sqrt'Result >= 0.0
44               and then (if X = 0.0 then Sqrt'Result = 0.0)
45               and then (if X = 1.0 then Sqrt'Result = 1.0);
46
47   function Log (X : Float_Type'Base) return Float_Type'Base
48   with
49     Post => (if X = 1.0 then Log'Result = 0.0);
50
51   function Log (X, Base : Float_Type'Base) return Float_Type'Base with
52     Post => (if X = 1.0 then Log'Result = 0.0);
53
54   function Exp (X : Float_Type'Base) return Float_Type'Base with
55     Post => (if X = 0.0 then Exp'Result = 1.0);
56
57   function "**" (Left, Right : Float_Type'Base) return Float_Type'Base with
58     Post => "**"'Result >= 0.0
59               and then (if Right = 0.0 then "**"'Result = 1.0)
60               and then (if Right = 1.0 then "**"'Result = Left)
61               and then (if Left = 1.0 then "**"'Result = 1.0)
62               and then (if Left = 0.0 then "**"'Result = 0.0);
63
64   function Sin (X : Float_Type'Base) return Float_Type'Base with
65     Post => Sin'Result in -1.0 .. 1.0
66               and then (if X = 0.0 then Sin'Result = 0.0);
67
68   function Sin (X, Cycle : Float_Type'Base) return Float_Type'Base with
69     Post => Sin'Result in -1.0 .. 1.0
70               and then (if X = 0.0 then Sin'Result = 0.0);
71
72   function Cos (X : Float_Type'Base) return Float_Type'Base with
73     Post => Cos'Result in -1.0 .. 1.0
74               and then (if X = 0.0 then Cos'Result = 1.0);
75
76   function Cos (X, Cycle : Float_Type'Base) return Float_Type'Base with
77     Post => Cos'Result in -1.0 .. 1.0
78               and then (if X = 0.0 then Cos'Result = 1.0);
79
80   function Tan (X : Float_Type'Base) return Float_Type'Base with
81     Post => (if X = 0.0 then Tan'Result = 0.0);
82
83   function Tan (X, Cycle : Float_Type'Base) return Float_Type'Base with
84     Post => (if X = 0.0 then Tan'Result = 0.0);
85
86   function Cot (X : Float_Type'Base) return Float_Type'Base;
87
88   function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base;
89
90   function Arcsin (X : Float_Type'Base) return Float_Type'Base with
91     Post => (if X = 0.0 then Arcsin'Result = 0.0);
92
93   function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base with
94     Post => (if X = 0.0 then Arcsin'Result = 0.0);
95
96   function Arccos (X : Float_Type'Base) return Float_Type'Base with
97     Post => (if X = 1.0 then Arccos'Result = 0.0);
98
99   function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base with
100     Post => (if X = 1.0 then Arccos'Result = 0.0);
101
102   function Arctan
103     (Y : Float_Type'Base;
104      X : Float_Type'Base := 1.0) return Float_Type'Base
105   with
106     Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
107
108   function Arctan
109     (Y     : Float_Type'Base;
110      X     : Float_Type'Base := 1.0;
111      Cycle : Float_Type'Base) return Float_Type'Base
112   with
113     Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
114
115   function Arccot
116     (X   : Float_Type'Base;
117      Y   : Float_Type'Base := 1.0) return Float_Type'Base
118   with
119     Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
120
121   function Arccot
122     (X     : Float_Type'Base;
123      Y     : Float_Type'Base := 1.0;
124      Cycle : Float_Type'Base) return Float_Type'Base
125   with
126     Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
127
128   function Sinh (X : Float_Type'Base) return Float_Type'Base with
129     Post => (if X = 0.0 then Sinh'Result = 0.0);
130
131   function Cosh (X : Float_Type'Base) return Float_Type'Base with
132     Post => Cosh'Result >= 1.0
133               and then (if X = 0.0 then Cosh'Result = 1.0);
134
135   function Tanh (X : Float_Type'Base) return Float_Type'Base with
136     Post => Tanh'Result in -1.0 .. 1.0
137               and then (if X = 0.0 then Tanh'Result = 0.0);
138
139   function Coth (X : Float_Type'Base) return Float_Type'Base with
140     Post => abs Coth'Result >= 1.0;
141
142   function Arcsinh (X : Float_Type'Base) return Float_Type'Base with
143     Post => (if X = 0.0 then Arcsinh'Result = 0.0);
144
145   function Arccosh (X : Float_Type'Base) return Float_Type'Base with
146     Post => Arccosh'Result >= 0.0
147               and then (if X = 1.0 then Arccosh'Result = 0.0);
148
149   function Arctanh (X : Float_Type'Base) return Float_Type'Base with
150     Post => (if X = 0.0 then Arctanh'Result = 0.0);
151
152   function Arccoth (X : Float_Type'Base) return Float_Type'Base;
153
154end Ada.Numerics.Generic_Elementary_Functions;
155