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-- CXG2005.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 floating point addition and multiplication
-- have the required accuracy.
--
-- TEST DESCRIPTION:
-- The check for the required precision is essentially a
-- check that a guard digit is used for the operations.
-- This test uses a generic package to check the addition
-- and multiplication results. The
-- generic package is instantiated with the standard FLOAT
-- type and a floating point type for the maximum number
-- of digits of precision.
--
-- APPLICABILITY CRITERIA:
-- This test applies only to implementations supporting the
-- Numerics Annex.
--
--
-- CHANGE HISTORY:
-- 14 FEB 96 SAIC Initial Release for 2.1
-- 16 SEP 99 RLB Repaired to avoid printing thousands of (almost)
-- identical failure messages.
--!
-- References:
--
-- Basic Concepts for Computational Software
-- W. J. Cody
-- Problems and Methodologies in Mathematical Software Production
-- editors P. C. Messina and A. Murli
-- Lecture Notes in Computer Science Vol 142
-- Springer Verlag, 1982
--
-- Software Manual for the Elementary Functions
-- William J. Cody and William Waite
-- Prentice-Hall, 1980
--
with System;
with Report;
procedure CXG2005 is
Verbose : constant Boolean := False;
generic
type Real is digits <>;
package Guard_Digit_Check is
procedure Do_Test;
end Guard_Digit_Check;
package body Guard_Digit_Check is
-- made global so that the compiler will be more likely
-- to keep the values in memory instead of in higher
-- precision registers.
X, Y, Z : Real;
OneX : Real;
Eps, BN : Real;
-- special constants - not declared as constants so that
-- the "stored" precision will be used instead of a "register"
-- precision.
Zero : Real := 0.0;
One : Real := 1.0;
Two : Real := 2.0;
Failure_Count : Natural := 0;
procedure Thwart_Optimization is
-- the purpose of this procedure is to reference the
-- global variables used by the test so
-- that the compiler is not likely to keep them in
-- a higher precision register for their entire lifetime.
begin
if Report.Ident_Bool (False) then
-- never executed
X := X + 5.0;
Y := Y + 6.0;
Z := Z + 1.0;
Eps := Eps + 2.0;
BN := BN + 2.0;
OneX := X + Y;
One := 12.34; Two := 56.78; Zero := 90.12;
end if;
end Thwart_Optimization;
procedure Addition_Test is
begin
for K in 1..10 loop
Eps := Real (K) * Real'Model_Epsilon;
for N in 1.. Real'Machine_EMax - 1 loop
BN := Real(Real'Machine_Radix) ** N;
X := (One + Eps) * BN;
Y := (One - Eps) * BN;
Z := X - Y; -- true value for Z is 2*Eps*BN
if Z /= Eps*BN + Eps*BN then
Report.Failed ("addition check failed. K=" &
Integer'Image (K) &
" N=" & Integer'Image (N) &
" difference=" & Real'Image (Z - 2.0*Eps*BN) &
" Eps*BN=" & Real'Image (Eps*BN) );
Failure_Count := Failure_Count + 1;
exit when Failure_Count > K*4; -- Avoid displaying dozens of messages.
end if;
end loop;
end loop;
exception
when others =>
Thwart_Optimization;
Report.Failed ("unexpected exception in addition test");
end Addition_Test;
procedure Multiplication_Test is
begin
X := Real (Real'Machine_Radix) ** (Real'Machine_EMax - 1);
OneX := One * X;
Thwart_Optimization;
if OneX /= X then
Report.Failed ("multiplication for large values");
end if;
X := Real (Real'Machine_Radix) ** (Real'Model_EMin + 1);
OneX := One * X;
Thwart_Optimization;
if OneX /= X then
Report.Failed ("multiplication for small values");
end if;
-- selection of "random" values between 1/radix and radix
Y := One / Real (Real'Machine_Radix);
Z := Real(Real'Machine_Radix) - One/Real(Real'Machine_Radix);
for I in 0..100 loop
X := Y + Real (I) / 100.0 * Z;
OneX := One * X;
Thwart_Optimization;
if OneX /= X then
Report.Failed ("multiplication for case" & Integer'Image (I));
exit when Failure_Count > 40+8; -- Avoid displaying dozens of messages.
end if;
end loop;
exception
when others =>
Thwart_Optimization;
Report.Failed ("unexpected exception in multiplication test");
end Multiplication_Test;
procedure Do_Test is
begin
Addition_Test;
Multiplication_Test;
end Do_Test;
end Guard_Digit_Check;
package Chk_Float is new Guard_Digit_Check (Float);
-- check the floating point type with the most digits
type A_Long_Float is digits System.Max_Digits;
package Chk_A_Long_Float is new Guard_Digit_Check (A_Long_Float);
begin
Report.Test ("CXG2005",
"Check the accuracy of floating point" &
" addition and multiplication");
if Verbose then
Report.Comment ("checking Standard.Float");
end if;
Chk_Float.Do_Test;
if Verbose then
Report.Comment ("checking a digits" &
Integer'Image (System.Max_Digits) &
" floating point type");
end if;
Chk_A_Long_Float.Do_Test;
Report.Result;
end CXG2005;
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