# Bitwise inversion of Bignum

**URL:** <https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411>\
**Category:** Ruby\
**Created:** [October 24, 2006, 3:49pm UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411 "2006-10-24T15:49:15Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![ianroddis](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/i/22d042/32.png) [@ianroddis](https://www.ruby-forum.com/u/ianroddis)\
**Post date:** [October 24, 2006, 3:49pm UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411/1 "2006-10-24T15:49:15Z")

</div>

A bitwise inversion of a Bignum sometimes yields odd results. As tested  
in 1.8.5:

./ruby -v

ruby 1.8.5 (2006-08-25) [i686-linux]  
./ruby -e 'a= “7fffff00”.hex ; b= “ffffff00”.hex ; printf “%b =\> %b\n”,  
a, ~a ;

printf “%b =\> %b\n”, b, ~b’  
1111111111111111111111100000000 =\> …10000000000000000000000011111111  
11111111111111111111111100000000 =\> …1

In the first case, the ‘…1’ is expected, as per the documentation, but  
annoying. Generally when I need to invert a number, I expect a result of  
the same length as the original. Since ruby number classes are  
inherently variable length I could not rely on the non-significant bits  
even if I wanted to. Is it possible to put in a vote for a Bignum ~  
operation to return a value of the same length as the largest argument?

The second case is just bizzare. Is this a bug?

---

<div class="post-metadata">

**Author:** ![ianroddis](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/i/22d042/32.png) [@ianroddis](https://www.ruby-forum.com/u/ianroddis)\
**Post date:** [October 24, 2006, 4:32pm UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411/2 "2006-10-24T16:32:42Z")

</div>

This seems to be a problem with inverting any 32 bit number. After  
looking at the source, the fix\_rev() function in numeric.c performs a  
shift-right before inverting, causing an overflow in many cases.

---

<div class="post-metadata">

**Author:** ![ianroddis](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/i/22d042/32.png) [@ianroddis](https://www.ruby-forum.com/u/ianroddis)\
**Post date:** [October 26, 2006, 8:35am UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411/3 "2006-10-26T08:35:37Z")

</div>

Hi,

In message “Re: Bitwise inversion of Bignum”  
on Tue, 24 Oct 2006 22:49:24 +0900, Ian Roddis  
[removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) writes:

|A bitwise inversion of a Bignum sometimes yields odd results. As tested  
|in 1.8.5:  
|  
|./ruby -v  
|  
|ruby 1.8.5 (2006-08-25) [i686-linux]  
|./ruby -e ‘a= “7fffff00”.hex ; b= “ffffff00”.hex ; printf “%b =\> %b\n”,  
|a, ~a ;  
|  
|printf “%b =\> %b\n”, b, ~b’  
|1111111111111111111111100000000 =\> …10000000000000000000000011111111  
|11111111111111111111111100000000 =\> …1  
|  
|In the first case, the ‘…1’ is expected, as per the documentation, but  
|annoying.

Both of them are as expected from my view point. What did you expect?

```
						matz.

```

---

<div class="post-metadata">

**Author:** ![ianroddis](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/i/22d042/32.png) [@ianroddis](https://www.ruby-forum.com/u/ianroddis)\
**Post date:** [October 26, 2006, 5:18pm UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411/4 "2006-10-26T17:18:11Z")

</div>

On 10/26/06, Yukihiro M. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote:

> |ruby 1.8.5 (2006-08-25) [i686-linux]  
> Both of them are as expected from my view point. What did you expect?  
> Perhaps I don’t understand:

irb(main):01:0\> sprintf(“%b”, “ffffff00”.hex) =\>  
“11111111111111111111111100000000”

irb(main):02:0\> “ffffff00”.hex =\> 4294967040  
So this is a positive number and the 2’s complement representation  
should have all zeroes in the msb’s.

So shouldn’t  
sprintf(“%b”, ~(“ffffff00”.hex))

give something like:

…100000000000000000000000011111111

What am I missing?

–  
Rick DeNatale

My blog on Ruby  
[http://talklikeaduck.denhaven2.com/](http://talklikeaduck.denhaven2.com/)

---

<div class="post-metadata">

**Author:** ![ianroddis](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/i/22d042/32.png) [@ianroddis](https://www.ruby-forum.com/u/ianroddis)\
**Post date:** [October 26, 2006, 5:48pm UTC](https://www.ruby-forum.com/t/bitwise-inversion-of-bignum/73411/5 "2006-10-26T17:48:15Z")

</div>

Hi,

In message “Re: Bitwise inversion of Bignum”  
on Fri, 27 Oct 2006 00:15:57 +0900, “Rick DeNatale”  
[removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) writes:

|So shouldn’t  
|sprintf(“%b”, ~(“ffffff00”.hex))  
|  
|give something like:  
|  
|…100000000000000000000000011111111  
|  
|What am I missing?

Oh, I was looking at wrong place. It is a bug. I will fix it soon.

```
						matz.

```