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--- 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;