Integer#single_bit? (Actually Fixnum#single_bit? and Bignum#single_bit?)
How about a new method Integer#single_bit?
(Actually Fixnum#single_bit? and Bignum#single_bit?)
n.single_bit? returns true for abs(n) is 1, 2, 4, ..., 2**i for some i.
Sometimes we need to test an integer contains only one bit or not.
It can be written as x != 0 && (x.abs & (x.abs-1)) == 0 but it is not
so easy to understand and it needs several Bignum allocations if x is Bignum.
I propose this method mainly because it assists
Integer#bit_length to determine an integer fits in a fixed size
two's complement format.
If Integer#bit_length works for abs(n) as I proposed as [Feature #8700],
-2**m should be tested for two's complement format and
Integer#single_bit? can be used for that without
(If Integer#bit_length works for two's complement number as Java,
Integer#single_bit? can be used to test abs(n).bit_length without Bignum
allocation. Integer#single_bit? is useful anyway.)
Integer#single_bit? has other use cases.
Some algorithms can be simplified if an input is a power of two.
For example, multiplication and division can be a bit shift.
Another example, FFT require input size is a power of two.
I think it can be used for various applications because
powers of two are special numbers for binary computer.
There are several method names I considered.
I feel power_of_two? returns false for negative numbers: (-1).power_of_two? => false.
So I choose single_bit?.
This method should behave for an absolute number
because I want to test -2**m.
I'd like to avoid n.abs.single_bit? because n.abs can allocate
a Bignum object.
I considered Integer#popcount which returns number of one bits in abs(n).
n.single_bit? can be implemented as n.popcount == 1.
I think Integer#popcount is interesting and good to have.
However Integer#single_bit? can be faster because it can return false
when it finds second one bit.
Also, n.popcount may need to allocate a Bignum if n is very big.
(n.bit_length also needs a Bignum allocation in such case, though.)
#3 Updated by Akira Tanaka over 2 years ago
2013/8/5 stomar (Marcus Stollsteimer) email@example.com:
Issue #8738 has been updated by stomar (Marcus Stollsteimer).
Regarding the naming, I find
8.single_bit? # => true
a little strange (that's 4 bits), power_of_2?/power_of_two? seem to be more to the point.
I feel power_of_two? returns false for all negative numbers.
But I want to determine negative powers of two.
So, if power_of_two? method will be added, I'd like to add
negative_power_of_two? method too.
(It returns true for -1, -2, -4, ...)
negative_power_of_two? can be combined with bit_length (absolute number) as
n.negative_power_of_two? ? n.bit_length <= 32 : n.bit_length < 32
to determine n fits in 32 bits signed integer with two's complement format.
It can be combined with bit_length (two's complement) as
n.negative_power_of_two? ? n.bit_length < 53 : n.bit_length <= 53
to determine n fits in 53 bits integer with absolute number format.
#4 Updated by Akira Tanaka over 2 years ago
matz (Yukihiro Matsumoto) wrote:
I don't see the use-case of this method. Is there any case that happens so frequently to have build-in method (maybe performance-wise)?
My intended use case is assists Integer#bit_length to determine
an integer fits an fixed size two's complement representation.
(I assume Integer#bit_lengthworks for absolute number.)
After some code searching I found several applications.
- Some application can be faster when input is a power of two. For example, integer to string (like Integer#to_s) can be implemented specially when radix is a power of two. In such case, the method can be used to decide the special case or not.
- Some library require input size be a power of two.
So application may want to test input size.
- FFT needs input size to be a power of two.
- A function in OpenGL require image width and height to be a power of two. http://www.khronos.org/opengles/sdk/docs/man/xhtml/glGenerateMipmap.xml
- Internal buffer size, table size, etc. tend to be a power of two. So application may want to assert the size is a power of two.
Several software provides this feature.
Squeak Smalltalk has isPowerOfTwo.
.NET has BigInteger.IsPowerOfTwo.
CLN has power2p.
NetBSD kernel has powerof2.