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author | upstream source tree <ports@midipix.org> | 2015-03-15 20:14:05 -0400 |
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committer | upstream source tree <ports@midipix.org> | 2015-03-15 20:14:05 -0400 |
commit | 554fd8c5195424bdbcabf5de30fdc183aba391bd (patch) | |
tree | 976dc5ab7fddf506dadce60ae936f43f58787092 /gcc/testsuite/ada/acats/tests/cxg/cxg2021.a | |
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Diffstat (limited to 'gcc/testsuite/ada/acats/tests/cxg/cxg2021.a')
-rw-r--r-- | gcc/testsuite/ada/acats/tests/cxg/cxg2021.a | 386 |
1 files changed, 386 insertions, 0 deletions
diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2021.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2021.a new file mode 100644 index 000000000..db49fc845 --- /dev/null +++ b/gcc/testsuite/ada/acats/tests/cxg/cxg2021.a @@ -0,0 +1,386 @@ +-- 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; |