## Feature #8700

### Integer#bitsize (actually Fixnum#bitsize and Bignum#bitsize)

**Description**

How about adding Integer#bitsize (actually Fixnum#bitsize and Bignum#bitsize)?

Integer#bitsize returns the position of the most significant bit in the absolute value.

(The position of the least significant bit is 1.)

It returns 0 if no bit set (i.e. the value 0).

Mathematically, n.bitsize is ceil(log2(abs(n)+1)).

Sometimes we want to know the size of a integer.

Determine the size of an integer in some format.

Although there are various formats, bitsize is a key property to determine the result size.

Several examples:- If a format is 4 bytes for absolute value, it overflows if 32 <= n.bitsize.
- If a format is 4 bytes for sign bit with absolute value, it overflows if 31 <= n.bitsize.
- If a format is 4 bytes for 2's complement format, it overflow if 31 <= n.bitsize && n != -2**31.
- BER-compressed integer needs (n.bitsize+6)/7 bytes when n > 0. BER-compressed integer is an example of VLQ. http://en.wikipedia.org/wiki/Variable-length_quantity
- Elias gamma coding needs 2*n.bitsize-1 bits. https://en.wikipedia.org/wiki/Elias_gamma_coding
- Elias delta coding needs 2*n.bitsize.bitsize+n.bitsize-2 bits. https://en.wikipedia.org/wiki/Elias_delta_coding

bitsize may be used to estimate the time or space cost of an algorithm.

For example, the result size of integer multiplication, x*y, is x.bitsize + y.bitsize.

The number of comparisons of binary search is sorted_array.length.bitsize, etc.

This is because n.bitsize is an approximation of log2(abs(n)).

So Math.log2 can be used for this purpose too.

However bitsize may be preferable if floating point error is not desirable.

There are several software which has similar feature.

Python 3.1 has int.bit_length().

http://docs.python.org/dev/library/stdtypes.html

http://docs.python.org/3.1/whatsnew/3.1.html

http://bugs.python.org/issue3439Java java.math.BigInteger has bitLength() method.

http://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html#bitLength()Mathematica has BitLength.

http://reference.wolfram.com/mathematica/ref/BitLength.htmlGMP has mpz_sizeinbase(n, base).

http://gmplib.org/manual/Miscellaneous-Integer-Functions.htmlNetBSD 5.0 has ilog2().

http://netbsd.gw.com/cgi-bin/man-cgi?ilog2++NetBSD-6.0

I think there are two concerns for this issue.

* method name

* behavior for zero and negative number

I named the method as bitsize, mainly because

there is Fixnum#size and Bignum#size.

However I'm open for other names such as:

* bitlength

* numbits

* ilog2

* maxbit

Some names may suggest different behavior, though.

The behavior for zero and negative number is not trivial.

Python adopts ceil(log2(abs(n)+1)) but

Java and Mathematica adopts ceil(log2(n < 0 ? -n : n+1)).

The difference is absolute number v.s. 2's complement number.

Some people may prefer ilog2, which name suggests ilog2(0) raise an error.

I choose ceil(log2(abs(n)+1)). (i.e. absolute number, same as Python).

I think absolute number is easier to understand than 2's complement for many people.

I attached the implementation as bitsize.patch.

The patch implements both Bignum#bitsize and Fixnum#bitsize in bignum.c.

It is because Fixnum#bitsize uses bitsize macro and it is defined in bignum.c.

Maybe, the macro should be moved to internal.h and the implementation of

Fixnum#bitsize should be moved to numeric.c.

Any comments?

### Associated revisions

- bignum.c (rb_big_bit_length): New method. (rb_fix_bit_length): Ditto. [Feature #8700]

- bignum.c (rb_big_bit_length): New method. (rb_fix_bit_length): Ditto. [Feature #8700]

- bignum.c (rb_big_bit_length): New method. (rb_fix_bit_length): Ditto. [Feature #8700]

### History

#### #1 [ruby-core:56249] Updated by Charles Nutter over 3 years ago

+1.

"bitlength" seems more in line with other platforms. Also, Fixnum#size represents octet size, not bit size.

For zero, bitlength == 0, always.

For negative numbers...we either decide to always return the bit length for a specific representation (two's complement or something else) or we provide a way to also query the representation. I prefer the former.

#### #2 [ruby-core:56250] Updated by Matthew Kerwin over 3 years ago

headius (Charles Nutter) wrote:

+1.

"bitlength" seems more in line with other platforms. Also, Fixnum#size represents octet size, not bit size.

For zero, bitlength == 0, always.

For negative numbers...we either decide to always return the bit length for a specific representation (two's complement or something else) or we provide a way to also query the representation. I prefer the former.

Alternatively, although no one else does it, the bitlength of a negative number could be negative the bitlength of the absolute value. E.g -1.bitlength==-1, -7.bitlength==-3

#### #3 [ruby-core:56303] Updated by Akira Tanaka over 3 years ago

**File**bitlength.patch View added

akr (Akira Tanaka) wrote:

There are several software which has similar feature.

Python 3.1 has int.bit_length().

http://docs.python.org/dev/library/stdtypes.html

http://docs.python.org/3.1/whatsnew/3.1.html

http://bugs.python.org/issue3439Java java.math.BigInteger has bitLength() method.

http://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html#bitLength()Mathematica has BitLength.

http://reference.wolfram.com/mathematica/ref/BitLength.htmlGMP has mpz_sizeinbase(n, base).

http://gmplib.org/manual/Miscellaneous-Integer-Functions.htmlNetBSD 5.0 has ilog2().

http://netbsd.gw.com/cgi-bin/man-cgi?ilog2++NetBSD-6.0

I look out more.

Go has BitLen.

http://golang.org/pkg/math/big/#Int.BitLenOpenSSL has BN_num_bits.

http://www.openssl.org/docs/crypto/BN_num_bytes.htmlLibTomMath has mp_count_bits.

http://libtom.org/gcrypt has gcry_mpi_get_nbits.

http://www.gnupg.org/documentation/manuals/gcrypt/Bit-manipulations.htmlScala has bitLength.

http://www.scala-lang.org/api/current/index.html#scala.math.BigIntCommonLisp has integer-length.

http://www.lispworks.com/documentation/HyperSpec/Body/f_intege.htmCLN has integer_length.

http://www.ginac.de/CLN/cln.html#Exact-numbers

They behaves on negative values for absolute value or two's complement as follows.

absolute value, ceil(log2(abs(n)+1)):

Python (bit_length)

Go (BitLen)

GMP (mpz_sizeinbase)

OpenSSL (BN_num_bits)

LibTomMath (mp_count_bits)

gcrypt (gcry_mpi_get_nbits)

two's complement, ceil(log2(n < 0 ? -n : n+1)):

Java (bitLength)

Scala (bitLength)

Mathematica (BitLength)

CommonLisp (integer-length)

CLN (integer_length)

It seems "bit length" is more common than other names.

So I changed the method name to "bitlength".

Both absolute value and two's complement are common.

I think it's difficult to say one is better.

(My patch's bitlength is absolute value.)

How do you think, matz?

#### #4 [ruby-core:56385] Updated by Akira Tanaka over 3 years ago

**File**bit_length.patch View added

I updated the patch because I change the method name to bit_length.

(I added an under score.)

#### #5 [ruby-core:56655] Updated by Akira Tanaka over 3 years ago

akr (Akira Tanaka) wrote:

- bitsize may be used to estimate the time or space cost of an algorithm. For example, the result size of integer multiplication, x*y, is x.bitsize + y.bitsize. The number of comparisons of binary search is sorted_array.length.bitsize, etc. This is because n.bitsize is an approximation of log2(abs(n)). So Math.log2 can be used for this purpose too. However bitsize may be preferable if floating point error is not desirable.

I found another reason bit_length is preferable over Math.log2.

Math.log2(n) returns Infinity when n is not representable as double.

% ./ruby -e 'n = 3**4; 10.times { n = n * n; p [n.class, n.size*8, n.bit_length, Math.log2(n)] }'

[Fixnum, 64, 13, 12.679700005769249]

[Fixnum, 64, 26, 25.359400011538497]

[Fixnum, 64, 51, 50.718800023076994]

[Bignum, 104, 102, 101.43760004615399]

[Bignum, 208, 203, 202.87520009230798]

[Bignum, 408, 406, 405.75040018461596]

[Bignum, 816, 812, 811.5008003692319]

[Bignum, 1624, 1624, Infinity]

[Bignum, 3248, 3247, Infinity]

[Bignum, 6496, 6493, Infinity]

#### #6 [ruby-core:56920] Updated by Yukihiro Matsumoto over 3 years ago

Accepted. It should be work as 2's complement for negative numbers.

Matz.

#### #7 Updated by Akira Tanaka over 3 years ago

**% Done**changed from*0*to*100***Status**changed from*Open*to*Closed*

#### #8 [ruby-core:57338] Updated by Fuad Saud over 3 years ago

I like it. Pretty neat for low level bit brushing stuff.

--

Fuad Saud

Sent with Sparrow (http://www.sparrowmailapp.com/?sig)

On Saturday, August 31, 2013 at 3:47 AM, matz (Yukihiro Matsumoto) wrote:

Issue #8700 has been updated by matz (Yukihiro Matsumoto).

Accepted. It should be work as 2's complement for negative numbers.

Matz.

Feature #8700: Integer#bitsize (actually Fixnum#bitsize and Bignum#bitsize)

https://bugs.ruby-lang.org/issues/8700#change-41474Author: akr (Akira Tanaka)

Status: Open

Priority: Normal

Assignee:

Category:

Target version:How about adding Integer#bitsize (actually Fixnum#bitsize and Bignum#bitsize)?

Integer#bitsize returns the position of the most significant bit in the absolute value.

(The position of the least significant bit is 1.)

It returns 0 if no bit set (i.e. the value 0).Mathematically, n.bitsize is ceil(log2(abs(n)+1)).

Sometimes we want to know the size of a integer.

- Determine the size of an integer in some format. Although there are various formats, bitsize is a key property to determine the result size. Several examples:
- If a format is 4 bytes for absolute value, it overflows if 32 <= n.bitsize.
- If a format is 4 bytes for sign bit with absolute value, it overflows if 31 <= n.bitsize.
- If a format is 4 bytes for 2's complement format, it overflow if 31 <= n.bitsize && n != -2**31.
- BER-compressed integer needs (n.bitsize+6)/7 bytes when n > 0. BER-compressed integer is an example of VLQ. http://en.wikipedia.org/wiki/Variable-length_quantity
- Elias gamma coding needs 2*n.bitsize-1 bits. https://en.wikipedia.org/wiki/Elias_gamma_coding
Elias delta coding needs 2*n.bitsize.bitsize+n.bitsize-2 bits.

https://en.wikipedia.org/wiki/Elias_delta_codingbitsize may be used to estimate the time or space cost of an algorithm.

For example, the result size of integer multiplication, x*y, is x.bitsize + y.bitsize.

The number of comparisons of binary search is sorted_array.length.bitsize, etc.

This is because n.bitsize is an approximation of log2(abs(n)).

So Math.log2 can be used for this purpose too.

However bitsize may be preferable if floating point error is not desirable.There are several software which has similar feature.

Python 3.1 has int.bit_length().

http://docs.python.org/dev/library/stdtypes.html

http://docs.python.org/3.1/whatsnew/3.1.html

http://bugs.python.org/issue3439Java java.math.BigInteger has bitLength() method.

http://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html#bitLength()Mathematica has BitLength.

http://reference.wolfram.com/mathematica/ref/BitLength.htmlGMP has mpz_sizeinbase(n, base).

http://gmplib.org/manual/Miscellaneous-Integer-Functions.htmlNetBSD 5.0 has ilog2().

http://netbsd.gw.com/cgi-bin/man-cgi?ilog2++NetBSD-6.0I think there are two concerns for this issue.

* method name

* behavior for zero and negative numberI named the method as bitsize, mainly because

there is Fixnum#size and Bignum#size.

However I'm open for other names such as:

* bitlength

* numbits

* ilog2

* maxbit

Some names may suggest different behavior, though.The behavior for zero and negative number is not trivial.

Python adopts ceil(log2(abs(n)+1)) but

Java and Mathematica adopts ceil(log2(n < 0 ? -n : n+1)).

The difference is absolute number v.s. 2's complement number.Some people may prefer ilog2, which name suggests ilog2(0) raise an error.

I choose ceil(log2(abs(n)+1)). (i.e. absolute number, same as Python).

I think absolute number is easier to understand than 2's complement for many people.I attached the implementation as bitsize.patch.

The patch implements both Bignum#bitsize and Fixnum#bitsize in bignum.c.

It is because Fixnum#bitsize uses bitsize macro and it is defined in bignum.c.

Maybe, the macro should be moved to internal.h and the implementation of

Fixnum#bitsize should be moved to numeric.c.Any comments?