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jeremybenn |
-- CXG2007.A
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--
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-- Grant of Unlimited Rights
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--
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-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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-- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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-- unlimited rights in the software and documentation contained herein.
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-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
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-- this public release, the Government intends to confer upon all
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-- recipients unlimited rights equal to those held by the Government.
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-- These rights include rights to use, duplicate, release or disclose the
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-- released technical data and computer software in whole or in part, in
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-- any manner and for any purpose whatsoever, and to have or permit others
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-- to do so.
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--
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-- DISCLAIMER
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--
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-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
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-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
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-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
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-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
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-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
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-- PARTICULAR PURPOSE OF SAID MATERIAL.
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--*
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--
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-- OBJECTIVE:
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-- Check that the complex Compose_From_Polar function returns
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-- results that are within the error bound allowed.
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-- Check that Argument_Error is raised if the Cycle parameter
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-- is less than or equal to zero.
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--
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-- TEST DESCRIPTION:
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-- This test uses a generic package to compute and check the
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-- values of the Compose_From_Polar function.
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--
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-- SPECIAL REQUIREMENTS
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-- The Strict Mode for the numerical accuracy must be
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-- selected. The method by which this mode is selected
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-- is implementation dependent.
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--
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-- APPLICABILITY CRITERIA:
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-- This test applies only to implementations supporting the
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-- Numerics Annex.
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-- This test only applies to the Strict Mode for numerical
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-- accuracy.
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--
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--
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-- CHANGE HISTORY:
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-- 23 FEB 96 SAIC Initial release for 2.1
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-- 23 APR 96 SAIC Fixed error checking
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-- 03 MAR 97 PWB.CTA Deleted checks with explicit Cycle => 2.0*Pi
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--
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-- CHANGE NOTE:
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-- According to Ken Dritz, author of the Numerics Annex of the RM,
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-- one should never specify the cycle 2.0*Pi for the trigonometric
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-- functions. In particular, if the machine number for the first
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-- argument is not an exact multiple of the machine number for the
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-- explicit cycle, then the specified exact results cannot be
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-- reasonably expected. The affected checks in this test have been
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-- marked as comments, with the additional notation "pwb-math".
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-- Phil Brashear
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--!
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with System;
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with Report;
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with Ada.Numerics;
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with Ada.Numerics.Generic_Complex_Types;
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procedure CXG2007 is
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Verbose : constant Boolean := False;
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-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
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Sqrt2 : constant :=
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1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
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Sqrt3 : constant :=
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1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
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Pi : constant := Ada.Numerics.Pi;
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generic
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type Real is digits <>;
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package Generic_Check is
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procedure Do_Test;
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end Generic_Check;
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package body Generic_Check is
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package Complex_Types is new
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Ada.Numerics.Generic_Complex_Types (Real);
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use Complex_Types;
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Maximum_Relative_Error : constant Real := 3.0;
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procedure Check (Actual, Expected : Real;
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Test_Name : String;
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MRE : Real;
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Arg_Error : Real) is
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-- Arg_Error is additional absolute error that is allowed beyond
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-- the MRE to account for error in the result that can be
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-- attributed to error in the arguments.
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Max_Error : Real;
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Rel_Error : Real;
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Abs_Error : Real;
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begin
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-- In the case where the expected result is very small or 0
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-- we compute the maximum error as a multiple of Model_Small instead
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-- of Model_Epsilon and Expected.
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Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
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Abs_Error := MRE * Real'Model_Epsilon;
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if Rel_Error > Abs_Error then
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Max_Error := Rel_Error;
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else
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Max_Error := Abs_Error;
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end if;
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Max_Error := Max_Error + Arg_Error;
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if abs (Actual - Expected) > Max_Error then
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Report.Failed (Test_Name &
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" actual: " & Real'Image (Actual) &
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" expected: " & Real'Image (Expected) &
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" difference: " & Real'Image (Actual - Expected) &
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" max err:" & Real'Image (Max_Error) );
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elsif Verbose then
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if Actual = Expected then
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Report.Comment (Test_Name & " exact result");
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else
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Report.Comment (Test_Name & " passed");
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end if;
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end if;
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end Check;
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procedure Check (Actual, Expected : Complex;
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Test_Name : String;
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MRE : Real;
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Arg_Error : Real) is
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-- Arg_Error is additional absolute error that is allowed beyond
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-- the MRE to account for error in the result that can be
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-- attributed to error in the arguments.
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begin
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Check (Actual.Re, Expected.Re,
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Test_Name & " real part",
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MRE, Arg_Error);
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Check (Actual.Im, Expected.Im,
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Test_Name & " imaginary part",
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MRE, Arg_Error);
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end Check;
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procedure Special_Cases is
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type Data_Point is
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record
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Re,
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Im,
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Modulus,
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Radians,
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Degrees,
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Arg_Error : Real;
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end record;
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-- shorthand names for various constants
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P4 : constant := Pi/4.0;
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P6 : constant := Pi/6.0;
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MER2 : constant Real := Real'Model_Epsilon * Sqrt2;
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type Test_Data_Type is array (Positive range <>) of Data_Point;
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-- the values in the following table only involve static
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-- expressions so no loss of precision occurs.
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Test_Data : constant Test_Data_Type := (
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--Re Im Modulus Radians Degrees Arg_Err
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( 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ), -- 1
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( 0.0, 0.0, 0.0, Pi, 180.0, 0.0 ), -- 2
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( 1.0, 0.0, 1.0, 0.0, 0.0, 0.0 ), -- 3
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(-1.0, 0.0, -1.0, 0.0, 0.0, 0.0 ), -- 4
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( 1.0, 1.0, Sqrt2, P4, 45.0, MER2), -- 5
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(-1.0, 1.0, -Sqrt2, -P4, -45.0, MER2), -- 6
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( 1.0, -1.0, Sqrt2, -P4, -45.0, MER2), -- 7
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(-1.0, -1.0, -Sqrt2, P4, 45.0, MER2), -- 8
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(-1.0, -1.0, Sqrt2, -3.0*P4,-135.0, MER2), -- 9
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(-1.0, 1.0, Sqrt2, 3.0*P4, 135.0, MER2), -- 10
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( 1.0, -1.0, -Sqrt2, 3.0*P4, 135.0, MER2), -- 11
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(-1.0, 0.0, 1.0, Pi, 180.0, 0.0 ), -- 12
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( 1.0, 0.0, -1.0, Pi, 180.0, 0.0 ) ); -- 13
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Z : Complex;
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Exp : Complex;
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begin
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for I in Test_Data'Range loop
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begin
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Exp := (Test_Data (I).Re, Test_Data (I).Im);
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Z := Compose_From_Polar (Test_Data (I).Modulus,
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Test_Data (I).Radians);
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Check (Z, Exp,
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"test" & Integer'Image (I) & " compose_from_polar(m,r)",
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Maximum_Relative_Error, Test_Data (I).Arg_Error);
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--pwb-math Z := Compose_From_Polar (Test_Data (I).Modulus,
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--pwb-math Test_Data (I).Radians,
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--pwb-math 2.0*Pi);
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--pwb-math Check (Z, Exp,
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--pwb-math "test" & Integer'Image (I) & " compose_from_polar(m,r,2pi)",
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--pwb-math Maximum_Relative_Error, Test_Data (I).Arg_Error);
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Z := Compose_From_Polar (Test_Data (I).Modulus,
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Test_Data (I).Degrees,
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360.0);
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Check (Z, Exp,
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"test" & Integer'Image (I) & " compose_from_polar(m,d,360)",
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Maximum_Relative_Error, Test_Data (I).Arg_Error);
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exception
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when Constraint_Error =>
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Report.Failed ("Constraint_Error raised in test" &
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Integer'Image (I));
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when others =>
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Report.Failed ("exception in test" &
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Integer'Image (I));
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end;
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end loop;
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end Special_Cases;
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procedure Exception_Cases is
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-- check that Argument_Error is raised if Cycle is <= 0
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Z : Complex;
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W : Complex;
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begin
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begin
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Z := Compose_From_Polar (3.0, 0.0, Cycle => 0.0);
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Report.Failed ("no exception for cycle = 0.0");
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exception
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when Ada.Numerics.Argument_Error => null;
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when others =>
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Report.Failed ("wrong exception for cycle = 0.0");
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end;
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begin
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W := Compose_From_Polar (6.0, 1.0, Cycle => -10.0);
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Report.Failed ("no exception for cycle < 0.0");
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exception
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when Ada.Numerics.Argument_Error => null;
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when others =>
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Report.Failed ("wrong exception for cycle < 0.0");
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end;
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if Report.Ident_Int (1) = 2 then
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-- not executed - used to make it appear that we use the
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-- results of the above computation
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Z := Z * W;
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Report.Failed(Real'Image (Z.Re + Z.Im));
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end if;
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end Exception_Cases;
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procedure Do_Test is
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begin
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Special_Cases;
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Exception_Cases;
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end Do_Test;
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end Generic_Check;
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package Chk_Float is new Generic_Check (Float);
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-- check the floating point type with the most digits
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type A_Long_Float is digits System.Max_Digits;
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package Chk_A_Long_Float is new Generic_Check (A_Long_Float);
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begin
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Report.Test ("CXG2007",
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"Check the accuracy of the Compose_From_Polar" &
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" function");
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if Verbose then
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Report.Comment ("checking Standard.Float");
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end if;
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Chk_Float.Do_Test;
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if Verbose then
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Report.Comment ("checking a digits" &
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Integer'Image (System.Max_Digits) &
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" floating point type");
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end if;
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Chk_A_Long_Float.Do_Test;
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Report.Result;
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end CXG2007;
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