| -- CXG2015.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 ARCSIN and ARCCOS 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 |
| -- several parts: |
| -- Special value checks where the result is a known constant. |
| -- Checks in a specific range where a Taylor series can be |
| -- used to compute an accurate result for comparison. |
| -- Exception checks. |
| -- The Taylor series tests are a direct translation of the |
| -- FORTRAN code found in the reference. |
| -- |
| -- 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: |
| -- 18 Mar 96 SAIC Initial release for 2.1 |
| -- 24 Apr 96 SAIC Fixed error bounds. |
| -- 17 Aug 96 SAIC Added reference information and improved |
| -- checking for machines with more than 23 |
| -- digits of precision. |
| -- 03 Feb 97 PWB.CTA Removed checks with explicit Cycle => 2.0*Pi |
| -- 22 Dec 99 RLB Added model range checking to "exact" results, |
| -- in order to avoid too strictly requiring a specific |
| -- result, and too weakly checking results. |
| -- |
| -- 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 |
| -- |
| -- CELEFUNT: A Portable Test Package for Complex Elementary Functions |
| -- ACM Collected Algorithms number 714 |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Elementary_Functions; |
| procedure CXG2015 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; |
| |
| -- relative error bound from G.2.4(7);6.0 |
| Minimum_Error : constant := 4.0; |
| |
| 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 Arcsin (X : Real) return Real renames |
| Elementary_Functions.Arcsin; |
| function Arcsin (X, Cycle : Real) return Real renames |
| Elementary_Functions.Arcsin; |
| function Arccos (X : Real) return Real renames |
| Elementary_Functions.ArcCos; |
| function Arccos (X, Cycle : Real) return Real renames |
| Elementary_Functions.ArcCos; |
| |
| -- needed for support |
| function Log (X, Base : Real) return Real renames |
| Elementary_Functions.Log; |
| |
| -- 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 |
| -- In the following tests the expected result is accurate |
| -- to the machine precision so the minimum guaranteed error |
| -- bound can be used. |
| |
| type Data_Point is |
| record |
| Degrees, |
| Radians, |
| Argument, |
| Error_Bound : Real; |
| end record; |
| |
| type Test_Data_Type is array (Positive range <>) of Data_Point; |
| |
| -- the values in the following tables only involve static |
| -- expressions so no loss of precision occurs. However, |
| -- rounding can be an issue with expressions involving Pi |
| -- and square roots. The error bound specified in the |
| -- table takes the sqrt error into account but not the |
| -- error due to Pi. The Pi error is added in in the |
| -- radians test below. |
| |
| Arcsin_Test_Data : constant Test_Data_Type := ( |
| -- degrees radians sine error_bound test # |
| --( 0.0, 0.0, 0.0, 0.0 ), -- 1 - In Exact_Result_Test. |
| ( 30.0, Pi/6.0, 0.5, 4.0 ), -- 2 |
| ( 60.0, Pi/3.0, Sqrt3/2.0, 5.0 ), -- 3 |
| --( 90.0, Pi/2.0, 1.0, 4.0 ), -- 4 - In Exact_Result_Test. |
| --(-90.0, -Pi/2.0, -1.0, 4.0 ), -- 5 - In Exact_Result_Test. |
| (-60.0, -Pi/3.0, -Sqrt3/2.0, 5.0 ), -- 6 |
| (-30.0, -Pi/6.0, -0.5, 4.0 ), -- 7 |
| ( 45.0, Pi/4.0, Sqrt2/2.0, 5.0 ), -- 8 |
| (-45.0, -Pi/4.0, -Sqrt2/2.0, 5.0 ) ); -- 9 |
| |
| Arccos_Test_Data : constant Test_Data_Type := ( |
| -- degrees radians cosine error_bound test # |
| --( 0.0, 0.0, 1.0, 0.0 ), -- 1 - In Exact_Result_Test. |
| ( 30.0, Pi/6.0, Sqrt3/2.0, 5.0 ), -- 2 |
| ( 60.0, Pi/3.0, 0.5, 4.0 ), -- 3 |
| --( 90.0, Pi/2.0, 0.0, 4.0 ), -- 4 - In Exact_Result_Test. |
| (120.0, 2.0*Pi/3.0, -0.5, 4.0 ), -- 5 |
| (150.0, 5.0*Pi/6.0, -Sqrt3/2.0, 5.0 ), -- 6 |
| --(180.0, Pi, -1.0, 4.0 ), -- 7 - In Exact_Result_Test. |
| ( 45.0, Pi/4.0, Sqrt2/2.0, 5.0 ), -- 8 |
| (135.0, 3.0*Pi/4.0, -Sqrt2/2.0, 5.0 ) ); -- 9 |
| |
| Cycle_Error, |
| Radian_Error : Real; |
| begin |
| for I in Arcsin_Test_Data'Range loop |
| |
| -- note exact result requirements A.5.1(38);6.0 and |
| -- G.2.4(12);6.0 |
| if Arcsin_Test_Data (I).Error_Bound = 0.0 then |
| Cycle_Error := 0.0; |
| Radian_Error := 0.0; |
| else |
| Cycle_Error := Arcsin_Test_Data (I).Error_Bound; |
| -- allow for rounding error in the specification of Pi |
| Radian_Error := Cycle_Error + 1.0; |
| end if; |
| |
| Check (Arcsin (Arcsin_Test_Data (I).Argument), |
| Arcsin_Test_Data (I).Radians, |
| "test" & Integer'Image (I) & |
| " arcsin(" & |
| Real'Image (Arcsin_Test_Data (I).Argument) & |
| ")", |
| Radian_Error); |
| --pwb-math Check (Arcsin (Arcsin_Test_Data (I).Argument, 2.0 * Pi), |
| --pwb-math Arcsin_Test_Data (I).Radians, |
| --pwb-math "test" & Integer'Image (I) & |
| --pwb-math " arcsin(" & |
| --pwb-math Real'Image (Arcsin_Test_Data (I).Argument) & |
| --pwb-math ", 2pi)", |
| --pwb-math Cycle_Error); |
| Check (Arcsin (Arcsin_Test_Data (I).Argument, 360.0), |
| Arcsin_Test_Data (I).Degrees, |
| "test" & Integer'Image (I) & |
| " arcsin(" & |
| Real'Image (Arcsin_Test_Data (I).Argument) & |
| ", 360)", |
| Cycle_Error); |
| end loop; |
| |
| |
| for I in Arccos_Test_Data'Range loop |
| |
| -- note exact result requirements A.5.1(39);6.0 and |
| -- G.2.4(12);6.0 |
| if Arccos_Test_Data (I).Error_Bound = 0.0 then |
| Cycle_Error := 0.0; |
| Radian_Error := 0.0; |
| else |
| Cycle_Error := Arccos_Test_Data (I).Error_Bound; |
| -- allow for rounding error in the specification of Pi |
| Radian_Error := Cycle_Error + 1.0; |
| end if; |
| |
| Check (Arccos (Arccos_Test_Data (I).Argument), |
| Arccos_Test_Data (I).Radians, |
| "test" & Integer'Image (I) & |
| " arccos(" & |
| Real'Image (Arccos_Test_Data (I).Argument) & |
| ")", |
| Radian_Error); |
| --pwb-math Check (Arccos (Arccos_Test_Data (I).Argument, 2.0 * Pi), |
| --pwb-math Arccos_Test_Data (I).Radians, |
| --pwb-math "test" & Integer'Image (I) & |
| --pwb-math " arccos(" & |
| --pwb-math Real'Image (Arccos_Test_Data (I).Argument) & |
| --pwb-math ", 2pi)", |
| --pwb-math Cycle_Error); |
| Check (Arccos (Arccos_Test_Data (I).Argument, 360.0), |
| Arccos_Test_Data (I).Degrees, |
| "test" & Integer'Image (I) & |
| " arccos(" & |
| Real'Image (Arccos_Test_Data (I).Argument) & |
| ", 360)", |
| Cycle_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(38) |
| Check_Exact (Arcsin (0.0), 0.0, 0.0, "arcsin(0)"); |
| Check_Exact (Arcsin (0.0, 45.0), 0.0, 0.0, "arcsin(0,45)"); |
| |
| -- A.5.1(39) |
| Check_Exact (Arccos (1.0), 0.0, 0.0, "arccos(1)"); |
| Check_Exact (Arccos (1.0, 75.0), 0.0, 0.0, "arccos(1,75)"); |
| |
| -- G.2.4(11-13) |
| Check_Exact (Arcsin (1.0), Half_PI_Low, Half_PI_High, "arcsin(1)"); |
| Check_Exact (Arcsin (1.0, 360.0), 90.0, 90.0, "arcsin(1,360)"); |
| |
| Check_Exact (Arcsin (-1.0), -Half_PI_High, -Half_PI_Low, "arcsin(-1)"); |
| Check_Exact (Arcsin (-1.0, 360.0), -90.0, -90.0, "arcsin(-1,360)"); |
| |
| Check_Exact (Arccos (0.0), Half_PI_Low, Half_PI_High, "arccos(0)"); |
| Check_Exact (Arccos (0.0, 360.0), 90.0, 90.0, "arccos(0,360)"); |
| |
| Check_Exact (Arccos (-1.0), PI_Low, PI_High, "arccos(-1)"); |
| Check_Exact (Arccos (-1.0, 360.0), 180.0, 180.0, "arccos(-1,360)"); |
| |
| 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 Arcsin_Taylor_Series_Test is |
| -- the following range is chosen so that the Taylor series |
| -- used will produce a result accurate to machine precision. |
| -- |
| -- The following formula is used for the Taylor series: |
| -- TS(x) = x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) + |
| -- (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] } |
| -- where xsq = x * x |
| -- |
| A : constant := -0.125; |
| B : constant := 0.125; |
| X : Real; |
| Y, Y_Sq : Real; |
| Actual, Sum, Xm : Real; |
| -- terms in Taylor series |
| K : constant Integer := Integer ( |
| Log ( |
| Real (Real'Machine_Radix) ** Real'Machine_Mantissa, |
| 10.0)) + 1; |
| begin |
| Accuracy_Error_Reported := False; -- reset |
| for I in 1..Max_Samples loop |
| -- make sure there is no error in x-1, x, and x+1 |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| |
| Y := X; |
| Y_Sq := Y * Y; |
| Sum := 0.0; |
| Xm := Real (K + K + 1); |
| for M in 1 .. K loop |
| Sum := Y_Sq * (Sum + 1.0/Xm); |
| Xm := Xm - 2.0; |
| Sum := Sum * (Xm /(Xm + 1.0)); |
| end loop; |
| Sum := Sum * Y; |
| Actual := Y + Sum; |
| Sum := (Y - Actual) + Sum; |
| if not Real'Machine_Rounds then |
| Actual := Actual + (Sum + Sum); |
| end if; |
| |
| Check (Actual, Arcsin (X), |
| "Taylor Series test" & Integer'Image (I) & ": arcsin(" & |
| Real'Image (X) & ") ", |
| Minimum_Error); |
| |
| 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; |
| |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in Arcsin_Taylor_Series_Test" & |
| " for X=" & Real'Image (X)); |
| when others => |
| Report.Failed ("exception in Arcsin_Taylor_Series_Test" & |
| " for X=" & Real'Image (X)); |
| end Arcsin_Taylor_Series_Test; |
| |
| |
| |
| procedure Arccos_Taylor_Series_Test is |
| -- the following range is chosen so that the Taylor series |
| -- used will produce a result accurate to machine precision. |
| -- |
| -- The following formula is used for the Taylor series: |
| -- TS(x) = x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) + |
| -- (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] } |
| -- arccos(x) = pi/2 - TS(x) |
| A : constant := -0.125; |
| B : constant := 0.125; |
| C1, C2 : Real; |
| X : Real; |
| Y, Y_Sq : Real; |
| Actual, Sum, Xm, S : Real; |
| -- terms in Taylor series |
| K : constant Integer := Integer ( |
| Log ( |
| Real (Real'Machine_Radix) ** Real'Machine_Mantissa, |
| 10.0)) + 1; |
| begin |
| if Real'Digits > 23 then |
| -- constants in this section only accurate to 23 digits |
| Error_Low_Bound := 0.00000_00000_00000_00000_001; |
| Report.Comment ("arctan accuracy checked to 23 digits"); |
| end if; |
| |
| -- C1 + C2 equals Pi/2 accurate to 23 digits |
| if Real'Machine_Radix = 10 then |
| C1 := 1.57; |
| C2 := 7.9632679489661923132E-4; |
| else |
| C1 := 201.0 / 128.0; |
| C2 := 4.8382679489661923132E-4; |
| end if; |
| |
| Accuracy_Error_Reported := False; -- reset |
| for I in 1..Max_Samples loop |
| -- make sure there is no error in x-1, x, and x+1 |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| |
| Y := X; |
| Y_Sq := Y * Y; |
| Sum := 0.0; |
| Xm := Real (K + K + 1); |
| for M in 1 .. K loop |
| Sum := Y_Sq * (Sum + 1.0/Xm); |
| Xm := Xm - 2.0; |
| Sum := Sum * (Xm /(Xm + 1.0)); |
| end loop; |
| Sum := Sum * Y; |
| |
| -- at this point we have arcsin(x). |
| -- We compute arccos(x) = pi/2 - arcsin(x). |
| -- The following code segment is translated directly from |
| -- the CELEFUNT FORTRAN implementation |
| |
| S := C1 + C2; |
| Sum := ((C1 - S) + C2) - Sum; |
| Actual := S + Sum; |
| Sum := ((S - Actual) + Sum) - Y; |
| S := Actual; |
| Actual := S + Sum; |
| Sum := (S - Actual) + Sum; |
| |
| if not Real'Machine_Rounds then |
| Actual := Actual + (Sum + Sum); |
| end if; |
| |
| Check (Actual, Arccos (X), |
| "Taylor Series test" & Integer'Image (I) & ": arccos(" & |
| Real'Image (X) & ") ", |
| Minimum_Error); |
| |
| -- only report the first error in this test in order to keep |
| -- lots of failures from producing a huge error log |
| exit when Accuracy_Error_Reported; |
| end loop; |
| Error_Low_Bound := 0.0; -- reset |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in Arccos_Taylor_Series_Test" & |
| " for X=" & Real'Image (X)); |
| when others => |
| Report.Failed ("exception in Arccos_Taylor_Series_Test" & |
| " for X=" & Real'Image (X)); |
| end Arccos_Taylor_Series_Test; |
| |
| |
| |
| procedure Identity_Test is |
| -- test the identity arcsin(-x) = -arcsin(x) |
| -- range chosen to be most of the valid range of the argument. |
| A : constant := -0.999; |
| B : constant := 0.999; |
| X : Real; |
| begin |
| Accuracy_Error_Reported := False; -- reset |
| for I in 1..Max_Samples loop |
| -- make sure there is no error in x-1, x, and x+1 |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| |
| Check (Arcsin(-X), -Arcsin (X), |
| "Identity test" & Integer'Image (I) & ": arcsin(" & |
| Real'Image (X) & ") ", |
| 8.0); -- 2 arcsin evaluations => twice the error bound |
| |
| 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 Identity_Test; |
| |
| |
| procedure Exception_Test is |
| X1, X2 : Real := 0.0; |
| begin |
| begin |
| X1 := Arcsin (1.1); |
| Report.Failed ("no exception for Arcsin (1.1)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error instead of " & |
| "Argument_Error for Arcsin (1.1)"); |
| when Ada.Numerics.Argument_Error => |
| null; -- expected result |
| when others => |
| Report.Failed ("wrong exception for Arcsin(1.1)"); |
| end; |
| |
| begin |
| X2 := Arccos (-1.1); |
| Report.Failed ("no exception for Arccos (-1.1)"); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error instead of " & |
| "Argument_Error for Arccos (-1.1)"); |
| when Ada.Numerics.Argument_Error => |
| null; -- expected result |
| when others => |
| Report.Failed ("wrong exception for Arccos(-1.1)"); |
| end; |
| |
| |
| -- optimizer thwarting |
| if Report.Ident_Bool (False) then |
| Report.Comment (Real'Image (X1 + X2)); |
| end if; |
| end Exception_Test; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Value_Test; |
| Exact_Result_Test; |
| Arcsin_Taylor_Series_Test; |
| Arccos_Taylor_Series_Test; |
| Identity_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 ("CXG2015", |
| "Check the accuracy of the ARCSIN and ARCCOS 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 CXG2015; |
