Implement unary operation for multiple precision integers
This commit is contained in:
parent
86c08e7af6
commit
b3fdd6fd4a
|
|
@ -10,10 +10,13 @@
|
|||
*/
|
||||
module tanya.math.mp;
|
||||
|
||||
import std.algorithm.comparison;
|
||||
import std.algorithm.iteration;
|
||||
import std.algorithm.searching;
|
||||
import std.algorithm.mutation;
|
||||
import std.experimental.allocator;
|
||||
import std.math;
|
||||
import std.range;
|
||||
import std.traits;
|
||||
import tanya.memory.allocator;
|
||||
import tanya.memory.types;
|
||||
|
||||
|
|
@ -22,6 +25,11 @@ struct Integer
|
|||
private RefCounted!(ubyte[]) rep;
|
||||
private bool sign;
|
||||
|
||||
invariant
|
||||
{
|
||||
assert(rep.length || !sign, "0 should be positive.");
|
||||
}
|
||||
|
||||
/**
|
||||
* Creates a multiple precision integer.
|
||||
*
|
||||
|
|
@ -29,7 +37,8 @@ struct Integer
|
|||
* value = Initial value.
|
||||
* allocator = Allocator.
|
||||
*/
|
||||
this(in uint value, IAllocator allocator = theAllocator)
|
||||
this(T)(in T value, IAllocator allocator = theAllocator)
|
||||
if (isIntegral!T)
|
||||
in
|
||||
{
|
||||
assert(allocator !is null);
|
||||
|
|
@ -39,8 +48,8 @@ struct Integer
|
|||
this(allocator);
|
||||
|
||||
immutable size = calculateSizeFromInt(value);
|
||||
rep = allocator.makeArray!ubyte(size);
|
||||
assignInt(size, value);
|
||||
allocator.resizeArray(rep, size);
|
||||
assignInt(value);
|
||||
}
|
||||
|
||||
///
|
||||
|
|
@ -61,8 +70,9 @@ struct Integer
|
|||
{
|
||||
this(allocator);
|
||||
|
||||
rep = allocator.makeArray!ubyte(value.length);
|
||||
allocator.resizeArray(rep, value.length);
|
||||
value.rep.get.copy(rep.get);
|
||||
sign = value.sign;
|
||||
}
|
||||
|
||||
/// Ditto.
|
||||
|
|
@ -74,14 +84,14 @@ struct Integer
|
|||
|
||||
/*
|
||||
* Figure out the minimum amount of space this value will take
|
||||
* up in bytes (leave at least one byte, though, if the value is 0).
|
||||
* up in bytes.
|
||||
*/
|
||||
pragma(inline, true)
|
||||
private ushort calculateSizeFromInt(in ref uint value)
|
||||
private ubyte calculateSizeFromInt(in ulong value)
|
||||
const pure nothrow @safe @nogc
|
||||
{
|
||||
ushort size = 4;
|
||||
for (uint mask = 0xff000000; mask > 0x000000ff; mask >>= 8)
|
||||
ubyte size = ulong.sizeof;
|
||||
for (ulong mask = 0xff00000000000000; mask >= 0xff; mask >>= 8)
|
||||
{
|
||||
if (value & mask)
|
||||
{
|
||||
|
|
@ -98,26 +108,35 @@ struct Integer
|
|||
* representation in big-endian format.
|
||||
*/
|
||||
pragma(inline, true)
|
||||
private void assignInt(in ref ushort size, in ref uint value)
|
||||
private void assignInt(T)(ref in T value)
|
||||
pure nothrow @safe @nogc
|
||||
in
|
||||
{
|
||||
uint mask = 0x00000000ff, shift;
|
||||
for (ushort i = size; i; --i)
|
||||
static assert(isIntegral!T);
|
||||
}
|
||||
body
|
||||
{
|
||||
uint mask = 0xff, shift;
|
||||
immutable absolute = abs(value);
|
||||
|
||||
sign = value < 0 ? true : false;
|
||||
for (auto i = length; i; --i)
|
||||
{
|
||||
rep[i - 1] = cast(ubyte) ((value & mask) >> shift);
|
||||
rep[i - 1] = cast(ubyte) ((absolute & mask) >> shift);
|
||||
mask <<= 8;
|
||||
shift += 8;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
ref Integer opAssign(in uint value)
|
||||
ref Integer opAssign(T)(in T value)
|
||||
if (isIntegral!T)
|
||||
{
|
||||
ushort size = calculateSizeFromInt(value);
|
||||
immutable size = calculateSizeFromInt(value);
|
||||
|
||||
checkAllocator();
|
||||
allocator.resizeArray(rep.get, size);
|
||||
assignInt(size, value);
|
||||
assignInt(value);
|
||||
|
||||
return this;
|
||||
}
|
||||
|
|
@ -125,9 +144,12 @@ struct Integer
|
|||
ref Integer opAssign(in Integer value)
|
||||
{
|
||||
checkAllocator();
|
||||
|
||||
allocator.resizeArray(rep, value.length);
|
||||
value.rep.get.copy(rep.get);
|
||||
|
||||
sign = value.sign;
|
||||
|
||||
return this;
|
||||
}
|
||||
|
||||
|
|
@ -147,8 +169,7 @@ struct Integer
|
|||
assert(h.rep[0] == 0b00000010 && h.rep[1] == 0b10110000);
|
||||
|
||||
h = 0;
|
||||
assert(h.length == 1);
|
||||
assert(h.rep[0] == 0);
|
||||
assert(h.length == 0);
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
@ -196,13 +217,11 @@ struct Integer
|
|||
{
|
||||
return -1;
|
||||
}
|
||||
|
||||
// Otherwise, keep searching through the representational integers
|
||||
// until one is bigger than another - once we've found one, it's
|
||||
// safe to stop, since the lower order bytes can't affect the
|
||||
// comparison
|
||||
int i = 0, j = 0;
|
||||
while (i < length && j < h.length)
|
||||
for (size_t i, j; i < length && j < h.length; ++i, ++j)
|
||||
{
|
||||
if (rep[i] < h.rep[j])
|
||||
{
|
||||
|
|
@ -212,8 +231,6 @@ struct Integer
|
|||
{
|
||||
return 1;
|
||||
}
|
||||
++i;
|
||||
++j;
|
||||
}
|
||||
// if we got all the way to the end without a comparison, the
|
||||
// two are equal
|
||||
|
|
@ -238,7 +255,8 @@ struct Integer
|
|||
* Assignment operators with another $(D_PSYMBOL Integer).
|
||||
*
|
||||
* Params:
|
||||
* h = The second integer.
|
||||
* op = Operation.
|
||||
* h = The second integer.
|
||||
*
|
||||
* Returns: $(D_KEYWORD this).
|
||||
*/
|
||||
|
|
@ -336,24 +354,23 @@ struct Integer
|
|||
}
|
||||
while (i);
|
||||
|
||||
if (borrow && i)
|
||||
if (borrow && i && rep[i - 1])
|
||||
{
|
||||
if (!(rep[i - 1])) // Don't borrow i
|
||||
{
|
||||
throw new Exception("Error, subtraction result is negative\n");
|
||||
}
|
||||
--rep[i - 1];
|
||||
}
|
||||
// Go through the representation array and see how many of the
|
||||
// left-most bytes are unused. Remove them and resize the array.
|
||||
immutable offset = rep.countUntil!(a => a != 0);
|
||||
immutable offset = rep.get.countUntil!((const ref a) => a != 0);
|
||||
if (offset > 0)
|
||||
{
|
||||
ubyte[] tmp;
|
||||
allocator.resizeArray(tmp, rep.length - offset);
|
||||
ubyte[] tmp = allocator.makeArray!ubyte(rep.length - offset);
|
||||
rep[offset .. $].copy(tmp);
|
||||
rep = tmp;
|
||||
}
|
||||
else if (offset == -1)
|
||||
{
|
||||
allocator.resizeArray(rep, 0);
|
||||
}
|
||||
return this;
|
||||
}
|
||||
|
||||
|
|
@ -371,6 +388,10 @@ struct Integer
|
|||
h2 = 4294967294;
|
||||
h1 -= h2;
|
||||
assert(h1.rep == [0x80, 0x00, 0x00, 0x01]);
|
||||
|
||||
h2 = h1;
|
||||
h1 -= h2;
|
||||
assert(h1.length == 0);
|
||||
}
|
||||
|
||||
/// Ditto.
|
||||
|
|
@ -427,8 +448,7 @@ struct Integer
|
|||
checkAllocator();
|
||||
if (step >= rep.length)
|
||||
{
|
||||
allocator.resizeArray(rep, 1);
|
||||
rep[0] = 0;
|
||||
allocator.resizeArray(rep, 0);
|
||||
return this;
|
||||
}
|
||||
|
||||
|
|
@ -450,7 +470,7 @@ struct Integer
|
|||
rep[j] = (rep[i] >> bit | oldCarry);
|
||||
++j;
|
||||
}
|
||||
rep.length = max(1, rep.length - n / 8 - (i == j ? 0 : 1));
|
||||
allocator.resizeArray(rep, rep.length - n / 8 - (i == j ? 0 : 1));
|
||||
|
||||
return this;
|
||||
}
|
||||
|
|
@ -474,32 +494,32 @@ struct Integer
|
|||
assert(h1.rep == [0x0f, 0xff]);
|
||||
|
||||
h1 >>= 20;
|
||||
assert(h1.rep == [0x00]);
|
||||
assert(h1.length == 0);
|
||||
|
||||
h1 >>= 2;
|
||||
assert(h1.rep == [0x00]);
|
||||
assert(h1.length == 0);
|
||||
|
||||
h1 = 1431655765;
|
||||
h1 >>= 16;
|
||||
assert(h1.rep == [0x55, 0x55]);
|
||||
|
||||
h1 >>= 16;
|
||||
assert(h1.rep == [0x00]);
|
||||
assert(h1.length == 0);
|
||||
}
|
||||
|
||||
/// Ditto.
|
||||
ref Integer opOpAssign(string op)(in Integer h)
|
||||
if (op == "*")
|
||||
{
|
||||
ubyte mask;
|
||||
auto i = h.rep.length;
|
||||
auto temp = Integer(this);
|
||||
auto temp = Integer(this, allocator);
|
||||
immutable sign = sign == h.sign ? false : true;
|
||||
|
||||
opAssign(0);
|
||||
do
|
||||
{
|
||||
--i;
|
||||
for (mask = 0x01; mask; mask <<= 1)
|
||||
for (ubyte mask = 0x01; mask; mask <<= 1)
|
||||
{
|
||||
if (mask & h.rep[i])
|
||||
{
|
||||
|
|
@ -509,6 +529,7 @@ struct Integer
|
|||
}
|
||||
}
|
||||
while (i);
|
||||
this.sign = sign;
|
||||
|
||||
return this;
|
||||
}
|
||||
|
|
@ -526,26 +547,24 @@ struct Integer
|
|||
ref Integer opOpAssign(string op)(in Integer h)
|
||||
if ((op == "/") || (op == "%"))
|
||||
{
|
||||
auto divisor = Integer(h);
|
||||
// "bit_position" keeps track of which bit, of the quotient,
|
||||
// is being set or cleared on the current operation.
|
||||
size_t bit_size;
|
||||
|
||||
checkAllocator();
|
||||
|
||||
// First, left-shift divisor until it's >= than the divident
|
||||
while (opCmp(divisor) > 0)
|
||||
auto divisor = Integer(h, allocator);
|
||||
size_t bitSize;
|
||||
|
||||
// First, left-shift divisor until it's >= than the dividend
|
||||
for (; opCmp(divisor) > 0; ++bitSize)
|
||||
{
|
||||
divisor <<= 1;
|
||||
++bit_size;
|
||||
}
|
||||
static if (op == "/")
|
||||
{
|
||||
auto quotient = allocator.makeArray!ubyte(bit_size / 8 + 1);
|
||||
auto quotient = allocator.makeArray!ubyte(bitSize / 8 + 1);
|
||||
}
|
||||
|
||||
auto bit_position = 8 - (bit_size % 8) - 1;
|
||||
|
||||
// "bitPosition" keeps track of which bit, of the quotient,
|
||||
// is being set or cleared on the current operation.
|
||||
auto bitPosition = 8 - (bitSize % 8) - 1;
|
||||
do
|
||||
{
|
||||
if (opCmp(divisor) >= 0)
|
||||
|
|
@ -553,21 +572,25 @@ struct Integer
|
|||
opOpAssign!"-"(divisor);
|
||||
static if (op == "/")
|
||||
{
|
||||
quotient[bit_position / 8] |= (0x80 >> (bit_position % 8));
|
||||
quotient[bitPosition / 8] |= (0x80 >> (bitPosition % 8));
|
||||
}
|
||||
}
|
||||
|
||||
if (bit_size)
|
||||
if (bitSize)
|
||||
{
|
||||
divisor >>= 1;
|
||||
}
|
||||
++bit_position;
|
||||
else
|
||||
{
|
||||
break;
|
||||
}
|
||||
++bitPosition, --bitSize;
|
||||
}
|
||||
while (bit_size--);
|
||||
while (true);
|
||||
|
||||
static if (op == "/")
|
||||
{
|
||||
rep = quotient;
|
||||
sign = sign == h.sign ? false : true;
|
||||
}
|
||||
return this;
|
||||
}
|
||||
|
|
@ -582,7 +605,7 @@ struct Integer
|
|||
|
||||
h1 = 8;
|
||||
h1 %= h2;
|
||||
assert(h1.rep == [0x00]);
|
||||
assert(h1.length == 0);
|
||||
|
||||
h1 = 7;
|
||||
h1 %= h2;
|
||||
|
|
@ -591,7 +614,7 @@ struct Integer
|
|||
h1 = 56088;
|
||||
h2 = 456;
|
||||
h1 /= h2;
|
||||
assert(h1.rep == [0x7b]); // 123
|
||||
assert(h1.rep == [0x7b]);
|
||||
}
|
||||
|
||||
/// Ditto.
|
||||
|
|
@ -599,8 +622,8 @@ struct Integer
|
|||
if (op == "^^")
|
||||
{
|
||||
auto i = exp.rep.length;
|
||||
auto tmp1 = Integer(this);
|
||||
Integer tmp2;
|
||||
auto tmp1 = Integer(this, allocator);
|
||||
auto tmp2 = Integer(allocator);
|
||||
|
||||
opAssign(1);
|
||||
|
||||
|
|
@ -637,5 +660,150 @@ struct Integer
|
|||
assert(h1.rep == [0x1b, 0x5c, 0xab, 0x9c, 0x31, 0x10]);
|
||||
}
|
||||
|
||||
/**
|
||||
* Unary operators.
|
||||
*
|
||||
* Params:
|
||||
* op = Operation.
|
||||
*
|
||||
* Returns: New $(D_PSYMBOL Integer).
|
||||
*/
|
||||
Integer opUnary(string op)()
|
||||
if ((op == "+") || (op == "-") || (op == "~"))
|
||||
{
|
||||
auto h = Integer(this, allocator);
|
||||
static if (op == "-")
|
||||
{
|
||||
h.sign = !h.sign;
|
||||
}
|
||||
else static if (op == "~")
|
||||
{
|
||||
h.rep.get.each!((ref a) => a = ~a);
|
||||
}
|
||||
return h;
|
||||
}
|
||||
|
||||
///
|
||||
unittest
|
||||
{
|
||||
auto h1 = Integer(79);
|
||||
Integer h2;
|
||||
|
||||
h2 = +h1;
|
||||
assert(h2.length == 1);
|
||||
assert(h2.rep[0] == 79);
|
||||
assert(!h2.sign);
|
||||
assert(h2 !is h1);
|
||||
|
||||
h2 = -h1;
|
||||
assert(h2.length == 1);
|
||||
assert(h2.rep[0] == 79);
|
||||
assert(h2.sign);
|
||||
|
||||
h1 = -h2;
|
||||
assert(h2.length == 1);
|
||||
assert(h2.rep[0] == 79);
|
||||
assert(h2.sign);
|
||||
assert(h2 !is h1);
|
||||
|
||||
h1 = -h2;
|
||||
assert(h1.length == 1);
|
||||
assert(h1.rep[0] == 79);
|
||||
assert(!h1.sign);
|
||||
|
||||
h2 = ~h1;
|
||||
assert(h2.rep[0] == ~cast(ubyte) 79);
|
||||
}
|
||||
|
||||
/**
|
||||
* Increment/decrement.
|
||||
*
|
||||
* Params:
|
||||
* op = Operation.
|
||||
*
|
||||
* Returns: $(D_KEYWORD this).
|
||||
*/
|
||||
ref Integer opUnary(string op)()
|
||||
if ((op == "++") || (op == "--"))
|
||||
{
|
||||
checkAllocator();
|
||||
|
||||
if (op == "++" || sign || length == 0)
|
||||
{
|
||||
static if (op == "--")
|
||||
{
|
||||
sign = true;
|
||||
}
|
||||
auto size = rep
|
||||
.get
|
||||
.retro
|
||||
.countUntil!((const ref a) => a != typeof(rep[0]).max);
|
||||
if (size == -1)
|
||||
{
|
||||
size = length;
|
||||
allocator.resizeArray(rep.get, rep.length + 1);
|
||||
rep[0] = 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
++rep[$ - size - 1];
|
||||
}
|
||||
rep[$ - size .. $] = 0;
|
||||
}
|
||||
else
|
||||
{
|
||||
immutable size = rep.get.retro.countUntil!((const ref a) => a != 0);
|
||||
if (rep[0] == 1)
|
||||
{
|
||||
allocator.resizeArray(rep, rep.length - 1);
|
||||
rep[0 .. $] = typeof(rep[0]).max;
|
||||
}
|
||||
else
|
||||
{
|
||||
--rep[$ - size - 1];
|
||||
rep[$ - size .. $] = typeof(rep[0]).max;
|
||||
}
|
||||
if (rep.length == 0)
|
||||
{
|
||||
sign = false;
|
||||
}
|
||||
}
|
||||
return this;
|
||||
}
|
||||
|
||||
///
|
||||
unittest
|
||||
{
|
||||
Integer h;
|
||||
|
||||
++h;
|
||||
assert(h.rep == [0x01]);
|
||||
assert(h.length == 1);
|
||||
|
||||
--h;
|
||||
assert(h.length == 0);
|
||||
|
||||
h = 511;
|
||||
++h;
|
||||
assert(h.rep == [0x02, 0x00]);
|
||||
|
||||
--h;
|
||||
assert(h.rep == [0x01, 0xff]);
|
||||
|
||||
h = 79;
|
||||
++h;
|
||||
assert(h.rep == [0x50]);
|
||||
|
||||
--h;
|
||||
assert(h.rep == [0x4f]);
|
||||
|
||||
h = 65535;
|
||||
++h;
|
||||
assert(h.rep == [0x01, 0x00, 0x00]);
|
||||
|
||||
--h;
|
||||
assert(h.rep == [0xff, 0xff]);
|
||||
}
|
||||
|
||||
mixin StructAllocator;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -10,6 +10,7 @@
|
|||
*/
|
||||
module tanya.memory.allocator;
|
||||
|
||||
import std.algorithm.mutation;
|
||||
import std.experimental.allocator;
|
||||
import std.typecons;
|
||||
|
||||
|
|
@ -136,26 +137,33 @@ abstract class Allocator : IAllocator
|
|||
|
||||
/**
|
||||
* Params:
|
||||
* T = Element type of the array being created.
|
||||
* allocator = The allocator used for getting memory.
|
||||
* array = A reference to the array being changed.
|
||||
* length = New array length.
|
||||
* T = Element type of the array being created.
|
||||
* allocator = The allocator used for getting memory.
|
||||
* array = A reference to the array being changed.
|
||||
* length = New array length.
|
||||
* init = The value to fill the new part of the array with if it becomes
|
||||
* larger.
|
||||
*
|
||||
* Returns: $(D_KEYWORD true) upon success, $(D_KEYWORD false) if memory could
|
||||
* not be reallocated. In the latter
|
||||
*/
|
||||
bool resizeArray(T)(IAllocator allocator,
|
||||
ref T[] array,
|
||||
in size_t length)
|
||||
in size_t length,
|
||||
T init = T.init)
|
||||
{
|
||||
void[] buf = array;
|
||||
immutable oldLength = array.length;
|
||||
|
||||
if (!allocator.reallocate(buf, length * T.sizeof))
|
||||
{
|
||||
return false;
|
||||
}
|
||||
array = cast(T[]) buf;
|
||||
|
||||
if (oldLength < length)
|
||||
{
|
||||
array[oldLength .. $].uninitializedFill(init);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
|
@ -194,7 +202,7 @@ mixin template StructAllocator()
|
|||
{
|
||||
private IAllocator allocator;
|
||||
|
||||
this(IAllocator allocator)
|
||||
this(IAllocator allocator) pure nothrow @safe @nogc
|
||||
in
|
||||
{
|
||||
assert(allocator !is null);
|
||||
|
|
|
|||
Loading…
Reference in New Issue