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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/cxg2016.a
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+-- CXG2016.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 ARCTAN 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 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.
+-- 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:
+-- 19 Mar 96 SAIC Initial release for 2.1
+-- 30 APR 96 SAIC Fixed optimization issue
+-- 17 AUG 96 SAIC Incorporated Reviewer's suggestions.
+-- 12 OCT 96 SAIC Incorporated Reviewer's suggestions.
+-- 02 DEC 97 EDS Remove procedure Identity_1_Test and calls to
+-- procedure.
+-- 29 JUN 98 EDS Replace -0.0 with call to ImpDef.Annex_G.Negative_Zero
+-- 28 APR 99 RLB Replaced comma accidentally deleted in above change.
+-- 15 DEC 99 RLB Added model range checking to "exact" results,
+-- in order to avoid too strictly requiring a specific
+-- result.
+--!
+
+--
+-- 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;
+with Impdef.Annex_G;
+procedure CXG2016 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;
+
+ Pi : constant := Ada.Numerics.Pi;
+
+ generic
+ type Real is digits <>;
+ Half_PI_Low : in Real; -- The machine number closest to, but not greater
+ -- than PI/2.0.
+ Half_PI_High : in Real;-- The machine number closest to, but not less
+ -- than PI/2.0.
+ PI_Low : in Real; -- The machine number closest to, but not greater
+ -- than PI.
+ PI_High : in Real; -- The machine number closest to, but not less
+ -- than PI.
+ 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 Arctan (Y : Real;
+ X : Real := 1.0) return Real renames
+ Elementary_Functions.Arctan;
+ function Arctan (Y : Real;
+ X : Real := 1.0;
+ Cycle : Real) return Real renames
+ Elementary_Functions.Arctan;
+
+ -- 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_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;
+
+ -- 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 Special_Value_Test is
+ -- If eta is very small, arctan(x + eta) ~= arctan(x) + eta/(1+x*x).
+ --
+ -- For tests 4 and 5, there is an error of 4.0ME for arctan + an
+ -- additional error of 1.0ME because pi is not exact for a total of 5.0ME.
+ --
+ -- In test 3 there is the error for pi plus an additional error
+ -- of (1.0ME)/4 since sqrt3 is not exact, for a total of 5.25ME.
+ --
+ -- In test 2 there is the error for pi plus an additional error
+ -- of (3/4)(1.0ME) since sqrt3 is not exact, for a total of 5.75ME.
+
+
+ type Data_Point is
+ record
+ Degrees,
+ Radians,
+ Tangent,
+ Allowed_Error : Real;
+ end record;
+
+ type Test_Data_Type is array (Positive range <>) of Data_Point;
+
+ -- the values in the following table only involve static
+ -- expressions so no additional loss of precision occurs.
+ Test_Data : constant Test_Data_Type := (
+ -- degrees radians tangent error test #
+ ( 0.0, 0.0, 0.0, 4.0 ), -- 1
+ ( 30.0, Pi/6.0, Sqrt3/3.0, 5.75), -- 2
+ ( 60.0, Pi/3.0, Sqrt3, 5.25), -- 3
+ ( 45.0, Pi/4.0, 1.0, 5.0 ), -- 4
+ (-45.0, -Pi/4.0, -1.0, 5.0 ) ); -- 5
+
+ begin
+ for I in Test_Data'Range loop
+ Check (Arctan (Test_Data (I).Tangent),
+ Test_Data (I).Radians,
+ "special value test" & Integer'Image (I) &
+ " arctan(" &
+ Real'Image (Test_Data (I).Tangent) &
+ ")",
+ Test_Data (I).Allowed_Error);
+ Check (Arctan (Test_Data (I).Tangent, Cycle => 360.0),
+ Test_Data (I).Degrees,
+ "special value test" & Integer'Image (I) &
+ " arctan(" &
+ Real'Image (Test_Data (I).Tangent) &
+ ", cycle=>360)",
+ Test_Data (I).Allowed_Error);
+ end loop;
+
+ 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 Check_Exact (Actual, Expected_Low, Expected_High : Real;
+ Test_Name : String) is
+ -- If the expected result is not a model number, then Expected_Low is
+ -- the first machine number less than the (exact) expected
+ -- result, and Expected_High is the first machine number greater than
+ -- the (exact) expected result. If the expected result is a model
+ -- number, Expected_Low = Expected_High = the result.
+ Model_Expected_Low : Real := Expected_Low;
+ Model_Expected_High : Real := Expected_High;
+ begin
+ -- Calculate the first model number nearest to, but below (or equal)
+ -- to the expected result:
+ while Real'Model (Model_Expected_Low) /= Model_Expected_Low loop
+ -- Try the next machine number lower:
+ Model_Expected_Low := Real'Adjacent(Model_Expected_Low, 0.0);
+ end loop;
+ -- Calculate the first model number nearest to, but above (or equal)
+ -- to the expected result:
+ while Real'Model (Model_Expected_High) /= Model_Expected_High loop
+ -- Try the next machine number higher:
+ Model_Expected_High := Real'Adjacent(Model_Expected_High, 100.0);
+ end loop;
+
+ if Actual < Model_Expected_Low or Actual > Model_Expected_High then
+ Accuracy_Error_Reported := True;
+ if Actual < Model_Expected_Low then
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected low: " & Real'Image (Model_Expected_Low) &
+ " expected high: " & Real'Image (Model_Expected_High) &
+ " difference: " & Real'Image (Actual - Expected_Low));
+ else
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected low: " & Real'Image (Model_Expected_Low) &
+ " expected high: " & Real'Image (Model_Expected_High) &
+ " difference: " & Real'Image (Expected_High - Actual));
+ end if;
+ elsif Verbose then
+ Report.Comment (Test_Name & " passed");
+ end if;
+ end Check_Exact;
+
+
+ procedure Exact_Result_Test is
+ begin
+ -- A.5.1(40);6.0
+ Check_Exact (Arctan (0.0, 1.0), 0.0, 0.0, "arctan(0,1)");
+ Check_Exact (Arctan (0.0, 1.0, 27.0), 0.0, 0.0, "arctan(0,1,27)");
+
+ -- G.2.4(11-13);6.0
+
+ Check_Exact (Arctan (1.0, 0.0), Half_PI_Low, Half_PI_High,
+ "arctan(1,0)");
+ Check_Exact (Arctan (1.0, 0.0, 360.0), 90.0, 90.0, "arctan(1,0,360)");
+
+ Check_Exact (Arctan (-1.0, 0.0), -Half_PI_High, -Half_PI_Low,
+ "arctan(-1,0)");
+ Check_Exact (Arctan (-1.0, 0.0, 360.0), -90.0, -90.0,
+ "arctan(-1,0,360)");
+
+ if Real'Signed_Zeros then
+ Check_Exact (Arctan (0.0, -1.0), PI_Low, PI_High, "arctan(+0,-1)");
+ Check_Exact (Arctan (0.0, -1.0, 360.0), 180.0, 180.0,
+ "arctan(+0,-1,360)");
+ Check_Exact (Arctan ( Real ( ImpDef.Annex_G.Negative_Zero ), -1.0),
+ -PI_High, -PI_Low, "arctan(-0,-1)");
+ Check_Exact (Arctan ( Real ( ImpDef.Annex_G.Negative_Zero ), -1.0,
+ 360.0), -180.0, -180.0, "arctan(-0,-1,360)");
+ else
+ Check_Exact (Arctan (0.0, -1.0), PI_Low, PI_High, "arctan(0,-1)");
+ Check_Exact (Arctan (0.0, -1.0, 360.0), 180.0, 180.0,
+ "arctan(0,-1,360)");
+ end if;
+ 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 Taylor_Series_Test is
+ -- This test checks the Arctan by using a taylor series expansion that
+ -- will produce a result accurate to 19 decimal digits for
+ -- the range under test.
+ --
+ -- The maximum relative error bound for this test is
+ -- 4 for the arctan operation and 2 for the Taylor series
+ -- for a total of 6 * Model_Epsilon
+
+ A : constant := -1.0/16.0;
+ B : constant := 1.0/16.0;
+ X : Real;
+ Actual, Expected : Real;
+ Sum, Em, X_Squared : Real;
+ begin
+ if Real'Digits > 19 then
+ -- Taylor series calculation produces result accurate to 19
+ -- digits. If type being tested has more digits then set
+ -- the error low bound to account for this.
+ -- The error low bound is conservatively set to 6*10**-19
+ Error_Low_Bound := 0.00000_00000_00000_0006;
+ Report.Comment ("arctan accuracy checked to 19 digits");
+ end if;
+
+ Accuracy_Error_Reported := False; -- reset
+ for I in 0..Max_Samples loop
+ X := (B - A) * Real (I) / Real (Max_Samples) + A;
+ X_Squared := X * X;
+ Em := 17.0;
+ Sum := X_Squared / Em;
+
+ for II in 1 .. 7 loop
+ Em := Em - 2.0;
+ Sum := (1.0 / Em - Sum) * X_Squared;
+ end loop;
+ Sum := -X * Sum;
+ Expected := X + Sum;
+ Sum := (X - Expected) + Sum;
+ if not Real'Machine_Rounds then
+ Expected := Expected + (Sum + Sum);
+ end if;
+
+ Actual := Arctan (X);
+
+ Check (Actual, Expected,
+ "Taylor_Series_Test " & Integer'Image (I) & ": arctan(" &
+ Real'Image (X) & ") ",
+ 6.0);
+
+ 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;
+ Error_Low_Bound := 0.0; -- reset
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Taylor_Series_Test");
+ when others =>
+ Report.Failed ("exception in Taylor_Series_Test");
+ end Taylor_Series_Test;
+
+
+ procedure Exception_Test is
+ X1, X2, X3 : Real := 0.0;
+ begin
+
+ begin -- A.5.1(20);6.0
+ X1 := Arctan(0.0, Cycle => 0.0);
+ Report.Failed ("no exception for cycle = 0.0");
+ exception
+ when Ada.Numerics.Argument_Error => null;
+ when others =>
+ Report.Failed ("wrong exception for cycle = 0.0");
+ end;
+
+ begin -- A.5.1(20);6.0
+ X2 := Arctan (0.0, Cycle => -1.0);
+ Report.Failed ("no exception for cycle < 0.0");
+ exception
+ when Ada.Numerics.Argument_Error => null;
+ when others =>
+ Report.Failed ("wrong exception for cycle < 0.0");
+ end;
+
+ begin -- A.5.1(25);6.0
+ X3 := Arctan (0.0, 0.0);
+ Report.Failed ("no exception for arctan(0,0)");
+ exception
+ when Ada.Numerics.Argument_Error => null;
+ when others =>
+ Report.Failed ("wrong exception for arctan(0,0)");
+ end;
+
+ -- optimizer thwarting
+ if Report.Ident_Bool (False) then
+ Report.Comment (Real'Image (X1 + X2 + X3));
+ end if;
+ end Exception_Test;
+
+
+ procedure Do_Test is
+ begin
+ Special_Value_Test;
+ Exact_Result_Test;
+ Taylor_Series_Test;
+ Exception_Test;
+ end Do_Test;
+ end Generic_Check;
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+ -- These expressions must be truly static, which is why we have to do them
+ -- outside of the generic, and we use the named numbers. Note that we know
+ -- that PI is not a machine number (it is irrational), and it should be
+ -- represented to more digits than supported by the target machine.
+ Float_Half_PI_Low : constant := Float'Adjacent(PI/2.0, 0.0);
+ Float_Half_PI_High : constant := Float'Adjacent(PI/2.0, 10.0);
+ Float_PI_Low : constant := Float'Adjacent(PI, 0.0);
+ Float_PI_High : constant := Float'Adjacent(PI, 10.0);
+ package Float_Check is new Generic_Check (Float,
+ Half_PI_Low => Float_Half_PI_Low,
+ Half_PI_High => Float_Half_PI_High,
+ PI_Low => Float_PI_Low,
+ PI_High => Float_PI_High);
+
+ -- check the Floating point type with the most digits
+ type A_Long_Float is digits System.Max_Digits;
+ A_Long_Float_Half_PI_Low : constant := A_Long_Float'Adjacent(PI/2.0, 0.0);
+ A_Long_Float_Half_PI_High : constant := A_Long_Float'Adjacent(PI/2.0, 10.0);
+ A_Long_Float_PI_Low : constant := A_Long_Float'Adjacent(PI, 0.0);
+ A_Long_Float_PI_High : constant := A_Long_Float'Adjacent(PI, 10.0);
+ package A_Long_Float_Check is new Generic_Check (A_Long_Float,
+ Half_PI_Low => A_Long_Float_Half_PI_Low,
+ Half_PI_High => A_Long_Float_Half_PI_High,
+ PI_Low => A_Long_Float_PI_Low,
+ PI_High => A_Long_Float_PI_High);
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+
+
+begin
+ Report.Test ("CXG2016",
+ "Check the accuracy of the ARCTAN 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 CXG2016;