-- CXG2010.A
|
-- CXG2010.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,
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-- 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.
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-- 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 exp function returns
|
-- Check that the exp function returns
|
-- results that are within the error bound allowed.
|
-- results that are within the error bound allowed.
|
--
|
--
|
-- TEST DESCRIPTION:
|
-- TEST DESCRIPTION:
|
-- This test contains three test packages that are almost
|
-- This test contains three test packages that are almost
|
-- identical. The first two packages differ only in the
|
-- identical. The first two packages differ only in the
|
-- floating point type that is being tested. The first
|
-- floating point type that is being tested. The first
|
-- and third package differ only in whether the generic
|
-- and third package differ only in whether the generic
|
-- elementary functions package or the pre-instantiated
|
-- elementary functions package or the pre-instantiated
|
-- package is used.
|
-- package is used.
|
-- The test package is not generic so that the arguments
|
-- The test package is not generic so that the arguments
|
-- and expected results for some of the test values
|
-- and expected results for some of the test values
|
-- can be expressed as universal real instead of being
|
-- can be expressed as universal real instead of being
|
-- computed at runtime.
|
-- computed at runtime.
|
--
|
--
|
-- 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 and where the Machine_Radix is 2, 4, 8, or 16.
|
-- Numerics Annex and where the Machine_Radix is 2, 4, 8, or 16.
|
-- 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:
|
-- 1 Mar 96 SAIC Initial release for 2.1
|
-- 1 Mar 96 SAIC Initial release for 2.1
|
-- 2 Sep 96 SAIC Improved check routine
|
-- 2 Sep 96 SAIC Improved check routine
|
--
|
--
|
--!
|
--!
|
|
|
--
|
--
|
-- 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
|
--
|
--
|
|
|
--
|
--
|
-- Notes on derivation of error bound for exp(p)*exp(-p)
|
-- Notes on derivation of error bound for exp(p)*exp(-p)
|
--
|
--
|
-- Let a = true value of exp(p) and ac be the computed value.
|
-- Let a = true value of exp(p) and ac be the computed value.
|
-- Then a = ac(1+e1), where |e1| <= 4*Model_Epsilon.
|
-- Then a = ac(1+e1), where |e1| <= 4*Model_Epsilon.
|
-- Similarly, let b = true value of exp(-p) and bc be the computed value.
|
-- Similarly, let b = true value of exp(-p) and bc be the computed value.
|
-- Then b = bc(1+e2), where |e2| <= 4*ME.
|
-- Then b = bc(1+e2), where |e2| <= 4*ME.
|
--
|
--
|
-- The product of x and y is (x*y)(1+e3), where |e3| <= 1.0ME
|
-- The product of x and y is (x*y)(1+e3), where |e3| <= 1.0ME
|
--
|
--
|
-- Hence, the computed ab is [ac(1+e1)*bc(1+e2)](1+e3) =
|
-- Hence, the computed ab is [ac(1+e1)*bc(1+e2)](1+e3) =
|
-- (ac*bc)[1 + e1 + e2 + e3 + e1e2 + e1e3 + e2e3 + e1e2e3).
|
-- (ac*bc)[1 + e1 + e2 + e3 + e1e2 + e1e3 + e2e3 + e1e2e3).
|
--
|
--
|
-- Throwing away the last four tiny terms, we have (ac*bc)(1 + eta),
|
-- Throwing away the last four tiny terms, we have (ac*bc)(1 + eta),
|
--
|
--
|
-- where |eta| <= (4+4+1)ME = 9.0Model_Epsilon.
|
-- where |eta| <= (4+4+1)ME = 9.0Model_Epsilon.
|
|
|
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 CXG2010 is
|
procedure CXG2010 is
|
Verbose : constant Boolean := False;
|
Verbose : constant Boolean := False;
|
Max_Samples : constant := 1000;
|
Max_Samples : constant := 1000;
|
Accuracy_Error_Reported : Boolean := False;
|
Accuracy_Error_Reported : Boolean := False;
|
|
|
package Float_Check is
|
package Float_Check is
|
subtype Real is Float;
|
subtype Real is Float;
|
procedure Do_Test;
|
procedure Do_Test;
|
end Float_Check;
|
end Float_Check;
|
|
|
package body Float_Check is
|
package body Float_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 Sqrt (X : Real) return Real renames
|
function Sqrt (X : Real) return Real renames
|
Elementary_Functions.Sqrt;
|
Elementary_Functions.Sqrt;
|
function Exp (X : Real) return Real renames
|
function Exp (X : Real) return Real renames
|
Elementary_Functions.Exp;
|
Elementary_Functions.Exp;
|
|
|
|
|
-- The following value is a lower bound on the accuracy
|
-- The following value is a lower bound on the accuracy
|
-- required. It is normally 0.0 so that the lower bound
|
-- required. It is normally 0.0 so that the lower bound
|
-- is computed from Model_Epsilon. However, for tests
|
-- is computed from Model_Epsilon. However, for tests
|
-- where the expected result is only known to a certain
|
-- where the expected result is only known to a certain
|
-- amount of precision this bound takes on a non-zero
|
-- amount of precision this bound takes on a non-zero
|
-- value to account for that level of precision.
|
-- value to account for that level of precision.
|
Error_Low_Bound : Real := 0.0;
|
Error_Low_Bound : Real := 0.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
Max_Error : Real;
|
Max_Error : Real;
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_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
|
-- we compute the maximum error as a multiple of Model_Epsilon
|
-- instead of Model_Epsilon and Expected.
|
-- instead 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;
|
|
|
-- take into account the low bound on the error
|
-- take into account the low bound on the error
|
if Max_Error < Error_Low_Bound then
|
if Max_Error < Error_Low_Bound then
|
Max_Error := Error_Low_Bound;
|
Max_Error := Error_Low_Bound;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if 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: " & Real'Image (Actual - Expected) &
|
" difference: " & Real'Image (Actual - Expected) &
|
" max err:" & Real'Image (Max_Error) );
|
" max err:" & 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 Argument_Range_Check_1 (A, B : Real;
|
procedure Argument_Range_Check_1 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 1.0 / 16.0;
|
V : constant := 1.0 / 16.0;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 1");
|
("Constraint_Error raised in argument range check 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 1");
|
Report.Failed ("exception in argument range check 1");
|
end Argument_Range_Check_1;
|
end Argument_Range_Check_1;
|
|
|
|
|
|
|
procedure Argument_Range_Check_2 (A, B : Real;
|
procedure Argument_Range_Check_2 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 45.0 / 16.0;
|
V : constant := 45.0 / 16.0;
|
-- 1/16 - Exp(45/16)
|
-- 1/16 - Exp(45/16)
|
Coeff : constant := 2.4453321046920570389E-3;
|
Coeff : constant := 2.4453321046920570389E-3;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 2");
|
("Constraint_Error raised in argument range check 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 2");
|
Report.Failed ("exception in argument range check 2");
|
end Argument_Range_Check_2;
|
end Argument_Range_Check_2;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(1.0);
|
Y := Exp(1.0);
|
-- normal accuracy requirements
|
-- normal accuracy requirements
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(16.0) * Exp(-16.0);
|
Y := Exp(16.0) * Exp(-16.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(0.0);
|
Y := Exp(0.0);
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
1.0,
|
1.0,
|
"5");
|
"5");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
--- test 6 ---
|
--- test 6 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_2 (1.0,
|
Argument_Range_Check_2 (1.0,
|
Sqrt(Real(Real'Machine_Radix)),
|
Sqrt(Real(Real'Machine_Radix)),
|
"6");
|
"6");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
end Do_Test;
|
end Do_Test;
|
end Float_Check;
|
end Float_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-- 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
|
package A_Long_Float_Check is
|
subtype Real is A_Long_Float;
|
subtype Real is A_Long_Float;
|
procedure Do_Test;
|
procedure Do_Test;
|
end A_Long_Float_Check;
|
end A_Long_Float_Check;
|
|
|
package body A_Long_Float_Check is
|
package body A_Long_Float_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 Sqrt (X : Real) return Real renames
|
function Sqrt (X : Real) return Real renames
|
Elementary_Functions.Sqrt;
|
Elementary_Functions.Sqrt;
|
function Exp (X : Real) return Real renames
|
function Exp (X : Real) return Real renames
|
Elementary_Functions.Exp;
|
Elementary_Functions.Exp;
|
|
|
|
|
-- The following value is a lower bound on the accuracy
|
-- The following value is a lower bound on the accuracy
|
-- required. It is normally 0.0 so that the lower bound
|
-- required. It is normally 0.0 so that the lower bound
|
-- is computed from Model_Epsilon. However, for tests
|
-- is computed from Model_Epsilon. However, for tests
|
-- where the expected result is only known to a certain
|
-- where the expected result is only known to a certain
|
-- amount of precision this bound takes on a non-zero
|
-- amount of precision this bound takes on a non-zero
|
-- value to account for that level of precision.
|
-- value to account for that level of precision.
|
Error_Low_Bound : Real := 0.0;
|
Error_Low_Bound : Real := 0.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
Max_Error : Real;
|
Max_Error : Real;
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_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
|
-- we compute the maximum error as a multiple of Model_Epsilon
|
-- instead of Model_Epsilon and Expected.
|
-- instead 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;
|
|
|
-- take into account the low bound on the error
|
-- take into account the low bound on the error
|
if Max_Error < Error_Low_Bound then
|
if Max_Error < Error_Low_Bound then
|
Max_Error := Error_Low_Bound;
|
Max_Error := Error_Low_Bound;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if 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: " & Real'Image (Actual - Expected) &
|
" difference: " & Real'Image (Actual - Expected) &
|
" max err:" & Real'Image (Max_Error) );
|
" max err:" & 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 Argument_Range_Check_1 (A, B : Real;
|
procedure Argument_Range_Check_1 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 1.0 / 16.0;
|
V : constant := 1.0 / 16.0;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 1");
|
("Constraint_Error raised in argument range check 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 1");
|
Report.Failed ("exception in argument range check 1");
|
end Argument_Range_Check_1;
|
end Argument_Range_Check_1;
|
|
|
|
|
|
|
procedure Argument_Range_Check_2 (A, B : Real;
|
procedure Argument_Range_Check_2 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 45.0 / 16.0;
|
V : constant := 45.0 / 16.0;
|
-- 1/16 - Exp(45/16)
|
-- 1/16 - Exp(45/16)
|
Coeff : constant := 2.4453321046920570389E-3;
|
Coeff : constant := 2.4453321046920570389E-3;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 2");
|
("Constraint_Error raised in argument range check 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 2");
|
Report.Failed ("exception in argument range check 2");
|
end Argument_Range_Check_2;
|
end Argument_Range_Check_2;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(1.0);
|
Y := Exp(1.0);
|
-- normal accuracy requirements
|
-- normal accuracy requirements
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(16.0) * Exp(-16.0);
|
Y := Exp(16.0) * Exp(-16.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(0.0);
|
Y := Exp(0.0);
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
1.0,
|
1.0,
|
"5");
|
"5");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
--- test 6 ---
|
--- test 6 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_2 (1.0,
|
Argument_Range_Check_2 (1.0,
|
Sqrt(Real(Real'Machine_Radix)),
|
Sqrt(Real(Real'Machine_Radix)),
|
"6");
|
"6");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
end Do_Test;
|
end Do_Test;
|
end A_Long_Float_Check;
|
end A_Long_Float_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
package Non_Generic_Check is
|
package Non_Generic_Check is
|
procedure Do_Test;
|
procedure Do_Test;
|
subtype Real is Float;
|
subtype Real is Float;
|
end Non_Generic_Check;
|
end Non_Generic_Check;
|
|
|
package body Non_Generic_Check is
|
package body Non_Generic_Check is
|
|
|
package Elementary_Functions renames
|
package Elementary_Functions renames
|
Ada.Numerics.Elementary_Functions;
|
Ada.Numerics.Elementary_Functions;
|
function Sqrt (X : Real) return Real renames
|
function Sqrt (X : Real) return Real renames
|
Elementary_Functions.Sqrt;
|
Elementary_Functions.Sqrt;
|
function Exp (X : Real) return Real renames
|
function Exp (X : Real) return Real renames
|
Elementary_Functions.Exp;
|
Elementary_Functions.Exp;
|
|
|
|
|
-- The following value is a lower bound on the accuracy
|
-- The following value is a lower bound on the accuracy
|
-- required. It is normally 0.0 so that the lower bound
|
-- required. It is normally 0.0 so that the lower bound
|
-- is computed from Model_Epsilon. However, for tests
|
-- is computed from Model_Epsilon. However, for tests
|
-- where the expected result is only known to a certain
|
-- where the expected result is only known to a certain
|
-- amount of precision this bound takes on a non-zero
|
-- amount of precision this bound takes on a non-zero
|
-- value to account for that level of precision.
|
-- value to account for that level of precision.
|
Error_Low_Bound : Real := 0.0;
|
Error_Low_Bound : Real := 0.0;
|
|
|
procedure Check (Actual, Expected : Real;
|
procedure Check (Actual, Expected : Real;
|
Test_Name : String;
|
Test_Name : String;
|
MRE : Real) is
|
MRE : Real) is
|
Max_Error : Real;
|
Max_Error : Real;
|
Rel_Error : Real;
|
Rel_Error : Real;
|
Abs_Error : Real;
|
Abs_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
|
-- we compute the maximum error as a multiple of Model_Epsilon
|
-- instead of Model_Epsilon and Expected.
|
-- instead 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;
|
|
|
-- take into account the low bound on the error
|
-- take into account the low bound on the error
|
if Max_Error < Error_Low_Bound then
|
if Max_Error < Error_Low_Bound then
|
Max_Error := Error_Low_Bound;
|
Max_Error := Error_Low_Bound;
|
end if;
|
end if;
|
|
|
if abs (Actual - Expected) > Max_Error then
|
if 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: " & Real'Image (Actual - Expected) &
|
" difference: " & Real'Image (Actual - Expected) &
|
" max err:" & Real'Image (Max_Error) );
|
" max err:" & 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 Argument_Range_Check_1 (A, B : Real;
|
procedure Argument_Range_Check_1 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 1.0 / 16.0;
|
V : constant := 1.0 / 16.0;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
One_Minus_Exp_Minus_V : constant := 6.058693718652421388E-2;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- ZX := Exp(X) - Exp(X) * (1 - Exp(-V);
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
ZX := ZX - ZX * One_Minus_Exp_Minus_V;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 1");
|
("Constraint_Error raised in argument range check 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 1");
|
Report.Failed ("exception in argument range check 1");
|
end Argument_Range_Check_1;
|
end Argument_Range_Check_1;
|
|
|
|
|
|
|
procedure Argument_Range_Check_2 (A, B : Real;
|
procedure Argument_Range_Check_2 (A, B : Real;
|
Test : String) is
|
Test : String) is
|
-- test a evenly distributed selection of
|
-- test a evenly distributed selection of
|
-- arguments selected from the range A to B.
|
-- arguments selected from the range A to B.
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- Test using identity: EXP(X-V) = EXP(X) * EXP (-V)
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- The parameter One_Minus_Exp_Minus_V is the value
|
-- 1.0 - Exp (-V)
|
-- 1.0 - Exp (-V)
|
-- accurate to machine precision.
|
-- accurate to machine precision.
|
-- This procedure is a translation of part of Cody's test
|
-- This procedure is a translation of part of Cody's test
|
X : Real;
|
X : Real;
|
Y : Real;
|
Y : Real;
|
ZX, ZY : Real;
|
ZX, ZY : Real;
|
V : constant := 45.0 / 16.0;
|
V : constant := 45.0 / 16.0;
|
-- 1/16 - Exp(45/16)
|
-- 1/16 - Exp(45/16)
|
Coeff : constant := 2.4453321046920570389E-3;
|
Coeff : constant := 2.4453321046920570389E-3;
|
|
|
begin
|
begin
|
Accuracy_Error_Reported := False;
|
Accuracy_Error_Reported := False;
|
for I in 1..Max_Samples loop
|
for I in 1..Max_Samples loop
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
X := (B - A) * Real (I) / Real (Max_Samples) + A;
|
Y := X - V;
|
Y := X - V;
|
if Y < 0.0 then
|
if Y < 0.0 then
|
X := Y + V;
|
X := Y + V;
|
end if;
|
end if;
|
|
|
ZX := Exp (X);
|
ZX := Exp (X);
|
ZY := Exp (Y);
|
ZY := Exp (Y);
|
|
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- ZX := Exp(X) * 1/16 - Exp(X) * Coeff;
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- where Coeff is 1/16 - Exp(45/16)
|
-- which simplifies to ZX := Exp (X-V);
|
-- which simplifies to ZX := Exp (X-V);
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
ZX := ZX * 0.0625 - ZX * Coeff;
|
|
|
-- 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.
|
Check (ZY, ZX,
|
Check (ZY, ZX,
|
"test " & Test & " -" &
|
"test " & Test & " -" &
|
Integer'Image (I) &
|
Integer'Image (I) &
|
" exp (" & Real'Image (X) & ")",
|
" exp (" & Real'Image (X) & ")",
|
9.0);
|
9.0);
|
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 argument range check 2");
|
("Constraint_Error raised in argument range check 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in argument range check 2");
|
Report.Failed ("exception in argument range check 2");
|
end Argument_Range_Check_2;
|
end Argument_Range_Check_2;
|
|
|
|
|
procedure Do_Test is
|
procedure Do_Test is
|
begin
|
begin
|
|
|
--- test 1 ---
|
--- test 1 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(1.0);
|
Y := Exp(1.0);
|
-- normal accuracy requirements
|
-- normal accuracy requirements
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
Check (Y, Ada.Numerics.e, "test 1 -- exp(1)", 4.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 1");
|
Report.Failed ("Constraint_Error raised in test 1");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 1");
|
Report.Failed ("exception in test 1");
|
end;
|
end;
|
|
|
--- test 2 ---
|
--- test 2 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(16.0) * Exp(-16.0);
|
Y := Exp(16.0) * Exp(-16.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
Check (Y, 1.0, "test 2 -- exp(16)*exp(-16)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 2");
|
Report.Failed ("Constraint_Error raised in test 2");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 2");
|
Report.Failed ("exception in test 2");
|
end;
|
end;
|
|
|
--- test 3 ---
|
--- test 3 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Y := Exp (Ada.Numerics.Pi) * Exp (-Ada.Numerics.Pi);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
Check (Y, 1.0, "test 3 -- exp(pi)*exp(-pi)", 9.0);
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 3");
|
Report.Failed ("Constraint_Error raised in test 3");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 3");
|
Report.Failed ("exception in test 3");
|
end;
|
end;
|
|
|
--- test 4 ---
|
--- test 4 ---
|
declare
|
declare
|
Y : Real;
|
Y : Real;
|
begin
|
begin
|
Y := Exp(0.0);
|
Y := Exp(0.0);
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
Check (Y, 1.0, "test 4 -- exp(0.0)",
|
0.0); -- no error allowed
|
0.0); -- no error allowed
|
exception
|
exception
|
when Constraint_Error =>
|
when Constraint_Error =>
|
Report.Failed ("Constraint_Error raised in test 4");
|
Report.Failed ("Constraint_Error raised in test 4");
|
when others =>
|
when others =>
|
Report.Failed ("exception in test 4");
|
Report.Failed ("exception in test 4");
|
end;
|
end;
|
|
|
--- test 5 ---
|
--- test 5 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
Argument_Range_Check_1 ( 1.0/Sqrt(Real(Real'Machine_Radix)),
|
1.0,
|
1.0,
|
"5");
|
"5");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
--- test 6 ---
|
--- test 6 ---
|
-- constants used here only have 19 digits of precision
|
-- constants used here only have 19 digits of precision
|
if Real'Digits > 19 then
|
if Real'Digits > 19 then
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Error_Low_Bound := 0.00000_00000_00000_0001;
|
Report.Comment ("exp accuracy checked to 19 digits");
|
Report.Comment ("exp accuracy checked to 19 digits");
|
end if;
|
end if;
|
|
|
Argument_Range_Check_2 (1.0,
|
Argument_Range_Check_2 (1.0,
|
Sqrt(Real(Real'Machine_Radix)),
|
Sqrt(Real(Real'Machine_Radix)),
|
"6");
|
"6");
|
Error_Low_Bound := 0.0; -- reset
|
Error_Low_Bound := 0.0; -- reset
|
|
|
end Do_Test;
|
end Do_Test;
|
end Non_Generic_Check;
|
end Non_Generic_Check;
|
|
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
-----------------------------------------------------------------------
|
|
|
begin
|
begin
|
Report.Test ("CXG2010",
|
Report.Test ("CXG2010",
|
"Check the accuracy of the exp function");
|
"Check the accuracy of the exp function");
|
|
|
-- the test only applies to machines with a radix of 2,4,8, or 16
|
-- the test only applies to machines with a radix of 2,4,8, or 16
|
case Float'Machine_Radix is
|
case Float'Machine_Radix is
|
when 2 | 4 | 8 | 16 => null;
|
when 2 | 4 | 8 | 16 => null;
|
when others =>
|
when others =>
|
Report.Not_Applicable ("only applicable to binary radix");
|
Report.Not_Applicable ("only applicable to binary radix");
|
Report.Result;
|
Report.Result;
|
return;
|
return;
|
end case;
|
end case;
|
|
|
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;
|
|
|
if Verbose then
|
if Verbose then
|
Report.Comment ("checking non-generic package");
|
Report.Comment ("checking non-generic package");
|
end if;
|
end if;
|
|
|
Non_Generic_Check.Do_Test;
|
Non_Generic_Check.Do_Test;
|
|
|
Report.Result;
|
Report.Result;
|
end CXG2010;
|
end CXG2010;
|
|
|
