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diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2014.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2014.a new file mode 100644 index 000000000..48499a255 --- /dev/null +++ b/gcc/testsuite/ada/acats/tests/cxg/cxg2014.a @@ -0,0 +1,399 @@ +-- 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; |