-- CXG2004.A
|
-- CXG2004.A
|
--
|
--
|
-- Grant of Unlimited Rights
|
-- Grant of Unlimited Rights
|
--
|
--
|
-- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
|
-- 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
|
-- 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 in the software and documentation contained herein.
|
-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
|
-- this public release, the Government intends to confer upon all
|
-- this public release, the Government intends to confer upon all
|
-- recipients unlimited rights equal to those held by the Government.
|
-- recipients unlimited rights equal to those held by the Government.
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- These rights include rights to use, duplicate, release or disclose the
|
-- released technical data and computer software in whole or in part, in
|
-- 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
|
-- any manner and for any purpose whatsoever, and to have or permit others
|
-- to do so.
|
-- to do so.
|
--
|
--
|
-- DISCLAIMER
|
-- DISCLAIMER
|
--
|
--
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
|
-- PARTICULAR PURPOSE OF SAID MATERIAL.
|
--*
|
--*
|
--
|
--
|
-- OBJECTIVE:
|
-- OBJECTIVE:
|
-- Check that the sin and cos functions return
|
-- Check that the sin and cos functions return
|
-- results that are within the error bound allowed.
|
-- results that are within the error bound allowed.
|
--
|
--
|
-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test consists of a generic package that is
|
-- This test consists of a generic package that is
|
-- instantiated to check both float and a long float type.
|
-- instantiated to check both float and a long float type.
|
-- The test for each floating point type is divided into
|
-- The test for each floating point type is divided into
|
-- the following parts:
|
-- the following parts:
|
-- Special value checks where the result is a known constant.
|
-- Special value checks where the result is a known constant.
|
-- Checks using an identity relationship.
|
-- Checks using an identity relationship.
|
--
|
--
|
-- SPECIAL REQUIREMENTS
|
-- SPECIAL REQUIREMENTS
|
-- The Strict Mode for the numerical accuracy must be
|
-- The Strict Mode for the numerical accuracy must be
|
-- selected. The method by which this mode is selected
|
-- selected. The method by which this mode is selected
|
-- is implementation dependent.
|
-- is implementation dependent.
|
--
|
--
|
-- APPLICABILITY CRITERIA:
|
-- APPLICABILITY CRITERIA:
|
-- This test applies only to implementations supporting the
|
-- This test applies only to implementations supporting the
|
-- Numerics Annex.
|
-- Numerics Annex.
|
-- This test only applies to the Strict Mode for numerical
|
-- This test only applies to the Strict Mode for numerical
|
-- accuracy.
|
-- accuracy.
|
--
|
--
|
--
|
--
|
-- CHANGE HISTORY:
|
-- CHANGE HISTORY:
|
-- 13 FEB 96 SAIC Initial release for 2.1
|
-- 13 FEB 96 SAIC Initial release for 2.1
|
-- 22 APR 96 SAIC Changed to generic implementation.
|
-- 22 APR 96 SAIC Changed to generic implementation.
|
-- 18 AUG 96 SAIC Improvements to commentary.
|
-- 18 AUG 96 SAIC Improvements to commentary.
|
-- 23 OCT 96 SAIC Exact results are not required unless the
|
-- 23 OCT 96 SAIC Exact results are not required unless the
|
-- cycle is specified.
|
-- cycle is specified.
|
-- 28 FEB 97 PWB.CTA Removed checks where cycle 2.0*Pi 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
|
-- 02 JUN 98 EDS Revised calculations to ensure that X is exactly
|
-- three times Y per advice of numerics experts.
|
-- three times Y per advice of numerics experts.
|
--
|
--
|
-- CHANGE NOTE:
|
-- CHANGE NOTE:
|
-- According to Ken Dritz, author of the Numerics Annex of the RM,
|
-- According to Ken Dritz, author of the Numerics Annex of the RM,
|
-- one should never specify the cycle 2.0*Pi for the trigonometric
|
-- one should never specify the cycle 2.0*Pi for the trigonometric
|
-- functions. In particular, if the machine number for the first
|
-- functions. In particular, if the machine number for the first
|
-- argument is not an exact multiple of the machine number for the
|
-- argument is not an exact multiple of the machine number for the
|
-- explicit cycle, then the specified exact results cannot be
|
-- explicit cycle, then the specified exact results cannot be
|
-- reasonably expected. The affected checks in this test have been
|
-- reasonably expected. The affected checks in this test have been
|
-- marked as comments, with the additional notation "pwb-math".
|
-- marked as comments, with the additional notation "pwb-math".
|
-- Phil Brashear
|
-- Phil Brashear
|
--!
|
--!
|
|
|
--
|
--
|
-- References:
|
-- References:
|
--
|
--
|
-- Software Manual for the Elementary Functions
|
-- Software Manual for the Elementary Functions
|
-- William J. Cody, Jr. and William Waite
|
-- William J. Cody, Jr. and William Waite
|
-- Prentice-Hall, 1980
|
-- Prentice-Hall, 1980
|
--
|
--
|
-- CRC Standard Mathematical Tables
|
-- CRC Standard Mathematical Tables
|
-- 23rd Edition
|
-- 23rd Edition
|
--
|
--
|
-- Implementation and Testing of Function Software
|
-- Implementation and Testing of Function Software
|
-- W. J. Cody
|
-- W. J. Cody
|
-- Problems and Methodologies in Mathematical Software Production
|
-- Problems and Methodologies in Mathematical Software Production
|
-- editors P. C. Messina and A. Murli
|
-- editors P. C. Messina and A. Murli
|
-- Lecture Notes in Computer Science Volume 142
|
-- Lecture Notes in Computer Science Volume 142
|
-- Springer Verlag, 1982
|
-- Springer Verlag, 1982
|
--
|
--
|
-- The sin and cos checks are translated directly from
|
-- The sin and cos checks are translated directly from
|
-- the netlib FORTRAN code that was written by W. Cody.
|
-- the netlib FORTRAN code that was written by W. Cody.
|
--
|
--
|
|
|
with System;
|
with System;
|
with Report;
|
with Report;
|
with Ada.Numerics.Generic_Elementary_Functions;
|
with Ada.Numerics.Generic_Elementary_Functions;
|
with Ada.Numerics.Elementary_Functions;
|
with Ada.Numerics.Elementary_Functions;
|
procedure CXG2004 is
|
procedure CXG2004 is
|
Verbose : constant Boolean := False;
|
Verbose : constant Boolean := False;
|
Number_Samples : constant := 1000;
|
Number_Samples : constant := 1000;
|
|
|
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
|
-- CRC Standard Mathematical Tables; 23rd Edition; pg 738
|
Sqrt2 : constant :=
|
Sqrt2 : constant :=
|
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
|
1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695;
|
Sqrt3 : constant :=
|
Sqrt3 : constant :=
|
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
|
1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039;
|
|
|
Pi : constant := Ada.Numerics.Pi;
|
Pi : constant := Ada.Numerics.Pi;
|
|
|
generic
|
generic
|
type Real is digits <>;
|
type Real is digits <>;
|
package Generic_Check is
|
package Generic_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
end Generic_Check;
|
end Generic_Check;
|
|
|
package body Generic_Check is
|
package body Generic_Check is
|
package Elementary_Functions is new
|
package Elementary_Functions is new
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
Ada.Numerics.Generic_Elementary_Functions (Real);
|
|
|
function Sin (X : Real) return Real renames
|
function Sin (X : Real) return Real renames
|
Elementary_Functions.Sin;
|
Elementary_Functions.Sin;
|
function Cos (X : Real) return Real renames
|
function Cos (X : Real) return Real renames
|
Elementary_Functions.Cos;
|
Elementary_Functions.Cos;
|
function Sin (X, Cycle : Real) return Real renames
|
function Sin (X, Cycle : Real) return Real renames
|
Elementary_Functions.Sin;
|
Elementary_Functions.Sin;
|
function Cos (X, Cycle : Real) return Real renames
|
function Cos (X, Cycle : Real) return Real renames
|
Elementary_Functions.Cos;
|
Elementary_Functions.Cos;
|
|
|
Accuracy_Error_Reported : Boolean := False;
|
Accuracy_Error_Reported : Boolean := False;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
Rel_Error,
|
Rel_Error,
|
Abs_Error,
|
Abs_Error,
|
Max_Error : Real;
|
Max_Error : Real;
|
begin
|
begin
|
|
|
-- In the case where the expected result is very small or 0
|
-- In the case where the expected result is very small or 0
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- we compute the maximum error as a multiple of Model_Epsilon instead
|
-- of Model_Epsilon and Expected.
|
-- of Model_Epsilon and Expected.
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Rel_Error := MRE * abs Expected * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
Abs_Error := MRE * Real'Model_Epsilon;
|
if Rel_Error > Abs_Error then
|
if Rel_Error > Abs_Error then
|
Max_Error := Rel_Error;
|
Max_Error := Rel_Error;
|
else
|
else
|
Max_Error := Abs_Error;
|
Max_Error := Abs_Error;
|
end if;
|
end if;
|
|
|
|
|
-- in addition to the relative error checks we apply the
|
-- in addition to the relative error checks we apply the
|
-- criteria of G.2.4(16)
|
-- criteria of G.2.4(16)
|
if abs (Actual) > 1.0 then
|
if abs (Actual) > 1.0 then
|
Accuracy_Error_Reported := True;
|
Accuracy_Error_Reported := True;
|
Report.Failed (Test_Name & " result > 1.0");
|
Report.Failed (Test_Name & " result > 1.0");
|
elsif abs (Actual - Expected) > Max_Error then
|
elsif abs (Actual - Expected) > Max_Error then
|
Accuracy_Error_Reported := True;
|
Accuracy_Error_Reported := True;
|
Report.Failed (Test_Name &
|
Report.Failed (Test_Name &
|
" actual: " & Real'Image (Actual) &
|
" actual: " & Real'Image (Actual) &
|
" expected: " & Real'Image (Expected) &
|
" expected: " & Real'Image (Expected) &
|
" difference: " &
|
" difference: " &
|
Real'Image (Actual - Expected) &
|
Real'Image (Actual - Expected) &
|
" mre:" &
|
" mre:" &
|
Real'Image (Max_Error) );
|
Real'Image (Max_Error) );
|
elsif Verbose then
|
elsif Verbose then
|
if Actual = Expected then
|
if Actual = Expected then
|
Report.Comment (Test_Name & " exact result");
|
Report.Comment (Test_Name & " exact result");
|
else
|
else
|
Report.Comment (Test_Name & " passed");
|
Report.Comment (Test_Name & " passed");
|
end if;
|
end if;
|
end if;
|
end if;
|
end Check;
|
end Check;
|
|
|
|
|
procedure Sin_Check (A, B : Real;
|
procedure Sin_Check (A, B : Real;
|
Arg_Range : String) is
|
Arg_Range : String) is
|
-- test a selection of
|
-- test a selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
--
|
--
|
-- This test uses the identity
|
-- This test uses the identity
|
-- sin(x) = sin(x/3)*(3 - 4 * sin(x/3)**2)
|
-- sin(x) = sin(x/3)*(3 - 4 * sin(x/3)**2)
|
--
|
--
|
-- Note that in this test we must take into account the
|
-- Note that in this test we must take into account the
|
-- error in the calculation of the expected result so
|
-- error in the calculation of the expected result so
|
-- the maximum relative error is larger than the
|
-- the maximum relative error is larger than the
|
-- accuracy required by the ARM.
|
-- accuracy required by the ARM.
|
|
|
X, Y, ZZ : Real;
|
X, Y, ZZ : Real;
|
Actual, Expected : Real;
|
Actual, Expected : Real;
|
MRE : Real;
|
MRE : Real;
|
Ran : Real;
|
Ran : Real;
|
begin
|
begin
|
Accuracy_Error_Reported := False; -- reset
|
Accuracy_Error_Reported := False; -- reset
|
for I in 1 .. Number_Samples loop
|
for I in 1 .. Number_Samples loop
|
-- Evenly distributed selection of arguments
|
-- Evenly distributed selection of arguments
|
Ran := Real (I) / Real (Number_Samples);
|
Ran := Real (I) / Real (Number_Samples);
|
|
|
-- make sure x and x/3 are both exactly representable
|
-- make sure x and x/3 are both exactly representable
|
-- on the machine. See "Implementation and Testing of
|
-- on the machine. See "Implementation and Testing of
|
-- Function Software" page 44.
|
-- Function Software" page 44.
|
X := (B - A) * Ran + A;
|
X := (B - A) * Ran + A;
|
Y := Real'Leading_Part
|
Y := Real'Leading_Part
|
( X/3.0,
|
( X/3.0,
|
Real'Machine_Mantissa - Real'Exponent (3.0) );
|
Real'Machine_Mantissa - Real'Exponent (3.0) );
|
X := Y * 3.0;
|
X := Y * 3.0;
|
|
|
Actual := Sin (X);
|
Actual := Sin (X);
|
|
|
ZZ := Sin(Y);
|
ZZ := Sin(Y);
|
Expected := ZZ * (3.0 - 4.0 * ZZ * ZZ);
|
Expected := ZZ * (3.0 - 4.0 * ZZ * ZZ);
|
|
|
-- note that since the expected value is computed, we
|
-- note that since the expected value is computed, we
|
-- must take the error in that computation into account.
|
-- must take the error in that computation into account.
|
-- See Cody pp 139-141.
|
-- See Cody pp 139-141.
|
MRE := 4.0;
|
MRE := 4.0;
|
|
|
Check (Actual, Expected,
|
Check (Actual, Expected,
|
"sin test of range" & Arg_Range &
|
"sin test of range" & Arg_Range &
|
Integer'Image (I),
|
Integer'Image (I),
|
MRE);
|
MRE);
|
exit when Accuracy_Error_Reported;
|
exit when Accuracy_Error_Reported;
|
end loop;
|
end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in sin check");
|
("Constraint_Error raised in sin check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in sin check");
|
Report.Failed ("exception in sin check");
|
end Sin_Check;
|
end Sin_Check;
|
|
|
|
|
|
|
procedure Cos_Check (A, B : Real;
|
procedure Cos_Check (A, B : Real;
|
Arg_Range : String) is
|
Arg_Range : String) is
|
-- test a selection of
|
-- test a selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
--
|
--
|
-- This test uses the identity
|
-- This test uses the identity
|
-- cos(x) = cos(x/3)*(4 * cos(x/3)**2 - 3)
|
-- cos(x) = cos(x/3)*(4 * cos(x/3)**2 - 3)
|
--
|
--
|
-- Note that in this test we must take into account the
|
-- Note that in this test we must take into account the
|
-- error in the calculation of the expected result so
|
-- error in the calculation of the expected result so
|
-- the maximum relative error is larger than the
|
-- the maximum relative error is larger than the
|
-- accuracy required by the ARM.
|
-- accuracy required by the ARM.
|
|
|
X, Y, ZZ : Real;
|
X, Y, ZZ : Real;
|
Actual, Expected : Real;
|
Actual, Expected : Real;
|
MRE : Real;
|
MRE : Real;
|
Ran : Real;
|
Ran : Real;
|
begin
|
begin
|
Accuracy_Error_Reported := False; -- reset
|
Accuracy_Error_Reported := False; -- reset
|
for I in 1 .. Number_Samples loop
|
for I in 1 .. Number_Samples loop
|
-- Evenly distributed selection of arguments
|
-- Evenly distributed selection of arguments
|
Ran := Real (I) / Real (Number_Samples);
|
Ran := Real (I) / Real (Number_Samples);
|
|
|
-- make sure x and x/3 are both exactly representable
|
-- make sure x and x/3 are both exactly representable
|
-- on the machine. See "Implementation and Testing of
|
-- on the machine. See "Implementation and Testing of
|
-- Function Software" page 44.
|
-- Function Software" page 44.
|
X := (B - A) * Ran + A;
|
X := (B - A) * Ran + A;
|
Y := Real'Leading_Part
|
Y := Real'Leading_Part
|
( X/3.0,
|
( X/3.0,
|
Real'Machine_Mantissa - Real'Exponent (3.0) );
|
Real'Machine_Mantissa - Real'Exponent (3.0) );
|
X := Y * 3.0;
|
X := Y * 3.0;
|
|
|
Actual := Cos (X);
|
Actual := Cos (X);
|
|
|
ZZ := Cos(Y);
|
ZZ := Cos(Y);
|
Expected := ZZ * (4.0 * ZZ * ZZ - 3.0);
|
Expected := ZZ * (4.0 * ZZ * ZZ - 3.0);
|
|
|
-- note that since the expected value is computed, we
|
-- note that since the expected value is computed, we
|
-- must take the error in that computation into account.
|
-- must take the error in that computation into account.
|
-- See Cody pp 141-143.
|
-- See Cody pp 141-143.
|
MRE := 6.0;
|
MRE := 6.0;
|
|
|
Check (Actual, Expected,
|
Check (Actual, Expected,
|
"cos test of range" & Arg_Range &
|
"cos test of range" & Arg_Range &
|
Integer'Image (I),
|
Integer'Image (I),
|
MRE);
|
MRE);
|
exit when Accuracy_Error_Reported;
|
exit when Accuracy_Error_Reported;
|
end loop;
|
end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed
|
Report.Failed
|
("Constraint_Error raised in cos check");
|
("Constraint_Error raised in cos check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in cos check");
|
Report.Failed ("exception in cos check");
|
end Cos_Check;
|
end Cos_Check;
|
|
|
|
|
procedure Special_Angle_Checks is
|
procedure Special_Angle_Checks is
|
type Data_Point is
|
type Data_Point is
|
record
|
record
|
Degrees,
|
Degrees,
|
Radians,
|
Radians,
|
Sine,
|
Sine,
|
Cosine : Real;
|
Cosine : Real;
|
Sin_Result_Error,
|
Sin_Result_Error,
|
Cos_Result_Error : Boolean;
|
Cos_Result_Error : Boolean;
|
end record;
|
end record;
|
|
|
type Test_Data_Type is array (Positive range <>) of Data_Point;
|
type Test_Data_Type is array (Positive range <>) of Data_Point;
|
|
|
-- the values in the following table only involve static
|
-- the values in the following table only involve static
|
-- expressions to minimize any loss of precision. However,
|
-- expressions to minimize any loss of precision. However,
|
-- there are two sources of error that must be accounted for
|
-- there are two sources of error that must be accounted for
|
-- in the following tests.
|
-- in the following tests.
|
-- First, when a cycle is not specified there can be a roundoff
|
-- First, when a cycle is not specified there can be a roundoff
|
-- error in the value of Pi used. This error does not apply
|
-- error in the value of Pi used. This error does not apply
|
-- when a cycle of 2.0 * Pi is explicitly provided.
|
-- when a cycle of 2.0 * Pi is explicitly provided.
|
-- Second, the expected results that involve sqrt values also
|
-- Second, the expected results that involve sqrt values also
|
-- have a potential roundoff error.
|
-- have a potential roundoff error.
|
-- The amount of error due to error in the argument is computed
|
-- The amount of error due to error in the argument is computed
|
-- as follows:
|
-- as follows:
|
-- sin(x+err) = sin(x)*cos(err) + cos(x)*sin(err)
|
-- sin(x+err) = sin(x)*cos(err) + cos(x)*sin(err)
|
-- ~= sin(x) + err * cos(x)
|
-- ~= sin(x) + err * cos(x)
|
-- similarly for cos the error due to error in the argument is
|
-- similarly for cos the error due to error in the argument is
|
-- computed as follows:
|
-- computed as follows:
|
-- cos(x+err) = cos(x)*cos(err) - sin(x)*sin(err)
|
-- cos(x+err) = cos(x)*cos(err) - sin(x)*sin(err)
|
-- ~= cos(x) - err * sin(x)
|
-- ~= cos(x) - err * sin(x)
|
-- In both cases the term "err" is bounded by 0.5 * argument.
|
-- In both cases the term "err" is bounded by 0.5 * argument.
|
|
|
Test_Data : constant Test_Data_Type := (
|
Test_Data : constant Test_Data_Type := (
|
-- degrees radians sine cosine sin_er cos_er test #
|
-- degrees radians sine cosine sin_er cos_er test #
|
( 0.0, 0.0, 0.0, 1.0, False, False ), -- 1
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( 0.0, 0.0, 0.0, 1.0, False, False ), -- 1
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( 30.0, Pi/6.0, 0.5, Sqrt3/2.0, False, True ), -- 2
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( 30.0, Pi/6.0, 0.5, Sqrt3/2.0, False, True ), -- 2
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( 60.0, Pi/3.0, Sqrt3/2.0, 0.5, True, False ), -- 3
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( 60.0, Pi/3.0, Sqrt3/2.0, 0.5, True, False ), -- 3
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( 90.0, Pi/2.0, 1.0, 0.0, False, False ), -- 4
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( 90.0, Pi/2.0, 1.0, 0.0, False, False ), -- 4
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(120.0, 2.0*Pi/3.0, Sqrt3/2.0, -0.5, True, False ), -- 5
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(120.0, 2.0*Pi/3.0, Sqrt3/2.0, -0.5, True, False ), -- 5
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(150.0, 5.0*Pi/6.0, 0.5, -Sqrt3/2.0, False, True ), -- 6
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(150.0, 5.0*Pi/6.0, 0.5, -Sqrt3/2.0, False, True ), -- 6
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(180.0, Pi, 0.0, -1.0, False, False ), -- 7
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(180.0, Pi, 0.0, -1.0, False, False ), -- 7
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(210.0, 7.0*Pi/6.0, -0.5, -Sqrt3/2.0, False, True ), -- 8
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(210.0, 7.0*Pi/6.0, -0.5, -Sqrt3/2.0, False, True ), -- 8
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(240.0, 8.0*Pi/6.0, -Sqrt3/2.0, -0.5, True, False ), -- 9
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(240.0, 8.0*Pi/6.0, -Sqrt3/2.0, -0.5, True, False ), -- 9
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(270.0, 9.0*Pi/6.0, -1.0, 0.0, False, False ), -- 10
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(270.0, 9.0*Pi/6.0, -1.0, 0.0, False, False ), -- 10
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(300.0, 10.0*Pi/6.0, -Sqrt3/2.0, 0.5, True, False ), -- 11
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(300.0, 10.0*Pi/6.0, -Sqrt3/2.0, 0.5, True, False ), -- 11
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(330.0, 11.0*Pi/6.0, -0.5, Sqrt3/2.0, False, True ), -- 12
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(330.0, 11.0*Pi/6.0, -0.5, Sqrt3/2.0, False, True ), -- 12
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(360.0, 2.0*Pi, 0.0, 1.0, False, False ), -- 13
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(360.0, 2.0*Pi, 0.0, 1.0, False, False ), -- 13
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( 45.0, Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 14
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( 45.0, Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 14
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(135.0, 3.0*Pi/4.0, Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 15
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(135.0, 3.0*Pi/4.0, Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 15
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(225.0, 5.0*Pi/4.0, -Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 16
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(225.0, 5.0*Pi/4.0, -Sqrt2/2.0, -Sqrt2/2.0, True, True ), -- 16
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(315.0, 7.0*Pi/4.0, -Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 17
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(315.0, 7.0*Pi/4.0, -Sqrt2/2.0, Sqrt2/2.0, True, True ), -- 17
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(405.0, 9.0*Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ) ); -- 18
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(405.0, 9.0*Pi/4.0, Sqrt2/2.0, Sqrt2/2.0, True, True ) ); -- 18
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Y : Real;
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Y : Real;
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Sin_Arg_Err,
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Sin_Arg_Err,
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Cos_Arg_Err,
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Cos_Arg_Err,
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Sin_Result_Err,
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Sin_Result_Err,
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Cos_Result_Err : Real;
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Cos_Result_Err : Real;
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begin
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begin
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for I in Test_Data'Range loop
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for I in Test_Data'Range loop
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-- compute error components
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-- compute error components
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Sin_Arg_Err := abs Test_Data (I).Cosine *
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Sin_Arg_Err := abs Test_Data (I).Cosine *
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abs Test_Data (I).Radians / 2.0;
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abs Test_Data (I).Radians / 2.0;
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Cos_Arg_Err := abs Test_Data (I).Sine *
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Cos_Arg_Err := abs Test_Data (I).Sine *
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abs Test_Data (I).Radians / 2.0;
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abs Test_Data (I).Radians / 2.0;
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|
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if Test_Data (I).Sin_Result_Error then
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if Test_Data (I).Sin_Result_Error then
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Sin_Result_Err := 0.5;
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Sin_Result_Err := 0.5;
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else
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else
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Sin_Result_Err := 0.0;
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Sin_Result_Err := 0.0;
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end if;
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end if;
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if Test_Data (I).Cos_Result_Error then
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if Test_Data (I).Cos_Result_Error then
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Cos_Result_Err := 1.0;
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Cos_Result_Err := 1.0;
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else
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else
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Cos_Result_Err := 0.0;
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Cos_Result_Err := 0.0;
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end if;
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end if;
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Y := Sin (Test_Data (I).Radians);
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Y := Sin (Test_Data (I).Radians);
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Check (Y, Test_Data (I).Sine,
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Check (Y, Test_Data (I).Sine,
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"test" & Integer'Image (I) & " sin(r)",
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"test" & Integer'Image (I) & " sin(r)",
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2.0 + Sin_Arg_Err + Sin_Result_Err);
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2.0 + Sin_Arg_Err + Sin_Result_Err);
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Y := Cos (Test_Data (I).Radians);
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Y := Cos (Test_Data (I).Radians);
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Check (Y, Test_Data (I).Cosine,
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Check (Y, Test_Data (I).Cosine,
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"test" & Integer'Image (I) & " cos(r)",
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"test" & Integer'Image (I) & " cos(r)",
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2.0 + Cos_Arg_Err + Cos_Result_Err);
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2.0 + Cos_Arg_Err + Cos_Result_Err);
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Y := Sin (Test_Data (I).Degrees, 360.0);
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Y := Sin (Test_Data (I).Degrees, 360.0);
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Check (Y, Test_Data (I).Sine,
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Check (Y, Test_Data (I).Sine,
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"test" & Integer'Image (I) & " sin(d,360)",
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"test" & Integer'Image (I) & " sin(d,360)",
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2.0 + Sin_Result_Err);
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2.0 + Sin_Result_Err);
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Y := Cos (Test_Data (I).Degrees, 360.0);
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Y := Cos (Test_Data (I).Degrees, 360.0);
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Check (Y, Test_Data (I).Cosine,
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Check (Y, Test_Data (I).Cosine,
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"test" & Integer'Image (I) & " cos(d,360)",
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"test" & Integer'Image (I) & " cos(d,360)",
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2.0 + Cos_Result_Err);
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2.0 + Cos_Result_Err);
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--pwb-math Y := Sin (Test_Data (I).Radians, 2.0*Pi);
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--pwb-math Y := Sin (Test_Data (I).Radians, 2.0*Pi);
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--pwb-math Check (Y, Test_Data (I).Sine,
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--pwb-math Check (Y, Test_Data (I).Sine,
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--pwb-math "test" & Integer'Image (I) & " sin(r,2pi)",
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--pwb-math "test" & Integer'Image (I) & " sin(r,2pi)",
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--pwb-math 2.0 + Sin_Result_Err);
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--pwb-math 2.0 + Sin_Result_Err);
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--pwb-math Y := Cos (Test_Data (I).Radians, 2.0*Pi);
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--pwb-math Y := Cos (Test_Data (I).Radians, 2.0*Pi);
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--pwb-math Check (Y, Test_Data (I).Cosine,
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--pwb-math Check (Y, Test_Data (I).Cosine,
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--pwb-math "test" & Integer'Image (I) & " cos(r,2pi)",
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--pwb-math "test" & Integer'Image (I) & " cos(r,2pi)",
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--pwb-math 2.0 + Cos_Result_Err);
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--pwb-math 2.0 + Cos_Result_Err);
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end loop;
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end loop;
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exception
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exception
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when Constraint_Error =>
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when Constraint_Error =>
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Report.Failed ("Constraint_Error raised in special angle test");
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Report.Failed ("Constraint_Error raised in special angle test");
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when others =>
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when others =>
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Report.Failed ("exception in special angle test");
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Report.Failed ("exception in special angle test");
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end Special_Angle_Checks;
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end Special_Angle_Checks;
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-- check the rule of A.5.1(41);6.0 which requires that the
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-- check the rule of A.5.1(41);6.0 which requires that the
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-- result be exact if the mathematical result is 0.0, 1.0,
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-- result be exact if the mathematical result is 0.0, 1.0,
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-- or -1.0
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-- or -1.0
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procedure Exact_Result_Checks is
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procedure Exact_Result_Checks is
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type Data_Point is
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type Data_Point is
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record
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record
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Degrees,
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Degrees,
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Sine,
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Sine,
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Cosine : Real;
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Cosine : Real;
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end record;
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end record;
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type Test_Data_Type is array (Positive range <>) of Data_Point;
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type Test_Data_Type is array (Positive range <>) of Data_Point;
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Test_Data : constant Test_Data_Type := (
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Test_Data : constant Test_Data_Type := (
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-- degrees sine cosine test #
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-- degrees sine cosine test #
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( 0.0, 0.0, 1.0 ), -- 1
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( 0.0, 0.0, 1.0 ), -- 1
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( 90.0, 1.0, 0.0 ), -- 2
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( 90.0, 1.0, 0.0 ), -- 2
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(180.0, 0.0, -1.0 ), -- 3
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(180.0, 0.0, -1.0 ), -- 3
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(270.0, -1.0, 0.0 ), -- 4
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(270.0, -1.0, 0.0 ), -- 4
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(360.0, 0.0, 1.0 ), -- 5
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(360.0, 0.0, 1.0 ), -- 5
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( 90.0 + 360.0, 1.0, 0.0 ), -- 6
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( 90.0 + 360.0, 1.0, 0.0 ), -- 6
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(180.0 + 360.0, 0.0, -1.0 ), -- 7
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(180.0 + 360.0, 0.0, -1.0 ), -- 7
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(270.0 + 360.0,-1.0, 0.0 ), -- 8
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(270.0 + 360.0,-1.0, 0.0 ), -- 8
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(360.0 + 360.0, 0.0, 1.0 ) ); -- 9
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(360.0 + 360.0, 0.0, 1.0 ) ); -- 9
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Y : Real;
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Y : Real;
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begin
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begin
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for I in Test_Data'Range loop
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for I in Test_Data'Range loop
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Y := Sin (Test_Data(I).Degrees, 360.0);
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Y := Sin (Test_Data(I).Degrees, 360.0);
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if Y /= Test_Data(I).Sine then
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if Y /= Test_Data(I).Sine then
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Report.Failed ("exact result for sin(" &
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Report.Failed ("exact result for sin(" &
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Real'Image (Test_Data(I).Degrees) &
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Real'Image (Test_Data(I).Degrees) &
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", 360.0) is not" &
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", 360.0) is not" &
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Real'Image (Test_Data(I).Sine) &
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Real'Image (Test_Data(I).Sine) &
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" Difference is " &
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" Difference is " &
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Real'Image (Y - Test_Data(I).Sine) );
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Real'Image (Y - Test_Data(I).Sine) );
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end if;
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end if;
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Y := Cos (Test_Data(I).Degrees, 360.0);
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Y := Cos (Test_Data(I).Degrees, 360.0);
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if Y /= Test_Data(I).Cosine then
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if Y /= Test_Data(I).Cosine then
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Report.Failed ("exact result for cos(" &
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Report.Failed ("exact result for cos(" &
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Real'Image (Test_Data(I).Degrees) &
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Real'Image (Test_Data(I).Degrees) &
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", 360.0) is not" &
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", 360.0) is not" &
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Real'Image (Test_Data(I).Cosine) &
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Real'Image (Test_Data(I).Cosine) &
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" Difference is " &
|
" Difference is " &
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Real'Image (Y - Test_Data(I).Cosine) );
|
Real'Image (Y - Test_Data(I).Cosine) );
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end if;
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end if;
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end loop;
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end loop;
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in exact result check");
|
Report.Failed ("Constraint_Error raised in exact result check");
|
when others =>
|
when others =>
|
Report.Failed ("exception in exact result check");
|
Report.Failed ("exception in exact result check");
|
end Exact_Result_Checks;
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end Exact_Result_Checks;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
Special_Angle_Checks;
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Special_Angle_Checks;
|
Sin_Check (0.0, Pi/2.0, "0..pi/2");
|
Sin_Check (0.0, Pi/2.0, "0..pi/2");
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Sin_Check (6.0*Pi, 6.5*Pi, "6pi..6.5pi");
|
Sin_Check (6.0*Pi, 6.5*Pi, "6pi..6.5pi");
|
Cos_Check (7.0*Pi, 7.5*Pi, "7pi..7.5pi");
|
Cos_Check (7.0*Pi, 7.5*Pi, "7pi..7.5pi");
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Exact_Result_Checks;
|
Exact_Result_Checks;
|
end Do_Test;
|
end Do_Test;
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end Generic_Check;
|
end Generic_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
package Float_Check is new Generic_Check (Float);
|
package Float_Check is new Generic_Check (Float);
|
|
|
-- check the floating point type with the most digits
|
-- check the floating point type with the most digits
|
type A_Long_Float is digits System.Max_Digits;
|
type A_Long_Float is digits System.Max_Digits;
|
package A_Long_Float_Check is new Generic_Check (A_Long_Float);
|
package A_Long_Float_Check is new Generic_Check (A_Long_Float);
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
|
|
begin
|
begin
|
Report.Test ("CXG2004",
|
Report.Test ("CXG2004",
|
"Check the accuracy of the sin and cos functions");
|
"Check the accuracy of the sin and cos functions");
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking Standard.Float");
|
Report.Comment ("checking Standard.Float");
|
end if;
|
end if;
|
|
|
Float_Check.Do_Test;
|
Float_Check.Do_Test;
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking a digits" &
|
Report.Comment ("checking a digits" &
|
Integer'Image (System.Max_Digits) &
|
Integer'Image (System.Max_Digits) &
|
" floating point type");
|
" floating point type");
|
end if;
|
end if;
|
|
|
A_Long_Float_Check.Do_Test;
|
A_Long_Float_Check.Do_Test;
|
|
|
Report.Result;
|
Report.Result;
|
end CXG2004;
|
end CXG2004;
|
|
|