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# Appendix

* <https://bugs.libre-soc.org/show_bug.cgi?id=574> Saturation
* <https://bugs.libre-soc.org/show_bug.cgi?id=558#c47> Parallel Prefix
* <https://bugs.libre-soc.org/show_bug.cgi?id=697> Reduce Modes
* <https://bugs.libre-soc.org/show_bug.cgi?id=809> OV sv.addex discussion

This is the appendix to [[sv/svp64]], providing explanations of modes
etc. leaving the main svp64 page's primary purpose as outlining the
instruction format.

Table of contents:

[[!toc]]

# XER, SO and other global flags

Vector systems are expected to be high performance.  This is achieved
through parallelism, which requires that elements in the vector be
independent.  XER SO/OV and other global "accumulation" flags (CR.SO) cause
Read-Write Hazards on single-bit global resources, having a significant
detrimental effect.

Consequently in SV, XER.SO behaviour is disregarded (including
in `cmp` instructions).  XER.SO is not read, but XER.OV may be written,
breaking the Read-Modify-Write Hazard Chain that complicates
microarchitectural implementations.
This includes when `scalar identity behaviour` occurs.  If precise
OpenPOWER v3.0/1 scalar behaviour is desired then OpenPOWER v3.0/1
instructions should be used without an SV Prefix.

TODO jacob add about OV https://www.intel.com/content/dam/www/public/us/en/documents/white-papers/ia-large-integer-arithmetic-paper.pdf

Of note here is that XER.SO and OV may already be disregarded in the
Power ISA v3.0/1 SFFS (Scalar Fixed and Floating) Compliancy Subset.
SVP64 simply makes it mandatory to disregard XER.SO even for other Subsets,
but only for SVP64 Prefixed Operations.

XER.CA/CA32 on the other hand is expected and required to be implemented
according to standard Power ISA Scalar behaviour.  Interestingly, due
to SVP64 being in effect a hardware for-loop around Scalar instructions
executing in precise Program Order, a little thought shows that a Vectorised
Carry-In-Out add is in effect a Big Integer Add, taking a single bit Carry In
and producing, at the end, a single bit Carry out.  High performance
implementations may exploit this observation to deploy efficient
Parallel Carry Lookahead.

    # assume VL=4, this results in 4 sequential ops (below)
    sv.adde r0.v, r4.v, r8.v

    # instructions that get executed in backend hardware:
    adde r0, r4, r8 # takes carry-in, produces carry-out
    adde r1, r5, r9 # takes carry from previous
    ...
    adde r3, r7, r11 # likewise

It can clearly be seen that the carry chains from one
64 bit add to the next, the end result being that a
256-bit "Big Integer Add" has been performed, and that
CA contains the 257th bit.  A one-instruction 512-bit Add
may be performed by setting VL=8, and a one-instruction
1024-bit add by setting VL=16, and so on.

# v3.0B/v3.1 relevant instructions

SV is primarily designed for use as an efficient hybrid 3D GPU / VPU /
CPU ISA.

Vectorisation of the VSX Packed SIMD system
likewise makes no sense whatsoever. SV *replaces* VSX and provides,
at the very minimum, predication (which VSX was designed without).
Thus all VSX Major Opcodes - all of them - are "unused" and must raise
illegal instruction exceptions in SV Prefix Mode.

Likewise, `lq` (Load Quad), and Load/Store Multiple make no sense to
have because they are not only provided by SV, the SV alternatives may
be predicated as well, making them far better suited to use in function
calls and context-switching.

Additionally, some v3.0/1 instructions simply make no sense at all in a
Vector context: `rfid` falls into this category,
as well as `sc` and `scv`.  Here there is simply no point
trying to Vectorise them: the standard OpenPOWER v3.0/1 instructions
should be called instead.

Fortuitously this leaves several Major Opcodes free for use by SV
to fit alternative future instructions.  In a 3D context this means
Vector Product, Vector Normalise, [[sv/mv.swizzle]], Texture LD/ST
operations, and others critical to an efficient, effective 3D GPU and
VPU ISA. With such instructions being included as standard in other
commercially-successful GPU ISAs it is likewise critical that a 3D
GPU/VPU based on svp64 also have such instructions.

Note however that svp64 is stand-alone and is in no way
critically dependent on the existence or provision of 3D GPU or VPU
instructions. These should be considered extensions, and their discussion
and specification is out of scope for this document.

Note, again: this is *only* under svp64 prefixing.  Standard v3.0B /
v3.1B is *not* altered by svp64 in any way.

## Major opcode map (v3.0B)

This table is taken from v3.0B.
Table 9: Primary Opcode Map (opcode bits 0:5)

```
    |  000   |   001 |  010  | 011   |  100  |    101 |  110  |  111
000 |        |       |  tdi  | twi   | EXT04 |        |       | mulli | 000
001 | subfic |       | cmpli | cmpi  | addic | addic. | addi  | addis | 001
010 | bc/l/a | EXT17 | b/l/a | EXT19 | rlwimi| rlwinm |       | rlwnm | 010
011 |  ori   | oris  | xori  | xoris | andi. | andis. | EXT30 | EXT31 | 011
100 |  lwz   | lwzu  | lbz   | lbzu  | stw   | stwu   | stb   | stbu  | 100
101 |  lhz   | lhzu  | lha   | lhau  | sth   | sthu   | lmw   | stmw  | 101
110 |  lfs   | lfsu  | lfd   | lfdu  | stfs  | stfsu  | stfd  | stfdu | 110
111 |  lq    | EXT57 | EXT58 | EXT59 | EXT60 | EXT61  | EXT62 | EXT63 | 111
    |  000   |   001 |   010 |  011  |   100 |   101  | 110   |  111
```

## Suitable for svp64-only

This is the same table containing v3.0B Primary Opcodes except those that
make no sense in a Vectorisation Context have been removed.  These removed
POs can, *in the SV Vector Context only*, be assigned to alternative
(Vectorised-only) instructions, including future extensions.
EXT04 retains the scalar `madd*` operations but would have all PackedSIMD
(aka VSX) operations removed.

Note, again, to emphasise: outside of svp64 these opcodes **do not**
change.  When not prefixed with svp64 these opcodes **specifically**
retain their v3.0B / v3.1B OpenPOWER Standard compliant meaning.

```
    |  000   |   001 |  010  | 011   |  100  |    101 |  110  |  111
000 |        |       |       |       | EXT04 |        |       | mulli | 000
001 | subfic |       | cmpli | cmpi  | addic | addic. | addi  | addis | 001
010 | bc/l/a |       |       | EXT19 | rlwimi| rlwinm |       | rlwnm | 010
011 |  ori   | oris  | xori  | xoris | andi. | andis. | EXT30 | EXT31 | 011
100 |  lwz   | lwzu  | lbz   | lbzu  | stw   | stwu   | stb   | stbu  | 100
101 |  lhz   | lhzu  | lha   | lhau  | sth   | sthu   |       |       | 101
110 |  lfs   | lfsu  | lfd   | lfdu  | stfs  | stfsu  | stfd  | stfdu | 110
111 |        |       | EXT58 | EXT59 |       | EXT61  |       | EXT63 | 111
    |  000   |   001 |   010 |  011  |   100 |   101  | 110   |  111
```

It is important to note that having a different v3.0B Scalar opcode
that is different from an SVP64 one is highly undesirable: the complexity
in the decoder is greatly increased.

# EXTRA Field Mapping

The purpose of the 9-bit EXTRA field mapping is to mark individual
registers (RT, RA, BFA) as either scalar or vector, and to extend
their numbering from 0..31 in Power ISA v3.0 to 0..127 in SVP64.
Three of the 9 bits may also be used up for a 2nd Predicate (Twin
Predication) leaving a mere 6 bits for qualifying registers. As can
be seen there is significant pressure on these (and in fact all) SVP64 bits.

In Power ISA v3.1 prefixing there are bits which describe and classify
the prefix in a fashion that is independent of the suffix. MLSS for
example.  For SVP64 there is insufficient space to make the SVP64 Prefix
"self-describing", and consequently every single Scalar instruction 
had to be individually analysed, by rote, to craft an EXTRA Field Mapping.
This process was semi-automated and is described in this section.
The final results, which are part of the SVP64 Specification, are here:

* [[openpower/opcode_regs_deduped]]

Firstly, every instruction's mnemonic (`add RT, RA, RB`) was analysed
from reading the markdown formatted version of the Scalar pseudocode
which is machine-readable and found in [[openpower/isatables]].  The
analysis gives, by instruction, a "Register Profile".  `add RT, RA, RB`
for example is given a designation `RM-2R-1W` because it requires
two GPR reads and one GPR write.

Secondly, the total number of registers was added up (2R-1W is 3 registers)
and if less than or equal to three then that instruction could be given an
EXTRA3 designation.  Four or more is given an EXTRA2 designation because
there are only 9 bits available.

Thirdly, the instruction was analysed to see if Twin or Single
Predication was suitable.  As a general rule this was if there
was only a single operand and a single result (`extw` and LD/ST)
however it was found that some 2 or 3 operand instructions also
qualify. Given that 3 of the 9 bits of EXTRA had to be sacrificed for use
in Twin Predication, some compromises were made, here.  LDST is
Twin but also has 3 operands in some operations, so only EXTRA2 can be used.

Fourthly, a packing format was decided: for 2R-1W an EXTRA3 indexing
could have been decided
that RA would be indexed 0 (EXTRA bits 0-2), RB indexed 1 (EXTRA bits 3-5)
and RT indexed 2 (EXTRA bits 6-8).  In some cases (LD/ST with update)
RA-as-a-source is given a **different** EXTRA index from RA-as-a-result
(because it is possible to do, and perceived to be useful). Rc=1
co-results (CR0, CR1) are always given the same EXTRA index as their
main result (RT, FRT).

Fifthly, in an automated process the results of the analysis
were outputted in CSV Format for use in machine-readable form
by sv_analysis.py <https://git.libre-soc.org/?p=openpower-isa.git;a=blob;f=src/openpower/sv/sv_analysis.py;hb=HEAD>

This process was laborious but logical, and, crucially, once a
decision is made (and ratified) cannot be reversed.
Qualifying future Power ISA Scalar instructions for SVP64
is **strongly** advised to utilise this same process and the same
sv_analysis.py program as a canonical method of maintaining the
relationships.  Alterations to that same program which
change the Designation is **prohibited** once finalised (ratified
through the Power ISA WG Process). It would
be similar to deciding that `add` should be changed from X-Form
to D-Form.

# Single Predication

This is a standard mode normally found in Vector ISAs.  every element in every source Vector and in the destination uses the same bit of one single predicate mask.

In SVSTATE, for Single-predication, implementors MUST increment both srcstep and dststep: unlike Twin-Predication the two must be equal at all times.

# Twin Predication

This is a novel concept that allows predication to be applied to a single
source and a single dest register.  The following types of traditional
Vector operations may be encoded with it, *without requiring explicit
opcodes to do so*

* VSPLAT (a single scalar distributed across a vector)
* VEXTRACT (like LLVM IR [`extractelement`](https://releases.llvm.org/11.0.0/docs/LangRef.html#extractelement-instruction))
* VINSERT (like LLVM IR [`insertelement`](https://releases.llvm.org/11.0.0/docs/LangRef.html#insertelement-instruction))
* VCOMPRESS (like LLVM IR [`llvm.masked.compressstore.*`](https://releases.llvm.org/11.0.0/docs/LangRef.html#llvm-masked-compressstore-intrinsics))
* VEXPAND (like LLVM IR [`llvm.masked.expandload.*`](https://releases.llvm.org/11.0.0/docs/LangRef.html#llvm-masked-expandload-intrinsics))

Those patterns (and more) may be applied to:

* mv (the usual way that V\* ISA operations are created)
* exts\* sign-extension
* rwlinm and other RS-RA shift operations (**note**: excluding
  those that take RA as both a src and dest. These are not
  1-src 1-dest, they are 2-src, 1-dest)
* LD and ST (treating AGEN as one source)
* FP fclass, fsgn, fneg, fabs, fcvt, frecip, fsqrt etc.
* Condition Register ops mfcr, mtcr and other similar

This is a huge list that creates extremely powerful combinations,
particularly given that one of the predicate options is `(1<<r3)`

Additional unusual capabilities of Twin Predication include a back-to-back
version of VCOMPRESS-VEXPAND which is effectively the ability to do
sequentially ordered multiple VINSERTs.  The source predicate selects a
sequentially ordered subset of elements to be inserted; the destination
predicate specifies the sequentially ordered recipient locations.
This is equivalent to
`llvm.masked.compressstore.*`
followed by
`llvm.masked.expandload.*`
with a single instruction.

This extreme power and flexibility comes down to the fact that SVP64
is not actually a Vector ISA: it is a loop-abstraction-concept that
is applied *in general* to Scalar operations, just like the x86
`REP` instruction (if put on steroids).

# Reduce modes

Reduction in SVP64 is deterministic and somewhat of a misnomer.  A normal
Vector ISA would have explicit Reduce opcodes with defined characteristics
per operation: in SX Aurora there is even an additional scalar argument
containing the initial reduction value, and the default is either 0
or 1 depending on the specifics of the explicit opcode.
SVP64 fundamentally has to
utilise *existing* Scalar Power ISA v3.0B operations, which presents some
unique challenges.

The solution turns out to be to simply define reduction as permitting
deterministic element-based schedules to be issued using the base Scalar
operations, and to rely on the underlying microarchitecture to resolve
Register Hazards at the element level.  This goes back to
the fundamental principle that SV is nothing more than a Sub-Program-Counter
sitting between Decode and Issue phases.

Microarchitectures *may* take opportunities to parallelise the reduction
but only if in doing so they preserve Program Order at the Element Level.
Opportunities where this is possible include an `OR` operation
or a MIN/MAX operation: it may be possible to parallelise the reduction,
but for Floating Point it is not permitted due to different results
being obtained if the reduction is not executed in strict Program-Sequential
Order.

In essence it becomes the programmer's responsibility to leverage the
pre-determined schedules to desired effect.

## Scalar result reduction and iteration

Scalar Reduction per se does not exist, instead is implemented in SVP64
as a simple and natural relaxation of the usual restriction on the Vector
Looping which would terminate if the destination was marked as a Scalar.
Scalar Reduction by contrast *keeps issuing Vector Element Operations*
even though the destination register is marked as scalar.
Thus it is up to the programmer to be aware of this, observe some
conventions, and thus end up achieving the desired outcome of scalar
reduction.

It is also important to appreciate that there is no
actual imposition or restriction on how this mode is utilised: there
will therefore be several valuable uses (including Vector Iteration
and "Reverse-Gear")
and it is up to the programmer to make best use of the
(strictly deterministic) capability
provided.

In this mode, which is suited to operations involving carry or overflow,
one register must be assigned, by convention by the programmer to be the
"accumulator".  Scalar reduction is thus categorised by:

* One of the sources is a Vector
* the destination is a scalar
* optionally but most usefully when one source scalar register is
  also the scalar destination (which may be informally termed
  the "accumulator")
* That the source register type is the same as the destination register
  type identified as the "accumulator".  Scalar reduction on `cmp`,
  `setb` or `isel` makes no sense for example because of the mixture
  between CRs and GPRs.

*Note that issuing instructions in Scalar reduce mode such as `setb`
are neither `UNDEFINED` nor prohibited, despite them not making much
sense at first glance.
Scalar reduce is strictly defined behaviour, and the cost in
hardware terms of prohibition of seemingly non-sensical operations is too great.  
Therefore it is permitted and required to be executed successfully.
Implementors **MAY** choose to optimise such instructions in instances
where their use results in "extraneous execution", i.e. where it is clear
that the sequence of operations, comprising multiple overwrites to
a scalar destination **without** cumulative, iterative, or reductive
behaviour (no "accumulator"), may discard all but the last element
operation.  Identification
of such is trivial to do for `setb` and `cmp`: the source register type is
a completely different register file from the destination.
Likewise Scalar reduction when the destination is a Vector
is as if the Reduction Mode was not requested.*

Typical applications include simple operations such as `ADD r3, r10.v,
r3` where, clearly, r3 is being used to accumulate the addition of all
elements of the vector starting at r10.

     # add RT, RA,RB but when RT==RA
     for i in range(VL):
          iregs[RA] += iregs[RB+i] # RT==RA

However, *unless* the operation is marked as "mapreduce" (`sv.add/mr`)
SV ordinarily
**terminates** at the first scalar operation.  Only by marking the
operation as "mapreduce" will it continue to issue multiple sub-looped
(element) instructions in `Program Order`.

To perform the loop in reverse order, the ```RG``` (reverse gear) bit must be set.  This may be useful in situations where the results may be different
(floating-point) if executed in a different order.  Given that there is
no actual prohibition on Reduce Mode being applied when the destination
is a Vector, the "Reverse Gear" bit turns out to be a way to apply Iterative
or Cumulative Vector operations in reverse. `sv.add/rg r3.v, r4.v, r4.v`
for example will start at the opposite end of the Vector and push
a cumulative series of overlapping add operations into the Execution units of
the underlying hardware.

Other examples include shift-mask operations where a Vector of inserts
into a single destination register is required (see [[sv/bitmanip]], bmset),
as a way to construct
a value quickly from multiple arbitrary bit-ranges and bit-offsets.
Using the same register as both the source and destination, with Vectors
of different offsets masks and values to be inserted has multiple
applications including Video, cryptography and JIT compilation.

    # assume VL=4:
    # * Vector of shift-offsets contained in RC (r12.v)
    # * Vector of masks contained in RB (r8.v)
    # * Vector of values to be masked-in in RA (r4.v)
    # * Scalar destination RT (r0) to receive all mask-offset values
    sv.bmset/mr r0, r4.v, r8.v, r12.v

Due to the Deterministic Scheduling,
Subtract and Divide are still permitted to be executed in this mode,
although from an algorithmic perspective it is strongly discouraged.
It would be better to use addition followed by one final subtract,
or in the case of divide, to get better accuracy, to perform a multiply
cascade followed by a final divide.

Note that single-operand or three-operand scalar-dest reduce is perfectly
well permitted: the programmer may still declare one register, used as
both a Vector source and Scalar destination, to be utilised as 
the "accumulator".  In the case of `sv.fmadds` and `sv.maddhw` etc
this naturally fits well with the normal expected usage of these
operations.

If an interrupt or exception occurs in the middle of the scalar mapreduce,
the scalar destination register **MUST** be updated with the current
(intermediate) result, because this is how ```Program Order``` is
preserved (Vector Loops are to be considered to be just another way of issuing instructions
in Program Order).  In this way, after return from interrupt,
the scalar mapreduce may continue where it left off.  This provides
"precise" exception behaviour.

Note that hardware is perfectly permitted to perform multi-issue
parallel optimisation of the scalar reduce operation: it's just that
as far as the user is concerned, all exceptions and interrupts **MUST**
be precise.

## Vector result reduce mode

Vector Reduce Mode issues a deterministic tree-reduction schedule to the underlying micro-architecture.  Like Scalar reduction, the "Scalar Base"
(Power ISA v3.0B) operation is leveraged, unmodified, to give the
*appearance* and *effect* of Reduction.

Given that the tree-reduction schedule is deterministic,
Interrupts and exceptions
can therefore also be precise.  The final result will be in the first
non-predicate-masked-out destination element, but due again to
the deterministic schedule programmers may find uses for the intermediate
results.

When Rc=1 a corresponding Vector of co-resultant CRs is also
created.  No special action is taken: the result and its CR Field
are stored "as usual" exactly as all other SVP64 Rc=1 operations.

## Sub-Vector Horizontal Reduction

Note that when SVM is clear and SUBVL!=1 the sub-elements are
*independent*, i.e. they are mapreduced per *sub-element* as a result.
illustration with a vec2, assuming RA==RT, e.g `sv.add/mr/vec2 r4, r4, r16`

    for i in range(0, VL):
        # RA==RT in the instruction. does not have to be
        iregs[RT].x = op(iregs[RT].x, iregs[RB+i].x)
        iregs[RT].y = op(iregs[RT].y, iregs[RB+i].y)

Thus logically there is nothing special or unanticipated about
`SVM=0`: it is expected behaviour according to standard SVP64
Sub-Vector rules.

By contrast, when SVM is set and SUBVL!=1, a Horizontal
Subvector mode is enabled, which behaves very much more
like a traditional Vector Processor Reduction instruction.
Example for a vec3:

    for i in range(VL):
        result = iregs[RA+i].x
        result = op(result, iregs[RA+i].y)
        result = op(result, iregs[RA+i].z)
        iregs[RT+i] = result

In this mode, when Rc=1 the Vector of CRs is as normal: each result
element creates a corresponding CR element (for the final, reduced, result).

# Fail-on-first

Data-dependent fail-on-first has two distinct variants: one for LD/ST
(see [[sv/ldst]],
the other for arithmetic operations (actually, CR-driven)
([[sv/normal]]) and CR operations ([[sv/cr_ops]]).
Note in each
case the assumption is that vector elements are required appear to be
executed in sequential Program Order, element 0 being the first.

* LD/ST ffirst treats the first LD/ST in a vector (element 0) as an
  ordinary one.  Exceptions occur "as normal".  However for elements 1
  and above, if an exception would occur, then VL is **truncated** to the
  previous element.
* Data-driven (CR-driven) fail-on-first activates when Rc=1 or other
  CR-creating operation produces a result (including cmp).  Similar to
  branch, an analysis of the CR is performed and if the test fails, the
  vector operation terminates and discards all element operations
  above the current one (and the current one if VLi is not set),
  and VL is truncated to either
  the *previous* element or the current one, depending on whether
  VLi (VL "inclusive") is set.

Thus the new VL comprises a contiguous vector of results, 
all of which pass the testing criteria (equal to zero, less than zero).

The CR-based data-driven fail-on-first is new and not found in ARM
SVE or RVV. It is extremely useful for reducing instruction count,
however requires speculative execution involving modifications of VL
to get high performance implementations.  An additional mode (RC1=1)
effectively turns what would otherwise be an arithmetic operation
into a type of `cmp`.  The CR is stored (and the CR.eq bit tested
against the `inv` field).
If the CR.eq bit is equal to `inv` then the Vector is truncated and
the loop ends.
Note that when RC1=1 the result elements are never stored, only the CRs.

VLi is only available as an option when `Rc=0` (or for instructions
which do not have Rc). When set, the current element is always
also included in the count (the new length that VL will be set to).
This may be useful in combination with "inv" to truncate the Vector
to `exclude` elements that fail a test, or, in the case of implementations
of strncpy, to include the terminating zero.

In CR-based data-driven fail-on-first there is only the option to select
and test one bit of each CR (just as with branch BO).  For more complex
tests this may be insufficient.  If that is the case, a vectorised crops
(crand, cror) may be used, and ffirst applied to the crop instead of to
the arithmetic vector.

One extremely important aspect of ffirst is:

* LDST ffirst may never set VL equal to zero.  This because on the first
  element an exception must be raised "as normal".
* CR-based data-dependent ffirst on the other hand **can** set VL equal
  to zero. This is the only means in the entirety of SV that VL may be set
  to zero (with the exception of via the SV.STATE SPR).  When VL is set
  zero due to the first element failing the CR bit-test, all subsequent
  vectorised operations are effectively `nops` which is
  *precisely the desired and intended behaviour*.

Another aspect is that for ffirst LD/STs, VL may be truncated arbitrarily
to a nonzero value for any implementation-specific reason.  For example:
it is perfectly reasonable for implementations to alter VL when ffirst
LD or ST operations are initiated on a nonaligned boundary, such that
within a loop the subsequent iteration of that loop begins subsequent
ffirst LD/ST operations on an aligned boundary.  Likewise, to reduce
workloads or balance resources.

CR-based data-dependent first on the other hand MUST not truncate VL
arbitrarily to a length decided by the hardware: VL MUST only be
truncated based explicitly on whether a test fails.
This because it is a precise test on which algorithms
will rely.

## Data-dependent fail-first on CR operations (crand etc)

Operations that actually produce or alter CR Field as a result
do not also in turn have an Rc=1 mode.  However it makes no
sense to try to test the 4 bits of a CR Field for being equal
or not equal to zero. Moreover, the result is already in the
form that is desired: it is a CR field.  Therefore,
CR-based operations have their own SVP64 Mode, described
in [[sv/cr_ops]]

There are two primary different types of CR operations:

* Those which have a 3-bit operand field (referring to a CR Field)
* Those which have a 5-bit operand (referring to a bit within the
   whole 32-bit CR)

More details can be found in [[sv/cr_ops]].

# pred-result mode

Predicate-result merges common CR testing with predication, saving on
instruction count.  In essence, a Condition Register Field test
is performed, and if it fails it is considered to have been
*as if* the destination predicate bit was zero.
Arithmetic and Logical Pred-result is covered in [[sv/normal]]

Ped-result mode may not be applied on CR ops.

Although CR operations (mtcr, crand, cror) may be Vectorised,
predicated, pred-result mode applies to operations that have
an Rc=1 mode, or make sense to add an RC1 option.

# CR Operations

CRs are slightly more involved than INT or FP registers due to the
possibility for indexing individual bits (crops BA/BB/BT).  Again however
the access pattern needs to be understandable in relation to v3.0B / v3.1B
numbering, with a clear linear relationship and mapping existing when
SV is applied.

## CR EXTRA mapping table and algorithm

Numbering relationships for CR fields are already complex due to being
in BE format (*the relationship is not clearly explained in the v3.0B
or v3.1 specification*).  However with some care and consideration
the exact same mapping used for INT and FP regfiles may be applied,
just to the upper bits, as explained below.  The notation
`CR{field number}` is used to indicate access to a particular
Condition Register Field (as opposed to the notation `CR[bit]`
which accesses one bit of the 32 bit Power ISA v3.0B
Condition Register)

`CR{n}` refers to `CR0` when `n=0` and consequently, for CR0-7, is defined, in v3.0B pseudocode, as:

     CR{7-n} = CR[32+n*4:35+n*4]

For SVP64 the relationship for the sequential
numbering of elements is to the CR **fields** within
the CR Register, not to individual bits within the CR register.

In OpenPOWER v3.0/1, BF/BT/BA/BB are all 5 bits.  The top 3 bits (0:2)
select one of the 8 CRs; the bottom 2 bits (3:4) select one of 4 bits
*in* that CR.  The numbering was determined (after 4 months of
analysis and research) to be as follows:

    CR_index = 7-(BA>>2)      # top 3 bits but BE
    bit_index = 3-(BA & 0b11) # low 2 bits but BE
    CR_reg = CR{CR_index}     # get the CR
    # finally get the bit from the CR.
    CR_bit = (CR_reg & (1<<bit_index)) != 0

When it comes to applying SV, it is the CR\_reg number to which SV EXTRA2/3
applies, **not** the CR\_bit portion (bits 3:4):

    if extra3_mode:
        spec = EXTRA3
    else:
        spec = EXTRA2<<1 | 0b0
    if spec[0]:
       # vector constructs "BA[0:2] spec[1:2] 00 BA[3:4]"
       return ((BA >> 2)<<6) | # hi 3 bits shifted up
              (spec[1:2]<<4) | # to make room for these
              (BA & 0b11)      # CR_bit on the end
    else:
       # scalar constructs "00 spec[1:2] BA[0:4]"
       return (spec[1:2] << 5) | BA

Thus, for example, to access a given bit for a CR in SV mode, the v3.0B
algorithm to determin CR\_reg is modified to as follows:

    CR_index = 7-(BA>>2)      # top 3 bits but BE
    if spec[0]:
        # vector mode, 0-124 increments of 4
        CR_index = (CR_index<<4) | (spec[1:2] << 2)
    else:
        # scalar mode, 0-32 increments of 1
        CR_index = (spec[1:2]<<3) | CR_index
    # same as for v3.0/v3.1 from this point onwards
    bit_index = 3-(BA & 0b11) # low 2 bits but BE
    CR_reg = CR{CR_index}     # get the CR
    # finally get the bit from the CR.
    CR_bit = (CR_reg & (1<<bit_index)) != 0

Note here that the decoding pattern to determine CR\_bit does not change.

Note: high-performance implementations may read/write Vectors of CRs in
batches of aligned 32-bit chunks (CR0-7, CR7-15).  This is to greatly
simplify internal design.  If instructions are issued where CR Vectors
do not start on a 32-bit aligned boundary, performance may be affected.

## CR fields as inputs/outputs of vector operations

CRs (or, the arithmetic operations associated with them)
may be marked as Vectorised or Scalar.  When Rc=1 in arithmetic operations that have no explicit EXTRA to cover the CR, the CR is Vectorised if the destination is Vectorised.  Likewise if the destination is scalar then so is the CR.

When vectorized, the CR inputs/outputs are sequentially read/written
to 4-bit CR fields.  Vectorised Integer results, when Rc=1, will begin
writing to CR8 (TBD evaluate) and increase sequentially from there.
This is so that:

* implementations may rely on the Vector CRs being aligned to 8. This
  means that CRs may be read or written in aligned batches of 32 bits
  (8 CRs per batch), for high performance implementations.
* scalar Rc=1 operation (CR0, CR1) and callee-saved CRs (CR2-4) are not
  overwritten by vector Rc=1 operations except for very large VL
* CR-based predication, from CR32, is also not interfered with
  (except by large VL).

However when the SV result (destination) is marked as a scalar by the
EXTRA field the *standard* v3.0B behaviour applies: the accompanying
CR when Rc=1 is written to.  This is CR0 for integer operations and CR1
for FP operations.

Note that yes, the CR Fields are genuinely Vectorised.  Unlike in SIMD VSX which
has a single CR (CR6) for a given SIMD result, SV Vectorised OpenPOWER
v3.0B scalar operations produce a **tuple** of element results: the
result of the operation as one part of that element *and a corresponding
CR element*.  Greatly simplified pseudocode:

    for i in range(VL):
         # calculate the vector result of an add
         iregs[RT+i] = iregs[RA+i] + iregs[RB+i]
         # now calculate CR bits
         CRs{8+i}.eq = iregs[RT+i] == 0
         CRs{8+i}.gt = iregs[RT+i] > 0
         ... etc

If a "cumulated" CR based analysis of results is desired (a la VSX CR6)
then a followup instruction must be performed, setting "reduce" mode on
the Vector of CRs, using cr ops (crand, crnor) to do so.  This provides far
more flexibility in analysing vectors than standard Vector ISAs.  Normal
Vector ISAs are typically restricted to "were all results nonzero" and
"were some results nonzero". The application of mapreduce to Vectorised
cr operations allows far more sophisticated analysis, particularly in
conjunction with the new crweird operations see [[sv/cr_int_predication]].

Note in particular that the use of a separate instruction in this way
ensures that high performance multi-issue OoO inplementations do not
have the computation of the cumulative analysis CR as a bottleneck and
hindrance, regardless of the length of VL.

Additionally,
SVP64 [[sv/branches]] may be used, even when the branch itself is to
the following instruction.  The combined side-effects of CTR reduction
and VL truncation provide several benefits.

(see [[discussion]].  some alternative schemes are described there)

## Rc=1 when SUBVL!=1

sub-vectors are effectively a form of Packed SIMD (length 2 to 4). Only 1 bit of
predicate is allocated per subvector; likewise only one CR is allocated
per subvector.

This leaves a conundrum as to how to apply CR computation per subvector,
when normally Rc=1 is exclusively applied to scalar elements.  A solution
is to perform a bitwise OR or AND of the subvector tests.  Given that
OE is ignored in SVP64, this field may (when available) be used to select OR or
AND behavior.

### Table of CR fields

CRn is the notation used by the OpenPower spec to refer to CR field #i,
so FP instructions with Rc=1 write to CR1 (n=1).

CRs are not stored in SPRs: they are registers in their own right.
Therefore context-switching the full set of CRs involves a Vectorised
mfcr or mtcr, using VL=8 to do so.  This is exactly as how
scalar OpenPOWER context-switches CRs: it is just that there are now
more of them.

The 64 SV CRs are arranged similarly to the way the 128 integer registers
are arranged.  TODO a python program that auto-generates a CSV file
which can be included in a table, which is in a new page (so as not to
overwhelm this one). [[svp64/cr_names]]

# Register Profiles

**NOTE THIS TABLE SHOULD NO LONGER BE HAND EDITED** see
<https://bugs.libre-soc.org/show_bug.cgi?id=548> for details.

Instructions are broken down by Register Profiles as listed in the
following auto-generated page: [[opcode_regs_deduped]].  "Non-SV"
indicates that the operations with this Register Profile cannot be
Vectorised (mtspr, bc, dcbz, twi)

TODO generate table which will be here [[svp64/reg_profiles]]

# SV pseudocode illilustration

## Single-predicated Instruction

illustration of normal mode add operation: zeroing not included, elwidth
overrides not included.  if there is no predicate, it is set to all 1s

    function op_add(rd, rs1, rs2) # add not VADD!
      int i, id=0, irs1=0, irs2=0;
      predval = get_pred_val(FALSE, rd);
      for (i = 0; i < VL; i++)
        STATE.srcoffs = i # save context
        if (predval & 1<<i) # predication uses intregs
           ireg[rd+id] <= ireg[rs1+irs1] + ireg[rs2+irs2];
        if (!int_vec[rd].isvec) break;
        if (rd.isvec)  { id += 1; }
        if (rs1.isvec) { irs1 += 1; }
        if (rs2.isvec) { irs2 += 1; }
        if (id == VL or irs1 == VL or irs2 == VL)
        {
          # end VL hardware loop
          STATE.srcoffs = 0; # reset
          return;
        }

This has several modes:

* RT.v = RA.v RB.v
* RT.v = RA.v RB.s (and RA.s RB.v)
* RT.v = RA.s RB.s
* RT.s = RA.v RB.v
* RT.s = RA.v RB.s (and RA.s RB.v)
* RT.s = RA.s RB.s

All of these may be predicated.  Vector-Vector is straightfoward.
When one of source is a Vector and the other a Scalar, it is clear that
each element of the Vector source should be added to the Scalar source,
each result placed into the Vector (or, if the destination is a scalar,
only the first nonpredicated result).

The one that is not obvious is RT=vector but both RA/RB=scalar.
Here this acts as a "splat scalar result", copying the same result into
all nonpredicated result elements.  If a fixed destination scalar was
intended, then an all-Scalar operation should be used.

See <https://bugs.libre-soc.org/show_bug.cgi?id=552>

# Assembly Annotation

Assembly code annotation is required for SV to be able to successfully
mark instructions as "prefixed".

A reasonable (prototype) starting point:

    svp64 [field=value]*

Fields:

* ew=8/16/32 - element width
* sew=8/16/32 - source element width
* vec=2/3/4 - SUBVL
* mode=reduce/satu/sats/crpred
* pred=1\<\<3/r3/~r3/r10/~r10/r30/~r30/lt/gt/le/ge/eq/ne
* spred={reg spec}

similar to x86 "rex" prefix.

For actual assembler:

    sv.asmcode/mode.vec{N}.ew=8,sw=16,m={pred},sm={pred} reg.v, src.s

Qualifiers:

* m={pred}: predicate mask mode
* sm={pred}: source-predicate mask mode (only allowed in Twin-predication)
* vec{N}: vec2 OR vec3 OR vec4 - sets SUBVL=2/3/4
* ew={N}: ew=8/16/32 - sets elwidth override
* sw={N}: sw=8/16/32 - sets source elwidth override
* ff={xx}: see fail-first mode
* pr={xx}: see predicate-result mode
* sat{x}: satu / sats - see saturation mode
* mr: see map-reduce mode
* mr.svm see map-reduce with sub-vector mode
* crm: see map-reduce CR mode
* crm.svm see map-reduce CR with sub-vector mode
* sz: predication with source-zeroing
* dz: predication with dest-zeroing

For modes:

* pred-result:
  - pm=lt/gt/le/ge/eq/ne/so/ns OR
  - pm=RC1 OR pm=~RC1
* fail-first
  - ff=lt/gt/le/ge/eq/ne/so/ns OR
  - ff=RC1 OR ff=~RC1
* saturation:
  - sats
  - satu
* map-reduce:
  - mr OR crm: "normal" map-reduce mode or CR-mode.
  - mr.svm OR crm.svm: when vec2/3/4 set, sub-vector mapreduce is enabled

# Proposed Parallel-reduction algorithm

**This algorithm contains a MV operation and may NOT be used.  Removal
of the MV operation may be achieved by using index-redirection as was
achieved in DCT and FFT REMAP**

```
/// reference implementation of proposed SimpleV reduction semantics.
///
                // reduction operation -- we still use this algorithm even
                // if the reduction operation isn't associative or
                // commutative.
    XXX VIOLATION OF SVP64 DESIGN PRINCIPLES               XXXX
/// XXX `pred` is a user-visible Vector Condition register XXXX
    XXX VIOLATION OF SVP64 DESIGN PRINCIPLES               XXXX
///
/// all input arrays have length `vl`
def reduce(vl, vec, pred):
    pred = copy(pred) # must not damage predicate
    step = 1;
    while step < vl
        step *= 2;
        for i in (0..vl).step_by(step)
            other = i + step / 2;
            other_pred = other < vl && pred[other];
            if pred[i] && other_pred
                vec[i] += vec[other];
            else if other_pred
                XXX VIOLATION OF SVP64 DESIGN XXX
                XXX vec[i] = vec[other];      XXX
                XXX VIOLATION OF SVP64 DESIGN XXX
            pred[i] |= other_pred;
```

The first principle in SVP64 being violated is that SVP64 is a fully-independent
Abstraction of hardware-looping in between issue and execute phases 
that has no relation to the operation it issues.  The above pseudocode
conditionally changes not only the type of element operation issued
(a MV in some cases) but also the number of arguments (2 for a MV).
At the very least, for Vertical-First Mode this will result in unanticipated and unexpected behaviour (maximise "surprises" for programmers) in
the middle of loops, that will be far too hard to explain.

The second principle being violated by the above algorithm is the expectation
that temporary storage is available for a modified predicate: there is no
such space, and predicates are read-only to reduce complexity at the
micro-architectural level.
SVP64 is founded on the principle that all operations are
"re-entrant" with respect to interrupts and exceptions: SVSTATE must
be saved and restored alongside PC and MSR, but nothing more. It is perfectly
fine to have context-switching back to the operation be somewhat slower,
through "reconstruction" of temporary internal state based on what SVSTATE
contains, but nothing more.

An alternative algorithm is therefore required that does not perform MVs,
and does not require additional state to be saved on context-switching.

```
def reduce(  vl,  vec, pred ):
    pred = copy(pred) # must not damage predicate
    j = 0
    vi = [] # array of lookup indices to skip nonpredicated
    for i, pbit in enumerate(pred):
       if pbit:
           vi[j] = i
           j += 1
    step = 2
    while step <= vl
        halfstep = step // 2
        for i in (0..vl).step_by(step)
            other = vi[i + halfstep]
            ir = vi[i]
            other_pred = other < vl && pred[other]
            if pred[i] && other_pred
                vec[ir] += vec[other]
            else if other_pred:
               vi[ir] = vi[other] # index redirection, no MV
            pred[ir] |= other_pred # reconstructed on context-switch
         step *= 2
```

In this version the need for an explicit MV is made unnecessary by instead
leaving elements *in situ*.  The internal modifications to the predicate may,
due to the reduction being entirely deterministic, be "reconstructed"
on a context-switch. This may make some implementations slower.

*Implementor's Note: many SIMD-based Parallel Reduction Algorithms are
implemented in hardware with MVs that ensure lane-crossing is minimised.
The mistake which would be catastrophic to SVP64 to make is to then
limit the Reduction Sequence for all implementors
based solely and exclusively on what one
specific internal microarchitecture does.
In SIMD ISAs the internal SIMD Architectural design is exposed and imposed on the programmer. Cray-style Vector ISAs on the other hand provide convenient,
compact and efficient encodings of abstract concepts.
It is the Implementor's responsibility to produce a design
that complies with the above algorithm,
utilising internal Micro-coding and other techniques to transparently
insert MV operations
if necessary or desired, to give the level of efficiency or performance
required.*

# Element-width overrides

Element-width overrides are best illustrated with a packed structure
union in the c programming language.  The following should be taken
literally, and assume always a little-endian layout:

    typedef union {
        uint8_t  b[];
        uint16_t s[];
        uint32_t i[];
        uint64_t l[];
        uint8_t actual_bytes[8];
    } el_reg_t;

    elreg_t int_regfile[128];

    get_polymorphed_reg(reg, bitwidth, offset):
        el_reg_t res;
        res.l = 0; // TODO: going to need sign-extending / zero-extending
        if bitwidth == 8:
            reg.b = int_regfile[reg].b[offset]
        elif bitwidth == 16:
            reg.s = int_regfile[reg].s[offset]
        elif bitwidth == 32:
            reg.i = int_regfile[reg].i[offset]
        elif bitwidth == 64:
            reg.l = int_regfile[reg].l[offset]
        return res

    set_polymorphed_reg(reg, bitwidth, offset, val):
        if (!reg.isvec):
            # not a vector: first element only, overwrites high bits
            int_regfile[reg].l[0] = val
        elif bitwidth == 8:
            int_regfile[reg].b[offset] = val
        elif bitwidth == 16:
            int_regfile[reg].s[offset] = val
        elif bitwidth == 32:
            int_regfile[reg].i[offset] = val
        elif bitwidth == 64:
            int_regfile[reg].l[offset] = val

In effect the GPR registers r0 to r127 (and corresponding FPRs fp0 
to fp127) are reinterpreted to be "starting points" in a byte-addressable
memory.  Vectors - which become just a virtual naming construct - effectively
overlap.

It is extremely important for implementors to note that the only circumstance
where upper portions of an underlying 64-bit register are zero'd out is
when the destination is a scalar.  The ideal register file has byte-level
write-enable lines, just like most SRAMs.

An example ADD operation with predication and element width overrides:

      for (i = 0; i < VL; i++)
        if (predval & 1<<i) # predication
           src1 = get_polymorphed_reg(RA, srcwid, irs1)
           src2 = get_polymorphed_reg(RB, srcwid, irs2)
           result = src1 + src2 # actual add here
           set_polymorphed_reg(RT, destwid, ird, result)
           if (!RT.isvec) break
        if (RT.isvec)  { id += 1; }
        if (RA.isvec)  { irs1 += 1; }
        if (RB.isvec)  { irs2 += 1; }

# Twin (implicit) result operations

Some operations in the Power ISA already target two 64-bit scalar
registers: `lq` for example. Some mathematical algorithms are more
efficient when there are two outputs rather than one, providing
feedback loops between elements.  64-bit multiply
for example actually internally produces a 128 bit result, which clearly
cannot be stored in a single 64 bit register.  Some ISAs recommend
"macro op fusion": the practice of setting a convention whereby if
two commonly used instructions (mullo, mulhi) use the same ALU but
one selects the low part of an identical operation and the other
selects the high part, then optimised micro-architectures may
"fuse" those two instructions together, using Micro-coding techniques,
internally.

The practice and convention of macro-op fusion however is not compatible
with SVP64 Horizontal-First, because Horizontal Mode may only
be applied to a single instruction at a time.  Thus it becomes
necessary to add explicit more complex single instructions with
more operands than would normally be seen in another ISA. If it
was not for Power ISA already having LD/ST with update as well as
Condition Codes and `lq` this would be hard to justify.

With limited space in the `EXTRA` Field, and Power ISA opcodes
being only 32 bit, 5 operands is quite an ask.  `lq` however sets
a precedent: `RTp` stands for "RT pair".  In other words the result
is stored in RT and RT+1.  For Scalar operations, following this
precedent is perfectly reasonable.  In Scalar mode,
`madded` therefore stores the two halves of the 128-bit multiply
into RT and RT+1.

What, then, of `sv.madded`? If the destination is hard-coded to
RT and RT+1 the instruction is not useful when Vectorised because
the output will be overwritten on the next element.  To solve this
is easy: define the destination registers as RT and RT+MAXVL
respectively.  This makes it easy for compilers to statically allocate
registers even when VL changes dynamically.

Bear in mind that both RT and RT+MAXVL are starting points for Vectors,
and bear in mind that element-width overrides still have to be taken
into consideration, the starting point for the implicit destination
is best illustrated in pseudocode:

      # demo of madded
      for (i = 0; i < VL; i++)
        if (predval & 1<<i) # predication
           src1 = get_polymorphed_reg(RA, srcwid, irs1)
           src2 = get_polymorphed_reg(RB, srcwid, irs2)
           src2 = get_polymorphed_reg(RC, srcwid, irs3)
           result = src1*src2 + src2
           destmask = (2<<destwid)-1
           # store two halves of result
           set_polymorphed_reg(RT, destwid, ird      , result&destmask)
           set_polymorphed_reg(RT, destwid, ird+MAXVL, result>>destwid)
           if (!RT.isvec) break
        if (RT.isvec)  { id += 1; }
        if (RA.isvec)  { irs1 += 1; }
        if (RB.isvec)  { irs2 += 1; }
        if (RC.isvec)  { irs3 += 1; }

The significant part here is that the second half is stored
starting not from RT+MAXVL at all: it is the *element* index
that is offset by MAXVL, both starting from RT.

* [[isa/svfixedarith]]
* [[isa/svfparith]]