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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/cxg2020.a
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+-- CXG2020.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 SQRT 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 complex numbers based upon
+-- 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:
+-- 24 Mar 96 SAIC Initial release for 2.1
+-- 17 Aug 96 SAIC Incorporated reviewer comments.
+-- 03 Jun 98 EDS Added parens to ensure that the expression is not
+-- evaluated by multiplying its two large terms
+-- together and overflowing.
+--!
+
+--
+-- References:
+--
+-- W. J. Cody
+-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
+-- Algorithm 714, Collected Algorithms from ACM.
+-- Published in Transactions On Mathematical Software,
+-- Vol. 19, No. 1, March, 1993, pp. 1-21.
+--
+-- CRC Standard Mathematical Tables
+-- 23rd Edition
+--
+
+with System;
+with Report;
+with Ada.Numerics.Generic_Complex_Types;
+with Ada.Numerics.Generic_Complex_Elementary_Functions;
+procedure CXG2020 is
+ Verbose : constant Boolean := False;
+ -- Note that Max_Samples is the number of samples taken in
+ -- both the real and imaginary directions. Thus, for Max_Samples
+ -- of 100 the number of values checked is 10000.
+ Max_Samples : constant := 100;
+
+ E : constant := Ada.Numerics.E;
+ Pi : constant := Ada.Numerics.Pi;
+
+ -- CRC Standard Mathematical Tables; 23rd Edition; pg 738
+ Sqrt2 : constant :=
+ 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
+ Sqrt3 : constant :=
+ 1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
+
+ generic
+ type Real is digits <>;
+ package Generic_Check is
+ procedure Do_Test;
+ end Generic_Check;
+
+ package body Generic_Check is
+ package Complex_Type is new
+ Ada.Numerics.Generic_Complex_Types (Real);
+ use Complex_Type;
+
+ package CEF is new
+ Ada.Numerics.Generic_Complex_Elementary_Functions (Complex_Type);
+
+ function Sqrt (X : Complex) return Complex renames CEF.Sqrt;
+
+ -- 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_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
+ 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 Check (Actual, Expected : Complex;
+ Test_Name : String;
+ MRE : Real) is
+ begin
+ Check (Actual.Re, Expected.Re, Test_Name & " real part", MRE);
+ Check (Actual.Im, Expected.Im, Test_Name & " imaginary part", MRE);
+ 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 if the argument is exact.
+ --
+ -- One or i is added to the actual and expected results in
+ -- order to prevent the expected result from having a
+ -- real or imaginary part of 0. This is to allow a reasonable
+ -- relative error for that component.
+ Minimum_Error : constant := 6.0;
+ Z1, Z2 : Complex;
+ begin
+ Check (Sqrt(9.0+0.0*i) + i,
+ 3.0+1.0*i,
+ "sqrt(9+0i)+i",
+ Minimum_Error);
+ Check (Sqrt (-2.0 + 0.0 * i) + 1.0,
+ 1.0 + Sqrt2 * i,
+ "sqrt(-2)+1 ",
+ Minimum_Error);
+
+ -- make sure no exception occurs when taking the sqrt of
+ -- very large and very small values.
+
+ Z1 := (Real'Safe_Last * 0.9, Real'Safe_Last * 0.9);
+ Z2 := Sqrt (Z1);
+ begin
+ Check (Z2 * Z2,
+ Z1,
+ "sqrt((big,big))",
+ Minimum_Error + 5.0); -- +5 for multiply
+ exception
+ when others =>
+ Report.Failed ("unexpected exception in sqrt((big,big))");
+ end;
+
+ Z1 := (Real'Model_Epsilon * 10.0, Real'Model_Epsilon * 10.0);
+ Z2 := Sqrt (Z1);
+ begin
+ Check (Z2 * Z2,
+ Z1,
+ "sqrt((little,little))",
+ Minimum_Error + 5.0); -- +5 for multiply
+ exception
+ when others =>
+ Report.Failed ("unexpected exception in " &
+ "sqrt((little,little))");
+ end;
+
+ 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
+ -- G.1.2(36);6.0
+ Check (Sqrt(0.0 + 0.0*i), 0.0 + 0.0 * i, "sqrt(0+0i)", No_Error);
+
+ -- G.1.2(37);6.0
+ Check (Sqrt(1.0 + 0.0*i), 1.0 + 0.0 * i, "sqrt(1+0i)", No_Error);
+
+ -- G.1.2(38-39);6.0
+ Check (Sqrt(-1.0 + 0.0*i), 0.0 + 1.0 * i, "sqrt(-1+0i)", No_Error);
+
+ -- G.1.2(40);6.0
+ if Real'Signed_Zeros then
+ Check (Sqrt(-1.0-0.0*i), 0.0 - 1.0 * i, "sqrt(-1-0i)", No_Error);
+ end if;
+ 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 (RA, RB, IA, IB : Real) is
+ -- Tests an identity over a range of values specified
+ -- by the 4 parameters. RA and RB denote the range for the
+ -- real part while IA and IB denote the range for the
+ -- imaginary part of the result.
+ --
+ -- For this test we use the identity
+ -- Sqrt(Z*Z) = Z
+ --
+
+ Scale : Real := Real (Real'Machine_Radix) ** (Real'Mantissa / 2 + 4);
+ W, X, Y, Z : Real;
+ CX : Complex;
+ Actual, Expected : Complex;
+ begin
+ Accuracy_Error_Reported := False; -- reset
+ for II in 1..Max_Samples loop
+ X := (RB - RA) * Real (II) / Real (Max_Samples) + RA;
+ for J in 1..Max_Samples loop
+ Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA;
+
+ -- purify the arguments to minimize roundoff error.
+ -- We construct the values so that the products X*X,
+ -- Y*Y, and X*Y are all exact machine numbers.
+ -- See Cody page 7 and CELEFUNT code.
+ Z := X * Scale;
+ W := Z + X;
+ X := W - Z;
+ Z := Y * Scale;
+ W := Z + Y;
+ Y := W - Z;
+ -- G.1.2(21);6.0 - real part of result is non-negative
+ Expected := Compose_From_Cartesian( abs X,Y);
+ Z := X*X - Y*Y;
+ W := X*Y;
+ CX := Compose_From_Cartesian(Z,W+W);
+
+ -- The arguments are now ready so on with the
+ -- identity computation.
+ Actual := Sqrt(CX);
+
+ Check (Actual, Expected,
+ "Identity_1_Test " & Integer'Image (II) &
+ Integer'Image (J) & ": Sqrt((" &
+ Real'Image (CX.Re) & ", " &
+ Real'Image (CX.Im) & ")) ",
+ 8.5); -- 6.0 from sqrt, 2.5 from argument.
+ -- See Cody pg 7-8 for analysis of additional error amount.
+
+ 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;
+ end loop;
+
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Identity_Test" &
+ " for X=(" & Real'Image (X) &
+ ", " & Real'Image (X) & ")");
+ when others =>
+ Report.Failed ("exception in Identity_Test" &
+ " for X=(" & Real'Image (X) &
+ ", " & Real'Image (X) & ")");
+ end Identity_Test;
+
+
+ procedure Do_Test is
+ begin
+ Special_Value_Test;
+ Exact_Result_Test;
+ -- ranges where the sign is the same and where it
+ -- differs.
+ Identity_Test ( 0.0, 10.0, 0.0, 10.0);
+ Identity_Test ( 0.0, 100.0, -100.0, 0.0);
+ 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 ("CXG2020",
+ "Check the accuracy of the complex 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;
+
+
+ Report.Result;
+end CXG2020;