# are ZSCO flags really fundamental?

By: Michael S (already5chosen.delete@this.yahoo.com), February 28, 2013 4:58 am
EduardoS (no.delete@this.spam.com) on February 27, 2013 11:07 pm wrote:
> Michael S (already5chosen.delete@this.yahoo.com) on February 27, 2013 4:24 pm wrote:
> > I say 12 rather than 14, because I don't think that negative/non-negative
> > conditions are really fundamental.
>
> The sign flag helps some times and is essentially free.
>
> > Now, do we really need 4 flag bits in order to implement 12 (or even all 14) fundamental
> > conditions? No, we don't. Up to 64 conditions, including all 14 defined in x86/ARM?SPARC,
> > can be easyly derived from just 7 distinct states = 3 bits.
> > For example, like those:
> > 0 - unsigned_less && signed_less. Implied non-overflow && negative
> > 1 - unsigned_less && signed_greater && non-overflow. Implied non-negative
> > 2 - unsigned_less && signed_greater && overflow. Implied negative
> > 3 - unsigned_greater && signed_less && non-overflow. Implied negative
> > 4 - unsigned_greater && signed_less && overflow. Implied non-negative
> > 5 - unsigned_greater && signed_greater. Implied non-overflow && non-negative
> > 6 - equal. Implied non-overflow && non-negative
>
> Encoding in three bits have the same "advantage" of killing the sign flag

I don't get what you're saying. Sign-of-result information is fully preserved in 3-bit encoding. Using encoding from my table above, SF = (0 || 2 || 3).

> at the expense
> of more complex (and time consuming) flag calculation, but the sign flag is free, so no
> real gain, also... 3 bitsT allow up to 8 resulting states, but there are 9, no?
>

You are right.
I was concerned only with sub/cmp and didn't pay attention to all combinations that can be generated by two-complement addition.
Specifically, my 7 states can not represent two additional zeros - ZF=1,CF=1,OF=0 and ZF=1,CF=1,OF=1. And there is only one 3-bit combination left so, without special measure, it's impossible to distinguish between the two states with just 3 bits.

One possible solution is definition of two separate addition instruction that behave identically except when faced with pair of 0x8000_0000 inputs in which case:
signed_add variant correctly detects carry and overflow, but leaves equivalent of ZF set;
unsigned_add variant correctly detects carry and ZF, but leaves equivalent of OF clear.

Then all 'C' compilers will happily ignore signed_add. All compiler for integer-overflow-paranoid languages will use signed_add when appropriated, being fully aware of the fact that ZF is not reliable after that. Anyway, ZF is most useful after sub/cmp, HLL compilers (unlike human coders) almost never exploit it after addition.

So, lets revisit my table:
0 - Z=0,S=1,C=0,B=1,O=0: unsigned_less && signed_less. Implied non-overflow && negative
1 - Z=0,S=0,C=0,B=1,O=0: unsigned_less && signed_greater && non-overflow. Implied non-negative
2 - Z=0,S=1,C=0,B=1,O=1: unsigned_less && signed_greater && overflow. Implied negative
3 - Z=0,S=1,C=1,B=0,O=0: unsigned_greater && signed_less && non-overflow. Implied negative
4 - Z=0,S=0,C=1,B=0,O=1: unsigned_greater && signed_less && overflow. Implied non-negative
5 - Z=0,S=0,C=1,B=0,O=0: unsigned_greater && signed_greater. Implied non-overflow && non-negative
6 - Z=1,S=0,C=0,B=0,O=0: equal. Implied non-overflow && non-negative
7 - Z=1,S=0,C=1,B=0,O=0: equal with carry && non-overflow. Implied non-negative

Plus:
As result of signed_add:
4 - Z=x,S=0,C=1,B=0,O=1: unsigned_greater && signed_less && overflow. Implied non-negative
As result of unsigned_add:
7 - Z=x,S=0,C=1,B=0,O=x: unsigned_greater && signed_less && overflow. Implied non-negative

So, let's look at your addition cases:

# 1
> mov eax, 1
> add eax, 1
>
> Non-Zero, Non-Negative, Non-Carry, Non-Overflow

1 - Z=0,S=0,C=0,B=1,O=0: unsigned_less && signed_greater && non-overflow. Implied non-negative

# 2
>
> mov eax, 0
> add eax, 0
>
> Zero, Non-Negative, Non-Carry, Non-Overflow

6 - Z=1,S=0,C=0,B=0,O=0: equal. Implied non-overflow && non-negative

# 3
> mov eax, -1
> add eax, 2
>
> Non-Zero, Non-Negative, Carry, Non-Overflow

5 - Z=0,S=0,C=1,B=0,O=0: unsigned_greater && signed_greater. Implied non-overflow && non-negative

# 4
>
> mov eax, -1
> add eax, 1
>
> Zero, Non-Negative, Carry, Non-Overflow

7 - Z=1,S=0,C=1,B=x,O=0: equal with carry. Implied overflow && non-negative

# 5
>
> mov eax, 80000000h
> add eax, 80000000h
>
> Zero, Non-Negative, Carry, Overflow

After unsigned_add:
7 - Z=1,S=0,C=1,B=x,O=0: equal with carry. Implied overflow && non-negative
After signed_add:
4 - Z=0,S=0,C=1,B=0,O=1: unsigned_greater && signed_less && overflow. Implied non-negative

# 6
>
> mov eax, 80000001h
> add eax, 80000000h
>
> Non-Zero, Non-Negative, Carry, Overflow

4 - Z=0,S=0,C=1,B=0,O=1: unsigned_greater && signed_less && overflow. Implied non-negative

#7
> mov eax, -2
> add eax, 1
>
> Non-Zero, Negative, Non-Carry, Non-Overflow
>

0 - Z=0,S=1,C=0,B=1,O=0: unsigned_less && signed_less. Implied non-overflow && negative

#8
> mov eax, 70000000h
> add eax, 70000000h
>
> Non-Zero, Negative, Non-Carry, Overflow
>

2 - Z=0,S=1,C=0,B=1,O=1: unsigned_less && signed_greater && overflow. Implied negative

#9
> mov eax, -1
> add eax, -1
>
> Non-Zero, Negative, Carry, Non-Overflow
>

3 - Z=0,S=1,C=1,B=0,O=0: unsigned_greater && signed_less && non-overflow. Implied negative

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What is wrong with ARM?dmsc2013/03/12 03:47 PM
What is wrong with ARM?dmsc2013/03/12 03:43 PM
ARMv8 cleanlinessMichael S2013/03/02 05:06 PM
ParityAndi Kleen2013/03/03 01:47 PM
ParityLinus Torvalds2013/03/03 03:06 PM
ParityAndi Kleen2013/03/03 07:15 PM
Except the borrow bitMatthew D2013/02/26 12:07 AM
Except the borrow bitrwessel2013/02/26 12:42 AM
Except the borrow bitLinus Torvalds2013/02/26 11:13 AM
are ZSCO flags really fundamental?Michael S2013/02/27 04:24 PM
are ZSCO flags really fundamental?Linus Torvalds2013/02/27 05:41 PM
are ZSCO flags really fundamental?Michael S2013/02/28 01:39 AM
are ZSCO flags really fundamental?2013/03/01 10:23 AM
are ZSCO flags really fundamental?EduardoS2013/02/27 11:07 PM
are ZSCO flags really fundamental?Michael S2013/02/28 04:58 AM
are ZSCO flags really fundamental?rwessel2013/02/28 12:29 AM
are ZSCO flags really fundamental?rwessel2013/02/28 12:32 AM
Bit numbering on big endian machinesKonrad Schwarz2013/02/28 01:49 AM
Bit numbering on big endian machinesrwessel2013/02/28 02:32 AM
ARMv8 cleanlinessWilco2013/02/25 05:54 AM
ARMv8 cleanlinessEduardoS2013/02/25 06:24 AM
ARMv8 cleanlinessWilco2013/02/25 07:36 AM
ARMv8 cleanlinessEduardoS2013/02/25 01:06 PM
ARMv8 cleanlinessWilco2013/02/25 05:24 PM
ARMv8 cleanlinessEduardoS2013/02/25 05:55 PM
Utility of data loss exceptionsPaul A. Clayton2013/02/25 08:18 PM
Utility of data loss exceptionsrwessel2013/02/26 01:00 AM
Excessively expensive mode changingPaul A. Clayton2013/02/26 06:15 AM
Utility of data loss exceptionsEduardoS2013/02/26 02:55 AM
Utility of data loss exceptionsTREZA2013/02/26 04:53 AM
Utility of data loss exceptionsEduardoS2013/02/26 05:37 AM
Utility of data loss exceptionsEtienne2013/02/26 06:01 AM
1b vs. 4b not a huge difference?Paul A. Clayton2013/02/25 09:57 AM
Possible benefit of multi-bit CCPaul A. Clayton2013/02/23 08:09 AM
ARMv8 cleanlinessrwessel2013/02/18 12:01 AM
ARMv8 cleanlinessWilco2013/02/18 05:33 PM
ARMv8 cleanlinessEduardoS2013/02/18 08:18 PM
ARMv8 cleanlinessWilco2013/02/25 06:19 AM
ARMv8 cleanlinessTREZA2013/02/15 04:21 AM
ARMv8 cleanliness2013/02/17 10:49 AM
ARMv8 cleanlinessLinus Torvalds2013/02/17 11:54 AM
ARMv8 cleanlinessLinus Torvalds2013/02/17 11:58 AM
ARMv8 cleanlinessnone2013/02/17 04:36 PM
ARMv8 cleanlinessTREZA2013/02/17 11:59 AM
ARMv8 cleanlinessWilco2013/02/17 12:30 PM
and-compare and or-comparePaul A. Clayton2013/02/17 05:28 PM
early branch resolutionanon2013/02/18 02:05 AM
My ignorance about compilers is vasterPaul A. Clayton2013/02/18 01:30 PM
early branch resolutionanon2013/02/18 05:12 PM
early branch resolution?EBFE2013/02/19 01:03 AM
Early resolution: some but limited potentialPaul A. Clayton2013/02/19 05:52 PM
Early resolution: some but limited potentialhobold2013/02/20 02:02 PM
PPC750 was an inspirationPaul A. Clayton2013/02/23 08:09 AM
ARMv8 cleanlinessTREZA2013/02/17 01:53 PM
ARMv8 cleanlinessExophase2013/02/17 04:49 PM
ARMv8 cleanlinessWilco2013/02/17 12:07 PM
ARMv8 cleanlinessbakaneko2013/02/17 12:43 PM
ARMv8 cleanlinessJouni Osmala2013/02/17 01:10 PM
-1 comparison true seems betterPaul A. Clayton2013/02/17 06:07 PM
ARMv8 cleanlinessEtienne2013/07/17 02:58 AM
ARM server benchmark- why Apache?Per Hesselgren2013/02/05 12:13 AM
ARM server benchmark- why Apache?anon2013/02/05 12:38 AM
ARM server benchmark- why Apache?Per Hesselgren2013/02/05 01:25 AM
ARM server benchmark- why Apache?Michael S2013/02/05 02:13 AM
ARM server benchmark- why Apache?Michael S2013/02/05 01:51 AM
I think that was debunked alreadyDavid Kanter2013/02/05 07:36 PM
ARM server benchmark- why Apache?bakaneko2013/02/06 02:37 AM
ARM server benchmark- why Apache?Michael S2013/02/06 03:43 AM
Marketing to PHBs?Paul A. Clayton2013/02/06 06:40 AM
ARM server benchmark- why Apache?bakaneko2013/02/06 07:08 AM
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