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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/cxg2002.a
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+-- CXG2002.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 complex "abs" or modulus function returns
+-- results that are within the error bound allowed.
+--
+-- TEST DESCRIPTION:
+-- This test uses a generic package to compute and check the
+-- values of the modulus function. In addition, a non-generic
+-- copy of this package is used to check the non-generic package
+-- Ada.Numerics.Complex_Types.
+-- Of special interest is the case where either the real or
+-- the imaginary part of the argument is very large while the
+-- other part is very small or 0.
+-- We want to check that the value is computed such that
+-- an overflow does not occur. If computed directly from the
+-- definition
+-- abs (x+yi) = sqrt(x**2 + y**2)
+-- then overflow or underflow is much more likely than if the
+-- argument is normalized first.
+--
+-- 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:
+-- 31 JAN 96 SAIC Initial release for 2.1
+-- 02 JUN 98 EDS Add parens to intermediate calculations.
+--!
+
+--
+-- Reference:
+-- 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_Complex_Types;
+with Ada.Numerics.Complex_Types;
+procedure CXG2002 is
+ Verbose : constant Boolean := False;
+ Maximum_Relative_Error : constant := 3.0;
+
+ generic
+ type Real is digits <>;
+ package Generic_Check is
+ procedure Do_Test;
+ end Generic_Check;
+
+ package body Generic_Check is
+ package Complex_Types is new
+ Ada.Numerics.Generic_Complex_Types (Real);
+ use Complex_Types;
+
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real := Maximum_Relative_Error) is
+ Rel_Error,
+ Abs_Error,
+ 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 (Expected - Actual) &
+ " 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 Do_Test is
+ Z : Complex;
+ X : Real;
+ T : Real;
+ begin
+
+ --- test 1 ---
+ begin
+ T := Real'Safe_Last;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T, "test 1 -- abs(bigreal + 0i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 1");
+ when others =>
+ Report.Failed ("exception in test 1");
+ end;
+
+ --- test 2 ---
+ begin
+ T := Real'Safe_Last;
+ Z := 0.0 + T*i;
+ X := Modulus (Z);
+ Check (X, T, "test 2 -- abs(0 + bigreal*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 2");
+ when others =>
+ Report.Failed ("exception in test 2");
+ end;
+
+ --- test 3 ---
+ begin
+ Z := 3.0 + 4.0*i;
+ X := abs Z;
+ Check (X, 5.0 , "test 3 -- abs(3 + 4*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 3");
+ when others =>
+ Report.Failed ("exception in test 3");
+ end;
+
+ --- test 4 ---
+ declare
+ S : Real;
+ begin
+ S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3);
+ Z := 3.0 * S + 4.0*S*i;
+ X := abs Z;
+ Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S",
+ 5.0*Real'Model_Epsilon);
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 4");
+ when others =>
+ Report.Failed ("exception in test 4");
+ end;
+
+ --- test 5 ---
+ begin
+ T := Real'Model_Small;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T , "test 5 -- abs(small + 0*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 5");
+ when others =>
+ Report.Failed ("exception in test 5");
+ end;
+
+ --- test 6 ---
+ begin
+ T := Real'Model_Small;
+ Z := 0.0 + T*i;
+ X := abs Z;
+ Check (X, T , "test 6 -- abs(0 + small*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 6");
+ when others =>
+ Report.Failed ("exception in test 6");
+ end;
+
+ --- test 7 ---
+ declare
+ S : Real;
+ begin
+ S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3);
+ Z := 3.0 * S + 4.0*S*i;
+ X := abs Z;
+ Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S",
+ 5.0*Real'Model_Epsilon);
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 7");
+ when others =>
+ Report.Failed ("exception in test 7");
+ end;
+
+ --- test 8 ---
+ declare
+ -- CRC Standard Mathematical Tables; 23rd Edition; pg 738
+ Sqrt2 : constant :=
+ 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
+ begin
+ Z := 1.0 + 1.0*i;
+ X := abs Z;
+ Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 8");
+ when others =>
+ Report.Failed ("exception in test 8");
+ end;
+
+ --- test 9 ---
+ begin
+ T := 0.0;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T , "test 5 -- abs(0 + 0*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 9");
+ when others =>
+ Report.Failed ("exception in test 9");
+ end;
+ end Do_Test;
+ end Generic_Check;
+
+ -----------------------------------------------------------------------
+ --- non generic copy of the above generic package
+ -----------------------------------------------------------------------
+
+ package Non_Generic_Check is
+ subtype Real is Float;
+ procedure Do_Test;
+ end Non_Generic_Check;
+
+ package body Non_Generic_Check is
+ use Ada.Numerics.Complex_Types;
+
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real := Maximum_Relative_Error) is
+ Rel_Error,
+ Abs_Error,
+ 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 (Expected - Actual) &
+ " 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 Do_Test is
+ Z : Complex;
+ X : Real;
+ T : Real;
+ begin
+
+ --- test 1 ---
+ begin
+ T := Real'Safe_Last;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T, "test 1 -- abs(bigreal + 0i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 1");
+ when others =>
+ Report.Failed ("exception in test 1");
+ end;
+
+ --- test 2 ---
+ begin
+ T := Real'Safe_Last;
+ Z := 0.0 + T*i;
+ X := Modulus (Z);
+ Check (X, T, "test 2 -- abs(0 + bigreal*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 2");
+ when others =>
+ Report.Failed ("exception in test 2");
+ end;
+
+ --- test 3 ---
+ begin
+ Z := 3.0 + 4.0*i;
+ X := abs Z;
+ Check (X, 5.0 , "test 3 -- abs(3 + 4*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 3");
+ when others =>
+ Report.Failed ("exception in test 3");
+ end;
+
+ --- test 4 ---
+ declare
+ S : Real;
+ begin
+ S := Real(Real'Machine_Radix) ** (Real'Machine_EMax - 3);
+ Z := 3.0 * S + 4.0*S*i;
+ X := abs Z;
+ Check (X, 5.0*S, "test 4 -- abs(3S + 4S*i) for large S",
+ 5.0*Real'Model_Epsilon);
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 4");
+ when others =>
+ Report.Failed ("exception in test 4");
+ end;
+
+ --- test 5 ---
+ begin
+ T := Real'Model_Small;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T , "test 5 -- abs(small + 0*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 5");
+ when others =>
+ Report.Failed ("exception in test 5");
+ end;
+
+ --- test 6 ---
+ begin
+ T := Real'Model_Small;
+ Z := 0.0 + T*i;
+ X := abs Z;
+ Check (X, T , "test 6 -- abs(0 + small*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 6");
+ when others =>
+ Report.Failed ("exception in test 6");
+ end;
+
+ --- test 7 ---
+ declare
+ S : Real;
+ begin
+ S := Real(Real'Machine_Radix) ** (Real'Model_EMin + 3);
+ Z := 3.0 * S + 4.0*S*i;
+ X := abs Z;
+ Check (X, 5.0*S, "test 7 -- abs(3S + 4S*i) for small S",
+ 5.0*Real'Model_Epsilon);
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 7");
+ when others =>
+ Report.Failed ("exception in test 7");
+ end;
+
+ --- test 8 ---
+ declare
+ -- CRC Standard Mathematical Tables; 23rd Edition; pg 738
+ Sqrt2 : constant :=
+ 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
+ begin
+ Z := 1.0 + 1.0*i;
+ X := abs Z;
+ Check (X, Sqrt2 , "test 8 -- abs(1 + 1*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 8");
+ when others =>
+ Report.Failed ("exception in test 8");
+ end;
+
+ --- test 9 ---
+ begin
+ T := 0.0;
+ Z := T + 0.0*i;
+ X := abs Z;
+ Check (X, T , "test 5 -- abs(0 + 0*i)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error raised in test 9");
+ when others =>
+ Report.Failed ("exception in test 9");
+ end;
+ end Do_Test;
+ end Non_Generic_Check;
+
+ -----------------------------------------------------------------------
+ --- end of "manual instantiation"
+ -----------------------------------------------------------------------
+ package Chk_Float is new Generic_Check (Float);
+
+ -- check the floating point type with the most digits
+ type A_Long_Float is digits System.Max_Digits;
+ package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
+begin
+ Report.Test ("CXG2002",
+ "Check the accuracy of the complex modulus" &
+ " function");
+
+ if Verbose then
+ Report.Comment ("checking Standard.Float");
+ end if;
+ Chk_Float.Do_Test;
+
+ if Verbose then
+ Report.Comment ("checking a digits" &
+ Integer'Image (System.Max_Digits) &
+ " floating point type");
+ end if;
+ Chk_A_Long_Float.Do_Test;
+
+ if Verbose then
+ Report.Comment ("checking non-generic package");
+ end if;
+ Non_Generic_Check.Do_Test;
+ Report.Result;
+end CXG2002;