cxg2011.a

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              -- 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 Taylor Series Test");
         when others =>
            Report.Failed ("exception in Taylor Series Test");
      end Taylor_Series_Test;



      procedure Log_Difference_Identity is
      -- Check using the identity ln(x) = ln(17x/16) - ln(17/16)
      -- over the range A to B.
      -- The selected range assures that both X and 17x/16 will
      -- have the same exponents and neither argument gets too close
      -- to 1.    Cody pg 50.
         A : constant Real := 1.0 / Sqrt (2.0);
         B : constant Real := 15.0 / 16.0;
         X : Real;
         Expected : Real;
         Actual : Real;
      begin
         Accuracy_Error_Reported := False;  -- reset
         for I in 1..Max_Samples loop
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
            -- magic argument purification
            X := Real'Machine (Real'Machine (X+8.0) - 8.0);
            
            Expected := Log (X + X / 16.0) - Log (17.0/16.0);

            Actual := Log (X);
            Check (Actual, Expected,
                   "Log Difference Identity -" &
                   Integer'Image (I) &
                   " log (" & Real'Image (X) & ")",
                   4.0);

            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 Log Difference Identity Test");
         when others =>
            Report.Failed ("exception in Log Difference Identity Test");
      end Log_Difference_Identity;


      procedure Log_Product_Identity is
      -- Check using the identity ln(x**2) = 2ln(x)
      -- over the range A to B.
      -- This large range is chosen to minimize the possibility of
      -- undetected systematic errors.   Cody pg 53.
         A : constant Real := 16.0;
         B : constant Real := 240.0;
         X : Real;
         Expected : Real;
         Actual : Real;
      begin
         Accuracy_Error_Reported := False;  -- reset
         for I in 1..Max_Samples loop
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
            -- magic argument purification
            X := Real'Machine (Real'Machine (X+8.0) - 8.0);
            
            Expected := 2.0 * Log (X);

            Actual := Log (X*X);
            Check (Actual, Expected,
                   "Log Product Identity -" &
                   Integer'Image (I) &
                   " log (" & Real'Image (X) & ")",
                   4.0);
            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 Log Product Identity Test");
         when others =>
            Report.Failed ("exception in Log Product Identity Test");
      end Log_Product_Identity;


      procedure Log10_Test is
      -- Check using the identity log(x) = log(11x/10) - log(1.1)
      -- over the range A to B.  See Cody pg 52.
         A : constant Real := 1.0 / Sqrt (10.0);
         B : constant Real := 0.9;
         X : Real;
         Expected : Real;
         Actual : Real;
      begin
         if Real'Digits > 17 then
             -- constant used below is accuract to 17 digits
            Error_Low_Bound := 0.00000_00000_00000_01;
            Report.Comment ("log accuracy checked to 19 digits");
         end if;
         Accuracy_Error_Reported := False;  -- reset
         for I in 1..Max_Samples loop
            X :=  (B - A) * Real (I) / Real (Max_Samples) + A;
            
            Expected := Log (X + X/10.0, 10.0)
                     - 3.77060_15822_50407_5E-4 - 21.0 / 512.0;

            Actual := Log (X, 10.0);
            Check (Actual, Expected,
                   "Log 10 Test -" &
                   Integer'Image (I) &
                   " log (" & Real'Image (X) & ")",
                   4.0);

              -- 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 Log 10 Test");
         when others =>
            Report.Failed ("exception in Log 10 Test");
      end Log10_Test;


      procedure Exception_Test is
         X1, X2, X3, X4 : Real;
      begin
         begin
            X1 := Log (0.0);
            Report.Failed ("exception not raised for LOG(0)");
         exception
            -- Log (0.0) must raise Constraint_Error, not Argument_Error,
            -- as per A.5.1(28,29).  Was incorrect in ACVC 2.1 release.
            when Ada.Numerics.Argument_Error =>
               Report.Failed ("Argument_Error raised instead of" &
                              " Constraint_Error for LOG(0)--A.5.1(28,29)");
            when Constraint_Error =>  null;  -- ok
            when others =>
               Report.Failed ("wrong exception raised for LOG(0)");
         end;

         begin
            X2 := Log ( 1.0, 0.0);
            Report.Failed ("exception not raised for LOG(1,0)");
         exception
            when Ada.Numerics.Argument_Error =>  null;  -- ok
            when Constraint_Error => 
               Report.Failed ("constraint_error raised instead of" &
                              " argument_error for LOG(1,0)");
            when others =>
               Report.Failed ("wrong exception raised for LOG(1,0)");
         end;

         begin
            X3 := Log (1.0, 1.0);
            Report.Failed ("exception not raised for LOG(1,1)");
         exception
            when Ada.Numerics.Argument_Error =>  null;  -- ok
            when Constraint_Error => 
               Report.Failed ("constraint_error raised instead of" &
                              " argument_error for LOG(1,1)");
            when others =>
               Report.Failed ("wrong exception raised for LOG(1,1)");
         end;

         begin
            X4 := Log (1.0, -10.0);
            Report.Failed ("exception not raised for LOG(1,-10)");
         exception
            when Ada.Numerics.Argument_Error =>  null;  -- ok
            when Constraint_Error => 
               Report.Failed ("constraint_error raised instead of" &
                              " argument_error for LOG(1,-10)");
            when others =>
               Report.Failed ("wrong exception raised for LOG(1,-10)");
         end;

         -- optimizer thwarting
         if Report.Ident_Bool (False) then
            Report.Comment (Real'Image (X1+X2+X3+X4));
         end if;
      end Exception_Test;


      procedure Do_Test is
      begin
         Special_Value_Test;
         Taylor_Series_Test;
         Log_Difference_Identity;
         Log_Product_Identity;
         Log10_Test;
         Exception_Test;
      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 ("CXG2011",
                "Check the accuracy of the log 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 CXG2011;