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-------------------------------------------------------------------------------
-- (C) Altran Praxis Limited
-------------------------------------------------------------------------------
--
-- The SPARK toolset is free software; you can redistribute it and/or modify it
-- under terms of the GNU General Public License as published by the Free
-- Software Foundation; either version 3, or (at your option) any later
-- version. The SPARK toolset is distributed in the hope that it will be
-- useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
-- Public License for more details. You should have received a copy of the GNU
-- General Public License distributed with the SPARK toolset; see file
-- COPYING3. If not, go to http://www.gnu.org/licenses for a complete copy of
-- the license.
--
--=============================================================================
with E_Strings;
with LexTokenManager;
use type LexTokenManager.Str_Comp_Result;
--# inherit E_Strings,
--# LexTokenManager,
--# SPARK_IO;
package Maths is
type Value is private;
NoValue : constant Value;
ZeroReal : constant Value;
ZeroInteger : constant Value;
OneInteger : constant Value;
ExactHalf : constant Value;
TrueValue : constant Value;
FalseValue : constant Value;
type ErrorCode is (
NoError,
IllegalValue, --ie. not a valid SPARK literal
IllegalOperation, --ie. wrong for Value types passed
OverFlow, --ie. too many digits for array
DivideByZero,
TypeMismatch,
ConstraintError); --eg. pred(t'base'first)
----------------------------------------------------------------------------
--Conversion of numeric literals
procedure LiteralToValue (Str : in LexTokenManager.Lex_String;
Num : out Value;
OK : out ErrorCode);
--# global in LexTokenManager.State;
--# derives Num,
--# OK from LexTokenManager.State,
--# Str;
-- post (Ok = NoError) or (Ok = illegalValue) or (Ok = overflow);
----------------------------------------------------------------------------
function IntegerToValue (I : Integer) return Value;
---------------------------------------------------------------------------
procedure StorageRep (Num : in Value;
Rep : out LexTokenManager.Lex_String);
--# global in out LexTokenManager.State;
--# derives LexTokenManager.State,
--# Rep from LexTokenManager.State,
--# Num;
----------------------------------------------------------------------------
function ValueRep (StoreRep : LexTokenManager.Lex_String) return Value;
--# global in LexTokenManager.State;
--caution, although this function turns a LexString into a value it is
--not the same as procedure LiteralToValue. This one converts only
--things which were first converted by StorageRep. LiteralToValue can parse
--any numeric literal to a value.
----------------------------------------------------------------------------
function HasNoValue (Num : Value) return Boolean;
pragma Inline (HasNoValue);
----------------------------------------------------------------------------
function ValueToString (Num : Value) return E_Strings.T;
----------------------------------------------------------------------------
procedure ValueToInteger (Num : in Value;
Int : out Integer;
Ok : out ErrorCode);
--# derives Int,
--# Ok from Num;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = overflow);
----------------------------------------------------------------------------
procedure Negate (Num : in out Value);
--# derives Num from *;
-- pre Num.Sort = IntegerValue or Num.Sort = RealValue;
----------------------------------------------------------------------------
procedure Absolute (Num : in out Value);
--# derives Num from *;
-- pre Num.Sort = IntegerValue or Num.Sort = RealValue;
----------------------------------------------------------------------------
procedure ConvertToInteger (Num : in out Value);
--# derives Num from *;
-- pre Num.Sort = IntegerValue or Num.Sort = RealValue;
----------------------------------------------------------------------------
procedure ConvertToReal (Num : in out Value);
--# derives Num from *;
-- pre Num.Sort = IntegerValue or Num.Sort = RealValue;
----------------------------------------------------------------------------
procedure Floor (Val : in Value;
Result : out Value;
OK : out ErrorCode);
--# derives OK,
--# Result from Val;
-- pre Val.Sort = IntegerValue or Val.Sort = RealValue;
-- post (Ok = NoError) or (Ok = Overflow)
----------------------------------------------------------------------------
procedure Ceiling (Val : in Value;
Result : out Value;
OK : out ErrorCode);
--# derives OK,
--# Result from Val;
-- pre Val.Sort = IntegerValue or Val.Sort = RealValue;
-- post (Ok = NoError) or (Ok = Overflow)
----------------------------------------------------------------------------
procedure Add (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = Overflow);
----------------------------------------------------------------------------
procedure Subtract (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = Overflow);
----------------------------------------------------------------------------
procedure Multiply (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = Overflow);
----------------------------------------------------------------------------
procedure Divide (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = Overflow) or
-- (Ok = DivideByZero);
----------------------------------------------------------------------------
procedure Modulus (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = IllegalOperation) or
-- (Ok = DivideByZero);
----------------------------------------------------------------------------
procedure Remainder (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch) or (Ok = IllegalOperation) or
-- (Ok = DivideByZero);
----------------------------------------------------------------------------
procedure Greater (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure Lesser (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure LesserOrEqual (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure GreaterOrEqual (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure InsideRange (Val, LowerBound, UpperBound : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from LowerBound,
--# UpperBound,
--# Val;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure OutsideRange (Val, LowerBound, UpperBound : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from LowerBound,
--# UpperBound,
--# Val;
-- post (Ok = NoError) or (Ok = TypeMismatch);
----------------------------------------------------------------------------
procedure RaiseByPower (FirstNum, SecondNum : in Value;
Result : out Value;
Ok : out ErrorCode);
--# derives Ok,
--# Result from FirstNum,
--# SecondNum;
-- post (Ok = NoError) or (Ok = IllegalOperation) or (Ok = OverFlow);
----------------------------------------------------------------------------
-- Support for non-numeric types
----------------------------------------------------------------------------
function AndOp (LeftVal, RightVal : Value) return Value;
----------------------------------------------------------------------------
function OrOp (LeftVal, RightVal : Value) return Value;
----------------------------------------------------------------------------
function XorOp (LeftVal, RightVal : Value) return Value;
----------------------------------------------------------------------------
procedure NotOp (TheVal : in out Value);
--# derives TheVal from *;
-- pre TheVal.Sort = TruthValue
----------------------------------------------------------------------------
procedure ModularNotOp (TheVal : in out Value;
TheModulus : in Value);
--# derives TheVal from *,
--# TheModulus;
-- pre TheVal.Sort = IntegerValue and IsAPositivePowerOf2 (TheModulus);
----------------------------------------------------------------------------
procedure ValueToBool (TheVal : in Value;
Result : out Boolean;
Ok : out ErrorCode);
--# derives Ok,
--# Result from TheVal;
-- post (Ok = NoError) or (Ok = TypeMismatch)
----------------------------------------------------------------------------
function BoolToValue (B : Boolean) return Value;
----------------------------------------------------------------------------
procedure PredOp (TheVal : in out Value;
Ok : out ErrorCode);
--# derives Ok,
--# TheVal from TheVal;
-- post (Ok = NoError) or (Ok = TypeMismatch)
----------------------------------------------------------------------------
procedure SuccOp (TheVal : in out Value;
Ok : out ErrorCode);
--# derives Ok,
--# TheVal from TheVal;
-- post (Ok = NoError) or (Ok = TypeMismatch)
----------------------------------------------------------------------------
function MakeEnum (Pos : Natural) return Value;
----------------------------------------------------------------------------
function IsIntegerValue (Val : Value) return Boolean;
function IsRealValue (Val : Value) return Boolean;
----------------------------------------------------------------------------
--converts real value to integer value rounding away from 0 as required by
--Ada 95 LRM 4.9(33) and LRM 4.9(40).
function Ada95RealToInteger (TheReal : Value) return Value;
----------------------------------------------------------------------------
-- returns True for 1, 2, 4, 8, 16 ... useful for wellformedness
-- of modular type declarations
function IsAPositivePowerOf2 (Num : in Value) return Boolean;
private
--------------- IMPORTANT -----------------------------------------------
-- MaxLength defines the size of the numbers that can be supported
-- to full precision.
--
-- If we want to support a floating point defined by
-- 1 sign bit
-- e exponent bits
-- s significand bits
-- The largest number that can be represented is 2 ** (2**(e-1))
-- The smallest number that can be represented is 2 ** -((2**(e-1))+s-1)
--
-- In order to represent any number in this range to the precision
-- implied by the smallest number then in the numerator/denominator format
-- the numerator must be able to represent 2 ** ((2**e) + s -1)
-- So we require MaxLength > ((2**e) + s-1) log 2
--
-- e s MaxLength >
-- IEEE Single Precision Float 8 23 84
-- IEEE Double Precision Float 11 52 632
-------------------------------------------------------------------------
MaxLength : constant Integer := 640;
subtype LengthRange is Integer range 0 .. MaxLength;
subtype PosRange is Integer range 1 .. MaxLength;
type Digit is range 0 .. 15;
for Digit'Size use 4;
type ValueType is (RealValue, IntegerValue, TruthValue, UnknownValue);
type ValueArray is array (PosRange) of Digit;
pragma Pack (ValueArray);
--NB. Values are stored with LSD in Numerals(1) and MSD in
-- Numerals(Length)
type Part is record
Numerals : ValueArray;
Length : LengthRange;
Overflowed : Boolean;
end record;
type Value is record
Numerator : Part;
Denominator : Part;
IsPositive : Boolean;
Sort : ValueType;
end record;
------------------------IMPORTANT--------------------------------------
-- Modular Type support
--
-- The largest modular type supported is 2**BinaryMaxLength.
--
-- The value of BinaryMaxLength has an upper bound of
-- |_ MaxLength / Log 2 _|
-- which is the largest power of 2 that can be evaluated in a ValueArray.
--
-- These values are stored with LSB in element 0,
-- and MSB in element BinaryMaxLength
-----------------------------------------------------------------------
BinaryMaxLength : constant Integer := 211;
subtype BinaryLengthRange is Integer range 0 .. BinaryMaxLength;
type Bits is array (BinaryLengthRange) of Boolean;
ZeroBits : constant Bits := Bits'(others => False);
ZeroPart : constant Part := Part'(Length => 1,
Numerals => ValueArray'(PosRange => 0),
Overflowed => False);
OnePart : constant Part := Part'(Length => 1,
Numerals => ValueArray'(1 => 1,
others => 0),
Overflowed => False);
TwoPart : constant Part := Part'(Length => 1,
Numerals => ValueArray'(1 => 2,
others => 0),
Overflowed => False);
ZeroReal : constant Value := Value'(Numerator => ZeroPart,
Denominator => OnePart,
IsPositive => True,
Sort => RealValue);
ExactHalf : constant Value := Value'(Numerator => OnePart,
Denominator => TwoPart,
IsPositive => True,
Sort => RealValue);
ZeroInteger : constant Value :=
Value'(Numerator => ZeroPart,
Denominator => OnePart,
IsPositive => True,
Sort => IntegerValue);
OneInteger : constant Value := Value'(Numerator => OnePart,
Denominator => OnePart,
IsPositive => True,
Sort => IntegerValue);
NoValue : constant Value := Value'(Numerator => ZeroPart,
Denominator => OnePart,
IsPositive => True,
Sort => UnknownValue);
FalseValue : constant Value := Value'(Numerator => ZeroPart,
Denominator => ZeroPart,
IsPositive => False,
Sort => TruthValue);
TrueValue : constant Value := Value'(Numerator => ZeroPart,
Denominator => ZeroPart,
IsPositive => True,
Sort => TruthValue);
end Maths;
|
