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-- CXG2019.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 complex LOG function returns
-- a result that is within the error bound allowed.
--
-- TEST DESCRIPTION:
-- This test consists of a generic package that is
-- instantiated to check complex numbers based upon
-- both Float and a long float type.
-- The test for each floating point type is divided into
-- several parts:
-- Special value checks where the result is a known constant.
-- Checks that use an identity for determining the result.
-- Exception conditions.
--
-- 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:
-- 22 Mar 96 SAIC Initial release for 2.1
--
--!
--
-- References:
--
-- W. J. Cody
-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
-- Algorithm 714, Collected Algorithms from ACM.
-- Published in Transactions On Mathematical Software,
-- Vol. 19, No. 1, March, 1993, pp. 1-21.
--
-- CRC Standard Mathematical Tables
-- 23rd Edition
--
with System;
with Report;
with Ada.Numerics.Generic_Complex_Types;
with Ada.Numerics.Generic_Complex_Elementary_Functions;
procedure CXG2019 is
Verbose : constant Boolean := False;
-- Note that Max_Samples is the number of samples taken in
-- both the real and imaginary directions. Thus, for Max_Samples
-- of 100 the number of values checked is 10000.
Max_Samples : constant := 100;
E : constant := Ada.Numerics.E;
Pi : constant := Ada.Numerics.Pi;
generic
type Real is digits <>;
package Generic_Check is
procedure Do_Test;
end Generic_Check;
package body Generic_Check is
package Complex_Type is new
Ada.Numerics.Generic_Complex_Types (Real);
use Complex_Type;
package CEF is new
Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
function Log (X : Complex) return Complex renames CEF.Log;
-- flag used to terminate some tests early
Accuracy_Error_Reported : Boolean := False;
procedure Check (Actual, Expected : Real;
Test_Name : String;
MRE : Real) is
Max_Error : Real;
Rel_Error : Real;
Abs_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_Small 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
Accuracy_Error_Reported := True;
Report.Failed (Test_Name &
" actual: " & Real'Image (Actual) &
" expected: " & Real'Image (Expected) &
" difference: " & Real'Image (Actual - Expected) &
" max err:" & Real'Image (Max_Error) );
elsif Verbose then
if Actual = Expected then
Report.Comment (Test_Name & " exact result");
else
Report.Comment (Test_Name & " passed");
end if;
end if;
end Check;
procedure Check (Actual, Expected : Complex;
Test_Name : String;
MRE : Real) is
begin
Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
end Check;
procedure Special_Value_Test is
-- In the following tests the expected result is accurate
-- to the machine precision so the minimum guaranteed error
-- bound can be used if the argument is exact.
--
-- When using pi there is an extra error of 1.0ME.
-- Although the real component has an error bound of 13.0,
-- the complex component must take into account this error
-- in the value for Pi.
--
-- One or i is added to the actual and expected results in
-- order to prevent the expected result from having a
-- real or imaginary part of 0. This is to allow a reasonable
-- relative error for that component.
Minimum_Error : constant := 13.0;
begin
Check (1.0 + Log (0.0 + i),
1.0 + Pi / 2.0 * i,
"1+log(0+i)",
Minimum_Error + 1.0);
Check (1.0 + Log ((-1.0, 0.0)),
1.0 + (Pi * i),
"log(-1+0i)+1 ",
Minimum_Error + 1.0);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in special value test");
when others =>
Report.Failed ("exception in special value test");
end Special_Value_Test;
procedure Exact_Result_Test is
No_Error : constant := 0.0;
begin
-- G.1.2(37);6.0
Check (Log(1.0 + 0.0*i), 0.0 + 0.0 * i, "log(1+0i)", No_Error);
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in Exact_Result Test");
when others =>
Report.Failed ("exception in Exact_Result Test");
end Exact_Result_Test;
procedure Identity_Test (RA, RB, IA, IB : Real) is
-- Tests an identity over a range of values specified
-- by the 4 parameters. RA and RB denote the range for the
-- real part while IA and IB denote the range for the
-- imaginary part.
--
-- For this test we use the identity
-- Log(Z*Z) = 2 * Log(Z)
--
Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);
W, X, Y, Z : Real;
CX, CY : Complex;
Actual1, Actual2 : Complex;
begin
Accuracy_Error_Reported := False; -- reset
for II in 1..Max_Samples loop
X := (RB - RA) * Real (II) / Real (Max_Samples) + RA;
for J in 1..Max_Samples loop
Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA;
-- purify the arguments to minimize roundoff error.
-- We construct the values so that the products X*X,
-- Y*Y, and X*Y are all exact machine numbers.
-- See Cody page 7 and CELEFUNT code.
Z := X * Scale;
W := Z + X;
X := W - Z;
Z := Y * Scale;
W := Z + Y;
Y := W - Z;
CX := Compose_From_Cartesian(X,Y);
Z := X*X - Y*Y;
W := X*Y;
CY := Compose_From_Cartesian(Z,W+W);
-- The arguments are now ready so on with the
-- identity computation.
Actual1 := Log(CX);
Actual2 := Log(CY) * 0.5;
Check (Actual1, Actual2,
"Identity_1_Test " & Integer'Image (II) &
Integer'Image (J) & ": Log((" &
Real'Image (CX.Re) & ", " &
Real'Image (CX.Im) & ")) ",
26.0); -- 2 logs = 2*13. no error from this multiply
if Accuracy_Error_Reported then
-- only report the first error in this test in order to keep
-- lots of failures from producing a huge error log
return;
end if;
end loop;
end loop;
exception
when Constraint_Error =>
Report.Failed
("Constraint_Error raised in Identity_Test" &
" for X=(" & Real'Image (X) &
", " & Real'Image (X) & ")");
when others =>
Report.Failed ("exception in Identity_Test" &
" for X=(" & Real'Image (X) &
", " & Real'Image (X) & ")");
end Identity_Test;
procedure Exception_Test is
-- Check that log((0,0)) causes constraint_error.
-- G.1.2(29);
X : Complex := (0.0, 0.0);
begin
if not Real'Machine_Overflows then
-- not applicable: G.1.2(28);6.0
return;
end if;
begin
X := Log ((0.0, 0.0));
Report.Failed ("exception not raised for log(0,0)");
exception
when Constraint_Error => null; -- ok
when others =>
Report.Failed ("wrong exception raised for log(0,0)");
end;
-- optimizer thwarting
if Report.Ident_Bool(False) then
Report.Comment (Real'Image (X.Re + X.Im));
end if;
end Exception_Test;
procedure Do_Test is
begin
Special_Value_Test;
Exact_Result_Test;
-- test regions that do not include the unit circle so that
-- the real part of LOG(Z) does not vanish
-- See Cody page 9.
Identity_Test ( 2.0, 10.0, 0.0, 10.0);
Identity_Test (1000.0, 2000.0, -4000.0, -1000.0);
Identity_Test (Real'Model_Epsilon, 0.25,
-0.25, -Real'Model_Epsilon);
Exception_Test;
end Do_Test;
end Generic_Check;
-----------------------------------------------------------------------
-----------------------------------------------------------------------
package Float_Check is new Generic_Check (Float);
-- check the floating point type with the most digits
type A_Long_Float is digits System.Max_Digits;
package A_Long_Float_Check is new Generic_Check (A_Long_Float);
-----------------------------------------------------------------------
-----------------------------------------------------------------------
begin
Report.Test ("CXG2019",
"Check the accuracy of the complex LOG function");
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 CXG2019;
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