ARM Architecture Reference Manual ARMv7-A and ARMv7-R edition

Pseudocode Definition
I.5.3 Bitstring manipulation
The following bitstring manipulation functions are defined:
Bitstring length and most significant bit
If x is a bitstring, the bitstring length function Len(x) returns its length as an integer, and TopBit(x) is the
leftmost bit of x (= x using bitstring extraction).
Bitstring concatenation and replication
If x and y are bitstrings of lengths N and M respectively, then x:y is the bitstring of length N+M constructed by
concatenating x and y in left-to-right order.
If x is a bitstring and n is an integer with n > 0, Replicate(x,n) is the bitstring of length n*Len(x) consisting
of n copies of x concatenated together, and Zeros(n) = Replicate(’0’,n), Ones(n) = Replicate(’1’,n).
Bitstring extraction
The bitstring extraction operator extracts a bitstring from either another bitstring or an integer. Its syntax is
x, where x is the integer or bitstring being extracted from, and is a list of
integers enclosed in angle brackets rather than the usual parentheses. The length of the resulting bitstring is
equal to the number of integers in . In x, each of the integers in
must be:
>= 0
< Len(x) if x is a bitstring.
The definition of x depends on whether integer_list contains more than one integer. If it
does, x is defined to be the concatenation:
x : x : x : ... : x
If integer_list consists of just one integer i, x is defined to be:
if x is a bitstring, '0' if bit i of x is a zero and '1' if bit i of x is a one.
if x is an integer, let y be the unique integer in the range 0 to 2^(i+1)-1 that is congruent to x modulo
2^(i+1). Then x is '0' if y < 2^i and '1' if y >= 2^i.
Loosely, this second definition treats an integer as equivalent to a sufficiently long two’s complement
representation of it as a bitstring.
In , the notation i:j with i >= j is shorthand for the integers in order from i down to j, both
ends inclusive. For example, instr is shorthand for instr.
The expression x is assignable provided x is an assignable bitstring and no integer appears
more than once in . In particular, x is assignable if x is an assignable bitstring and 0