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# Normal SVP64 Modes, for Arithmetic and Logical Operations

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

## Mode

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

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

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

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

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

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

Fields:

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

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

## Rounding, clamp and saturate

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

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

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

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

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

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

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

## Reduce mode

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

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

## Data-dependent Fail-on-first

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

Data-driven (CR-driven) fail-on-first activates when Rc=1 or other
CR-creating operation produces a result (including cmp).  Similar to
branch, an analysis of the CR is performed and if the test fails, the
vector operation terminates and discards all element operations **at and
above the current one**, and VL is truncated to either the *previous*
element or the current one, depending on whether VLi (VL "inclusive")
is clear or set, respectively.

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

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

The CR-based data-driven fail-on-first is "new" and not found in ARM SVE
or RVV. At the same time it is "old" because it is almost identical to
a generalised form of Z80's `CPIR` instruction.  It is extremely useful
for reducing instruction count, however requires speculative execution
involving modifications of VL to get high performance implementations.
An additional mode (RC1=1) effectively turns what would otherwise be an
arithmetic operation into a type of `cmp`.  The CR is stored (and the
CR.eq bit tested against the `inv` field).  If the CR.eq bit is equal to
`inv` then the Vector is truncated and the loop ends.

VLi is only available as an option when `Rc=0` (or for instructions
which do not have Rc). When set, the current element is always also
included in the count (the new length that VL will be set to).  This may
be useful in combination with "inv" to truncate the Vector to *exclude*
elements that fail a test, or, in the case of implementations of strncpy,
to include the terminating zero.

In CR-based data-driven fail-on-first there is only the option to select
and test one bit of each CR (just as with branch BO).  For more complex
tests this may be insufficient.  If that is the case, a vectorised crop
such as crand, cror or [[sv/cr_int_predication]] crweirder may be used,
and ffirst applied to the crop instead of to the arithmetic vector. Note
that crops are covered by the [[sv/cr_ops]] Mode format.

Use of Fail-on-first with Vertical-First Mode is not prohibited but is
not really recommended.  The effect of truncating VL
may have unintended and unexpected consequences on subsequent instructions.
VLi set will be fine: it is when VLi is clear that problems may be faced.

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

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

Two extremely important aspects of ffirst are:

* LDST ffirst may never set VL equal to zero.  This because on the first
  element an exception must be raised "as normal".
* CR-based data-dependent ffirst on the other hand **can** set VL equal
  to zero. This is the only means in the entirety of SV that VL may be set
  to zero (with the exception of via the SV.STATE SPR).  When VL is set
  zero due to the first element failing the CR bit-test, all subsequent
  vectorised operations are effectively `nops` which is
  *precisely the desired and intended behaviour*.

The second crucial aspect, compared to LDST Ffirst:

* LD/ST Failfirst may (beyond the initial first element
  conditions) truncate VL for any architecturally suitable reason. Beyond
  the first element LD/ST Failfirst is arbitrarily speculative and 100%
  non-deterministic.
* CR-based data-dependent first on the other hand MUST NOT truncate VL
  arbitrarily to a length decided by the hardware: VL MUST only be
  truncated based explicitly on whether a test fails.  This because it is
  a precise Deterministic test on which algorithms can and will will rely.

**Floating-point Exceptions**

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

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

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

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

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

## pred-result mode

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

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

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

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

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

--------

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[[!tag opf_rfc]]