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Merge math.mp.Integer changes from the crypto branch

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Eugen Wissner 2017-03-21 19:25:12 +01:00
parent 85380ac3fc
commit b90517580e
2 changed files with 1363 additions and 1155 deletions
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source/tanya/math/mp.d
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source/tanya/math/package.d
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@ -3,11 +3,11 @@
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */ * 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/, * License: $(LINK2 https://www.mozilla.org/en-US/MPL/2.0/,
* Mozilla Public License, v. 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; module tanya.math;
import std.traits; import std.traits;
@ -16,7 +16,7 @@ public import tanya.math.random;
version (unittest) version (unittest)
{ {
import std.algorithm.iteration; import std.algorithm.iteration;
} }
/** /**
@ -26,12 +26,12 @@ version (unittest)
* is used to allocate the result. * is used to allocate the result.
* *
* Params: * Params:
* I = Base type. * I = Base type.
* G = Exponent type. * G = Exponent type.
* H = Divisor type: * H = Divisor type:
* x = Base. * x = Base.
* y = Exponent. * y = Exponent.
* z = Divisor. * z = Divisor.
* *
* Returns: Reminder of the division of $(D_PARAM x) to the power $(D_PARAM y) * Returns: Reminder of the division of $(D_PARAM x) to the power $(D_PARAM y)
* by $(D_PARAM z). * by $(D_PARAM z).
@ -39,134 +39,162 @@ version (unittest)
* Precondition: $(D_INLINECODE z > 0) * 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) 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 in
{ {
assert(z > 0, "Division by zero."); assert(z > 0, "Division by zero.");
} }
body body
{ {
G mask = G.max / 2 + 1; G mask = G.max / 2 + 1;
H result; H result;
if (y == 0) if (y == 0)
{ {
return 1 % z; return 1 % z;
} }
else if (y == 1) else if (y == 1)
{ {
return x % z; return x % z;
} }
do do
{ {
immutable bit = y & mask; immutable bit = y & mask;
if (!result && bit) if (!result && bit)
{ {
result = x; result = x;
continue; continue;
} }
result *= result; result *= result;
if (bit) if (bit)
{ {
result *= x; result *= x;
} }
result %= z; result %= z;
} }
while (mask >>= 1); while (mask >>= 1);
return result; return result;
} }
/// Ditto. /// Ditto.
I pow(I)(in auto ref I x, in auto ref I y, in auto ref I z) I pow(I)(const auto ref I x, const auto ref I y, const auto ref I z)
if (is(I == Integer)) if (is(I == Integer))
in in
{ {
assert(z.length > 0, "Division by zero."); assert(z.length > 0, "Division by zero.");
} }
body body
{ {
size_t i = y.length; size_t i = y.length;
auto tmp2 = Integer(x.allocator), tmp1 = Integer(x, x.allocator); auto tmp1 = Integer(x, x.allocator);
Integer result = Integer(x.allocator); auto result = Integer(x.allocator);
if (x.length == 0 && i != 0) if (x.length == 0 && i != 0)
{ {
i = 0; i = 0;
} }
else else
{ {
result = 1; result = 1;
} }
while (i) while (i)
{ {
--i; --i;
for (ubyte mask = 0x01; mask; mask <<= 1) for (ubyte mask = 0x01; mask; mask <<= 1)
{ {
if (y.rep[i] & mask) if (y.rep[i] & mask)
{ {
result *= tmp1; result *= tmp1;
result %= z; result %= z;
} }
tmp2 = tmp1; auto tmp2 = tmp1;
tmp1 *= tmp2; tmp1 *= tmp2;
tmp1 %= z; tmp1 %= z;
} }
} }
return result; return result;
} }
/// ///
pure nothrow @safe @nogc unittest pure nothrow @safe @nogc unittest
{ {
assert(pow(3, 5, 7) == 5); assert(pow(3, 5, 7) == 5);
assert(pow(2, 2, 1) == 0); assert(pow(2, 2, 1) == 0);
assert(pow(3, 3, 3) == 0); assert(pow(3, 3, 3) == 0);
assert(pow(7, 4, 2) == 1); assert(pow(7, 4, 2) == 1);
assert(pow(53, 0, 2) == 1); assert(pow(53, 0, 2) == 1);
assert(pow(53, 1, 3) == 2); assert(pow(53, 1, 3) == 2);
assert(pow(53, 2, 5) == 4); assert(pow(53, 2, 5) == 4);
assert(pow(0, 0, 5) == 1); assert(pow(0, 0, 5) == 1);
assert(pow(0, 5, 5) == 0); assert(pow(0, 5, 5) == 0);
} }
/// ///
unittest unittest
{ {
assert(cast(long) pow(Integer(3), Integer(5), Integer(7)) == 5); assert(pow(Integer(3), Integer(5), Integer(7)) == 5);
assert(cast(long) pow(Integer(2), Integer(2), Integer(1)) == 0); assert(pow(Integer(2), Integer(2), Integer(1)) == 0);
assert(cast(long) pow(Integer(3), Integer(3), Integer(3)) == 0); assert(pow(Integer(3), Integer(3), Integer(3)) == 0);
assert(cast(long) pow(Integer(7), Integer(4), Integer(2)) == 1); assert(pow(Integer(7), Integer(4), Integer(2)) == 1);
assert(cast(long) pow(Integer(53), Integer(0), Integer(2)) == 1); assert(pow(Integer(53), Integer(0), Integer(2)) == 1);
assert(cast(long) pow(Integer(53), Integer(1), Integer(3)) == 2); assert(pow(Integer(53), Integer(1), Integer(3)) == 2);
assert(cast(long) pow(Integer(53), Integer(2), Integer(5)) == 4); assert(pow(Integer(53), Integer(2), Integer(5)) == 4);
assert(cast(long) pow(Integer(0), Integer(0), Integer(5)) == 1); assert(pow(Integer(0), Integer(0), Integer(5)) == 1);
assert(cast(long) pow(Integer(0), Integer(5), Integer(5)) == 0); assert(pow(Integer(0), Integer(5), Integer(5)) == 0);
} }
/** /**
* Checks if $(D_PARAM x) is a prime. * Checks if $(D_PARAM x) is a prime.
* *
* Params: * 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, * Returns: $(D_KEYWORD true) if $(D_PARAM x) is a prime number,
* $(D_KEYWORD false) otherwise. * $(D_KEYWORD false) otherwise.
*/ */
bool isPseudoprime(ulong x) nothrow pure @safe @nogc bool isPseudoprime(ulong x) nothrow pure @safe @nogc
{ {
return pow(2, x - 1, x) == 1; return pow(2, x - 1, x) == 1;
} }
/// ///
unittest unittest
{ {
uint[30] known = [74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719, uint[30] known = [74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719,
74843, 74747, 74759, 74761, 74771, 74779, 74797, 74821, 74843, 74747, 74759, 74761, 74771, 74779, 74797, 74821,
74827, 9973, 104729, 15485867, 49979693, 104395303, 74827, 9973, 104729, 15485867, 49979693, 104395303,
593441861, 104729, 15485867, 49979693, 104395303, 593441861, 104729, 15485867, 49979693, 104395303,
593441861, 899809363, 982451653]; 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;
} }