(no commit message)

[libreriscv.git] / openpower / sv / svp64.mdwn

# SVP64 Zero-Overhead Loop Prefix Subsystem

* **DRAFT STATUS v0.1 18sep2021** Release notes <https://bugs.libre-soc.org/show_bug.cgi?id=699>

This document describes [[SV|sv]] augmentation of the [[Power|openpower]] v3.0B [[ISA|openpower/isa/]]. It is in Draft Status and
will be submitted to the [[!wikipedia OpenPOWER_Foundation]] ISA WG
via the External RFC Process.

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:

* <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.
* <https://bugs.libre-soc.org/show_bug.cgi?id=905> TODO [[sv/svp64-single]]
* <https://bugs.libre-soc.org/show_bug.cgi?id=1045> External RFC ls010
* [[sv/branches]] chapter
* [[sv/ldst]] chapter


Table of contents

[[!toc]]

## 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 naively viewed one-dimensionally as an
actual Vector ISA it introduces over 1.5 million 64-bit True-Scalable
Vector instructions on the SFFS Subset and closer to 10 million 64-bit
True-Scalable Vector instructions if introduced on VSX.  SVP64, the
instruction format used by Simple-V, 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 32-bit instructions
(Defined Words) 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 (*Note the intention to release that bit
and move Post-Increment instructions to EXT2xx, as part of [[ls011]]*).
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.  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.

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`.

UnVectorised instructions are required to be detected as such if
Prefixed (either SVP64 or SVP64Single) and an Illegal Instruction
Trap raised.

*Architectural Note: Given that a "pre-classification" Decode Phase is
required (identifying whether the Suffix - Defined Word - is
Arithmetic/Logical, CR-op, Load/Store or Branch-Conditional),
adding "UnVectorised" to this phase is not unreasonable.*

## Definition of Strict Program Order

Strict Program Order is defined as giving the appearance, as far
as programs are concerned, that instructions were executed
strictly in the sequence that they occurred.  A "Precise"
out-of-order
Micro-architecture goes to considerable lengths to ensure that
this is the case.

Many Vector ISAs allow interrupts to occur in the middle of
processing of large Vector operations, only under the condition
that partial results are cleanly discarded, and continuation on return
from the Trap Handler will restart the entire operation.
The reason is that saving of full Architectural State is
not practical.

Simple-V operates on an entirely different paradigm from traditional
Vector ISAs: as a Sub-Program Counter where "Elements" are synonymous
with Scalar instructions. With this in mind it is critical for
implementations to observe Strict Element-Level Program Order
at all times
(often simply referred to as just "Strict Program Order"
throughout
this Chapter).
*Any* element is Interruptible and Simple-V has
been carefully designed to guarantee that Architectural State may
be fully preserved and restored regardless of that same State, but
it is not necessarily guaranteed that the amount of time needed to recover
will be low latency (particularly if REMAP
is active).

Interrupts still only save `MSR` and `PC` in `SRR0` and `SRR1`
but the full SVP64 Architectural State may be saved and
restored through manual copying of `SVSTATE` (and the four
REMAP SPRs if in use at the time)
Whilst this initially sounds unsafe in reality
all that Trap Handlers (and function call stack save/restore)
need do is avoid
use of SVP64 Prefixed instructions to perform the necessary
save/restore of Simple-V Architectural State.
This capability also allows nested function calls to be made from
inside Vector loops, which is very rare for Vector ISAs.

Strict Program Order is also preserved by the Parallel Reduction
REMAP Schedule, but only at the cost of requiring the destination
Vector to be used (Deterministically) to store partial progress of the
Parallel Reduction.

The only major caveat for REMAP is that
after an explicit change to
Architectural State caused by writing to the
Simple-V SPRs, some implementations may find
it easier to take longer to calculate where in a given Schedule
the re-mapping Indices were.  Obvious examples include Interrupts occuring
in the middle of a non-RADIX2 Matrix Multiply Schedule (5x3 by 3x3
for example), which
will force implementations to perform divide and modulo
calculations.

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

The relationship between register files, elements, and element-width
overrides is expressed as follows:

* register files are considered to be *byte-level* contiguous SRAMs,
  accessed exclusively in Little-Endian  Byte-Order at all times
* elements are sequential contiguous unbounded arrays starting at the "address"
  of any given 64-bit GPR or FPR, numbered from 0 as the first,
  "spilling" into numerically-sequentially-increasing GPRs
* element-width overrides set the width of the *elements* in the
  sequentially-numbered contiguous array.

The relationship is best defined in Canonical form, below, in ANSI c as a
union data structure.  A key difference is that VSR elements are bounded
fixed at 128-bit, where SVP64 elements are conceptually unbounded and
only limited by the Maximum Vector Length.

*Future specification note: SVP64 may be defined on top of VSRs in future.
At which point VSX also gains conceptually unbounded VSR register elements*

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.

The only major impact on Arithmetic and Logical operations is that all
Scalar operations are defined, where practical and workable, to have
three new widths: elwidth=32, elwidth=16, elwidth=8.  The default of
elwidth=64 is the pre-existing (Scalar) behaviour which remains 100%
unchanged. Thus, `addi` is now joined by a 32-bit, 16-bit, and 8-bit
variant of `addi`, but the sole exclusive difference is the width.
*In no way* is the actual `addi` instruction fundamentally altered.
FP Operations elwidth overrides are also defined, as explained in
the [[svp64/appendix]].

To be absolutely clear:

```
    There are 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
```

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 needed to express the fact that
elements are LSB0-sequential 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.
Note the deliberate similarity to how VSX register elements are defined,
from Figure 97, Book I, Section 6.3, Page 258:

```
    #pragma pack
    typedef union {
        uint8_t actual_bytes[8];
        // all of these are very deliberately unbounded arrays
        // that intentionally "wrap" into subsequent actual_bytes...
        uint8_t  bytes[]; // elwidth 8
        uint16_t hwords[]; // elwidth 16
        uint32_t words[]; // elwidth 32
        uint64_t dwords[]; // elwidth 64

    } el_reg_t;

    // ... here, as packed statically-defined GPRs.
    elreg_t int_regfile[128];

    // use element 0 as the destination
    void get_register_element(el_reg_t* el, int gpr, int element, int width) {
        switch (width) {
            case 64: el->dwords[0] = int_regfile[gpr].dwords[element];
            case 32: el->words[0] = int_regfile[gpr].words[element];
            case 16: el->hwords[0] = int_regfile[gpr].hwords[element];
            case 8 : el->bytes[0] = int_regfile[gpr].bytes[element];
        }
    }

    // use element 0 as the source
    void set_register_element(el_reg_t* el, int gpr, int element, int width) {
        switch (width) {
            case 64: int_regfile[gpr].dwords[element] = el->dwords[0];
            case 32: int_regfile[gpr].words[element] = el->words[0];
            case 16: int_regfile[gpr].hwords[element] = el->hwords[0];
            case 8 : int_regfile[gpr].bytes[element] = el->bytes[0];
        }
    }
```

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

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

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

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

The most fundamental aspect here to understand is that the wrapping
into subsequent Scalar GPRs that occurs on larger-numbered elements
including and especially on smaller element widths is **deliberate
and intentional**.  From this Canonical definition it should be clear
that sequential elements begin at the LSB end of any given underlying
Scalar GPR, progress to the MSB end, and then to the LSB end of the
*next numerically-larger Scalar GPR*.  In the example above if VL=5
and RT=1 then the contents of GPR(1) and GPR(2) will be as follows.
For clarity in the table below:

* Both MSB0-ordered bitnumbering *and* LSB-ordered bitnumbering are shown
* The GPR-numbering is considered LSB0-ordered
* The Element-numbering (result0-result4) is LSB0-ordered
* Each of the results (result0-result4) are 16-bit
* "same" indicates "no change as a result of the Vectorised add"

```
    | MSB0:  | 0:15    | 16:31   | 32:47   | 48:63   |
    | LSB0:  | 63:48   | 47:32   | 31:16   | 15:0    |
    |--------|---------|---------|---------|---------|
    | GPR(0) | same    | same    | same    | same    |
    | GPR(1) | result3 | result2 | result1 | result0 |
    | GPR(2) | same    | same    | same    | result4 |
    | GPR(3) | same    | same    | same    | same    |
    | ...    | ...     | ...     | ...     | ...     |
    | ...    | ...     | ...     | ...     | ...     |
```

Note that the upper 48 bits of GPR(2) would **not** be modified due to
the example having VL=5.  Thus on "wrapping" - sequential progression
from GPR(1) into GPR(2) - the 5th result modifies **only** the bottom
16 LSBs of GPR(1).

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.  Overall it helps to think of the register files
as being much more akin to a byte-level-addressable SRAM.

If the 16-bit operation were to be followed up with a 32-bit Vectorised
Operation, the exact same contents would be viewed as follows:

```
    | MSB0:  | 0:31                 | 32:63                |
    | LSB0:  | 63:32                | 31:0                 |
    |--------|----------------------|----------------------|
    | GPR(0) | same                 | same                 |
    | GPR(1) | (result3 || result2) | (result1 || result0) |
    | GPR(2) | same                 | (same    || result4) |
    | GPR(3) | same                 | same                 |
    | ...    | ...                  | ...                  |
    | ...    | ...                  | ...                  |
```

In other words, this perspective really is no different from the situation
where the actual Register File is treated as an Industry-standard
byte-level-addressable Little-Endian-addressed SRAM.  Note that
this perspective does **not** involve `MSR.LE` in any way shape or
form because `MSR.LE` is directly in control of the Memory-to-Register
byte-ordering. This section is exclusively about how to correctly perceive
Simple-V-Augmented **Register** Files.

**Comparative equivalent using VSR registers**

For a comparative data point the VSR Registers may be expressed in the
same fashion. The c code below is directly an expression of Figure 97 in
Power ISA Public v3.1 Book I Section 6.3 page 258, *after compensating
for MSB0 numbering in both bits and elements, adapting in full to LSB0
numbering, and obeying LE ordering*.

**Crucial to understanding why the subtraction from 1,3,7,15 is present is
because the Power ISA numbers VSX Registers elements also in MSB0 order**.
SVP64 very specifically numbers elements in **LSB0** order with the first
element (numbered zero) being at the bitwise-numbered **LSB** end of the
register, where VSX does the reverse: places the numerically-*highest*
(last-numbered) element at the LSB end of the register.


```
    #pragma pack
    typedef union {
        // these do NOT match their Power ISA VSX numbering directly, they are all reversed
        // bytes[15] is actually VSR.byte[0] for example.  if this convention is not
        // followed then everything ends up in the wrong place
        uint8_t  bytes[16]; // elwidth 8, QTY 16 FIXED total
        uint16_t hwords[8]; // elwidth 16, QTY 8 FIXED total
        uint32_t words[4]; // elwidth 32, QTY 8 FIXED total
        uint64_t dwords[2]; // elwidth 64, QTY 2 FIXED total
        uint8_t actual_bytes[16]; // totals 128-bit
    } el_reg_t;

    elreg_t VSR_regfile[64];

    static void check_num_elements(int elt, int width) {
        switch (width) {
            case 64: assert elt < 2;
            case 32: assert elt < 4;
            case 16: assert elt < 8;
            case 8 : assert elt < 16;
        }
    }
    void get_VSR_element(el_reg_t* el, int gpr, int elt, int width) {
        check_num_elements(elt, width);
        switch (width) {
            case 64: el->dwords[0] = VSR_regfile[gpr].dwords[1-elt];
            case 32: el->words[0] = VSR_regfile[gpr].words[3-elt];
            case 16: el->hwords[0] = VSR_regfile[gpr].hwords[7-elt];
            case 8 : el->bytes[0] = VSR_regfile[gpr].bytes[15-elt];
        }
    }
    void set_VSR_element(el_reg_t* el, int gpr, int elt, int width) {
        check_num_elements(elt, width);
        switch (width) {
            case 64: VSR_regfile[gpr].dwords[1-elt] = el->dwords[0];
            case 32: VSR_regfile[gpr].words[3-elt] = el->words[0];
            case 16: VSR_regfile[gpr].hwords[7-elt] = el->hwords[0];
            case 8 : VSR_regfile[gpr].bytes[15-elt] = el->bytes[0];
        }
    }
```

For VSR Registers one key difference is that the overlay of different
element widths is clearly a *bounded static quantity*, whereas for
Simple-V the elements are unrestrained and permitted to flow into
*successive underlying Scalar registers*.  This difference is absolutely
critical to a full understanding of the entire Simple-V paradigm and
why element-ordering, bit-numbering *and register numbering* are all so
strictly defined.

Implementations are not permitted to violate the Canonical
definition. Software will be critically relying on the wrapped (overflow)
behaviour inherently implied by the unbounded variable-length c arrays.

Illustrating the exact same loop with the exact same effect as achieved
by Simple-V we are first forced to create wrapper functions, to cater
for the fact that VSR register elements are static bounded:

```
    int calc_VSR_reg_offs(int elt, int width) {
        switch (width) {
            case 64: return floor(elt / 2);
            case 32: return floor(elt / 4);
            case 16: return floor(elt / 8);
            case 8 : return floor(elt / 16);
        }
    }
    int calc_VSR_elt_offs(int elt, int width) {
        switch (width) {
            case 64: return (elt % 2);
            case 32: return (elt % 4);
            case 16: return (elt % 8);
            case 8 : return (elt % 16);
        }
    }
    void _set_VSR_element(el_reg_t* el, int gpr, int elt, int width) {
        int new_elt = calc_VSR_elt_offs(elt, width);
        int new_reg = calc_VSR_reg_offs(elt, width);
        set_VSR_element(el, gpr+new_reg, new_elt, width);
    }
```

And finally use these functions:

```
    # VSX-add RT, RA, RB using the "uint64_t" union member "hwords"
    for i in range(VL):
         el_reg_t result, ra, rb;
        _get_VSR_element(&ra, RA, i, 16);
        _get_VSR_element(&rb, RB, i, 16);
         result.hwords[0] = ra.hwords[0] + rb.hwords[0]; // use array 0 elements
        _set_VSR_element(&result, RT, i, 16);

```

## 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.

**Condition Register(s)**

The Scalar Power ISA Condition Register is a 64 bit register where
the top 32 MSBs (numbered 0:31 in MSB0 numbering) are not used.
This convention is *preserved* in SVP64 and an additional 15 Condition
Registers provided in order to store the new CR Fields, CR8-CR15,
CR16-CR23 etc. sequentially.  The top 32 MSBs in each new SVP64 Condition
Register are *also* not used: only the bottom 32 bits (numbered 32:63
in MSB0 numbering).

*Programmer's note: using `sv.mfcr` without element-width overrides
to take into account the fact that the top 32 MSBs are zero and thus
effectively doubling the number of GPR registers required to hold all 128
CR Fields would seem the only option because a source elwidth override
to 32-bit would take only the bottom 16 LSBs of the Condition Register
and set the top 16 LSBs to zeros.  However in this case it
is possible to use destination element-width overrides (for `sv.mfcr`.
source overrides would be used on the GPR of `sv.mtocrf`), whereupon
truncation of the 64-bit Condition Register(s) occurs, throwing away
the zeros and storing the remaining (valid, desired) 32-bit values
sequentially into (LSB0-convention) lower-numbered and upper-numbered
halves of GPRs respectively.  The programmer is expected to be aware
however that the full width of the entire 64-bit Condition Register
is considered to be "an element".  This is **not** like any other
Condition-Register instructions because all other CR instructions,
on closer investigation, will be observed to all be CR-bit or CR-Field
related. Thus a `VL` of 16 must be used*

**Condition Register Fields as Predicate Masks**

Condition Register Fields perform an additional duty in Simple-V: they are
used for Predicate Masks.  ARM's Scalar Instruction Set calls single-bit
predication "Conditional Execution", and utilises Condition Codes for
exactly this purpose to solve the problem caused by Branch Speculation.
In a Vector ISA context the concept of Predication is naturally extended
from single-bit to multi-bit, and the (well-known) benefits become all the
more critical given that parallel branches in Vector ISAs are impossible
(even a Vector ISA can only have Scalar branches).

However the Scalar Power ISA does not have Conditional Execution (for
which, if it had ever been considered, Condition Register bits would be
a perfect natural fit).  Thus, when adding Predication using CR Fields
via Simple-V it becomes a somewhat disruptive addition to the Power ISA.

To ameliorate this situation, particularly for pre-existing Hardware
designs implementing up to Scalar Power ISA v3.1, some rules are set that
allow those pre-existing designs not to require heavy modification to
their existing Scalar pipelines.  These rules effectively allow Hardware
Architects to add the additional CR Fields CR8 to CR127 as if they were
an **entirely separate register file**.

* any instruction involving more than 1 source 1 destination
  where one of the operands is a Condition Register is prohibited from
  using registers from both the CR0-7 group and the CR8-127 group at
  the same time.
* any instruction involving 1 source 1 destination where either the
  source or the destination is a Condition Register is prohibited
  from setting CR0-7 as a Vector.
* prohibitions are required to be enforced by raising Illegal Instruction
  Traps

Examples of permitted instructions:

```
    sv.crand *cr8.eq, *cr16.le, *cr40.so # all CR8-CR127
    sv.mfcr cr5, *cr40                   # only one source (CR40) copied to CR5
    sv.mfcr *cr16, cr40                  # Vector-Splat CR40 onto CR16,17,18...
    sv.mfcr *cr16, cr3                  # Vector-Splat CR3 onto CR16,17,18...
```

Examples of prohibited instructions:

```
    sv.mfcr *cr0, cr40        # Vector-Splat onto CR0,1,2
    sv.crand cr7, cr9, cr10   # crosses over between CR0-7 and CR8-127
```

## 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
in some way as long as the reputation of Power ISA for full backwards
binary interoperability is preserved. Backwards binary compatibility
may be achieved with a PCR bit (Program Compatibility Register) or an
MSR bit analogous to SF.  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 a future version of the Power ISA to 256-bit,
512-bit and 1024-bit operations, as well as doubling or quadrupling the
number of VSX registers to 128 or 256. Again further discussion is out
of scope for this version of SVP64.

--------

\newpage{}

## SVP64 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 EXT1xx 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 *length*
of anything in the 64-bit space has been kept brutally simple (EXT009),
and further decoding of any number of 64-bit Encodings in parallel at
that point is fully independent.

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".

`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 |

`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]].

**Please note the following**:

```
    Machine-readable CSV files have been autogenerated which will make the
    task of creating SV-aware ISA decoders, documentation, assembler tools
    compiler tools Simulators documentation all aspects of SVP64 easier
    and less prone to mistakes.  Please avoid manual re-creation of
    information from the written specification wording in this chapter,
    and use the CSV files or use the Canonical tool which creates the CSV
    files, named sv_analysis.py. The information contained within
    sv_analysis.py is considered to be part of this Specification, even
    encoded as it is in python3.
```


The 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.

| Field Name | Field bits | Description                 |
|------------|------------|----------------------------|
| Rsrc1_EXTRA3 | `10:12`    | extends Rsrc1             |
| Rsrc2_EXTRA3 | `13:15`    | extends Rsrc2             |
| MASK_SRC     | `16:18`    | Execution Mask for Source |

### 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     |

**RM-2P-1S2D:**

For RM-2P-1S2D dest2 is in bits 14:15

| Field Name | Field bits | Description                     |
|------------|------------|----------------------------|
| Rdest_EXTRA2 | `10:11`  | extends Rdest (R\*\_EXTRA2 Encoding)   |
| Rsrc1_EXTRA2 | `12:13`  | extends Rsrc1 (R\*\_EXTRA2 Encoding)   |
| Rdest2_EXTRA2 | `14:15`  | extends Rdest22 (R\*\_EXTRA2 Encoding)   |
| MASK_SRC     | `16:18`  | Execution Mask for Source     |

**RM-2P-3S:**

Also that for RM-2P-3S (to cover `stdx` etc.) the names are switched to 3 src:
Rsrc1_EXTRA2, Rsrc2_EXTRA2, Rsrc3_EXTRA2.

| Field Name | Field bits | Description                     |
|------------|------------|----------------------------|
| Rsrc1_EXTRA2 | `10:11`  | extends Rsrc1 (R\*\_EXTRA2 Encoding)   |
| Rsrc2_EXTRA2 | `12:13`  | extends Rsrc2 (R\*\_EXTRA2 Encoding)   |
| Rsrc3_EXTRA2 | `14:15`  | extends Rsrc3 (R\*\_EXTRA2 Encoding)   |
| MASK_SRC     | `16:18`  | Execution Mask for Source     |

Note also that LD with update indexed, which takes 2 src and
creates 2 dest registers (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 (GPR) is extended from r0-31 to r0-127
* FP (FPR) 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)

Encoding shown in LSB0: MSB down to LSB (MSB 6..0 LSB)

| 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:

Encoding shown in LSB0: MSB down to LSB (MSB 6..0 LSB)

| 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 in LSB0: MSB down to LSB (MSB 8..5 4..2 1..0 LSB),
BA ranges are in MSB0.

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.
Note that Vectors may only start from CR0, CR8, CR16, CR24, CR32...

Encoding shown in LSB0: MSB down to LSB (MSB 8..5 4..2 1..0 LSB),
BA ranges are in MSB0.

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   |

## Appendix

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

--------

[[!tag standards]]

\newpage{}