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# SVP64 Branch Conditional behaviour

**DRAFT STATUS**

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

Links

* <https://bugs.libre-soc.org/show_bug.cgi?id=664>
* <http://lists.libre-soc.org/pipermail/libre-soc-dev/2021-August/003416.html>
* [[openpower/isa/branch]]

# Rationale

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

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

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

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

# Overview

When considering an "array" of branch-tests, there are four useful modes:
AND, OR, NAND and NOR of all Conditions.
NAND and NOR may be synthesised from AND and OR by
inverting `BO[2]` which just leaves two modes:

* Branch takes place on the first CR Field test to succeed
  (a Great Big OR of all condition tests)
* Branch takes place only if **all** CR field tests succeed:
  a Great Big AND of all condition tests
  (including those where the predicate is masked out
   and the corresponding CR Field is considered to be
   set to `SNZ`)

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

*Note: Early-exit is **MANDATORY** (required) behaviour.
Branches **MUST** exit at the first failure point, for
exactly the same reasons for which it is mandatory in
programming languages doing early-exit: to avoid
damaging side-effects. Speculative testing of Condition
Register Fields is permitted, as is speculative updating
of CTR, as long as, as usual in any Out-of-Order microarchitecture,
that speculative testing is cancelled should an early-exit occur.*

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

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

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

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

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

# Format and fields

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

SVP64 RM `MODE` (includes `ELWIDTH` and `ELWIDTH_SRC` bits) for Branch
Conditional:

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

Brief description of fields:

* **sz=1** if predication is enabled and `sz=1` and a predicate
  element bit is zero, `SNZ` will
  be substituted in place of the CR bit selected by `BI`,
  as the Condition tested.
  Contrast this with
  normal SVP64 `sz=1` behaviour, where *only* a zero is put in
  place of masked-out predicate bits.
* **sz=0** When `sz=0` skipping occurs as usual on
  masked-out elements, but unlike all
  other SVP64 behaviour which entirely skips an element with
  no related side-effects at all, there are certain
  special circumstances where CTR
  may be decremented.  See CTR-test Mode, below.
* **ALL** when set, all branch conditional tests must pass in order for
  the branch to succeed. When clear, it is the first sequentially
  encountered successful test that causes the branch to succeed.
  This is identical behaviour to how programming languages perform
  early-exit on Boolean Logic chains.
* **VLI** VLSET is identical to Data-dependent Fail-First mode.
  In VLSET mode, VL is set equal (truncated) to the first point
  where, assuming Conditions are tested sequentially, the branch succeeds
  *or fails* depending if VSb is set.
  If VLI (Vector Length Inclusive) is clear,
  VL is truncated to *exclude* the current element, otherwise it is
  included. SVSTATE.MVL is not changed: only VL.
* **LRu**: Link Register Update. When set, Link Register will
  only be updated if the Branch Condition succeeds. This avoids
  destruction of LR during loops (particularly Vertical-First
  ones).
* **VSb** is most relevant for Vertical-First VLSET Mode. After testing,
  if VSb is set, VL is truncated if the branch succeeds.  If VSb is clear,
  VL is truncated if the branch did **not** take place.
* **CTi** CTR inversion. CTR-test Mode normally decrements per element
  tested. CTR inversion decrements if a test *fails*. Only relevant
  in CTR-test Mode.

# Vectorised CR Field numbering, and Scalar behaviour

It is important to keep in mind that just like all SVP64 instructions,
the `BI` field of the base v3.0B Branch Conditional instruction
may be extended by SVP64 EXTRA augmentation, as well as be marked
as either Scalar or Vector.

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

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

In other words, the fact that this is a Branch
Operation (instead of an arithmetic one) does not result, ultimately,
in significant changes as to
how SVP64 is fundamentally applied, except with respect to 
the unique properties associated with conditionally
 changing the Program
Counter (aka "a Branch"), resulting in early-out
opportunities and CTR-testing, which are outlined below.

# Horizontal-First and Vertical-First Modes

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

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

# Description and Modes

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

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

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

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

If both CTR-test and VLSET Modes are requested, then because the CTR decrement is on a per element basis, the total amount that CTR is decremented
by will end up being VL *after* truncation (should that occur). In
other words, the order is strictly (as can be seen in pseudocode, below):

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

CTR-test mode and CTi interaction is as follows: note that
`BO[2]` is still required to be clear for decrements to be
considered.

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

`CTR-test=0, CTi=1, sz=0` requires special emphasis because it is the
only time in the entirety of SVP64 that has side-effects when
a predicate mask bit is clear.  **All** other SVP64 operations
entirely skip an element when sz=0 and a predicate mask bit is zero.

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

Also, the unconditional bit `BO[0]` is still relevant when Predication
is applied to the Branch because in `ALL` mode all nonmasked bits have
to be tested. Even when VLSET mode is not used, CTR
may still be decremented by the total number of nonmasked elements.
In short, Vectorised Branch becomes an extremely powerful tool.

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

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

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

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

# Boolean Logic combinations

There are an extraordinary number of different combinations which
provide completely different and useful behaviour.
Available options to combine:

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

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

# Pseudocode and examples

Pseudocode for Horizontal-First Mode:

```
cond_ok = not SVRMmode.ALL
for srcstep in range(VL):
    # select predicate bit or zero/one
    if predicate[srcstep]:
        # get SVP64 extended CR field 0..127
        SVCRf = SVP64EXTRA(BI>>2)
        CRbits = CR{SVCRf}
        testbit = CRbits[BI & 0b11]
        # testbit = CR[BI+32+srcstep*4]
    else if not SVRMmode.sz:
      # inverted CTR test skip mode
      if ¬BO[2] & CTRtest & ¬CTI then
         CTR = CTR - 1
        continue
    else
        testbit = SVRMmode.SNZ
    # actual element test here
    el_cond_ok <- BO[0] | ¬(testbit ^ BO[1])
    # merge in the test
    if SVRMmode.ALL:
        cond_ok &= el_cond_ok
    else
        cond_ok |= el_cond_ok
    # test for VL to be set (and exit)
    if VLSET and VSb = el_cond_ok then
        if SVRMmode.VLI
            SVSTATE.VL = srcstep+1
        else
            SVSTATE.VL = srcstep
        break
    # early exit?
    if SVRMmode.ALL:
        if ~el_cond_ok:
            break
    else
        if el_cond_ok:
            break
    if SVCRf.scalar:
       break
```

Pseudocode for Vertical-First Mode:

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

v3.0B branch pseudocode including LRu and CTR skipping

```
if (mode_is_64bit) then M <- 0
else M <- 32
cond_ok <- BO[0] | ¬(CR[BI+32] ^ BO[1])
ctrdec = ¬BO[2]
if CTRtest & (cond_ok ^ CTi) then
   ctrdec = 0b0
if ctrdec then CTR <- CTR - 1
ctr_ok <- BO[2] | ((CTR[M:63] != 0) ^ BO[3])
lr_ok <- SVRMmode.LRu
if ctr_ok & cond_ok then
  if AA then NIA <-iea EXTS(BD || 0b00)
  else       NIA <-iea CIA + EXTS(BD || 0b00)
  lr_ok <- 0b1
if LK & lr_ok then LR <-iea CIA + 4
```

# Example Shader code

```
while(a > 2) {
    if(b < 5)
        f();
    else
        g();
    h();
}
```

which compiles to something like:

```
vec<i32> a, b;
// ...
pred loop_pred = a > 2;
while(loop_pred.any()) {
    pred if_pred = loop_pred & (b < 5);
    if(if_pred.any()) {
        f(if_pred);
    }
label1:
    pred else_pred = loop_pred & ~if_pred;
    if(else_pred.any()) {
        g(else_pred);
    }
    h(loop_pred);
}
```

which will end up as:

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