summaryrefslogtreecommitdiff
path: root/gcc/testsuite/ada/acats/tests/cxg/cxg2018.a
diff options
context:
space:
mode:
authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
commit554fd8c5195424bdbcabf5de30fdc183aba391bd (patch)
tree976dc5ab7fddf506dadce60ae936f43f58787092 /gcc/testsuite/ada/acats/tests/cxg/cxg2018.a
downloadcbb-gcc-4.6.4-554fd8c5195424bdbcabf5de30fdc183aba391bd.tar.bz2
cbb-gcc-4.6.4-554fd8c5195424bdbcabf5de30fdc183aba391bd.tar.xz
obtained gcc-4.6.4.tar.bz2 from upstream website;upstream
verified gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream tarball. downloading a git-generated archive based on the 'upstream' tag should provide you with a source tree that is binary identical to the one extracted from the above tarball. if you have obtained the source via the command 'git clone', however, do note that line-endings of files in your working directory might differ from line-endings of the respective files in the upstream repository.
Diffstat (limited to 'gcc/testsuite/ada/acats/tests/cxg/cxg2018.a')
-rw-r--r--gcc/testsuite/ada/acats/tests/cxg/cxg2018.a355
1 files changed, 355 insertions, 0 deletions
diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2018.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2018.a
new file mode 100644
index 000000000..be4f1a82f
--- /dev/null
+++ b/gcc/testsuite/ada/acats/tests/cxg/cxg2018.a
@@ -0,0 +1,355 @@
+-- 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;