Set the number of bits - set

How can I set a variable to have a certain number of bits? For example I want to set x to have 3 bits, and if I copy 9=1001 in x, x will hold 100.

In C you can do something like this:
struct foo {
int field1:3;
}
And field1 of a foo would only occupy 3 bits.

Related

xoring a slice in Go

So I'm trying to xor random, which is 4 bytes, with every four bytes of something. The thing is, I want to change random to ans (which is the result of the xor) and then keep going. So basically the random variable will be a fixed number the first time but will change afterwards until the loop ends. My code seems to have the correct logic, however, I keep getting
(operator ^ not defined on slice)
random := 4 bytes
for j:=0;j<len(something);j+=4{
ans:=something[j:j+4] ^ random
random=ans
}
My guess is, slice doesn't allow xor, and something will have to be slice since I'm kind of slicing the array into multiple bytes. Any idea how to solve this problem?
The application should xor the individual bytes. Something like this:
var random [4]byte
for i, b := range something {
random[i&3] ^= b // xor b on element of random
}
This sets
random[0] = random[0] ^ something[0] ^ something[4] ....
random[1] = random[1] ^ something[1] ^ something[5] ...
... and so on

How to generate a random number within a range in D

How do i generate a random number within a range in D?
int number = randomNumber(0,1);
Something like this. So number would be equal to either 0 or 1.
int number = uniform!"[]"(0,1);
http://dlang.org/phobos/std_random.html#.uniform

Pass two integers as one integer

I have two integers that I need to pass through one integer and then get the values of two integers back.
I am thinking of using Logic Operators (AND, OR, XOR, etc) .
Using the C programming language, it could be done as follows assuming that the two integers are less than 65535.
void take2IntegersAsOne(int x)
{
// int1 is stored in the bottom half of x, so take just that part.
int int1 = x & 0xFFFF;
// int2 is stored in the top half of x, so slide that part of the number
// into the bottom half, and take just that part.
int int2 = (x >> 16) & 0xFFFF
// use int1 and int2 here. They must both be less than 0xFFFF or 65535 in decimal
}
void pass2()
{
int int1 = 345;
int int2 = 2342;
take2Integers( int1 | (int2 << 16) );
}
This relies on the fact that in C an integer is stored in 4 bytes. So, the example uses the first two bytes to store one of the integers, and the next two bytes for the second. This does impose the limit though that each of the integers must have a small enough value so that they will each fit into just 2 bytes.
The shift operators << and >> are used to slide the bits of an integer up and down. Shifting by 16, moves the bits by two bytes (as there are 8 bits per byte).
Using 0xFFFF represents the bit pattern where all of the bits in the lower two bytes of the number are 1s So, ANDing (with with & operator) causes all the bits that are not in these bottom two bytes to be switched off (back to zero). This can be used to remove any parts of the 'other integer' from the one you're currently extracting.
There are two parts to this question. First, how do you bitmask two 32-bit Integers into a 64-bit Long Integer?
As others have stated, let's say I have a function that takes an X and Y coordinate, and returns a longint representing that Point's linear value. I tend to call this linearization of 2d data:
public long asLong(int x, int y) {
return ( ((long)x) << 32 ) | y;
}
public int getX(long location) {
return (int)((location >> 32) & 0xFFFFFFFF);
}
public int getY(long location) {
return (int)(location & 0xFFFFFFFF);
}
Forgive me if I'm paranoid about order of operations, sometimes other operations are greedier than <<, causing things to shift further than they should.
Why does this work? When might it fail?
It's convenient that integers tend to be exactly half the size of longints. What we're doing is casting x to a long, shifting it left until it sits entirely to the left of y, and then doing a union operation (OR) to combine the bits of both.
Let's pretend they're 4-bit numbers being combined into an 8-bit number:
x = 14 : 1110
y = 5 : 0101
x = x << 4 : 1110 0000
p = x | y : 1110 0000
OR 0101
---------
1110 0101
Meanwhile, the reverse:
p = 229 : 1110 0101
x = p >> 4 : 1111 1110 //depending on your language and data type, sign extension
//can cause the bits to smear on the left side as they're
//shifted, as shown here. Doesn't happen in unsigned types
x = x & 0xF:
1111 1110
AND 0000 1111
-------------
0000 1110 //AND selects only the bits we have in common
y = p & 0xF:
1110 0101
AND 0000 1111
-------------
0000 0101 //AND strikes again
This sort of approach came into being a long time ago, in environments that needed to squeeze every bit out of their storage or transmission space. If you're not on an embedded system or immediately packing this data for transmission over a network, the practicality of this whole procedure starts to break down really rapidly:
It's way too much work just for boxing a return value that almost always immediately needs to be unboxed and read by the caller. That's kind of like digging a hole and then filling it in.
It greatly reduces your code readability. "What type is returned?" Uh... an int.. and another int... in a long.
It can introduce hard-to-trace bugs down the line. For instance, if you use unsigned types and ignore the sign extension, then later on migrate to a platform that causes those types to go two's complement. If you save off the longint, and try to read it later in another part of your code, you might hit an off-by-one error on the bitshift and spend an hour debugging your function only to find out it's the parameter that's wrong.
If it's so bad, what are the alternatives?
This is why people were asking you about your language. Ideally, if you're in something like C or C++, it'd be best to say
struct Point { int x; int y; };
public Point getPosition() {
struct Point result = { 14,5 };
return result;
}
Otherwise, in HLLs like Java, you might wind up with an inner class to achieve the same functionality:
public class Example {
public class Point {
public int x;
public int y;
public Point(int x, int y) { this.x=x; this.y=y; }
}
public Point getPosition() {
return new Point(14,5);
}
}
In this case, getPosition returns an Example.Point - if you keep using Point often, promote it to a full class of its own. In fact, java.awt has several Point classes already, including Point and Point.Float
Finally, many modern languages now have syntactic sugar for either boxing multiple values into tuples or directly returning multiple values from a function. This is kind of a last resort. In my experience, any time you pretend that data isn't what it is, you wind up with problems down the line. But if your method absolutely must return two numbers that really aren't part of the same data at all, tuples or arrays are the way to go.
The reference for the c++ stdlib tuple can be found at
http://www.cplusplus.com/reference/std/tuple/
Well.. #Felice is right, but if they both fit in 16 bit there's a way:
output_int = (first_int << 16) | second_int
^
means 'or'
to pack them, and
first_int = output_int & 0xffff
second_int = (output int >> 16) & 0xffff
^
means 'and'
to extract them.
Two integer can't fit one integer, or at least you cant get back the two original one.
But anyway, if the two original integer are bounded to a sure number of bits you can ( in pseudocode ):
First integer
OR with
(Second integer SHIFTLEFT(nOfBits))
for getting back the two integer
mask the merged integer with a number that is binary represented by nOfBitsOne and you obtain the first integer, then
ShiftRight by nOfBits the merged integer, and you have back the second.
You could store 2 16-bit integers within a 32-bit integer. First one i 16 first bits and second one in the last 16 bits. To retrieve and compose the value you use shift-operators.

Efficient Indexing method for a 2 by 2 matrix

If I fill numbers from 1 to 4 in a 2 by 2 matrix, there are 16 possible combinations. What I want to do is store values in an array of size 24 corresponding to each matrix. So given a
2 by 2 matrix, I want a efficient indexing method to index into the array directly.( I dont want comparing all 4 elements for each of 16 positions). Something similar to bit vector ? but not able to figure out how?
I want it for a 4 by 4 matrix also filling from 1 to 9
to clarify: you're looking for an efficient hash function for 2x2 matrices. you want to use the results of the hash function to compare matrices to see if they're the same.
first, lets assume you actually want the numbers 0 to 3 instead of 1 to 4 - this makes it easier, and is more computer-sciency. Next, 16 is not right. there are 24 possible permutations of the numbers 0-3. There are 4^4 = 256 possible strings of length 4 that use a four-letter alphabet (you can repeat already-used numbers).
either one is trivial to encode into a single byte. Let the first 2 bits represent the (0,0) position, the next 2 bits represent (0,1), and so forth. Than, to hash your 2x2 matrix, simply do:
hash = m[0][0] | (m[0][1] << 2) | (m[1][0] << 4) | (m[1][1] << 6
random example: the number 54 in binary is 00110110 which represents a matrix like:
2 1
3 0
When you need efficiency, sometimes code clarity goes out the window :)
First you need to be sure you want efficiency - you have profiling info to be sure that the simple comparison code is too inefficient for you?
You can simply treat it as an array of bytes of the same size. memcmp does comparisons of arbitary memory:
A data structure such as:
int matrix[2][2];
is stored the same as:
int matrix[2*2];
which could be dynamically allocated as:
typedef int matrix[2*2];
matrix* m = (matrix*)malloc(sizeof(matrix));
I'm not suggesting you dynamically allocate them, I'm illustrating how the bytes in your original type is actually layed out in memory.
Therefore, the following is valid:
matrix lookup[16];
int matrix_cmp(const void* a,const void* b) {
return memcmp(a,b,sizeof(matrix));
}
void init_matrix_lookup() {
int i;
for(i=0; i<16; i++) {
...
}
qsort(lookup,16,sizeof(matrix),matrix_cmp));
}
int matrix_to_lookup(matrix* m) {
// in this example I'm sorting them so we can bsearch;
// but with only 16 elements, its probably not worth the effort,
// and you could safely just loop over them...
return bsearch(m,lookup,16,sizeof(matrix),matrix_cmp);
}

Convert string to integer (not atoi!)

I want to be able to take, as input, a character pointer to a number in base 2 through 16 and as a second parameter, what base the number is in and then convert that to it's representation in base 2. The integer can be of arbitrary length. My solution now does what the atoi() function does, but I was curious purely out of academic interest if a lookup table solution is possible.
I have found that this is simple for binary, octal, and hexadecimal. I can simply use a lookup table for each digit to get a series of bits. For instance:
0xF1E ---> (F = 1111) (1 = 0001) (E = 1110) ---> 111100011110
0766 ---> (7 = 111) (6 = 110) (6 = 110) ---> 111110110
1000 ---> ??? ---> 1111101000
However, my problem is that I want to do this look up table method for odd bases, like base 10. I know that I could write the algorithm like atoi does and do a bunch of multiplies and adds, but for this specific problem I'm trying to see if I can do it with a look up table. It's definitely not so obvious with base 10, though. I was curious if anyone had any clever way to figure out how to generate a generic look up table for Base X -> Base 2. I know that for base 10, you can't just give it one digit at a time, so the solution would likely have to lookup a group of digits at a time.
I am aware of the multiply and add solution but since these are arbitrary length numbers, the multiply and add operations are not free so I'd like to avoid them, if at all possible.
You will have to use a look up table with an input width of m base b symbols returning n bits so that
n = log2(b) * m
for positive integers b, n and m. So if b is not a power of two, there will be no (simple) look up table solution.
I do not think that there is a solution. The following example with base 10 illustrates why.
65536 = 1 0000 0000 0000 0000
Changing the last digit from 6 to 5 will flip all bits.
65535 = 0 1111 1111 1111 1111
And almost the same will hold if you process the input starting from the end. Changing the first digit from 6 to 5 flips a significant number of bits.
55535 = 0 1101 1000 1111 0000
This is not possible in bases that aren't powers of two to convert to base-2. The reason that it is possible for base 8 (and 16) is that the way the conversion works is following:
octal ABC = 8^2*A + 8^1*B + 8^0*C (decimal)
= 0b10000000*A + 0b1000*B + C (binary)
so if you have the lookup table of A = (0b000 to 0b111), then the multiplication is always by 1 and some trailing zeros, so the multiplication is simple (just shifting left).
However, consider the 'odd' base of 10. When you look at the powers of 10:
10^1 = 0b1010
10^2 = 0b1100100
10^3 = 0b1111101000
10^4 = 0b10011100010000
..etc
You'll notice that the multiplication never gets simple, so you can't have any lookup tables and do bitshifts and ors, no matter how big you group them. It will always overlap. The best you can do is have a lookup table of the form: (a,b) where a is the digit position, and b is the digit (0..9). Then, you are only reduced to adding n numbers, rather than multiplying and adding n numbers (plus the cost of the memory of the lookup table)
How big are the strings? You can potentially convert the multiply-and-add to a lookup-and-add by doing something like this:
Store the numbers 0-9, 10, 20, 30, 40, ... 90, 100, 200, ... 900, 1000, 2000, ... , 9000, 10000, ... in the target base in a table.
For each character starting with the rightmost, index appropriately into the table and add it to a running result.
Of course I'm not sure how well this will actually perform, but it's a thought.
The algorithm is quite simple. Language agnostic would be:
total = 0
base <- input_base
for each character in input:
total <- total*base + number(char)
In C++:
// Helper to convert a digit to a number
unsigned int number( char ch )
{
if ( ch >= '0' && ch <= '9' ) return ch-'0';
ch = toupper(ch);
if ( ch >= 'A' && ch <= 'F' ) return 10 + (ch-'A');
}
unsigned int parse( std::string const & input, unsigned int base )
{
unsigned int total = 0;
for ( int i = 0; i < input.size(); ++i )
{
total = total*base + number(input[i]);
}
return total;
}
Of course, you should take care of possible errors (incoherent input: base 2 and input string 'af12') or any other exceptional condition.
Start with a running count of 0.
For each character in the string (reading left to right)
Multiply count by base.
Convert character to int value (0 through base)
Add character value to running count.
How accurate do you need to be?
If you're looking for perfection, then multiply-and-add is really your only recourse. And I'd be very surprised if it's the slowest part of your application.
If order-of-magnitude is good enough, use a lookup table to find the closest power of 2.
Example 1: 1234, closest power of 2 is 1024.
Example 2: 98765, closest is 65536
You could also drive this by counting the number of digits, and multiplying the appropriate power of 2 by the leftmost digit. This can be implemented as a left-shift:
Example 3: 98765 has 5 digits, closest power of 2 to 10000 is 8192 (2^13), so result is 9 << 13
I wrote this before your clarifying comment so it probably isn't quite is applicable. I'm not sure if a lookup table approach is possible or not. If you really don't need arbitrary precision, then take advantage of the runtime.
If a C/C++ solution is acceptable, I believe that the following is what you are looking for is something like the following. It probably contains bugs in edge cases, but it does compile and work as expected at least for positive numbers. Making it really work is an exercise for the reader.
/*
* NAME
* convert_num - convert a numerical string (str) of base (b) to
* a printable binary representation
* SYNOPSIS
* int convert_num(char const* s, int b, char** o)
* DESCRIPTION
* Generates a printable binary representation of an input number
* from an arbitrary base. The input number is passed as the ASCII
* character string `s'. The input string consists of characters
* from the ASCII character set {'0'..'9','A'..('A'+b-10)} where
* letter characters may be in either upper or lower case.
* RETURNS
* The number of characters from the input string `s' which were
* consumed by this operation. The output string is placed into
* newly allocated storage which is pointed to by `*o' upon successful
* completion. An error is signalled by returning `-1'.
*/
int
convert_num(char const *str, int b, char **out)
{
int rc = -1;
char *endp = NULL;
char *outp = NULL;
unsigned long num = strtoul(str, &endp, b);
if (endp != str) { /* then we have some numbers */
int numdig = -1;
rc = (endp - str); /* we have this many base `b' digits! */
frexp((double)num, &numdig); /* we need this many base 2 digits */
if ((outp=malloc(numdig+1)) == NULL) {
return -1;
}
*out = outp; /* return the buffer */
outp += numdig; /* make sure it is NUL terminated */
*outp-- = '\0';
while (numdig-- != 0) { /* fill it in from LSb to MSb */
*outp-- = ((num & 1) ? '1' : '0');
num >>= 1;
}
}
return rc;
}

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