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

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[1] 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

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. Truncation of VL takes place around the early-exit point.
  • 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.

Predicate skipping or zeroing may, as usual with SVP64, be controlled by sz. Where the predicate is masked out and zeroing is enabled, then in such circumstances the same Boolean Logic Analysis dictates that rather than testing only against zero, the option to test against one is also prudent. This introduces a new immediate field, SNZ, which works in conjunction with sz.

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.

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

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 SNZ / / 0 0 / LRu sz normal mode
ALL SNZ / VSb 0 1 VLI LRu sz VLSET mode
ALL SNZ CTi / 1 0 / LRu sz CTR-test mode
ALL SNZ CTi VSb 1 1 VLI LRu 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 may (depending on VSb) be truncated. If VLI (Vector Length Inclusive) is clear, VL is truncated to exclude the current element, otherwise it is included. SVSTATE.MVL is not altered: 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 In 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 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
  • CTR-testing

Both 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.

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, and when sz=0 skipping occurs. Even when VLSET mode is not used, CTR may still be decremented by the total number of nonmasked elements, acting in effect as either a popcount or cntlz depending on which mode bits are set. In short, Vectorised Branch becomes an extremely powerful tool.

CTR-test

Where a standard Scalar v3.0B branch unconditionally decrements CTR when BO[2] is clear, CTR-test Mode introduces more flexibility which allows CTR to be used for many more types of Vector loops constructs.

CTR-test mode and CTi interaction is as follows: note that BO[2] is still required to be clear for CTR decrements to be considered, exactly as is the case in Scalar Power ISA v3.0B

  • 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 and sz=0).
  • 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. It is also critical to emphasise that in this unusual mode, no other side-effects occur: only CTR is decremented, i.e. the rest of the Branch operation iss skipped.

VLSET Mode

VLSET Mode truncates the Vector Length so that subsequent instructions operate on a reduced Vector Length. This is similar to Data-dependent Fail-First and LD/ST Fail-First, where for VLSET the truncation occurs at the Branch decision-point.

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.

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.

In the case of a Vertical-First branch-back (loop), with VSb=0 the branch takes place if success conditions are met, but on exit from that loop (branch condition fails), VL will be truncated. This is extremely useful.

VLSET mode with Horizontal-First when VSb=0 is still useful, because it can be used to truncate VL to the first predicated (non-masked-out) element.

The truncation point for VL, when VLi is clear, must not include skipped elements that preceded the current element being tested. Example: sz=0, VLi=0, predicate mask = 0b110010 and the Condition failure point is at element 4.

  • Testing at element 0 is skipped because its predicate bit is zero
  • Testing at element 1 passed
  • Testing elements 2 and 3 are skipped because their respective predicate mask bits are zero
  • Testing element 4 fails therefore VL is truncated to 2 not 4 due to elements 2 and 3 being skipped.

If sz=1 in the above example then VL would have been set to 4 because in non-zeroing mode the zero'd elements are still effectively part of the Vector (with their respective elements set to SNZ)

If VLI=1 then VL would be set to 5 regardless of sz, due to being inclusive of the element actually being tested.

VLSET and CTR-test combined

If both CTR-test and VLSET Modes are requested, it's important to observe the correct order. What occurs depends on whether VLi is enabled, because VLi affects the length, VL.

If VLi (VL truncate inclusive) is set:

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

If VLi is clear, then when a test fails that element and any following it should not be considered part of the Vector. Consequently:

  1. compute the branch test including whether CTR triggers
  2. if the test fails against VSb, truncate VL to the previous element, and terminate looping. No further steps executed.
  3. (optionally) decrement CTR
  4. decide whether to branch.

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