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Absolute value (ABS)
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ABS, Absolute value instructions
It is often necessary to take the absolute value.
Calculating this with a branch
if(v < 0 ) v = -v
costs extra instructions, and may produce costly branch mispredictions.
Branchless ABS
In IEEE FP representations, calculating the absolute value may involve just AND-masking off the sign bit. NaNs may make this more complicated.
In 2's compliment integer representation, calculating the absolute value without a branch is a bit more complicated.
The instruction count overhead of branchless absolute value, in combination with branch mispredictions, and NaN and overflow semantics, motivates a special instruction.
2's complement branchless ABS
result = (v ^ (v>>31)) - (v>>31)
supposedly patented. TBD find patent.
Instruction Forms
- scalar ABS
- dest := ABS(src)
- scalar ABSDIFF
- dest := ABS(src1-src2)
- since ABS is often found right after a SUBtract
- vector ABS
- destV := vector-ABS( v1 - v2 )
- vector SAD - sum-of-absolute-difference
- destV := SUM-reduce( vector-ABS( vector-SUB( v1 - v2 )))
- accumulating vector SAD sum-of-absolute-difference
- Acc += SUM-reduce( vector-ABS( vector-SUB( v1 - v2 )))
- See MPSADBW
Issue: signed integer ABS overflow
N-bit 2's compliment integers range from -2^(N-1) to +2^(N-1)-1. This means that ABS of the most negative integer is not representable as a signed 2's compliment integer
There are several ways of handling this.
One way is to consider ABS(signed)->unsigned, which removes the possibility of overflow - or at least defers it to the next calculations.
Another way would be to throw to throw an exception; barring that, treat the ABS instruction as returning an unsigned integer
unsigned ABS( signed );
and to return the bit pattern 10...00, which is the appropraite unsigned value.
It may be desirable to set a condition code to indicate this condition. This is particularly appropriate for ABS instruction flavours such as accumulating-sum-of-absolute-differences
Acc += SUM-reduce( vector-ABS( vector-SUB( v1 - v2 )))
where you may want to distinguish overflow of the accumulator from possible
NEGABS
Occasionally one sees negative absolute value (NEGABS) and NEGABSDIFF and sum-neg-absdiff (SNAD) instructions, to cope with the fact that in standard 2's complement there is one more negative value than there is a positive value. I.i. ABS and ABSDIFF can overflow, but NAGABS and NEGABSDIFF cannot.
Also calls NABS, as in NABS (Negative Absolute value)
Cyrix PMAGW
Cyrix 6x86MX's PMAGW instruction is an interesting variant on ABS instructions: it does, for all vector elements i
vdest[i] := ( abs(src1[i]) > abs(src2[i]) ? src1[i] : src2[i]
i.e. it compares absolute values, without saturation, and then selects the non-absolute value that is greatest.
rather like an abs-select-max.
