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1 294 jeremybenn
-- CXG2017.A
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--
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--                             Grant of Unlimited Rights
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--
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--     Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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--     F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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--     unlimited rights in the software and documentation contained herein.
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--     Unlimited rights are defined in DFAR 252.227-7013(a)(19).  By making
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--     this public release, the Government intends to confer upon all
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--     recipients unlimited rights  equal to those held by the Government.
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--     These rights include rights to use, duplicate, release or disclose the
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--     released technical data and computer software in whole or in part, in
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--     any manner and for any purpose whatsoever, and to have or permit others
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--     to do so.
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--
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--                                    DISCLAIMER
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--
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--     ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
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--     DISCLOSED ARE AS IS.  THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
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--     WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
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--     SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
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--     OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
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--     PARTICULAR PURPOSE OF SAID MATERIAL.
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--*
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--
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-- OBJECTIVE:
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--      Check that the TANH function returns
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--      a result that is within the error bound allowed.
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--
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-- TEST DESCRIPTION:
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--      This test consists of a generic package that is
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--      instantiated to check both Float and a long float type.
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--      The test for each floating point type is divided into
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--      several parts:
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--         Special value checks where the result is a known constant.
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--         Checks that use an identity for determining the result.
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--
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-- SPECIAL REQUIREMENTS
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--      The Strict Mode for the numerical accuracy must be
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--      selected.  The method by which this mode is selected
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--      is implementation dependent.
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--
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-- APPLICABILITY CRITERIA:
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--      This test applies only to implementations supporting the
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--      Numerics Annex.
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--      This test only applies to the Strict Mode for numerical
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--      accuracy.
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--
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--
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-- CHANGE HISTORY:
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--      20 Mar 96   SAIC    Initial release for 2.1
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--      17 Aug 96   SAIC    Incorporated reviewer comments.
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--      03 Jun 98   EDS     Add parens to remove the potential for overflow.
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--                          Remove the invocation of Identity_Test that checks
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--                          Tanh values that are too close to zero for the
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--                          test's error bounds.
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--!
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--
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-- References:
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--
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-- Software Manual for the Elementary Functions
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-- William J. Cody, Jr. and William Waite
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-- Prentice-Hall, 1980
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--
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-- CRC Standard Mathematical Tables
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-- 23rd Edition
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--
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-- Implementation and Testing of Function Software
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-- W. J. Cody
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-- Problems and Methodologies in Mathematical Software Production
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-- editors P. C. Messina and A. Murli
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-- Lecture Notes in Computer Science   Volume 142
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-- Springer Verlag, 1982
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--
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with System;
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with Report;
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with Ada.Numerics.Generic_Elementary_Functions;
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procedure CXG2017 is
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   Verbose : constant Boolean := False;
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   Max_Samples : constant := 1000;
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84
   E  : constant := Ada.Numerics.E;
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   generic
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      type Real is digits <>;
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   package Generic_Check is
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      procedure Do_Test;
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   end Generic_Check;
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   package body Generic_Check is
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      package Elementary_Functions is new
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           Ada.Numerics.Generic_Elementary_Functions (Real);
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96
      function Tanh (X : Real) return Real renames
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           Elementary_Functions.Tanh;
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99
      function Log (X : Real) return Real renames
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           Elementary_Functions.Log;
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      -- flag used to terminate some tests early
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      Accuracy_Error_Reported : Boolean := False;
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105
 
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      -- The following value is a lower bound on the accuracy
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      -- required.  It is normally 0.0 so that the lower bound
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      -- is computed from Model_Epsilon.  However, for tests
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      -- where the expected result is only known to a certain
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      -- amount of precision this bound takes on a non-zero
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      -- value to account for that level of precision.
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      Error_Low_Bound : Real := 0.0;
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114
      procedure Check (Actual, Expected : Real;
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                       Test_Name : String;
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                       MRE : Real) is
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         Max_Error : Real;
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         Rel_Error : Real;
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         Abs_Error : Real;
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      begin
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         -- In the case where the expected result is very small or 0
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         -- we compute the maximum error as a multiple of Model_Small instead
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         -- of Model_Epsilon and Expected.
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         Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
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         Abs_Error := MRE * Real'Model_Small;
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         if Rel_Error > Abs_Error then
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            Max_Error := Rel_Error;
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         else
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            Max_Error := Abs_Error;
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         end if;
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         -- take into account the low bound on the error
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         if Max_Error < Error_Low_Bound then
133
            Max_Error := Error_Low_Bound;
134
         end if;
135
 
136
         if abs (Actual - Expected) > Max_Error then
137
            Accuracy_Error_Reported := True;
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            Report.Failed (Test_Name &
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                           " actual: " & Real'Image (Actual) &
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                           " expected: " & Real'Image (Expected) &
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                           " difference: " & Real'Image (Actual - Expected) &
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                           " max err:" & Real'Image (Max_Error) );
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         elsif Verbose then
144
            if Actual = Expected then
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               Report.Comment (Test_Name & "  exact result");
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            else
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               Report.Comment (Test_Name & "  passed");
148
            end if;
149
         end if;
150
      end Check;
151
 
152
 
153
      procedure Special_Value_Test is
154
         -- In the following tests the expected result is accurate
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         -- to the machine precision so the minimum guaranteed error
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         -- bound can be used.
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         Minimum_Error : constant := 8.0;
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         E2 : constant := E * E;
159
      begin
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         Check (Tanh (1.0),
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                (E - 1.0 / E) / (E + 1.0 / E),
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                "tanh(1)",
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                Minimum_Error);
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         Check (Tanh (2.0),
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                (E2 - 1.0 / E2) / (E2 + 1.0 / E2),
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                "tanh(2)",
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                Minimum_Error);
168
      exception
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         when Constraint_Error =>
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            Report.Failed ("Constraint_Error raised in special value test");
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         when others =>
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            Report.Failed ("exception in special value test");
173
      end Special_Value_Test;
174
 
175
 
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177
      procedure Exact_Result_Test is
178
         No_Error : constant := 0.0;
179
      begin
180
         -- A.5.1(38);6.0
181
         Check (Tanh (0.0),  0.0, "tanh(0)", No_Error);
182
      exception
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         when Constraint_Error =>
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            Report.Failed ("Constraint_Error raised in Exact_Result Test");
185
         when others =>
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            Report.Failed ("exception in Exact_Result Test");
187
      end Exact_Result_Test;
188
 
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190
      procedure Identity_Test (A, B : Real) is
191
      -- For this test we use the identity
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      --    TANH(u+v) = [TANH(u) + TANH(v)] / [1 + TANH(u)*TANH(v)]
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      -- which is transformed to
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      --    TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]
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      -- where C = TANH(1/8) and y = x - 1/8
196
      --
197
      -- see Cody pg 248-249 for details on the error analysis.
198
      -- The net result is a relative error bound of 16 * Model_Epsilon.
199
      --
200
      -- The second part of this test checks the identity
201
      --    TANH(-x) = -TANH(X)
202
 
203
         X, Y : Real;
204
         Actual1, Actual2 : Real;
205
         C : constant := 1.2435300177159620805e-1;
206
      begin
207
         if Real'Digits > 20 then
208
            -- constant C is accurate to 20 digits.  Set the low bound
209
            -- on the error to 16*10**-20
210
            Error_Low_Bound := 0.00000_00000_00000_00016;
211
            Report.Comment ("tanh accuracy checked to 20 digits");
212
         end if;
213
 
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         Accuracy_Error_Reported := False;  -- reset
215
         for I in 1..Max_Samples loop
216
            X :=  (B - A) * (Real (I) / Real (Max_Samples)) + A;
217
            Actual1 := Tanh(X);
218
 
219
            -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]
220
            Y := X - (1.0 / 8.0);
221
            Actual2 := (Tanh (Y) + C) / (1.0 + Tanh(Y) * C);
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223
            Check (Actual1, Actual2,
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                   "Identity_1_Test " & Integer'Image (I) & ": tanh(" &
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                   Real'Image (X) & ") ",
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                   16.0);
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            -- TANH(-x) = -TANH(X)
229
            Actual2 := Tanh(-X);
230
            Check (-Actual1, Actual2,
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                   "Identity_2_Test " & Integer'Image (I) & ": tanh(" &
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                   Real'Image (X) & ") ",
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                   16.0);
234
 
235
            if Accuracy_Error_Reported then
236
              -- only report the first error in this test in order to keep
237
              -- lots of failures from producing a huge error log
238
              return;
239
            end if;
240
 
241
         end loop;
242
         Error_Low_Bound := 0.0;   -- reset
243
      exception
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         when Constraint_Error =>
245
            Report.Failed
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               ("Constraint_Error raised in Identity_Test" &
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                " for X=" & Real'Image (X));
248
         when others =>
249
            Report.Failed ("exception in Identity_Test" &
250
                " for X=" & Real'Image (X));
251
      end Identity_Test;
252
 
253
 
254
 
255
      procedure Do_Test is
256
      begin
257
         Special_Value_Test;
258
         Exact_Result_Test;
259
            -- cover a large range
260
         Identity_Test (1.0, Real'Safe_Last);
261
      end Do_Test;
262
   end Generic_Check;
263
 
264
   -----------------------------------------------------------------------
265
   -----------------------------------------------------------------------
266
   package Float_Check is new Generic_Check (Float);
267
 
268
   -- check the floating point type with the most digits
269
   type A_Long_Float is digits System.Max_Digits;
270
   package A_Long_Float_Check is new Generic_Check (A_Long_Float);
271
 
272
   -----------------------------------------------------------------------
273
   -----------------------------------------------------------------------
274
 
275
 
276
begin
277
   Report.Test ("CXG2017",
278
                "Check the accuracy of the TANH function");
279
 
280
   if Verbose then
281
      Report.Comment ("checking Standard.Float");
282
   end if;
283
 
284
   Float_Check.Do_Test;
285
 
286
   if Verbose then
287
      Report.Comment ("checking a digits" &
288
                      Integer'Image (System.Max_Digits) &
289
                      " floating point type");
290
   end if;
291
 
292
   A_Long_Float_Check.Do_Test;
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   Report.Result;
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end CXG2017;

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