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   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
  36 generic
  37    type Float_Type is digits <>;
  38
  39 package 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
 154 end Ada.Numerics.Generic_Elementary_Functions;