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-- CXG2012.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 exponentiation operator returns
-- results that are within the error bound allowed.
--
-- TEST DESCRIPTION:
-- This test consists of a generic package that is
-- instantiated to check 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 checks.
-- While this test concentrates on the "**" operator
-- defined in Generic_Elementary_Functions, a check is also
-- performed on the standard "**" operator.
--
-- 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:
-- 7 Mar 96 SAIC Initial release for 2.1
-- 2 Sep 96 SAIC Improvements as suggested by reviewers
-- 3 Jun 98 EDS Add parens to ensure that the expression is not
-- evaluated by multiplying its two large terms
-- together and overflowing.
-- 3 Dec 01 RLB Added 'Machine to insure that equality tests
-- are certain to work.
--
--!
--
-- References:
--
-- Software Manual for the Elementary Functions
-- William J. Cody, Jr. and William Waite
-- Prentice-Hall, 1980
--
-- CRC Standard Mathematical Tables
-- 23rd Edition
--
-- Implementation and Testing of Function Software
-- W. J. Cody
-- Problems and Methodologies in Mathematical Software Production
-- editors P. C. Messina and A. Murli
-- Lecture Notes in Computer Science Volume 142
-- Springer Verlag, 1982
--
with System;
with Report;
with Ada.Numerics.Generic_Elementary_Functions;
procedure CXG2012 is
Verbose : constant Boolean := False;
Max_Samples : constant := 1000;
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
Sqrt2 : constant :=
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
Sqrt3 : constant :=
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
generic
type Real is digits <>;
package Generic_Check is
procedure Do_Test;
end Generic_Check;
package body Generic_Check is
package Elementary_Functions is new
Ada.Numerics.Generic_Elementary_Functions (Real);
function Sqrt (X : Real) return Real renames
Elementary_Functions.Sqrt;
function Exp (X : Real) return Real renames
Elementary_Functions.Exp;
function Log (X : Real) return Real renames
Elementary_Functions.Log;
function "**" (L, R : Real) return Real renames
Elementary_Functions."**";
-- 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_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
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;
-- the following version of Check computes the allowed error bound
-- using the operands
procedure Check (Actual, Expected : Real;
Left, Right : Real;
Test_Name : String;
MRE_Factor : Real := 1.0) is
MRE : Real;
begin
MRE := MRE_Factor * (4.0 + abs (Right * Log(Left)) / 32.0);
Check (Actual, Expected, Test_Name, MRE);
end Check;
procedure Real_To_Integer_Test is
type Int_Check is
record
Left : Real;
Right : Integer;
Expected : Real;
end record;
type Int_Checks is array (Positive range <>) of Int_Check;
-- the following tests use only model numbers so the result
-- is expected to be exact.
IC : constant Int_Checks :=
( ( 2.0, 5, 32.0),
( -2.0, 5, -32.0),
( 0.5, -5, 32.0),
( 2.0, 0, 1.0),
( 0.0, 0, 1.0) );
begin
for I in IC'Range loop
declare
Y : Real;
begin
Y := IC (I).Left ** IC (I).Right;
Check (Y, IC (I).Expected,
"real to integer test" &
Real'Image (IC (I).Left) & " ** " &
Integer'Image (IC (I).Right),
0.0); -- no error allowed
exception
when Constraint_Error =>
Report.Failed ("Constraint_Error raised in rtoi test " &
Integer'Image (I));
when others =>
Report.Failed ("exception in rtoi test " &
Integer'Image (I));
end;
end loop;
end Real_To_Integer_Test;
procedure Special_Value_Test is
No_Error : constant := 0.0;
begin
Check (0.0 ** 1.0, 0.0, "0**1", No_Error);
Check (1.0 ** 0.0, 1.0, "1**0", No_Error);
Check ( 2.0 ** 5.0, 32.0, 2.0, 5.0, "2**5");
Check ( 0.5**(-5.0), 32.0, 0.5, -5.0, "0.5**-5");
Check (Sqrt2 ** 4.0, 4.0, Sqrt2, 4.0, "Sqrt2**4");
Check (Sqrt3 ** 6.0, 27.0, Sqrt3, 6.0, "Sqrt3**6");
Check (2.0 ** 0.5, Sqrt2, 2.0, 0.5, "2.0**0.5");
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 Small_Range_Test is
-- Several checks over the range 1/radix .. 1
A : constant Real := 1.0 / Real (Real'Machine_Radix);
B : constant Real := 1.0;
X : Real;
-- In the cases below where the expected result is
-- inexact we allow an additional error amount of
-- 1.0 * Model_Epsilon to account for that error.
-- This is accomplished by the factor of 1.25 times
-- the computed error bound (which is > 4.0) thus
-- increasing the error bound by at least
-- 1.0 * Model_Epsilon
begin
Accuracy_Error_Reported := False; -- reset
for I in 0..Max_Samples loop
X := Real'Machine((B - A) * Real (I) / Real (Max_Samples) + A);
Check (X ** 1.0, X, -- exact result required
"Small range" & Integer'Image (I) & ": " &
Real'Image (X) & " ** 1.0",
0.0);
Check ((X*X) ** 1.5, X**3, X*X, 1.5,
"Small range" & Integer'Image (I) & ": " &
Real'Image (X*X) & " ** 1.5",
1.25);
Check (X ** 13.5, 1.0 / (X ** (-13.5)), X, 13.5,
"Small range" & Integer'Image (I) & ": " &
Real'Image (X) & " ** 13.5",
2.0); -- 2 ** computations
Check ((X*X) ** 1.25, X**(2.5), X*X, 1.25,
"Small range" & Integer'Image (I) & ": " &
Real'Image (X*X) & " ** 1.25",
2.0); -- 2 ** computations
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;
exception
when Constraint_Error =>
Report.Failed
("Constraint_Error raised in Small Range Test");
when others =>
Report.Failed ("exception in Small Range Test");
end Small_Range_Test;
procedure Large_Range_Test is
-- Check over the range A to B where A is 1.0 and
-- B is a large value.
A : constant Real := 1.0;
B : Real;
X : Real;
Iteration : Integer := 0;
Subtest : Character := 'X';
begin
-- upper bound of range should be as large as possible where
-- B**3 is still valid.
B := Real'Safe_Last ** 0.333;
Accuracy_Error_Reported := False; -- reset
for I in 0..Max_Samples loop
Iteration := I;
Subtest := 'X';
X := Real'Machine((B - A) * (Real (I) / Real (Max_Samples)) + A);
Subtest := 'A';
Check (X ** 1.0, X, -- exact result required
"Large range" & Integer'Image (I) & ": " &
Real'Image (X) & " ** 1.0",
0.0);
Subtest := 'B';
Check ((X*X) ** 1.5, X**3, X*X, 1.5,
"Large range" & Integer'Image (I) & ": " &
Real'Image (X*X) & " ** 1.5",
1.25); -- inexact expected result
Subtest := 'C';
Check ((X*X) ** 1.25, X**(2.5), X*X, 1.25,
"Large range" & Integer'Image (I) & ": " &
Real'Image (X*X) & " ** 1.25",
2.0); -- two ** operators
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;
exception
when Constraint_Error =>
Report.Failed
("Constraint_Error raised in Large Range Test" &
Integer'Image (Iteration) & Subtest);
when others =>
Report.Failed ("exception in Large Range Test" &
Integer'Image (Iteration) & Subtest);
end Large_Range_Test;
procedure Exception_Test is
X1, X2, X3, X4 : Real;
begin
begin
X1 := 0.0 ** (-1.0);
Report.Failed ("exception not raised for 0**-1");
exception
when Ada.Numerics.Argument_Error =>
Report.Failed ("argument_error raised instead of" &
" constraint_error for 0**-1");
when Constraint_Error => null; -- ok
when others =>
Report.Failed ("wrong exception raised for 0**-1");
end;
begin
X2 := 0.0 ** 0.0;
Report.Failed ("exception not raised for 0**0");
exception
when Ada.Numerics.Argument_Error => null; -- ok
when Constraint_Error =>
Report.Failed ("constraint_error raised instead of" &
" argument_error for 0**0");
when others =>
Report.Failed ("wrong exception raised for 0**0");
end;
begin
X3 := (-1.0) ** 1.0;
Report.Failed ("exception not raised for -1**1");
exception
when Ada.Numerics.Argument_Error => null; -- ok
when Constraint_Error =>
Report.Failed ("constraint_error raised instead of" &
" argument_error for -1**1");
when others =>
Report.Failed ("wrong exception raised for -1**1");
end;
begin
X4 := (-2.0) ** 2.0;
Report.Failed ("exception not raised for -2**2");
exception
when Ada.Numerics.Argument_Error => null; -- ok
when Constraint_Error =>
Report.Failed ("constraint_error raised instead of" &
" argument_error for -2**2");
when others =>
Report.Failed ("wrong exception raised for -2**2");
end;
-- optimizer thwarting
if Report.Ident_Bool (False) then
Report.Comment (Real'Image (X1+X2+X3+X4));
end if;
end Exception_Test;
procedure Do_Test is
begin
Real_To_Integer_Test;
Special_Value_Test;
Small_Range_Test;
Large_Range_Test;
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 ("CXG2012",
"Check the accuracy of the ** operator");
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 CXG2012;
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