URL
https://opencores.org/ocsvn/openrisc_me/openrisc_me/trunk
Subversion Repositories openrisc_me
[/] [openrisc/] [trunk/] [gnu-src/] [gcc-4.5.1/] [gcc/] [testsuite/] [ada/] [acats/] [tests/] [cxg/] [cxg2018.a] - Rev 316
Go to most recent revision | Compare with Previous | Blame | View Log
-- CXG2018.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 EXP 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.
--
-- 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:
-- 21 Mar 96 SAIC Initial release for 2.1
-- 17 Aug 96 SAIC Incorporated reviewer comments.
-- 27 Aug 99 RLB Repair on the error result of checks.
-- 02 Apr 03 RLB Added code to discard excess precision in the
-- construction of the test value for the
-- Identity_Test.
--
--!
--
-- 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 CXG2018 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 Exp (X : Complex) return Complex renames CEF.Exp;
function Exp (X : Imaginary) return Complex renames CEF.Exp;
-- flag used to terminate some tests early
Accuracy_Error_Reported : Boolean := False;
-- The following value is a lower bound on the accuracy
-- required. It is normally 0.0 so that the lower bound
-- is computed from Model_Epsilon. However, for tests
-- where the expected result is only known to a certain
-- amount of precision this bound takes on a non-zero
-- value to account for that level of precision.
Error_Low_Bound : Real := 0.0;
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;
-- take into account the low bound on the error
if Max_Error < Error_Low_Bound then
Max_Error := Error_Low_Bound;
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.
--
-- The error bounds given assumed z is exact. When using
-- pi there is an extra error of 1.0ME.
-- The pi inside the exp call requires that the complex
-- component have an extra error allowance of 1.0*angle*ME.
-- Thus for pi/2,the Minimum_Error_I is
-- (2.0 + 1.0(pi/2))ME <= 3.6ME.
-- For pi, it is (2.0 + 1.0*pi)ME <= 5.2ME,
-- and for 2pi, it is (2.0 + 1.0(2pi))ME <= 8.3ME.
-- The addition of 1 or i to a result is so that neither of
-- the components of an expected result is 0. This is so
-- that a reasonable relative error is allowed.
Minimum_Error_C : constant := 7.0; -- for exp(Complex)
Minimum_Error_I : constant := 2.0; -- for exp(Imaginary)
begin
Check (Exp (1.0 + 0.0*i) + i,
E + i,
"exp(1+0i)",
Minimum_Error_C);
Check (Exp ((Pi / 2.0) * i) + 1.0,
1.0 + 1.0*i,
"exp(pi/2*i)",
3.6);
Check (Exp (Pi * i) + i,
-1.0 + 1.0*i,
"exp(pi*i)",
5.2);
Check (Exp (Pi * 2.0 * i) + i,
1.0 + i,
"exp(2pi*i)",
8.3);
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(36);6.0
Check (Exp(0.0 + 0.0*i), 1.0 + 0.0 * i, "exp(0+0i)", No_Error);
Check (Exp( 0.0*i), 1.0 + 0.0 * i, "exp(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 (A, B : Real) is
-- For this test we use the identity
-- Exp(Z) = Exp(Z-W) * Exp (W)
-- where W = (1+i)/16
--
-- The second part of this test checks the identity
-- Exp(Z) * Exp(-Z) = 1
--
X, Y : Complex;
Actual1, Actual2 : Complex;
W : constant Complex := (0.0625, 0.0625);
-- the following constant was taken from the CELEFUNC EXP test.
-- This is the value EXP(W) - 1
C : constant Complex := (6.2416044877018563681e-2,
6.6487597751003112768e-2);
begin
if Real'Digits > 20 then
-- constant ExpW is accurate to 20 digits.
-- The low bound is 19 * 10**-20
Error_Low_Bound := 0.00000_00000_00019;
Report.Comment ("complex exp accuracy checked to 20 digits");
end if;
Accuracy_Error_Reported := False; -- reset
for II in 1..Max_Samples loop
X.Re := Real'Machine ((B - A) * Real (II) / Real (Max_Samples)
+ A);
for J in 1..Max_Samples loop
X.Im := Real'Machine ((B - A) * Real (J) / Real (Max_Samples)
+ A);
Actual1 := Exp(X);
-- Exp(X) = Exp(X-W) * Exp (W)
-- = Exp(X-W) * (1 - (1-Exp(W))
-- = Exp(X-W) * (1 + (Exp(W) - 1))
-- = Exp(X-W) * (1 + C)
Y := X - W;
Actual2 := Exp(Y);
Actual2 := Actual2 + Actual2 * C;
Check (Actual1, Actual2,
"Identity_1_Test " & Integer'Image (II) &
Integer'Image (J) & ": Exp((" &
Real'Image (X.Re) & ", " &
Real'Image (X.Im) & ")) ",
20.0); -- 2 exp and 1 multiply and 1 add = 2*7+1*5+1
-- Note: The above is not strictly correct, as multiply
-- has a box error, rather than a relative error.
-- Supposedly, the interval is chosen to avoid the need
-- to worry about this.
-- Exp(X) * Exp(-X) + i = 1 + i
-- The addition of i is to allow a reasonable relative
-- error in the imaginary part
Actual2 := (Actual1 * Exp(-X)) + i;
Check (Actual2, (1.0, 1.0),
"Identity_2_Test " & Integer'Image (II) &
Integer'Image (J) & ": Exp((" &
Real'Image (X.Re) & ", " &
Real'Image (X.Im) & ")) ",
20.0); -- 2 exp and 1 multiply and one add = 2*7+1*5+1
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;
Error_Low_Bound := 0.0;
exception
when Constraint_Error =>
Report.Failed
("Constraint_Error raised in Identity_Test" &
" for X=(" & Real'Image (X.Re) &
", " & Real'Image (X.Im) & ")");
when others =>
Report.Failed ("exception in Identity_Test" &
" for X=(" & Real'Image (X.Re) &
", " & Real'Image (X.Im) & ")");
end Identity_Test;
procedure Do_Test is
begin
Special_Value_Test;
Exact_Result_Test;
-- test regions where we can avoid cancellation error problems
-- See Cody page 10.
Identity_Test (0.0625, 1.0);
Identity_Test (15.0, 17.0);
Identity_Test (1.625, 3.0);
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 ("CXG2018",
"Check the accuracy of the complex EXP 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 CXG2018;
Go to most recent revision | Compare with Previous | Blame | View Log