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425 | with Ada.Assertions;
with Ada.Text_IO;
package body Very_Longs.Test is
use Ada.Assertions;
subtype Hex_String is String(1 .. 48);
Bad_Hex_Digit : exception;
--
-- Test procedures
--
procedure Test_Natural_Constructor is
type Test_Case is
record
N : Integer;
Expected : Hex_String;
end record;
subtype Test_Index is Integer range 1 .. 5;
Test_Cases : array(Test_Index) of Test_Case :=
(( N => 1, Expected => "000000000000000000000000000000000000000000000001"),
( N => 16#FFFF#, Expected => "00000000000000000000000000000000000000000000FFFF"),
( N => 16#10000#, Expected => "000000000000000000000000000000000000000000010000"),
( N => 16#5A5A5A5A#, Expected => "00000000000000000000000000000000000000005A5A5A5A"),
( N => 16#7FFFFFFF#, Expected => "00000000000000000000000000000000000000007FFFFFFF"));
Number : Very_Long(24);
begin
Number := Make_From_Natural(Number => 0, Length => 24);
for I in Test_Index loop
Number := Make_From_Natural(Number => Test_Cases(I).N, Length => 24);
end loop;
end Test_Natural_Constructor;
procedure Test_String_Constructor is
type Test_Case is
record
N : Hex_String;
end record;
subtype Test_Index is Integer range 1 .. 4;
Test_Cases : array(Test_Index) of Test_Case :=
((N => "000000000000000000000000000000000000000000000005"),
(N => "000000000000000000000000000000000000000100000000"),
(N => "00000000000000000000000000000000FFFFFFFFFFFFFFFF"),
(N => "000000000000000000000000000000010000000000000000"));
Number : Very_Long(24);
Valid : Boolean;
Bad_Digits : String := "000000001122334455667788990x11223344556677889900";
begin
for I in Test_Index loop
Make_From_Hex_String(Test_Cases(I).N, Number, Valid);
Assert(Valid, "Bad hex string in Test_String_Constructor");
end loop;
Make_From_Hex_String(Bad_Digits, Number, Valid);
Assert(not Valid, "Hex string with bad digits accepted as valid");
end Test_String_Constructor;
procedure Test_Relationals is
Number1, Number2 : Very_Long(24);
begin
Number1 := Make_From_Natural(Number => 0, Length => 24);
Number2 := Make_From_Natural(Number => 2, Length => 24);
-- Compare: 0 op 2 (for op in { <, =, <=, >, >= }).
Assert( (Number1 < Number2), "Bad relational ( 1)");
Assert(not (Number1 = Number2), "Bad relational ( 2)");
Assert( (Number1 <= Number2), "Bad relational ( 3)");
Assert(not (Number1 > Number2), "Bad relational ( 4)");
Assert(not (Number1 >= Number2), "Bad relational ( 5)");
-- Compare them in the other order.
Assert(not (Number2 < Number1), "Bad relational ( 6)");
Assert(not (Number2 = Number1), "Bad relational ( 7)");
Assert(not (Number2 <= Number1), "Bad relational ( 8)");
Assert( (Number2 > Number1), "Bad relational ( 9)");
Assert( (Number2 >= Number1), "Bad relational (10)");
-- Compare: 1 op 2
Number1 := Make_From_Natural(Number => 1, Length => 24);
Assert( (Number1 < Number2), "Bad relational (11)");
Assert(not (Number1 = Number2), "Bad relational (12)");
Assert( (Number1 <= Number2), "Bad relational (13)");
Assert(not (Number1 > Number2), "Bad relational (14)");
Assert(not (Number1 >= Number2), "Bad relational (15)");
-- Compare: 2 op 2
Number1 := Make_From_Natural(Number => 2, Length => 24);
Assert(not (Number1 < Number2), "Bad relational (16)");
Assert( (Number1 = Number2), "Bad relational (17)");
Assert( (Number1 <= Number2), "Bad relational (18)");
Assert(not (Number1 > Number2), "Bad relational (19)");
Assert( (Number1 >= Number2), "Bad relational (20)");
end Test_Relationals;
procedure Test_Addition is
type Test_Case is
record
X : Hex_String;
Y : Hex_String;
Z : Hex_String; -- Z = X + Y
end record;
subtype Test_Index is Integer range 1 .. 9;
Test_Cases : array(Test_Index) of Test_Case :=
(1 => (X => "000000000000000000000000000000000000000000000000",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000001"),
2 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000000",
Z => "000000000000000000000000000000000000000000000001"),
3 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000002",
Z => "000000000000000000000000000000000000000000000003"),
4 => (X => "000000000000000000000000000001234567890987654321",
Y => "000000000000000000000000000000000000000000000000",
Z => "000000000000000000000000000001234567890987654321"),
5 => (X => "000000000000000000000000000001234567890987654321",
Y => "000000000000000000000000000001234567890987654321",
Z => "000000000000000000000000000002468ACF12130ECA8642"),
6 => (X => "00000000000000000000000000000000000000000000FFFF",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000010000"),
7 => (X => "0000000000000000000000000000000000000000ffffffff", -- Also check lower case letters.
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000100000000"),
8 => (X => "00000000000000000000000000000000ffFFffFFffFFffFF",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000010000000000000000"),
9 => (X => "FFFFFFFFFfFfFfFfFfFfFfFfFfFffFfFfFfFfFfFfFfFfFfF",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000000"));
X, Y, Sum : Very_Long(24);
Expected : Very_Long(24);
Valid : Boolean;
begin
for I in Test_Index loop
-- I'm just going to assume the conversions work (the strings are hard coded literals, after all)!
Make_From_Hex_String(Test_Cases(I).X, X, Valid);
Make_From_Hex_String(Test_Cases(I).Y, Y, Valid);
Make_From_Hex_String(Test_Cases(I).Z, Expected, Valid);
Sum := ModAdd(X, Y);
Assert(Sum = Expected, "Bad addition in case #" & Integer'Image(I));
end loop;
end Test_Addition;
procedure Test_Subtraction is
type Test_Case is
record
X : Hex_String;
Y : Hex_String;
Z : Hex_String; -- Z = X - Y
end record;
subtype Test_Index is Integer range 1 .. 9;
Test_Cases : array(Test_Index) of Test_Case :=
(1 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000000"),
2 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000000",
Z => "000000000000000000000000000000000000000000000001"),
3 => (X => "000000000000000000000000000000000000000000000003",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000002"),
4 => (X => "000000000000000000000000000001234567890987654321",
Y => "000000000000000000000000000000000000000000000000",
Z => "000000000000000000000000000001234567890987654321"),
5 => (X => "000000000000000000000000000002468ACF12130ECA8642",
Y => "000000000000000000000000000001234567890987654321",
Z => "000000000000000000000000000001234567890987654321"),
6 => (X => "000000000000000000000000000000000000000000010000",
Y => "000000000000000000000000000000000000000000000001",
Z => "00000000000000000000000000000000000000000000FFFF"),
7 => (X => "000000000000000000000000000000000000000100000000",
Y => "000000000000000000000000000000000000000000000001",
Z => "0000000000000000000000000000000000000000ffffffff"), -- Also check lower case letters.
8 => (X => "000000000000000000000000000000010000000000000000",
Y => "000000000000000000000000000000000000000000000001",
Z => "00000000000000000000000000000000ffFFffFFffFFffFF"),
9 => (X => "000000000000000000000000000000000000000000000000",
Y => "000000000000000000000000000000000000000000000001",
Z => "FfFfFfFfFfFfFfFfFfFfFfFfFfFffFfFfFfFfFfFfFfFfFfF"));
X, Y, Difference : Very_Long(24);
Expected : Very_Long(24);
Valid : Boolean;
begin
for I in Test_Index loop
-- I'm just going to assume the conversions work (the strings are hard coded literals, after all)!
Make_From_Hex_String(Test_Cases(I).X, X, Valid);
Make_From_Hex_String(Test_Cases(I).Y, Y, Valid);
Make_From_Hex_String(Test_Cases(I).Z, Expected, Valid);
Difference := ModSubtract(X, Y);
Assert(Difference = Expected, "Bad subtraction in case #" & Integer'Image(I));
end loop;
end Test_Subtraction;
procedure Test_Multiplication is
type Test_Case is
record
X : Hex_String;
Y : Hex_String;
Z : Hex_String; -- Z = X * Y
end record;
subtype Test_Index is Integer range 1 .. 5;
Test_Cases : array(Test_Index) of Test_Case :=
(1 => (X => "000000000000000000000000000000000000000000000000",
Y => "000000000000000000000000000000000000000000000000",
Z => "000000000000000000000000000000000000000000000000"),
2 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000001"),
3 => (X => "000000000000000000000000000000000000000000000001",
Y => "000000000000000000000000000000000000000000000002",
Z => "000000000000000000000000000000000000000000000002"),
4 => (X => "000000000000000000000000000000000000000000000002",
Y => "000000000000000000000000000000000000000000000001",
Z => "000000000000000000000000000000000000000000000002"),
5 => (X => "00000000000000000000000000000000112210F4B16C1CB1",
Y => "000000000000000000000000000000004ECF8A71CED0C6E2",
Z => "0000000000000000054644FA3EEF2D71E014744CFD723A42"));
X, Y, Product : Very_Long(24);
Expected : Very_Long(24);
Valid : Boolean;
begin
for I in Test_Index loop
-- I'm just going to assume the conversions work (the strings are hard coded literals, after all)!
Make_From_Hex_String(Test_Cases(I).X, X, Valid);
Make_From_Hex_String(Test_Cases(I).Y, Y, Valid);
Make_From_Hex_String(Test_Cases(I).Z, Expected, Valid);
Product := ModMultiply(X, Y);
Assert(Product = Expected, "Bad multiplication in case #" & Integer'Image(I));
end loop;
end Test_Multiplication;
procedure Test_Multiplication_Full is
type Test_Case is
record
X : Hex_String;
Y : Hex_String;
Z : String(1 .. 96); -- Z = X * Y
end record;
-- Test cases were computed with the 'dc' program.
subtype Test_Index is Integer range 1 .. 2;
Test_Cases : array(Test_Index) of Test_Case :=
(1 => (X => "00000000000000000000000000000000112210F4B16C1CB1",
Y => "000000000000000000000000000000004ECF8A71CED0C6E2",
Z => "0000000000000000000000000000000000000000000000000000000000000000054644FA3EEF2D71E014744CFD723A42"),
2 => (X => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
Y => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
Z => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE000000000000000000000000000000000000000000000001"));
X, Y : Very_Long(24);
Product : Very_Long(48);
Expected : Very_Long(48);
Valid : Boolean;
begin
for I in Test_Index loop
-- I'm just going to assume the conversions work (the strings are hard coded literals, after all)!
Make_From_Hex_String(Test_Cases(I).X, X, Valid);
Make_From_Hex_String(Test_Cases(I).Y, Y, Valid);
Make_From_Hex_String(Test_Cases(I).Z, Expected, Valid);
Product := X * Y;
Assert(Product = Expected, "Bad full multiplication in case #" & Integer'Image(I));
end loop;
end Test_Multiplication_Full;
procedure Test_Division is
type Test_Case is
record
U : String(1 .. 96);
V : Hex_String;
Q : String(1 .. 96); -- Q = floor(U / V);
R : Hex_String; -- R = U mod V;
end record;
-- Just "typical" test cases for now. Must also exercise the "Add Back" step in Knuth's algorithm. That step occurs with
-- low probability so it is necessary to construct special test cases to exercise it. Test cases below created with the
-- 'dc' program on Ubuntu Linux 12.04.
--
subtype Test_Index is Integer range 1 .. 12;
Test_Cases : array(Test_Index) of Test_Case :=
-- Non-trivial with pattern.
(1 => (U => "010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748",
V => "00112233445566778899AABBCCDDEEFF0011223344556677",
Q => "00000000000000000000000000000000000000000000000F0F0F0F0F0F0F0F0F690F0F0F0F0FFF0F0F0F690F0F0F8CB8",
R => "000870D941B118811958202890FA67E9D23AD31179E28DC0"),
-- "Random."
2 => (U => "73D89CAA0082F227719B9992DD37782001844A43C784B99C512A83C422A34B860CAD328659287BB21FEE282A9DF2E483",
V => "428BB453A749C933FDC291A77CBE892001B5882345829AC7",
Q => "000000000000000000000000000000000000000000000001BDA85E584B55AB859B1C09C3FC3BB62C84478E492FDDC56B",
R => "39A4E4D22AD4C10B9264E0B9D8CDA672E9CB9C05E8761056"),
-- Random with MSD of V at 01.
3 => (U => "73D89CAA0082F227719B9992DD37782001844A43C784B99C512A83C422A34B860CAD328659287BB21FEE282A9DF2E483",
V => "018BB453A749C933FDC291A77CBE892001B5882345829AC7",
Q => "00000000000000000000000000000000000000000000004AF245E1C2BC1C960C537D183E413EBBA181FEDF9330BA8924",
R => "00C52A8CE858768071B369671E296953AE9EEBD32E2AA187"),
-- Random with MSD of V at 7F.
4 => (U => "73D89CAA0082F227719B9992DD37782001844A43C784B99C512A83C422A34B860CAD328659287BB21FEE282A9DF2E483",
V => "7F8BB453A749C933FDC291A77CBE892001B5882345829AC7",
Q => "000000000000000000000000000000000000000000000000E8847ADA09C5AA87714598019D0E62B296D3D7E3EF103639",
R => "201C036A415218687F43B0CF3F2AA96884E0C18821C87434"),
-- Random with MSD of V at 80.
5 => (U => "73D89CAA0082F227719B9992DD37782001844A43C784B99C512A83C422A34B860CAD328659287BB21FEE282A9DF2E483",
V => "808BB453A749C933FDC291A77CBE892001B5882345829AC7",
Q => "000000000000000000000000000000000000000000000000E6B56B4B96E478E4114477F727940CD4E3116D085DBC239F",
R => "48D3931409995E53691BB2A658DE8966F037B865A1878DEA"),
-- Random with MSD of V at FF.
6 => (U => "73D89CAA0082F227719B9992DD37782001844A43C784B99C512A83C422A34B860CAD328659287BB21FEE282A9DF2E483",
V => "FF8BB453A749C933FDC291A77CBE892001B5882345829AC7",
Q => "000000000000000000000000000000000000000000000000740D55028EBFAE1701477EEE2CF64D0428EFF6728935DF82",
R => "9FED98AA125DA4842160F1C365245FCA03FADD380299F275"),
-- Largest possible U, smallest possible V using the "full" algorithm.
7 => (U => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
V => "000000000000000000000000000000000000000000000100",
Q => "00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
R => "0000000000000000000000000000000000000000000000FF"),
-- Largest possible U, largest possible V.
8 => (U => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
V => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
Q => "000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000001",
R => "000000000000000000000000000000000000000000000000"),
-- Smallest possible U, smallest possible V using the "full" algorithm.
9 => (U => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
V => "000000000000000000000000000000000000000000000100",
Q => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
R => "000000000000000000000000000000000000000000000001"),
-- Smallest possible U, largest possible V.
10 => (U => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
V => "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
Q => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
R => "000000000000000000000000000000000000000000000001"),
-- Partial U, similar V, quotient of 1.
11 => (U => "000000000000000000000000000000000000000000000000800000000000000000000000000000000000000000000000",
V => "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
Q => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
R => "000000000000000000000000000000000000000000000001"),
-- Partial U, similar V, quotient of 0.
12 => (U => "0000000000000000000000000000000000000000000000007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
V => "800000000000000000000000000000000000000000000000",
Q => "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
R => "7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"));
U : Very_Long(48);
V : Very_Long(24);
Q : Very_Long(48);
R : Very_Long(24);
Expected_Q : Very_Long(48);
Expected_R : Very_Long(24);
Valid : Boolean;
begin
for I in Test_Index loop
-- I'm just going to assume the conversions work (the strings are hard coded literals, after all)!
Make_From_Hex_String(Test_Cases(I).U, U, Valid);
Make_From_Hex_String(Test_Cases(I).V, V, Valid);
Make_From_Hex_String(Test_Cases(I).Q, Expected_Q, Valid);
Make_From_Hex_String(Test_Cases(I).R, Expected_R, Valid);
Divide(U, V, Q, R);
Assert(Q = Expected_Q, "Bad division: incorrect quotient in case #" & Integer'Image(I));
Assert(R = Expected_R, "Bad division: incorrect remainder in case #" & Integer'Image(I));
end loop;
end Test_Division;
procedure Execute is
begin
Ada.Text_IO.Put_Line("... Natural constructor"); Test_Natural_Constructor;
Ada.Text_IO.Put_Line("... String constructor"); Test_String_Constructor;
Ada.Text_IO.Put_Line("... Relational operators"); Test_Relationals;
Ada.Text_IO.Put_Line("... Addition"); Test_Addition;
Ada.Text_IO.Put_Line("... Subtraction"); Test_Subtraction;
Ada.Text_IO.Put_Line("... Multiplication"); Test_Multiplication;
Ada.Text_IO.Put_Line("... Multiplication (Full)"); Test_Multiplication_Full;
Ada.Text_IO.Put_Line("... Division"); Test_Division;
end Execute;
end Very_Longs.Test;
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