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