Merge math.mp.Integer changes from the crypto branch

This commit is contained in:
Eugen Wissner 2017-03-21 19:25:12 +01:00
parent 85380ac3fc
commit b90517580e
2 changed files with 1363 additions and 1155 deletions

File diff suppressed because it is too large Load Diff

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@ -3,10 +3,10 @@
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/**
* Copyright: Eugene Wissner 2016.
* Copyright: Eugene Wissner 2016-2017.
* License: $(LINK2 https://www.mozilla.org/en-US/MPL/2.0/,
* Mozilla Public License, v. 2.0).
* Authors: $(LINK2 mailto:belka@caraus.de, Eugene Wissner)
* Authors: $(LINK2 mailto:info@caraus.de, Eugene Wissner)
*/
module tanya.math;
@ -16,7 +16,7 @@ public import tanya.math.random;
version (unittest)
{
import std.algorithm.iteration;
import std.algorithm.iteration;
}
/**
@ -26,12 +26,12 @@ version (unittest)
* is used to allocate the result.
*
* Params:
* I = Base type.
* G = Exponent type.
* H = Divisor type:
* x = Base.
* y = Exponent.
* z = Divisor.
* I = Base type.
* G = Exponent type.
* H = Divisor type:
* x = Base.
* y = Exponent.
* z = Divisor.
*
* Returns: Reminder of the division of $(D_PARAM x) to the power $(D_PARAM y)
* by $(D_PARAM z).
@ -39,134 +39,162 @@ version (unittest)
* Precondition: $(D_INLINECODE z > 0)
*/
H pow(I, G, H)(in auto ref I x, in auto ref G y, in auto ref H z)
if (isIntegral!I && isIntegral!G && isIntegral!H)
if (isIntegral!I && isIntegral!G && isIntegral!H)
in
{
assert(z > 0, "Division by zero.");
assert(z > 0, "Division by zero.");
}
body
{
G mask = G.max / 2 + 1;
H result;
G mask = G.max / 2 + 1;
H result;
if (y == 0)
{
return 1 % z;
}
else if (y == 1)
{
return x % z;
}
do
{
immutable bit = y & mask;
if (!result && bit)
{
result = x;
continue;
}
if (y == 0)
{
return 1 % z;
}
else if (y == 1)
{
return x % z;
}
do
{
immutable bit = y & mask;
if (!result && bit)
{
result = x;
continue;
}
result *= result;
if (bit)
{
result *= x;
}
result %= z;
}
while (mask >>= 1);
result *= result;
if (bit)
{
result *= x;
}
result %= z;
}
while (mask >>= 1);
return result;
return result;
}
/// Ditto.
I pow(I)(in auto ref I x, in auto ref I y, in auto ref I z)
if (is(I == Integer))
I pow(I)(const auto ref I x, const auto ref I y, const auto ref I z)
if (is(I == Integer))
in
{
assert(z.length > 0, "Division by zero.");
assert(z.length > 0, "Division by zero.");
}
body
{
size_t i = y.length;
auto tmp2 = Integer(x.allocator), tmp1 = Integer(x, x.allocator);
Integer result = Integer(x.allocator);
size_t i = y.length;
auto tmp1 = Integer(x, x.allocator);
auto result = Integer(x.allocator);
if (x.length == 0 && i != 0)
{
i = 0;
}
else
{
result = 1;
}
while (i)
{
--i;
for (ubyte mask = 0x01; mask; mask <<= 1)
{
if (y.rep[i] & mask)
{
result *= tmp1;
result %= z;
}
tmp2 = tmp1;
tmp1 *= tmp2;
tmp1 %= z;
}
}
return result;
if (x.length == 0 && i != 0)
{
i = 0;
}
else
{
result = 1;
}
while (i)
{
--i;
for (ubyte mask = 0x01; mask; mask <<= 1)
{
if (y.rep[i] & mask)
{
result *= tmp1;
result %= z;
}
auto tmp2 = tmp1;
tmp1 *= tmp2;
tmp1 %= z;
}
}
return result;
}
///
pure nothrow @safe @nogc unittest
{
assert(pow(3, 5, 7) == 5);
assert(pow(2, 2, 1) == 0);
assert(pow(3, 3, 3) == 0);
assert(pow(7, 4, 2) == 1);
assert(pow(53, 0, 2) == 1);
assert(pow(53, 1, 3) == 2);
assert(pow(53, 2, 5) == 4);
assert(pow(0, 0, 5) == 1);
assert(pow(0, 5, 5) == 0);
assert(pow(3, 5, 7) == 5);
assert(pow(2, 2, 1) == 0);
assert(pow(3, 3, 3) == 0);
assert(pow(7, 4, 2) == 1);
assert(pow(53, 0, 2) == 1);
assert(pow(53, 1, 3) == 2);
assert(pow(53, 2, 5) == 4);
assert(pow(0, 0, 5) == 1);
assert(pow(0, 5, 5) == 0);
}
///
unittest
{
assert(cast(long) pow(Integer(3), Integer(5), Integer(7)) == 5);
assert(cast(long) pow(Integer(2), Integer(2), Integer(1)) == 0);
assert(cast(long) pow(Integer(3), Integer(3), Integer(3)) == 0);
assert(cast(long) pow(Integer(7), Integer(4), Integer(2)) == 1);
assert(cast(long) pow(Integer(53), Integer(0), Integer(2)) == 1);
assert(cast(long) pow(Integer(53), Integer(1), Integer(3)) == 2);
assert(cast(long) pow(Integer(53), Integer(2), Integer(5)) == 4);
assert(cast(long) pow(Integer(0), Integer(0), Integer(5)) == 1);
assert(cast(long) pow(Integer(0), Integer(5), Integer(5)) == 0);
assert(pow(Integer(3), Integer(5), Integer(7)) == 5);
assert(pow(Integer(2), Integer(2), Integer(1)) == 0);
assert(pow(Integer(3), Integer(3), Integer(3)) == 0);
assert(pow(Integer(7), Integer(4), Integer(2)) == 1);
assert(pow(Integer(53), Integer(0), Integer(2)) == 1);
assert(pow(Integer(53), Integer(1), Integer(3)) == 2);
assert(pow(Integer(53), Integer(2), Integer(5)) == 4);
assert(pow(Integer(0), Integer(0), Integer(5)) == 1);
assert(pow(Integer(0), Integer(5), Integer(5)) == 0);
}
/**
* Checks if $(D_PARAM x) is a prime.
*
* Params:
* x = The number should be checked.
* x = The number should be checked.
*
* Returns: $(D_KEYWORD true) if $(D_PARAM x) is a prime number,
* $(D_KEYWORD false) otherwise.
*/
bool isPseudoprime(ulong x) nothrow pure @safe @nogc
{
return pow(2, x - 1, x) == 1;
return pow(2, x - 1, x) == 1;
}
///
unittest
{
uint[30] known = [74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719,
74843, 74747, 74759, 74761, 74771, 74779, 74797, 74821,
74827, 9973, 104729, 15485867, 49979693, 104395303,
593441861, 104729, 15485867, 49979693, 104395303,
593441861, 899809363, 982451653];
uint[30] known = [74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719,
74843, 74747, 74759, 74761, 74771, 74779, 74797, 74821,
74827, 9973, 104729, 15485867, 49979693, 104395303,
593441861, 104729, 15485867, 49979693, 104395303,
593441861, 899809363, 982451653];
known.each!((ref x) => assert(isPseudoprime(x)));
known.each!((ref x) => assert(isPseudoprime(x)));
}
/**
* Params:
* I = Value type.
* x = Value.
*
* Returns: The absolute value of a number.
*/
I abs(I : Integer)(const auto ref I x)
{
auto result = Integer(x, x.allocator);
result.sign = Sign.positive;
return result;
}
/// Ditto.
I abs(I : Integer)(I x)
{
x.sign = Sign.positive;
return x;
}
/// Ditto.
I abs(I)(const I x)
if (isIntegral!I)
{
return x >= 0 ? x : -x;
}