cxg2015.a

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         -- 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;