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diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a new file mode 100644 index 000000000..832b11822 --- /dev/null +++ b/gcc/testsuite/ada/acats/tests/cxg/cxg2016.a @@ -0,0 +1,482 @@ +-- 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; |