Pascal Sommer - 2 months ago 8

C Question

I came across this code:

`int __min(int a, int b) {`

return ((a)-(((a)-(b))&((b)-(a))>>31));

}

I can imagine that it has something to do with the 2s complement, and that it only works for signed 32 bit integers, but after that I'm lost.

I found this question, but I don't think that the functions are related, or am I wrong?

So I have 2 questions:

- Why does this function work?
- Is there a situation where wouldn't work and this function would, or is this function just overcomplicated for fun?
`(a<b)?a:b`

Answer

This is designed to work for 32 bit signed values. Let's break this down one step at a time.

```
((b)-(a))>>31)
```

The right shift operator essentially takes the highest bit in the 32 bit value, and sign-extends it to the remaining 31 bits. That's how the right shift operator works for signed values.

If `b`

is greater than `a`

, the result of the subtraction will be positive, the highest bit will be 0, and the result of this is 0.

If `b`

is less than `a`

, the result of the subtraction will be negative, the highest bit will be 1, and the result of this is -1. The highest bit gets shifted down to all the remaining bits. All bits in the 32 bit value will be set, which is -1.

You can verify this by yourself by writing a short program that places either a positive or a negative value into a 32 bit `int`

, right-shifts it by 31 bits; then observing that the result will be either 0 or -1. As you know, in two-s complement arithmetic, the value `-1`

has all of its bits set.

```
((a)-(b)) & (0 or -1, as the result of the previous operation).
```

So, if `b`

is less than `a`

, the right hand side value has all bits set, and the result of the bitwise `&`

operator is the left hand side value. or `a-b`

.

If `b`

is greater then `a`

the right hand side value has all bits 0, and the result of the `&`

is 0.

In conclusion:

If `b`

is less than `a`

, the above expression evaluates to:

```
a-(a-b)
or
a-a+b
or
b
```

And if `b`

is greater than `a`

, the result of the expression is

```
a - 0
or
a
```