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# RFC ls009 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

This document focuses on the encoding of [[SV|sv]], and assumes familiarity with the same. It does not cover how SV works (merely the instruction encoding), and is therefore best read in conjunction with the [[sv/overview]], as well as the [[sv/svp64_quirks]] section.
It is also crucial to note that whilst this format augments instruction
behaviour it works in conjunction with SVSTATE and other [[sv/sprs]].

All bit numbers are 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 used
elsewhere in the Power ISA.

64-bit instructions are split into two 32-bit words, the prefix and the
suffix. The prefix always comes before the suffix in PC order.

| 0:5    | 6:31         | 32:63        |
|--------|--------------|--------------|
| EXT01  | v3.1  Prefix | v3.0/1  Suffix |

svp64 fits into the "reserved" portions of the v3.1 prefix, making it possible for svp64, v3.0B (or v3.1 including 64 bit prefixed) instructions  to co-exist in the same binary without conflict.

Subset implementations in hardware are permitted, as long as certain
rules are followed, allowing for full soft-emulation including future
revisions.  Details in the [[svp64/appendix]].

## 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.

This document focusses specifically on how that fits into available space.  The [[svp64/appendix]] explains more of the details, whilst the [[sv/overview]] gives the basics.

# 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.

# 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").

# Register Naming and size

SV Registers are simply the INT, FP and CR register files extended
linearly to larger sizes; SV Vectorisation iterates sequentially through these registers.

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.

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

To allow relatively easy remapping of which portions of the Prefix Opcode
Map are used for SVP64 without needing to rewrite a large portion of the
SVP64 spec, a mapping is defined from the OpenPower v3.1 prefix bits to
a new 24-bit Remapped Encoding denoted `RM[0]` at the MSB to `RM[23]`
at the LSB.

The mapping from the OpenPower v3.1 prefix bits to the Remapped Encoding
is defined in the Prefix Fields section.

## Prefix Opcode Map (64-bit instruction encoding)

In the original table in the v3.1B Power ISA Spec on p1350, Table 12, prefix bits 6:11 are shown, with their allocations to different v3.1B pregix "modes".

The table below hows both PowerISA v3.1 instructions as well as new SVP instructions fit;
empty spaces are yet-to-be-allocated Illegal Instructions.  

| 6:11 | ---000 | ---001 | ---010 | ---011 | ---100 | ---101 | ---110 | ---111 |
|------|--------|--------|--------|--------|--------|--------|--------|--------|
|000---| 8LS    | 8LS    | 8LS    | 8LS    | 8LS    | 8LS    | 8LS    | 8LS    |
|001---|        |        |        |        |        |        |        |        |
|010---| 8RR    |        |        |        | `SVP64`| `SVP64`| `SVP64`| `SVP64`|
|011---|        |        |        |        | `SVP64`| `SVP64`| `SVP64`| `SVP64`|
|100---| MLS    | MLS    | MLS    | MLS    | MLS    | MLS    | MLS    | MLS    |
|101---|        |        |        |        |        |        |        |        |
|110---| MRR    |        |        |        | `SVP64`| `SVP64`| `SVP64`| `SVP64`|
|111---|        | MMIRR  |        |        | `SVP64`| `SVP64`| `SVP64`| `SVP64`|

Note that by taking up a block of 16, where in every case bits 7 and 9 are set, this allows svp64 to utilise four bits of the v3.1B Prefix space and "allocate" them to svp64's Remapped Encoding field, instead.

## Prefix Fields

To "activate" svp64 (in a way that does not conflict with v3.1B 64 bit Prefix mode), fields within the v3.1B Prefix Opcode Map are set
(see Prefix Opcode Map, above), leaving 24 bits "free" for use by SV.
This is achieved by setting bits 7 and 9 to 1:  

| Name       | Bits    | Value | Description                    |
|------------|---------|-------|--------------------------------|
| EXT01      | `0:5`   | `1`   | Indicates Prefixed 64-bit      |
| `RM[0]`    | `6`     |       | Bit 0 of Remapped Encoding     |
| SVP64_7    | `7`     | `1`   | Indicates this is SVP64        |
| `RM[1]`    | `8`     |       | Bit 1 of Remapped Encoding     |
| SVP64_9    | `9`     | `1`   | Indicates this is SVP64        |
| `RM[2:23]` | `10:31` |       | Bits 2-23 of Remapped Encoding |

Laid out bitwise, this is as follows, showing how the 32-bits of the prefix
are constructed:

| 0:5    | 6     | 7 | 8     | 9 | 10:31    |
|--------|-------|---|-------|---|----------|
| EXT01  | RM    | 1 | RM    | 1 | RM       |
| 000001 | RM[0] | 1 | RM[1] | 1 | RM[2:23] |

Following the prefix will be the suffix: this is simply a 32-bit v3.0B / v3.1
instruction.  That instruction becomes "prefixed" with the SVP context: the
Remapped Encoding field (RM).

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.

Extreme caution and care must therefore 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:

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

TODO: rename MASK_KIND to MASKMODE

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.  See [[svp64/appendix]] for explanation and pseudocode.
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[4:2] | BA[1:0] |
| 001   | Scalar | `CR8-CR15`/1  | 0b0001    | BA[4:2] | BA[1:0] |
| 010   | Scalar | `CR16-CR23`/1 | 0b0010    | BA[4:2] | BA[1:0] |
| 011   | Scalar | `CR24-CR31`/1 | 0b0011    | BA[4:2] | BA[1:0] |
| 100   | Vector | `CR0-CR112`/16 | BA[4:2] 0 | 0b000   | BA[1:0] |
| 101   | Vector | `CR4-CR116`/16 | BA[4:2] 0 | 0b100   | BA[1:0] |
| 110   | Vector | `CR8-CR120`/16 | BA[4:2] 1 | 0b000   | BA[1:0] |
| 111   | Vector | `CR12-CR124`/16 | BA[4:2] 1 | 0b100   | BA[1:0] |

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.  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[4:2] | BA[1:0] |
| 01    | Scalar | `CR8-CR15`/1   | 0b0001  | BA[4:2] | BA[1:0] |
| 10    | Vector | `CR0-CR112`/16 | BA[4:2] 0 | 0b000   | BA[1:0] |
| 11    | Vector | `CR8-CR120`/16 | BA[4:2] 1 | 0b000   | BA[1:0] |

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   |

# Appendix

Now at its own page: [[svp64/appendix]]