Integer to byte string - Speed improvements

I'm writing code that needs to store an integer as a sequence of bytes.
Array#pack works for 1-, 2-, and 4-byte integers, but I want to be able
to support Bignums as well.

I have working code below. I'm happy with it. However, I thought I'd
pose the question to the list: how much faster can you make the below
code run?

# The natural log of 2 (for base-2 logarithms)
Math::LOG2 = Math.log( 2 )

class Integer
# Converts the integer into a string, where the value of each
character
# is a byte in the bit representation of the integer.
# Low-order bytes appear first in the string.
#
# If the number of characters is not specified, the fewest number of
# characters that can represent the integer is used.
#
#
def to_bytestring( num_chars=nil )
unless num_chars
bits_needed = Math.log( self ) / Math::LOG2
num_chars = ( bits_needed / 8.0 ).ceil
end
if pack_code = { 1=>'C', 2=>'S', 4=>'L' }[ num_chars ]
[ self ].pack( pack_code )
else
(0...(num_chars)).map{ |i|
(( self >> i*8 ) & 0xFF ).chr
}.join
end
end

# Creates an integer from a byte string.
# See Integer#to_bytestring for more information.
def self.from_bytestring( str )
val = 0
index = 0
str.each_byte{ |b|
val += b << 8 * index
index += 1
}
val
end

end

[
0x48,
0x6948,
0x646c726f57206f6c6c6548,
0x217962755220666f207463657073612074656577732061207369206d756e676942
].each{ |i| puts i, i.to_bytestring, '' }

#=> 72
#=> H

#=> 26952
#=> Hi

#=> 121404708493354166158910792
#=> Hello World
#=>
3876042760240808297111079005855559646422331404814505579794973210389374306838850
#=> Bignum is a sweet aspect of Ruby!

.

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