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-- CXG2014.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 SINH and COSH functions return
-- 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.
--
-- 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:
-- 15 Mar 96 SAIC Initial release for 2.1
-- 03 Jun 98 EDS In line 80, change 1000 to 1024, making it a model
-- number. Add Taylor Series terms in line 281.
-- 15 Feb 99 RLB Repaired Subtraction_Error_Test to avoid precision
-- problems.
--!
--
-- 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 CXG2014 is
Verbose : constant Boolean := False;
Max_Samples : constant := 1024;
E : constant := Ada.Numerics.E;
Cosh1 : constant := (E + 1.0 / E) / 2.0; -- cosh(1.0)
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 Sinh (X : Real) return Real renames
Elementary_Functions.Sinh;
function Cosh (X : Real) return Real renames
Elementary_Functions.Cosh;
function Log (X : Real) return Real renames
Elementary_Functions.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_Small;
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 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.
Minimum_Error : constant := 8.0;
begin
Check (Sinh (1.0),
(E - 1.0 / E) / 2.0,
"sinh(1)",
Minimum_Error);
Check (Cosh (1.0),
Cosh1,
"cosh(1)",
Minimum_Error);
Check (Sinh (2.0),
(E * E - (1.0 / (E * E))) / 2.0,
"sinh(2)",
Minimum_Error);
Check (Cosh (2.0),
(E * E + (1.0 / (E * E))) / 2.0,
"cosh(2)",
Minimum_Error);
Check (Sinh (-1.0),
(1.0 / E - E) / 2.0,
"sinh(-1)",
Minimum_Error);
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
-- A.5.1(38);6.0
Check (Sinh (0.0), 0.0, "sinh(0)", No_Error);
Check (Cosh (0.0), 1.0, "cosh(0)", 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_1_Test is
-- For the Sinh test use the identity
-- 2 * Sinh(x) * Cosh(1) = Sinh(x+1) + Sinh (x-1)
-- which is transformed to
-- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
-- where C = 1/(2*Cosh(1))
--
-- For the Cosh test use the identity
-- 2 * Cosh(x) * Cosh(1) = Cosh(x+1) + Cosh(x-1)
-- which is transformed to
-- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
-- where C is the same as above
--
-- see Cody pg 230-231 for details on the error analysis.
-- The net result is a relative error bound of 16 * Model_Epsilon.
A : constant := 3.0;
-- large upper bound but not so large as to cause Cosh(B)
-- to overflow
B : constant Real := Log(Real'Safe_Last) - 2.0;
X_Minus_1, X, X_Plus_1 : Real;
Actual1, Actual2 : Real;
C : constant := 1.0 / (2.0 * Cosh1);
begin
Accuracy_Error_Reported := False; -- reset
for I in 1..Max_Samples loop
-- make sure there is no error in x-1, x, and x+1
X_Plus_1 := (B - A) * Real (I) / Real (Max_Samples) + A;
X_Plus_1 := Real'Machine (X_Plus_1);
X := Real'Machine (X_Plus_1 - 1.0);
X_Minus_1 := Real'Machine (X - 1.0);
-- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
Actual1 := Sinh(X);
Actual2 := C * (Sinh(X_Plus_1) + Sinh(X_Minus_1));
Check (Actual1, Actual2,
"Identity_1_Test " & Integer'Image (I) & ": sinh(" &
Real'Image (X) & ") ",
16.0);
-- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
Actual1 := Cosh (X);
Actual2 := C * (Cosh(X_Plus_1) + Cosh (X_Minus_1));
Check (Actual1, Actual2,
"Identity_1_Test " & Integer'Image (I) & ": cosh(" &
Real'Image (X) & ") ",
16.0);
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 Identity_1_Test" &
" for X=" & Real'Image (X));
when others =>
Report.Failed ("exception in Identity_1_Test" &
" for X=" & Real'Image (X));
end Identity_1_Test;
procedure Subtraction_Error_Test is
-- This test detects the error resulting from subtraction if
-- the obvious algorithm was used for computing sinh. That is,
-- it it is computed as (e**x - e**-x)/2.
-- We check the result by using a Taylor series expansion that
-- will produce a result accurate to the machine precision for
-- the range under test.
--
-- The maximum relative error bound for this test is
-- 8 for the sinh operation and 7 for the Taylor series
-- for a total of 15 * Model_Epsilon
A : constant := 0.0;
B : constant := 0.5;
X : Real;
X_Squared : Real;
Actual, Expected : Real;
begin
if Real'digits > 15 then
return; -- The approximation below is not accurate beyond
-- 15 digits. Adding more terms makes the error
-- larger, so it makes the test worse for more normal
-- values. Thus, we skip this subtest for larger than
-- 15 digits.
end if;
Accuracy_Error_Reported := False; -- reset
for I in 1..Max_Samples loop
X := (B - A) * Real (I) / Real (Max_Samples) + A;
X_Squared := X * X;
Actual := Sinh(X);
-- The Taylor series regrouped a bit
Expected :=
X * (1.0 + (X_Squared / 6.0) *
(1.0 + (X_Squared/20.0) *
(1.0 + (X_Squared/42.0) *
(1.0 + (X_Squared/72.0) *
(1.0 + (X_Squared/110.0) *
(1.0 + (X_Squared/156.0)
))))));
Check (Actual, Expected,
"Subtraction_Error_Test " & Integer'Image (I) & ": sinh(" &
Real'Image (X) & ") ",
15.0);
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 Subtraction_Error_Test");
when others =>
Report.Failed ("exception in Subtraction_Error_Test");
end Subtraction_Error_Test;
procedure Exception_Test is
X1, X2 : Real := 0.0;
begin
-- this part of the test is only applicable if 'Machine_Overflows
-- is true.
if Real'Machine_Overflows then
begin
X1 := Sinh (Real'Safe_Last / 2.0);
Report.Failed ("no exception for sinh overflow");
exception
when Constraint_Error => null;
when others =>
Report.Failed ("wrong exception sinh overflow");
end;
begin
X2 := Cosh (Real'Safe_Last / 2.0);
Report.Failed ("no exception for cosh overflow");
exception
when Constraint_Error => null;
when others =>
Report.Failed ("wrong exception cosh overflow");
end;
end if;
-- optimizer thwarting
if Report.Ident_Bool (False) then
Report.Comment (Real'Image (X1 + X2));
end if;
end Exception_Test;
procedure Do_Test is
begin
Special_Value_Test;
Exact_Result_Test;
Identity_1_Test;
Subtraction_Error_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 ("CXG2014",
"Check the accuracy of the SINH and COSH 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 CXG2014;