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+------------------------------------------------------------------------------
+-- --
+-- GNAT RUN-TIME COMPONENTS --
+-- --
+-- ADA.NUMERICS.GENERIC_ELEMENTARY_FUNCTIONS --
+-- --
+-- S p e c --
+-- --
+-- Copyright (C) 2012, Free Software Foundation, Inc. --
+-- --
+-- This specification is derived from the Ada Reference Manual for use with --
+-- GNAT. The copyright notice above, and the license provisions that follow --
+-- apply solely to the Post aspects that have been added to the spec. --
+-- --
+-- 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. --
+-- --
+------------------------------------------------------------------------------
+
+generic
+ type Float_Type is digits <>;
+
+package Ada.Numerics.Generic_Elementary_Functions is
+ pragma Pure;
+
+ function Sqrt (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Sqrt'Result >= 0.0
+ and then (if X = 0.0 then Sqrt'Result = 0.0)
+ and then (if X = 1.0 then Sqrt'Result = 1.0);
+
+ function Log (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 1.0 then Log'Result = 0.0);
+
+ function Log (X, Base : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 1.0 then Log'Result = 0.0);
+
+ function Exp (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Exp'Result = 1.0);
+
+ function "**" (Left, Right : Float_Type'Base) return Float_Type'Base
+ with
+ Post => "**"'Result >= 0.0
+ and then (if Right = 0.0 then "**"'Result = 1.0)
+ and then (if Right = 1.0 then "**"'Result = Left)
+ and then (if Left = 1.0 then "**"'Result = 1.0)
+ and then (if Left = 0.0 then "**"'Result = 0.0);
+
+ function Sin (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Sin'Result in -1.0 .. 1.0
+ and then (if X = 0.0 then Sin'Result = 0.0);
+
+ function Sin (X, Cycle : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Sin'Result in -1.0 .. 1.0
+ and then (if X = 0.0 then Sin'Result = 0.0);
+
+ function Cos (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Cos'Result in -1.0 .. 1.0
+ and then (if X = 0.0 then Cos'Result = 1.0);
+
+ function Cos (X, Cycle : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Cos'Result in -1.0 .. 1.0
+ and then (if X = 0.0 then Cos'Result = 1.0);
+
+ function Tan (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Tan'Result = 0.0);
+
+ function Tan (X, Cycle : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Tan'Result = 0.0);
+
+ function Cot (X : Float_Type'Base) return Float_Type'Base;
+
+ function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base;
+
+ function Arcsin (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Arcsin'Result = 0.0);
+
+ function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Arcsin'Result = 0.0);
+
+ function Arccos (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 1.0 then Arccos'Result = 0.0);
+
+ function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 1.0 then Arccos'Result = 0.0);
+
+ function Arctan
+ (Y : Float_Type'Base;
+ X : Float_Type'Base := 1.0)
+ return Float_Type'Base
+ with
+ Post => (if X > 0.0 and Y = 0.0 then Arctan'Result = 0.0);
+
+ function Arctan
+ (Y : Float_Type'Base;
+ X : Float_Type'Base := 1.0;
+ Cycle : Float_Type'Base)
+ return Float_Type'Base
+ with
+ Post => (if X > 0.0 and Y = 0.0 then Arctan'Result = 0.0);
+
+ function Arccot
+ (X : Float_Type'Base;
+ Y : Float_Type'Base := 1.0)
+ return Float_Type'Base
+ with
+ Post => (if X > 0.0 and Y = 0.0 then Arccot'Result = 0.0);
+
+ function Arccot
+ (X : Float_Type'Base;
+ Y : Float_Type'Base := 1.0;
+ Cycle : Float_Type'Base)
+ return Float_Type'Base
+ with
+ Post => (if X > 0.0 and Y = 0.0 then Arccot'Result = 0.0);
+
+ function Sinh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Sinh'Result = 0.0);
+
+ function Cosh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Cosh'Result >= 1.0
+ and then (if X = 0.0 then Cosh'Result = 1.0);
+
+ function Tanh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Tanh'Result in -1.0 .. 1.0
+ and then (if X = 0.0 then Tanh'Result = 0.0);
+
+ function Coth (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => abs Coth'Result >= 1.0;
+
+ function Arcsinh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Arcsinh'Result = 0.0);
+
+ function Arccosh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => Arccosh'Result >= 0.0
+ and then (if X = 1.0 then Arccosh'Result = 0.0);
+
+ function Arctanh (X : Float_Type'Base) return Float_Type'Base
+ with
+ Post => (if X = 0.0 then Arctanh'Result = 0.0);
+
+ function Arccoth (X : Float_Type'Base) return Float_Type'Base;
+
+end Ada.Numerics.Generic_Elementary_Functions;