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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/cxg2021.a
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+-- CXG2021.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 SIN and COS functions return
+-- 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:
+-- 27 Mar 96 SAIC Initial release for 2.1
+-- 22 Aug 96 SAIC No longer skips test for systems with
+-- more than 20 digits of precision.
+--
+--!
+
+--
+-- 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 CXG2021 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;
+
+ 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 Sin (X : Complex) return Complex renames CEF.Sin;
+ function Cos (X : Complex) return Complex renames CEF.Cos;
+
+ -- flag used to terminate some tests early
+ Accuracy_Error_Reported : Boolean := False;
+
+ -- The following value is a lower bound on the accuracy
+ -- required. It is normally 0.0 so that the lower bound
+ -- is computed from Model_Epsilon. However, for tests
+ -- where the expected result is only known to a certain
+ -- amount of precision this bound takes on a non-zero
+ -- value to account for that level of precision.
+ Error_Low_Bound : Real := 0.0;
+
+ -- the E_Factor is an additional amount added to the Expected
+ -- value prior to computing the maximum relative error.
+ -- This is needed because the error analysis (Cody pg 17-20)
+ -- requires this additional allowance.
+ procedure Check (Actual, Expected : Real;
+ Test_Name : String;
+ MRE : Real;
+ E_Factor : Real := 0.0) 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 * Real'Model_Epsilon * (abs Expected + E_Factor);
+ Abs_Error := MRE * Real'Model_Epsilon;
+ if Rel_Error > Abs_Error then
+ Max_Error := Rel_Error;
+ else
+ Max_Error := Abs_Error;
+ end if;
+
+ -- take into account the low bound on the error
+ if Max_Error < Error_Low_Bound then
+ Max_Error := Error_Low_Bound;
+ 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) &
+ " efactor:" & Real'Image (E_Factor) );
+ elsif Verbose then
+ if Actual = Expected then
+ Report.Comment (Test_Name & " exact result");
+ else
+ Report.Comment (Test_Name & " passed" &
+ " actual: " & Real'Image (Actual) &
+ " expected: " & Real'Image (Expected) &
+ " difference: " & Real'Image (Actual - Expected) &
+ " max err:" & Real'Image (Max_Error) &
+ " efactor:" & Real'Image (E_Factor) );
+ end if;
+ end if;
+ end Check;
+
+
+ procedure Check (Actual, Expected : Complex;
+ Test_Name : String;
+ MRE : Real;
+ R_Factor, I_Factor : Real := 0.0) is
+ begin
+ Check (Actual.Re, Expected.Re, Test_Name & " real part",
+ MRE, R_Factor);
+ Check (Actual.Im, Expected.Im, Test_Name & " imaginary part",
+ MRE, I_Factor);
+ 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.
+ -- Since the argument involves Pi, we must allow for this
+ -- inexact argument.
+ Minimum_Error : constant := 11.0;
+ begin
+ Check (Sin (Pi/2.0 + 0.0*i),
+ 1.0 + 0.0*i,
+ "sin(pi/2+0i)",
+ Minimum_Error + 1.0);
+ Check (Cos (Pi/2.0 + 0.0*i),
+ 0.0 + 0.0*i,
+ "cos(pi/2+0i)",
+ Minimum_Error + 1.0);
+ 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 (Sin(0.0 + 0.0*i), 0.0 + 0.0 * i, "sin(0+0i)", No_Error);
+ Check (Cos(0.0 + 0.0*i), 1.0 + 0.0 * i, "cos(0+0i)", 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_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.
+ --
+ -- For this test we use the identity
+ -- Sin(Z) = Sin(Z-W) * Cos(W) + Cos(Z-W) * Sin(W)
+ -- and
+ -- Cos(Z) = Cos(Z-W) * Cos(W) - Sin(Z-W) * Sin(W)
+ --
+
+ X, Y : Real;
+ Z : Complex;
+ W : constant Complex := Compose_From_Cartesian(0.0625, 0.0625);
+ ZmW : Complex; -- Z - W
+ Sin_ZmW,
+ Cos_ZmW : Complex;
+ Actual1, Actual2 : Complex;
+ R_Factor : Real; -- additional real error factor
+ I_Factor : Real; -- additional imaginary error factor
+ Sin_W : constant Complex := (6.2581348413276935585E-2,
+ 6.2418588008436587236E-2);
+ -- numeric stability is enhanced by using Cos(W) - 1.0 instead of
+ -- Cos(W) in the computation.
+ Cos_W_m_1 : constant Complex := (-2.5431314180235545803E-6,
+ -3.9062493377261771826E-3);
+
+
+ begin
+ if Real'Digits > 20 then
+ -- constants used here accurate to 20 digits. Allow 1
+ -- additional digit of error for computation.
+ Error_Low_Bound := 0.00000_00000_00000_0001;
+ Report.Comment ("accuracy checked to 19 digits");
+ end if;
+
+ Accuracy_Error_Reported := False; -- reset
+ for II in 0..Max_Samples loop
+ X := (RB - RA) * Real (II) / Real (Max_Samples) + RA;
+ for J in 0..Max_Samples loop
+ Y := (IB - IA) * Real (J) / Real (Max_Samples) + IA;
+
+ Z := Compose_From_Cartesian(X,Y);
+ ZmW := Z - W;
+ Sin_ZmW := Sin (ZmW);
+ Cos_ZmW := Cos (ZmW);
+
+ -- now for the first identity
+ -- Sin(Z) = Sin(Z-W) * Cos(W) + Cos(Z-W) * Sin(W)
+ -- = Sin(Z-W) * (1+(Cos(W)-1)) + Cos(Z-W) * Sin(W)
+ -- = Sin(Z-W) + Sin(Z-W)*(Cos(W)-1) + Cos(Z-W)*Sin(W)
+
+
+ Actual1 := Sin (Z);
+ Actual2 := Sin_ZmW + (Sin_ZmW * Cos_W_m_1 + Cos_ZmW * Sin_W);
+
+ -- The computation of the additional error factors are taken
+ -- from Cody pages 17-20.
+
+ R_Factor := abs (Re (Sin_ZmW) * Re (1.0 - Cos_W_m_1)) +
+ abs (Im (Sin_ZmW) * Im (1.0 - Cos_W_m_1)) +
+ abs (Re (Cos_ZmW) * Re (Sin_W)) +
+ abs (Re (Cos_ZmW) * Re (1.0 - Cos_W_m_1));
+
+ I_Factor := abs (Re (Sin_ZmW) * Im (1.0 - Cos_W_m_1)) +
+ abs (Im (Sin_ZmW) * Re (1.0 - Cos_W_m_1)) +
+ abs (Re (Cos_ZmW) * Im (Sin_W)) +
+ abs (Im (Cos_ZmW) * Re (1.0 - Cos_W_m_1));
+
+ Check (Actual1, Actual2,
+ "Identity_1_Test " & Integer'Image (II) &
+ Integer'Image (J) & ": Sin((" &
+ Real'Image (Z.Re) & ", " &
+ Real'Image (Z.Im) & ")) ",
+ 11.0, R_Factor, I_Factor);
+
+ -- now for the second identity
+ -- Cos(Z) = Cos(Z-W) * Cos(W) - Sin(Z-W) * Sin(W)
+ -- = Cos(Z-W) * (1+(Cos(W)-1) - Sin(Z-W) * Sin(W)
+ Actual1 := Cos (Z);
+ Actual2 := Cos_ZmW + (Cos_ZmW * Cos_W_m_1 - Sin_ZmW * Sin_W);
+
+ -- The computation of the additional error factors are taken
+ -- from Cody pages 17-20.
+
+ R_Factor := abs (Re (Sin_ZmW) * Re (Sin_W)) +
+ abs (Im (Sin_ZmW) * Im (Sin_W)) +
+ abs (Re (Cos_ZmW) * Re (1.0 - Cos_W_m_1)) +
+ abs (Im (Cos_ZmW) * Im (1.0 - Cos_W_m_1));
+
+ I_Factor := abs (Re (Sin_ZmW) * Im (Sin_W)) +
+ abs (Im (Sin_ZmW) * Re (Sin_W)) +
+ abs (Re (Cos_ZmW) * Im (1.0 - Cos_W_m_1)) +
+ abs (Im (Cos_ZmW) * Re (1.0 - Cos_W_m_1));
+
+ Check (Actual1, Actual2,
+ "Identity_2_Test " & Integer'Image (II) &
+ Integer'Image (J) & ": Cos((" &
+ Real'Image (Z.Re) & ", " &
+ Real'Image (Z.Im) & ")) ",
+ 11.0, R_Factor, I_Factor);
+
+ 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
+ Error_Low_Bound := 0.0; -- reset
+ return;
+ end if;
+ end loop;
+ end loop;
+
+ Error_Low_Bound := 0.0; -- reset
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Identity_Test" &
+ " for Z=(" & Real'Image (X) &
+ ", " & Real'Image (Y) & ")");
+ when others =>
+ Report.Failed ("exception in Identity_Test" &
+ " for Z=(" & Real'Image (X) &
+ ", " & Real'Image (Y) & ")");
+ end Identity_Test;
+
+
+ procedure Do_Test is
+ begin
+ Special_Value_Test;
+ Exact_Result_Test;
+ -- test regions where sin and cos have the same sign and
+ -- about the same magnitude. This will minimize subtraction
+ -- errors in the identities.
+ -- See Cody page 17.
+ Identity_Test (0.0625, 10.0, 0.0625, 10.0);
+ Identity_Test ( 16.0, 17.0, 16.0, 17.0);
+ 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 ("CXG2021",
+ "Check the accuracy of the complex SIN and COS 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 CXG2021;