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Diffstat (limited to 'gcc/testsuite/ada/acats/tests/cxg/cxg2016.a')
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diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a deleted file mode 100644 index 832b118224a..00000000000 --- a/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a +++ /dev/null @@ -1,482 +0,0 @@ --- 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; |