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authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
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tree976dc5ab7fddf506dadce60ae936f43f58787092 /gcc/testsuite/ada/acats/tests/cxg/cxg2017.a
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+-- CXG2017.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 TANH function returns
+-- a result that is within the error bound allowed.
+--
+-- TEST DESCRIPTION:
+-- This test consists of a generic package that is
+-- instantiated to check both Float and a long float type.
+-- The test for each floating point type is divided into
+-- several parts:
+-- Special value checks where the result is a known constant.
+-- Checks that use an identity for determining the result.
+--
+-- 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.
+-- This test only applies to the Strict Mode for numerical
+-- accuracy.
+--
+--
+-- CHANGE HISTORY:
+-- 20 Mar 96 SAIC Initial release for 2.1
+-- 17 Aug 96 SAIC Incorporated reviewer comments.
+-- 03 Jun 98 EDS Add parens to remove the potential for overflow.
+-- Remove the invocation of Identity_Test that checks
+-- Tanh values that are too close to zero for the
+-- test's error bounds.
+--!
+
+--
+-- 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
+--
+
+with System;
+with Report;
+with Ada.Numerics.Generic_Elementary_Functions;
+procedure CXG2017 is
+ Verbose : constant Boolean := False;
+ Max_Samples : constant := 1000;
+
+ E : constant := Ada.Numerics.E;
+
+ generic
+ type Real is digits <>;
+ package Generic_Check is
+ procedure Do_Test;
+ end Generic_Check;
+
+ package body Generic_Check is
+ package Elementary_Functions is new
+ Ada.Numerics.Generic_Elementary_Functions (Real);
+
+ function Tanh (X : Real) return Real renames
+ Elementary_Functions.Tanh;
+
+ function Log (X : Real) return Real renames
+ Elementary_Functions.Log;
+
+ -- flag used to terminate some tests early
+ Accuracy_Error_Reported : Boolean := False;
+
+
+ -- 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_Small instead
+ -- of Model_Epsilon and Expected.
+ Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
+ Abs_Error := MRE * Real'Model_Small;
+ 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 Special_Value_Test is
+ -- In the following tests the expected result is accurate
+ -- to the machine precision so the minimum guaranteed error
+ -- bound can be used.
+ Minimum_Error : constant := 8.0;
+ E2 : constant := E * E;
+ begin
+ Check (Tanh (1.0),
+ (E - 1.0 / E) / (E + 1.0 / E),
+ "tanh(1)",
+ Minimum_Error);
+ Check (Tanh (2.0),
+ (E2 - 1.0 / E2) / (E2 + 1.0 / E2),
+ "tanh(2)",
+ Minimum_Error);
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in special value test");
+ when others =>
+ Report.Failed ("exception in special value test");
+ end Special_Value_Test;
+
+
+
+ procedure Exact_Result_Test is
+ No_Error : constant := 0.0;
+ begin
+ -- A.5.1(38);6.0
+ Check (Tanh (0.0), 0.0, "tanh(0)", No_Error);
+ 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 Identity_Test (A, B : Real) is
+ -- For this test we use the identity
+ -- TANH(u+v) = [TANH(u) + TANH(v)] / [1 + TANH(u)*TANH(v)]
+ -- which is transformed to
+ -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]
+ -- where C = TANH(1/8) and y = x - 1/8
+ --
+ -- see Cody pg 248-249 for details on the error analysis.
+ -- The net result is a relative error bound of 16 * Model_Epsilon.
+ --
+ -- The second part of this test checks the identity
+ -- TANH(-x) = -TANH(X)
+
+ X, Y : Real;
+ Actual1, Actual2 : Real;
+ C : constant := 1.2435300177159620805e-1;
+ begin
+ if Real'Digits > 20 then
+ -- constant C is accurate to 20 digits. Set the low bound
+ -- on the error to 16*10**-20
+ Error_Low_Bound := 0.00000_00000_00000_00016;
+ Report.Comment ("tanh accuracy checked to 20 digits");
+ end if;
+
+ Accuracy_Error_Reported := False; -- reset
+ for I in 1..Max_Samples loop
+ X := (B - A) * (Real (I) / Real (Max_Samples)) + A;
+ Actual1 := Tanh(X);
+
+ -- TANH(x) = [TANH(y)+C] / [1 + TANH(y) * C]
+ Y := X - (1.0 / 8.0);
+ Actual2 := (Tanh (Y) + C) / (1.0 + Tanh(Y) * C);
+
+ Check (Actual1, Actual2,
+ "Identity_1_Test " & Integer'Image (I) & ": tanh(" &
+ Real'Image (X) & ") ",
+ 16.0);
+
+ -- TANH(-x) = -TANH(X)
+ Actual2 := Tanh(-X);
+ Check (-Actual1, Actual2,
+ "Identity_2_Test " & Integer'Image (I) & ": tanh(" &
+ Real'Image (X) & ") ",
+ 16.0);
+
+ 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;
+ Error_Low_Bound := 0.0; -- reset
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Identity_Test" &
+ " for X=" & Real'Image (X));
+ when others =>
+ Report.Failed ("exception in Identity_Test" &
+ " for X=" & Real'Image (X));
+ end Identity_Test;
+
+
+
+ procedure Do_Test is
+ begin
+ Special_Value_Test;
+ Exact_Result_Test;
+ -- cover a large range
+ Identity_Test (1.0, Real'Safe_Last);
+ 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 ("CXG2017",
+ "Check the accuracy of the TANH 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 CXG2017;