------------------------------------------------------------------------------
-- --
-- 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. --
-- --
-- --
-- --
-- --
-- --
-- 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;