Trying to understand an inline function - c

I am studying the following function:
inline xint dtally(xint x)
{
xint t = 0;
while (x) t += 1 << ((x % 10) * 6), x /= 10;
return t;
}
I just want to know what makes this feature i.e. which computes and stored in the variable t.

This counts the number of base 10 digits in the number x in t, separated by 6-width bit fields.
Note that each shift length is a multiple of 6. So if a digit is 0 the shift is 0, if the digit is 1 the shift is 6, if the digit is 9 the shift is 54, and so forth.
The reason 6 is used I think is so it fits under 64 bits.

Related

Problems about check a integer is zero or negative with only operator in C?

/*
* isPower2 - returns 1 if x is a power of 2, and 0 otherwise
* Examples: isPower2(5) = 0, isPower2(8) = 1, isPower2(0) = 0
* Note that no negative number is a power of 2.
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 4
*/
int isPower2(int x) {
/*
* Variable a checks if x is power of 2, x and x - 1 won't have a 1
* in the same place if it's power of 2. Variable b checks if x is
* negative or zero. Use & to combine !a and b to complete the function.
*/
int a = x &(x+(~1+1));
int b = ((x+(~1+1))>> 31)+1;
return (!a)&b;
}
Hello every one, I am self-learning a course called CSE351 form Washton University and am finishing the lab1 about data manipulation in C. As you
can see about this question, I need to use the variable b to tell whether or not
the int x is zero.
And then I think that for zero or negative, if you minus one and then right shift 31 bits, adding one, you will get zero if the int is 0, and 1 if it is positive.
But however, my code didn't work, but I found a line of code works.
int b = ((!(x >> 31)) & (~(!x)));
I am really confused why my code don't work, can somebody tell me why?
Edit: Sorry, I didn't mention the environment of this lab is based on int with 32 bits and 2's complement for negative.
Several things to note (in your code):
first, (~1 + 1) is the same as ~0, and the same as -1 (in two's complement). Simpler, right?
x + (~0) is the same as x - 1. Simpler, right?
x & (x - 1) is 1 all the bits that don't change and are 1, when x is decremented. I think what you pretend here is to write x ^ (x - 1) that is, the set of bits that carry to the next on a decrement. This is the bits that change in a decrement. It happens that all bits change iff the number is a power of two. In case you want the bits that don't change, instead of using ^, just use & (bits that are 1 and don't change on a decrement which must be the empty set in case of a power of two ---we have to complement the result, as this boolean gives the opposite) This expression could be the result to get a power of two, if you consider the special case of 0 that is returned as a power of two. As with negatives, and 0, the logarithm does not exist, so we can simply say if (x <= 0) return 0; else return !(x & (x - 1)); (THIS CAN BE THE REQUESTED SOLUTION) or more compact return x <= 0 ? 0 : !(x&(x-1));.
~a as a consequence is _all the bits that do change OR are 0 when x is decremented. I'm lost completely here on what you pretend. I think you want to get if x <= 0 but that's so easy to write in C, instead of the complications you show.
So, your intentions (I guess) is to use the number of 1 bits that don't change on a decrement, because all bits do change for powers of two. Then, a possible implementation should be:
#include <stdio.h>
/*
* isPower2 - returns 1 if x is a power of 2, and 0 otherwise
* Examples: isPower2(5) = 0, isPower2(8) = 1, isPower2(0) = 0
* Note that no negative number is a power of 2. (and zero also, there's no logarithm of zero)
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 4
*/
int isPower2(int x) {
return x <= 0
? 0
: !(x&(x-1));
}
/* please, always post complete and verifiable code, with header files,
* and the like, so we can test it without having to first modify it.
*/
int main()
{
for (;;) {
int a;
scanf("%d", &a);
printf("isPower2(a=%d) => %d\n", a, isPower2(a));
}
}
NOTE
Anyway, I don't have a clear idea of the result you want to get, as you entitle the question as Problems about check a integer is zero or negative... and then you show partial code (see How to create a Minimal, Complete, and Verifiable example) about how to detect if some given integer is a power of two but then, you show then some strange code to check if a number is negative. It suffices to do:
if (x <= 0) do_bla_bla();
and this doesn't produce undefined behaviour with 31 bit right shifts.
NOTE
if you need to use only the operators in the list, just change <= by the following:
#define SIGNBIT (~(~0>>1)) /* ALL ONES, SHIFTED ONE BIT RIGHT AND COMPLEMENTED */
return
x & SIGNBIT /* sign bit on, negative number */
|| !x /* OR x == 0 */
? 0
: !(x&(x-1));
The final code is:
#include <stdio.h>
/*
* isPower2 - returns 1 if x is a power of 2, and 0 otherwise
* Examples: isPower2(5) = 0, isPower2(8) = 1, isPower2(0) = 0
* Note that no negative number is a power of 2. (and zero also, there's no logarithm of zero)
* Legal ops: ! ~ & ^ | + << >>
* Max ops: 20
* Rating: 4
*/
#define SIGNBIT (~(~0>>1))
int isPower2(int x) {
return x & SIGNBIT || !x ? 0 : !(x&(x-1));
/* if anybody tells you are using ? and || operators, just write:
* if (x & SIGNBIT) return 0;
* if (!x) return 0;
* return !(x&(x-1));
*/
}
/* please, always post complete and verifiable code, with header files,
* and the like, so we can test it without having to first modify it.
*/
int main()
{
for (;;) {
int a;
scanf("%d", &a);
printf("isPower2(a=%d) => %d\n", a, isPower2(a));
}
}

How can i change mod with bitwise AND [duplicate]

Is it possible to divide an unsigned integer by 10 by using pure bit shifts, addition, subtraction and maybe multiply? Using a processor with very limited resources and slow divide.
Editor's note: this is not actually what compilers do, and gives the wrong answer for large positive integers ending with 9, starting with div10(1073741829) = 107374183 not 107374182. It is exact for smaller inputs, though, which may be sufficient for some uses.
Compilers (including MSVC) do use fixed-point multiplicative inverses for constant divisors, but they use a different magic constant and shift on the high-half result to get an exact result for all possible inputs, matching what the C abstract machine requires. See Granlund & Montgomery's paper on the algorithm.
See Why does GCC use multiplication by a strange number in implementing integer division? for examples of the actual x86 asm gcc, clang, MSVC, ICC, and other modern compilers make.
This is a fast approximation that's inexact for large inputs
It's even faster than the exact division via multiply + right-shift that compilers use.
You can use the high half of a multiply result for divisions by small integral constants. Assume a 32-bit machine (code can be adjusted accordingly):
int32_t div10(int32_t dividend)
{
int64_t invDivisor = 0x1999999A;
return (int32_t) ((invDivisor * dividend) >> 32);
}
What's going here is that we're multiplying by a close approximation of 1/10 * 2^32 and then removing the 2^32. This approach can be adapted to different divisors and different bit widths.
This works great for the ia32 architecture, since its IMUL instruction will put the 64-bit product into edx:eax, and the edx value will be the wanted value. Viz (assuming dividend is passed in eax and quotient returned in eax)
div10 proc
mov edx,1999999Ah ; load 1/10 * 2^32
imul eax ; edx:eax = dividend / 10 * 2 ^32
mov eax,edx ; eax = dividend / 10
ret
endp
Even on a machine with a slow multiply instruction, this will be faster than a software or even hardware divide.
Though the answers given so far match the actual question, they do not match the title. So here's a solution heavily inspired by Hacker's Delight that really uses only bit shifts.
unsigned divu10(unsigned n) {
unsigned q, r;
q = (n >> 1) + (n >> 2);
q = q + (q >> 4);
q = q + (q >> 8);
q = q + (q >> 16);
q = q >> 3;
r = n - (((q << 2) + q) << 1);
return q + (r > 9);
}
I think that this is the best solution for architectures that lack a multiply instruction.
Of course you can if you can live with some loss in precision. If you know the value range of your input values you can come up with a bit shift and a multiplication which is exact.
Some examples how you can divide by 10, 60, ... like it is described in this blog to format time the fastest way possible.
temp = (ms * 205) >> 11; // 205/2048 is nearly the same as /10
to expand Alois's answer a bit, we can expand the suggested y = (x * 205) >> 11 for a few more multiples/shifts:
y = (ms * 1) >> 3 // first error 8
y = (ms * 2) >> 4 // 8
y = (ms * 4) >> 5 // 8
y = (ms * 7) >> 6 // 19
y = (ms * 13) >> 7 // 69
y = (ms * 26) >> 8 // 69
y = (ms * 52) >> 9 // 69
y = (ms * 103) >> 10 // 179
y = (ms * 205) >> 11 // 1029
y = (ms * 410) >> 12 // 1029
y = (ms * 820) >> 13 // 1029
y = (ms * 1639) >> 14 // 2739
y = (ms * 3277) >> 15 // 16389
y = (ms * 6554) >> 16 // 16389
y = (ms * 13108) >> 17 // 16389
y = (ms * 26215) >> 18 // 43699
y = (ms * 52429) >> 19 // 262149
y = (ms * 104858) >> 20 // 262149
y = (ms * 209716) >> 21 // 262149
y = (ms * 419431) >> 22 // 699059
y = (ms * 838861) >> 23 // 4194309
y = (ms * 1677722) >> 24 // 4194309
y = (ms * 3355444) >> 25 // 4194309
y = (ms * 6710887) >> 26 // 11184819
y = (ms * 13421773) >> 27 // 67108869
each line is a single, independent, calculation, and you'll see your first "error"/incorrect result at the value shown in the comment. you're generally better off taking the smallest shift for a given error value as this will minimise the extra bits needed to store the intermediate value in the calculation, e.g. (x * 13) >> 7 is "better" than (x * 52) >> 9 as it needs two less bits of overhead, while both start to give wrong answers above 68.
if you want to calculate more of these, the following (Python) code can be used:
def mul_from_shift(shift):
mid = 2**shift + 5.
return int(round(mid / 10.))
and I did the obvious thing for calculating when this approximation starts to go wrong with:
def first_err(mul, shift):
i = 1
while True:
y = (i * mul) >> shift
if y != i // 10:
return i
i += 1
(note that // is used for "integer" division, i.e. it truncates/rounds towards zero)
the reason for the "3/1" pattern in errors (i.e. 8 repeats 3 times followed by 9) seems to be due to the change in bases, i.e. log2(10) is ~3.32. if we plot the errors we get the following:
where the relative error is given by: mul_from_shift(shift) / (1<<shift) - 0.1
Considering Kuba Ober’s response, there is another one in the same vein.
It uses iterative approximation of the result, but I wouldn’t expect any surprising performances.
Let say we have to find x where x = v / 10.
We’ll use the inverse operation v = x * 10 because it has the nice property that when x = a + b, then x * 10 = a * 10 + b * 10.
Let use x as variable holding the best approximation of result so far. When the search ends, x Will hold the result. We’ll set each bit b of x from the most significant to the less significant, one by one, end compare (x + b) * 10 with v. If its smaller or equal to v, then the bit b is set in x. To test the next bit, we simply shift b one position to the right (divide by two).
We can avoid the multiplication by 10 by holding x * 10 and b * 10 in other variables.
This yields the following algorithm to divide v by 10.
uin16_t x = 0, x10 = 0, b = 0x1000, b10 = 0xA000;
while (b != 0) {
uint16_t t = x10 + b10;
if (t <= v) {
x10 = t;
x |= b;
}
b10 >>= 1;
b >>= 1;
}
// x = v / 10
Edit: to get the algorithm of Kuba Ober which avoids the need of variable x10 , we can subtract b10 from v and v10 instead. In this case x10 isn’t needed anymore. The algorithm becomes
uin16_t x = 0, b = 0x1000, b10 = 0xA000;
while (b != 0) {
if (b10 <= v) {
v -= b10;
x |= b;
}
b10 >>= 1;
b >>= 1;
}
// x = v / 10
The loop may be unwinded and the different values of b and b10 may be precomputed as constants.
On architectures that can only shift one place at a time, a series of explicit comparisons against decreasing powers of two multiplied by 10 might work better than the solution form hacker's delight. Assuming a 16 bit dividend:
uint16_t div10(uint16_t dividend) {
uint16_t quotient = 0;
#define div10_step(n) \
do { if (dividend >= (n*10)) { quotient += n; dividend -= n*10; } } while (0)
div10_step(0x1000);
div10_step(0x0800);
div10_step(0x0400);
div10_step(0x0200);
div10_step(0x0100);
div10_step(0x0080);
div10_step(0x0040);
div10_step(0x0020);
div10_step(0x0010);
div10_step(0x0008);
div10_step(0x0004);
div10_step(0x0002);
div10_step(0x0001);
#undef div10_step
if (dividend >= 5) ++quotient; // round the result (optional)
return quotient;
}
Well division is subtraction, so yes. Shift right by 1 (divide by 2). Now subtract 5 from the result, counting the number of times you do the subtraction until the value is less than 5. The result is number of subtractions you did. Oh, and dividing is probably going to be faster.
A hybrid strategy of shift right then divide by 5 using the normal division might get you a performance improvement if the logic in the divider doesn't already do this for you.
I've designed a new method in AVR assembly, with lsr/ror and sub/sbc only. It divides by 8, then sutracts the number divided by 64 and 128, then subtracts the 1,024th and the 2,048th, and so on and so on. Works very reliable (includes exact rounding) and quick (370 microseconds at 1 MHz).
The source code is here for 16-bit-numbers:
http://www.avr-asm-tutorial.net/avr_en/beginner/DIV10/div10_16rd.asm
The page that comments this source code is here:
http://www.avr-asm-tutorial.net/avr_en/beginner/DIV10/DIV10.html
I hope that it helps, even though the question is ten years old.
brgs, gsc
elemakil's comments' code can be found here: https://doc.lagout.org/security/Hackers%20Delight.pdf
page 233. "Unsigned divide by 10 [and 11.]"

Bitwise bit shifting and why this solution works

I've been doing code fights on codefights.com and I came upon this problem below. I have figured out the problem on my own, but when i researched other peoples solutions I found one that was much shorter than mine, but I cant seem to understand why they did what they did.
The question goes:
You are given an array of up to four non-negative integers, each less than 256.
Your task is to pack these integers into one number M in the following way:
The first element of the array occupies the first 8 bits of M;
The second element occupies next 8 bits, and so on.
Return the obtained integer M.
Note: the phrase "first bits of M" refers to the least significant bits of M - the right-most bits of an integer. For further clarification see the following example.
Example
For a = [24, 85, 0], the output should be
arrayPacking(a) = 21784.
An array [24, 85, 0] looks like [00011000, 01010101, 00000000] in binary.
After packing these into one number we get 00000000 01010101 00011000 (spaces are placed for convenience), which equals to 21784.
Their answer was:
func arrayPacking(a []int) (sum int) {
for i := range a {
sum += a[len(a) - i - 1] << uint((len(a) - i - 1) * 8)
}
return
}
How is this code returning the right amount of shift just by using 0, 8, 16, etc. intervals? I've been researching bitwise a lot lately, but I still can't seem to reason why this works.
First, write the solution in Go. We convert little-endian, base-256 digits to a base-2 (binary) number. Shifting left by 8 bits multiplies by 256.
package main
import (
"fmt"
)
func pack(digits []int) (number int) {
// digits are little-endian, base-256 (1 << 8 = 256)
for i, digit := range digits {
number += digit << uint(i*8)
}
return number
}
func main() {
a := []int{24, 85, 0}
m := pack(a)
fmt.Println(m)
}
Playground: https://play.golang.org/p/oo_n7CiAHwG
Output:
21784
Now you should be able to figure out their ugly looking answer:
func arrayPacking(a []int) (sum int) {
for i := range a {
sum += a[len(a) - i - 1] << uint((len(a) - i - 1) * 8)
}
return
}
the bitshifting by multiples of 8 is the same as muliplying by multiples of 256, e.g. x << 0*8 == x * 256⁰, x << 1*8 == x * 256¹, x << 2*8 == x * 256² etc., so the code can be rewritten like this, using math.Pow:
func arrayPacking(a []int) (sum int) {
for i := range a {
sum += a[len(a) - i - 1] * int(math.Pow(256, (len(a) - i - 1)))
}
return
}
Or is your question why this sort of packing works?

How to get position of right most set bit in C

int a = 12;
for eg: binary of 12 is 1100 so answer should be 3 as 3rd bit from right is set.
I want the position of the last most set bit of a. Can anyone tell me how can I do so.
NOTE : I want position only, here I don't want to set or reset the bit. So it is not duplicate of any question on stackoverflow.
This answer Unset the rightmost set bit tells both how to get and unset rightmost set bit for an unsigned integer or signed integer represented as two's complement.
get rightmost set bit,
x & -x
// or
x & (~x + 1)
unset rightmost set bit,
x &= x - 1
// or
x -= x & -x // rhs is rightmost set bit
why it works
x: leading bits 1 all 0
~x: reversed leading bits 0 all 1
~x + 1 or -x: reversed leading bits 1 all 0
x & -x: all 0 1 all 0
eg, let x = 112, and choose 8-bit for simplicity, though the idea is same for all size of integer.
// example for get rightmost set bit
x: 01110000
~x: 10001111
-x or ~x + 1: 10010000
x & -x: 00010000
// example for unset rightmost set bit
x: 01110000
x-1: 01101111
x & (x-1): 01100000
Finding the (0-based) index of the least significant set bit is equivalent to counting how many trailing zeros a given integer has. Depending on your compiler there are builtin functions for this, for example gcc and clang support __builtin_ctz.
For MSVC you would need to implement your own version, this answer to a different question shows a solution making use of MSVC intrinsics.
Given that you are looking for the 1-based index, you simply need to add 1 to ctz's result in order to achieve what you want.
int a = 12;
int least_bit = __builtin_ctz(a) + 1; // least_bit = 3
Note that this operation is undefined if a == 0. Furthermore there exist __builtin_ctzl and __builtin_ctzll which you should use if you are working with long and long long instead of int.
One can use the property of 2s-complement here.
Fastest way to find 2s-complement of a number is to get the rightmost set bit and flip everything to the left of it.
For example: consider a 4 bit system
/* Number in binary */
4 = 0100
/* 2s complement of 4 */
complement = 1100
/* which nothing but */
complement == -4
/* Result */
4 & (-4) = 0100
Notice that there is only one set bit and its at rightmost set bit of 4.
Similarly we can generalise this for n.
n&(-n) will contain only one set bit which is actually at the rightmost set bit position of n.
Since there is only one set bit in n&(-n), it is a power of 2.
So finally we can get the bit position by:
log2(n&(-n))+1
The leftmost bit of n can be obtained using the formulae:
n & ~(n-1)
This works because when you calculate (n-1) .. you are actually making all the zeros till the rightmost bit to 1, and the rightmost bit to 0.
Then you take a NOT of it .. which leaves you with the following:
x= ~(bits from the original number) + (rightmost 1 bit) + trailing zeros
Now, if you do (n & x), you get what you need, as the only bit that is 1 in both n and x is the rightmost bit.
Phewwwww .. :sweat_smile:
http://www.catonmat.net/blog/low-level-bit-hacks-you-absolutely-must-know/
helped me understand this.
There is a neat trick in Knuth 7.1.3 where you multiply by a "magic" number (found by a brute-force search) that maps the first few bits of the number to a unique value for each position of the rightmost bit, and then you can use a small lookup table. Here is an implementation of that trick for 32-bit values, adapted from the nlopt library (MIT/expat licensed).
/* Return position (0, 1, ...) of rightmost (least-significant) one bit in n.
*
* This code uses a 32-bit version of algorithm to find the rightmost
* one bit in Knuth, _The Art of Computer Programming_, volume 4A
* (draft fascicle), section 7.1.3, "Bitwise tricks and
* techniques."
*
* Assumes n has a 1 bit, i.e. n != 0
*
*/
static unsigned rightone32(uint32_t n)
{
const uint32_t a = 0x05f66a47; /* magic number, found by brute force */
static const unsigned decode[32] = { 0, 1, 2, 26, 23, 3, 15, 27, 24, 21, 19, 4, 12, 16, 28, 6, 31, 25, 22, 14, 20, 18, 11, 5, 30, 13, 17, 10, 29, 9, 8, 7 };
n = a * (n & (-n));
return decode[n >> 27];
}
Try this
int set_bit = n ^ (n&(n-1));
Explanation:
As noted in this answer, n&(n-1) unsets the last set bit.
So, if we unset the last set bit and xor it with the number; by the nature of the xor operation, the last set bit will become 1 and the rest of the bits will return 0
1- Subtract 1 form number: (a-1)
2- Take it's negation : ~(a-1)
3- Take 'AND' operation with original number:
int last_set_bit = a & ~(a-1)
The reason behind subtraction is, when you take negation it set its last bit 1, so when take 'AND' it gives last set bit.
Check if a & 1 is 0. If so, shift right by one until it's not zero. The number of times you shift is how many bits from the right is the rightmost bit that is set.
You can find the position of rightmost set bit by doing bitwise xor of n and (n&(n-1) )
int pos = n ^ (n&(n-1));
I inherited this one, with a note that it came from HAKMEM (try it out here). It works on both signed and unsigned integers, logical or arithmetic right shift. It's also pretty efficient.
#include <stdio.h>
int rightmost1(int n) {
int pos, temp;
for (pos = 0, temp = ~n & (n - 1); temp > 0; temp >>= 1, ++pos);
return pos;
}
int main()
{
int pos = rightmost1(16);
printf("%d", pos);
}
You must check all 32 bits starting at index 0 and working your way to the left. If you can bitwise-and your a with a one bit at that position and get a non-zero value back, it means the bit is set.
#include <limits.h>
int last_set_pos(int a) {
for (int i = 0; i < sizeof a * CHAR_BIT; ++i) {
if (a & (0x1 << i)) return i;
}
return -1; // a == 0
}
On typical systems int will be 32 bits, but doing sizeof a * CHAR_BIT will get you the right number of bits in a even if it's a different size
Accourding to dbush's solution, Try this:
int rightMostSet(int a){
if (!a) return -1; //means there isn't any 1-bit
int i=0;
while(a&1==0){
i++;
a>>1;
}
return i;
}
return log2(((num-1)^num)+1);
explanation with example: 12 - 1100
num-1 = 11 = 1011
num^ (num-1) = 12^11 = 7 (111)
num^ (num-1))+1 = 8 (1000)
log2(1000) = 3 (answer).
x & ~(x-1) isolates the lowest bit that is one.
int main(int argc, char **argv)
{
int setbit;
unsigned long d;
unsigned long n1;
unsigned long n = 0xFFF7;
double nlog2 = log(2);
while(n)
{
n1 = (unsigned long)n & (unsigned long)(n -1);
d = n - n1;
n = n1;
setbit = log(d) / nlog2;
printf("Set bit: %d\n", setbit);
}
return 0;
}
And the result is as below.
Set bit: 0
Set bit: 1
Set bit: 2
Set bit: 4
Set bit: 5
Set bit: 6
Set bit: 7
Set bit: 8
Set bit: 9
Set bit: 10
Set bit: 11
Set bit: 12
Set bit: 13
Set bit: 14
Set bit: 15
Let x be your integer input.
Bitwise AND by 1.
If it's even ie 0, 0&1 returns you 0.
If it's odd ie 1, 1&1 returns you 1.
if ( (x & 1) == 0) )
{
std::cout << "The rightmost bit is 0 ie even \n";
}
else
{
std::cout<< "The rightmost bit is 1 ie odd \n";
}```
Alright, so number systems is just working with logarithms and exponents. So I'll dive down into an approach that really makes sense to me.
I would prefer you read this because I write there about how I interpret logarithms as.
When you perform the x & -x operation, it gives you the value which has the right most bit as 1 (for example, it can be 0001000 or 0000010. Now according to how I interpret logarithms as, this value of the right most set bit, is the final value after I grow at the rate of 2. Now we are interested in finding the number of digits in this answer because whatever that is, if you subtract 1 from it, that is precisely the bit-count of set bit (bit count begins with 0 here and the digit count begins with 1, so yeah). But the number of digits is precisely the time you expanded for + 1 (in accordance with my logic) or just the formula I mentioned in the previous link. But now, as we don't really need the digits, but need the bit count, and we also don't have to worry about values of bits which potentially can be real (if the number is 65) because the number is always some multiple of 2 (except 1). So if you just take the logarithm of the value x & -x, we get the bit count! I did see an answer before that mentioned this, but diving down to why it really works was something I felt like writing down.
P.S: You could also count the number of digits and then subtract 1 from it to get the bit-count.

How to multiply a given number by 2 without using arithmetic operators in c?

How to multiply a given number by 2 without using arithmetic operators in c language?
Use bit wise << operator:
x = x << 1;
This works for integer and long numbers (not floating point numbers).
It basically shifts the binary contents one position to the left, which is equivalent to multiplying by 2
Left shift.
But why would you want to do that? Leave that kind of optimization to the compiler.
List of operators and plenty of examples on wikipedia.
Just to extend on kgiannakakis post:
The shift operator << works because it shifts at the binary level - effectively in base 2. Just as moving a number by one place to the left in decimal (base 10) is the same as multiplying by 10. For example:
23 (move to left one digit) = 230 = 23 * 10
For the example (using the prefix 0b to represent binary numbers):
3 * 2 = 6
0b11 << 1 = 0b110
Shifting by other numbers is equivalent to multiplying by 2 'n' times, or multiplying by 2 to the nth power (2^n)
3 * 8 = 3 * 2^3 = 24
0b11 * 8 = 0b11 << 3 = 0b11000 (note the trailing zeros)
And an example in decimal to finish it off:
23 (move to left 3 places) = 23 * 1000 = 23 * 10^3 = 23000
Caution: Shifting might not work for signed variables,
int x;
int tmp;
if (x < 0) {
tmp = -x;
tmp = tmp << 1;
x = -tmp;
}
else {
x = x << 1;
}
Just to make sure we are all clear, to do this as everyone has suggested, bitwise shift left (<<)
Every time you shift left, you are multiplying by a factor of two essentially.
int x;
int result;
x = 5;
// result = 10 (multiply by a factor of 2 or 2^1=2)
result = 5<<1;
//result = 20 (multiply by a factor of 4 or 2^2=4)
result = 5<<2;
//result = 40 (multiply by a factor of 8 or 2^3=8)
result = 5<<3;

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