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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) 2012-2014, 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        --  Finally if X is positive, the result of Sqrt is positive (because
  48        --  the sqrt of numbers greater than 1 is greater than or equal to 1,
  49        --  and the sqrt of numbers less than 1 is greater than the argument).
  50
  51        --  This property is useful in particular for static analysis. The
  52        --  property that X is positive is not expressed as (X > 0.0), as
  53        --  the value X may be held in registers that have larger range and
  54        --  precision on some architecture (for example, on x86 using x387
  55        --  FPU, as opposed to SSE2). So, it might be possible for X to be
  56        --  2.0**(-5000) or so, which could cause the number to compare as
  57        --  greater than 0, but Sqrt would still return a zero result.
  58
  59        --  Note: we use the comparison with Succ (0.0) here because this is
  60        --  more amenable to CodePeer analysis than the use of 'Machine.
  61
  62        and then (if X >= Float_Type'Succ (0.0) then Sqrt'Result > 0.0);
  63
  64    function Log (X : Float_Type'Base) return Float_Type'Base
  65    with
  66      Post => (if X = 1.0 then Log'Result = 0.0);
  67
  68    function Log (X, Base : Float_Type'Base) return Float_Type'Base with
  69      Post => (if X = 1.0 then Log'Result = 0.0);
  70
  71    function Exp (X : Float_Type'Base) return Float_Type'Base with
  72      Post => (if X = 0.0 then Exp'Result = 1.0);
  73
  74    function "**" (Left, Right : Float_Type'Base) return Float_Type'Base with
  75      Post => "**"'Result >= 0.0
  76        and then (if Right = 0.0 then "**"'Result = 1.0)
  77        and then (if Right = 1.0 then "**"'Result = Left)
  78        and then (if Left  = 1.0 then "**"'Result = 1.0)
  79        and then (if Left  = 0.0 then "**"'Result = 0.0);
  80
  81    function Sin (X : Float_Type'Base) return Float_Type'Base with
  82      Post => Sin'Result in -1.0 .. 1.0
  83        and then (if X = 0.0 then Sin'Result = 0.0);
  84
  85    function Sin (X, Cycle : Float_Type'Base) return Float_Type'Base with
  86      Post => Sin'Result in -1.0 .. 1.0
  87        and then (if X = 0.0 then Sin'Result = 0.0);
  88
  89    function Cos (X : Float_Type'Base) return Float_Type'Base with
  90      Post => Cos'Result in -1.0 .. 1.0
  91        and then (if X = 0.0 then Cos'Result = 1.0);
  92
  93    function Cos (X, Cycle : Float_Type'Base) return Float_Type'Base with
  94      Post => Cos'Result in -1.0 .. 1.0
  95        and then (if X = 0.0 then Cos'Result = 1.0);
  96
  97    function Tan (X : Float_Type'Base) return Float_Type'Base with
  98      Post => (if X = 0.0 then Tan'Result = 0.0);
  99
 100    function Tan (X, Cycle : Float_Type'Base) return Float_Type'Base with
 101      Post => (if X = 0.0 then Tan'Result = 0.0);
 102
 103    function Cot (X : Float_Type'Base) return Float_Type'Base;
 104
 105    function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base;
 106
 107    function Arcsin (X : Float_Type'Base) return Float_Type'Base with
 108      Post => (if X = 0.0 then Arcsin'Result = 0.0);
 109
 110    function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base with
 111      Post => (if X = 0.0 then Arcsin'Result = 0.0);
 112
 113    function Arccos (X : Float_Type'Base) return Float_Type'Base with
 114      Post => (if X = 1.0 then Arccos'Result = 0.0);
 115
 116    function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base with
 117      Post => (if X = 1.0 then Arccos'Result = 0.0);
 118
 119    function Arctan
 120      (Y : Float_Type'Base;
 121       X : Float_Type'Base := 1.0) return Float_Type'Base
 122    with
 123      Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
 124
 125    function Arctan
 126      (Y     : Float_Type'Base;
 127       X     : Float_Type'Base := 1.0;
 128       Cycle : Float_Type'Base) return Float_Type'Base
 129    with
 130      Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
 131
 132    function Arccot
 133      (X   : Float_Type'Base;
 134       Y   : Float_Type'Base := 1.0) return Float_Type'Base
 135    with
 136      Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
 137
 138    function Arccot
 139      (X     : Float_Type'Base;
 140       Y     : Float_Type'Base := 1.0;
 141       Cycle : Float_Type'Base) return Float_Type'Base
 142    with
 143      Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
 144
 145    function Sinh (X : Float_Type'Base) return Float_Type'Base with
 146      Post => (if X = 0.0 then Sinh'Result = 0.0);
 147
 148    function Cosh (X : Float_Type'Base) return Float_Type'Base with
 149      Post => Cosh'Result >= 1.0
 150        and then (if X = 0.0 then Cosh'Result = 1.0);
 151
 152    function Tanh (X : Float_Type'Base) return Float_Type'Base with
 153      Post => Tanh'Result in -1.0 .. 1.0
 154        and then (if X = 0.0 then Tanh'Result = 0.0);
 155
 156    function Coth (X : Float_Type'Base) return Float_Type'Base with
 157      Post => abs Coth'Result >= 1.0;
 158
 159    function Arcsinh (X : Float_Type'Base) return Float_Type'Base with
 160      Post => (if X = 0.0 then Arcsinh'Result = 0.0);
 161
 162    function Arccosh (X : Float_Type'Base) return Float_Type'Base with
 163      Post => Arccosh'Result >= 0.0
 164        and then (if X = 1.0 then Arccosh'Result = 0.0);
 165
 166    function Arctanh (X : Float_Type'Base) return Float_Type'Base with
 167      Post => (if X = 0.0 then Arctanh'Result = 0.0);
 168
 169    function Arccoth (X : Float_Type'Base) return Float_Type'Base;
 170
 171 end Ada.Numerics.Generic_Elementary_Functions;