cxg2010.a

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	    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;