| -- CXG2010.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 exp function returns |
| -- results that are within the error bound allowed. |
| -- |
| -- TEST DESCRIPTION: |
| -- This test contains three test packages that are almost |
| -- identical. The first two packages differ only in the |
| -- floating point type that is being tested. The first |
| -- and third package differ only in whether the generic |
| -- elementary functions package or the pre-instantiated |
| -- package is used. |
| -- The test package is not generic so that the arguments |
| -- and expected results for some of the test values |
| -- can be expressed as universal real instead of being |
| -- computed at runtime. |
| -- |
| -- 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 and where the Machine_Radix is 2, 4, 8, or 16. |
| -- This test only applies to the Strict Mode for numerical |
| -- accuracy. |
| -- |
| -- |
| -- CHANGE HISTORY: |
| -- 1 Mar 96 SAIC Initial release for 2.1 |
| -- 2 Sep 96 SAIC Improved check routine |
| -- |
| --! |
| |
| -- |
| -- 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 |
| -- |
| |
| -- |
| -- Notes on derivation of error bound for exp(p)*exp(-p) |
| -- |
| -- Let a = true value of exp(p) and ac be the computed value. |
| -- Then a = ac(1+e1), where |e1| <= 4*Model_Epsilon. |
| -- Similarly, let b = true value of exp(-p) and bc be the computed value. |
| -- Then b = bc(1+e2), where |e2| <= 4*ME. |
| -- |
| -- The product of x and y is (x*y)(1+e3), where |e3| <= 1.0ME |
| -- |
| -- Hence, the computed ab is [ac(1+e1)*bc(1+e2)](1+e3) = |
| -- (ac*bc)[1 + e1 + e2 + e3 + e1e2 + e1e3 + e2e3 + e1e2e3). |
| -- |
| -- Throwing away the last four tiny terms, we have (ac*bc)(1 + eta), |
| -- |
| -- where |eta| <= (4+4+1)ME = 9.0Model_Epsilon. |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Elementary_Functions; |
| with Ada.Numerics.Elementary_Functions; |
| procedure CXG2010 is |
| Verbose : constant Boolean := False; |
| Max_Samples : constant := 1000; |
| Accuracy_Error_Reported : Boolean := False; |
| |
| package Float_Check is |
| subtype Real is Float; |
| procedure Do_Test; |
| end Float_Check; |
| |
| package body Float_Check is |
| package Elementary_Functions is new |
| Ada.Numerics.Generic_Elementary_Functions (Real); |
| function Sqrt (X : Real) return Real renames |
| Elementary_Functions.Sqrt; |
| function Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| |
| |
| -- 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 Argument_Range_Check_1 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 1.0 / 16.0; |
| One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX - ZX * One_Minus_Exp_Minus_V; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 1"); |
| when others => |
| Report.Failed ("exception in argument range check 1"); |
| end Argument_Range_Check_1; |
| |
| |
| |
| procedure Argument_Range_Check_2 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 45.0 / 16.0; |
| -- 1/16 - Exp(45/16) |
| Coeff : constant := 2.4453321046920570389E-3; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; |
| -- where Coeff is 1/16 - Exp(45/16) |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX * 0.0625 - ZX * Coeff; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 2"); |
| when others => |
| Report.Failed ("exception in argument range check 2"); |
| end Argument_Range_Check_2; |
| |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(1.0); |
| -- normal accuracy requirements |
| Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(16.0) * Exp(-16.0); |
| Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); |
| Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(0.0); |
| Check (Y, 1.0, "test 4 -- exp(0.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 4"); |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| --- test 5 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), |
| 1.0, |
| "5"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| --- test 6 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_2 (1.0, |
| Sqrt(Real(Real'Machine_Radix)), |
| "6"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| end Do_Test; |
| end Float_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| -- check the floating point type with the most digits |
| type A_Long_Float is digits System.Max_Digits; |
| |
| |
| package A_Long_Float_Check is |
| subtype Real is A_Long_Float; |
| procedure Do_Test; |
| end A_Long_Float_Check; |
| |
| package body A_Long_Float_Check is |
| package Elementary_Functions is new |
| Ada.Numerics.Generic_Elementary_Functions (Real); |
| function Sqrt (X : Real) return Real renames |
| Elementary_Functions.Sqrt; |
| function Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| |
| |
| -- 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 Argument_Range_Check_1 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 1.0 / 16.0; |
| One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX - ZX * One_Minus_Exp_Minus_V; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 1"); |
| when others => |
| Report.Failed ("exception in argument range check 1"); |
| end Argument_Range_Check_1; |
| |
| |
| |
| procedure Argument_Range_Check_2 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 45.0 / 16.0; |
| -- 1/16 - Exp(45/16) |
| Coeff : constant := 2.4453321046920570389E-3; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; |
| -- where Coeff is 1/16 - Exp(45/16) |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX * 0.0625 - ZX * Coeff; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 2"); |
| when others => |
| Report.Failed ("exception in argument range check 2"); |
| end Argument_Range_Check_2; |
| |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(1.0); |
| -- normal accuracy requirements |
| Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(16.0) * Exp(-16.0); |
| Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); |
| Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(0.0); |
| Check (Y, 1.0, "test 4 -- exp(0.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 4"); |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| --- test 5 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), |
| 1.0, |
| "5"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| --- test 6 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_2 (1.0, |
| Sqrt(Real(Real'Machine_Radix)), |
| "6"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| end Do_Test; |
| end A_Long_Float_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| package Non_Generic_Check is |
| procedure Do_Test; |
| subtype Real is Float; |
| end Non_Generic_Check; |
| |
| package body Non_Generic_Check is |
| |
| package Elementary_Functions renames |
| Ada.Numerics.Elementary_Functions; |
| function Sqrt (X : Real) return Real renames |
| Elementary_Functions.Sqrt; |
| function Exp (X : Real) return Real renames |
| Elementary_Functions.Exp; |
| |
| |
| -- 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 Argument_Range_Check_1 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 1.0 / 16.0; |
| One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) - Exp(X) * (1 - Exp(-V); |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX - ZX * One_Minus_Exp_Minus_V; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 1"); |
| when others => |
| Report.Failed ("exception in argument range check 1"); |
| end Argument_Range_Check_1; |
| |
| |
| |
| procedure Argument_Range_Check_2 (A, B : Real; |
| Test : String) is |
| -- test a evenly distributed selection of |
| -- arguments selected from the range A to B. |
| -- Test using identity: EXP(X-V) = EXP(X) * EXP (-V) |
| -- The parameter One_Minus_Exp_Minus_V is the value |
| -- 1.0 - Exp (-V) |
| -- accurate to machine precision. |
| -- This procedure is a translation of part of Cody's test |
| X : Real; |
| Y : Real; |
| ZX, ZY : Real; |
| V : constant := 45.0 / 16.0; |
| -- 1/16 - Exp(45/16) |
| Coeff : constant := 2.4453321046920570389E-3; |
| |
| begin |
| Accuracy_Error_Reported := False; |
| for I in 1..Max_Samples loop |
| X := (B - A) * Real (I) / Real (Max_Samples) + A; |
| Y := X - V; |
| if Y < 0.0 then |
| X := Y + V; |
| end if; |
| |
| ZX := Exp (X); |
| ZY := Exp (Y); |
| |
| -- ZX := Exp(X) * 1/16 - Exp(X) * Coeff; |
| -- where Coeff is 1/16 - Exp(45/16) |
| -- which simplifies to ZX := Exp (X-V); |
| ZX := ZX * 0.0625 - ZX * Coeff; |
| |
| -- note that since the expected value is computed, we |
| -- must take the error in that computation into account. |
| Check (ZY, ZX, |
| "test " & Test & " -" & |
| Integer'Image (I) & |
| " exp (" & Real'Image (X) & ")", |
| 9.0); |
| exit when Accuracy_Error_Reported; |
| end loop; |
| exception |
| when Constraint_Error => |
| Report.Failed |
| ("Constraint_Error raised in argument range check 2"); |
| when others => |
| Report.Failed ("exception in argument range check 2"); |
| end Argument_Range_Check_2; |
| |
| |
| procedure Do_Test is |
| begin |
| |
| --- test 1 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(1.0); |
| -- normal accuracy requirements |
| Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(16.0) * Exp(-16.0); |
| Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi); |
| Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 3"); |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| Y : Real; |
| begin |
| Y := Exp(0.0); |
| Check (Y, 1.0, "test 4 -- exp(0.0)", |
| 0.0); -- no error allowed |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 4"); |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| --- test 5 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)), |
| 1.0, |
| "5"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| --- test 6 --- |
| -- constants used here only have 19 digits of precision |
| if Real'Digits > 19 then |
| Error_Low_Bound := 0.00000_00000_00000_0001; |
| Report.Comment ("exp accuracy checked to 19 digits"); |
| end if; |
| |
| Argument_Range_Check_2 (1.0, |
| Sqrt(Real(Real'Machine_Radix)), |
| "6"); |
| Error_Low_Bound := 0.0; -- reset |
| |
| end Do_Test; |
| end Non_Generic_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| begin |
| Report.Test ("CXG2010", |
| "Check the accuracy of the exp function"); |
| |
| -- the test only applies to machines with a radix of 2,4,8, or 16 |
| case Float'Machine_Radix is |
| when 2 | 4 | 8 | 16 => null; |
| when others => |
| Report.Not_Applicable ("only applicable to binary radix"); |
| Report.Result; |
| return; |
| end case; |
| |
| 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; |
| |
| if Verbose then |
| Report.Comment ("checking non-generic package"); |
| end if; |
| |
| Non_Generic_Check.Do_Test; |
| |
| Report.Result; |
| end CXG2010; |
