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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/cxg2014.a
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+-- CXG2014.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 SINH and COSH functions return
+-- results that are 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.
+-- Exception checks.
+--
+-- 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:
+-- 15 Mar 96 SAIC Initial release for 2.1
+-- 03 Jun 98 EDS In line 80, change 1000 to 1024, making it a model
+-- number. Add Taylor Series terms in line 281.
+-- 15 Feb 99 RLB Repaired Subtraction_Error_Test to avoid precision
+-- problems.
+--!
+
+--
+-- 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 CXG2014 is
+ Verbose : constant Boolean := False;
+ Max_Samples : constant := 1024;
+
+ E : constant := Ada.Numerics.E;
+ Cosh1 : constant := (E + 1.0 / E) / 2.0; -- cosh(1.0)
+
+ 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 Sinh (X : Real) return Real renames
+ Elementary_Functions.Sinh;
+ function Cosh (X : Real) return Real renames
+ Elementary_Functions.Cosh;
+ function Log (X : Real) return Real renames
+ Elementary_Functions.Log;
+
+ -- flag used to terminate some tests early
+ Accuracy_Error_Reported : Boolean := False;
+
+
+ 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;
+
+ 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;
+ begin
+ Check (Sinh (1.0),
+ (E - 1.0 / E) / 2.0,
+ "sinh(1)",
+ Minimum_Error);
+ Check (Cosh (1.0),
+ Cosh1,
+ "cosh(1)",
+ Minimum_Error);
+ Check (Sinh (2.0),
+ (E * E - (1.0 / (E * E))) / 2.0,
+ "sinh(2)",
+ Minimum_Error);
+ Check (Cosh (2.0),
+ (E * E + (1.0 / (E * E))) / 2.0,
+ "cosh(2)",
+ Minimum_Error);
+ Check (Sinh (-1.0),
+ (1.0 / E - E) / 2.0,
+ "sinh(-1)",
+ 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 (Sinh (0.0), 0.0, "sinh(0)", No_Error);
+ Check (Cosh (0.0), 1.0, "cosh(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_1_Test is
+ -- For the Sinh test use the identity
+ -- 2 * Sinh(x) * Cosh(1) = Sinh(x+1) + Sinh (x-1)
+ -- which is transformed to
+ -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
+ -- where C = 1/(2*Cosh(1))
+ --
+ -- For the Cosh test use the identity
+ -- 2 * Cosh(x) * Cosh(1) = Cosh(x+1) + Cosh(x-1)
+ -- which is transformed to
+ -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
+ -- where C is the same as above
+ --
+ -- see Cody pg 230-231 for details on the error analysis.
+ -- The net result is a relative error bound of 16 * Model_Epsilon.
+
+ A : constant := 3.0;
+ -- large upper bound but not so large as to cause Cosh(B)
+ -- to overflow
+ B : constant Real := Log(Real'Safe_Last) - 2.0;
+ X_Minus_1, X, X_Plus_1 : Real;
+ Actual1, Actual2 : Real;
+ C : constant := 1.0 / (2.0 * Cosh1);
+ 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_Plus_1 := (B - A) * Real (I) / Real (Max_Samples) + A;
+ X_Plus_1 := Real'Machine (X_Plus_1);
+ X := Real'Machine (X_Plus_1 - 1.0);
+ X_Minus_1 := Real'Machine (X - 1.0);
+
+ -- Sinh(x) = ((Sinh(x+1) + Sinh(x-1)) * C
+ Actual1 := Sinh(X);
+ Actual2 := C * (Sinh(X_Plus_1) + Sinh(X_Minus_1));
+
+ Check (Actual1, Actual2,
+ "Identity_1_Test " & Integer'Image (I) & ": sinh(" &
+ Real'Image (X) & ") ",
+ 16.0);
+
+ -- Cosh(x) = C * (Cosh(x+1) + Cosh(x-1))
+ Actual1 := Cosh (X);
+ Actual2 := C * (Cosh(X_Plus_1) + Cosh (X_Minus_1));
+ Check (Actual1, Actual2,
+ "Identity_1_Test " & Integer'Image (I) & ": cosh(" &
+ 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;
+
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Identity_1_Test" &
+ " for X=" & Real'Image (X));
+ when others =>
+ Report.Failed ("exception in Identity_1_Test" &
+ " for X=" & Real'Image (X));
+ end Identity_1_Test;
+
+
+
+ procedure Subtraction_Error_Test is
+ -- This test detects the error resulting from subtraction if
+ -- the obvious algorithm was used for computing sinh. That is,
+ -- it it is computed as (e**x - e**-x)/2.
+ -- We check the result by using a Taylor series expansion that
+ -- will produce a result accurate to the machine precision for
+ -- the range under test.
+ --
+ -- The maximum relative error bound for this test is
+ -- 8 for the sinh operation and 7 for the Taylor series
+ -- for a total of 15 * Model_Epsilon
+ A : constant := 0.0;
+ B : constant := 0.5;
+ X : Real;
+ X_Squared : Real;
+ Actual, Expected : Real;
+ begin
+ if Real'digits > 15 then
+ return; -- The approximation below is not accurate beyond
+ -- 15 digits. Adding more terms makes the error
+ -- larger, so it makes the test worse for more normal
+ -- values. Thus, we skip this subtest for larger than
+ -- 15 digits.
+ end if;
+ Accuracy_Error_Reported := False; -- reset
+ for I in 1..Max_Samples loop
+ X := (B - A) * Real (I) / Real (Max_Samples) + A;
+ X_Squared := X * X;
+
+ Actual := Sinh(X);
+
+ -- The Taylor series regrouped a bit
+ Expected :=
+ X * (1.0 + (X_Squared / 6.0) *
+ (1.0 + (X_Squared/20.0) *
+ (1.0 + (X_Squared/42.0) *
+ (1.0 + (X_Squared/72.0) *
+ (1.0 + (X_Squared/110.0) *
+ (1.0 + (X_Squared/156.0)
+ ))))));
+
+ Check (Actual, Expected,
+ "Subtraction_Error_Test " & Integer'Image (I) & ": sinh(" &
+ Real'Image (X) & ") ",
+ 15.0);
+
+ 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 Subtraction_Error_Test");
+ when others =>
+ Report.Failed ("exception in Subtraction_Error_Test");
+ end Subtraction_Error_Test;
+
+
+ procedure Exception_Test is
+ X1, X2 : Real := 0.0;
+ begin
+ -- this part of the test is only applicable if 'Machine_Overflows
+ -- is true.
+ if Real'Machine_Overflows then
+
+ begin
+ X1 := Sinh (Real'Safe_Last / 2.0);
+ Report.Failed ("no exception for sinh overflow");
+ exception
+ when Constraint_Error => null;
+ when others =>
+ Report.Failed ("wrong exception sinh overflow");
+ end;
+
+ begin
+ X2 := Cosh (Real'Safe_Last / 2.0);
+ Report.Failed ("no exception for cosh overflow");
+ exception
+ when Constraint_Error => null;
+ when others =>
+ Report.Failed ("wrong exception cosh overflow");
+ end;
+
+ end if;
+
+ -- 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;
+ Identity_1_Test;
+ Subtraction_Error_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 ("CXG2014",
+ "Check the accuracy of the SINH and COSH 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 CXG2014;