| -- CXG2008.A |
| -- |
| -- Grant of Unlimited Rights |
| -- |
| -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687, |
| -- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained |
| -- unlimited rights in the software and documentation contained herein. |
| -- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making |
| -- this public release, the Government intends to confer upon all |
| -- recipients unlimited rights equal to those held by the Government. |
| -- These rights include rights to use, duplicate, release or disclose the |
| -- released technical data and computer software in whole or in part, in |
| -- any manner and for any purpose whatsoever, and to have or permit others |
| -- to do so. |
| -- |
| -- DISCLAIMER |
| -- |
| -- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR |
| -- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED |
| -- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE |
| -- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE |
| -- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A |
| -- PARTICULAR PURPOSE OF SAID MATERIAL. |
| --* |
| -- |
| -- OBJECTIVE: |
| -- Check that the complex multiplication and division |
| -- operations return results that are within the allowed |
| -- error bound. |
| -- Check that all the required pure Numerics packages are pure. |
| -- |
| -- TEST DESCRIPTION: |
| -- This test contains three test packages that are almost |
| -- identical. The first two packages differ only in the |
| -- floating point type that is being tested. The first |
| -- and third package differ only in whether the generic |
| -- complex types package or the pre-instantiated |
| -- package is used. |
| -- The test package is not generic so that the arguments |
| -- and expected results for some of the test values |
| -- can be expressed as universal real instead of being |
| -- computed at runtime. |
| -- |
| -- SPECIAL REQUIREMENTS |
| -- The Strict Mode for the numerical accuracy must be |
| -- selected. The method by which this mode is selected |
| -- is implementation dependent. |
| -- |
| -- APPLICABILITY CRITERIA: |
| -- This test applies only to implementations supporting the |
| -- Numerics Annex. |
| -- This test only applies to the Strict Mode for numerical |
| -- accuracy. |
| -- |
| -- |
| -- CHANGE HISTORY: |
| -- 24 FEB 96 SAIC Initial release for 2.1 |
| -- 03 JUN 98 EDS Correct the test program's incorrect assumption |
| -- that Constraint_Error must be raised by complex |
| -- division by zero, which is contrary to the |
| -- allowance given by the Ada 95 standard G.1.1(40). |
| -- 13 MAR 01 RLB Replaced commented out Pure check on non-generic |
| -- packages, as required by Defect Report |
| -- 8652/0020 and as reflected in Technical |
| -- Corrigendum 1. |
| --! |
| |
| ------------------------------------------------------------------------------ |
| -- Check that the required pure packages are pure by withing them from a |
| -- pure package. The non-generic versions of those packages are required to |
| -- be pure by Defect Report 8652/0020, Technical Corrigendum 1 [A.5.1(9/1) and |
| -- G.1.1(25/1)]. |
| with Ada.Numerics.Generic_Elementary_Functions; |
| with Ada.Numerics.Elementary_Functions; |
| with Ada.Numerics.Generic_Complex_Types; |
| with Ada.Numerics.Complex_Types; |
| with Ada.Numerics.Generic_Complex_Elementary_Functions; |
| with Ada.Numerics.Complex_Elementary_Functions; |
| package CXG2008_0 is |
| pragma Pure; |
| -- CRC Standard Mathematical Tables; 23rd Edition; pg 738 |
| Sqrt2 : constant := |
| 1.41421_35623_73095_04880_16887_24209_69807_85696_71875_37695; |
| Sqrt3 : constant := |
| 1.73205_08075_68877_29352_74463_41505_87236_69428_05253_81039; |
| end CXG2008_0; |
| |
| ------------------------------------------------------------------------------ |
| |
| with System; |
| with Report; |
| with Ada.Numerics.Generic_Complex_Types; |
| with Ada.Numerics.Complex_Types; |
| with CXG2008_0; use CXG2008_0; |
| procedure CXG2008 is |
| Verbose : constant Boolean := False; |
| |
| package Float_Check is |
| subtype Real is Float; |
| procedure Do_Test; |
| end Float_Check; |
| |
| package body Float_Check is |
| package Complex_Types is new |
| Ada.Numerics.Generic_Complex_Types (Real); |
| use Complex_Types; |
| |
| -- keep track if an accuracy failure has occurred so the test |
| -- can be short-circuited to avoid thousands of error messages. |
| Failure_Detected : Boolean := False; |
| |
| Mult_MBE : constant Real := 5.0; |
| Divide_MBE : constant Real := 13.0; |
| |
| |
| procedure Check (Actual, Expected : Complex; |
| Test_Name : String; |
| MBE : Real) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_Error : Real; |
| begin |
| -- In the case where the expected result is very small or 0 |
| -- we compute the maximum error as a multiple of Model_Epsilon instead |
| -- of Model_Epsilon and Expected. |
| Rel_Error := MBE * abs Expected.Re * Real'Model_Epsilon; |
| Abs_Error := MBE * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| |
| if abs (Actual.Re - Expected.Re) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.re: " & Real'Image (Actual.Re) & |
| " expected.re: " & Real'Image (Expected.Re) & |
| " difference.re " & |
| Real'Image (Actual.Re - Expected.Re) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for real part"); |
| else |
| Report.Comment (Test_Name & " passed for real part"); |
| end if; |
| end if; |
| |
| Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| if abs (Actual.Im - Expected.Im) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.im: " & Real'Image (Actual.Im) & |
| " expected.im: " & Real'Image (Expected.Im) & |
| " difference.im " & |
| Real'Image (Actual.Im - Expected.Im) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for imaginary part"); |
| else |
| Report.Comment (Test_Name & " passed for imaginary part"); |
| end if; |
| end if; |
| end Check; |
| |
| |
| procedure Special_Values is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : Complex := (0.0, 0.0); |
| X : Complex := (0.0, 0.0); |
| Y : Complex := (Big, Big); |
| Z : Complex; |
| begin |
| Z := X * Y; |
| Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)", |
| Mult_MBE); |
| Z := Y * X; |
| Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Expected : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| Z := U * X; |
| Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| B : Complex := (Big, Big); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := B / X; |
| Report.Failed ("test 3 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := U / X; |
| Report.Failed ("test 4 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| |
| --- test 5 --- |
| declare |
| X : Complex := (Sqrt2, Sqrt2); |
| Z : Complex; |
| Expected : constant Complex := (0.0, 4.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : Complex := Sqrt3 - Sqrt3 * i; |
| Z : Complex; |
| Expected : constant Complex := (0.0, -6.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 --- |
| declare |
| X : Complex := Sqrt2 + Sqrt2 * i; |
| Y : Complex := Sqrt2 - Sqrt2 * i; |
| Z : Complex; |
| Expected : constant Complex := 0.0 + i; |
| begin |
| Z := X / Y; |
| Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)", |
| Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 7"); |
| when others => |
| Report.Failed ("exception in test 7"); |
| end; |
| end Special_Values; |
| |
| |
| procedure Do_Mult_Div (X, Y : Complex) is |
| Z : Complex; |
| Args : constant String := |
| "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " & |
| "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ; |
| begin |
| Z := (X * X) / X; |
| Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / X; |
| Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / Y; |
| Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args); |
| when others => |
| Report.Failed ("exception in Do_Mult_Div for " & Args); |
| end Do_Mult_Div; |
| |
| -- select complex values X and Y where the real and imaginary |
| -- parts are selected from the ranges (1/radix..1) and |
| -- (1..radix). This translates into quite a few combinations. |
| procedure Mult_Div_Check is |
| Samples : constant := 17; |
| Radix : constant Real := Real(Real'Machine_Radix); |
| Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix); |
| Low_Sample : Real; -- (1/radix .. 1) |
| High_Sample : Real; -- (1 .. radix) |
| Sample : array (1..2) of Real; |
| X, Y : Complex; |
| begin |
| for I in 1 .. Samples loop |
| Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) + |
| Inv_Radix; |
| Sample (1) := Low_Sample; |
| for J in 1 .. Samples loop |
| High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) + |
| Radix; |
| Sample (2) := High_Sample; |
| for K in 1 .. 2 loop |
| for L in 1 .. 2 loop |
| X := Complex'(Sample (K), Sample (L)); |
| Y := Complex'(Sample (L), Sample (K)); |
| Do_Mult_Div (X, Y); |
| if Failure_Detected then |
| return; -- minimize flood of error messages |
| end if; |
| end loop; |
| end loop; |
| end loop; -- J |
| end loop; -- I |
| end Mult_Div_Check; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Values; |
| Mult_Div_Check; |
| end Do_Test; |
| end Float_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| -- check the floating point type with the most digits |
| |
| package A_Long_Float_Check is |
| type A_Long_Float is digits System.Max_Digits; |
| subtype Real is A_Long_Float; |
| procedure Do_Test; |
| end A_Long_Float_Check; |
| |
| package body A_Long_Float_Check is |
| |
| package Complex_Types is new |
| Ada.Numerics.Generic_Complex_Types (Real); |
| use Complex_Types; |
| |
| -- keep track if an accuracy failure has occurred so the test |
| -- can be short-circuited to avoid thousands of error messages. |
| Failure_Detected : Boolean := False; |
| |
| Mult_MBE : constant Real := 5.0; |
| Divide_MBE : constant Real := 13.0; |
| |
| |
| procedure Check (Actual, Expected : Complex; |
| Test_Name : String; |
| MBE : Real) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_Error : Real; |
| begin |
| -- In the case where the expected result is very small or 0 |
| -- we compute the maximum error as a multiple of Model_Epsilon instead |
| -- of Model_Epsilon and Expected. |
| Rel_Error := MBE * abs Expected.Re * Real'Model_Epsilon; |
| Abs_Error := MBE * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| |
| if abs (Actual.Re - Expected.Re) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.re: " & Real'Image (Actual.Re) & |
| " expected.re: " & Real'Image (Expected.Re) & |
| " difference.re " & |
| Real'Image (Actual.Re - Expected.Re) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for real part"); |
| else |
| Report.Comment (Test_Name & " passed for real part"); |
| end if; |
| end if; |
| |
| Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| if abs (Actual.Im - Expected.Im) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.im: " & Real'Image (Actual.Im) & |
| " expected.im: " & Real'Image (Expected.Im) & |
| " difference.im " & |
| Real'Image (Actual.Im - Expected.Im) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for imaginary part"); |
| else |
| Report.Comment (Test_Name & " passed for imaginary part"); |
| end if; |
| end if; |
| end Check; |
| |
| |
| procedure Special_Values is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : Complex := (0.0, 0.0); |
| X : Complex := (0.0, 0.0); |
| Y : Complex := (Big, Big); |
| Z : Complex; |
| begin |
| Z := X * Y; |
| Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)", |
| Mult_MBE); |
| Z := Y * X; |
| Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Expected : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| Z := U * X; |
| Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| B : Complex := (Big, Big); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := B / X; |
| Report.Failed ("test 3 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := U / X; |
| Report.Failed ("test 4 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| |
| --- test 5 --- |
| declare |
| X : Complex := (Sqrt2, Sqrt2); |
| Z : Complex; |
| Expected : constant Complex := (0.0, 4.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : Complex := Sqrt3 - Sqrt3 * i; |
| Z : Complex; |
| Expected : constant Complex := (0.0, -6.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 --- |
| declare |
| X : Complex := Sqrt2 + Sqrt2 * i; |
| Y : Complex := Sqrt2 - Sqrt2 * i; |
| Z : Complex; |
| Expected : constant Complex := 0.0 + i; |
| begin |
| Z := X / Y; |
| Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)", |
| Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 7"); |
| when others => |
| Report.Failed ("exception in test 7"); |
| end; |
| end Special_Values; |
| |
| |
| procedure Do_Mult_Div (X, Y : Complex) is |
| Z : Complex; |
| Args : constant String := |
| "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " & |
| "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ; |
| begin |
| Z := (X * X) / X; |
| Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / X; |
| Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / Y; |
| Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args); |
| when others => |
| Report.Failed ("exception in Do_Mult_Div for " & Args); |
| end Do_Mult_Div; |
| |
| -- select complex values X and Y where the real and imaginary |
| -- parts are selected from the ranges (1/radix..1) and |
| -- (1..radix). This translates into quite a few combinations. |
| procedure Mult_Div_Check is |
| Samples : constant := 17; |
| Radix : constant Real := Real(Real'Machine_Radix); |
| Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix); |
| Low_Sample : Real; -- (1/radix .. 1) |
| High_Sample : Real; -- (1 .. radix) |
| Sample : array (1..2) of Real; |
| X, Y : Complex; |
| begin |
| for I in 1 .. Samples loop |
| Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) + |
| Inv_Radix; |
| Sample (1) := Low_Sample; |
| for J in 1 .. Samples loop |
| High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) + |
| Radix; |
| Sample (2) := High_Sample; |
| for K in 1 .. 2 loop |
| for L in 1 .. 2 loop |
| X := Complex'(Sample (K), Sample (L)); |
| Y := Complex'(Sample (L), Sample (K)); |
| Do_Mult_Div (X, Y); |
| if Failure_Detected then |
| return; -- minimize flood of error messages |
| end if; |
| end loop; |
| end loop; |
| end loop; -- J |
| end loop; -- I |
| end Mult_Div_Check; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Values; |
| Mult_Div_Check; |
| end Do_Test; |
| end A_Long_Float_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| package Non_Generic_Check is |
| subtype Real is Float; |
| procedure Do_Test; |
| end Non_Generic_Check; |
| |
| package body Non_Generic_Check is |
| |
| use Ada.Numerics.Complex_Types; |
| |
| -- keep track if an accuracy failure has occurred so the test |
| -- can be short-circuited to avoid thousands of error messages. |
| Failure_Detected : Boolean := False; |
| |
| Mult_MBE : constant Real := 5.0; |
| Divide_MBE : constant Real := 13.0; |
| |
| |
| procedure Check (Actual, Expected : Complex; |
| Test_Name : String; |
| MBE : Real) is |
| Rel_Error : Real; |
| Abs_Error : Real; |
| Max_Error : Real; |
| begin |
| -- In the case where the expected result is very small or 0 |
| -- we compute the maximum error as a multiple of Model_Epsilon instead |
| -- of Model_Epsilon and Expected. |
| Rel_Error := MBE * abs Expected.Re * Real'Model_Epsilon; |
| Abs_Error := MBE * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| |
| if abs (Actual.Re - Expected.Re) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.re: " & Real'Image (Actual.Re) & |
| " expected.re: " & Real'Image (Expected.Re) & |
| " difference.re " & |
| Real'Image (Actual.Re - Expected.Re) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for real part"); |
| else |
| Report.Comment (Test_Name & " passed for real part"); |
| end if; |
| end if; |
| |
| Rel_Error := MBE * abs Expected.Im * Real'Model_Epsilon; |
| if Rel_Error > Abs_Error then |
| Max_Error := Rel_Error; |
| else |
| Max_Error := Abs_Error; |
| end if; |
| if abs (Actual.Im - Expected.Im) > Max_Error then |
| Failure_Detected := True; |
| Report.Failed (Test_Name & |
| " actual.im: " & Real'Image (Actual.Im) & |
| " expected.im: " & Real'Image (Expected.Im) & |
| " difference.im " & |
| Real'Image (Actual.Im - Expected.Im) & |
| " mre:" & Real'Image (Max_Error) ); |
| elsif Verbose then |
| if Actual = Expected then |
| Report.Comment (Test_Name & " exact result for imaginary part"); |
| else |
| Report.Comment (Test_Name & " passed for imaginary part"); |
| end if; |
| end if; |
| end Check; |
| |
| |
| procedure Special_Values is |
| begin |
| |
| --- test 1 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| Expected : Complex := (0.0, 0.0); |
| X : Complex := (0.0, 0.0); |
| Y : Complex := (Big, Big); |
| Z : Complex; |
| begin |
| Z := X * Y; |
| Check (Z, Expected, "test 1a -- (0+0i) * (big+big*i)", |
| Mult_MBE); |
| Z := Y * X; |
| Check (Z, Expected, "test 1b -- (big+big*i) * (0+0i)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 1"); |
| when others => |
| Report.Failed ("exception in test 1"); |
| end; |
| |
| --- test 2 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Expected : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| Z := U * X; |
| Check (Z, Expected, "test 2 -- (tiny,tiny) * (0,0)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 2"); |
| when others => |
| Report.Failed ("exception in test 2"); |
| end; |
| |
| --- test 3 --- |
| declare |
| T : constant := (Real'Machine_EMax - 1) / 2; |
| Big : constant := (1.0 * Real'Machine_Radix) ** (2 * T); |
| B : Complex := (Big, Big); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := B / X; |
| Report.Failed ("test 3 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 3"); |
| end; |
| |
| --- test 4 --- |
| declare |
| T : constant := Real'Model_EMin + 1; |
| Tiny : constant := (1.0 * Real'Machine_Radix) ** T; |
| U : Complex := (Tiny, Tiny); |
| X : Complex := (0.0, 0.0); |
| Z : Complex; |
| begin |
| if Real'Machine_Overflows then |
| Z := U / X; |
| Report.Failed ("test 4 - Constraint_Error not raised"); |
| Check (Z, Z, "not executed - optimizer thwarting", 0.0); |
| end if; |
| exception |
| when Constraint_Error => null; -- expected |
| when others => |
| Report.Failed ("exception in test 4"); |
| end; |
| |
| |
| --- test 5 --- |
| declare |
| X : Complex := (Sqrt2, Sqrt2); |
| Z : Complex; |
| Expected : constant Complex := (0.0, 4.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 5 -- (sqrt2,sqrt2) * (sqrt2,sqrt2)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 5"); |
| when others => |
| Report.Failed ("exception in test 5"); |
| end; |
| |
| --- test 6 --- |
| declare |
| X : Complex := Sqrt3 - Sqrt3 * i; |
| Z : Complex; |
| Expected : constant Complex := (0.0, -6.0); |
| begin |
| Z := X * X; |
| Check (Z, Expected, "test 6 -- (sqrt3,-sqrt3) * (sqrt3,-sqrt3)", |
| Mult_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 6"); |
| when others => |
| Report.Failed ("exception in test 6"); |
| end; |
| |
| --- test 7 --- |
| declare |
| X : Complex := Sqrt2 + Sqrt2 * i; |
| Y : Complex := Sqrt2 - Sqrt2 * i; |
| Z : Complex; |
| Expected : constant Complex := 0.0 + i; |
| begin |
| Z := X / Y; |
| Check (Z, Expected, "test 7 -- (sqrt2,sqrt2) / (sqrt2,-sqrt2)", |
| Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error raised in test 7"); |
| when others => |
| Report.Failed ("exception in test 7"); |
| end; |
| end Special_Values; |
| |
| |
| procedure Do_Mult_Div (X, Y : Complex) is |
| Z : Complex; |
| Args : constant String := |
| "X=(" & Real'Image (X.Re) & "," & Real'Image (X.Im) & ") " & |
| "Y=(" & Real'Image (Y.Re) & "," & Real'Image (Y.Im) & ") " ; |
| begin |
| Z := (X * X) / X; |
| Check (Z, X, "X*X/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / X; |
| Check (Z, Y, "X*Y/X " & Args, Mult_MBE + Divide_MBE); |
| Z := (X * Y) / Y; |
| Check (Z, X, "X*Y/Y " & Args, Mult_MBE + Divide_MBE); |
| exception |
| when Constraint_Error => |
| Report.Failed ("Constraint_Error in Do_Mult_Div for " & Args); |
| when others => |
| Report.Failed ("exception in Do_Mult_Div for " & Args); |
| end Do_Mult_Div; |
| |
| -- select complex values X and Y where the real and imaginary |
| -- parts are selected from the ranges (1/radix..1) and |
| -- (1..radix). This translates into quite a few combinations. |
| procedure Mult_Div_Check is |
| Samples : constant := 17; |
| Radix : constant Real := Real(Real'Machine_Radix); |
| Inv_Radix : constant Real := 1.0 / Real(Real'Machine_Radix); |
| Low_Sample : Real; -- (1/radix .. 1) |
| High_Sample : Real; -- (1 .. radix) |
| Sample : array (1..2) of Real; |
| X, Y : Complex; |
| begin |
| for I in 1 .. Samples loop |
| Low_Sample := (1.0 - Inv_Radix) / Real (Samples) * Real (I) + |
| Inv_Radix; |
| Sample (1) := Low_Sample; |
| for J in 1 .. Samples loop |
| High_Sample := (Radix - 1.0) / Real (Samples) * Real (I) + |
| Radix; |
| Sample (2) := High_Sample; |
| for K in 1 .. 2 loop |
| for L in 1 .. 2 loop |
| X := Complex'(Sample (K), Sample (L)); |
| Y := Complex'(Sample (L), Sample (K)); |
| Do_Mult_Div (X, Y); |
| if Failure_Detected then |
| return; -- minimize flood of error messages |
| end if; |
| end loop; |
| end loop; |
| end loop; -- J |
| end loop; -- I |
| end Mult_Div_Check; |
| |
| |
| procedure Do_Test is |
| begin |
| Special_Values; |
| Mult_Div_Check; |
| end Do_Test; |
| end Non_Generic_Check; |
| |
| ----------------------------------------------------------------------- |
| ----------------------------------------------------------------------- |
| |
| begin |
| Report.Test ("CXG2008", |
| "Check the accuracy of the complex multiplication and" & |
| " division operators"); |
| |
| if Verbose then |
| Report.Comment ("checking Standard.Float"); |
| end if; |
| |
| Float_Check.Do_Test; |
| |
| if Verbose then |
| Report.Comment ("checking a digits" & |
| Integer'Image (System.Max_Digits) & |
| " floating point type"); |
| end if; |
| |
| A_Long_Float_Check.Do_Test; |
| |
| if Verbose then |
| Report.Comment ("checking non-generic package"); |
| end if; |
| |
| Non_Generic_Check.Do_Test; |
| |
| Report.Result; |
| end CXG2008; |
