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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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9
Task/Miller-Rabin-primality-test/Ada/miller-rabin-primality-test-1.ada Normal file
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generic
type Number is range <>;
package Miller_Rabin is
type Result_Type is (Composite, Probably_Prime);
function Is_Prime (N : Number; K : Positive := 10) return Result_Type;
end Miller_Rabin;

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Task/Miller-Rabin-primality-test/Ada/miller-rabin-primality-test-2.ada Normal file
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with Ada.Numerics.Discrete_Random;
package body Miller_Rabin is
function Is_Prime (N : Number; K : Positive := 10)
return Result_Type
is
subtype Number_Range is Number range 2 .. N - 1;
package Random is new Ada.Numerics.Discrete_Random (Number_Range);
function Mod_Exp (Base, Exponent, Modulus : Number) return Number is
Result : Number := 1;
begin
for E in 1 .. Exponent loop
Result := Result * Base mod Modulus;
end loop;
return Result;
end Mod_Exp;
Generator : Random.Generator;
D : Number := N - 1;
S : Natural := 0;
X : Number;
begin
-- exclude 2 and even numbers
if N = 2 then
return Probably_Prime;
elsif N mod 2 = 0 then
return Composite;
end if;
-- write N-1 as 2**S * D, with D mod 2 /= 0
while D mod 2 = 0 loop
D := D / 2;
S := S + 1;
end loop;
-- initialize RNG
Random.Reset (Generator);
for Loops in 1 .. K loop
X := Mod_Exp(Random.Random (Generator), D, N);
if X /= 1 and X /= N - 1 then
Inner : for R in 1 .. S - 1 loop
X := Mod_Exp (X, 2, N);
if X = 1 then return Composite; end if;
exit Inner when X = N - 1;
end loop Inner;
if X /= N - 1 then return Composite; end if;
end if;
end loop;
return Probably_Prime;
end Is_Prime;
end Miller_Rabin;

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Task/Miller-Rabin-primality-test/Ada/miller-rabin-primality-test-3.ada Normal file
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with Ada.Text_IO, Miller_Rabin;
procedure Mr_Tst is
type Number is range 0 .. (2**48)-1;
package Num_IO is new Ada.Text_IO.Integer_IO (Number);
package Pos_IO is new Ada.Text_IO.Integer_IO (Positive);
package MR is new Miller_Rabin(Number); use MR;
N : Number;
K : Positive;
begin
for I in Number(2) .. 1000 loop
if Is_Prime (I) = Probably_Prime then
Ada.Text_IO.Put (Number'Image (I));
end if;
end loop;
Ada.Text_IO.Put_Line (".");
Ada.Text_IO.Put ("Enter a Number: "); Num_IO.Get (N);
Ada.Text_IO.Put ("Enter the count of loops: "); Pos_IO.Get (K);
Ada.Text_IO.Put_Line ("What is it? " & Result_Type'Image (Is_Prime(N, K)));
end MR_Tst;

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Task/Miller-Rabin-primality-test/Ada/miller-rabin-primality-test-4.ada Normal file
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with Ada.Text_IO, Crypto.Types.Big_Numbers, Ada.Numerics.Discrete_Random;
procedure Miller_Rabin is
Bound: constant Positive := 256; -- can be any multiple of 32
package LN is new Crypto.Types.Big_Numbers (Bound);
use type LN.Big_Unsigned; -- all computations "mod 2**Bound"
function "+"(S: String) return LN.Big_Unsigned
renames LN.Utils.To_Big_Unsigned;
function Is_Prime (N : LN.Big_Unsigned; K : Positive := 10) return Boolean is
subtype Mod_32 is Crypto.Types.Mod_Type;
use type Mod_32;
package R_32 is new Ada.Numerics.Discrete_Random (Mod_32);
Generator : R_32.Generator;
function Random return LN.Big_Unsigned is
X: LN.Big_Unsigned := LN.Big_Unsigned_Zero;
begin
for I in 1 .. Bound/32 loop
X := (X * 2**16) * 2**16;
X := X + R_32.Random(Generator);
end loop;
return X;
end Random;
D: LN.Big_Unsigned := N - LN.Big_Unsigned_One;
S: Natural := 0;
A, X: LN.Big_Unsigned;
begin
-- exclude 2 and even numbers
if N = 2 then
return True;
elsif N mod 2 = LN.Big_Unsigned_Zero then
return False;
else
-- write N-1 as 2**S * D, with odd D
while D mod 2 = LN.Big_Unsigned_Zero loop
D := D / 2;
S := S + 1;
end loop;
-- initialize RNG
R_32.Reset (Generator);
-- run the real test
for Loops in 1 .. K loop
loop
A := Random;
exit when (A > 1) and (A < (N - 1));
end loop;
X := LN.Mod_Utils.Pow(A, D, N); -- X := (Random**D) mod N
if X /= 1 and X /= N - 1 then
Inner:
for R in 1 .. S - 1 loop
X := LN.Mod_Utils.Pow(X, LN.Big_Unsigned_Two, N);
if X = 1 then
return False;
end if;
exit Inner when X = N - 1;
end loop Inner;
if X /= N - 1 then
return False;
end if;
end if;
end loop;
end if;
return True;
end Is_Prime;
S: constant String :=
"4547337172376300111955330758342147474062293202868155909489";
T: constant String :=
"4547337172376300111955330758342147474062293202868155909393";
K: constant Positive := 10;
begin
Ada.Text_IO.Put_Line("Prime(" & S & ")=" & Boolean'Image(Is_Prime(+S, K)));
Ada.Text_IO.Put_Line("Prime(" & T & ")=" & Boolean'Image(Is_Prime(+T, K)));
end Miller_Rabin;

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Task/Miller-Rabin-primality-test/Ada/miller-rabin-primality-test-5.ada Normal file
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with Ada.Text_IO, Crypto.Types.Big_Numbers, Ada.Numerics.Discrete_Random;
procedure Miller_Rabin is
Bound: constant Positive := 256; -- can be any multiple of 32
package LN is new Crypto.Types.Big_Numbers (Bound);
use type LN.Big_Unsigned; -- all computations "mod 2**Bound"
function "+"(S: String) return LN.Big_Unsigned
renames LN.Utils.To_Big_Unsigned;
S: constant String :=
"4547337172376300111955330758342147474062293202868155909489";
T: constant String :=
"4547337172376300111955330758342147474062293202868155909393";
K: constant Positive := 10;
begin
Ada.Text_IO.Put_Line("Prime(" & S & ")="
& Boolean'Image (LN.Mod_Utils.Passed_Miller_Rabin_Test(+S, K)));
Ada.Text_IO.Put_Line("Prime(" & T & ")="
& Boolean'Image (LN.Mod_Utils.Passed_Miller_Rabin_Test(+T, K)));
end Miller_Rabin;