-- CXG2009.A
|
-- CXG2009.A
|
--
|
--
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-- Grant of Unlimited Rights
|
-- Grant of Unlimited Rights
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--
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--
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-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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-- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
|
-- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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-- unlimited rights in the software and documentation contained herein.
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-- unlimited rights in the software and documentation contained herein.
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-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- this public release, the Government intends to confer upon all
|
-- this public release, the Government intends to confer upon all
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-- recipients unlimited rights equal to those held by the Government.
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-- recipients unlimited rights equal to those held by the Government.
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-- These rights include rights to use, duplicate, release or disclose the
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-- These rights include rights to use, duplicate, release or disclose the
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-- released technical data and computer software in whole or in part, in
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-- released technical data and computer software in whole or in part, in
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-- any manner and for any purpose whatsoever, and to have or permit others
|
-- any manner and for any purpose whatsoever, and to have or permit others
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-- to do so.
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-- to do so.
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--
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--
|
-- DISCLAIMER
|
-- DISCLAIMER
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--
|
--
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
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-- PARTICULAR PURPOSE OF SAID MATERIAL.
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--*
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--*
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--
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--
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-- OBJECTIVE:
|
-- OBJECTIVE:
|
-- Check that the real sqrt and complex modulus functions
|
-- Check that the real sqrt and complex modulus functions
|
-- return results that are within the allowed
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-- return results that are within the allowed
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-- error bound.
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-- error bound.
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--
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--
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-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test checks the accuracy of the sqrt and modulus functions
|
-- This test checks the accuracy of the sqrt and modulus functions
|
-- by computing the norm of various vectors where the result
|
-- by computing the norm of various vectors where the result
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-- is known in advance.
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-- is known in advance.
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-- This test uses real and complex math together as would an
|
-- This test uses real and complex math together as would an
|
-- actual application. Considerable use of generics is also
|
-- actual application. Considerable use of generics is also
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-- employed.
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-- employed.
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--
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--
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-- SPECIAL REQUIREMENTS
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-- SPECIAL REQUIREMENTS
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-- The Strict Mode for the numerical accuracy must be
|
-- The Strict Mode for the numerical accuracy must be
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-- selected. The method by which this mode is selected
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-- selected. The method by which this mode is selected
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-- is implementation dependent.
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-- is implementation dependent.
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--
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--
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-- APPLICABILITY CRITERIA:
|
-- APPLICABILITY CRITERIA:
|
-- This test applies only to implementations supporting the
|
-- This test applies only to implementations supporting the
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-- Numerics Annex.
|
-- Numerics Annex.
|
-- This test only applies to the Strict Mode for numerical
|
-- This test only applies to the Strict Mode for numerical
|
-- accuracy.
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-- accuracy.
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--
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--
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--
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--
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-- CHANGE HISTORY:
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-- CHANGE HISTORY:
|
-- 26 FEB 96 SAIC Initial release for 2.1
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-- 26 FEB 96 SAIC Initial release for 2.1
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-- 22 AUG 96 SAIC Revised Check procedure
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-- 22 AUG 96 SAIC Revised Check procedure
|
--
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--
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--!
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--!
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|
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------------------------------------------------------------------------------
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------------------------------------------------------------------------------
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|
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with System;
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with System;
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with Report;
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with Report;
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with Ada.Numerics.Generic_Complex_Types;
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with Ada.Numerics.Generic_Complex_Types;
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with Ada.Numerics.Generic_Elementary_Functions;
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with Ada.Numerics.Generic_Elementary_Functions;
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procedure CXG2009 is
|
procedure CXG2009 is
|
Verbose : constant Boolean := False;
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Verbose : constant Boolean := False;
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|
|
--=====================================================================
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--=====================================================================
|
|
|
generic
|
generic
|
type Real is digits <>;
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type Real is digits <>;
|
package Generic_Real_Norm_Check is
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package Generic_Real_Norm_Check is
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procedure Do_Test;
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procedure Do_Test;
|
end Generic_Real_Norm_Check;
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end Generic_Real_Norm_Check;
|
|
|
-----------------------------------------------------------------------
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-----------------------------------------------------------------------
|
|
|
package body Generic_Real_Norm_Check is
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package body Generic_Real_Norm_Check is
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type Vector is array (Integer range <>) of Real;
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type Vector is array (Integer range <>) of Real;
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|
|
package GEF is new Ada.Numerics.Generic_Elementary_Functions (Real);
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package GEF is new Ada.Numerics.Generic_Elementary_Functions (Real);
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function Sqrt (X : Real) return Real renames GEF.Sqrt;
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function Sqrt (X : Real) return Real renames GEF.Sqrt;
|
|
|
function One_Norm (V : Vector) return Real is
|
function One_Norm (V : Vector) return Real is
|
-- sum of absolute values of the elements of the vector
|
-- sum of absolute values of the elements of the vector
|
Result : Real := 0.0;
|
Result : Real := 0.0;
|
begin
|
begin
|
for I in V'Range loop
|
for I in V'Range loop
|
Result := Result + abs V(I);
|
Result := Result + abs V(I);
|
end loop;
|
end loop;
|
return Result;
|
return Result;
|
end One_Norm;
|
end One_Norm;
|
|
|
function Inf_Norm (V : Vector) return Real is
|
function Inf_Norm (V : Vector) return Real is
|
-- greatest absolute vector element
|
-- greatest absolute vector element
|
Result : Real := 0.0;
|
Result : Real := 0.0;
|
begin
|
begin
|
for I in V'Range loop
|
for I in V'Range loop
|
if abs V(I) > Result then
|
if abs V(I) > Result then
|
Result := abs V(I);
|
Result := abs V(I);
|
end if;
|
end if;
|
end loop;
|
end loop;
|
return Result;
|
return Result;
|
end Inf_Norm;
|
end Inf_Norm;
|
|
|
function Two_Norm (V : Vector) return Real is
|
function Two_Norm (V : Vector) return Real is
|
-- if greatest absolute vector element is 0 then return 0
|
-- if greatest absolute vector element is 0 then return 0
|
-- else return greatest * sqrt (sum((element / greatest) ** 2)))
|
-- else return greatest * sqrt (sum((element / greatest) ** 2)))
|
-- where greatest is Inf_Norm of the vector
|
-- where greatest is Inf_Norm of the vector
|
Inf_N : Real;
|
Inf_N : Real;
|
Sum_Squares : Real;
|
Sum_Squares : Real;
|
Term : Real;
|
Term : Real;
|
begin
|
begin
|
Inf_N := Inf_Norm (V);
|
Inf_N := Inf_Norm (V);
|
if Inf_N = 0.0 then
|
if Inf_N = 0.0 then
|
return 0.0;
|
return 0.0;
|
end if;
|
end if;
|
Sum_Squares := 0.0;
|
Sum_Squares := 0.0;
|
for I in V'Range loop
|
for I in V'Range loop
|
Term := V (I) / Inf_N;
|
Term := V (I) / Inf_N;
|
Sum_Squares := Sum_Squares + Term * Term;
|
Sum_Squares := Sum_Squares + Term * Term;
|
end loop;
|
end loop;
|
return Inf_N * Sqrt (Sum_Squares);
|
return Inf_N * Sqrt (Sum_Squares);
|
end Two_Norm;
|
end Two_Norm;
|
|
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real;
|
MRE : Real;
|
Vector_Length : Integer) is
|
Vector_Length : Integer) is
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_Error : Real;
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if abs (Actual - Expected) > Max_Error then
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" VectLength:" &
|
" VectLength:" &
|
Integer'Image (Vector_Length) &
|
Integer'Image (Vector_Length) &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" & Real'Image (Max_Error) );
|
" mre:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
Report.Comment (Test_Name & " vector length" &
|
Report.Comment (Test_Name & " vector length" &
|
Integer'Image (Vector_Length));
|
Integer'Image (Vector_Length));
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
for Vector_Length in 1 .. 10 loop
|
for Vector_Length in 1 .. 10 loop
|
declare
|
declare
|
V : Vector (1..Vector_Length) := (1..Vector_Length => 0.0);
|
V : Vector (1..Vector_Length) := (1..Vector_Length => 0.0);
|
V1 : Vector (1..Vector_Length) := (1..Vector_Length => 1.0);
|
V1 : Vector (1..Vector_Length) := (1..Vector_Length => 1.0);
|
begin
|
begin
|
Check (One_Norm (V), 0.0, "one_norm (z)", 0.0, Vector_Length);
|
Check (One_Norm (V), 0.0, "one_norm (z)", 0.0, Vector_Length);
|
Check (Inf_Norm (V), 0.0, "inf_norm (z)", 0.0, Vector_Length);
|
Check (Inf_Norm (V), 0.0, "inf_norm (z)", 0.0, Vector_Length);
|
|
|
for J in 1..Vector_Length loop
|
for J in 1..Vector_Length loop
|
V := (1..Vector_Length => 0.0);
|
V := (1..Vector_Length => 0.0);
|
V (J) := 1.0;
|
V (J) := 1.0;
|
Check (One_Norm (V), 1.0, "one_norm (010)",
|
Check (One_Norm (V), 1.0, "one_norm (010)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Inf_Norm (V), 1.0, "inf_norm (010)",
|
Check (Inf_Norm (V), 1.0, "inf_norm (010)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Two_Norm (V), 1.0, "two_norm (010)",
|
Check (Two_Norm (V), 1.0, "two_norm (010)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
end loop;
|
end loop;
|
|
|
Check (One_Norm (V1), Real (Vector_Length), "one_norm (1)",
|
Check (One_Norm (V1), Real (Vector_Length), "one_norm (1)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Inf_Norm (V1), 1.0, "inf_norm (1)",
|
Check (Inf_Norm (V1), 1.0, "inf_norm (1)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
|
|
-- error in computing Two_Norm and expected result
|
-- error in computing Two_Norm and expected result
|
-- are as follows (ME is Model_Epsilon * Expected_Value):
|
-- are as follows (ME is Model_Epsilon * Expected_Value):
|
-- 2ME from expected Sqrt
|
-- 2ME from expected Sqrt
|
-- 2ME from Sqrt in Two_Norm times the error in the
|
-- 2ME from Sqrt in Two_Norm times the error in the
|
-- vector calculation.
|
-- vector calculation.
|
-- The vector calculation contains the following error
|
-- The vector calculation contains the following error
|
-- based upon the length N of the vector:
|
-- based upon the length N of the vector:
|
-- N*1ME from squaring terms in Two_Norm
|
-- N*1ME from squaring terms in Two_Norm
|
-- N*1ME from the division of each term in Two_Norm
|
-- N*1ME from the division of each term in Two_Norm
|
-- (N-1)*1ME from the sum of the terms
|
-- (N-1)*1ME from the sum of the terms
|
-- This gives (2 + 2 * (N + N + (N-1)) ) * ME
|
-- This gives (2 + 2 * (N + N + (N-1)) ) * ME
|
-- which simplifies to (2 + 2N + 2N + 2N - 2) * ME
|
-- which simplifies to (2 + 2N + 2N + 2N - 2) * ME
|
-- or 6*N*ME
|
-- or 6*N*ME
|
Check (Two_Norm (V1), Sqrt (Real(Vector_Length)),
|
Check (Two_Norm (V1), Sqrt (Real(Vector_Length)),
|
"two_norm (1)",
|
"two_norm (1)",
|
(Real (6 * Vector_Length)),
|
(Real (6 * Vector_Length)),
|
Vector_Length);
|
Vector_Length);
|
exception
|
exception
|
when others => Report.Failed ("exception for vector length" &
|
when others => Report.Failed ("exception for vector length" &
|
Integer'Image (Vector_Length) );
|
Integer'Image (Vector_Length) );
|
end;
|
end;
|
end loop;
|
end loop;
|
end Do_Test;
|
end Do_Test;
|
end Generic_Real_Norm_Check;
|
end Generic_Real_Norm_Check;
|
|
|
--=====================================================================
|
--=====================================================================
|
|
|
generic
|
generic
|
type Real is digits <>;
|
type Real is digits <>;
|
package Generic_Complex_Norm_Check is
|
package Generic_Complex_Norm_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Generic_Complex_Norm_Check;
|
end Generic_Complex_Norm_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
package body Generic_Complex_Norm_Check is
|
package body Generic_Complex_Norm_Check is
|
package Complex_Types is new Ada.Numerics.Generic_Complex_Types (Real);
|
package Complex_Types is new Ada.Numerics.Generic_Complex_Types (Real);
|
use Complex_Types;
|
use Complex_Types;
|
type Vector is array (Integer range <>) of Complex;
|
type Vector is array (Integer range <>) of Complex;
|
|
|
package GEF is new Ada.Numerics.Generic_Elementary_Functions (Real);
|
package GEF is new Ada.Numerics.Generic_Elementary_Functions (Real);
|
function Sqrt (X : Real) return Real renames GEF.Sqrt;
|
function Sqrt (X : Real) return Real renames GEF.Sqrt;
|
|
|
function One_Norm (V : Vector) return Real is
|
function One_Norm (V : Vector) return Real is
|
Result : Real := 0.0;
|
Result : Real := 0.0;
|
begin
|
begin
|
for I in V'Range loop
|
for I in V'Range loop
|
Result := Result + abs V(I);
|
Result := Result + abs V(I);
|
end loop;
|
end loop;
|
return Result;
|
return Result;
|
end One_Norm;
|
end One_Norm;
|
|
|
function Inf_Norm (V : Vector) return Real is
|
function Inf_Norm (V : Vector) return Real is
|
Result : Real := 0.0;
|
Result : Real := 0.0;
|
begin
|
begin
|
for I in V'Range loop
|
for I in V'Range loop
|
if abs V(I) > Result then
|
if abs V(I) > Result then
|
Result := abs V(I);
|
Result := abs V(I);
|
end if;
|
end if;
|
end loop;
|
end loop;
|
return Result;
|
return Result;
|
end Inf_Norm;
|
end Inf_Norm;
|
|
|
function Two_Norm (V : Vector) return Real is
|
function Two_Norm (V : Vector) return Real is
|
Inf_N : Real;
|
Inf_N : Real;
|
Sum_Squares : Real;
|
Sum_Squares : Real;
|
Term : Real;
|
Term : Real;
|
begin
|
begin
|
Inf_N := Inf_Norm (V);
|
Inf_N := Inf_Norm (V);
|
if Inf_N = 0.0 then
|
if Inf_N = 0.0 then
|
return 0.0;
|
return 0.0;
|
end if;
|
end if;
|
Sum_Squares := 0.0;
|
Sum_Squares := 0.0;
|
for I in V'Range loop
|
for I in V'Range loop
|
Term := abs (V (I) / Inf_N );
|
Term := abs (V (I) / Inf_N );
|
Sum_Squares := Sum_Squares + Term * Term;
|
Sum_Squares := Sum_Squares + Term * Term;
|
end loop;
|
end loop;
|
return Inf_N * Sqrt (Sum_Squares);
|
return Inf_N * Sqrt (Sum_Squares);
|
end Two_Norm;
|
end Two_Norm;
|
|
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real;
|
MRE : Real;
|
Vector_Length : Integer) is
|
Vector_Length : Integer) is
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_Error : Real;
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if abs (Actual - Expected) > Max_Error then
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" VectLength:" &
|
" VectLength:" &
|
Integer'Image (Vector_Length) &
|
Integer'Image (Vector_Length) &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" & Real'Image (Max_Error) );
|
" mre:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
Report.Comment (Test_Name & " vector length" &
|
Report.Comment (Test_Name & " vector length" &
|
Integer'Image (Vector_Length));
|
Integer'Image (Vector_Length));
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
for Vector_Length in 1 .. 10 loop
|
for Vector_Length in 1 .. 10 loop
|
declare
|
declare
|
V : Vector (1..Vector_Length) :=
|
V : Vector (1..Vector_Length) :=
|
(1..Vector_Length => (0.0, 0.0));
|
(1..Vector_Length => (0.0, 0.0));
|
X, Y : Vector (1..Vector_Length);
|
X, Y : Vector (1..Vector_Length);
|
begin
|
begin
|
Check (One_Norm (V), 0.0, "one_norm (z)", 0.0, Vector_Length);
|
Check (One_Norm (V), 0.0, "one_norm (z)", 0.0, Vector_Length);
|
Check (Inf_Norm (V), 0.0, "inf_norm (z)", 0.0, Vector_Length);
|
Check (Inf_Norm (V), 0.0, "inf_norm (z)", 0.0, Vector_Length);
|
|
|
for J in 1..Vector_Length loop
|
for J in 1..Vector_Length loop
|
X := (1..Vector_Length => (0.0, 0.0) );
|
X := (1..Vector_Length => (0.0, 0.0) );
|
Y := X; -- X and Y are now both zeroed
|
Y := X; -- X and Y are now both zeroed
|
X (J).Re := 1.0;
|
X (J).Re := 1.0;
|
Y (J).Im := 1.0;
|
Y (J).Im := 1.0;
|
Check (One_Norm (X), 1.0, "one_norm (0x0)",
|
Check (One_Norm (X), 1.0, "one_norm (0x0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Inf_Norm (X), 1.0, "inf_norm (0x0)",
|
Check (Inf_Norm (X), 1.0, "inf_norm (0x0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Two_Norm (X), 1.0, "two_norm (0x0)",
|
Check (Two_Norm (X), 1.0, "two_norm (0x0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (One_Norm (Y), 1.0, "one_norm (0y0)",
|
Check (One_Norm (Y), 1.0, "one_norm (0y0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Inf_Norm (Y), 1.0, "inf_norm (0y0)",
|
Check (Inf_Norm (Y), 1.0, "inf_norm (0y0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
Check (Two_Norm (Y), 1.0, "two_norm (0y0)",
|
Check (Two_Norm (Y), 1.0, "two_norm (0y0)",
|
0.0, Vector_Length);
|
0.0, Vector_Length);
|
end loop;
|
end loop;
|
|
|
V := (1..Vector_Length => (3.0, 4.0));
|
V := (1..Vector_Length => (3.0, 4.0));
|
|
|
-- error in One_Norm is 3*N*ME for abs computation +
|
-- error in One_Norm is 3*N*ME for abs computation +
|
-- (N-1)*ME for the additions
|
-- (N-1)*ME for the additions
|
-- which gives (4N-1) * ME
|
-- which gives (4N-1) * ME
|
Check (One_Norm (V), 5.0 * Real (Vector_Length),
|
Check (One_Norm (V), 5.0 * Real (Vector_Length),
|
"one_norm ((3,4))",
|
"one_norm ((3,4))",
|
Real (4*Vector_Length - 1),
|
Real (4*Vector_Length - 1),
|
Vector_Length);
|
Vector_Length);
|
|
|
-- error in Inf_Norm is from abs of single element (3ME)
|
-- error in Inf_Norm is from abs of single element (3ME)
|
Check (Inf_Norm (V), 5.0,
|
Check (Inf_Norm (V), 5.0,
|
"inf_norm ((3,4))",
|
"inf_norm ((3,4))",
|
3.0,
|
3.0,
|
Vector_Length);
|
Vector_Length);
|
|
|
-- error in following comes from:
|
-- error in following comes from:
|
-- 2ME in sqrt of expected result
|
-- 2ME in sqrt of expected result
|
-- 3ME in Inf_Norm calculation
|
-- 3ME in Inf_Norm calculation
|
-- 2ME in sqrt of vector calculation
|
-- 2ME in sqrt of vector calculation
|
-- vector calculation has following error
|
-- vector calculation has following error
|
-- 3N*ME for abs
|
-- 3N*ME for abs
|
-- N*ME for squaring
|
-- N*ME for squaring
|
-- N*ME for division
|
-- N*ME for division
|
-- (N-1)ME for sum
|
-- (N-1)ME for sum
|
-- this results in [2 + 3 + 2(6N-1) ] * ME
|
-- this results in [2 + 3 + 2(6N-1) ] * ME
|
-- or (12N + 3)ME
|
-- or (12N + 3)ME
|
Check (Two_Norm (V), 5.0 * Sqrt (Real(Vector_Length)),
|
Check (Two_Norm (V), 5.0 * Sqrt (Real(Vector_Length)),
|
"two_norm ((3,4))",
|
"two_norm ((3,4))",
|
(12.0 * Real (Vector_Length) + 3.0),
|
(12.0 * Real (Vector_Length) + 3.0),
|
Vector_Length);
|
Vector_Length);
|
exception
|
exception
|
when others => Report.Failed ("exception for complex " &
|
when others => Report.Failed ("exception for complex " &
|
"vector length" &
|
"vector length" &
|
Integer'Image (Vector_Length) );
|
Integer'Image (Vector_Length) );
|
end;
|
end;
|
end loop;
|
end loop;
|
end Do_Test;
|
end Do_Test;
|
end Generic_Complex_Norm_Check;
|
end Generic_Complex_Norm_Check;
|
|
|
--=====================================================================
|
--=====================================================================
|
|
|
generic
|
generic
|
type Real is digits <>;
|
type Real is digits <>;
|
package Generic_Norm_Check is
|
package Generic_Norm_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Generic_Norm_Check;
|
end Generic_Norm_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
package body Generic_Norm_Check is
|
package body Generic_Norm_Check is
|
package RNC is new Generic_Real_Norm_Check (Real);
|
package RNC is new Generic_Real_Norm_Check (Real);
|
package CNC is new Generic_Complex_Norm_Check (Real);
|
package CNC is new Generic_Complex_Norm_Check (Real);
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
RNC.Do_Test;
|
RNC.Do_Test;
|
CNC.Do_Test;
|
CNC.Do_Test;
|
end Do_Test;
|
end Do_Test;
|
end Generic_Norm_Check;
|
end Generic_Norm_Check;
|
|
|
--=====================================================================
|
--=====================================================================
|
|
|
package Float_Check is new Generic_Norm_Check (Float);
|
package Float_Check is new Generic_Norm_Check (Float);
|
|
|
type A_Long_Float is digits System.Max_Digits;
|
type A_Long_Float is digits System.Max_Digits;
|
package A_Long_Float_Check is new Generic_Norm_Check (A_Long_Float);
|
package A_Long_Float_Check is new Generic_Norm_Check (A_Long_Float);
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
begin
|
begin
|
Report.Test ("CXG2009",
|
Report.Test ("CXG2009",
|
"Check the accuracy of the real sqrt and complex " &
|
"Check the accuracy of the real sqrt and complex " &
|
" modulus functions");
|
" modulus functions");
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking Standard.Float");
|
Report.Comment ("checking Standard.Float");
|
end if;
|
end if;
|
|
|
Float_Check.Do_Test;
|
Float_Check.Do_Test;
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking a digits" &
|
Report.Comment ("checking a digits" &
|
Integer'Image (System.Max_Digits) &
|
Integer'Image (System.Max_Digits) &
|
" floating point type");
|
" floating point type");
|
end if;
|
end if;
|
|
|
A_Long_Float_Check.Do_Test;
|
A_Long_Float_Check.Do_Test;
|
|
|
Report.Result;
|
Report.Result;
|
end CXG2009;
|
end CXG2009;
|
|
|
