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# RFC ls010 SVP64 Zero-Overhead Loop Prefix Subsystem

Credits and acknowledgements:

* Luke Leighton
* Jacob Lifshay
* Hendrik Boom
* Richard Wilbur
* Alexandre Oliva
* Cesar Strauss
* NLnet Foundation, for funding
* OpenPOWER Foundation
* Paul Mackerras
* Toshaan Bharvani
* IBM for the Power ISA itself

Links:

* <https://bugs.libre-soc.org/show_bug.cgi?id=1045>

# Introduction

Simple-V is a type of Vectorisation best described as a "Prefix Loop
Subsystem" similar to the 5 decades-old Zilog Z80 `LDIR` instruction and to the 8086 `REP`
Prefix instruction.  More advanced features are similar to the Z80
`CPIR` instruction. If viewed one-dimensionally as an actual Vector ISA it introduces
over 1.5 million 64-bit Vector instructions.  SVP64, the instruction
format, is therefore best viewed as an orthogonal RISC-paradigm "Prefixing"
subsystem instead.

Except where explicitly stated all bit numbers remain as in the rest of
the Power ISA: in MSB0 form (the bits are numbered from 0 at the MSB on
the left and counting up as you move rightwards to the LSB end). All bit
ranges are inclusive (so `4:6` means bits 4, 5, and 6, in MSB0 order).
**All register numbering and element numbering however is LSB0 ordering**
which is a different convention from that used elsewhere in the Power ISA.

The SVP64 prefix always comes before the suffix in PC order and must be
considered an independent "Defined word" that augments the behaviour of
the following instruction, but does **not** change the actual Decoding
of that following instruction.  **All prefixed instructions retain their
non-prefixed encoding and definition**.

Two apparent exceptions to the above hard rule exist: SV Branch-Conditional
operations and LD/ST-update "Post-Increment" Mode.  Post-Increment
was considered sufficiently high priority (significantly reducing hot-loop
instruction count) that one bit in the Prefix is reserved for it.
Vectorised Branch-Conditional operations "embed" the original Scalar
Branch-Conditional behaviour into a much more advanced variant that
is highly suited to High-Performance Computation (HPC), Supercomputing,
and parallel GPU Workloads.

*Architectural Resource Allocation note: it is prohibited to accept RFCs
which fundamentally violate this hard requirement.  Under no circumstances
must the Suffix space have an alternate instruction encoding allocated
within SVP64 that is entirely different from the non-prefixed Defined
Word. Hardware Implementors critically rely on this inviolate guarantee
to implement High-Performance Multi-Issue micro-architectures that can
sustain 100% throughput*

Subset implementations in hardware are permitted, as long as certain
rules are followed, allowing for full soft-emulation including future
revisions.  Compliancy Subsets exist to ensure minimum levels of binary
interoperability expectations within certain environments.

## SVP64 encoding features

A number of features need to be compacted into a very small space of
only 24 bits:

* Independent per-register Scalar/Vector tagging and range extension on
  every register
* Element width overrides on both source and destination
* Predication on both source and destination
* Two different sources of predication: INT and CR Fields
* SV Modes including saturation (for Audio, Video and DSP), mapreduce,
  fail-first and predicate-result mode.

Different classes of operations require different formats. The earlier
sections cover the common formats and the four separate modes follow:
CR operations (crops), Arithmetic/Logical (termed "normal"), Load/Store
and Branch-Conditional.

## Definition of Reserved in this spec.

For the new fields added in SVP64, instructions that have any of their
fields set to a reserved value must cause an illegal instruction trap,
to allow emulation of future instruction sets, or for subsets of SVP64 to
be implemented in hardware and the rest emulated.  This includes SVP64
SPRs: reading or writing values which are not supported in hardware
must also raise illegal instruction traps in order to allow emulation.
Unless otherwise stated, reserved values are always all zeros.

This is unlike OpenPower ISA v3.1, which in many instances does not
require a trap if reserved fields are nonzero.  Where the standard Power
ISA definition is intended the red keyword `RESERVED` is used.

##  Definition of "UnVectoriseable"

Any operation that inherently makes no sense if repeated is termed
"UnVectoriseable" or "UnVectorised".  Examples include `sc` or `sync`
which have no registers. `mtmsr` is also classed as UnVectoriseable
because there is only one `MSR`.

## Register files, elements, and Element-width Overrides

In the Upper Compliancy Levels of SVP64 the size of the GPR and FPR Register
files are expanded from 32 to 128 entries, and the number of CR Fields
expanded from CR0-CR7 to CR0-CR127. (Note: A future version of SVP64 is anticipated
to extend the VSR register file).

Memory access remains exactly the same: the effects of `MSR.LE` remain
exactly the same, affecting as they already do and remain **only**
on the Load and Store memory-register operation byte-order, and having
nothing to do with the ordering of the contents of register files or
register-register operations.

To be absolutely clear:

```
    No conceptual arithmetic ordering or other changes over the Scalar
    Power ISA definitions to registers or register files or to arithmetic
    or Logical Operations beyond element-width subdivision and sequential
    element numbering are expressed or implied
```

Element offset
numbering is naturally **LSB0-sequentially-incrementing from zero, not
MSB0-incrementing** including when element-width overrides are used,
at which point the elements progress through each register
sequentially from the LSB end
(confusingly numbered the highest in MSB0 ordering) and progress
incrementally to the MSB end (confusingly numbered the lowest in
MSB0 ordering).

When exclusively using MSB0-numbering, SVP64
becomes unnecessarily complex to both express and subsequently understand:
the required conditional subtractions from 63,
31, 15 and 7 unfortunately become a hostile minefield, obscuring both
intent and meaning. Therefore for the
purposes of this section the more natural **LSB0 numbering is assumed**
and it is left to the reader to translate to MSB0 numbering.

The Canonical specification for how element-sequential numbering and
element-width overrides is defined is expressed in the following c
structure, assuming a Little-Endian system, and naturally using LSB0
numbering everywhere because the ANSI c specification is inherently LSB0:

```
    #pragma pack
    typedef union {
        uint8_t  b[]; // elwidth 8
        uint16_t s[]; // elwidth 16
        uint32_t i[]; // elwidth 32
        uint64_t l[]; // elwidth 64
        uint8_t actual_bytes[8];
    } el_reg_t;

    elreg_t int_regfile[128];

    void get_register_element(el_reg_t* el, int gpr, int element, int width) {
        switch (width) {
            case 64: el->l = int_regfile[gpr].l[element];
            case 32: el->i = int_regfile[gpr].i[element];
            case 16: el->s = int_regfile[gpr].s[element];
            case 8 : el->b = int_regfile[gpr].b[element];
        }
    }
    void set_register_element(el_reg_t* el, int gpr, int element, int width) {
        switch (width) {
            case 64: int_regfile[gpr].l[element] = el->l;
            case 32: int_regfile[gpr].i[element] = el->i;
            case 16: int_regfile[gpr].s[element] = el->s;
            case 8 : int_regfile[gpr].b[element] = el->b;
        }
    }
```

Example Vector-looped add operation implementation when elwidths are 64-bit:

```
 # add RT, RA,RB using the "uint64_t" union member, "l"
 for i in range(VL):
      int_regfile[RT].l[i] = int_regfile[RA].l[i] + int_regfile[RB].l[i]
```

However if elwidth overrides are set to 16 for both source and destination:

```
 # add RT, RA, RB using the "uint64_t" union member "s"
 for i in range(VL):
      int_regfile[RT].s[i] = int_regfile[RA].s[i] + int_regfile[RB].s[i]
```

Hardware Architectural note: to avoid a Read-Modify-Write at the register
file it is strongly recommended to implement byte-level write-enable lines
exactly as has been implemented in DRAM ICs for many decades. Additionally
the predicate mask bit is advised to be associated with the element
operation and alongside the result ultimately passed to the register file.
When element-width is set to 64-bit the relevant predicate mask bit
may be repeated eight times and pull all eight write-port byte-level
lines HIGH. Clearly when element-width is set to 8-bit the relevant
predicate mask bit corresponds directly with one single byte-level
write-enable line.  It is up to the Hardware Architect to then amortise
(merge) elements together into both PredicatedSIMD Pipelines as well
as simultaneous non-overlapping Register File writes, to achieve High
Performance designs.

## Scalar Identity Behaviour

SVP64 is designed so that when the prefix is all zeros, and
 VL=1, no effect or
influence occurs (no augmentation) such that all standard Power ISA
v3.0/v3 1 instructions covered by the prefix are "unaltered". This
is termed `scalar identity behaviour` (based on the mathematical
definition for "identity", as in, "identity matrix" or better "identity
transformation").

Note that this is completely different from when VL=0.  VL=0 turns all
operations under its influence into `nops` (regardless of the prefix)
whereas when VL=1 and the SV prefix is all zeros, the operation simply
acts as if SV had not been applied at all to the instruction  (an
"identity transformation").

The fact that `VL` is dynamic and can be set to any value at runtime based
on program conditions and behaviour means very specifically that
`scalar identity behaviour` is **not** a redundant encoding. If the
only means by which VL could be set was by way of static-compiled
immediates then this assertion would be false.  VL should not
be confused with MAXVL when understanding this key aspect of SimpleV.

## Register Naming and size

As indicated above SV Registers are simply the GPR, FPR and CR
register files extended linearly to larger sizes; SV Vectorisation
iterates sequentially through these registers (LSB0 sequential ordering
from 0 to VL-1).

Where the integer regfile in standard scalar Power ISA v3.0B/v3.1B is
r0 to r31, SV extends this as r0 to r127.  Likewise FP registers are
extended to 128 (fp0 to fp127), and CR Fields are extended to 128 entries,
CR0 thru CR127.

The names of the registers therefore reflects a simple linear extension
of the Power ISA v3.0B / v3.1B register naming, and in hardware this
would be reflected by a linear increase in the size of the underlying
SRAM used for the regfiles.

Note: when an EXTRA field (defined below) is zero, SV is deliberately
designed so that the register fields are identical to as if SV was not in
effect i.e. under these circumstances (EXTRA=0) the register field names
RA, RB etc. are interpreted and treated as v3.0B / v3.1B scalar registers.
This is part of `scalar identity behaviour` described above.

## Future expansion.

With the way that EXTRA fields are defined and applied to register fields,
future versions of SV may involve 256 or greater registers. Backwards
binary compatibility may be achieved with a PCR bit (Program Compatibility
Register).  Further discussion is out of scope for this version of SVP64.

Additionally, a future variant of SVP64 will be applied to the Scalar
(Quad-precision and 128-bit) VSX instructions. Element-width overrides
are an opportunity to expand the Power ISA to 256-bit, 512-bit and
1024-bit operations.

--------

\newpage{}

# New 64-bit Instruction Encoding spaces

The following seven new areas are defined within Primary Opcode 9 (EXT009) as a
new 64-bit encoding space, alongside EXT1xx.

| 0-5 | 6 | 7 | 8-31  | 32| Description                        |
|-----|---|---|-------|---|------------------------------------|
| PO  | 0 | x | xxxx  | 0 | EXT200-232 or `RESERVED2` (56-bit) |
| PO  | 0 | 0 | !zero | 1 | SVP64Single:EXT232-263, or `RESERVED3` |
| PO  | 0 | 0 | 0000  | 1 | Scalar EXT232-263               |
| PO  | 0 | 1 | nnnn  | 1 | SVP64:EXT232-263     |
| PO  | 1 | 0 | 0000  | x | EXT300-363 or `RESERVED1` (32-bit) |
| PO  | 1 | 0 | !zero | n | SVP64Single:EXT000-063 or `RESERVED4` |
| PO  | 1 | 1 | nnnn  | n | SVP64:EXT000-063       |

Note that for the future SVP64Single Encoding (currently RESERVED) it
is prohibited to have bits 8-31 be zero, unlike for SVP64 Vector space,
for which bits 8-31
can be zero (termed `scalar identity behaviour`). This
prohibition allows SVP64Single to share its
Encoding space with Scalar Ext232-263 and Scalar EXT300-363.

*Architectural Resource Allocation Note: **under no circumstances** must
different Defined Words be allocated within any `EXT{z}` prefixed
or unprefixed space for a given value of `z`. Even if UnVectoriseable
an instruction Defined Word space must have the exact same Instruction
and exact same Instruction Encoding in all spaces (including
being RESERVED if UnVectoriseable) or not be allocated at all.
This is required as an inviolate hard rule governing Primary Opcode 9
that may not be revoked under any circumstances. A useful way to think
of this is that the Prefix Encoding is, like the 8086 REP instruction,
an independent 32-bit Defined Word.*

# Remapped Encoding (`RM[0:23]`)

In the SVP64 Vector Prefix spaces, the 24 bits 8-31 are termed `RM`. Bits 32-37 are
the Primary Opcode of the Suffix "Defined Word". 38-63 are the remainder of the
Defined Word.  Note that the new EXT232-263 SVP64 area it is obviously mandatory
that bit 32 is required to be set to 1.

| 0-5 | 6 | 7 | 8-31     | 32-37  | 38-64    |Description                        |
|-----|---|---|----------|--------|----------|-----------------------|
| PO  | 0 | 1 | RM[0:23] | 1nnnnn | xxxxxxxx | SVP64:EXT232-263     |
| PO  | 1 | 1 | RM[0:23] | nnnnnn | xxxxxxxx | SVP64:EXT000-063       |

It is important to note that unlike v3.1 64-bit prefixed instructions
there is insufficient space in `RM` to provide identification of any SVP64
Fields without first partially decoding the 32-bit suffix.  Similar to
the "Forms" (X-Form, D-Form) the `RM` format is individually associated
with every instruction. However this still does not adversely affect Multi-Issue
Decoding because the identification of the 64-bit space has been kept brutally
simple.

Extreme caution and care must be taken when extending SVP64
in future, to not create unnecessary relationships between prefix and
suffix that could complicate decoding, adding latency.

## Common RM fields

The following fields are common to all Remapped Encodings:

| Field Name | Field bits | Description                            |
|------------|------------|----------------------------------------|
| MASKMODE   | `0`        | Execution (predication) Mask Kind      |
| MASK       | `1:3`      | Execution Mask                      |
| SUBVL      | `8:9`      | Sub-vector length                   |

The following fields are optional or encoded differently depending
on context after decoding of the Scalar suffix:

| Field Name | Field bits | Description                            |
|------------|------------|----------------------------------------|
| ELWIDTH       | `4:5`      | Element Width                       |
| ELWIDTH_SRC   | `6:7`      | Element Width for Source      |
| EXTRA         | `10:18`    | Register Extra encoding                |
| MODE          | `19:23`    | changes Vector behaviour               |

* MODE changes the behaviour of the SV operation (result saturation,
  mapreduce)
* SUBVL groups elements together into vec2, vec3, vec4 for use in 3D
  and Audio/Video DSP work
* ELWIDTH and ELWIDTH_SRC overrides the instruction's destination and
  source operand width
* MASK (and MASK_SRC) and MASKMODE provide predication (two types of
  sources: scalar INT and Vector CR).
* Bits 10 to 18 (EXTRA) are further decoded depending on the RM category
  for the instruction, which is determined only by decoding the Scalar 32
  bit suffix.

Similar to Power ISA `X-Form` etc. EXTRA bits are given designations,
such as `RM-1P-3S1D` which indicates for this example that the operation
is to be single-predicated and that there are 3 source operand EXTRA
tags and one destination operand tag.

Note that if ELWIDTH != ELWIDTH_SRC this may result in reduced performance
or increased latency in some implementations due to lane-crossing.

## Mode

Mode is an augmentation of SV behaviour.  Different types of instructions
have different needs, similar to Power ISA v3.1 64 bit prefix 8LS and MTRR
formats apply to different instruction types.  Modes include Reduction,
Iteration, arithmetic saturation, and Fail-First.  More specific details
in each section and in the SVP64 appendix

* For condition register operations see [[sv/cr_ops]]
* For LD/ST Modes, see [[sv/ldst]].
* For Branch modes, see [[sv/branches]]
* For arithmetic and logical, see [[sv/normal]]

## ELWIDTH Encoding

Default behaviour is set to 0b00 so that zeros follow the convention
of `scalar identity behaviour`.  In this case it means that elwidth
overrides are not applicable.  Thus if a 32 bit instruction operates
on 32 bit, `elwidth=0b00` specifies that this behaviour is unmodified.
Likewise when a processor is switched from 64 bit to 32 bit mode,
`elwidth=0b00` states that, again, the behaviour is not to be modified.

Only when elwidth is nonzero is the element width overridden to the
explicitly required value.

### Elwidth for Integers:

| Value | Mnemonic       | Description                        |
|-------|----------------|------------------------------------|
| 00    | DEFAULT        | default behaviour for operation    |
| 01    | `ELWIDTH=w`    | Word: 32-bit integer                 |
| 10    | `ELWIDTH=h`    | Halfword: 16-bit integer             |
| 11    | `ELWIDTH=b`    | Byte: 8-bit integer                  |

This encoding is chosen such that the byte width may be computed as
`8<<(3-ew)`

### Elwidth for FP Registers:

| Value | Mnemonic       | Description                        |
|-------|----------------|------------------------------------|
| 00    | DEFAULT        | default behaviour for FP operation     |
| 01    | `ELWIDTH=f32`  | 32-bit IEEE 754 Single floating-point  |
| 10    | `ELWIDTH=f16`  | 16-bit IEEE 754 Half floating-point   |
| 11    | `ELWIDTH=bf16` | Reserved for `bf16` |

Note:
[`bf16`](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format)
is reserved for a future implementation of SV

Note that any IEEE754 FP operation in Power ISA ending in "s" (`fadds`) shall
perform its operation at **half** the ELWIDTH then padded back out
to ELWIDTH.  `sv.fadds/ew=f32` shall perform an IEEE754 FP16 operation that is then "padded" to fill out to an IEEE754 FP32. When ELWIDTH=DEFAULT
clearly the behaviour of `sv.fadds` is performed at 32-bit accuracy
then padded back out to fit in IEEE754 FP64, exactly as for Scalar
v3.0B "single" FP.  Any FP operation ending in "s" where ELWIDTH=f16
or ELWIDTH=bf16 is reserved and must raise an illegal instruction
(IEEE754 FP8 or BF8 are not defined).

### Elwidth for CRs (no meaning)

Element-width overrides for CR Fields has no meaning. The bits
are therefore used for other purposes, or when Rc=1, the Elwidth
applies to the result being tested (a GPR or FPR), but not to the
Vector of CR Fields.

## SUBVL Encoding

The default for SUBVL is 1 and its encoding is 0b00 to indicate that
SUBVL is effectively disabled (a SUBVL for-loop of only one element). this
lines up in combination with all other "default is all zeros" behaviour.

| Value | Mnemonic  | Subvec  | Description            |
|-------|-----------|---------|------------------------|
| 00    | `SUBVL=1` | single  | Sub-vector length of 1 |
| 01    | `SUBVL=2` | vec2    | Sub-vector length of 2 |
| 10    | `SUBVL=3` | vec3    | Sub-vector length of 3 |
| 11    | `SUBVL=4` | vec4    | Sub-vector length of 4 |

The SUBVL encoding value may be thought of as an inclusive range of a
sub-vector.  SUBVL=2 represents a vec2, its encoding is 0b01, therefore
this may be considered to be elements 0b00 to 0b01 inclusive.

## MASK/MASK_SRC & MASKMODE Encoding

One bit (`MASKMODE`) indicates the mode: CR or Int predication.   The two
types may not be mixed.

Special note: to disable predication this field must be set to zero in
combination with Integer Predication also being set to 0b000. this has the
effect of enabling "all 1s" in the predicate mask, which is equivalent to
"not having any predication at all" and consequently, in combination with
all other default zeros, fully disables SV (`scalar identity behaviour`).

`MASKMODE` may be set to one of 2 values:

| Value | Description                                          |
|-----------|------------------------------------------------------|
| 0         | MASK/MASK_SRC are encoded using Integer Predication  |
| 1         | MASK/MASK_SRC are encoded using CR-based Predication |

Integer Twin predication has a second set of 3 bits that uses the same
encoding thus allowing either the same register (r3, r10 or r31) to be
used for both src and dest, or different regs (one for src, one for dest).

Likewise CR based twin predication has a second set of 3 bits, allowing
a different test to be applied.

Note that it is assumed that Predicate Masks (whether INT or CR) are
read *before* the operations proceed.  In practice (for CR Fields)
this creates an unnecessary block on parallelism.  Therefore, it is up
to the programmer to ensure that the CR fields used as Predicate Masks
are not being written to by any parallel Vector Loop.  Doing so results
in **UNDEFINED** behaviour, according to the definition outlined in the
Power ISA v3.0B Specification.

Hardware Implementations are therefore free and clear to delay reading
of individual CR fields until the actual predicated element operation
needs to take place, safe in the knowledge that no programmer will have
issued a Vector Instruction where previous elements could have overwritten
(destroyed) not-yet-executed CR-Predicated element operations.

### Integer Predication (MASKMODE=0)

When the predicate mode bit is zero the 3 bits are interpreted as below.
Twin predication has an identical 3 bit field similarly encoded.

`MASK` and `MASK_SRC` may be set to one of 8 values, to provide the
following meaning:

| Value | Mnemonic | Element `i` enabled if:      |
|-------|----------|------------------------------|
| 000   | ALWAYS   | predicate effectively all 1s |
| 001   | 1 << R3  | `i == R3`                    |
| 010   | R3       | `R3 & (1 << i)` is non-zero  |
| 011   | ~R3      | `R3 & (1 << i)` is zero      |
| 100   | R10      | `R10 & (1 << i)` is non-zero |
| 101   | ~R10     | `R10 & (1 << i)` is zero     |
| 110   | R30      | `R30 & (1 << i)` is non-zero |
| 111   | ~R30     | `R30 & (1 << i)` is zero     |

r10 and r30 are at the high end of temporary and unused registers,
so as not to interfere with register allocation from ABIs.

### CR-based Predication (MASKMODE=1)

When the predicate mode bit is one the 3 bits are interpreted as below.
Twin predication has an identical 3 bit field similarly encoded.

`MASK` and `MASK_SRC` may be set to one of 8 values, to provide the
following meaning:

| Value | Mnemonic | Element `i` is enabled if     |
|-------|----------|--------------------------|
| 000   | lt       | `CR[offs+i].LT` is set   |
| 001   | nl/ge    | `CR[offs+i].LT` is clear |
| 010   | gt       | `CR[offs+i].GT` is set   |
| 011   | ng/le    | `CR[offs+i].GT` is clear |
| 100   | eq       | `CR[offs+i].EQ` is set   |
| 101   | ne       | `CR[offs+i].EQ` is clear |
| 110   | so/un    | `CR[offs+i].FU` is set   |
| 111   | ns/nu    | `CR[offs+i].FU` is clear |

CR based predication.  TODO: select alternate CR for twin predication? see
[[discussion]]  Overlap of the two CR based predicates must be taken
into account, so the starting point for one of them must be suitably
high, or accept that for twin predication VL must not exceed the range
where overlap will occur, *or* that they use the same starting point
but select different *bits* of the same CRs

`offs` is defined as CR32 (4x8) so as to mesh cleanly with Vectorised
Rc=1 operations (see below).  Rc=1 operations start from CR8 (TBD).

The CR Predicates chosen must start on a boundary that Vectorised CR
operations can access cleanly, in full.  With EXTRA2 restricting starting
points to multiples of 8 (CR0, CR8, CR16...) both Vectorised Rc=1 and
CR Predicate Masks have to be adapted to fit on these boundaries as well.

## Extra Remapped Encoding <a name="extra_remap"> </a>

Shows all instruction-specific fields in the Remapped Encoding
`RM[10:18]` for all instruction variants.  Note that due to the very
tight space, the encoding mode is *not* included in the prefix itself.
The mode is "applied", similar to Power ISA "Forms" (X-Form, D-Form)
on a per-instruction basis, and, like "Forms" are given a designation
(below) of the form `RM-nP-nSnD`. The full list of which instructions
use which remaps is here [[opcode_regs_deduped]]. (*Machine-readable CSV
files have been provided which will make the task of creating SV-aware
ISA decoders easier*).

These mappings are part of the SVP64 Specification in exactly the same
way as X-Form, D-Form. New Scalar instructions added to the Power ISA
will need a corresponding SVP64 Mapping, which can be derived by-rote
from examining the Register "Profile" of the instruction.

There are two categories:  Single and Twin Predication.  Due to space
considerations further subdivision of Single Predication is based on
whether the number of src operands is 2 or 3.  With only 9 bits available
some compromises have to be made.

* `RM-1P-3S1D` Single Predication dest/src1/2/3, applies to 4-operand
   instructions (fmadd, isel, madd).
* `RM-1P-2S1D` Single Predication dest/src1/2 applies to 3-operand 
   instructions (src1 src2 dest)
* `RM-2P-1S1D` Twin Predication (src=1, dest=1)
* `RM-2P-2S1D` Twin Predication (src=2, dest=1) primarily for LDST (Indexed)
* `RM-2P-1S2D` Twin Predication (src=1, dest=2) primarily for LDST Update

### RM-1P-3S1D

| Field Name | Field bits | Description                            |
|------------|------------|----------------------------------------|
| Rdest\_EXTRA2 | `10:11` | extends Rdest (R\*\_EXTRA2 Encoding)   |
| Rsrc1\_EXTRA2 | `12:13` | extends Rsrc1 (R\*\_EXTRA2 Encoding)   |
| Rsrc2\_EXTRA2 | `14:15` | extends Rsrc2 (R\*\_EXTRA2 Encoding)   |
| Rsrc3\_EXTRA2 | `16:17` | extends Rsrc3 (R\*\_EXTRA2 Encoding)   |
| EXTRA2_MODE   | `18`    | used by `divmod2du` and `maddedu` for RS   |

These are for 3 operand in and either 1 or 2 out instructions.
3-in 1-out includes `madd RT,RA,RB,RC`. (DRAFT) instructions
such as `maddedu` have an implicit second destination, RS, the
selection of which is determined by bit 18.

### RM-1P-2S1D

| Field Name | Field bits | Description                               |
|------------|------------|-------------------------------------------|
| Rdest\_EXTRA3 | `10:12` | extends Rdest  |
| Rsrc1\_EXTRA3 | `13:15` | extends Rsrc1  |
| Rsrc2\_EXTRA3 | `16:18` | extends Rsrc3  |

These are for 2 operand 1 dest instructions, such as `add RT, RA,
RB`. However also included are unusual instructions with an implicit
dest that is identical to its src reg, such as `rlwinmi`.

Normally, with instructions such as `rlwinmi`, the scalar v3.0B ISA would
not have sufficient bit fields to allow an alternative destination.
With SV however this becomes possible.  Therefore, the fact that the
dest is implicitly also a src should not mislead: due to the *prefix*
they are different SV regs.

* `rlwimi RA, RS, ...`
* Rsrc1_EXTRA3 applies to RS as the first src
* Rsrc2_EXTRA3 applies to RA as the secomd src
* Rdest_EXTRA3 applies to RA to create an **independent** dest.

With the addition of the EXTRA bits, the three registers
each may be *independently* made vector or scalar, and be independently
augmented to 7 bits in length.

### RM-2P-1S1D/2S

| Field Name | Field bits | Description                 |
|------------|------------|----------------------------|
| Rdest_EXTRA3 | `10:12`    | extends Rdest             |
| Rsrc1_EXTRA3 | `13:15`    | extends Rsrc1             |
| MASK_SRC     | `16:18`    | Execution Mask for Source |

`RM-2P-2S` is for `stw` etc. and is Rsrc1 Rsrc2.

### RM-1P-2S1D

single-predicate, three registers (2 read, 1 write)

| Field Name | Field bits | Description                 |
|------------|------------|----------------------------|
| Rdest_EXTRA3 | `10:12`    | extends Rdest             |
| Rsrc1_EXTRA3 | `13:15`    | extends Rsrc1             |
| Rsrc2_EXTRA3 | `16:18`    | extends Rsrc2             |

### RM-2P-2S1D/1S2D/3S

The primary purpose for this encoding is for Twin Predication on LOAD
and STORE operations.  see [[sv/ldst]] for detailed anslysis.

RM-2P-2S1D:

| Field Name | Field bits | Description                     |
|------------|------------|----------------------------|
| Rdest_EXTRA2 | `10:11`  | extends Rdest (R\*\_EXTRA2 Encoding)   |
| Rsrc1_EXTRA2 | `12:13`  | extends Rsrc1 (R\*\_EXTRA2 Encoding)   |
| Rsrc2_EXTRA2 | `14:15`  | extends Rsrc2 (R\*\_EXTRA2 Encoding)   |
| MASK_SRC     | `16:18`  | Execution Mask for Source     |

Note that for 1S2P the EXTRA2 dest and src names are switched (Rsrc_EXTRA2
is in bits 10:11, Rdest1_EXTRA2 in 12:13)

Also that for 3S (to cover `stdx` etc.) the names are switched to 3 src:
Rsrc1_EXTRA2, Rsrc2_EXTRA2, Rsrc3_EXTRA2.

Note also that LD with update indexed, which takes 2 src and 2 dest
(e.g. `lhaux RT,RA,RB`), does not have room for 4 registers and also
Twin Predication.  therefore these are treated as RM-2P-2S1D and the
src spec for RA is also used for the same RA as a dest.

Note that if ELWIDTH != ELWIDTH_SRC this may result in reduced performance
or increased latency in some implementations due to lane-crossing.

## R\*\_EXTRA2/3

EXTRA is the means by which two things are achieved:

1. Registers are marked as either Vector *or Scalar*
2. Register field numbers (limited typically to 5 bit)
   are extended in range, both for Scalar and Vector.

The register files are therefore extended:

* INT is extended from r0-31 to r0-127
* FP is extended from fp0-32 to fp0-fp127
* CR Fields are extended from CR0-7 to CR0-127

However due to pressure in `RM.EXTRA` not all these registers
are accessible by all instructions, particularly those with
a large number of operands (`madd`, `isel`).

In the following tables register numbers are constructed from the
standard v3.0B / v3.1B 32 bit register field (RA, FRA) and the EXTRA2 or
EXTRA3 field from the SV Prefix, determined by the specific RM-xx-yyyy
designation for a given instruction.  The prefixing is arranged so that
interoperability between prefixing and nonprefixing of scalar registers
is direct and convenient (when the EXTRA field is all zeros).

A pseudocode algorithm explains the relationship, for INT/FP (see
SVP64 appendix for CRs)

```
    if extra3_mode:
        spec = EXTRA3
    else:
        spec = EXTRA2 << 1 # same as EXTRA3, shifted
    if spec[0]: # vector
         return (RA << 2) | spec[1:2]
    else:         # scalar
         return (spec[1:2] << 5) | RA
```

Future versions may extend to 256 by shifting Vector numbering up.
Scalar will not be altered.

Note that in some cases the range of starting points for Vectors
is limited.

### INT/FP EXTRA3

If EXTRA3 is zero, maps to "scalar identity" (scalar Power ISA field
naming).

Fields are as follows:

* Value: R_EXTRA3
* Mode: register is tagged as scalar or vector
* Range/Inc: the range of registers accessible from this EXTRA
  encoding, and the "increment" (accessibility). "/4" means
  that this EXTRA encoding may only give access (starting point)
  every 4th register.
* MSB..LSB: the bit field showing how the register opcode field
  combines with EXTRA to give (extend) the register number (GPR)

| Value     | Mode  | Range/Inc     | 6..0 |
|-----------|-------|---------------|---------------------|
| 000       | Scalar | `r0-r31`/1 | `0b00 RA`      |
| 001       | Scalar | `r32-r63`/1 | `0b01 RA`      |
| 010       | Scalar | `r64-r95`/1 | `0b10 RA`      |
| 011       | Scalar | `r96-r127`/1 | `0b11 RA`      |
| 100       | Vector | `r0-r124`/4 | `RA 0b00`      |
| 101       | Vector | `r1-r125`/4 | `RA 0b01`      |
| 110       | Vector | `r2-r126`/4 | `RA 0b10`      |
| 111       | Vector | `r3-r127`/4 | `RA 0b11`      |

### INT/FP EXTRA2

If EXTRA2 is zero will map to
"scalar identity behaviour" i.e Scalar Power ISA register naming:

| Value    | Mode  | Range/inc     | 6..0 |
|----------|-------|---------------|-----------|
| 00       | Scalar | `r0-r31`/1 | `0b00 RA`     |
| 01       | Scalar | `r32-r63`/1 | `0b01 RA`      |
| 10       | Vector | `r0-r124`/4 | `RA 0b00`      |
| 11       | Vector | `r2-r126`/4 | `RA 0b10`   |

**Note that unlike in EXTRA3, in EXTRA2**:

* the GPR Vectors may only start from
  `r0, r2, r4, r6, r8` and likewise FPR Vectors.
* the GPR Scalars may only go from `r0, r1, r2.. r63` and likewise FPR Scalars.

as there is insufficient bits to cover the full range.

### CR Field EXTRA3

CR Field encoding is essentially the same but made more complex due to CRs
being bit-based, because the application of SVP64 element-numbering applies
to the CR *Field* numbering not the CR register *bit* numbering.
Note that Vectors may only start from `CR0, CR4, CR8, CR12, CR16, CR20`...
and Scalars may only go from `CR0, CR1, ... CR31`

Encoding shown MSB down to LSB

For a 5-bit operand (BA, BB, BT):

| Value | Mode | Range/Inc     | 8..5      | 4..2    | 1..0    |
|-------|------|---------------|-----------| --------|---------|
| 000   | Scalar | `CR0-CR7`/1   | 0b0000    | BA[0:2] | BA[3:4] |
| 001   | Scalar | `CR8-CR15`/1  | 0b0001    | BA[0:2] | BA[3:4] |
| 010   | Scalar | `CR16-CR23`/1 | 0b0010    | BA[0:2] | BA[3:4] |
| 011   | Scalar | `CR24-CR31`/1 | 0b0011    | BA[0:2] | BA[3:4] |
| 100   | Vector | `CR0-CR112`/16 | BA[0:2] 0 | 0b000   | BA[3:4] |
| 101   | Vector | `CR4-CR116`/16 | BA[0:2] 0 | 0b100   | BA[3:4] |
| 110   | Vector | `CR8-CR120`/16 | BA[0:2] 1 | 0b000   | BA[3:4] |
| 111   | Vector | `CR12-CR124`/16 | BA[0:2] 1 | 0b100   | BA[3:4] |

For a 3-bit operand (e.g. BFA):

| Value | Mode | Range/Inc     | 6..3      | 2..0    |
|-------|------|---------------|-----------| --------|
| 000   | Scalar | `CR0-CR7`/1   | 0b0000    | BFA   |
| 001   | Scalar | `CR8-CR15`/1  | 0b0001    | BFA      |
| 010   | Scalar | `CR16-CR23`/1 | 0b0010    | BFA      |
| 011   | Scalar | `CR24-CR31`/1 | 0b0011    | BFA      |
| 100   | Vector | `CR0-CR112`/16 | BFA 0 | 0b000   |
| 101   | Vector | `CR4-CR116`/16 | BFA 0 | 0b100   |
| 110   | Vector | `CR8-CR120`/16 | BFA 1 | 0b000   |
| 111   | Vector | `CR12-CR124`/16 | BFA 1 | 0b100   |

### CR EXTRA2

CR encoding is essentially the same but made more complex due to CRs
being bit-based, because the application of SVP64 element-numbering applies
to the CR *Field* numbering not the CR register *bit* numbering.
See separate section for explanation and pseudocode.
Note that Vectors may only start from CR0, CR8, CR16, CR24, CR32...

Encoding shown MSB down to LSB

For a 5-bit operand (BA, BB, BC):

| Value | Mode   | Range/Inc      | 8..5    | 4..2    | 1..0    |
|-------|--------|----------------|---------|---------|---------|
| 00    | Scalar | `CR0-CR7`/1    | 0b0000  | BA[0:2] | BA[3:4] |
| 01    | Scalar | `CR8-CR15`/1   | 0b0001  | BA[0:2] | BA[3:4] |
| 10    | Vector | `CR0-CR112`/16 | BA[0:2] 0 | 0b000   | BA[3:4] |
| 11    | Vector | `CR8-CR120`/16 | BA[0:2] 1 | 0b000   | BA[3:4] |

For a 3-bit operand (e.g. BFA):

| Value | Mode | Range/Inc     | 6..3      | 2..0    |
|-------|------|---------------|-----------| --------|
| 00    | Scalar | `CR0-CR7`/1   | 0b0000  | BFA   |
| 01    | Scalar | `CR8-CR15`/1  | 0b0001  | BFA     |
| 10    | Vector | `CR0-CR112`/16 | BFA 0 | 0b000   |
| 11    | Vector | `CR8-CR120`/16 | BFA 1 | 0b000   |

--------

\newpage{}


# Normal SVP64 Modes, for Arithmetic and Logical Operations

Normal SVP64 Mode covers Arithmetic and Logical operations
to provide suitable additional behaviour.  The Mode
field is bits 19-23 of the [[svp64]] RM Field.

## Mode

Mode is an augmentation of SV behaviour, providing additional
functionality.  Some of these alterations are element-based (saturation),
others involve post-analysis (predicate result) and others are
Vector-based (mapreduce, fail-on-first).

[[sv/ldst]], [[sv/cr_ops]] and [[sv/branches]] are covered separately:
the following Modes apply to Arithmetic and Logical SVP64 operations:

* **simple** mode is straight vectorisation.  no augmentations: the
  vector comprises an array of independently created results.
* **ffirst** or data-dependent fail-on-first: see separate section.
  the vector may be truncated depending on certain criteria.
  *VL is altered as a result*.
* **sat mode** or saturation: clamps each element result to a min/max
  rather than overflows / wraps.  allows signed and unsigned clamping
  for both INT and FP.
* **reduce mode**. if used correctly, a mapreduce (or a prefix sum)
  is performed.    see [[svp64/appendix]].
  note that there are comprehensive caveats when using this mode.
* **pred-result** will test the result (CR testing selects a bit of CR
  and inverts it, just like branch conditional testing) and if the
  test fails it is as if the *destination* predicate bit was zero even
  before starting the operation.  When Rc=1 the CR element however is
  still stored in the CR regfile, even if the test failed.  See appendix
  for details.

Note that ffirst and reduce modes are not anticipated to be
high-performance in some implementations.  ffirst due to interactions
with VL, and reduce due to it requiring additional operations to produce
a result.  simple, saturate and pred-result are however inter-element
independent and may easily be parallelised to give high performance,
regardless of the value of VL.

The Mode table for Arithmetic and Logical operations is laid out as
follows:

| 0-1 |  2  |  3   4  |  description              |
| --- | --- |---------|-------------------------- |
| 00  |   0 |  dz  sz | simple mode                      |
| 00  |   1 | 0  RG   | scalar reduce mode (mapreduce) |
| 00  |   1 | 1  /    | reserved     |
| 01  | inv | CR-bit  | Rc=1: ffirst CR sel              |
| 01  | inv | VLi RC1 |  Rc=0: ffirst z/nonz |
| 10  |   N | dz   sz |  sat mode: N=0/1 u/s |
| 11  | inv | CR-bit  |  Rc=1: pred-result CR sel |
| 11  | inv | zz  RC1 |  Rc=0: pred-result z/nonz |

Fields:

* **sz / dz**  if predication is enabled will put zeros into the dest
  (or as src in the case of twin pred) when the predicate bit is zero.
  otherwise the element is ignored or skipped, depending on context.
* **zz**: both sz and dz are set equal to this flag
* **inv CR bit** just as in branches (BO) these bits allow testing of
  a CR bit and whether it is set (inv=0) or unset (inv=1)
* **RG** inverts the Vector Loop order (VL-1 downto 0) rather
  than the normal 0..VL-1
* **N** sets signed/unsigned saturation.
* **RC1** as if Rc=1, enables access to `VLi`.
* **VLi** VL inclusive: in fail-first mode, the truncation of
  VL *includes* the current element at the failure point rather
  than excludes it from the count.

For LD/ST Modes, see [[sv/ldst]].  For Condition Registers see
[[sv/cr_ops]].  For Branch modes, see [[sv/branches]].

## Rounding, clamp and saturate

To help ensure for example that audio quality is not compromised by
overflow, "saturation" is provided, as well as a way to detect when
saturation occurred if desired (Rc=1). When Rc=1 there will be a *vector*
of CRs, one CR per element in the result (Note: this is different from
VSX which has a single CR per block).

When N=0 the result is saturated to within the maximum range of an
unsigned value.  For integer ops this will be 0 to 2^elwidth-1. Similar
logic applies to FP operations, with the result being saturated to
maximum rather than returning INF, and the minimum to +0.0

When N=1 the same occurs except that the result is saturated to the min
or max of a signed result, and for FP to the min and max value rather
than returning +/- INF.

When Rc=1, the CR "overflow" bit is set on the CR associated with the
element, to indicate whether saturation occurred.  Note that due to
the hugely detrimental effect it has on parallel processing, XER.SO is
**ignored** completely and is **not** brought into play here.  The CR
overflow bit is therefore simply set to zero if saturation did not occur,
and to one if it did.  This behaviour (ignoring XER.SO) is actually optional in
the SFFS Compliancy Subset: for SVP64 it is made mandatory *but only on
Vectorised instructions*.

Note also that saturate on operations that set OE=1 must raise an Illegal
Instruction due to the conflicting use of the CR.so bit for storing if
saturation occurred. Vectorised Integer Operations that produce a Carry-Out (CA,
CA32): these two bits will be `UNDEFINED` if saturation is also requested.

Note that the operation takes place at the maximum bitwidth (max of
src and dest elwidth) and that truncation occurs to the range of the
dest elwidth.

*Programmer's Note: Post-analysis of the Vector of CRs to find out if any
given element hit saturation may be done using a mapreduced CR op (cror),
or by using the new crrweird instruction with Rc=1, which will transfer
the required CR bits to a scalar integer and update CR0, which will allow
testing the scalar integer for nonzero.  see [[sv/cr_int_predication]].
Alternatively, a Data-Dependent Fail-First may be used to truncate the
Vector Length to non-saturated elements, greatly increasing the productivity
of parallelised inner hot-loops.*

## Reduce mode

Reduction in SVP64 is similar in essence to other Vector Processing ISAs,
but leverages the underlying scalar Base v3.0B operations.  Thus it is
more a convention that the programmer may utilise to give the appearance
and effect of a Horizontal Vector Reduction. Due to the unusual decoupling
it is also possible to perform prefix-sum (Fibonacci Series) in certain
circumstances. Details are in the SVP64 appendix

Reduce Mode should not be confused with Parallel Reduction [[sv/remap]].
As explained in the [[sv/appendix]] Reduce Mode switches off the check
which would normally stop looping if the result register is scalar.
Thus, the result scalar register, if also used as a source scalar,
may be used to perform sequential accumulation.  This *deliberately*
sets up a chain of Register Hazard Dependencies, whereas Parallel Reduce
[[sv/remap]] deliberately issues a Tree-Schedule of operations that may
be parallelised.

## Data-dependent Fail-on-first

Data-dependent fail-on-first is very different from LD/ST Fail-First
(also known as Fault-First) and is actually CR-field-driven.
Vector elements are required to appear
to be executed in sequential Program Order. When REMAP is not active,
element 0 would be the first.

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 **at and
above the current one**, and VL is truncated to either the *previous*
element or the current one, depending on whether VLi (VL "inclusive")
is clear or set, respectively.

Thus the new VL comprises a contiguous vector of results, all of which
pass the testing criteria (equal to zero, less than zero etc as defined
by the CR-bit test).

*Note: when VLi is clear, the behaviour at first seems counter-intuitive.
A result is calculated but if the test fails it is prohibited from being
actually written.  This becomes intuitive again when it is remembered
that the length that VL is set to is the number of *written* elements, and
only when VLI is set will the current element be included in that count.*

The CR-based data-driven fail-on-first is "new" and not found in ARM SVE
or RVV. At the same time it is "old" because it is almost identical to
a generalised form of Z80's `CPIR` instruction.  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.

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 crop
such as crand, cror or [[sv/cr_int_predication]] crweirder may be used,
and ffirst applied to the crop instead of to the arithmetic vector. Note
that crops are covered by the [[sv/cr_ops]] Mode format.

*Programmer's note: `VLi` is only accessible in normal operations which in
turn limits the CR field bit-testing to only `EQ/NE`.  [[sv/cr_ops]] are
not so limited.  Thus it is possible to use for example `sv.cror/ff=gt/vli
*0,*0,*0`, which is not a `nop` because it allows Fail-First Mode to
perform a test and truncate VL.*

*Hardware implementor's note: effective Sequential Program Order must be preserved.
Speculative Execution is perfectly permitted as long as the speculative elements
are held back from writing to register files (kept in Resevation Stations),
until such time as the relevant
CR Field bit(s) has been analysed. All Speculative elements sequentially beyond the
test-failure point **MUST** be cancelled. This is no different from standard
Out-of-Order Execution and the modification effort to efficiently support 
Data-Dependent Fail-First within a pre-existing Multi-Issue Out-of-Order Engine
is anticipated to be minimal. In-Order systems on the other hand are expected,
unavoidably, to be low-performance*.

Two extremely important aspects of ffirst are:

* 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*.

The second crucial aspect, compared to LDST Ffirst:

* LD/ST Failfirst may (beyond the initial first element
  conditions) truncate VL for any architecturally suitable reason. Beyond
  the first element LD/ST Failfirst is arbitrarily speculative and 100%
  non-deterministic.
* 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 Deterministic test on which algorithms can and will will rely.

**Floating-point Exceptions**

When Floating-point exceptions are enabled VL must be truncated at
the point where the Exception appears not to have occurred. If `VLi`
is set then VL must include the faulting element, and thus the faulting
element will always raise its exception.  If however `VLi` is clear then
VL **excludes** the faulting element and thus the exception will **never**
be raised.

Although very strongly discouraged the Exception Mode that permits
Floating Point Exception notification to arrive too late to unwind
is permitted (under protest, due it violating the otherwise 100%
Deterministic nature of Data-dependent Fail-first) and is `UNDEFINED`
behaviour.

**Use of lax FP Exception Notification Mode could result in parallel
computations proceeding with invalid results that have to be explicitly
detected, whereas with the strict FP Execption Mode enabled, FFirst
truncates VL, allows subsequent parallel computation to avoid the
exceptions entirely**

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

Operations that actually produce or alter CR Field as a result have
their own SVP64 Mode, described in [[sv/cr_ops]].

## pred-result mode

This mode merges common CR testing with predication, saving on instruction
count. Below is the pseudocode excluding predicate zeroing and elwidth
overrides. Note that the pseudocode for SVP64 CR-ops is slightly different.

```
    for i in range(VL):
        # predication test, skip all masked out elements.
        if predicate_masked_out(i):
             continue
        result = op(iregs[RA+i], iregs[RB+i])
        CRnew = analyse(result) # calculates eq/lt/gt
        # Rc=1 always stores the CR field
        if Rc=1 or RC1:
            CR.field[offs+i] = CRnew
        # now test CR, similar to branch
        if RC1 or CR.field[BO[0:1]] != BO[2]:
            continue # test failed: cancel store
        # result optionally stored but CR always is
        iregs[RT+i] = result
```

The reason for allowing the CR element to be stored is so that
post-analysis of the CR Vector may be carried out.  For example:
Saturation may have occurred (and been prevented from updating, by the
test) but it is desirable to know *which* elements fail saturation.

Note that RC1 Mode basically turns all operations into `cmp`.  The
calculation is performed but it is only the CR that is written. The
element result is *always* discarded, never written (just like `cmp`).

Note that predication is still respected: predicate zeroing is slightly
different: elements that fail the CR test *or* are masked out are zero'd.

--------

\newpage{}

# SV Load and Store

**Rationale**

All Vector ISAs dating back fifty years have extensive and comprehensive
Load and Store operations that go far beyond the capabilities of Scalar
RISC and most CISC processors, yet at their heart on an individual element
basis may be found to be no different from RISC Scalar equivalents.

The resource savings from Vector LD/ST are significant and stem
from the fact that one single instruction can trigger a dozen (or in
some microarchitectures such as Cray or NEC SX Aurora) hundreds of
element-level Memory accesses.

Additionally, and simply: if the Arithmetic side of an ISA supports
Vector Operations, then in order to keep the ALUs 100% occupied the
Memory infrastructure (and the ISA itself) correspondingly needs Vector
Memory Operations as well.

Vectorised Load and Store also presents an extra dimension (literally)
which creates scenarios unique to Vector applications, that a Scalar
(and even a SIMD) ISA simply never encounters.  SVP64 endeavours to add
the modes typically found in *all* Scalable Vector ISAs, without changing
the behaviour of the underlying Base (Scalar) v3.0B operations in any way.

## Modes overview

Vectorisation of Load and Store requires creation, from scalar operations,
a number of different modes:

* **fixed aka "unit" stride** - contiguous sequence with no gaps
* **element strided** - sequential but regularly offset, with gaps
* **vector indexed** - vector of base addresses and vector of offsets
* **Speculative fail-first** - where it makes sense to do so
* **Structure Packing** - covered in SV by [[sv/remap]] and Pack/Unpack Mode.

*Despite being constructed from Scalar LD/ST none of these Modes exist
or make sense in any Scalar ISA. They **only** exist in Vector ISAs*

Also included in SVP64 LD/ST is both signed and unsigned Saturation,
as well as Element-width overrides and Twin-Predication.

Note also that Indexed [[sv/remap]] mode may be applied to both v3.0
LD/ST Immediate instructions *and* v3.0 LD/ST Indexed instructions.
LD/ST-Indexed should not be conflated with Indexed REMAP mode:
clarification is provided below.

**Determining the LD/ST Modes**

A minor complication (caused by the retro-fitting of modern Vector
features to a Scalar ISA) is that certain features do not exactly make
sense or are considered a security risk.  Fail-first on Vector Indexed
would allow attackers to probe large numbers of pages from userspace,
where strided fail-first (by creating contiguous sequential LDs) does not.

In addition, reduce mode makes no sense.  Realistically we need an
alternative table definition for [[sv/svp64]] `RM.MODE`.  The following
modes make sense:

* saturation
* predicate-result (mostly for cache-inhibited LD/ST)
* simple (no augmentation)
* fail-first (where Vector Indexed is banned)
* Signed Effective Address computation (Vector Indexed only)

More than that however it is necessary to fit the usual Vector ISA
capabilities onto both Power ISA LD/ST with immediate and to LD/ST
Indexed. They present subtly different Mode tables, which, due to lack
of space, have the following quirks:

* LD/ST Immediate has no individual control over src/dest zeroing,
  whereas LD/ST Indexed does.
* LD/ST Immediate has no Saturated Pack/Unpack (Arithmetic Mode does)
* LD/ST Indexed has no Pack/Unpack (REMAP may be used instead)

## Format and fields

Fields used in tables below:

* **sz / dz**  if predication is enabled will put zeros into the dest
  (or as src in the case of twin pred) when the predicate bit is zero.
  otherwise the element is ignored or skipped, depending on context.
* **zz**: both sz and dz are set equal to this flag.
* **inv CR bit** just as in branches (BO) these bits allow testing of
  a CR bit and whether it is set (inv=0) or unset (inv=1)
* **N** sets signed/unsigned saturation.
* **RC1** as if Rc=1, stores CRs *but not the result*
* **SEA** - Signed Effective Address, if enabled performs sign-extension on
  registers that have been reduced due to elwidth overrides
* **PI** - post-increment mode (applies to LD/ST with update only).
  the Effective Address utilised is always just RA, i.e. the computation of
  EA is stored in RA **after** it is actually used.
* **LF** - Load/Store Fail or Fault First: for any reason Load or Store Vectors
  may be truncated to (at least) one element, and VL altered to indicate such.

**LD/ST immediate**

The table for [[sv/svp64]] for `immed(RA)` which is `RM.MODE`
(bits 19:23 of `RM`) is:

| 0-1 |  2  |  3   4  |  description               |
| --- | --- |---------|--------------------------- |
| 00  | 0   |  zz els | simple mode                |
| 00  | 1   | PI  LF  | post-increment and Fault-First  |
| 01  | inv | CR-bit  | Rc=1: ffirst CR sel        |
| 01  | inv | els RC1 |  Rc=0: ffirst z/nonz       |
| 10  |   N | zz  els |  sat mode: N=0/1 u/s       |
| 11  | inv | CR-bit  |  Rc=1: pred-result CR sel  |
| 11  | inv | els RC1 |  Rc=0: pred-result z/nonz  |

The `els` bit is only relevant when `RA.isvec` is clear: this indicates
whether stride is unit or element:

```
    if RA.isvec:
        svctx.ldstmode = indexed
    elif els == 0:
        svctx.ldstmode = unitstride
    elif immediate != 0:
        svctx.ldstmode = elementstride
```

An immediate of zero is a safety-valve to allow `LD-VSPLAT`: in effect
the multiplication of the immediate-offset by zero results in reading from
the exact same memory location, *even with a Vector register*. (Normally
this type of behaviour is reserved for the mapreduce modes)

For `LD-VSPLAT`, on non-cache-inhibited Loads, the read can occur just
the once and be copied, rather than hitting the Data Cache multiple
times with the same memory read at the same location.  The benefit of
Cache-inhibited LD-splats is that it allows for memory-mapped peripherals
to have multiple data values read in quick succession and stored in
sequentially numbered registers (but, see Note below).

For non-cache-inhibited ST from a vector source onto a scalar destination:
with the Vector loop effectively creating multiple memory writes to
the same location, we can deduce that the last of these will be the
"successful" one. Thus, implementations are free and clear to optimise
out the overwriting STs, leaving just the last one as the "winner".
Bear in mind that predicate masks will skip some elements (in source
non-zeroing mode).  Cache-inhibited ST operations on the other hand
**MUST** write out a Vector source multiple successive times to the exact
same Scalar destination. Just like Cache-inhibited LDs, multiple values
may be written out in quick succession to a memory-mapped peripheral
from sequentially-numbered registers.

Note that any memory location may be Cache-inhibited
(Power ISA v3.1, Book III, 1.6.1, p1033)

*Programmer's Note: an immediate also with a Scalar source as a "VSPLAT"
mode is simply not possible: there are not enough Mode bits. One single
Scalar Load operation may be used instead, followed by any arithmetic
operation (including a simple mv) in "Splat" mode.*

**LD/ST Indexed**

The modes for `RA+RB` indexed version are slightly different
but are the same `RM.MODE` bits (19:23 of `RM`):

| 0-1 |  2  |  3   4  |  description              |
| --- | --- |---------|-------------------------- |
| 00  | SEA |  dz  sz | simple mode        |
| 01  | SEA | dz sz   | Strided (scalar only source)   |
| 10  |   N | dz   sz |  sat mode: N=0/1 u/s |
| 11  | inv | CR-bit  |  Rc=1: pred-result CR sel |
| 11  | inv | zz  RC1 |  Rc=0: pred-result z/nonz |

Vector Indexed Strided Mode is qualified as follows:

    if mode = 0b01 and !RA.isvec and !RB.isvec:
        svctx.ldstmode = elementstride

A summary of the effect of Vectorisation of src or dest:

```
    imm(RA)  RT.v   RA.v   no stride allowed
    imm(RA)  RT.s   RA.v   no stride allowed
    imm(RA)  RT.v   RA.s   stride-select allowed
    imm(RA)  RT.s   RA.s   not vectorised
    RA,RB    RT.v  {RA|RB}.v Standard Indexed
    RA,RB    RT.s  {RA|RB}.v Indexed but single LD (no VSPLAT)
    RA,RB    RT.v  {RA&RB}.s VSPLAT possible. stride selectable
    RA,RB    RT.s  {RA&RB}.s not vectorised (scalar identity)
```

Signed Effective Address computation is only relevant for Vector Indexed
Mode, when elwidth overrides are applied.  The source override applies to
RB, and before adding to RA in order to calculate the Effective Address,
if SEA is set RB is sign-extended from elwidth bits to the full 64 bits.
For other Modes (ffirst, saturate), all EA computation with elwidth
overrides is unsigned.

Note that cache-inhibited LD/ST  when VSPLAT is activated will perform
**multiple** LD/ST operations, sequentially.  Even with scalar src
a Cache-inhibited LD will read the same memory location *multiple
times*, storing the result in successive Vector destination registers.
This because the cache-inhibit instructions are typically used to read
and write memory-mapped peripherals.  If a genuine cache-inhibited
LD-VSPLAT is required then a single *scalar* cache-inhibited LD should
be performed, followed by a VSPLAT-augmented mv, copying the one *scalar*
value into multiple register destinations.

Note also that cache-inhibited VSPLAT with Predicate-result is possible.
This allows for example to issue a massive batch of memory-mapped
peripheral reads, stopping at the first NULL-terminated character and
truncating VL to that point. No branch is needed to issue that large
burst of LDs, which may be valuable in Embedded scenarios.

## Vectorisation of Scalar Power ISA v3.0B

Scalar Power ISA Load/Store operations may be seen from their
pseudocode to be of the form:

```
    lbux RT, RA, RB
    EA <- (RA) + (RB)
    RT <- MEM(EA)
```

and for immediate variants:

```
    lb RT,D(RA)
    EA <- RA + EXTS(D)
    RT <- MEM(EA)
```

Thus in the first example, the source registers may each be independently
marked as scalar or vector, and likewise the destination; in the second
example only the one source and one dest may be marked as scalar or
vector.

Thus we can see that Vector Indexed may be covered, and, as demonstrated
with the pseudocode below, the immediate can be used to give unit
stride or element stride.  With there being no way to tell which from
the Power v3.0B Scalar opcode alone, the choice is provided instead by
the SV Context.

```
    # LD not VLD!  format - ldop RT, immed(RA)
    # op_width: lb=1, lh=2, lw=4, ld=8
    op_load(RT, RA, op_width, immed, svctx, RAupdate):
      ps = get_pred_val(FALSE, RA); # predication on src
      pd = get_pred_val(FALSE, RT); # ... AND on dest
      for (i=0, j=0, u=0; i < VL && j < VL;):
        # skip nonpredicates elements
        if (RA.isvec) while (!(ps & 1<<i)) i++;
        if (RAupdate.isvec) while (!(ps & 1<<u)) u++;
        if (RT.isvec) while (!(pd & 1<<j)) j++;
        if postinc:
            offs = 0; # added afterwards
            if RA.isvec: srcbase = ireg[RA+i]
            else         srcbase = ireg[RA]
        elif svctx.ldstmode == elementstride:
          # element stride mode
          srcbase = ireg[RA]
          offs = i * immed              # j*immed for a ST
        elif svctx.ldstmode == unitstride:
          # unit stride mode
          srcbase = ireg[RA]
          offs = immed + (i * op_width) # j*op_width for ST
        elif RA.isvec:
          # quirky Vector indexed mode but with an immediate
          srcbase = ireg[RA+i]
          offs = immed;
        else
          # standard scalar mode (but predicated)
          # no stride multiplier means VSPLAT mode
          srcbase = ireg[RA]
          offs = immed

        # compute EA
        EA = srcbase + offs
        # load from memory
        ireg[RT+j] <= MEM[EA];
        # check post-increment of EA
        if postinc: EA = srcbase + immed;
        # update RA?
        if RAupdate: ireg[RAupdate+u] = EA;
        if (!RT.isvec)
            break # destination scalar, end now
        if (RA.isvec) i++;
        if (RAupdate.isvec) u++;
        if (RT.isvec) j++;
```

Indexed LD is:

```
    # format: ldop RT, RA, RB
    function op_ldx(RT, RA, RB, RAupdate=False) # LD not VLD!
      ps = get_pred_val(FALSE, RA); # predication on src
      pd = get_pred_val(FALSE, RT); # ... AND on dest
      for (i=0, j=0, k=0, u=0; i < VL && j < VL && k < VL):
        # skip nonpredicated RA, RB and RT
        if (RA.isvec) while (!(ps & 1<<i)) i++;
        if (RAupdate.isvec) while (!(ps & 1<<u)) u++;
        if (RB.isvec) while (!(ps & 1<<k)) k++;
        if (RT.isvec) while (!(pd & 1<<j)) j++;
        if svctx.ldstmode == elementstride:
            EA = ireg[RA] + ireg[RB]*j   # register-strided
        else
            EA = ireg[RA+i] + ireg[RB+k] # indexed address
        if RAupdate: ireg[RAupdate+u] = EA
        ireg[RT+j] <= MEM[EA];
        if (!RT.isvec)
            break # destination scalar, end immediately
        if (RA.isvec) i++;
        if (RAupdate.isvec) u++;
        if (RB.isvec) k++;
        if (RT.isvec) j++;
```

Note that Element-Strided uses the Destination Step because with both
sources being Scalar as a prerequisite condition of activation of
Element-Stride Mode, the source step (being Scalar) would never advance.

Note in both cases that [[sv/svp64]] allows RA-as-a-dest in "update"
mode (`ldux`) to be effectively a *completely different* register from
RA-as-a-source.  This because there is room in svp64 to extend RA-as-src
as well as RA-as-dest, both independently as scalar or vector *and*
independently extending their range.

*Programmer's note: being able to set RA-as-a-source as separate from
RA-as-a-destination as Scalar is **extremely valuable** once it is
remembered that Simple-V element operations must be in Program Order,
especially in loops, for saving on multiple address computations. Care
does have to be taken however that RA-as-src is not overwritten by
RA-as-dest unless intentionally desired, especially in element-strided
Mode.*

## LD/ST Indexed vs Indexed REMAP

Unfortunately the word "Indexed" is used twice in completely different
contexts, potentially causing confusion.

* There has existed instructions in the Power ISA `ld RT,RA,RB` since
  its creation: these are called "LD/ST Indexed" instructions and their
  name and meaning is well-established.
* There now exists, in Simple-V, a REMAP mode called "Indexed"
  Mode that can be applied to *any* instruction **including those
  named LD/ST Indexed**.

Whilst it may be costly in terms of register reads to allow REMAP Indexed
Mode to be applied to any Vectorised LD/ST Indexed operation such as
`sv.ld *RT,RA,*RB`, or even misleadingly labelled  as redundant, firstly
the strict application of the RISC Paradigm that Simple-V follows makes
it awkward to consider *preventing* the application of Indexed REMAP to
such operations, and secondly they are not actually the same at all.

Indexed REMAP, as applied to RB in the instruction `sv.ld *RT,RA,*RB`
effectively performs an *in-place* re-ordering of the offsets, RB.
To achieve the same effect without Indexed REMAP would require taking
a *copy* of the Vector of offsets starting at RB, manually explicitly
reordering them, and finally using the copy of re-ordered offsets in a
non-REMAP'ed `sv.ld`.  Using non-strided LD as an example, pseudocode
showing what actually occurs, where the pseudocode for `indexed_remap`
may be found in [[sv/remap]]:

```
    # sv.ld *RT,RA,*RB with Index REMAP applied to RB
    for i in 0..VL-1:
        if remap.indexed:
            rb_idx = indexed_remap(i) # remap
        else:
            rb_idx = i # use the index as-is
        EA = GPR(RA) + GPR(RB+rb_idx)
        GPR(RT+i) = MEM(EA, 8)
```

Thus it can be seen that the use of Indexed REMAP saves copying
and manual reordering of the Vector of RB offsets.

## LD/ST ffirst

LD/ST ffirst treats the first LD/ST in a vector (element 0 if REMAP
is not active) as an ordinary one, with all behaviour with respect to
Interrupts Exceptions Page Faults Memory Management being identical
in every regard to Scalar v3.0 Power ISA LD/ST. However for elements
1 and above, if an exception would occur, then VL is **truncated**
to the previous element: the exception is **not** then raised because
the LD/ST that would otherwise have caused an exception is *required*
to be cancelled. Additionally an implementor may choose to truncate VL
for any arbitrary reason *except for the very first*.

ffirst LD/ST to multiple pages via a Vectorised Index base is
considered a security risk due to the abuse of probing multiple
pages in rapid succession and getting speculative feedback on which
pages would fail.  Therefore Vector Indexed LD/ST is prohibited
entirely, and the Mode bit instead used for element-strided LD/ST.

```
    for(i = 0; i < VL; i++)
        reg[rt + i] = mem[reg[ra] + i * reg[rb]];
```

High security implementations where any kind of speculative probing of
memory pages is considered a risk should take advantage of the fact
that implementations may truncate VL at any point, without requiring
software to be rewritten and made non-portable. Such implementations may
choose to *always* set VL=1 which will have the effect of terminating
any speculative probing (and also adversely affect performance), but
will at least not require applications to be rewritten.

Low-performance simpler hardware implementations may also choose (always)
to also set VL=1 as the bare minimum compliant implementation of LD/ST
Fail-First. It is however critically important to remember that the first
element LD/ST **MUST** be treated as an ordinary LD/ST, i.e.  **MUST**
raise exceptions exactly like an ordinary LD/ST.

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 the following ffirst LD/ST
operations on an aligned boundary such as the beginning of a cache line,
or beginning of a Virtual Memory page. Likewise, to reduce workloads or
balance resources.

Vertical-First Mode is slightly strange in that only one element at a time
is ever executed anyway.  Given that programmers may legitimately choose
to alter srcstep and dststep in non-sequential order as part of explicit
loops, it is neither possible nor safe to make speculative assumptions
about future LD/STs.  Therefore, Fail-First LD/ST in Vertical-First is
`UNDEFINED`.  This is very different from Arithmetic (Data-dependent)
FFirst where Vertical-First Mode is fully deterministic, not speculative.

## LOAD/STORE Elwidths <a name="elwidth"></a>

Loads and Stores are almost unique in that the Power Scalar ISA
provides a width for the operation (lb, lh, lw, ld).  Only `extsb` and
others like it provide an explicit operation width.  There are therefore
*three* widths involved:

* operation width (lb=8, lh=16, lw=32, ld=64)
* src element width override (8/16/32/default)
* destination element width override (8/16/32/default)

Some care is therefore needed to express and make clear the transformations,
which are expressly in this order:

* Calculate the Effective Address from RA at full width
  but (on Indexed Load) allow srcwidth overrides on RB
* Load at the operation width (lb/lh/lw/ld) as usual
* byte-reversal as usual
* Non-saturated mode:
   - zero-extension or truncation from operation width to dest elwidth
   - place result in destination at dest elwidth
* Saturated mode:
   - Sign-extension or truncation from operation width to dest width
   - signed/unsigned saturation down to dest elwidth

In order to respect Power v3.0B Scalar behaviour the memory side
is treated effectively as completely separate and distinct from SV
augmentation.  This is primarily down to quirks surrounding LE/BE and
byte-reversal.

It is rather unfortunately possible to request an elwidth override on
the memory side which does not mesh with the overridden operation width:
these result in `UNDEFINED` behaviour.  The reason is that the effect
of attempting a 64-bit `sv.ld` operation with a source elwidth override
of 8/16/32 would result in overlapping memory requests, particularly
on unit and element strided operations.  Thus it is `UNDEFINED` when
the elwidth is smaller than the memory operation width. Examples include
`sv.lw/sw=16/els` which requests (overlapping) 4-byte memory reads offset
from each other at 2-byte intervals.  Store likewise is also `UNDEFINED`
where the dest elwidth override is less than the operation width.

Note the following regarding the pseudocode to follow:

* `scalar identity behaviour` SV Context parameter conditions turn this
  into a straight absolute fully-compliant Scalar v3.0B LD operation
* `brev` selects whether the operation is the byte-reversed variant (`ldbrx`
  rather than `ld`)
* `op_width` specifies the operation width (`lb`, `lh`, `lw`, `ld`) as
  a "normal" part of Scalar v3.0B LD
* `imm_offs` specifies the immediate offset `ld r3, imm_offs(r5)`, again
  as a "normal" part of Scalar v3.0B LD
* `svctx` specifies the SV Context and includes VL as well as
  source and destination elwidth overrides.

Below is the pseudocode for Unit-Strided LD (which includes Vector
capability). Observe in particular that RA, as the base address in both
Immediate and Indexed LD/ST, does not have element-width overriding
applied to it.

Note that predication, predication-zeroing, and other modes except
saturation have all been removed, for clarity and simplicity:

```
    # LD not VLD!
    # this covers unit stride mode and a type of vector offset
    function op_ld(RT, RA, op_width, imm_offs, svctx)
      for (int i = 0, int j = 0; i < svctx.VL && j < svctx.VL):
        if not svctx.unit/el-strided:
            # strange vector mode, compute 64 bit address which is
            # not polymorphic! elwidth hardcoded to 64 here
            srcbase = get_polymorphed_reg(RA, 64, i)
        else:
            # unit / element stride mode, compute 64 bit address
            srcbase = get_polymorphed_reg(RA, 64, 0)
            # adjust for unit/el-stride
            srcbase += ....

        # read the underlying memory
        memread <= MEM(srcbase + imm_offs, op_width)

        # check saturation.
        if svpctx.saturation_mode:
            # ... saturation adjustment...
            memread = clamp(memread, op_width, svctx.dest_elwidth)
        else:
            # truncate/extend to over-ridden dest width.
            memread = adjust_wid(memread, op_width, svctx.dest_elwidth)

        # takes care of inserting memory-read (now correctly byteswapped)
        # into regfile underlying LE-defined order, into the right place
        # within the NEON-like register, respecting destination element
        # bitwidth, and the element index (j)
        set_polymorphed_reg(RT, svctx.dest_elwidth, j, memread)

        # increments both src and dest element indices (no predication here)
        i++;
        j++;
```

Note above that the source elwidth is *not used at all* in LD-immediate.

For LD/Indexed, the key is that in the calculation of the Effective Address,
RA has no elwidth override but RB does.  Pseudocode below is simplified
for clarity: predication and all modes except saturation are removed:

```
    # LD not VLD! ld*rx if brev else ld*
    function op_ld(RT, RA, RB, op_width, svctx, brev)
      for (int i = 0, int j = 0; i < svctx.VL && j < svctx.VL):
        if not svctx.el-strided:
            # RA not polymorphic! elwidth hardcoded to 64 here
            srcbase = get_polymorphed_reg(RA, 64, i)
        else:
            # element stride mode, again RA not polymorphic
            srcbase = get_polymorphed_reg(RA, 64, 0)
        # RB *is* polymorphic
        offs = get_polymorphed_reg(RB, svctx.src_elwidth, i)
        # sign-extend
        if svctx.SEA: offs = sext(offs, svctx.src_elwidth, 64)

        # takes care of (merges) processor LE/BE and ld/ldbrx
        bytereverse = brev XNOR MSR.LE

        # read the underlying memory
        memread <= MEM(srcbase + offs, op_width)

        # optionally performs byteswap at op width
        if (bytereverse):
            memread = byteswap(memread, op_width)

        if svpctx.saturation_mode:
            # ... saturation adjustment...
            memread = clamp(memread, op_width, svctx.dest_elwidth)
        else:
            # truncate/extend to over-ridden dest width.
            memread = adjust_wid(memread, op_width, svctx.dest_elwidth)

        # takes care of inserting memory-read (now correctly byteswapped)
        # into regfile underlying LE-defined order, into the right place
        # within the NEON-like register, respecting destination element
        # bitwidth, and the element index (j)
        set_polymorphed_reg(RT, svctx.dest_elwidth, j, memread)

        # increments both src and dest element indices (no predication here)
        i++;
        j++;
```

## Remapped LD/ST

In the [[sv/remap]] page the concept of "Remapping" is described.  Whilst
it is expensive to set up (2 64-bit opcodes minimum) it provides a way to
arbitrarily perform 1D, 2D and 3D "remapping" of up to 64 elements worth
of LDs or STs.  The usual interest in such re-mapping is for example in
separating out 24-bit RGB channel data into separate contiguous registers.

REMAP easily covers this capability, and with dest elwidth overrides
and saturation may do so with built-in conversion that would normally
require additional width-extension, sign-extension and min/max Vectorised
instructions as post-processing stages.

Thus we do not need to provide specialist LD/ST "Structure Packed" opcodes
because the generic abstracted concept of "Remapping", when applied to
LD/ST, will give that same capability, with far more flexibility.

It is worth noting that Pack/Unpack Modes of SVSTATE, which may be
established through `svstep`, are also an easy way to perform regular
Structure Packing, at the vec2/vec3/vec4 granularity level.  Beyond that,
REMAP will need to be used.

--------

\newpage{}

# Condition Register SVP64 Operations

Condition Register Fields are only 4 bits wide: this presents some
interesting conceptual challenges for SVP64, which was designed
primarily for vectors of arithmetic and logical operations. However
if predicates may be bits of CR Fields it makes sense to extend
Simple-V to cover CR Operations, especially given that Vectorised Rc=1
may be processed by Vectorised CR Operations tbat usefully in turn
may become Predicate Masks to yet more Vector operations, like so:

```
    sv.cmpi/ew=8 *B,*ra,0    # compare bytes against zero
    sv.cmpi/ew=8 *B2,*ra,13. # and against newline
    sv.cror PM.EQ,B.EQ,B2.EQ # OR compares to create mask
    sv.stb/sm=EQ    ...      # store only nonzero/newline
```

Element width however is clearly meaningless for a 4-bit collation of
Conditions, EQ LT GE SO. Likewise, arithmetic saturation (an important
part of Arithmetic SVP64) has no meaning. An alternative Mode Format is
required, and given that elwidths are meaningless for CR Fields the bits
in SVP64 `RM` may be used for other purposes.

This alternative mapping **only** applies to instructions that **only**
reference a CR Field or CR bit as the sole exclusive result. This section
**does not** apply to instructions which primarily produce arithmetic
results that also, as an aside, produce a corresponding CR Field (such as
when Rc=1).  Instructions that involve Rc=1 are definitively arithmetic
in nature, where the corresponding Condition Register Field can be
considered to be a "co-result". Such CR Field "co-result" arithmeric
operations are firmly out of scope for this section, being covered fully
by [[sv/normal]].

* Examples of v3.0B instructions to which this section does
  apply is
  - `mfcr` and `cmpi` (3 bit operands) and
  - `crnor` and `crand` (5 bit operands).
* Examples to which this section does **not** apply include
  `fadds.` and `subf.` which both produce arithmetic results
  (and a CR Field co-result).

The CR Mode Format still applies to `sv.cmpi` because despite
taking a GPR as input, the output from the Base Scalar v3.0B `cmpi`
instruction is purely to a Condition Register Field.

Other modes are still applicable and include:

* **Data-dependent fail-first**.
  useful to truncate VL based on analysis of a Condition Register result bit.
* **Reduction**.
  Reduction is useful for analysing a Vector of Condition Register Fields
  and reducing it to one single Condition Register Field.

Predicate-result does not make any sense because when Rc=1 a co-result
is created (a CR Field). Testing the co-result allows the decision to
be made to store or not store the main result, and for CR Ops the CR
Field result *is* the main result.

## Format

SVP64 RM `MODE` (includes `ELWIDTH_SRC` bits) for CR-based operations:

|6 | 7 |19-20|  21 | 22   23 |  description     |
|--|---|-----| --- |---------|----------------- |
|/ | / |0 RG |   0 | dz  sz  | simple mode                      |
|/ | / |0 RG |   1 | dz  sz  | scalar reduce mode (mapreduce) |
|zz|SNZ|1 VLI| inv |  CR-bit | Ffirst 3-bit mode      |
|/ |SNZ|1 VLI| inv |  dz sz  | Ffirst 5-bit mode (implies CR-bit from result) |

Fields:

* **sz / dz**  if predication is enabled will put zeros into the dest
 (or as src in the case of twin pred) when the predicate bit is zero.
  otherwise the element is ignored or skipped, depending on context.
* **zz** set both sz and dz equal to this flag
* **SNZ** In fail-first mode, on the bit being tested, when sz=1 and
  SNZ=1 a value "1" is put in place of "0".
* **inv CR-bit** just as in branches (BO) these bits allow testing of
  a CR bit and whether it is set (inv=0) or unset (inv=1)
* **RG** inverts the Vector Loop order (VL-1 downto 0) rather
  than the normal 0..VL-1
* **SVM** sets "subvector" reduce mode
* **VLi** VL inclusive: in fail-first mode, the truncation of
  VL *includes* the current element at the failure point rather
  than excludes it from the count.

## Data-dependent fail-first on CR operations

The principle of data-dependent fail-first is that if, during the course
of sequentially evaluating an element's Condition Test, one such test
is encountered which fails, then VL (Vector Length) is truncated (set)
at that point. In the case of Arithmetic SVP64 Operations the Condition
Register Field generated from Rc=1 is used as the basis for the truncation
decision.  However with CR-based operations that CR Field result to be
tested is provided *by the operation itself*.

Data-dependent SVP64 Vectorised Operations involving the creation
or modification of a CR can require an extra two bits, which are not
available in the compact space of the SVP64 RM `MODE` Field. With the
concept of element width overrides being meaningless for CR Fields it
is possible to use the `ELWIDTH` field for alternative purposes.

Condition Register based operations such as `sv.mfcr` and `sv.crand`
can thus be made more flexible.  However the rules that apply in this
section also apply to future CR-based instructions.

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)

Examining these two types it is observed that the difference may
be considered to be that the 5-bit variant *already* provides the
prerequisite information about which CR Field bit (EQ, GE, LT, SO) is
to be operated on by the instruction.  Thus, logically, we may set the
following rule:

* When a 5-bit CR Result field is used in an instruction, the
  5-bit variant of Data-Dependent Fail-First
  must be used. i.e. the bit of the CR field to be tested is
  the one that has just been modified (created) by the operation.
* When a 3-bit CR Result field is used the 3-bit variant
  must be used, providing as it does the missing `CRbit` field
  in order to select which CR Field bit of the result shall
  be tested (EQ, LE, GE, SO)

The reason why the 3-bit CR variant needs the additional CR-bit field
should be obvious from the fact that the 3-bit CR Field from the base
Power ISA v3.0B operation clearly does not contain and is missing the
two CR Field Selector bits. Thus, these two bits (to select EQ, LE,
GE or SO) must be provided in another way.

Examples of the former type:

* crand, cror, crnor. These all are 5-bit (BA, BB, BT). The bit
  to be tested against `inv` is the one selected by `BT`
* mcrf. This has only 3-bit (BF, BFA). In order to select the
  bit to be tested, the alternative encoding must be used.
  With `CRbit` coming from the SVP64 RM bits 22-23 the bit
  of BF to be tested is identified.

Just as with SVP64 [[sv/branches]] there is the option to truncate
VL to include the element being tested (`VLi=1`) and to exclude it
(`VLi=0`).

Also exactly as with [[sv/normal]] fail-first, VL cannot, unlike
[[sv/ldst]], be set to an arbitrary value.  Deterministic behaviour
is *required*.

## Reduction and Iteration

Bearing in mind as described in the svp64 Appendix, SVP64 Horizontal
Reduction is a deterministic schedule on top of base Scalar v3.0
operations, the same rules apply to CR Operations, i.e. that programmers
must follow certain conventions in order for an *end result* of a
reduction to be achieved.  Unlike other Vector ISAs *there are no explicit
reduction opcodes* in SVP64: Schedules however achieve the same effect.

Due to these conventions only reduction on operations such as `crand`
and `cror` are meaningful because these have Condition Register Fields
as both input and output.  Meaningless operations are not prohibited
because the cost in hardware of doing so is prohibitive, but neither
are they `UNDEFINED`. Implementations are still required to execute them
but are at liberty to optimise out any operations that would ultimately
be overwritten, as long as Strict Program Order is still obvservable by
the programmer.

Also bear in mind that 'Reverse Gear' may be enabled, which can be
used in combination with overlapping CR operations to iteratively
accumulate results.  Issuing a `sv.crand` operation for example with
`BA` differing from `BB` by one Condition Register Field would result
in a cascade effect, where the first-encountered CR Field would set the
result to zero, and also all subsequent CR Field elements thereafter:

```
    # sv.crand/mr/rg CR4.ge.v, CR5.ge.v, CR4.ge.v
    for i in VL-1 downto 0 # reverse gear
         CR.field[4+i].ge &= CR.field[5+i].ge
```

`sv.crxor` with reduction would be particularly useful for parity
calculation for example, although there are many ways in which the same
calculation could be carried out after transferring a vector of CR Fields
to a GPR using crweird operations.

Implementations are free and clear to optimise these reductions in any way
they see fit, as long as the end-result is compatible with Strict Program
Order being observed, and Interrupt latency is not adversely impacted.

## Unusual and quirky CR operations

**cmp and other compare ops**

`cmp` and `cmpi` etc take GPRs as sources and create a CR Field as a result.

    cmpli BF,L,RA,UI
    cmpeqb BF,RA,RB

With `ELWIDTH` applying to the source GPR operands this is perfectly fine.

**crweird operations**

There are 4 weird CR-GPR operations and one reasonable one in
the [[cr_int_predication]] set:

* crrweird
* mtcrweird
* crweirder
* crweird
* mcrfm - reasonably normal and referring to CR Fields for src and dest.

The "weird" operations have a non-standard behaviour, being able to
treat *individual bits* of a GPR effectively as elements.  They are
expected to be Micro-coded by most Hardware implementations.


--------

\newpage{}

# SVP64 Branch Conditional behaviour

Please note: although similar, SVP64 Branch instructions should be
considered completely separate and distinct from standard scalar
OpenPOWER-approved v3.0B branches.  **v3.0B branches are in no way
impacted, altered, changed or modified in any way, shape or form by the
SVP64 Vectorised Variants**.

It is also extremely important to note that Branches are the sole
pseudo-exception in SVP64 to `Scalar Identity Behaviour`.  SVP64 Branches
contain additional modes that are useful for scalar operations (i.e. even
when VL=1 or when using single-bit predication).

**Rationale**

Scalar 3.0B Branch Conditional operations, `bc`, `bctar` etc. test
a Condition Register.  However for parallel processing it is simply
impossible to perform multiple independent branches: the Program
Counter simply cannot branch to multiple destinations based on multiple
conditions.  The best that can be done is to test multiple Conditions
and make a decision of a *single* branch, based on analysis of a *Vector*
of CR Fields which have just been calculated from a *Vector* of results.

In 3D Shader binaries, which are inherently parallelised and predicated,
testing all or some results and branching based on multiple tests is
extremely common, and a fundamental part of Shader Compilers.  Example:
without such multi-condition test-and-branch, if a predicate mask is
all zeros a large batch of instructions may be masked out to `nop`,
and it would waste CPU cycles to run them.  3D GPU ISAs can test for
this scenario and, with the appropriate predicate-analysis instruction,
jump over fully-masked-out operations, by spotting that *all* Conditions
are false.

Unless Branches are aware and capable of such analysis, additional
instructions would be required which perform Horizontal Cumulative
analysis of Vectorised Condition Register Fields, in order to reduce
the Vector of CR Fields down to one single yes or no decision that a
Scalar-only v3.0B Branch-Conditional could cope with.  Such instructions
would be unavoidable, required, and costly by comparison to a single
Vector-aware Branch.  Therefore, in order to be commercially competitive,
`sv.bc` and other Vector-aware Branch Conditional instructions are a
high priority for 3D GPU (and OpenCL-style) workloads.

Given that Power ISA v3.0B is already quite powerful, particularly
the Condition Registers and their interaction with Branches, there are
opportunities to create extremely flexible and compact Vectorised Branch
behaviour.  In addition, the side-effects (updating of CTR, truncation
of VL, described below) make it a useful instruction even if the branch
points to the next instruction (no actual branch).

## Overview

When considering an "array" of branch-tests, there are four
primarily-useful modes: AND, OR, NAND and NOR of all Conditions.
NAND and NOR may be synthesised from AND and OR by inverting `BO[1]`
which just leaves two modes:

* Branch takes place on the **first** CR Field test to succeed
  (a Great Big OR of all condition tests). Exit occurs
  on the first **successful** test.
* Branch takes place only if **all** CR field tests succeed:
  a Great Big AND of all condition tests.  Exit occurs
  on the first **failed** test.

Early-exit is enacted such that the Vectorised Branch does not
perform needless extra tests, which will help reduce reads on
the Condition Register file.

*Note: Early-exit is **MANDATORY** (required) behaviour.  Branches
**MUST** exit at the first sequentially-encountered failure point,
for exactly the same reasons for which it is mandatory in programming
languages doing early-exit: to avoid damaging side-effects and to provide
deterministic behaviour. Speculative testing of Condition Register
Fields is permitted, as is speculative calculation of CTR, as long as,
as usual in any Out-of-Order microarchitecture, that speculative testing
is cancelled should an early-exit occur.  i.e. the speculation must be
"precise": Program Order must be preserved*

Also note that when early-exit occurs in Horizontal-first Mode, srcstep,
dststep etc. are all reset, ready to begin looping from the beginning
for the next instruction. However for Vertical-first Mode srcstep
etc. are incremented "as usual" i.e. an early-exit has no special impact,
regardless of whether the branch occurred or not. This can leave srcstep
etc. in what may be considered an unusual state on exit from a loop and
it is up to the programmer to reset srcstep, dststep etc. to known-good
values *(easily achieved with `setvl`)*.

Additional useful behaviour involves two primary Modes (both of which
may be enabled and combined):

* **VLSET Mode**: identical to Data-Dependent Fail-First Mode
  for Arithmetic SVP64 operations, with more
  flexibility and a close interaction and integration into the
  underlying base Scalar v3.0B Branch instruction.
  Truncation of VL takes place around the early-exit point.
* **CTR-test Mode**: gives much more flexibility over when and why
  CTR is decremented, including options to decrement if a Condition
  test succeeds *or if it fails*.

With these side-effects, basic Boolean Logic Analysis advises that it
is important to provide a means to enact them each based on whether
testing succeeds *or fails*. This results in a not-insignificant number
of additional Mode Augmentation bits, accompanying VLSET and CTR-test
Modes respectively.

Predicate skipping or zeroing may, as usual with SVP64, be controlled by
`sz`.  Where the predicate is masked out and zeroing is enabled, then in
such circumstances the same Boolean Logic Analysis dictates that rather
than testing only against zero, the option to test against one is also
prudent. This introduces a new immediate field, `SNZ`, which works in
conjunction with `sz`.

Vectorised Branches can be used in either SVP64 Horizontal-First or
Vertical-First Mode. Essentially, at an element level, the behaviour
is identical in both Modes, although the `ALL` bit is meaningless in
Vertical-First Mode.

It is also important to bear in mind that, fundamentally, Vectorised
Branch-Conditional is still extremely close to the Scalar v3.0B
Branch-Conditional instructions, and that the same v3.0B Scalar
Branch-Conditional instructions are still *completely separate and
independent*, being unaltered and unaffected by their SVP64 variants in
every conceivable way.

*Programming note: One important point is that SVP64 instructions are
64 bit.  (8 bytes not 4). This needs to be taken into consideration
when computing branch offsets: the offset is relative to the start of
the instruction, which **includes** the SVP64 Prefix*

## Format and fields

With element-width overrides being meaningless for Condition Register
Fields, bits 4 thru 7 of SVP64 RM may be used for additional Mode bits.

SVP64 RM `MODE` (includes repurposing `ELWIDTH` bits 4:5, and
`ELWIDTH_SRC` bits 6-7 for *alternate* uses) for Branch Conditional:

| 4 | 5 | 6 | 7 | 17 | 18 | 19 | 20 |  21 | 22  23 |  description     |
| - | - | - | - | -- | -- | -- | -- | --- |--------|----------------- |
|ALL|SNZ| / | / | SL |SLu | 0  | 0  | /   | LRu sz | simple mode      |
|ALL|SNZ| / |VSb| SL |SLu | 0  | 1  | VLI | LRu sz | VLSET mode       |
|ALL|SNZ|CTi| / | SL |SLu | 1  | 0  | /   | LRu sz | CTR-test mode         |
|ALL|SNZ|CTi|VSb| SL |SLu | 1  | 1  | VLI | LRu sz | CTR-test+VLSET mode   |

Brief description of fields:

* **sz=1** if predication is enabled and `sz=1` and a predicate
  element bit is zero, `SNZ` will
  be substituted in place of the CR bit selected by `BI`,
  as the Condition tested.
  Contrast this with
  normal SVP64 `sz=1` behaviour, where *only* a zero is put in
  place of masked-out predicate bits.
* **sz=0** When `sz=0` skipping occurs as usual on
  masked-out elements, but unlike all
  other SVP64 behaviour which entirely skips an element with
  no related side-effects at all, there are certain
  special circumstances where CTR
  may be decremented.  See CTR-test Mode, below.
* **ALL** when set, all branch conditional tests must pass in order for
  the branch to succeed. When clear, it is the first sequentially
  encountered successful test that causes the branch to succeed.
  This is identical behaviour to how programming languages perform
  early-exit on Boolean Logic chains.
* **VLI** VLSET is identical to Data-dependent Fail-First mode.
  In VLSET mode, VL *may* (depending on `VSb`) be truncated.
  If VLI (Vector Length Inclusive) is clear,
  VL is truncated to *exclude* the current element, otherwise it is
  included. SVSTATE.MVL is not altered: only VL.
* **SL** identical to `LR` except applicable to SVSTATE. If `SL`
  is set, SVSTATE is transferred to SVLR (conditionally on
  whether `SLu` is set).
* **SLu**: SVSTATE Link Update, like `LRu` except applies to SVSTATE.
* **LRu**: Link Register Update, used in conjunction with LK=1
  to make LR update conditional
* **VSb** In VLSET Mode, after testing,
  if VSb is set, VL is truncated if the test succeeds.  If VSb is clear,
  VL is truncated if a test *fails*. Masked-out (skipped)
  bits are not considered
  part of testing when `sz=0`
* **CTi** CTR inversion. CTR-test Mode normally decrements per element
  tested. CTR inversion decrements if a test *fails*. Only relevant
  in CTR-test Mode.

LRu and CTR-test modes are where SVP64 Branches subtly differ from
Scalar v3.0B Branches. `sv.bcl` for example will always update LR,
whereas `sv.bcl/lru` will only update LR if the branch succeeds.

Of special interest is that when using ALL Mode (Great Big AND of all
Condition Tests), if `VL=0`, which is rare but can occur in Data-Dependent
Modes, the Branch will always take place because there will be no failing
Condition Tests to prevent it. Likewise when not using ALL Mode (Great
Big OR of all Condition Tests) and `VL=0` the Branch is guaranteed not
to occur because there will be no *successful* Condition Tests to make
it happen.

## Vectorised CR Field numbering, and Scalar behaviour

It is important to keep in mind that just like all SVP64 instructions,
the `BI` field of the base v3.0B Branch Conditional instruction may be
extended by SVP64 EXTRA augmentation, as well as be marked as either
Scalar or Vector. It is also crucially important to keep in mind that for
CRs, SVP64 sequentially increments the CR *Field* numbers.  CR *Fields*
are treated as elements, not bit-numbers of the CR *register*.

The `BI` operand of Branch Conditional operations is five bits, in scalar
v3.0B this would select one bit of the 32 bit CR, comprising eight CR
Fields of 4 bits each.  In SVP64 there are 16 32 bit CRs, containing
128 4-bit CR Fields.  Therefore, the 2 LSBs of `BI` select the bit from
the CR Field (EQ LT GT SO), and the top 3 bits are extended to either
scalar or vector and to select CR Fields 0..127 as specified in SVP64
[[sv/svp64/appendix]].

When the CR Fields selected by SVP64-Augmented `BI` is marked as scalar,
then as the usual SVP64 rules apply: the Vector loop ends at the first
element tested (the first CR *Field*), after taking predication into
consideration. Thus, also as usual, when a predicate mask is given, and
`BI` marked as scalar, and `sz` is zero, srcstep skips forward to the
first non-zero predicated element, and only that one element is tested.

In other words, the fact that this is a Branch Operation (instead of an
arithmetic one) does not result, ultimately, in significant changes as
to how SVP64 is fundamentally applied, except with respect to:

* the unique properties associated with conditionally
 changing the Program Counter (aka "a Branch"), resulting in early-out
 opportunities
* CTR-testing

Both are outlined below, in later sections.

## Horizontal-First and Vertical-First Modes

In SVP64 Horizontal-First Mode, the first failure in ALL mode (Great Big
AND) results in early exit: no more updates to CTR occur (if requested);
no branch occurs, and LR is not updated (if requested). Likewise for
non-ALL mode (Great Big Or) on first success early exit also occurs,
however this time with the Branch proceeding.  In both cases the testing
of the Vector of CRs should be done in linear sequential order (or in
REMAP re-sequenced order): such that tests that are sequentially beyond
the exit point are *not* carried out. (*Note: it is standard practice
in Programming languages to exit early from conditional tests, however a
little unusual to consider in an ISA that is designed for Parallel Vector
Processing. The reason is to have strictly-defined guaranteed behaviour*)

In Vertical-First Mode, setting the `ALL` bit results in `UNDEFINED`
behaviour. Given that only one element is being tested at a time in
Vertical-First Mode, a test designed to be done on multiple bits is
meaningless.

## Description and Modes

Predication in both INT and CR modes may be applied to `sv.bc` and other
SVP64 Branch Conditional operations, exactly as they may be applied to
other SVP64 operations.  When `sz` is zero, any masked-out Branch-element
operations are not included in condition testing, exactly like all other
SVP64 operations, *including* side-effects such as potentially updating
LR or CTR, which will also be skipped. There is *one* exception here,
which is when `BO[2]=0, sz=0, CTR-test=0, CTi=1` and the relevant element
predicate mask bit is also zero: under these special circumstances CTR
will also decrement.

When `sz` is non-zero, this normally requests insertion of a zero in
place of the input data, when the relevant predicate mask bit is zero.
This would mean that a zero is inserted in place of `CR[BI+32]` for
testing against `BO`, which may not be desirable in all circumstances.
Therefore, an extra field is provided `SNZ`, which, if set, will insert
a **one** in place of a masked-out element, instead of a zero.

(*Note: Both options are provided because it is useful to deliberately
cause the Branch-Conditional Vector testing to fail at a specific point,
controlled by the Predicate mask. This is particularly useful in `VLSET`
mode, which will truncate SVSTATE.VL at the point of the first failed
test.*)

Normally, CTR mode will decrement once per Condition Test, resulting under
normal circumstances that CTR reduces by up to VL in Horizontal-First
Mode. Just as when v3.0B Branch-Conditional saves at least one instruction
on tight inner loops through auto-decrementation of CTR, likewise it
is also possible to save instruction count for SVP64 loops in both
Vertical-First and Horizontal-First Mode, particularly in circumstances
where there is conditional interaction between the element computation
and testing, and the continuation (or otherwise) of a given loop. The
potential combinations of interactions is why CTR testing options have
been added.

Also, the unconditional bit `BO[0]` is still relevant when Predication
is applied to the Branch because in `ALL` mode all nonmasked bits have
to be tested, and when `sz=0` skipping occurs.  Even when VLSET mode is
not used, CTR may still be decremented by the total number of nonmasked
elements, acting in effect as either a popcount or cntlz depending
on which mode bits are set.  In short, Vectorised Branch becomes an
extremely powerful tool.

**Micro-Architectural Implementation Note**: *when implemented on top
of a Multi-Issue Out-of-Order Engine it is possible to pass a copy of
the predicate and the prerequisite CR Fields to all Branch Units, as
well as the current value of CTR at the time of multi-issue, and for
each Branch Unit to compute how many times CTR would be subtracted,
in a fully-deterministic and parallel fashion. A SIMD-based Branch
Unit, receiving and processing multiple CR Fields covered by multiple
predicate bits, would do the exact same thing. Obviously, however, if
CTR is modified within any given loop (mtctr) the behaviour of CTR is
no longer deterministic.*

### Link Register Update

For a Scalar Branch, unconditional updating of the Link Register LR
is useful and practical. However, if a loop of CR Fields is tested,
unconditional updating of LR becomes problematic.

For example when using `bclr` with `LRu=1,LK=0` in Horizontal-First Mode,
LR's value will be unconditionally overwritten after the first element,
such that for execution (testing) of the second element, LR has the value
`CIA+8`. This is covered in the `bclrl` example, in a later section.

The addition of a LRu bit modifies behaviour in conjunction with LK,
as follows:

* `sv.bc` When LRu=0,LK=0, Link Register is not updated
* `sv.bcl` When LRu=0,LK=1, Link Register is updated unconditionally
* `sv.bcl/lru` When LRu=1,LK=1, Link Register will
  only be updated if the Branch Condition fails.
* `sv.bc/lru` When LRu=1,LK=0, Link Register will only be updated if
  the Branch Condition succeeds.

This avoids destruction of LR during loops (particularly Vertical-First
ones).

**SVLR and SVSTATE**

For precisely the reasons why `LK=1` was added originally to the Power
ISA, with SVSTATE being a peer of the Program Counter it becomes necessary
to also add an SVLR (SVSTATE Link Register) and corresponding control bits
`SL` and `SLu`.

### CTR-test

Where a standard Scalar v3.0B branch unconditionally decrements CTR when
`BO[2]` is clear, CTR-test Mode introduces more flexibility which allows
CTR to be used for many more types of Vector loops constructs.

CTR-test mode and CTi interaction is as follows: note that `BO[2]`
is still required to be clear for CTR decrements to be considered,
exactly as is the case in Scalar Power ISA v3.0B

* **CTR-test=0, CTi=0**: CTR decrements on a per-element basis
  if `BO[2]` is zero. Masked-out elements when `sz=0` are
  skipped (i.e. CTR is *not* decremented when the predicate
  bit is zero and `sz=0`).
* **CTR-test=0, CTi=1**: CTR decrements on a per-element basis
  if `BO[2]` is zero and a masked-out element is skipped
  (`sz=0` and predicate bit is zero). This one special case is the
  **opposite** of other combinations, as well as being
  completely different from normal SVP64 `sz=0` behaviour)
* **CTR-test=1, CTi=0**: CTR decrements on a per-element basis
  if `BO[2]` is zero and the Condition Test succeeds.
  Masked-out elements when `sz=0` are skipped (including
  not decrementing CTR)
* **CTR-test=1, CTi=1**: CTR decrements on a per-element basis
  if `BO[2]` is zero and the Condition Test *fails*.
  Masked-out elements when `sz=0` are skipped (including
  not decrementing CTR)

`CTR-test=0, CTi=1, sz=0` requires special emphasis because it is the
only time in the entirety of SVP64 that has side-effects when
a predicate mask bit is clear.  **All** other SVP64 operations
entirely skip an element when sz=0 and a predicate mask bit is zero.
It is also critical to emphasise that in this unusual mode,
no other side-effects occur: **only** CTR is decremented, i.e. the
rest of the Branch operation is skipped.

### VLSET Mode

VLSET Mode truncates the Vector Length so that subsequent instructions
operate on a reduced Vector Length. This is similar to Data-dependent
Fail-First and LD/ST Fail-First, where for VLSET the truncation occurs
at the Branch decision-point.

Interestingly, due to the side-effects of `VLSET` mode it is actually
useful to use Branch Conditional even to perform no actual branch
operation, i.e to point to the instruction after the branch. Truncation of
VL would thus conditionally occur yet control flow alteration would not.

`VLSET` mode with Vertical-First is particularly unusual. Vertical-First
is designed to be used for explicit looping, where an explicit call to
`svstep` is required to move both srcstep and dststep on to the next
element, until VL (or other condition) is reached.  Vertical-First Looping
is expected (required) to terminate if the end of the Vector, VL, is
reached. If however that loop is terminated early because VL is truncated,
VLSET with Vertical-First becomes meaningless.  Resolving this would
require two branches: one Conditional, the other branching unconditionally
to create the loop, where the Conditional one jumps over it.

Therefore, with `VSb`, the option to decide whether truncation should
occur if the branch succeeds *or* if the branch condition fails allows
for the flexibility required.  This allows a Vertical-First Branch to
*either* be used as a branch-back (loop) *or* as part of a conditional
exit or function call from *inside* a loop, and for VLSET to be integrated
into both types of decision-making.

In the case of a Vertical-First branch-back (loop), with `VSb=0` the
branch takes place if success conditions are met, but on exit from that
loop (branch condition fails), VL will be truncated. This is extremely
useful.

`VLSET` mode with Horizontal-First when `VSb=0` is still useful, because
it can be used to truncate VL to the first predicated (non-masked-out)
element.

The truncation point for VL, when VLi is clear, must not include skipped
elements that preceded the current element being tested.  Example:
`sz=0, VLi=0, predicate mask = 0b110010` and the Condition Register
failure point is at CR Field element 4.

* Testing at element 0 is skipped because its predicate bit is zero
* Testing at element 1 passed
* Testing elements 2 and 3 are skipped because their
  respective predicate mask bits are zero
* Testing element 4 fails therefore VL is truncated to **2**
  not 4 due to elements 2 and 3 being skipped.

If `sz=1` in the above example *then* VL would have been set to 4 because
in non-zeroing mode the zero'd elements are still effectively part of the
Vector (with their respective elements set to `SNZ`)

If `VLI=1` then VL would be set to 5 regardless of sz, due to being inclusive
of the element actually being tested.

### VLSET and CTR-test combined

If both CTR-test and VLSET Modes are requested, it is important to
observe the correct order. What occurs depends on whether VLi is enabled,
because VLi affects the length, VL.

If VLi (VL truncate inclusive) is set:

1. compute the test including whether CTR triggers
2. (optionally) decrement CTR
3. (optionally) truncate VL (VSb inverts the decision)
4. decide (based on step 1) whether to terminate looping
   (including not executing step 5)
5. decide whether to branch.

If VLi is clear, then when a test fails that element
and any following it
should **not** be considered part of the Vector. Consequently:

1. compute the branch test including whether CTR triggers
2. if the test fails against VSb, truncate VL to the *previous*
   element, and terminate looping. No further steps executed.
3. (optionally) decrement CTR
4. decide whether to branch.

## Boolean Logic combinations

In a Scalar ISA, Branch-Conditional testing even of vector results may be
performed through inversion of tests. NOR of all tests may be performed
by inversion of the scalar condition and branching *out* from the scalar
loop around elements, using scalar operations.

In a parallel (Vector) ISA it is the ISA itself which must perform
the prerequisite logic manipulation.  Thus for SVP64 there are an
extraordinary number of nesessary combinations which provide completely
different and useful behaviour.  Available options to combine:

* `BO[0]` to make an unconditional branch would seem irrelevant if
  it were not for predication and for side-effects (CTR Mode
  for example)
* Enabling CTR-test Mode and setting `BO[2]` can still result in the
  Branch
  taking place, not because the Condition Test itself failed, but
  because CTR reached zero **because**, as required by CTR-test mode,
  CTR was decremented as a  **result** of Condition Tests failing.
* `BO[1]` to select whether the CR bit being tested is zero or nonzero
* `R30` and `~R30` and other predicate mask options including CR and
  inverted CR bit testing
* `sz` and `SNZ` to insert either zeros or ones in place of masked-out
  predicate bits
* `ALL` or `ANY` behaviour corresponding to `AND` of all tests and
  `OR` of all tests, respectively.
* Predicate Mask bits, which combine in effect with the CR being
  tested.
* Inversion of Predicate Masks (`~r3` instead of `r3`, or using
  `NE` rather than `EQ`) which results in an additional
  level of possible ANDing, ORing etc. that would otherwise
  need explicit instructions.

The most obviously useful combinations here are to set `BO[1]` to zero
in order to turn `ALL` into Great-Big-NAND and `ANY` into Great-Big-NOR.
Other Mode bits which perform behavioural inversion then have to work
round the fact that the Condition Testing is NOR or NAND.  The alternative
to not having additional behavioural inversion (`SNZ`, `VSb`, `CTi`)
would be to have a second (unconditional) branch directly after the first,
which the first branch jumps over.  This contrivance is avoided by the
behavioural inversion bits.

## Pseudocode and examples

Please see the SVP64 appendix regarding CR bit ordering and for
the definition of `CR{n}`

For comparative purposes this is a copy of the v3.0B `bc` pseudocode

```
    if (mode_is_64bit) then M <- 0
    else M <- 32
    if ¬BO[2] then CTR <- CTR - 1
    ctr_ok <- BO[2] | ((CTR[M:63] != 0) ^ BO[3])
    cond_ok <- BO[0] | ¬(CR[BI+32] ^ BO[1])
    if ctr_ok & cond_ok then
      if AA then NIA <-iea EXTS(BD || 0b00)
      else       NIA <-iea CIA + EXTS(BD || 0b00)
    if LK then LR  <-iea  CIA + 4
```

Simplified pseudocode including LRu and CTR skipping, which illustrates
clearly that SVP64 Scalar Branches (VL=1) are **not** identical to
v3.0B Scalar Branches.  The key areas where differences occur are the
inclusion of predication (which can still be used when VL=1), in when and
why CTR is decremented (CTRtest Mode) and whether LR is updated (which
is unconditional in v3.0B when LK=1, and conditional in SVP64 when LRu=1).

Inline comments highlight the fact that the Scalar Branch behaviour and
pseudocode is still clearly visible and embedded within the Vectorised
variant:

```
    if (mode_is_64bit) then M <- 0
    else M <- 32
    # the bit of CR to test, if the predicate bit is zero,
    # is overridden
    testbit = CR[BI+32]
    if ¬predicate_bit then testbit = SVRMmode.SNZ
    # otherwise apart from the override ctr_ok and cond_ok
    # are exactly the same
    ctr_ok <- BO[2] | ((CTR[M:63] != 0) ^ BO[3])
    cond_ok <- BO[0] | ¬(testbit ^ BO[1])
    if ¬predicate_bit & ¬SVRMmode.sz then
      # this is entirely new: CTR-test mode still decrements CTR
      # even when predicate-bits are zero
      if ¬BO[2] & CTRtest & ¬CTi then
        CTR = CTR - 1
      # instruction finishes here
    else
      # usual BO[2] CTR-mode now under CTR-test mode as well
      if ¬BO[2] & ¬(CTRtest & (cond_ok ^ CTi)) then CTR <- CTR - 1
      # new VLset mode, conditional test truncates VL
      if VLSET and VSb = (cond_ok & ctr_ok) then
        if SVRMmode.VLI then SVSTATE.VL = srcstep+1
        else                 SVSTATE.VL = srcstep
      # usual LR is now conditional, but also joined by SVLR
      lr_ok <- LK
      svlr_ok <- SVRMmode.SL
      if ctr_ok & cond_ok then
        if AA then NIA <-iea EXTS(BD || 0b00)
        else       NIA <-iea CIA + EXTS(BD || 0b00)
        if SVRMmode.LRu then lr_ok <- ¬lr_ok
        if SVRMmode.SLu then svlr_ok <- ¬svlr_ok
      if lr_ok   then LR   <-iea CIA + 4
      if svlr_ok then SVLR <- SVSTATE
```

Below is the pseudocode for SVP64 Branches, which is a little less
obvious but identical to the above. The lack of obviousness is down to
the early-exit opportunities.

Effective pseudocode for Horizontal-First Mode:

```
    if (mode_is_64bit) then M <- 0
    else M <- 32
    cond_ok = not SVRMmode.ALL
    for srcstep in range(VL):
        # select predicate bit or zero/one
        if predicate[srcstep]:
            # get SVP64 extended CR field 0..127
            SVCRf = SVP64EXTRA(BI>>2)
            CRbits = CR{SVCRf}
            testbit = CRbits[BI & 0b11]
            # testbit = CR[BI+32+srcstep*4]
        else if not SVRMmode.sz:
            # inverted CTR test skip mode
            if ¬BO[2] & CTRtest & ¬CTI then
              CTR = CTR - 1
            continue # skip to next element
        else
            testbit = SVRMmode.SNZ
        # actual element test here
        ctr_ok <- BO[2] | ((CTR[M:63] != 0) ^ BO[3])
        el_cond_ok <- BO[0] | ¬(testbit ^ BO[1])
        # check if CTR dec should occur
        ctrdec = ¬BO[2]
        if CTRtest & (el_cond_ok ^ CTi) then
           ctrdec = 0b0
        if ctrdec then CTR <- CTR - 1
        # merge in the test
        if SVRMmode.ALL:
            cond_ok &= (el_cond_ok & ctr_ok)
        else
            cond_ok |= (el_cond_ok & ctr_ok)
        # test for VL to be set (and exit)
        if VLSET and VSb = (el_cond_ok & ctr_ok) then
            if SVRMmode.VLI then SVSTATE.VL = srcstep+1
            else                 SVSTATE.VL = srcstep
            break
        # early exit?
        if SVRMmode.ALL != (el_cond_ok & ctr_ok):
             break
        # SVP64 rules about Scalar registers still apply!
        if SVCRf.scalar:
           break
    # loop finally done, now test if branch (and update LR)
    lr_ok <- LK
    svlr_ok <- SVRMmode.SL
    if cond_ok then
        if AA then NIA <-iea EXTS(BD || 0b00)
        else       NIA <-iea CIA + EXTS(BD || 0b00)
        if SVRMmode.LRu then lr_ok <- ¬lr_ok
        if SVRMmode.SLu then svlr_ok <- ¬svlr_ok
    if lr_ok then LR <-iea CIA + 4
    if svlr_ok then SVLR <- SVSTATE
```

Pseudocode for Vertical-First Mode:

```
    # get SVP64 extended CR field 0..127
    SVCRf = SVP64EXTRA(BI>>2)
    CRbits = CR{SVCRf}
    # select predicate bit or zero/one
    if predicate[srcstep]:
        if BRc = 1 then # CR0 vectorised
            CR{SVCRf+srcstep} = CRbits
        testbit = CRbits[BI & 0b11]
    else if not SVRMmode.sz:
        # inverted CTR test skip mode
        if ¬BO[2] & CTRtest & ¬CTI then
           CTR = CTR - 1
        SVSTATE.srcstep = new_srcstep
        exit # no branch testing
    else
        testbit = SVRMmode.SNZ
    # actual element test here
    cond_ok <- BO[0] | ¬(testbit ^ BO[1])
    # test for VL to be set (and exit)
    if VLSET and cond_ok = VSb then
        if SVRMmode.VLI
            SVSTATE.VL = new_srcstep+1
        else
            SVSTATE.VL = new_srcstep
```

### Example Shader code

```
    // assume f() g() or h() modify a and/or b
    while(a > 2) {
        if(b < 5)
            f();
        else
            g();
        h();
    }
```

which compiles to something like:

```
    vec<i32> a, b;
    // ...
    pred loop_pred = a > 2;
    // loop continues while any of a elements greater than 2
    while(loop_pred.any()) {
        // vector of predicate bits
        pred if_pred = loop_pred & (b < 5);
        // only call f() if at least 1 bit set
        if(if_pred.any()) {
            f(if_pred);
        }
    label1:
        // loop mask ANDs with inverted if-test
        pred else_pred = loop_pred & ~if_pred;
        // only call g() if at least 1 bit set
        if(else_pred.any()) {
            g(else_pred);
        }
        h(loop_pred);
    }
```

which will end up as:

```
       # start from while loop test point
       b looptest
    while_loop:
       sv.cmpi CR80.v, b.v, 5     # vector compare b into CR64 Vector
       sv.bc/m=r30/~ALL/sz CR80.v.LT skip_f # skip when none
       # only calculate loop_pred & pred_b because needed in f()
       sv.crand CR80.v.SO, CR60.v.GT, CR80.V.LT # if = loop & pred_b
       f(CR80.v.SO)
    skip_f:
       # illustrate inversion of pred_b. invert r30, test ALL
       # rather than SOME, but masked-out zero test would FAIL,
       # therefore masked-out instead is tested against 1 not 0
       sv.bc/m=~r30/ALL/SNZ CR80.v.LT skip_g
       # else = loop & ~pred_b, need this because used in g()
       sv.crternari(A&~B) CR80.v.SO, CR60.v.GT, CR80.V.LT
       g(CR80.v.SO)
    skip_g:
       # conditionally call h(r30) if any loop pred set
       sv.bclr/m=r30/~ALL/sz BO[1]=1 h()
    looptest:
       sv.cmpi CR60.v a.v, 2      # vector compare a into CR60 vector
       sv.crweird r30, CR60.GT # transfer GT vector to r30
       sv.bc/m=r30/~ALL/sz BO[1]=1 while_loop
    end:
```

### LRu example

show why LRu would be useful in a loop.  Imagine the following
c code:

```
    for (int i = 0; i < 8; i++) {
        if (x < y) break;
    }
```

Under these circumstances exiting from the loop is not only based on
CTR it has become conditional on a CR result.  Thus it is desirable that
NIA *and* LR only be modified if the conditions are met

v3.0 pseudocode for `bclrl`:

```
    if (mode_is_64bit) then M <- 0
    else M <- 32
    if ¬BO[2]  then CTR <- CTR - 1
    ctr_ok <- BO[2] | ((CTR[M:63] != 0) ^ BO[3])
    cond_ok <- BO[0] | ¬(CR[BI+32] ^  BO[1])
    if ctr_ok & cond_ok then NIA <-iea LR[0:61] || 0b00
    if LK then LR <-iea CIA + 4
```

the latter part for SVP64 `bclrl` becomes:

```
    for i in 0 to VL-1:
        ...
        ...
        cond_ok <- BO[0] | ¬(CR[BI+32] ^  BO[1])
        lr_ok <- LK
        if ctr_ok & cond_ok then
           NIA <-iea LR[0:61] || 0b00
           if SVRMmode.LRu then lr_ok <- ¬lr_ok
        if lr_ok then LR <-iea CIA + 4
        # if NIA modified exit loop
```

The reason why should be clear from this being a Vector loop:
unconditional destruction of LR when LK=1 makes `sv.bclrl` ineffective,
because the intention going into the loop is that the branch should be to
the copy of LR set at the *start* of the loop, not half way through it.
However if the change to LR only occurs if the branch is taken then it
becomes a useful instruction.

The following pseudocode should **not** be implemented because it
violates the fundamental principle of SVP64 which is that SVP64 looping
is a thin wrapper around Scalar Instructions.  The pseducode below is
more an actual Vector ISA Branch and as such is not at all appropriate:

```
    for i in 0 to VL-1:
        ...
        ...
        cond_ok <- BO[0] | ¬(CR[BI+32] ^  BO[1])
        if ctr_ok & cond_ok then NIA <-iea LR[0:61] || 0b00
    # only at the end of looping is LK checked.
    # this completely violates the design principle of SVP64
    # and would actually need to be a separate (scalar)
    # instruction "set LR to CIA+4 but retrospectively"
    # which is clearly impossible
    if LK then LR <-iea CIA + 4
```

[[!tag opf_rfc]]