-- CXG2020.A -- -- Grant of Unlimited Rights -- -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687 and -- F08630-91-C-0015, 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 SQRT 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: -- 24 Mar 96 SAIC Initial release for 2.1 -- 17 Aug 96 SAIC Incorporated reviewer comments. -- --! -- -- 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 CXG2020 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; -- 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; 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 Sqrt (X : Complex) return Complex renames CEF.Sqrt; -- flag used to terminate some tests early Accuracy_Error_Reported : Boolean := False; 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; 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 if the argument is exact. -- -- One or i is added to the actual and expected results in -- order to prevent the expected result from having a -- real or imaginary part of 0. This is to allow a reasonable -- relative error for that component. Minimum_Error : constant := 6.0; Z1, Z2 : Complex; begin Check (Sqrt(9.0+0.0*i) + i, 3.0+1.0*i, "sqrt(9+0i)+i", Minimum_Error); Check (Sqrt (-2.0 + 0.0 * i) + 1.0, 1.0 + Sqrt2 * i, "sqrt(-2)+1 ", Minimum_Error); -- make sure no exception occurs when taking the sqrt of -- very large and very small values. Z1 := (Real'Safe_Last * 0.9, Real'Safe_Last * 0.9); Z2 := Sqrt (Z1); begin Check (Z2 * Z2, Z1, "sqrt((big,big))", Minimum_Error + 5.0); -- +5 for multiply exception when others => Report.Failed ("unexpected exception in sqrt((big,big))"); end; Z1 := (Real'Model_Epsilon * 10.0, Real'Model_Epsilon * 10.0); Z2 := Sqrt (Z1); begin Check (Z2 * Z2, Z1, "sqrt((little,little))", Minimum_Error + 5.0); -- +5 for multiply exception when others => Report.Failed ("unexpected exception in " & "sqrt((little,little))"); end; 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 (Sqrt(0.0 + 0.0*i), 0.0 + 0.0 * i, "sqrt(0+0i)", No_Error); -- G.1.2(37);6.0 Check (Sqrt(1.0 + 0.0*i), 1.0 + 0.0 * i, "sqrt(1+0i)", No_Error); -- G.1.2(38-39);6.0 Check (Sqrt(-1.0 + 0.0*i), 0.0 + 1.0 * i, "sqrt(-1+0i)", No_Error); -- G.1.2(40);6.0 if Real'Signed_Zeros then Check (Sqrt(-1.0-0.0*i), 0.0 - 1.0 * i, "sqrt(-1-0i)", No_Error); 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 Identity_Test (RA, RB, IA, IB : Real) is -- Tests an identity over a range of values specified -- by the 4 parameters. RA and RB denote the range for the -- real part while IA and IB denote the range for the -- imaginary part of the result. -- -- For this test we use the identity -- Sqrt(Z*Z) = Z -- Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4); W, X, Y, Z : Real; CX : Complex; Actual, Expected : Complex; begin Accuracy_Error_Reported := False; -- reset for II in 1..Max_Samples loop X := (RB - RA) * Real (II) / Real (Max_Samples) + RA; for J in 1..Max_Samples loop Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA; -- purify the arguments to minimize roundoff error. -- We construct the values so that the products X*X, -- Y*Y, and X*Y are all exact machine numbers. -- See Cody page 7 and CELEFUNT code. Z := X * Scale; W := Z + X; X := W - Z; Z := Y * Scale; W := Z + Y; Y := W - Z; -- G.1.2(21);6.0 - real part of result is non-negative Expected := Compose_From_Cartesian( abs X,Y); Z := X*X - Y*Y; W := X*Y; CX := Compose_From_Cartesian(Z,W+W); -- The arguments are now ready so on with the -- identity computation. Actual := Sqrt(CX); Check (Actual, Expected, "Identity_1_Test " & Integer'Image (II) & Integer'Image (J) & ": Sqrt((" & Real'Image (CX.Re) & ", " & Real'Image (CX.Im) & ")) ", 8.5); -- 6.0 from sqrt, 2.5 from argument. -- See Cody pg 7-8 for analysis of additional error amount. 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; exception when Constraint_Error => Report.Failed ("Constraint_Error raised in Identity_Test" & " for X=(" & Real'Image (X) & ", " & Real'Image (X) & ")"); when others => Report.Failed ("exception in Identity_Test" & " for X=(" & Real'Image (X) & ", " & Real'Image (X) & ")"); end Identity_Test; procedure Do_Test is begin Special_Value_Test; Exact_Result_Test; -- ranges where the sign is the same and where it -- differs. Identity_Test ( 0.0, 10.0, 0.0, 10.0); Identity_Test ( 0.0, 100.0, -100.0, 0.0); 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 ("CXG2020", "Check the accuracy of the complex SQRT 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 CXG2020;