-- CXG2019.A
|
-- CXG2019.A
|
--
|
--
|
-- Grant of Unlimited Rights
|
-- Grant of Unlimited Rights
|
--
|
--
|
-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
|
-- 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
|
-- 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 in the software and documentation contained herein.
|
-- 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
|
-- recipients unlimited rights equal to those held by the Government.
|
-- recipients unlimited rights equal to those held by the Government.
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- released technical data and computer software in whole or in part, in
|
-- 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
|
-- any manner and for any purpose whatsoever, and to have or permit others
|
-- to do so.
|
-- to do so.
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--
|
--
|
-- DISCLAIMER
|
-- DISCLAIMER
|
--
|
--
|
-- 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.
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
|
--*
|
--*
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--
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--
|
-- OBJECTIVE:
|
-- OBJECTIVE:
|
-- Check that the complex LOG function returns
|
-- Check that the complex LOG function returns
|
-- a result that is within the error bound allowed.
|
-- a result that is within the error bound allowed.
|
--
|
--
|
-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test consists of a generic package that is
|
-- This test consists of a generic package that is
|
-- instantiated to check complex numbers based upon
|
-- instantiated to check complex numbers based upon
|
-- both Float and a long float type.
|
-- both Float and a long float type.
|
-- The test for each floating point type is divided into
|
-- The test for each floating point type is divided into
|
-- several parts:
|
-- several parts:
|
-- Special value checks where the result is a known constant.
|
-- Special value checks where the result is a known constant.
|
-- Checks that use an identity for determining the result.
|
-- Checks that use an identity for determining the result.
|
-- Exception conditions.
|
-- Exception conditions.
|
--
|
--
|
-- SPECIAL REQUIREMENTS
|
-- SPECIAL REQUIREMENTS
|
-- The Strict Mode for the numerical accuracy must be
|
-- The Strict Mode for the numerical accuracy must be
|
-- selected. The method by which this mode is selected
|
-- selected. The method by which this mode is selected
|
-- is implementation dependent.
|
-- is implementation dependent.
|
--
|
--
|
-- APPLICABILITY CRITERIA:
|
-- APPLICABILITY CRITERIA:
|
-- This test applies only to implementations supporting the
|
-- This test applies only to implementations supporting the
|
-- 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.
|
-- accuracy.
|
--
|
--
|
--
|
--
|
-- CHANGE HISTORY:
|
-- CHANGE HISTORY:
|
-- 22 Mar 96 SAIC Initial release for 2.1
|
-- 22 Mar 96 SAIC Initial release for 2.1
|
--
|
--
|
--!
|
--!
|
|
|
--
|
--
|
-- References:
|
-- References:
|
--
|
--
|
-- W. J. Cody
|
-- W. J. Cody
|
-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
|
-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
|
-- Algorithm 714, Collected Algorithms from ACM.
|
-- Algorithm 714, Collected Algorithms from ACM.
|
-- Published in Transactions On Mathematical Software,
|
-- Published in Transactions On Mathematical Software,
|
-- Vol. 19, No. 1, March, 1993, pp. 1-21.
|
-- Vol. 19, No. 1, March, 1993, pp. 1-21.
|
--
|
--
|
-- CRC Standard Mathematical Tables
|
-- CRC Standard Mathematical Tables
|
-- 23rd Edition
|
-- 23rd Edition
|
--
|
--
|
|
|
with System;
|
with System;
|
with Report;
|
with Report;
|
with Ada.Numerics.Generic_Complex_Types;
|
with Ada.Numerics.Generic_Complex_Types;
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with Ada.Numerics.Generic_Complex_Elementary_Functions;
|
with Ada.Numerics.Generic_Complex_Elementary_Functions;
|
procedure CXG2019 is
|
procedure CXG2019 is
|
Verbose : constant Boolean := False;
|
Verbose : constant Boolean := False;
|
-- Note that Max_Samples is the number of samples taken in
|
-- Note that Max_Samples is the number of samples taken in
|
-- both the real and imaginary directions. Thus, for Max_Samples
|
-- both the real and imaginary directions. Thus, for Max_Samples
|
-- of 100 the number of values checked is 10000.
|
-- of 100 the number of values checked is 10000.
|
Max_Samples : constant := 100;
|
Max_Samples : constant := 100;
|
|
|
E : constant := Ada.Numerics.E;
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E : constant := Ada.Numerics.E;
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Pi : constant := Ada.Numerics.Pi;
|
Pi : constant := Ada.Numerics.Pi;
|
|
|
generic
|
generic
|
type Real is digits <>;
|
type Real is digits <>;
|
package Generic_Check is
|
package Generic_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Generic_Check;
|
end Generic_Check;
|
|
|
package body Generic_Check is
|
package body Generic_Check is
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package Complex_Type is new
|
package Complex_Type is new
|
Ada.Numerics.Generic_Complex_Types (Real);
|
Ada.Numerics.Generic_Complex_Types (Real);
|
use Complex_Type;
|
use Complex_Type;
|
|
|
package CEF is new
|
package CEF is new
|
Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
|
Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
|
|
|
function Log (X : Complex) return Complex renames CEF.Log;
|
function Log (X : Complex) return Complex renames CEF.Log;
|
|
|
-- flag used to terminate some tests early
|
-- flag used to terminate some tests early
|
Accuracy_Error_Reported : Boolean := False;
|
Accuracy_Error_Reported : Boolean := False;
|
|
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
Max_Error : Real;
|
Max_Error : Real;
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_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_Small instead
|
-- we compute the maximum error as a multiple of Model_Small 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
|
Accuracy_Error_Reported := True;
|
Accuracy_Error_Reported := True;
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " & Real'Image (Actual - Expected) &
|
" difference: " & Real'Image (Actual - Expected) &
|
" max err:" & Real'Image (Max_Error) );
|
" max err:" & Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
if Actual = Expected then
|
if Actual = Expected then
|
Report.Comment (Test_Name & " exact result");
|
Report.Comment (Test_Name & " exact result");
|
else
|
else
|
Report.Comment (Test_Name & " passed");
|
Report.Comment (Test_Name & " passed");
|
end if;
|
end if;
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Check (Actual, Expected : Complex;
|
procedure Check (Actual, Expected : Complex;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
begin
|
begin
|
Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
|
Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
|
Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
|
Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
|
end Check;
|
end Check;
|
|
|
|
|
procedure Special_Value_Test is
|
procedure Special_Value_Test is
|
-- In the following tests the expected result is accurate
|
-- In the following tests the expected result is accurate
|
-- to the machine precision so the minimum guaranteed error
|
-- to the machine precision so the minimum guaranteed error
|
-- bound can be used if the argument is exact.
|
-- bound can be used if the argument is exact.
|
--
|
--
|
-- When using pi there is an extra error of 1.0ME.
|
-- When using pi there is an extra error of 1.0ME.
|
-- Although the real component has an error bound of 13.0,
|
-- Although the real component has an error bound of 13.0,
|
-- the complex component must take into account this error
|
-- the complex component must take into account this error
|
-- in the value for Pi.
|
-- in the value for Pi.
|
--
|
--
|
-- One or i is added to the actual and expected results in
|
-- One or i is added to the actual and expected results in
|
-- order to prevent the expected result from having a
|
-- order to prevent the expected result from having a
|
-- real or imaginary part of 0. This is to allow a reasonable
|
-- real or imaginary part of 0. This is to allow a reasonable
|
-- relative error for that component.
|
-- relative error for that component.
|
Minimum_Error : constant := 13.0;
|
Minimum_Error : constant := 13.0;
|
begin
|
begin
|
Check (1.0 + Log (0.0 + i),
|
Check (1.0 + Log (0.0 + i),
|
1.0 + Pi / 2.0 * i,
|
1.0 + Pi / 2.0 * i,
|
"1+log(0+i)",
|
"1+log(0+i)",
|
Minimum_Error + 1.0);
|
Minimum_Error + 1.0);
|
Check (1.0 + Log ((-1.0, 0.0)),
|
Check (1.0 + Log ((-1.0, 0.0)),
|
1.0 + (Pi * i),
|
1.0 + (Pi * i),
|
"log(-1+0i)+1 ",
|
"log(-1+0i)+1 ",
|
Minimum_Error + 1.0);
|
Minimum_Error + 1.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in special value test");
|
Report.Failed ("Constraint_Error raised in special value test");
|
when others =>
|
when others =>
|
Report.Failed ("exception in special value test");
|
Report.Failed ("exception in special value test");
|
end Special_Value_Test;
|
end Special_Value_Test;
|
|
|
|
|
|
|
procedure Exact_Result_Test is
|
procedure Exact_Result_Test is
|
No_Error : constant := 0.0;
|
No_Error : constant := 0.0;
|
begin
|
begin
|
-- G.1.2(37);6.0
|
-- G.1.2(37);6.0
|
Check (Log(1.0 + 0.0*i), 0.0 + 0.0 * i, "log(1+0i)", No_Error);
|
Check (Log(1.0 + 0.0*i), 0.0 + 0.0 * i, "log(1+0i)", No_Error);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in Exact_Result Test");
|
Report.Failed ("Constraint_Error raised in Exact_Result Test");
|
when others =>
|
when others =>
|
Report.Failed ("exception in Exact_Result Test");
|
Report.Failed ("exception in Exact_Result Test");
|
end Exact_Result_Test;
|
end Exact_Result_Test;
|
|
|
|
|
procedure Identity_Test (RA, RB, IA, IB : Real) is
|
procedure Identity_Test (RA, RB, IA, IB : Real) is
|
-- Tests an identity over a range of values specified
|
-- Tests an identity over a range of values specified
|
-- by the 4 parameters. RA and RB denote the range for the
|
-- by the 4 parameters. RA and RB denote the range for the
|
-- real part while IA and IB denote the range for the
|
-- real part while IA and IB denote the range for the
|
-- imaginary part.
|
-- imaginary part.
|
--
|
--
|
-- For this test we use the identity
|
-- For this test we use the identity
|
-- Log(Z*Z) = 2 * Log(Z)
|
-- Log(Z*Z) = 2 * Log(Z)
|
--
|
--
|
|
|
Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);
|
Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);
|
W, X, Y, Z : Real;
|
W, X, Y, Z : Real;
|
CX, CY : Complex;
|
CX, CY : Complex;
|
Actual1, Actual2 : Complex;
|
Actual1, Actual2 : Complex;
|
begin
|
begin
|
Accuracy_Error_Reported := False; -- reset
|
Accuracy_Error_Reported := False; -- reset
|
for II in 1..Max_Samples loop
|
for II in 1..Max_Samples loop
|
X := (RB - RA) * Real (II) / Real (Max_Samples) + RA;
|
X := (RB - RA) * Real (II) / Real (Max_Samples) + RA;
|
for J in 1..Max_Samples loop
|
for J in 1..Max_Samples loop
|
Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA;
|
Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA;
|
|
|
-- purify the arguments to minimize roundoff error.
|
-- purify the arguments to minimize roundoff error.
|
-- We construct the values so that the products X*X,
|
-- We construct the values so that the products X*X,
|
-- Y*Y, and X*Y are all exact machine numbers.
|
-- Y*Y, and X*Y are all exact machine numbers.
|
-- See Cody page 7 and CELEFUNT code.
|
-- See Cody page 7 and CELEFUNT code.
|
Z := X * Scale;
|
Z := X * Scale;
|
W := Z + X;
|
W := Z + X;
|
X := W - Z;
|
X := W - Z;
|
Z := Y * Scale;
|
Z := Y * Scale;
|
W := Z + Y;
|
W := Z + Y;
|
Y := W - Z;
|
Y := W - Z;
|
CX := Compose_From_Cartesian(X,Y);
|
CX := Compose_From_Cartesian(X,Y);
|
Z := X*X - Y*Y;
|
Z := X*X - Y*Y;
|
W := X*Y;
|
W := X*Y;
|
CY := Compose_From_Cartesian(Z,W+W);
|
CY := Compose_From_Cartesian(Z,W+W);
|
|
|
-- The arguments are now ready so on with the
|
-- The arguments are now ready so on with the
|
-- identity computation.
|
-- identity computation.
|
Actual1 := Log(CX);
|
Actual1 := Log(CX);
|
|
|
Actual2 := Log(CY) * 0.5;
|
Actual2 := Log(CY) * 0.5;
|
|
|
Check (Actual1, Actual2,
|
Check (Actual1, Actual2,
|
"Identity_1_Test " & Integer'Image (II) &
|
"Identity_1_Test " & Integer'Image (II) &
|
Integer'Image (J) & ": Log((" &
|
Integer'Image (J) & ": Log((" &
|
Real'Image (CX.Re) & ", " &
|
Real'Image (CX.Re) & ", " &
|
Real'Image (CX.Im) & ")) ",
|
Real'Image (CX.Im) & ")) ",
|
26.0); -- 2 logs = 2*13. no error from this multiply
|
26.0); -- 2 logs = 2*13. no error from this multiply
|
|
|
if Accuracy_Error_Reported then
|
if Accuracy_Error_Reported then
|
-- only report the first error in this test in order to keep
|
-- only report the first error in this test in order to keep
|
-- lots of failures from producing a huge error log
|
-- lots of failures from producing a huge error log
|
return;
|
return;
|
end if;
|
end if;
|
end loop;
|
end loop;
|
end loop;
|
end loop;
|
|
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in Identity_Test" &
|
("Constraint_Error raised in Identity_Test" &
|
" for X=(" & Real'Image (X) &
|
" for X=(" & Real'Image (X) &
|
", " & Real'Image (X) & ")");
|
", " & Real'Image (X) & ")");
|
when others =>
|
when others =>
|
Report.Failed ("exception in Identity_Test" &
|
Report.Failed ("exception in Identity_Test" &
|
" for X=(" & Real'Image (X) &
|
" for X=(" & Real'Image (X) &
|
", " & Real'Image (X) & ")");
|
", " & Real'Image (X) & ")");
|
end Identity_Test;
|
end Identity_Test;
|
|
|
|
|
procedure Exception_Test is
|
procedure Exception_Test is
|
-- Check that log((0,0)) causes constraint_error.
|
-- Check that log((0,0)) causes constraint_error.
|
-- G.1.2(29);
|
-- G.1.2(29);
|
|
|
X : Complex := (0.0, 0.0);
|
X : Complex := (0.0, 0.0);
|
begin
|
begin
|
if not Real'Machine_Overflows then
|
if not Real'Machine_Overflows then
|
-- not applicable: G.1.2(28);6.0
|
-- not applicable: G.1.2(28);6.0
|
return;
|
return;
|
end if;
|
end if;
|
|
|
begin
|
begin
|
X := Log ((0.0, 0.0));
|
X := Log ((0.0, 0.0));
|
Report.Failed ("exception not raised for log(0,0)");
|
Report.Failed ("exception not raised for log(0,0)");
|
exception
|
exception
|
when Constraint_Error => null; -- ok
|
when Constraint_Error => null; -- ok
|
when others =>
|
when others =>
|
Report.Failed ("wrong exception raised for log(0,0)");
|
Report.Failed ("wrong exception raised for log(0,0)");
|
end;
|
end;
|
|
|
-- optimizer thwarting
|
-- optimizer thwarting
|
if Report.Ident_Bool(False) then
|
if Report.Ident_Bool(False) then
|
Report.Comment (Real'Image (X.Re + X.Im));
|
Report.Comment (Real'Image (X.Re + X.Im));
|
end if;
|
end if;
|
end Exception_Test;
|
end Exception_Test;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
Special_Value_Test;
|
Special_Value_Test;
|
Exact_Result_Test;
|
Exact_Result_Test;
|
-- test regions that do not include the unit circle so that
|
-- test regions that do not include the unit circle so that
|
-- the real part of LOG(Z) does not vanish
|
-- the real part of LOG(Z) does not vanish
|
-- See Cody page 9.
|
-- See Cody page 9.
|
Identity_Test ( 2.0, 10.0, 0.0, 10.0);
|
Identity_Test ( 2.0, 10.0, 0.0, 10.0);
|
Identity_Test (1000.0, 2000.0, -4000.0, -1000.0);
|
Identity_Test (1000.0, 2000.0, -4000.0, -1000.0);
|
Identity_Test (Real'Model_Epsilon, 0.25,
|
Identity_Test (Real'Model_Epsilon, 0.25,
|
-0.25, -Real'Model_Epsilon);
|
-0.25, -Real'Model_Epsilon);
|
Exception_Test;
|
Exception_Test;
|
end Do_Test;
|
end Do_Test;
|
end Generic_Check;
|
end Generic_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
package Float_Check is new Generic_Check (Float);
|
package Float_Check is new Generic_Check (Float);
|
|
|
-- check the floating point type with the most digits
|
-- check the floating point type with the most digits
|
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_Check (A_Long_Float);
|
package A_Long_Float_Check is new Generic_Check (A_Long_Float);
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
|
|
begin
|
begin
|
Report.Test ("CXG2019",
|
Report.Test ("CXG2019",
|
"Check the accuracy of the complex LOG function");
|
"Check the accuracy of the complex LOG function");
|
|
|
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 CXG2019;
|
end CXG2019;
|
|
|
