171 lines
7.9 KiB
Ada
171 lines
7.9 KiB
Ada
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------------------------------------------------------------------------------
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-- --
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-- GNAT RUN-TIME COMPONENTS --
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-- --
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-- ADA.NUMERICS.GENERIC_ELEMENTARY_FUNCTIONS --
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-- --
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-- S p e c --
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-- --
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-- Copyright (C) 2012-2015, Free Software Foundation, Inc. --
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-- --
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-- This specification is derived from the Ada Reference Manual for use with --
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-- GNAT. The copyright notice above, and the license provisions that follow --
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-- apply solely to the Post aspects that have been added to the spec. --
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-- --
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-- GNAT is free software; you can redistribute it and/or modify it under --
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-- terms of the GNU General Public License as published by the Free Soft- --
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-- ware Foundation; either version 3, or (at your option) any later ver- --
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-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE. --
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-- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- additional permissions described in the GCC Runtime Library Exception, --
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-- version 3.1, as published by the Free Software Foundation. --
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-- --
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-- You should have received a copy of the GNU General Public License and --
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-- a copy of the GCC Runtime Library Exception along with this program; --
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-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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-- <http://www.gnu.org/licenses/>. --
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-- --
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-- GNAT was originally developed by the GNAT team at New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc. --
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-- --
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------------------------------------------------------------------------------
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generic
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type Float_Type is digits <>;
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package Ada.Numerics.Generic_Elementary_Functions is
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pragma Pure;
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function Sqrt (X : Float_Type'Base) return Float_Type'Base with
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Post => Sqrt'Result >= 0.0
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and then (if X = 0.0 then Sqrt'Result = 0.0)
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and then (if X = 1.0 then Sqrt'Result = 1.0)
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-- Finally if X is positive, the result of Sqrt is positive (because
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-- the sqrt of numbers greater than 1 is greater than or equal to 1,
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-- and the sqrt of numbers less than 1 is greater than the argument).
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-- This property is useful in particular for static analysis. The
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-- property that X is positive is not expressed as (X > 0.0), as
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-- the value X may be held in registers that have larger range and
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-- precision on some architecture (for example, on x86 using x387
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-- FPU, as opposed to SSE2). So, it might be possible for X to be
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-- 2.0**(-5000) or so, which could cause the number to compare as
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-- greater than 0, but Sqrt would still return a zero result.
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-- Note: we use the comparison with Succ (0.0) here because this is
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-- more amenable to CodePeer analysis than the use of 'Machine.
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and then (if X >= Float_Type'Succ (0.0) then Sqrt'Result > 0.0);
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function Log (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 1.0 then Log'Result = 0.0);
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function Log (X, Base : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 1.0 then Log'Result = 0.0);
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function Exp (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Exp'Result = 1.0);
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function "**" (Left, Right : Float_Type'Base) return Float_Type'Base with
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Post => "**"'Result >= 0.0
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and then (if Right = 0.0 then "**"'Result = 1.0)
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and then (if Right = 1.0 then "**"'Result = Left)
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and then (if Left = 1.0 then "**"'Result = 1.0)
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and then (if Left = 0.0 then "**"'Result = 0.0);
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function Sin (X : Float_Type'Base) return Float_Type'Base with
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Post => Sin'Result in -1.0 .. 1.0
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and then (if X = 0.0 then Sin'Result = 0.0);
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function Sin (X, Cycle : Float_Type'Base) return Float_Type'Base with
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Post => Sin'Result in -1.0 .. 1.0
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and then (if X = 0.0 then Sin'Result = 0.0);
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function Cos (X : Float_Type'Base) return Float_Type'Base with
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Post => Cos'Result in -1.0 .. 1.0
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and then (if X = 0.0 then Cos'Result = 1.0);
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function Cos (X, Cycle : Float_Type'Base) return Float_Type'Base with
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Post => Cos'Result in -1.0 .. 1.0
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and then (if X = 0.0 then Cos'Result = 1.0);
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function Tan (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Tan'Result = 0.0);
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function Tan (X, Cycle : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Tan'Result = 0.0);
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function Cot (X : Float_Type'Base) return Float_Type'Base;
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function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base;
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function Arcsin (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Arcsin'Result = 0.0);
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function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Arcsin'Result = 0.0);
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function Arccos (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 1.0 then Arccos'Result = 0.0);
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function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 1.0 then Arccos'Result = 0.0);
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function Arctan
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(Y : Float_Type'Base;
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X : Float_Type'Base := 1.0) return Float_Type'Base
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with
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Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
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function Arctan
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(Y : Float_Type'Base;
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X : Float_Type'Base := 1.0;
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Cycle : Float_Type'Base) return Float_Type'Base
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with
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Post => (if X > 0.0 and then Y = 0.0 then Arctan'Result = 0.0);
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function Arccot
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(X : Float_Type'Base;
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Y : Float_Type'Base := 1.0) return Float_Type'Base
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with
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Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
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function Arccot
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(X : Float_Type'Base;
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Y : Float_Type'Base := 1.0;
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Cycle : Float_Type'Base) return Float_Type'Base
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with
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Post => (if X > 0.0 and then Y = 0.0 then Arccot'Result = 0.0);
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function Sinh (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Sinh'Result = 0.0);
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function Cosh (X : Float_Type'Base) return Float_Type'Base with
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Post => Cosh'Result >= 1.0
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and then (if X = 0.0 then Cosh'Result = 1.0);
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function Tanh (X : Float_Type'Base) return Float_Type'Base with
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Post => Tanh'Result in -1.0 .. 1.0
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and then (if X = 0.0 then Tanh'Result = 0.0);
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function Coth (X : Float_Type'Base) return Float_Type'Base with
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Post => abs Coth'Result >= 1.0;
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function Arcsinh (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Arcsinh'Result = 0.0);
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function Arccosh (X : Float_Type'Base) return Float_Type'Base with
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Post => Arccosh'Result >= 0.0
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and then (if X = 1.0 then Arccosh'Result = 0.0);
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function Arctanh (X : Float_Type'Base) return Float_Type'Base with
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Post => (if X = 0.0 then Arctanh'Result = 0.0);
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function Arccoth (X : Float_Type'Base) return Float_Type'Base;
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end Ada.Numerics.Generic_Elementary_Functions;
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