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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
commit554fd8c5195424bdbcabf5de30fdc183aba391bd (patch)
tree976dc5ab7fddf506dadce60ae936f43f58787092 /gcc/testsuite/ada/acats/tests/cxg/cxg2003.a
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+-- CXG2003.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 sqrt function returns
+-- results that are within the error bound allowed.
+--
+-- TEST DESCRIPTION:
+-- This test contains three test packages that are almost
+-- identical. The first two packages differ only in the
+-- floating point type that is being tested. The first
+-- and third package differ only in whether the generic
+-- elementary functions package or the pre-instantiated
+-- package is used.
+-- The test package is not generic so that the arguments
+-- and expected results for some of the test values
+-- can be expressed as universal real instead of being
+-- computed at runtime.
+--
+-- 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:
+-- 2 FEB 96 SAIC Initial release for 2.1
+-- 18 AUG 96 SAIC Made Check consistent with other tests.
+--
+--!
+
+with System;
+with Report;
+with Ada.Numerics.Generic_Elementary_Functions;
+with Ada.Numerics.Elementary_Functions;
+procedure CXG2003 is
+ Verbose : constant Boolean := False;
+
+ package Float_Check is
+ subtype Real is Float;
+ procedure Do_Test;
+ end Float_Check;
+
+ package body Float_Check is
+ package Elementary_Functions is new
+ Ada.Numerics.Generic_Elementary_Functions (Real);
+ function Sqrt (X : Real) return Real renames
+ Elementary_Functions.Sqrt;
+ function Log (X : Real) return Real renames
+ Elementary_Functions.Log;
+ function Exp (X : Real) return Real renames
+ Elementary_Functions.Exp;
+
+ -- The default Maximum Relative Error is the value specified
+ -- in the LRM.
+ Default_MRE : constant Real := 2.0;
+
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real := Default_MRE) is
+ Rel_Error : Real;
+ Abs_Error : Real;
+ Max_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_Epsilon instead
+ -- of Model_Epsilon and Expected.
+ Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
+ Abs_Error := MRE * Real'Model_Epsilon;
+ if Rel_Error > Abs_Error then
+ Max_Error := Rel_Error;
+ else
+ Max_Error := Abs_Error;
+ end if;
+
+ if abs (Actual - Expected) > Max_Error then
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected: " & Real'Image (Expected) &
+ " difference: " &
+ Real'Image (Actual - Expected) &
+ " mre:" & 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 Argument_Range_Check (A, B : Real;
+ Test : String) is
+ -- test a logarithmically distributed selection of
+ -- arguments selected from the range A to B.
+ X : Real;
+ Expected : Real;
+ Y : Real;
+ C : Real := Log(B/A);
+ Max_Samples : constant := 1000;
+
+ begin
+ for I in 1..Max_Samples loop
+ Expected := A * Exp(C * Real (I) / Real (Max_Samples));
+ X := Expected * Expected;
+ Y := Sqrt (X);
+
+ -- note that since the expected value is computed, we
+ -- must take the error in that computation into account.
+ Check (Y, Expected,
+ "test " & Test & " -" &
+ Integer'Image (I) &
+ " of argument range",
+ 3.0);
+ end loop;
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in argument range check");
+ when others =>
+ Report.Failed ("exception in argument range check");
+ end Argument_Range_Check;
+
+ procedure Do_Test is
+ begin
+
+ --- test 1 ---
+ declare
+ T : constant := (Real'Machine_EMax - 1) / 2;
+ X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Real'Machine_Radix) ** T;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 1");
+ when others =>
+ Report.Failed ("exception in test 1");
+ end;
+
+ --- test 2 ---
+ declare
+ T : constant := (Real'Model_EMin + 1) / 2;
+ X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Real'Machine_Radix) ** T;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 2");
+ when others =>
+ Report.Failed ("exception in test 2");
+ end;
+
+ --- test 3 ---
+ declare
+ X : constant := 1.0;
+ Expected : constant := 1.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ Check (Y, Expected, "test 3 -- sqrt(1.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 3");
+ when others =>
+ Report.Failed ("exception in test 3");
+ end;
+
+ --- test 4 ---
+ declare
+ X : constant := 0.0;
+ Expected : constant := 0.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ Check (Y, Expected, "test 4 -- sqrt(0.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 4");
+ when others =>
+ Report.Failed ("exception in test 4");
+ end;
+
+ --- test 5 ---
+ declare
+ X : constant := -1.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ -- the following code should not be executed.
+ -- The call to Check is to keep the call to Sqrt from
+ -- appearing to be dead code.
+ Check (Y, -1.0, "test 5 -- sqrt(-1)" );
+ Report.Failed ("test 5 - argument_error expected");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 5");
+ when Ada.Numerics.Argument_Error =>
+ if Verbose then
+ Report.Comment ("test 5 correctly got argument_error");
+ end if;
+ when others =>
+ Report.Failed ("exception in test 5");
+ end;
+
+ --- test 6 ---
+ declare
+ X : constant := Ada.Numerics.Pi ** 2;
+ Expected : constant := Ada.Numerics.Pi;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 6 -- sqrt(pi**2)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 6");
+ when others =>
+ Report.Failed ("exception in test 6");
+ end;
+
+ --- test 7 & 8 ---
+ Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
+ 1.0,
+ "7");
+ Argument_Range_Check (1.0,
+ Sqrt(Real(Real'Machine_Radix)),
+ "8");
+ end Do_Test;
+ end Float_Check;
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+ -- check the floating point type with the most digits
+ type A_Long_Float is digits System.Max_Digits;
+
+
+ package A_Long_Float_Check is
+ subtype Real is A_Long_Float;
+ procedure Do_Test;
+ end A_Long_Float_Check;
+
+ package body A_Long_Float_Check is
+ package Elementary_Functions is new
+ Ada.Numerics.Generic_Elementary_Functions (Real);
+ function Sqrt (X : Real) return Real renames
+ Elementary_Functions.Sqrt;
+ function Log (X : Real) return Real renames
+ Elementary_Functions.Log;
+ function Exp (X : Real) return Real renames
+ Elementary_Functions.Exp;
+
+ -- The default Maximum Relative Error is the value specified
+ -- in the LRM.
+ Default_MRE : constant Real := 2.0;
+
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real := Default_MRE) is
+ Rel_Error : Real;
+ Abs_Error : Real;
+ Max_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_Epsilon instead
+ -- of Model_Epsilon and Expected.
+ Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
+ Abs_Error := MRE * Real'Model_Epsilon;
+ if Rel_Error > Abs_Error then
+ Max_Error := Rel_Error;
+ else
+ Max_Error := Abs_Error;
+ end if;
+
+ if abs (Actual - Expected) > Max_Error then
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected: " & Real'Image (Expected) &
+ " difference: " &
+ Real'Image (Actual - Expected) &
+ " mre:" & 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 Argument_Range_Check (A, B : Real;
+ Test : String) is
+ -- test a logarithmically distributed selection of
+ -- arguments selected from the range A to B.
+ X : Real;
+ Expected : Real;
+ Y : Real;
+ C : Real := Log(B/A);
+ Max_Samples : constant := 1000;
+
+ begin
+ for I in 1..Max_Samples loop
+ Expected := A * Exp(C * Real (I) / Real (Max_Samples));
+ X := Expected * Expected;
+ Y := Sqrt (X);
+
+ -- note that since the expected value is computed, we
+ -- must take the error in that computation into account.
+ Check (Y, Expected,
+ "test " & Test & " -" &
+ Integer'Image (I) &
+ " of argument range",
+ 3.0);
+ end loop;
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in argument range check");
+ when others =>
+ Report.Failed ("exception in argument range check");
+ end Argument_Range_Check;
+
+
+ procedure Do_Test is
+ begin
+
+ --- test 1 ---
+ declare
+ T : constant := (Real'Machine_EMax - 1) / 2;
+ X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Real'Machine_Radix) ** T;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 1");
+ when others =>
+ Report.Failed ("exception in test 1");
+ end;
+
+ --- test 2 ---
+ declare
+ T : constant := (Real'Model_EMin + 1) / 2;
+ X : constant := (1.0 * Real'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Real'Machine_Radix) ** T;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 2");
+ when others =>
+ Report.Failed ("exception in test 2");
+ end;
+
+ --- test 3 ---
+ declare
+ X : constant := 1.0;
+ Expected : constant := 1.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ Check (Y, Expected, "test 3 -- sqrt(1.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 3");
+ when others =>
+ Report.Failed ("exception in test 3");
+ end;
+
+ --- test 4 ---
+ declare
+ X : constant := 0.0;
+ Expected : constant := 0.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ Check (Y, Expected, "test 4 -- sqrt(0.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 4");
+ when others =>
+ Report.Failed ("exception in test 4");
+ end;
+
+ --- test 5 ---
+ declare
+ X : constant := -1.0;
+ Y : Real;
+ begin
+ Y := Sqrt(X);
+ -- the following code should not be executed.
+ -- The call to Check is to keep the call to Sqrt from
+ -- appearing to be dead code.
+ Check (Y, -1.0, "test 5 -- sqrt(-1)" );
+ Report.Failed ("test 5 - argument_error expected");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 5");
+ when Ada.Numerics.Argument_Error =>
+ if Verbose then
+ Report.Comment ("test 5 correctly got argument_error");
+ end if;
+ when others =>
+ Report.Failed ("exception in test 5");
+ end;
+
+ --- test 6 ---
+ declare
+ X : constant := Ada.Numerics.Pi ** 2;
+ Expected : constant := Ada.Numerics.Pi;
+ Y : Real;
+ begin
+ Y := Sqrt (X);
+ Check (Y, Expected, "test 6 -- sqrt(pi**2)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 6");
+ when others =>
+ Report.Failed ("exception in test 6");
+ end;
+
+ --- test 7 & 8 ---
+ Argument_Range_Check (1.0/Sqrt(Real(Real'Machine_Radix)),
+ 1.0,
+ "7");
+ Argument_Range_Check (1.0,
+ Sqrt(Real(Real'Machine_Radix)),
+ "8");
+ end Do_Test;
+ end A_Long_Float_Check;
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+
+ package Non_Generic_Check is
+ procedure Do_Test;
+ end Non_Generic_Check;
+
+ package body Non_Generic_Check is
+ package EF renames
+ Ada.Numerics.Elementary_Functions;
+ subtype Real is Float;
+
+ -- The default Maximum Relative Error is the value specified
+ -- in the LRM.
+ Default_MRE : constant Real := 2.0;
+
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real := Default_MRE) is
+ Rel_Error : Real;
+ Abs_Error : Real;
+ Max_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_Epsilon instead
+ -- of Model_Epsilon and Expected.
+ Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
+ Abs_Error := MRE * Real'Model_Epsilon;
+ if Rel_Error > Abs_Error then
+ Max_Error := Rel_Error;
+ else
+ Max_Error := Abs_Error;
+ end if;
+
+ if abs (Actual - Expected) > Max_Error then
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected: " & Real'Image (Expected) &
+ " difference: " &
+ Real'Image (Actual - Expected) &
+ " mre:" & 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 Argument_Range_Check (A, B : Float;
+ Test : String) is
+ -- test a logarithmically distributed selection of
+ -- arguments selected from the range A to B.
+ X : Float;
+ Expected : Float;
+ Y : Float;
+ C : Float := EF.Log(B/A);
+ Max_Samples : constant := 1000;
+
+ begin
+ for I in 1..Max_Samples loop
+ Expected := A * EF.Exp(C * Float (I) / Float (Max_Samples));
+ X := Expected * Expected;
+ Y := EF.Sqrt (X);
+
+ -- note that since the expected value is computed, we
+ -- must take the error in that computation into account.
+ Check (Y, Expected,
+ "test " & Test & " -" &
+ Integer'Image (I) &
+ " of argument range",
+ 3.0);
+ end loop;
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in argument range check");
+ when others =>
+ Report.Failed ("exception in argument range check");
+ end Argument_Range_Check;
+
+
+ procedure Do_Test is
+ begin
+
+ --- test 1 ---
+ declare
+ T : constant := (Float'Machine_EMax - 1) / 2;
+ X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Float'Machine_Radix) ** T;
+ Y : Float;
+ begin
+ Y := EF.Sqrt (X);
+ Check (Y, Expected, "test 1 -- sqrt(radix**((emax-1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 1");
+ when others =>
+ Report.Failed ("exception in test 1");
+ end;
+
+ --- test 2 ---
+ declare
+ T : constant := (Float'Model_EMin + 1) / 2;
+ X : constant := (1.0 * Float'Machine_Radix) ** (2 * T);
+ Expected : constant := (1.0 * Float'Machine_Radix) ** T;
+ Y : Float;
+ begin
+ Y := EF.Sqrt (X);
+ Check (Y, Expected, "test 2 -- sqrt(radix**((emin+1)/2))");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 2");
+ when others =>
+ Report.Failed ("exception in test 2");
+ end;
+
+ --- test 3 ---
+ declare
+ X : constant := 1.0;
+ Expected : constant := 1.0;
+ Y : Float;
+ begin
+ Y := EF.Sqrt(X);
+ Check (Y, Expected, "test 3 -- sqrt(1.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 3");
+ when others =>
+ Report.Failed ("exception in test 3");
+ end;
+
+ --- test 4 ---
+ declare
+ X : constant := 0.0;
+ Expected : constant := 0.0;
+ Y : Float;
+ begin
+ Y := EF.Sqrt(X);
+ Check (Y, Expected, "test 4 -- sqrt(0.0)",
+ 0.0); -- no error allowed
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 4");
+ when others =>
+ Report.Failed ("exception in test 4");
+ end;
+
+ --- test 5 ---
+ declare
+ X : constant := -1.0;
+ Y : Float;
+ begin
+ Y := EF.Sqrt(X);
+ -- the following code should not be executed.
+ -- The call to Check is to keep the call to Sqrt from
+ -- appearing to be dead code.
+ Check (Y, -1.0, "test 5 -- sqrt(-1)" );
+ Report.Failed ("test 5 - argument_error expected");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 5");
+ when Ada.Numerics.Argument_Error =>
+ if Verbose then
+ Report.Comment ("test 5 correctly got argument_error");
+ end if;
+ when others =>
+ Report.Failed ("exception in test 5");
+ end;
+
+ --- test 6 ---
+ declare
+ X : constant := Ada.Numerics.Pi ** 2;
+ Expected : constant := Ada.Numerics.Pi;
+ Y : Float;
+ begin
+ Y := EF.Sqrt (X);
+ Check (Y, Expected, "test 6 -- sqrt(pi**2)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 6");
+ when others =>
+ Report.Failed ("exception in test 6");
+ end;
+
+ --- test 7 & 8 ---
+ Argument_Range_Check (1.0/EF.Sqrt(Float(Float'Machine_Radix)),
+ 1.0,
+ "7");
+ Argument_Range_Check (1.0,
+ EF.Sqrt(Float(Float'Machine_Radix)),
+ "8");
+ end Do_Test;
+ end Non_Generic_Check;
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+
+begin
+ Report.Test ("CXG2003",
+ "Check the accuracy of the sqrt 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;
+
+ if Verbose then
+ Report.Comment ("checking non-generic package");
+ end if;
+
+ Non_Generic_Check.Do_Test;
+
+ Report.Result;
+end CXG2003;