Fixnum's binary representation

[camsight]

Hi, people!

As far as I know, Ruby's Fixnum is 30-bit signed integer.
One bit is used as a flag for whether it's a direct value.
Another bit is used for non-Fixnum direct values.
I wondered how Fixnum#[] works and tested it.

def show_binary(i)
result = ''
32.times do |b|
result = i.to_s + result
if (b % 8 == 7) and (b != 31)
result = " " + result
end
end
puts result + ": " + i.to_s
end

show_binary(1)
show_binary(-1)
show_binary(2 ** 31 - 1)
show_binary((2 ** 31 - 1) * (-1))

Result:

00000000 00000000 00000000 00000001: 1
11111111 11111111 11111111 11111111: -1
01111111 11111111 11111111 11111111: 2147483647
10000000 00000000 00000000 00000001: -2147483647

This is exactly how 32-bit signed integer's binary representations look
like.
My guess is that Fixnum#[] works as if it's 32-bit signed integer.
It's not showing its real binary representation.
Is my guess true?

My another question is that even if (2 ** 31 - 1) is not a Fixnum, the
above code works for it (Actually Bignum#[]).
If the number is bigger than that, [] doesn't work.
Fixnum#[] and Bignum#[] are cleverly hiding the internal facts and are
made to simulate 32-bit signed integers?

Thanks.
Sam

 

[camsight]

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?
I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

Thanks again.

Sam

 

[Robert Klemme]

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?

Well, since Bignums can be arbitrary size, you have to decide. The values
returned by Fixnum#[] and Bignum#[] represent bits of a two complement's
arbitrary size binary number. If you view it from this perspective, you'll
see that there is no single sign bit. Negative numbers have *all* the
higher bits set to 1.

I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

Not at all.

n = -(1<<100) => -1267650600228229401496703205376
200.times{|i| print i, " ", n, "\n"}

0 0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
....
95 0
96 0
97 0
98 0
99 0
100 1
101 1
102 1
103 1
104 1
....
195 1
196 1
197 1
198 1
199 1
=> 200

As you clearly see, the representation is ok.

Btw, you'll notice the same effect with Fixnum#[] - because these methods do
not represent the actual binary representation in mem but try to represent
the general concept of signed binary numbers:

(-1)[100] => 1
(-1)[1<<100]

=> 1

Kind regards

robert

 

[Mark Hubbart]

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?
I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

IIUC, it's not precisely a "sign bit"; it's more like an entire
bit-flip. -1 is zero, bit-flipped. So if you are trying to use
Integer#[] to get determine the sign of a number, the question is
simply: how high do you want to go? integer[512] will correctly
determine sign for numbers in the range of (-(2**512-1)..2**512) (that
is, a 512 bit integer). There no way (that I can think of) to use
Integer#[] to return the correct sign on *any* integer usable in Ruby.

hth,
Mark

 

[Ara.T.Howard]

Hi, people!

As far as I know, Ruby's Fixnum is 30-bit signed integer.
One bit is used as a flag for whether it's a direct value.
Another bit is used for non-Fixnum direct values.
I wondered how Fixnum#[] works and tested it.

def show_binary(i)
result = ''
32.times do |b|
result = i.to_s + result
if (b % 8 == 7) and (b != 31)
result = " " + result
end
end
puts result + ": " + i.to_s
end

show_binary(1)
show_binary(-1)
show_binary(2 ** 31 - 1)
show_binary((2 ** 31 - 1) * (-1))

Result:

00000000 00000000 00000000 00000001: 1
11111111 11111111 11111111 11111111: -1
01111111 11111111 11111111 11111111: 2147483647
10000000 00000000 00000000 00000001: -2147483647

don't deny yourself the joys of printf ;-)

harp:~ > cat a.rb
[ (1), (-1), (2 ** 31 - 1), ((2 ** 31 - 1) * (-1)) ].each{|n| printf "%32.32b\n", n}

harp:~ > ruby a.rb
00000000000000000000000000000001
11111111111111111111111111111111
01111111111111111111111111111111
10000000000000000000000000000001

cheers.

-a
--
===============================================================================
| email :: ara [dot] t [dot] howard [at] noaa [dot] gov
| phone :: 303.497.6469
| renunciation is not getting rid of the things of this world, but accepting
| that they pass away. --aitken roshi
===============================================================================

 

[Phil Tomson]

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?
I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

IIUC, it's not precisely a "sign bit"; it's more like an entire
bit-flip. -1 is zero, bit-flipped.

It's 2's complement, isn't it?


Phil

 

[camsight]

Wow, that's great.
I have to learn more...

Thanks.
Sam

 

[camsight]

Now I understand what you mean.
Thanks a lot!

Sam

 

[Mark Hubbart]

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?
I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

IIUC, it's not precisely a "sign bit"; it's more like an entire
bit-flip. -1 is zero, bit-flipped.

It's 2's complement, isn't it?

(looking it up)

yeah! that's what it is. IANACSM (I am not a CS major) and I still
have terminology to learn. I am woefully ignorant of it, and really
should read some programming theory. When I get the time.

cheers,
Mark

 

[Eric Hodel]

Hi, people!

As far as I know, Ruby's Fixnum is 30-bit signed integer.
One bit is used as a flag for whether it's a direct value.
Another bit is used for non-Fixnum direct values.

My guess is that Fixnum#[] works as if it's 32-bit signed integer.
It's not showing its real binary representation.
Is my guess true?

$ ruby
puts (-10..10).map { |i| "#{i}: #{i.object_id}" }.join("\n")
-5: -9
-4: -7
-3: -5
-2: -3
-1: -1
0: 1
1: 3
2: 5
3: 7
4: 9
5: 11

A Fixnum's object_id is 2N+1 its value, so if you want a Fixnum's
binary representation, use its object_id. (So long as the object_id is
a Fixnum.)

#define FIXNUM_FLAG 0x01
#define INT2FIX(i) ((VALUE)(((long)(i))<<1 | FIXNUM_FLAG))

Also, a Fixnum always has an odd object_id, while any other VALUE has
an even object_id.

 

[Andrew Ballantine]

Guy's this is very neat and it also brings back some memories.

Some years ago I did quite a lot of programming on CDC 6600 & 7600 at the
ULCC. These machines use exactly the same notation. I remember revelling in
having two zeros because I used to use one to mean null (-1) and the other
zero. Yes programming in FORTRAN and writing COMPASS assembler subroutines
when FORTRAN was stumped. Mmm about 1974-1976 I think.

Kind regards,

Andrew Ballantine
----- Original Message -----
From: "Robert Klemme" <[email protected]>
Newsgroups: comp.lang.ruby
To: "ruby-talk ML" <[email protected]>
Sent: Wednesday, May 04, 2005 6:09 PM
Subject: Re: Fixnum's binary representation

Thanks, Robert!

For which numbers do you have problems? I don't see any so far

I mean...
If Bignum#[] is made to simulate 32-bit signed integers, it can't show
numbers with more than 32-bit representation.
Well, positive numbers will be okay.
But what about negative numbers?
When can I expect the sign bit?

Well, since Bignums can be arbitrary size, you have to decide. The values
returned by Fixnum#[] and Bignum#[] represent bits of a two complement's
arbitrary size binary number. If you view it from this perspective, you'll
see that there is no single sign bit. Negative numbers have *all* the
higher bits set to 1.

I assume that numbers beyond 32-bit are not suitable for Bignum#[].
Do you agree?

Not at all.

n = -(1<<100) => -1267650600228229401496703205376
200.times{|i| print i, " ", n, "\n"}

0 0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
....
95 0
96 0
97 0
98 0
99 0
100 1
101 1
102 1
103 1
104 1
....
195 1
196 1
197 1
198 1
199 1
=> 200

As you clearly see, the representation is ok.

Btw, you'll notice the same effect with Fixnum#[] - because these methods do
not represent the actual binary representation in mem but try to represent
the general concept of signed binary numbers:

(-1)[100] => 1
(-1)[1<<100]

=> 1

Kind regards

robert

 

[camsight]

Hmmm... this is very interesting.
Thanks.

Sam