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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=864> parallel prefix simulator
* <https://bugs.libre-soc.org/show_bug.cgi?id=809> OV sv.addex discussion
* ARM SVE Fault-first <https://alastairreid.github.io/papers/sve-ieee-micro-2017.pdf>

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]]

## Partial Implementations

It is perfectly legal to implement subsets of SVP64 as long as illegal
instruction traps are always raised on unimplemented features,
so that soft-emulation is possible,
even for future revisions of SVP64. With SVP64 being partly controlled
through contextual SPRs, a little care has to be taken.

**All** SPRs
not implemented including reserved ones for future use must raise an illegal
instruction trap if read or written. This allows software the
opportunity to emulate the context created by the given SPR.

See [[sv/compliancy_levels]] for full details.

## 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 with Carry" has been performed, and that
CA contains the 257th bit.  A one-instruction 512-bit Add-with-Carry
may be performed by setting VL=8, and a one-instruction
1024-bit Add-with-Carry by setting VL=16, and so on.  More on
this in [[openpower/sv/biginteger]]

## 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 <a name="1p"> </a>

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, but depending on whether sz and/or dz are set,
srcstep and dststep can still potentially become different indices.
Only when sz=dz is srcstep guaranteed to equal dststep at all times.

Note that in some Mode Formats there is only one flag (zz). This indicates
that *both* sz *and* dz are set to the same.

Example 1:

* VL=4
* mask=0b1101
* sz=0, dz=1

The following schedule for srcstep and dststep will occur:

| srcstep | dststep | comment      |
| ----    | -----   | --------      |
| 0       | 0       | both mask[src=0] and mask[dst=0] are 1 |
| 1       | 2       | sz=1 but dz=0: dst skips mask[1], src soes not |
| 2       | 3       | mask[src=2] and mask[dst=3] are 1 |
| end     | end     | loop has ended because dst reached VL-1 |

Example 2:

* VL=4
* mask=0b1101
* sz=1, dz=0

The following schedule for srcstep and dststep will occur:

| srcstep | dststep | comment      |
| ----    | -----   | --------      |
| 0       | 0       | both mask[src=0] and mask[dst=0] are 1 |
| 2       | 1       | sz=0 but dz=1: src skips mask[1], dst does not |
| 3       | 2       | mask[src=3] and mask[dst=2] are 1 |
| end     | end     | loop has ended because src reached VL-1 |

In both these examples it is crucial to note that despite there being
a single predicate mask, with sz and dz being different, srcstep and
dststep are being requested to react differently.

Example 3:

* VL=4
* mask=0b1101
* sz=0, dz=0

The following schedule for srcstep and dststep will occur:

| srcstep | dststep | comment      |
| ----    | -----   | --------      |
| 0       | 0       | both mask[src=0] and mask[dst=0] are 1 |
| 2       | 2       | sz=0 and dz=0: both src and dst skip mask[1] |
| 3       | 3       | mask[src=3] and mask[dst=3] are 1 |
| end     | end     | loop has ended because src and dst reached VL-1 |

Here, both srcstep and dststep remain in lockstep because sz=dz=1

## Twin Predication <a name="2p"> </a>

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, but abstracted out from Load/Store and applicable
in general to any 2P 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).

## Pack/Unpack

The pack/unpack concept of VSX `vpack` is abstracted out as Sub-Vector
reordering.  Two bits in the `SVSHAPE` [[sv/spr]] enable either "packing"
or "unpacking" on the subvectors vec2/3/4.

First, illustrating a "normal" SVP64 operation with `SUBVL!=1:` (assuming
no elwidth overrides), note that the VL loop is outer and the SUBVL
loop inner:

```
    def index():
        for i in range(VL):
            for j in range(SUBVL):
                yield i*SUBVL+j

    for idx in index():
        operation_on(RA+idx)
```

For pack/unpack (again, no elwidth overrides), note that now there is the
option to swap the SUBVL and VL loop orders.
In effect the Pack/Unpack performs a Transpose of the subvector elements.
Illustrated this time with a GPR mv operation:

```
    # yield an outer-SUBVL or inner VL loop with SUBVL
    def index_p(outer):
        if outer:
            for j in range(SUBVL):   # subvl is outer
                for i in range(VL):  # vl is inner
                    yield i+VL*j
        else:
            for i in range(VL):        # vl is outer
                for j in range(SUBVL): # subvl is inner
                    yield i*SUBVL+j

     # walk through both source and dest indices simultaneously
     for src_idx, dst_idx in zip(index_p(PACK), index_p(UNPACK)):
         move_operation(RT+dst_idx, RA+src_idx)
```

"yield" from python is used here for simplicity and clarity.
The two Finite State Machines for the generation of the source
and destination element offsets progress incrementally in
lock-step.

Example VL=2, SUBVL=3, PACK_en=1 - elements grouped by
vec3 will be redistributed such that Sub-elements 0 are
packed together, Sub-elements 1 are packed together, as
are Sub-elements 2.
            
```
     srcstep=0   srcstep=1
     0   1   2   3   4   5

     dststep=0  dststep=1  dststep=2
     0   3      1   4      2   5
```

Setting of both `PACK` and `UNPACK` is neither prohibited nor `UNDEFINED`
because the reordering is fully deterministic, and additional REMAP
reordering may be applied. Combined with Matrix REMAP this would give
potentially up to 4 Dimensions of reordering.

Pack/Unpack has quirky interactions on [[sv/mv.swizzle]] because it can
set a different subvector length for destination, and has a slightly
different pseudocode algorithm for Vertical-First Mode.

Ordering is as follows:

* SVSHAPE srcstep, dststep, ssubstep and dsubstep are advanced sequentially
  depending on PACK/UNPACK.
* srcstep and dststep are pushed through REMAP to compute actual Element offsets.
* Swizzle is independently applied to ssubstep and dsubstep

Pack/Unpack is enabled (set up) through [[sv/svstep]].

## 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.

For Scalar Reduction, Microarchitectures *may* take opportunities to
parallelise the reduction but only if in doing so they preserve strict
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 *and*
the same register is used as a source register.  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 by
  convention 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. However it would clearly be unacceptable to perform
such optimisations on cache-inhibited LD/ST, so some considerable care
needs to be taken.*

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.

## Fail-on-first <a name="fail-first"> </a>

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 (not to be confused with *Data-Dependent* LD/ST ffirst)
  treats the first LD/ST in a vector (element 0) as an ordinary one.
  Exceptions occur "as normal" on the first element.  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. At the same time it is also
"old" because it is a generalisation of the Z80 [Block
compare](https://rvbelzen.tripod.com/z80prgtemp/z80prg04.htm)
instructions, especially
[CPIR](http://z80-heaven.wikidot.com/instructions-set:cpir) which is
based on CP (compare) as the ultimate "element" (suffix) operation
to which the repeat (prefix) is applied.  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.

*Note: there is no reverse-direction for Data-dependent Fail-First.  REMAP
will need to be activated to invert the ordering of element traversal.*

### 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

Pred-result mode may not be applied on CR-based operations.

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.

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.  Given that there are no CR-based
operations that produce Rc=1 co-results, there can be no pred-result
mode  for mtcr and other CR-based instructions

Arithmetic and Logical Pred-result, which does have Rc=1 or for which
RC1 Mode makes sense, is covered in [[sv/normal]]

## 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 <a name="cr_extra"></a>

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.  Firstly and most importantly a new
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{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.

The `CR{n}` notation is designed to give *linear sequential
numbering* in the Vector domain on a straight sequential Vector Loop.

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 (EQ/LT/GT/SO).  The numbering was determined (after 4 months of
analysis and research) to be as follows:

```
    CR_index = (BA>>2)      # top 3 bits
    bit_index = (BA & 0b11) # low 2 bits
    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 Field* number `CR_reg`
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 determine CR\_reg is modified to as follows:

```
    CR_index = (BA>>2)      # top 3 bits 
    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 = (BA & 0b11) # low 2 bits
    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

Instructions are broken down by Register Profiles as listed in the
following auto-generated page: [[opcode_regs_deduped]].  These tables,
despite being auto-generated, are part of the Specification.

## SV pseudocode illustration

### 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=mr/satu/sats/crpred
* pred=1\<\<3/r3/~r3/r10/~r10/r30/~r30/lt/gt/le/ge/eq/ne

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
* mrr: map-reduce, reverse-gear (VL-1 downto 0)
* 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
  - RC1 mode
* fail-first
  - ff=lt/gt/le/ge/eq/ne/so/ns
  - RC1 mode
* 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

## Parallel-reduction algorithm

The principle of SVP64 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.
Additional state cannot be saved on context-switching beyond that
of SVSTATE, making things slightly tricky.

Executable demo pseudocode, full version
[here](https://git.libre-soc.org/?p=libreriscv.git;a=blob;f=openpower/sv/test_preduce.py;hb=HEAD)

```
[[!inline pages="openpower/sv/preduce.py" raw="yes" ]]
```

This algorithm works by noting when data remains in-place rather than
being reduced, and referring to that alternative position on subsequent
layers of reduction.  It is re-entrant. If however interrupted and
restored, some implementations may take longer to re-establish the
context.

Its application by default is that:

* RA, FRA or BFA is the first register as the first operand
  (ci index offset in the above pseudocode)
* RB, FRB or BFB is the second (co index offset)
* RT (result) also uses ci **if RA==RT**

For more complex applications a REMAP Schedule must be used

*Programmers's note: if passed a predicate mask with only one bit set,
this algorithm takes no action, similar to when a predicate mask is
all zero.*

*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 micro-architectural lane-crossing Move operations
if necessary or desired, to give the level of efficiency or performance
required.**

## Element-width overrides <a name="elwidth"> </>

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:

```
    #pragma pack
    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];
```

Accessing (get and set) of registers given a value, register (in `elreg_t`
form), and that all arithmetic, numbering and pseudo-Memory format is
LE-endian and LSB0-numbered below:

```
    elreg_t& get_polymorphed_reg(elreg_t const& reg, bitwidth, offset):
        el_reg_t res; // result
        res.l = 0; // TODO: going to need sign-extending / zero-extending
        if !reg.isvec: // scalar access has no element offset
            offset = 0
        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 reg

    set_polymorphed_reg(elreg_t& reg, bitwidth, offset, val):
        if (!reg.isvec):
            # for safety mask out hi bits
            bytemask = (8 << bitwidth) - 1
            val &= bytemask
            # not a vector: first element only, overwrites high bits.
            # and with the *Architectural* definition being LE,
            # storing in the first DWORD works perfectly.
            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, in order to avoid READ-MODIFY-WRITE.

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; }
```

Thus it can be clearly seen that elements are packed by their
element width, and the packing starts from the source (or destination)
specified by the instruction.

## Twin (implicit) result operations

Some operations in the Power ISA already target two 64-bit scalar
registers: `lq` for example, and LD with update.  Some mathematical
algorithms are more efficient when there are two outputs rather than one,
providing feedback loops between elements (the most well-known being add
with carry).  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, and SVP64 is based on the principle of
strict Program Order even at the element level.  Thus it becomes necessary
to add explicit more complex single instructions with more operands than
would normally be seen in the average RISC ISA (3-in, 2-out, in some
cases). 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, `maddedu` therefore stores the two halves of the 128-bit
multiply into RT and RT+1.

What, then, of `sv.maddedu`? 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 maddedu
     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, both start from RT.
           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 halves actually starting from RT.
If VL is 3, MAXVL is 5, RT is 1, and dest elwidth is 32 then the elements
RT0 to RT2 are stored:

```
     LSB0:  63:32     31:0
     MSB0:  0:31      32:63
     r0    unchanged unchanged
     r1    RT1.lo    RT0.lo
     r2    unchanged RT2.lo
     r3    RT0.hi    unchanged
     r4    RT2.hi    RT1.hi
     r5    unchanged unchanged
```

Note that all of the LO halves start from r1, but that the HI halves
start from half-way into r3. The reason is that with MAXVL bring 5 and
elwidth being 32, this is the 5th element offset (in 32 bit quantities)
counting from r1.

*Programmer's note: accessing registers that have been placed starting
on a non-contiguous boundary (half-way along a scalar register) can
be inconvenient: REMAP can provide an offset but it requires extra
instructions to set up.  A simple solution is to ensure that MAXVL is
rounded up such that the Vector ends cleanly on a contiguous register
boundary.  MAXVL=6 in the above example would achieve that*

Additional DRAFT Scalar instructions in 3-in 2-out form with an implicit
2nd destination:

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

[[!tag standards]]

------

\newpage{}