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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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+-- CXG2015.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 ARCSIN and ARCCOS 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
+-- several parts:
+-- Special value checks where the result is a known constant.
+-- Checks in a specific range where a Taylor series can be
+-- used to compute an accurate result for comparison.
+-- Exception checks.
+-- The Taylor series tests are a direct translation of the
+-- FORTRAN code found in the reference.
+--
+-- 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:
+-- 18 Mar 96 SAIC Initial release for 2.1
+-- 24 Apr 96 SAIC Fixed error bounds.
+-- 17 Aug 96 SAIC Added reference information and improved
+-- checking for machines with more than 23
+-- digits of precision.
+-- 03 Feb 97 PWB.CTA Removed checks with explicit Cycle => 2.0*Pi
+-- 22 Dec 99 RLB Added model range checking to "exact" results,
+-- in order to avoid too strictly requiring a specific
+-- result, and too weakly checking results.
+--
+-- 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
+--
+-- CELEFUNT: A Portable Test Package for Complex Elementary Functions
+-- ACM Collected Algorithms number 714
+
+with System;
+with Report;
+with Ada.Numerics.Generic_Elementary_Functions;
+procedure CXG2015 is
+ Verbose : constant Boolean := False;
+ Max_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;
+
+ -- relative error bound from G.2.4(7);6.0
+ Minimum_Error : constant := 4.0;
+
+ generic
+ type Real is digits <>;
+ Half_PI_Low : in Real; -- The machine number closest to, but not greater
+ -- than PI/2.0.
+ Half_PI_High : in Real;-- The machine number closest to, but not less
+ -- than PI/2.0.
+ PI_Low : in Real; -- The machine number closest to, but not greater
+ -- than PI.
+ PI_High : in Real; -- The machine number closest to, but not less
+ -- than PI.
+ 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 Arcsin (X : Real) return Real renames
+ Elementary_Functions.Arcsin;
+ function Arcsin (X, Cycle : Real) return Real renames
+ Elementary_Functions.Arcsin;
+ function Arccos (X : Real) return Real renames
+ Elementary_Functions.ArcCos;
+ function Arccos (X, Cycle : Real) return Real renames
+ Elementary_Functions.ArcCos;
+
+ -- needed for support
+ function Log (X, Base : Real) return Real renames
+ Elementary_Functions.Log;
+
+ -- 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;
+
+
+ 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;
+
+ -- 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) );
+ 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 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.
+
+ type Data_Point is
+ record
+ Degrees,
+ Radians,
+ Argument,
+ Error_Bound : Real;
+ end record;
+
+ type Test_Data_Type is array (Positive range <>) of Data_Point;
+
+ -- the values in the following tables only involve static
+ -- expressions so no loss of precision occurs. However,
+ -- rounding can be an issue with expressions involving Pi
+ -- and square roots. The error bound specified in the
+ -- table takes the sqrt error into account but not the
+ -- error due to Pi. The Pi error is added in in the
+ -- radians test below.
+
+ Arcsin_Test_Data : constant Test_Data_Type := (
+ -- degrees radians sine error_bound test #
+ --( 0.0, 0.0, 0.0, 0.0 ), -- 1 - In Exact_Result_Test.
+ ( 30.0, Pi/6.0, 0.5, 4.0 ), -- 2
+ ( 60.0, Pi/3.0, Sqrt3/2.0, 5.0 ), -- 3
+ --( 90.0, Pi/2.0, 1.0, 4.0 ), -- 4 - In Exact_Result_Test.
+ --(-90.0, -Pi/2.0, -1.0, 4.0 ), -- 5 - In Exact_Result_Test.
+ (-60.0, -Pi/3.0, -Sqrt3/2.0, 5.0 ), -- 6
+ (-30.0, -Pi/6.0, -0.5, 4.0 ), -- 7
+ ( 45.0, Pi/4.0, Sqrt2/2.0, 5.0 ), -- 8
+ (-45.0, -Pi/4.0, -Sqrt2/2.0, 5.0 ) ); -- 9
+
+ Arccos_Test_Data : constant Test_Data_Type := (
+ -- degrees radians cosine error_bound test #
+ --( 0.0, 0.0, 1.0, 0.0 ), -- 1 - In Exact_Result_Test.
+ ( 30.0, Pi/6.0, Sqrt3/2.0, 5.0 ), -- 2
+ ( 60.0, Pi/3.0, 0.5, 4.0 ), -- 3
+ --( 90.0, Pi/2.0, 0.0, 4.0 ), -- 4 - In Exact_Result_Test.
+ (120.0, 2.0*Pi/3.0, -0.5, 4.0 ), -- 5
+ (150.0, 5.0*Pi/6.0, -Sqrt3/2.0, 5.0 ), -- 6
+ --(180.0, Pi, -1.0, 4.0 ), -- 7 - In Exact_Result_Test.
+ ( 45.0, Pi/4.0, Sqrt2/2.0, 5.0 ), -- 8
+ (135.0, 3.0*Pi/4.0, -Sqrt2/2.0, 5.0 ) ); -- 9
+
+ Cycle_Error,
+ Radian_Error : Real;
+ begin
+ for I in Arcsin_Test_Data'Range loop
+
+ -- note exact result requirements A.5.1(38);6.0 and
+ -- G.2.4(12);6.0
+ if Arcsin_Test_Data (I).Error_Bound = 0.0 then
+ Cycle_Error := 0.0;
+ Radian_Error := 0.0;
+ else
+ Cycle_Error := Arcsin_Test_Data (I).Error_Bound;
+ -- allow for rounding error in the specification of Pi
+ Radian_Error := Cycle_Error + 1.0;
+ end if;
+
+ Check (Arcsin (Arcsin_Test_Data (I).Argument),
+ Arcsin_Test_Data (I).Radians,
+ "test" & Integer'Image (I) &
+ " arcsin(" &
+ Real'Image (Arcsin_Test_Data (I).Argument) &
+ ")",
+ Radian_Error);
+--pwb-math Check (Arcsin (Arcsin_Test_Data (I).Argument, 2.0 * Pi),
+--pwb-math Arcsin_Test_Data (I).Radians,
+--pwb-math "test" & Integer'Image (I) &
+--pwb-math " arcsin(" &
+--pwb-math Real'Image (Arcsin_Test_Data (I).Argument) &
+--pwb-math ", 2pi)",
+--pwb-math Cycle_Error);
+ Check (Arcsin (Arcsin_Test_Data (I).Argument, 360.0),
+ Arcsin_Test_Data (I).Degrees,
+ "test" & Integer'Image (I) &
+ " arcsin(" &
+ Real'Image (Arcsin_Test_Data (I).Argument) &
+ ", 360)",
+ Cycle_Error);
+ end loop;
+
+
+ for I in Arccos_Test_Data'Range loop
+
+ -- note exact result requirements A.5.1(39);6.0 and
+ -- G.2.4(12);6.0
+ if Arccos_Test_Data (I).Error_Bound = 0.0 then
+ Cycle_Error := 0.0;
+ Radian_Error := 0.0;
+ else
+ Cycle_Error := Arccos_Test_Data (I).Error_Bound;
+ -- allow for rounding error in the specification of Pi
+ Radian_Error := Cycle_Error + 1.0;
+ end if;
+
+ Check (Arccos (Arccos_Test_Data (I).Argument),
+ Arccos_Test_Data (I).Radians,
+ "test" & Integer'Image (I) &
+ " arccos(" &
+ Real'Image (Arccos_Test_Data (I).Argument) &
+ ")",
+ Radian_Error);
+--pwb-math Check (Arccos (Arccos_Test_Data (I).Argument, 2.0 * Pi),
+--pwb-math Arccos_Test_Data (I).Radians,
+--pwb-math "test" & Integer'Image (I) &
+--pwb-math " arccos(" &
+--pwb-math Real'Image (Arccos_Test_Data (I).Argument) &
+--pwb-math ", 2pi)",
+--pwb-math Cycle_Error);
+ Check (Arccos (Arccos_Test_Data (I).Argument, 360.0),
+ Arccos_Test_Data (I).Degrees,
+ "test" & Integer'Image (I) &
+ " arccos(" &
+ Real'Image (Arccos_Test_Data (I).Argument) &
+ ", 360)",
+ Cycle_Error);
+ end loop;
+
+ 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 Check_Exact (Actual, Expected_Low, Expected_High : Real;
+ Test_Name : String) is
+ -- If the expected result is not a model number, then Expected_Low is
+ -- the first machine number less than the (exact) expected
+ -- result, and Expected_High is the first machine number greater than
+ -- the (exact) expected result. If the expected result is a model
+ -- number, Expected_Low = Expected_High = the result.
+ Model_Expected_Low : Real := Expected_Low;
+ Model_Expected_High : Real := Expected_High;
+ begin
+ -- Calculate the first model number nearest to, but below (or equal)
+ -- to the expected result:
+ while Real'Model (Model_Expected_Low) /= Model_Expected_Low loop
+ -- Try the next machine number lower:
+ Model_Expected_Low := Real'Adjacent(Model_Expected_Low, 0.0);
+ end loop;
+ -- Calculate the first model number nearest to, but above (or equal)
+ -- to the expected result:
+ while Real'Model (Model_Expected_High) /= Model_Expected_High loop
+ -- Try the next machine number higher:
+ Model_Expected_High := Real'Adjacent(Model_Expected_High, 100.0);
+ end loop;
+
+ if Actual < Model_Expected_Low or Actual > Model_Expected_High then
+ Accuracy_Error_Reported := True;
+ if Actual < Model_Expected_Low then
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected low: " & Real'Image (Model_Expected_Low) &
+ " expected high: " & Real'Image (Model_Expected_High) &
+ " difference: " & Real'Image (Actual - Expected_Low));
+ else
+ Report.Failed (Test_Name &
+ " actual: " & Real'Image (Actual) &
+ " expected low: " & Real'Image (Model_Expected_Low) &
+ " expected high: " & Real'Image (Model_Expected_High) &
+ " difference: " & Real'Image (Expected_High - Actual));
+ end if;
+ elsif Verbose then
+ Report.Comment (Test_Name & " passed");
+ end if;
+ end Check_Exact;
+
+
+ procedure Exact_Result_Test is
+ begin
+ -- A.5.1(38)
+ Check_Exact (Arcsin (0.0), 0.0, 0.0, "arcsin(0)");
+ Check_Exact (Arcsin (0.0, 45.0), 0.0, 0.0, "arcsin(0,45)");
+
+ -- A.5.1(39)
+ Check_Exact (Arccos (1.0), 0.0, 0.0, "arccos(1)");
+ Check_Exact (Arccos (1.0, 75.0), 0.0, 0.0, "arccos(1,75)");
+
+ -- G.2.4(11-13)
+ Check_Exact (Arcsin (1.0), Half_PI_Low, Half_PI_High, "arcsin(1)");
+ Check_Exact (Arcsin (1.0, 360.0), 90.0, 90.0, "arcsin(1,360)");
+
+ Check_Exact (Arcsin (-1.0), -Half_PI_High, -Half_PI_Low, "arcsin(-1)");
+ Check_Exact (Arcsin (-1.0, 360.0), -90.0, -90.0, "arcsin(-1,360)");
+
+ Check_Exact (Arccos (0.0), Half_PI_Low, Half_PI_High, "arccos(0)");
+ Check_Exact (Arccos (0.0, 360.0), 90.0, 90.0, "arccos(0,360)");
+
+ Check_Exact (Arccos (-1.0), PI_Low, PI_High, "arccos(-1)");
+ Check_Exact (Arccos (-1.0, 360.0), 180.0, 180.0, "arccos(-1,360)");
+
+ 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 Arcsin_Taylor_Series_Test is
+ -- the following range is chosen so that the Taylor series
+ -- used will produce a result accurate to machine precision.
+ --
+ -- The following formula is used for the Taylor series:
+ -- TS(x) = x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) +
+ -- (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] }
+ -- where xsq = x * x
+ --
+ A : constant := -0.125;
+ B : constant := 0.125;
+ X : Real;
+ Y, Y_Sq : Real;
+ Actual, Sum, Xm : Real;
+ -- terms in Taylor series
+ K : constant Integer := Integer (
+ Log (
+ Real (Real'Machine_Radix) ** Real'Machine_Mantissa,
+ 10.0)) + 1;
+ begin
+ Accuracy_Error_Reported := False; -- reset
+ for I in 1..Max_Samples loop
+ -- make sure there is no error in x-1, x, and x+1
+ X := (B - A) * Real (I) / Real (Max_Samples) + A;
+
+ Y := X;
+ Y_Sq := Y * Y;
+ Sum := 0.0;
+ Xm := Real (K + K + 1);
+ for M in 1 .. K loop
+ Sum := Y_Sq * (Sum + 1.0/Xm);
+ Xm := Xm - 2.0;
+ Sum := Sum * (Xm /(Xm + 1.0));
+ end loop;
+ Sum := Sum * Y;
+ Actual := Y + Sum;
+ Sum := (Y - Actual) + Sum;
+ if not Real'Machine_Rounds then
+ Actual := Actual + (Sum + Sum);
+ end if;
+
+ Check (Actual, Arcsin (X),
+ "Taylor Series test" & Integer'Image (I) & ": arcsin(" &
+ Real'Image (X) & ") ",
+ Minimum_Error);
+
+ 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;
+
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Arcsin_Taylor_Series_Test" &
+ " for X=" & Real'Image (X));
+ when others =>
+ Report.Failed ("exception in Arcsin_Taylor_Series_Test" &
+ " for X=" & Real'Image (X));
+ end Arcsin_Taylor_Series_Test;
+
+
+
+ procedure Arccos_Taylor_Series_Test is
+ -- the following range is chosen so that the Taylor series
+ -- used will produce a result accurate to machine precision.
+ --
+ -- The following formula is used for the Taylor series:
+ -- TS(x) = x { 1 + (xsq/2) [ (1/3) + (3/4)xsq { (1/5) +
+ -- (5/6)xsq [ (1/7) + (7/8)xsq/9 ] } ] }
+ -- arccos(x) = pi/2 - TS(x)
+ A : constant := -0.125;
+ B : constant := 0.125;
+ C1, C2 : Real;
+ X : Real;
+ Y, Y_Sq : Real;
+ Actual, Sum, Xm, S : Real;
+ -- terms in Taylor series
+ K : constant Integer := Integer (
+ Log (
+ Real (Real'Machine_Radix) ** Real'Machine_Mantissa,
+ 10.0)) + 1;
+ begin
+ if Real'Digits > 23 then
+ -- constants in this section only accurate to 23 digits
+ Error_Low_Bound := 0.00000_00000_00000_00000_001;
+ Report.Comment ("arctan accuracy checked to 23 digits");
+ end if;
+
+ -- C1 + C2 equals Pi/2 accurate to 23 digits
+ if Real'Machine_Radix = 10 then
+ C1 := 1.57;
+ C2 := 7.9632679489661923132E-4;
+ else
+ C1 := 201.0 / 128.0;
+ C2 := 4.8382679489661923132E-4;
+ end if;
+
+ Accuracy_Error_Reported := False; -- reset
+ for I in 1..Max_Samples loop
+ -- make sure there is no error in x-1, x, and x+1
+ X := (B - A) * Real (I) / Real (Max_Samples) + A;
+
+ Y := X;
+ Y_Sq := Y * Y;
+ Sum := 0.0;
+ Xm := Real (K + K + 1);
+ for M in 1 .. K loop
+ Sum := Y_Sq * (Sum + 1.0/Xm);
+ Xm := Xm - 2.0;
+ Sum := Sum * (Xm /(Xm + 1.0));
+ end loop;
+ Sum := Sum * Y;
+
+ -- at this point we have arcsin(x).
+ -- We compute arccos(x) = pi/2 - arcsin(x).
+ -- The following code segment is translated directly from
+ -- the CELEFUNT FORTRAN implementation
+
+ S := C1 + C2;
+ Sum := ((C1 - S) + C2) - Sum;
+ Actual := S + Sum;
+ Sum := ((S - Actual) + Sum) - Y;
+ S := Actual;
+ Actual := S + Sum;
+ Sum := (S - Actual) + Sum;
+
+ if not Real'Machine_Rounds then
+ Actual := Actual + (Sum + Sum);
+ end if;
+
+ Check (Actual, Arccos (X),
+ "Taylor Series test" & Integer'Image (I) & ": arccos(" &
+ Real'Image (X) & ") ",
+ Minimum_Error);
+
+ -- only report the first error in this test in order to keep
+ -- lots of failures from producing a huge error log
+ exit when Accuracy_Error_Reported;
+ end loop;
+ Error_Low_Bound := 0.0; -- reset
+ exception
+ when Constraint_Error =>
+ Report.Failed
+ ("Constraint_Error raised in Arccos_Taylor_Series_Test" &
+ " for X=" & Real'Image (X));
+ when others =>
+ Report.Failed ("exception in Arccos_Taylor_Series_Test" &
+ " for X=" & Real'Image (X));
+ end Arccos_Taylor_Series_Test;
+
+
+
+ procedure Identity_Test is
+ -- test the identity arcsin(-x) = -arcsin(x)
+ -- range chosen to be most of the valid range of the argument.
+ A : constant := -0.999;
+ B : constant := 0.999;
+ X : Real;
+ begin
+ Accuracy_Error_Reported := False; -- reset
+ for I in 1..Max_Samples loop
+ -- make sure there is no error in x-1, x, and x+1
+ X := (B - A) * Real (I) / Real (Max_Samples) + A;
+
+ Check (Arcsin(-X), -Arcsin (X),
+ "Identity test" & Integer'Image (I) & ": arcsin(" &
+ Real'Image (X) & ") ",
+ 8.0); -- 2 arcsin evaluations => twice the error bound
+
+ 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 Identity_Test;
+
+
+ procedure Exception_Test is
+ X1, X2 : Real := 0.0;
+ begin
+ begin
+ X1 := Arcsin (1.1);
+ Report.Failed ("no exception for Arcsin (1.1)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error instead of " &
+ "Argument_Error for Arcsin (1.1)");
+ when Ada.Numerics.Argument_Error =>
+ null; -- expected result
+ when others =>
+ Report.Failed ("wrong exception for Arcsin(1.1)");
+ end;
+
+ begin
+ X2 := Arccos (-1.1);
+ Report.Failed ("no exception for Arccos (-1.1)");
+ exception
+ when Constraint_Error =>
+ Report.Failed ("Constraint_Error instead of " &
+ "Argument_Error for Arccos (-1.1)");
+ when Ada.Numerics.Argument_Error =>
+ null; -- expected result
+ when others =>
+ Report.Failed ("wrong exception for Arccos(-1.1)");
+ end;
+
+
+ -- optimizer thwarting
+ if Report.Ident_Bool (False) then
+ Report.Comment (Real'Image (X1 + X2));
+ end if;
+ end Exception_Test;
+
+
+ procedure Do_Test is
+ begin
+ Special_Value_Test;
+ Exact_Result_Test;
+ Arcsin_Taylor_Series_Test;
+ Arccos_Taylor_Series_Test;
+ Identity_Test;
+ Exception_Test;
+ end Do_Test;
+ end Generic_Check;
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+ -- These expressions must be truly static, which is why we have to do them
+ -- outside of the generic, and we use the named numbers. Note that we know
+ -- that PI is not a machine number (it is irrational), and it should be
+ -- represented to more digits than supported by the target machine.
+ Float_Half_PI_Low : constant := Float'Adjacent(PI/2.0, 0.0);
+ Float_Half_PI_High : constant := Float'Adjacent(PI/2.0, 10.0);
+ Float_PI_Low : constant := Float'Adjacent(PI, 0.0);
+ Float_PI_High : constant := Float'Adjacent(PI, 10.0);
+ package Float_Check is new Generic_Check (Float,
+ Half_PI_Low => Float_Half_PI_Low,
+ Half_PI_High => Float_Half_PI_High,
+ PI_Low => Float_PI_Low,
+ PI_High => Float_PI_High);
+
+ -- check the floating point type with the most digits
+ type A_Long_Float is digits System.Max_Digits;
+ A_Long_Float_Half_PI_Low : constant := A_Long_Float'Adjacent(PI/2.0, 0.0);
+ A_Long_Float_Half_PI_High : constant := A_Long_Float'Adjacent(PI/2.0, 10.0);
+ A_Long_Float_PI_Low : constant := A_Long_Float'Adjacent(PI, 0.0);
+ A_Long_Float_PI_High : constant := A_Long_Float'Adjacent(PI, 10.0);
+ package A_Long_Float_Check is new Generic_Check (A_Long_Float,
+ Half_PI_Low => A_Long_Float_Half_PI_Low,
+ Half_PI_High => A_Long_Float_Half_PI_High,
+ PI_Low => A_Long_Float_PI_Low,
+ PI_High => A_Long_Float_PI_High);
+
+ -----------------------------------------------------------------------
+ -----------------------------------------------------------------------
+
+
+begin
+ Report.Test ("CXG2015",
+ "Check the accuracy of the ARCSIN and ARCCOS 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 CXG2015;