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diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a deleted file mode 100644 index 2df296d3d42..00000000000 --- a/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a +++ /dev/null @@ -1,499 +0,0 @@ --- CXG2004.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 sin and cos functions return --- results that are 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 --- the following parts: --- Special value checks where the result is a known constant. --- Checks using an identity relationship. --- --- 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: --- 13 FEB 96 SAIC Initial release for 2.1 --- 22 APR 96 SAIC Changed to generic implementation. --- 18 AUG 96 SAIC Improvements to commentary. --- 23 OCT 96 SAIC Exact results are not required unless the --- cycle is specified. --- 28 FEB 97 PWB.CTA Removed checks where cycle 2.0*Pi is specified --- 02 JUN 98 EDS Revised calculations to ensure that X is exactly --- three times Y per advice of numerics experts. --- --- CHANGE NOTE: --- According to Ken Dritz, author of the Numerics Annex of the RM, --- one should never specify the cycle 2.0*Pi for the trigonometric --- functions. In particular, if the machine number for the first --- argument is not an exact multiple of the machine number for the --- explicit cycle, then the specified exact results cannot be --- reasonably expected. The affected checks in this test have been --- marked as comments, with the additional notation "pwb-math". --- Phil Brashear ---! - --- --- 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 --- --- The sin and cos checks are translated directly from --- the netlib FORTRAN code that was written by W. Cody. --- - -with System; -with Report; -with Ada.Numerics.Generic_Elementary_Functions; -with Ada.Numerics.Elementary_Functions; -procedure CXG2004 is - Verbose : constant Boolean := False; - Number_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 <>; - 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 Sin (X : Real) return Real renames - Elementary_Functions.Sin; - function Cos (X : Real) return Real renames - Elementary_Functions.Cos; - function Sin (X, Cycle : Real) return Real renames - Elementary_Functions.Sin; - function Cos (X, Cycle : Real) return Real renames - Elementary_Functions.Cos; - - Accuracy_Error_Reported : Boolean := False; - - procedure Check (Actual, Expected : Real; - Test_Name : String; - MRE : Real) is - Rel_Error, - Abs_Error, - Max_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; - - - -- in addition to the relative error checks we apply the - -- criteria of G.2.4(16) - if abs (Actual) > 1.0 then - Accuracy_Error_Reported := True; - Report.Failed (Test_Name & " result > 1.0"); - elsif 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) & - " mre:" & - 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 Sin_Check (A, B : Real; - Arg_Range : String) is - -- test a selection of - -- arguments selected from the range A to B. - -- - -- This test uses the identity - -- sin(x) = sin(x/3)*(3 - 4 * sin(x/3)**2) - -- - -- Note that in this test we must take into account the - -- error in the calculation of the expected result so - -- the maximum relative error is larger than the - -- accuracy required by the ARM. - - X, Y, ZZ : Real; - Actual, Expected : Real; - MRE : Real; - Ran : Real; - begin - Accuracy_Error_Reported := False; -- reset - for I in 1 .. Number_Samples loop - -- Evenly distributed selection of arguments - Ran := Real (I) / Real (Number_Samples); - - -- make sure x and x/3 are both exactly representable - -- on the machine. See "Implementation and Testing of - -- Function Software" page 44. - X := (B - A) * Ran + A; - Y := Real'Leading_Part - ( X/3.0, - Real'Machine_Mantissa - Real'Exponent (3.0) ); - X := Y * 3.0; - - Actual := Sin (X); - - ZZ := Sin(Y); - Expected := ZZ * (3.0 - 4.0 * ZZ * ZZ); - - -- note that since the expected value is computed, we - -- must take the error in that computation into account. - -- See Cody pp 139-141. - MRE := 4.0; - - Check (Actual, Expected, - "sin test of range" & Arg_Range & - Integer'Image (I), - MRE); - exit when Accuracy_Error_Reported; - end loop; - exception - when Constraint_Error => - Report.Failed - ("Constraint_Error raised in sin check"); - when others => - Report.Failed ("exception in sin check"); - end Sin_Check; - - - - procedure Cos_Check (A, B : Real; - Arg_Range : String) is - -- test a selection of - -- arguments selected from the range A to B. - -- - -- This test uses the identity - -- cos(x) = cos(x/3)*(4 * cos(x/3)**2 - 3) - -- - -- Note that in this test we must take into account the - -- error in the calculation of the expected result so - -- the maximum relative error is larger than the - -- accuracy required by the ARM. - - X, Y, ZZ : Real; - Actual, Expected : Real; - MRE : Real; - Ran : Real; - begin - Accuracy_Error_Reported := False; -- reset - for I in 1 .. Number_Samples loop - -- Evenly distributed selection of arguments - Ran := Real (I) / Real (Number_Samples); - - -- make sure x and x/3 are both exactly representable - -- on the machine. See "Implementation and Testing of - -- Function Software" page 44. - X := (B - A) * Ran + A; - Y := Real'Leading_Part - ( X/3.0, - Real'Machine_Mantissa - Real'Exponent (3.0) ); - X := Y * 3.0; - - Actual := Cos (X); - - ZZ := Cos(Y); - Expected := ZZ * (4.0 * ZZ * ZZ - 3.0); - - -- note that since the expected value is computed, we - -- must take the error in that computation into account. - -- See Cody pp 141-143. - MRE := 6.0; - - Check (Actual, Expected, - "cos test of range" & Arg_Range & - Integer'Image (I), - MRE); - exit when Accuracy_Error_Reported; - end loop; - exception - when Constraint_Error => - Report.Failed - ("Constraint_Error raised in cos check"); - when others => - Report.Failed ("exception in cos check"); - end Cos_Check; - - - procedure Special_Angle_Checks is - type Data_Point is - record - Degrees, - Radians, - Sine, - Cosine : Real; - Sin_Result_Error, - Cos_Result_Error : Boolean; - end record; - - type Test_Data_Type is array (Positive range <>) of Data_Point; - - -- the values in the following table only involve static - -- expressions to minimize any loss of precision. However, - -- there are two sources of error that must be accounted for - -- in the following tests. - -- First, when a cycle is not specified there can be a roundoff - -- error in the value of Pi used. This error does not apply - -- when a cycle of 2.0 * Pi is explicitly provided. - -- Second, the expected results that involve sqrt values also - -- have a potential roundoff error. - -- The amount of error due to error in the argument is computed - -- as follows: - -- sin(x+err) = sin(x)*cos(err) + cos(x)*sin(err) - -- ~= sin(x) + err * cos(x) - -- similarly for cos the error due to error in the argument is - -- computed as follows: - -- cos(x+err) = cos(x)*cos(err) - sin(x)*sin(err) - -- ~= cos(x) - err * sin(x) - -- In both cases the term "err" is bounded by 0.5 * argument. - - Test_Data : constant Test_Data_Type := ( --- degrees radians sine cosine sin_er cos_er test # - ( 0.0, 0.0, 0.0, 1.0, False, False ), -- 1 - ( 30.0, Pi/6.0, 0.5, Sqrt3/2.0, False, True ), -- 2 - ( 60.0, Pi/3.0, Sqrt3/2.0, 0.5, True, False ), -- 3 - ( 90.0, Pi/2.0, 1.0, 0.0, False, False ), -- 4 - (120.0, 2.0*Pi/3.0, Sqrt3/2.0, -0.5, True, False ), -- 5 - (150.0, 5.0*Pi/6.0, 0.5, -Sqrt3/2.0, False, True ), -- 6 - (180.0, Pi, 0.0, -1.0, False, False ), -- 7 - (210.0, 7.0*Pi/6.0, -0.5, -Sqrt3/2.0, False, True ), -- 8 - (240.0, 8.0*Pi/6.0, -Sqrt3/2.0, -0.5, True, False ), -- 9 - (270.0, 9.0*Pi/6.0, -1.0, 0.0, False, False ), -- 10 - (300.0, 10.0*Pi/6.0, -Sqrt3/2.0, 0.5, True, False ), -- 11 - (330.0, 11.0*Pi/6.0, -0.5, Sqrt3/2.0, False, True ), -- 12 - (360.0, 2.0*Pi, 0.0, 1.0, False, False ), -- 13 - ( 45.0, Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 14 - (135.0, 3.0*Pi/4.0, Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 15 - (225.0, 5.0*Pi/4.0, -Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 16 - (315.0, 7.0*Pi/4.0, -Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 17 - (405.0, 9.0*Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ) ); -- 18 - - - Y : Real; - Sin_Arg_Err, - Cos_Arg_Err, - Sin_Result_Err, - Cos_Result_Err : Real; - begin - for I in Test_Data'Range loop - -- compute error components - Sin_Arg_Err := abs Test_Data (I).Cosine * - abs Test_Data (I).Radians / 2.0; - Cos_Arg_Err := abs Test_Data (I).Sine * - abs Test_Data (I).Radians / 2.0; - - if Test_Data (I).Sin_Result_Error then - Sin_Result_Err := 0.5; - else - Sin_Result_Err := 0.0; - end if; - - if Test_Data (I).Cos_Result_Error then - Cos_Result_Err := 1.0; - else - Cos_Result_Err := 0.0; - end if; - - - - Y := Sin (Test_Data (I).Radians); - Check (Y, Test_Data (I).Sine, - "test" & Integer'Image (I) & " sin(r)", - 2.0 + Sin_Arg_Err + Sin_Result_Err); - Y := Cos (Test_Data (I).Radians); - Check (Y, Test_Data (I).Cosine, - "test" & Integer'Image (I) & " cos(r)", - 2.0 + Cos_Arg_Err + Cos_Result_Err); - Y := Sin (Test_Data (I).Degrees, 360.0); - Check (Y, Test_Data (I).Sine, - "test" & Integer'Image (I) & " sin(d,360)", - 2.0 + Sin_Result_Err); - Y := Cos (Test_Data (I).Degrees, 360.0); - Check (Y, Test_Data (I).Cosine, - "test" & Integer'Image (I) & " cos(d,360)", - 2.0 + Cos_Result_Err); ---pwb-math Y := Sin (Test_Data (I).Radians, 2.0*Pi); ---pwb-math Check (Y, Test_Data (I).Sine, ---pwb-math "test" & Integer'Image (I) & " sin(r,2pi)", ---pwb-math 2.0 + Sin_Result_Err); ---pwb-math Y := Cos (Test_Data (I).Radians, 2.0*Pi); ---pwb-math Check (Y, Test_Data (I).Cosine, ---pwb-math "test" & Integer'Image (I) & " cos(r,2pi)", ---pwb-math 2.0 + Cos_Result_Err); - end loop; - exception - when Constraint_Error => - Report.Failed ("Constraint_Error raised in special angle test"); - when others => - Report.Failed ("exception in special angle test"); - end Special_Angle_Checks; - - - -- check the rule of A.5.1(41);6.0 which requires that the - -- result be exact if the mathematical result is 0.0, 1.0, - -- or -1.0 - procedure Exact_Result_Checks is - type Data_Point is - record - Degrees, - Sine, - Cosine : Real; - end record; - - type Test_Data_Type is array (Positive range <>) of Data_Point; - Test_Data : constant Test_Data_Type := ( - -- degrees sine cosine test # - ( 0.0, 0.0, 1.0 ), -- 1 - ( 90.0, 1.0, 0.0 ), -- 2 - (180.0, 0.0, -1.0 ), -- 3 - (270.0, -1.0, 0.0 ), -- 4 - (360.0, 0.0, 1.0 ), -- 5 - ( 90.0 + 360.0, 1.0, 0.0 ), -- 6 - (180.0 + 360.0, 0.0, -1.0 ), -- 7 - (270.0 + 360.0,-1.0, 0.0 ), -- 8 - (360.0 + 360.0, 0.0, 1.0 ) ); -- 9 - - Y : Real; - begin - for I in Test_Data'Range loop - Y := Sin (Test_Data(I).Degrees, 360.0); - if Y /= Test_Data(I).Sine then - Report.Failed ("exact result for sin(" & - Real'Image (Test_Data(I).Degrees) & - ", 360.0) is not" & - Real'Image (Test_Data(I).Sine) & - " Difference is " & - Real'Image (Y - Test_Data(I).Sine) ); - end if; - - Y := Cos (Test_Data(I).Degrees, 360.0); - if Y /= Test_Data(I).Cosine then - Report.Failed ("exact result for cos(" & - Real'Image (Test_Data(I).Degrees) & - ", 360.0) is not" & - Real'Image (Test_Data(I).Cosine) & - " Difference is " & - Real'Image (Y - Test_Data(I).Cosine) ); - end if; - end loop; - exception - when Constraint_Error => - Report.Failed ("Constraint_Error raised in exact result check"); - when others => - Report.Failed ("exception in exact result check"); - end Exact_Result_Checks; - - - procedure Do_Test is - begin - Special_Angle_Checks; - Sin_Check (0.0, Pi/2.0, "0..pi/2"); - Sin_Check (6.0*Pi, 6.5*Pi, "6pi..6.5pi"); - Cos_Check (7.0*Pi, 7.5*Pi, "7pi..7.5pi"); - Exact_Result_Checks; - 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 ("CXG2004", - "Check the accuracy of the sin and cos functions"); - - 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 CXG2004; |