| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT RUN-TIME COMPONENTS -- |
| -- -- |
| -- ADA.NUMERICS.GENERIC_ELEMENTARY_FUNCTIONS -- |
| -- -- |
| -- S p e c -- |
| -- -- |
| -- Copyright (C) 2012-2022, 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 with |
| SPARK_Mode => On |
| is |
| pragma Pure; |
| |
| -- Preconditions in this unit are meant for analysis only, not for run-time |
| -- checking, so that the expected exceptions are raised when calling |
| -- Assert. This is enforced by setting the corresponding assertion policy |
| -- to Ignore. This is done in the generic spec so that it applies to all |
| -- instances. |
| |
| pragma Assertion_Policy (Pre => Ignore); |
| |
| function Sqrt (X : Float_Type'Base) return Float_Type'Base with |
| Pre => X >= 0.0, |
| 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) |
| |
| -- Finally if X is positive, the result of Sqrt is positive (because |
| -- the sqrt of numbers greater than 1 is greater than or equal to 1, |
| -- and the sqrt of numbers less than 1 is greater than the argument). |
| |
| -- This property is useful in particular for static analysis. The |
| -- property that X is positive is not expressed as (X > 0.0), as |
| -- the value X may be held in registers that have larger range and |
| -- precision on some architecture (for example, on x86 using x387 |
| -- FPU, as opposed to SSE2). So, it might be possible for X to be |
| -- 2.0**(-5000) or so, which could cause the number to compare as |
| -- greater than 0, but Sqrt would still return a zero result. |
| |
| -- Note: we use the comparison with Succ (0.0) here because this is |
| -- more amenable to CodePeer analysis than the use of 'Machine. |
| |
| and then (if X >= Float_Type'Succ (0.0) then Sqrt'Result > 0.0); |
| |
| function Log (X : Float_Type'Base) return Float_Type'Base with |
| Pre => X > 0.0, |
| Post => (if X = 1.0 then Log'Result = 0.0); |
| |
| function Log (X, Base : Float_Type'Base) return Float_Type'Base with |
| Pre => X > 0.0 and Base > 0.0 and Base /= 1.0, |
| 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 |
| Pre => (if Left = 0.0 then Right > 0.0) and Left >= 0.0, |
| 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 |
| Inline, |
| 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 |
| Pre => Cycle > 0.0, |
| 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 |
| Inline, |
| 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 |
| Pre => Cycle > 0.0, |
| 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 |
| Pre => Cycle > 0.0 |
| and then abs Float_Type'Base'Remainder (X, Cycle) /= 0.25 * Cycle, |
| Post => (if X = 0.0 then Tan'Result = 0.0); |
| |
| function Cot (X : Float_Type'Base) return Float_Type'Base with |
| Pre => X /= 0.0; |
| |
| function Cot (X, Cycle : Float_Type'Base) return Float_Type'Base with |
| Pre => Cycle > 0.0 |
| and then X /= 0.0 |
| and then Float_Type'Base'Remainder (X, Cycle) /= 0.0 |
| and then abs Float_Type'Base'Remainder (X, Cycle) /= 0.5 * Cycle; |
| |
| function Arcsin (X : Float_Type'Base) return Float_Type'Base with |
| Pre => abs X <= 1.0, |
| Post => (if X = 0.0 then Arcsin'Result = 0.0); |
| |
| function Arcsin (X, Cycle : Float_Type'Base) return Float_Type'Base with |
| Pre => Cycle > 0.0 and abs X <= 1.0, |
| Post => (if X = 0.0 then Arcsin'Result = 0.0); |
| |
| function Arccos (X : Float_Type'Base) return Float_Type'Base with |
| Pre => abs X <= 1.0, |
| Post => (if X = 1.0 then Arccos'Result = 0.0); |
| |
| function Arccos (X, Cycle : Float_Type'Base) return Float_Type'Base with |
| Pre => Cycle > 0.0 and abs X <= 1.0, |
| 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 |
| Pre => X /= 0.0 or Y /= 0.0, |
| Post => (if X > 0.0 and then 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 |
| Pre => Cycle > 0.0 and (X /= 0.0 or Y /= 0.0), |
| Post => (if X > 0.0 and then 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 |
| Pre => X /= 0.0 or Y /= 0.0, |
| Post => (if X > 0.0 and then 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 |
| Pre => Cycle > 0.0 and (X /= 0.0 or Y /= 0.0), |
| Post => (if X > 0.0 and then 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 |
| Pre => X /= 0.0, |
| 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 |
| Pre => X >= 1.0, |
| 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 |
| Pre => abs X < 1.0, |
| Post => (if X = 0.0 then Arctanh'Result = 0.0); |
| |
| function Arccoth (X : Float_Type'Base) return Float_Type'Base with |
| Pre => abs X > 1.0; |
| |
| end Ada.Numerics.Generic_Elementary_Functions; |