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

Pseudocode Definition
If x is a bitstring and i is an integer, then SignExtend(x,i) is x extended to a length of i bits, by adding
sufficient copies of its leftmost bit to its left. That is, if i == Len(x), then SignExtend(x,i) = x, and if i >
Len(x), then:
SignExtend(x,i) = Replicate(TopBit(x), i-Len(x)) : x
It is a pseudocode error to use either ZeroExtend(x,i) or SignExtend(x,i) in a context where it is possible
that i < Len(x).
Converting bitstrings to integers
If x is a bitstring, SInt(x) is the integer whose two’s complement representation is x:
// SInt()
// ======
integer SInt(bits(N) x)
result = 0;
for i = 0 to N-1
if x == ‘1’ then result = result + 2^i;
if x == ‘1’ then result = result - 2^N;
return result;
UInt(x) is the integer whose unsigned representation is x:
// UInt()
// ======
integer UInt(bits(N) x)
result = 0;
for i = 0 to N-1
if x == ‘1’ then result = result + 2^i;
return result;
Int(x, unsigned) returns either SInt(x) or UInt(x) depending on the value of its second argument:
// Int()
// =====
integer Int(bits(N) x, boolean unsigned)
result = if unsigned then UInt(x) else SInt(x);
return result;
I.5.4 Arithmetic
Most pseudocode arithmetic is performed on integer or real values, with operands being obtained by
conversions from bitstrings and results converted back to bitstrings afterwards. As these data types are the
unbounded mathematical types, no issues arise about overflow or similar errors.
AppxI-14 Copyright © 1996-1998, 2000, 2004-2008 ARM Limited. All rights reserved. ARM DDI 0406B