From 554fd8c5195424bdbcabf5de30fdc183aba391bd Mon Sep 17 00:00:00 2001 From: upstream source tree Date: Sun, 15 Mar 2015 20:14:05 -0400 Subject: obtained gcc-4.6.4.tar.bz2 from upstream website; verified gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream tarball. downloading a git-generated archive based on the 'upstream' tag should provide you with a source tree that is binary identical to the one extracted from the above tarball. if you have obtained the source via the command 'git clone', however, do note that line-endings of files in your working directory might differ from line-endings of the respective files in the upstream repository. --- gcc/testsuite/ada/acats/tests/cxg/cxg2004.a | 499 ++++++++++++++++++++++++++++ 1 file changed, 499 insertions(+) create mode 100644 gcc/testsuite/ada/acats/tests/cxg/cxg2004.a (limited to 'gcc/testsuite/ada/acats/tests/cxg/cxg2004.a') diff --git a/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a b/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a new file mode 100644 index 000000000..2df296d3d --- /dev/null +++ b/gcc/testsuite/ada/acats/tests/cxg/cxg2004.a @@ -0,0 +1,499 @@ +-- CXG2004.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 sin and cos functions return +-- results that are within the error bound allowed. +-- +-- TEST DESCRIPTION: +-- This test consists of a generic package that is +-- instantiated to check both float and a long float type. +-- The test for each floating point type is divided into +-- the following parts: +-- Special value checks where the result is a known constant. +-- Checks using an identity relationship. +-- +-- 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: +-- 13 FEB 96 SAIC Initial release for 2.1 +-- 22 APR 96 SAIC Changed to generic implementation. +-- 18 AUG 96 SAIC Improvements to commentary. +-- 23 OCT 96 SAIC Exact results are not required unless the +-- cycle is specified. +-- 28 FEB 97 PWB.CTA Removed checks where cycle 2.0*Pi is specified +-- 02 JUN 98 EDS Revised calculations to ensure that X is exactly +-- three times Y per advice of numerics experts. +-- +-- CHANGE NOTE: +-- According to Ken Dritz, author of the Numerics Annex of the RM, +-- one should never specify the cycle 2.0*Pi for the trigonometric +-- functions. In particular, if the machine number for the first +-- argument is not an exact multiple of the machine number for the +-- explicit cycle, then the specified exact results cannot be +-- reasonably expected. The affected checks in this test have been +-- marked as comments, with the additional notation "pwb-math". +-- Phil Brashear +--! + +-- +-- References: +-- +-- Software Manual for the Elementary Functions +-- William J. Cody, Jr. and William Waite +-- Prentice-Hall, 1980 +-- +-- CRC Standard Mathematical Tables +-- 23rd Edition +-- +-- Implementation and Testing of Function Software +-- W. J. Cody +-- Problems and Methodologies in Mathematical Software Production +-- editors P. C. Messina and A. Murli +-- Lecture Notes in Computer Science Volume 142 +-- Springer Verlag, 1982 +-- +-- The sin and cos checks are translated directly from +-- the netlib FORTRAN code that was written by W. Cody. +-- + +with System; +with Report; +with Ada.Numerics.Generic_Elementary_Functions; +with Ada.Numerics.Elementary_Functions; +procedure CXG2004 is + Verbose : constant Boolean := False; + Number_Samples : constant := 1000; + + -- 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; + + 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 Elementary_Functions is new + Ada.Numerics.Generic_Elementary_Functions (Real); + + function Sin (X : Real) return Real renames + Elementary_Functions.Sin; + function Cos (X : Real) return Real renames + Elementary_Functions.Cos; + function Sin (X, Cycle : Real) return Real renames + Elementary_Functions.Sin; + function Cos (X, Cycle : Real) return Real renames + Elementary_Functions.Cos; + + Accuracy_Error_Reported : Boolean := False; + + procedure Check (Actual, Expected : Real; + Test_Name : String; + MRE : Real) 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; + + + -- in addition to the relative error checks we apply the + -- criteria of G.2.4(16) + if abs (Actual) > 1.0 then + Accuracy_Error_Reported := True; + Report.Failed (Test_Name & " result > 1.0"); + elsif 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) & + " 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 Sin_Check (A, B : Real; + Arg_Range : String) is + -- test a selection of + -- arguments selected from the range A to B. + -- + -- This test uses the identity + -- sin(x) = sin(x/3)*(3 - 4 * sin(x/3)**2) + -- + -- Note that in this test we must take into account the + -- error in the calculation of the expected result so + -- the maximum relative error is larger than the + -- accuracy required by the ARM. + + X, Y, ZZ : Real; + Actual, Expected : Real; + MRE : Real; + Ran : Real; + begin + Accuracy_Error_Reported := False; -- reset + for I in 1 .. Number_Samples loop + -- Evenly distributed selection of arguments + Ran := Real (I) / Real (Number_Samples); + + -- make sure x and x/3 are both exactly representable + -- on the machine. See "Implementation and Testing of + -- Function Software" page 44. + X := (B - A) * Ran + A; + Y := Real'Leading_Part + ( X/3.0, + Real'Machine_Mantissa - Real'Exponent (3.0) ); + X := Y * 3.0; + + Actual := Sin (X); + + ZZ := Sin(Y); + Expected := ZZ * (3.0 - 4.0 * ZZ * ZZ); + + -- note that since the expected value is computed, we + -- must take the error in that computation into account. + -- See Cody pp 139-141. + MRE := 4.0; + + Check (Actual, Expected, + "sin test of range" & Arg_Range & + Integer'Image (I), + MRE); + exit when Accuracy_Error_Reported; + end loop; + exception + when Constraint_Error => + Report.Failed + ("Constraint_Error raised in sin check"); + when others => + Report.Failed ("exception in sin check"); + end Sin_Check; + + + + procedure Cos_Check (A, B : Real; + Arg_Range : String) is + -- test a selection of + -- arguments selected from the range A to B. + -- + -- This test uses the identity + -- cos(x) = cos(x/3)*(4 * cos(x/3)**2 - 3) + -- + -- Note that in this test we must take into account the + -- error in the calculation of the expected result so + -- the maximum relative error is larger than the + -- accuracy required by the ARM. + + X, Y, ZZ : Real; + Actual, Expected : Real; + MRE : Real; + Ran : Real; + begin + Accuracy_Error_Reported := False; -- reset + for I in 1 .. Number_Samples loop + -- Evenly distributed selection of arguments + Ran := Real (I) / Real (Number_Samples); + + -- make sure x and x/3 are both exactly representable + -- on the machine. See "Implementation and Testing of + -- Function Software" page 44. + X := (B - A) * Ran + A; + Y := Real'Leading_Part + ( X/3.0, + Real'Machine_Mantissa - Real'Exponent (3.0) ); + X := Y * 3.0; + + Actual := Cos (X); + + ZZ := Cos(Y); + Expected := ZZ * (4.0 * ZZ * ZZ - 3.0); + + -- note that since the expected value is computed, we + -- must take the error in that computation into account. + -- See Cody pp 141-143. + MRE := 6.0; + + Check (Actual, Expected, + "cos test of range" & Arg_Range & + Integer'Image (I), + MRE); + exit when Accuracy_Error_Reported; + end loop; + exception + when Constraint_Error => + Report.Failed + ("Constraint_Error raised in cos check"); + when others => + Report.Failed ("exception in cos check"); + end Cos_Check; + + + procedure Special_Angle_Checks is + type Data_Point is + record + Degrees, + Radians, + Sine, + Cosine : Real; + Sin_Result_Error, + Cos_Result_Error : Boolean; + end record; + + type Test_Data_Type is array (Positive range <>) of Data_Point; + + -- the values in the following table only involve static + -- expressions to minimize any loss of precision. However, + -- there are two sources of error that must be accounted for + -- in the following tests. + -- First, when a cycle is not specified there can be a roundoff + -- error in the value of Pi used. This error does not apply + -- when a cycle of 2.0 * Pi is explicitly provided. + -- Second, the expected results that involve sqrt values also + -- have a potential roundoff error. + -- The amount of error due to error in the argument is computed + -- as follows: + -- sin(x+err) = sin(x)*cos(err) + cos(x)*sin(err) + -- ~= sin(x) + err * cos(x) + -- similarly for cos the error due to error in the argument is + -- computed as follows: + -- cos(x+err) = cos(x)*cos(err) - sin(x)*sin(err) + -- ~= cos(x) - err * sin(x) + -- In both cases the term "err" is bounded by 0.5 * argument. + + Test_Data : constant Test_Data_Type := ( +-- degrees radians sine cosine sin_er cos_er test # + ( 0.0, 0.0, 0.0, 1.0, False, False ), -- 1 + ( 30.0, Pi/6.0, 0.5, Sqrt3/2.0, False, True ), -- 2 + ( 60.0, Pi/3.0, Sqrt3/2.0, 0.5, True, False ), -- 3 + ( 90.0, Pi/2.0, 1.0, 0.0, False, False ), -- 4 + (120.0, 2.0*Pi/3.0, Sqrt3/2.0, -0.5, True, False ), -- 5 + (150.0, 5.0*Pi/6.0, 0.5, -Sqrt3/2.0, False, True ), -- 6 + (180.0, Pi, 0.0, -1.0, False, False ), -- 7 + (210.0, 7.0*Pi/6.0, -0.5, -Sqrt3/2.0, False, True ), -- 8 + (240.0, 8.0*Pi/6.0, -Sqrt3/2.0, -0.5, True, False ), -- 9 + (270.0, 9.0*Pi/6.0, -1.0, 0.0, False, False ), -- 10 + (300.0, 10.0*Pi/6.0, -Sqrt3/2.0, 0.5, True, False ), -- 11 + (330.0, 11.0*Pi/6.0, -0.5, Sqrt3/2.0, False, True ), -- 12 + (360.0, 2.0*Pi, 0.0, 1.0, False, False ), -- 13 + ( 45.0, Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 14 + (135.0, 3.0*Pi/4.0, Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 15 + (225.0, 5.0*Pi/4.0, -Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 16 + (315.0, 7.0*Pi/4.0, -Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 17 + (405.0, 9.0*Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ) ); -- 18 + + + Y : Real; + Sin_Arg_Err, + Cos_Arg_Err, + Sin_Result_Err, + Cos_Result_Err : Real; + begin + for I in Test_Data'Range loop + -- compute error components + Sin_Arg_Err := abs Test_Data (I).Cosine * + abs Test_Data (I).Radians / 2.0; + Cos_Arg_Err := abs Test_Data (I).Sine * + abs Test_Data (I).Radians / 2.0; + + if Test_Data (I).Sin_Result_Error then + Sin_Result_Err := 0.5; + else + Sin_Result_Err := 0.0; + end if; + + if Test_Data (I).Cos_Result_Error then + Cos_Result_Err := 1.0; + else + Cos_Result_Err := 0.0; + end if; + + + + Y := Sin (Test_Data (I).Radians); + Check (Y, Test_Data (I).Sine, + "test" & Integer'Image (I) & " sin(r)", + 2.0 + Sin_Arg_Err + Sin_Result_Err); + Y := Cos (Test_Data (I).Radians); + Check (Y, Test_Data (I).Cosine, + "test" & Integer'Image (I) & " cos(r)", + 2.0 + Cos_Arg_Err + Cos_Result_Err); + Y := Sin (Test_Data (I).Degrees, 360.0); + Check (Y, Test_Data (I).Sine, + "test" & Integer'Image (I) & " sin(d,360)", + 2.0 + Sin_Result_Err); + Y := Cos (Test_Data (I).Degrees, 360.0); + Check (Y, Test_Data (I).Cosine, + "test" & Integer'Image (I) & " cos(d,360)", + 2.0 + Cos_Result_Err); +--pwb-math Y := Sin (Test_Data (I).Radians, 2.0*Pi); +--pwb-math Check (Y, Test_Data (I).Sine, +--pwb-math "test" & Integer'Image (I) & " sin(r,2pi)", +--pwb-math 2.0 + Sin_Result_Err); +--pwb-math Y := Cos (Test_Data (I).Radians, 2.0*Pi); +--pwb-math Check (Y, Test_Data (I).Cosine, +--pwb-math "test" & Integer'Image (I) & " cos(r,2pi)", +--pwb-math 2.0 + Cos_Result_Err); + end loop; + exception + when Constraint_Error => + Report.Failed ("Constraint_Error raised in special angle test"); + when others => + Report.Failed ("exception in special angle test"); + end Special_Angle_Checks; + + + -- check the rule of A.5.1(41);6.0 which requires that the + -- result be exact if the mathematical result is 0.0, 1.0, + -- or -1.0 + procedure Exact_Result_Checks is + type Data_Point is + record + Degrees, + Sine, + Cosine : Real; + end record; + + type Test_Data_Type is array (Positive range <>) of Data_Point; + Test_Data : constant Test_Data_Type := ( + -- degrees sine cosine test # + ( 0.0, 0.0, 1.0 ), -- 1 + ( 90.0, 1.0, 0.0 ), -- 2 + (180.0, 0.0, -1.0 ), -- 3 + (270.0, -1.0, 0.0 ), -- 4 + (360.0, 0.0, 1.0 ), -- 5 + ( 90.0 + 360.0, 1.0, 0.0 ), -- 6 + (180.0 + 360.0, 0.0, -1.0 ), -- 7 + (270.0 + 360.0,-1.0, 0.0 ), -- 8 + (360.0 + 360.0, 0.0, 1.0 ) ); -- 9 + + Y : Real; + begin + for I in Test_Data'Range loop + Y := Sin (Test_Data(I).Degrees, 360.0); + if Y /= Test_Data(I).Sine then + Report.Failed ("exact result for sin(" & + Real'Image (Test_Data(I).Degrees) & + ", 360.0) is not" & + Real'Image (Test_Data(I).Sine) & + " Difference is " & + Real'Image (Y - Test_Data(I).Sine) ); + end if; + + Y := Cos (Test_Data(I).Degrees, 360.0); + if Y /= Test_Data(I).Cosine then + Report.Failed ("exact result for cos(" & + Real'Image (Test_Data(I).Degrees) & + ", 360.0) is not" & + Real'Image (Test_Data(I).Cosine) & + " Difference is " & + Real'Image (Y - Test_Data(I).Cosine) ); + end if; + end loop; + exception + when Constraint_Error => + Report.Failed ("Constraint_Error raised in exact result check"); + when others => + Report.Failed ("exception in exact result check"); + end Exact_Result_Checks; + + + procedure Do_Test is + begin + Special_Angle_Checks; + Sin_Check (0.0, Pi/2.0, "0..pi/2"); + Sin_Check (6.0*Pi, 6.5*Pi, "6pi..6.5pi"); + Cos_Check (7.0*Pi, 7.5*Pi, "7pi..7.5pi"); + Exact_Result_Checks; + 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 ("CXG2004", + "Check the accuracy of the 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 CXG2004; -- cgit v1.2.3