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# SVP64 for OpenPOWER ISA v3.0B

This document describes [[SV|sv]] augmentation of the [[OpenPOWER|openpower]] v3.0B [[ISA|openpower/isa/]]. Permission to create commercial v3.1B implementations has not yet been granted through the issuance of a v3.1B EULA by the [[!wikipedia OpenPOWER_Foundation]] (only v3.0B)

Links:

* <http://lists.libre-soc.org/pipermail/libre-soc-dev/2020-December/001498.html>>
* [[svp64/discussion]]
* [[svp64/appendix]]
* <http://lists.libre-soc.org/pipermail/libre-soc-dev/2020-December/001650.html>
* <https://bugs.libre-soc.org/show_bug.cgi?id=550>
* <https://bugs.libre-soc.org/show_bug.cgi?id=573> TODO elwidth "infinite" discussion
* <https://bugs.libre-soc.org/show_bug.cgi?id=574> Saturating description. 

Table of contents

[[!toc]]

# Introduction

This document focuses on the encoding of [[SV|sv]], and assumes familiarity with the same. It is best read in conjunction with the [[sv/overview]] which explains the background.

The plan is to create an encoding for SVP64, then to create an encoding
for SVP48, then to reorganize them both to improve field overlap,
reducing the amount of decoder hardware necessary.

All bit numbers are in MSB0 form (the bits are numbered from 0 at the MSB
and counting up as you move to the LSB end). All bit ranges are inclusive
(so `4:6` means bits 4, 5, and 6).

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         | 0:31         |
|--------|--------------|--------------|
| EXT01  | v3.1B Prefix | v3.1B Suffix |

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

## 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 *types* of predication: INT and CR
* SV Modes including saturation (for A/V 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.  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.

# 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 OpenPOWER
v3.0/1B 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 operation").

The significance of identity behaviour is that instructions added under svp64 to the 32 bit suffix are not only accessible to svp64: as long as implementors conform to identity behaviour (set the prefix to all zeros) they may use the instructions without needing to actually implement SV itself.

# 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
OpenPOWER 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 CRs are
extended to 64 entries, CR0 thru CR63.

The names of the registers therefore reflects a simple linear extension
of the OpenPOWER 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.  To accommodate 256 registers, numbering of Vectors will simply shift up by one bit, without
requiring additional prefix bits.  Backwards binary compatibility may be achieved with a PCR bit (Program Compatibility Register).  Beyond this, 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 OpenPOWER 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 / v3.1B
instruction.  That instruction becomes "prefixed" with the SVP context: the
Remapped Encoding field (RM).

# 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                      |
| ELWIDTH       | `4:5`      | Element Width                       |
| ELWIDTH_SRC   | `6:7`      | Element Width for Source      |
| SUBVL         | `8:9`      | Sub-vector length                   |                          
| 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 are further decoded depending on RM category for the instruction.
Similar to OpenPOWER `X-Form` etc. these 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.  Some of these alterations are element-based (saturation), others involve post-analysis (predicate result) and others are Vector-based (mapreduce, fail-on-first).

These are the modes:

* **normal** 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 elemrnt result to a min/max rather than overflows / wraps.  allows signed and unsigned clamping. 
* **reduce mode**. a mapreduce is performed.  the result is a scalar.  a result vector however is required, as the upper elements may be used to store intermediary computations.  the result of the mapreduce is in the first element with a nonzero predicate bit.  see [[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 testing) and if the test fails it is as if the predicate bit was zero.  When Rc=1 the CR element however is still stored in the CR regfile, even if the test failed.  This scheme does not apply to crops (crand, cror).  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.  normal, 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 is laid out as follows:

| 0-1 |  2  |  3   4  |  description              |
| --- | --- |---------|-------------------------- |
| 00  |   0 |  sz  dz | normal mode                      |
| 00  |   1 | sz CRM  | reduce mode (mapreduce), SUBVL=1 |
| 00  |   1 | SVM CRM | subvector reduce mode, SUBVL>1   |
| 01  | inv | CR-bit  | Rc=1: ffirst CR sel              |
| 01  | inv | sz  RC1 |  Rc=0: ffirst z/nonz |
| 10  |   N | sz   dz |  sat mode: N=0/1 u/s |
| 11  | inv | CR-bit  |  Rc=1: pred-result CR sel |
| 11  | inv | sz  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.
* **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)
* **CRM** affects the CR on reduce mode when Rc=1
* **SVM** sets "subvector" reduce mode
* **N** sets signed/unsigned saturation.
**RC1** as if Rc=1, stores CRs *but not the result*

## LD/ST ffirst

ffirst LD/ST to multiple pages via a Vectorised base is considered a security risk due to the abuse of probing multiple pages in rapid succession and getting feedback on which pages would fail.  Therefore in these special circumstances requesting ffirst eith a vector base is instead interpreted as element-strided LD/ST.  See <https://bugs.libre-soc.org/show_bug.cgi?id=561>

# 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 `(3-ew)<<8`

## 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

## Elwidth for CRs:

TODO, important, particularly for crops, mfcr and mtcr, what elwidth
even means.  instead it may be possible to use the bits as extra indices
(add to EXTRA2/3) to access the full 64 CRs at the bit level.  TBD, several ideas

The actual width of the CRs cannot be altered: they are 4 bit.  Also,
for Rc=1 operations that produce a result (in RT or FRT) and corresponding CR, it is
the INT/FP result to which the elwidth override applies, *not* the CR.
This therefore inherently places Rc=1 operations firmly out of scope as far as a "meaning" for elwidth on CRs is concerned.

As mentioned TBD, this leaves crops etc. to have a meaning defined for
elwidth, because these ops are pure explicit CR based.

Examples: mfxm may take the extra bits and use them as extra mask bits.

Example: hypothetically, operations could be modified to be considered 2-bit or 1-bit per CR.  This would need a very comprehensive review.

# 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 or r10) 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.

## 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).

Notes from Jacob: CR6-7 allows Scalar ops to refer to these without having to do a transfer (v3.0B).  Another idea: the DepMatrices treat scalar CRs as one "thing" and treat the Vectors as a completely separate "thing".

# Extra Remapped Encoding

Shows all instruction-specific fields in the Remapped Encoding `RM[8:18]` 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 OpenPOWER "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*).

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.  

* `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)   |
| reserved      | `18` | reserved                               |

## 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-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.

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.  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[2]: # vector
         return (RA << 2) | spec[0:1]
    else:         # scalar
         return (spec[0:1] << 5) | RA

## INT/FP EXTRA3

alternative which is understandable and, if EXTRA3 is zero, maps to
"no effect" (scalar OpenPOWER ISA field naming).  also, these are the
encodings used in the original SV Prefix scheme.  the reason why they
were chosen is so that scalar registers in v3.0B and prefixed scalar
registers have access to the same 32 registers.

| R\*\_EXTRA3 | Mode | Range | MSB downto LSB |
|-----------|-------|---------------|---------------------|
| 000       | Scalar | `r0-r31` | `0b00 RA`      |
| 001       | Scalar | `r32-r63` | `0b01 RA`      |
| 010       | Scalar | `r64-r95` | `0b10 RA`      |
| 011       | Scalar | `r96-r127` | `0b11 RA`      |
| 100       | Vector | `r0-r124` | `RA 0b00`      |
| 101       | Vector | `r1-r125` | `RA 0b01`      |
| 110       | Vector | `r2-r126` | `RA 0b10`      |
| 111       | Vector | `r3-r127` | `RA 0b11`      |

## INT/FP EXTRA2

alternative which is understandable and, if EXTRA2 is zero will map to
"no effect" i.e Scalar OpenPOWER register naming:

| R\*\_EXTRA2 | Mode | Range | MSB down to LSB |
|-----------|-------|---------------|---------------------|
| 00       | Scalar | `r0-r31` | `0b00 RA`                |
| 01       | Scalar | `r32-r63` | `0b01 RA`      |
| 10       | Vector | `r0-r124` | `RA 0b00`      |
| 11       | Vector | `r2-r126` | `RA 0b10`   |

## CR EXTRA3

CR encoding is essentially the same but made more complex due to CRs being bit-based.  See separate section for explanation and pseudocode.

 Encoding shown MSB down to LSB

| R\*\_EXTRA3 | Mode | 7..5    | 4..2    | 1..0    |
|-------------|------|---------| --------|---------|
| 000       | Scalar | 0b000   | BA[4:2] | BA[1:0] |
| 001       | Scalar | 0b001   | BA[4:2] | BA[1:0] |
| 010       | Scalar | 0b010   | BA[4:2] | BA[1:0] |
| 011       | Scalar | 0b011   | BA[4:2] | BA[1:0] |
| 100       | Vector | BA[4:2] | 0b000   | BA[1:0] |
| 101       | Vector | BA[4:2] | 0b010   | BA[1:0] |
| 110       | Vector | BA[4:2] | 0b100   | BA[1:0] |
| 111       | Vector | BA[4:2] | 0b110   | BA[1:0] |

## 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.

Encoding shown MSB down to LSB

| R\*\_EXTRA2 | Mode   | 7..5    | 4..2    | 1..0    |
|-------------|--------|---------|---------|---------|
| 00          | Scalar | 0b000   | BA[4:2] | BA[1:0] |
| 01          | Scalar | 0b001   | BA[4:2] | BA[1:0] |
| 10          | Vector | BA[4:2] | 0b000   | BA[1:0] |
| 11          | Vector | BA[4:2] | 0b100   | BA[1:0] |

# Appendix

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