Appendix

This is the appendix to svp64, providing explanations of modes etc. leaving the main svp64 page's primary purpose as outlining the instruction format.

Table of contents:

  1. Appendix

Partial Implementations

It is perfectly legal to implement subsets of SVP64 as long as illegal instruction traps are always raised on unimplemented features, so that soft-emulation is possible, even for future revisions of SVP64. With SVP64 being partly controlled through contextual SPRs, a little care has to be taken.

All SPRs not implemented including reserved ones for future use must raise an illegal instruction trap if read or written. This allows software the opportunity to emulate the context created by the given SPR.

See compliancy levels for full details.

XER, SO and other global flags

Vector systems are expected to be high performance. This is achieved through parallelism, which requires that elements in the vector be independent. XER SO/OV and other global "accumulation" flags (CR.SO) cause Read-Write Hazards on single-bit global resources, having a significant detrimental effect.

Consequently in SV, XER.SO behaviour is disregarded (including in cmp instructions). XER.SO is not read, but XER.OV may be written, breaking the Read-Modify-Write Hazard Chain that complicates microarchitectural implementations. This includes when scalar identity behaviour occurs. If precise OpenPOWER v3.0/1 scalar behaviour is desired then OpenPOWER v3.0/1 instructions should be used without an SV Prefix.

TODO jacob add about OV https://www.intel.com/content/dam/www/public/us/en/documents/white-papers/ia-large-integer-arithmetic-paper.pdf

Of note here is that XER.SO and OV may already be disregarded in the Power ISA v3.0/1 SFFS (Scalar Fixed and Floating) Compliancy Subset. SVP64 simply makes it mandatory to disregard XER.SO even for other Subsets, but only for SVP64 Prefixed Operations.

XER.CA/CA32 on the other hand is expected and required to be implemented according to standard Power ISA Scalar behaviour. Interestingly, due to SVP64 being in effect a hardware for-loop around Scalar instructions executing in precise Program Order, a little thought shows that a Vectorized Carry-In-Out add is in effect a Big Integer Add, taking a single bit Carry In and producing, at the end, a single bit Carry out. High performance implementations may exploit this observation to deploy efficient Parallel Carry Lookahead.

    # assume VL=4, this results in 4 sequential ops (below)
    sv.adde r0.v, r4.v, r8.v

    # instructions that get executed in backend hardware:
    adde r0, r4, r8 # takes carry-in, produces carry-out
    adde r1, r5, r9 # takes carry from previous
    ...
    adde r3, r7, r11 # likewise

It can clearly be seen that the carry chains from one 64 bit add to the next, the end result being that a 256-bit "Big Integer Add with Carry" has been performed, and that CA contains the 257th bit. A one-instruction 512-bit Add-with-Carry may be performed by setting VL=8, and a one-instruction 1024-bit Add-with-Carry by setting VL=16, and so on. More on this in biginteger

EXTRA Field Mapping

The purpose of the 9-bit EXTRA field mapping is to mark individual registers (RT, RA, BFA) as either scalar or vector, and to extend their numbering from 0..31 in Power ISA v3.0 to 0..127 in SVP64. Three of the 9 bits may also be used up for a 2nd Predicate (Twin Predication) leaving a mere 6 bits for qualifying registers. As can be seen there is significant pressure on these (and in fact all) SVP64 bits.

In Power ISA v3.1 prefixing there are bits which describe and classify the prefix in a fashion that is independent of the suffix. MLSS for example. For SVP64 there is insufficient space to make the SVP64 Prefix "self-describing", and consequently every single Scalar instruction had to be individually analysed, by rote, to craft an EXTRA Field Mapping. This process was semi-automated and is described in this section. The final results, which are part of the SVP64 Specification, are here: opcode regs deduped

  • Firstly, every instruction's mnemonic (add RT, RA, RB) was analysed from reading the markdown formatted version of the Scalar pseudocode which is machine-readable and found in isatables. The analysis gives, by instruction, a "Register Profile". add RT, RA, RB for example is given a designation RM-2R-1W because it requires two GPR reads and one GPR write.
  • Secondly, the total number of registers was added up (2R-1W is 3 registers) and if less than or equal to three then that instruction could be given an EXTRA3 designation. Four or more is given an EXTRA2 designation because there are only 9 bits available.
  • Thirdly, the instruction was analysed to see if Twin or Single Predication was suitable. As a general rule this was if there was only a single operand and a single result (extw and LD/ST) however it was found that some 2 or 3 operand instructions also qualify. Given that 3 of the 9 bits of EXTRA had to be sacrificed for use in Twin Predication, some compromises were made, here. LDST is Twin but also has 3 operands in some operations, so only EXTRA2 can be used.
  • Fourthly, a packing format was decided: for 2R-1W an EXTRA3 indexing could have been decided that RA would be indexed 0 (EXTRA bits 0-2), RB indexed 1 (EXTRA bits 3-5) and RT indexed 2 (EXTRA bits 6-8). In some cases (LD/ST with update) RA-as-a-source is given a different EXTRA index from RA-as-a-result (because it is possible to do, and perceived to be useful). Rc=1 co-results (CR0, CR1) are always given the same EXTRA index as their main result (RT, FRT).
  • Fifthly, in an automated process the results of the analysis were outputted in CSV Format for use in machine-readable form by sv_analysis.py https://git.libre-soc.org/?p=openpower-isa.git;a=blob;f=src/openpower/sv/sv_analysis.py;hb=HEAD

This process was laborious but logical, and, crucially, once a decision is made (and ratified) cannot be reversed. Qualifying future Power ISA Scalar instructions for SVP64 is strongly advised to utilise this same process and the same sv_analysis.py program as a canonical method of maintaining the relationships. Alterations to that same program which change the Designation is prohibited once finalised (ratified through the Power ISA WG Process). It would be similar to deciding that add should be changed from X-Form to D-Form.

Single Predication

This is a standard mode normally found in Vector ISAs. every element in every source Vector and in the destination uses the same bit of one single predicate mask.

In SVSTATE, for Single-predication, implementors MUST increment both srcstep and dststep, but depending on whether sz and/or dz are set, srcstep and dststep can still potentially become different indices. Only when sz=dz is srcstep guaranteed to equal dststep at all times.

Note that in some Mode Formats there is only one flag (zz). This indicates that both sz and dz are set to the same.

Example 1:

  • VL=4
  • mask=0b1101
  • sz=0, dz=1

The following schedule for srcstep and dststep will occur:

srcstep dststep comment
0 0 both mask[src=0] and mask[dst=0] are 1
1 2 sz=1 but dz=0: dst skips mask[1], src soes not
2 3 mask[src=2] and mask[dst=3] are 1
3 end loop has ended because dst reached VL-1

Example 2:

  • VL=4
  • mask=0b1101
  • sz=1, dz=0

The following schedule for srcstep and dststep will occur:

srcstep dststep comment
0 0 both mask[src=0] and mask[dst=0] are 1
2 1 sz=0 but dz=1: src skips mask[1], dst does not
3 2 mask[src=3] and mask[dst=2] are 1
end 3 loop has ended because src reached VL-1

In both these examples it is crucial to note that despite there being a single predicate mask, with sz and dz being different, srcstep and dststep are being requested to react differently.

Example 3:

  • VL=4
  • mask=0b1101
  • sz=0, dz=0

The following schedule for srcstep and dststep will occur:

srcstep dststep comment
0 0 both mask[src=0] and mask[dst=0] are 1
2 2 sz=0 and dz=0: both src and dst skip mask[1]
3 3 mask[src=3] and mask[dst=3] are 1
end end loop has ended because src and dst reached VL-1

Here, both srcstep and dststep remain in lockstep because sz=dz=0

Twin Predication

This is a novel concept that allows predication to be applied to a single source and a single dest register. The following types of traditional Vector operations may be encoded with it, without requiring explicit opcodes to do so

Those patterns (and more) may be applied to:

  • mv (the usual way that V* ISA operations are created)
  • exts* sign-extension
  • rwlinm and other RS-RA shift operations (note: excluding those that take RA as both a src and dest. These are not 1-src 1-dest, they are 2-src, 1-dest)
  • LD and ST (treating AGEN as one source)
  • FP fclass, fsgn, fneg, fabs, fcvt, frecip, fsqrt etc.
  • Condition Register ops mfcr, mtcr and other similar

This is a huge list that creates extremely powerful combinations, particularly given that one of the predicate options is (1<<r3)

Additional unusual capabilities of Twin Predication include a back-to-back version of VCOMPRESS-VEXPAND which is effectively the ability to do sequentially ordered multiple VINSERTs. The source predicate selects a sequentially ordered subset of elements to be inserted; the destination predicate specifies the sequentially ordered recipient locations. This is equivalent to llvm.masked.compressstore.* followed by llvm.masked.expandload.* with a single instruction, but abstracted out from Load/Store and applicable in general to any 2P instruction.

This extreme power and flexibility comes down to the fact that SVP64 is not actually a Vector ISA: it is a loop-abstraction-concept that is applied in general to Scalar operations, just like the x86 REP instruction (if put on steroids).

Pack/Unpack

The pack/unpack concept of VSX vpack is abstracted out as Sub-Vector reordering. Two bits in the SVSHAPE ?spr enable either "packing" or "unpacking" on the subvectors vec2/3/4.

First, illustrating a "normal" SVP64 operation with SUBVL!=1: (assuming no elwidth overrides), note that the VL loop is outer and the SUBVL loop inner:

    def index():
        for i in range(VL):
            for j in range(SUBVL):
                yield i*SUBVL+j

    for idx in index():
        operation_on(RA+idx)

For pack/unpack (again, no elwidth overrides), note that now there is the option to swap the SUBVL and VL loop orders. In effect the Pack/Unpack performs a Transpose of the subvector elements. Illustrated this time with a GPR mv operation:

    # yield an outer-SUBVL or inner VL loop with SUBVL
    def index_p(outer):
        if outer:
            for j in range(SUBVL):   # subvl is outer
                for i in range(VL):  # vl is inner
                    yield i+VL*j
        else:
            for i in range(VL):        # vl is outer
                for j in range(SUBVL): # subvl is inner
                    yield i*SUBVL+j

     # walk through both source and dest indices simultaneously
     for src_idx, dst_idx in zip(index_p(PACK), index_p(UNPACK)):
         move_operation(RT+dst_idx, RA+src_idx)

"yield" from python is used here for simplicity and clarity. The two Finite State Machines for the generation of the source and destination element offsets progress incrementally in lock-step.

Example VL=2, SUBVL=3, PACK_en=1 - elements grouped by vec3 will be redistributed such that Sub-elements 0 are packed together, Sub-elements 1 are packed together, as are Sub-elements 2.

     srcstep=0   srcstep=1
     0   1   2   3   4   5

     dststep=0  dststep=1  dststep=2
     0   3      1   4      2   5

Setting of both PACK and UNPACK is neither prohibited nor UNDEFINED because the reordering is fully deterministic, and additional REMAP reordering may be applied. Combined with Matrix REMAP this would give potentially up to 4 Dimensions of reordering.

Pack/Unpack has quirky interactions on mv.swizzle because it can set a different subvector length for destination, and has a slightly different pseudocode algorithm for Vertical-First Mode.

Ordering is as follows:

  • SVSHAPE srcstep, dststep, ssubstep and dsubstep are advanced sequentially depending on PACK/UNPACK.
  • srcstep and dststep are pushed through REMAP to compute actual Element offsets.
  • Swizzle is independently applied to ssubstep and dsubstep

Pack/Unpack is enabled (set up) through svstep.

Reduce modes

Reduction in SVP64 is deterministic and somewhat of a misnomer. A normal Vector ISA would have explicit Reduce opcodes with defined characteristics per operation: in SX Aurora there is even an additional scalar argument containing the initial reduction value, and the default is either 0 or 1 depending on the specifics of the explicit opcode. SVP64 fundamentally has to utilise existing Scalar Power ISA v3.0B operations, which presents some unique challenges.

The solution turns out to be to simply define reduction as permitting deterministic element-based schedules to be issued using the base Scalar operations, and to rely on the underlying microarchitecture to resolve Register Hazards at the element level. This goes back to the fundamental principle that SV is nothing more than a Sub-Program-Counter sitting between Decode and Issue phases.

For Scalar Reduction, Microarchitectures may take opportunities to parallelise the reduction but only if in doing so they preserve strict Program Order at the Element Level. Opportunities where this is possible include an OR operation or a MIN/MAX operation: it may be possible to parallelise the reduction, but for Floating Point it is not permitted due to different results being obtained if the reduction is not executed in strict Program-Sequential Order.

In essence it becomes the programmer's responsibility to leverage the pre-determined schedules to desired effect.

Scalar result reduction and iteration

Scalar Reduction per se does not exist, instead is implemented in SVP64 as a simple and natural relaxation of the usual restriction on the Vector Looping which would terminate if the destination was marked as a Scalar. Scalar Reduction by contrast keeps issuing Vector Element Operations even though the destination register is marked as scalar and the same register is used as a source register. Thus it is up to the programmer to be aware of this, observe some conventions, and thus end up achieving the desired outcome of scalar reduction.

It is also important to appreciate that there is no actual imposition or restriction on how this mode is utilised: there will therefore be several valuable uses (including Vector Iteration and "Reverse-Gear") and it is up to the programmer to make best use of the (strictly deterministic) capability provided.

In this mode, which is suited to operations involving carry or overflow, one register must be assigned, by convention by the programmer to be the "accumulator". Scalar reduction is thus categorised by:

  • One of the sources is a Vector
  • the destination is a scalar
  • optionally but most usefully when one source scalar register is also the scalar destination (which may be informally termed by convention the "accumulator")
  • That the source register type is the same as the destination register type identified as the "accumulator". Scalar reduction on cmp, setb or isel makes no sense for example because of the mixture between CRs and GPRs.

Note that issuing instructions in Scalar reduce mode such as setb are neither UNDEFINED nor prohibited, despite them not making much sense at first glance. Scalar reduce is strictly defined behaviour, and the cost in hardware terms of prohibition of seemingly non-sensical operations is too great. Therefore it is permitted and required to be executed successfully. Implementors MAY choose to optimise such instructions in instances where their use results in "extraneous execution", i.e. where it is clear that the sequence of operations, comprising multiple overwrites to a scalar destination without cumulative, iterative, or reductive behaviour (no "accumulator"), may discard all but the last element operation. Identification of such is trivial to do for setb and cmp: the source register type is a completely different register file from the destination. Likewise Scalar reduction when the destination is a Vector is as if the Reduction Mode was not requested. However it would clearly be unacceptable to perform such optimisations on cache-inhibited LD/ST, so some considerable care needs to be taken.

Typical applications include simple operations such as ADD r3, r10.v, r3 where, clearly, r3 is being used to accumulate the addition of all elements of the vector starting at r10.

     # add RT, RA,RB but when RT==RA
     for i in range(VL):
          iregs[RA] += iregs[RB+i] # RT==RA

However, unless the operation is marked as "mapreduce" (sv.add/mr) SV ordinarily terminates at the first scalar operation. Only by marking the operation as "mapreduce" will it continue to issue multiple sub-looped (element) instructions in Program Order.

To perform the loop in reverse order, the RG (reverse gear) bit must be set. This may be useful in situations where the results may be different (floating-point) if executed in a different order. Given that there is no actual prohibition on Reduce Mode being applied when the destination is a Vector, the "Reverse Gear" bit turns out to be a way to apply Iterative or Cumulative Vector operations in reverse. sv.add/rg r3.v, r4.v, r4.v for example will start at the opposite end of the Vector and push a cumulative series of overlapping add operations into the Execution units of the underlying hardware.

Other examples include shift-mask operations where a Vector of inserts into a single destination register is required (see bitmanip, bmset), as a way to construct a value quickly from multiple arbitrary bit-ranges and bit-offsets. Using the same register as both the source and destination, with Vectors of different offsets masks and values to be inserted has multiple applications including Video, cryptography and JIT compilation.

    # assume VL=4:
    # * Vector of shift-offsets contained in RC (r12.v)
    # * Vector of masks contained in RB (r8.v)
    # * Vector of values to be masked-in in RA (r4.v)
    # * Scalar destination RT (r0) to receive all mask-offset values
    sv.bmset/mr r0, r4.v, r8.v, r12.v

Due to the Deterministic Scheduling, Subtract and Divide are still permitted to be executed in this mode, although from an algorithmic perspective it is strongly discouraged. It would be better to use addition followed by one final subtract, or in the case of divide, to get better accuracy, to perform a multiply cascade followed by a final divide.

Note that single-operand or three-operand scalar-dest reduce is perfectly well permitted: the programmer may still declare one register, used as both a Vector source and Scalar destination, to be utilised as the "accumulator". In the case of sv.fmadds and sv.maddhw etc this naturally fits well with the normal expected usage of these operations.

If an interrupt or exception occurs in the middle of the scalar mapreduce, the scalar destination register MUST be updated with the current (intermediate) result, because this is how Program Order is preserved (Vector Loops are to be considered to be just another way of issuing instructions in Program Order). In this way, after return from interrupt, the scalar mapreduce may continue where it left off. This provides "precise" exception behaviour.

Note that hardware is perfectly permitted to perform multi-issue parallel optimisation of the scalar reduce operation: it's just that as far as the user is concerned, all exceptions and interrupts MUST be precise.

Fail-on-first

Data-dependent fail-on-first has two distinct variants: one for LD/ST (see ldst, the other for arithmetic operations (actually, CR-driven) normal and CR operations cr ops. Note in each case the assumption is that vector elements are required appear to be executed in sequential Program Order, element 0 being the first.

  • LD/ST ffirst (not to be confused with Data-Dependent LD/ST ffirst) treats the first LD/ST in a vector (element 0) as an ordinary one. Exceptions occur "as normal" on the first element. However for elements 1 and above, if an exception would occur, then VL is truncated to the previous element.
  • 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 above the current one (and the current one if VLi is not set), and VL is truncated to either the previous element or the current one, depending on whether VLi (VL "inclusive") is set.

Thus the new VL comprises a contiguous vector of results, all of which pass the testing criteria (equal to zero, less than zero). Demonstrated approximately in pseudocode, where the normal Vector-looping is just:

for i in range(VL):
   GPR[RT+i], CR[i] = operation(GPR[RA+i]... )

Data-depedendent Fail-First is, in principle, the sequentially-ordered "early-termination" of looping, which is near-identical to the Z80 LDIR and CPIR instructions, but generalised:

for i in range(VL):
   GPR[RT+i], CR[i] = operation(GPR[RA+i]... )
   if test(CR[i]) == failure:
      VL = i+VLi
      break

The CR-based data-driven fail-on-first is new and not found in ARM SVE or RVV. At the same time it is also "old" because it is a generalisation of the Z80 Block compare instructions, especially CPIR which is based on CP (compare) as the ultimate "element" (suffix) operation to which the repeat (prefix) is applied. 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. Note that when RC1=1 the result elements are never stored, only the CRs.

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 vectorized crops (crand, cror) may be used, and ffirst applied to the crop instead of to the arithmetic vector.

One extremely important aspect of ffirst is:

  • 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 vectorized operations are effectively nops which is precisely the desired and intended behaviour.

Another aspect is that for ffirst LD/STs, VL may be truncated arbitrarily to a nonzero value for any implementation-specific reason. For example: it is perfectly reasonable for implementations to alter VL when ffirst LD or ST operations are initiated on a nonaligned boundary, such that within a loop the subsequent iteration of that loop begins subsequent ffirst LD/ST operations on an aligned boundary. Likewise, to reduce workloads or balance resources.

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 test on which algorithms will rely.

Note: there is no reverse-direction for Data-dependent Fail-First. REMAP will need to be activated to invert the ordering of element traversal.

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

Operations that actually produce or alter CR Field as a result do not also in turn have an Rc=1 mode. However it makes no sense to try to test the 4 bits of a CR Field for being equal or not equal to zero. Moreover, the result is already in the form that is desired: it is a CR field. Therefore, CR-based operations have their own SVP64 Mode, described in cr ops

There are two primary different types of CR operations:

  • Those which have a 3-bit operand field (referring to a CR Field)
  • Those which have a 5-bit operand (referring to a bit within the whole 32-bit CR)

More details can be found in cr ops.

CR Operations

CRs are slightly more involved than INT or FP registers due to the possibility for indexing individual bits (crops BA/BB/BT). Again however the access pattern needs to be understandable in relation to v3.0B / v3.1B numbering, with a clear linear relationship and mapping existing when SV is applied.

CR EXTRA mapping table and algorithm

Numbering relationships for CR fields are already complex due to being in BE format (the relationship is not clearly explained in the v3.0B or v3.1 specification). However with some care and consideration the exact same mapping used for INT and FP regfiles may be applied, just to the upper bits, as explained below. Firstly and most importantly a new notation CR{field number} is used to indicate access to a particular Condition Register Field (as opposed to the notation CR[bit] which accesses one bit of the 32 bit Power ISA v3.0B Condition Register).

CR{n} refers to CR0 when n=0 and consequently, for CR0-7, is defined, in v3.0B pseudocode, as:

     CR{n} = CR[32+n*4:35+n*4]

For SVP64 the relationship for the sequential numbering of elements is to the CR fields within the CR Register, not to individual bits within the CR register.

The CR{n} notation is designed to give linear sequential numbering in the Vector domain on a straight sequential Vector Loop.

In OpenPOWER v3.0/1, BF/BT/BA/BB are all 5 bits. The top 3 bits (0:2) select one of the 8 CRs; the bottom 2 bits (3:4) select one of 4 bits in that CR (EQ/LT/GT/SO). The numbering was determined (after 4 months of analysis and research) to be as follows:

    CR_index = (BA>>2)      # top 3 bits
    bit_index = (BA & 0b11) # low 2 bits
    CR_reg = CR{CR_index}     # get the CR
    # finally get the bit from the CR.
    CR_bit = (CR_reg & (1<<bit_index)) != 0

When it comes to applying SV, it is the CR Field number CR_reg to which SV EXTRA2/3 applies, not the CR_bit portion (bits 3-4):

    if extra3_mode:
        spec = EXTRA3
    elif EXTRA2[0]:  # vector mode
        spec = EXTRA2 << 1  # same as EXTRA3, shifted
    else:            # scalar mode
        spec = (EXTRA2[0] << 2) | EXTRA2[1]
    if spec[0]:
       # vector constructs "BA[0:2] spec[1:2] 00 BA[3:4]"
       return ((BA >> 2)<<6) | # hi 3 bits shifted up
              (spec[1:2]<<4) | # to make room for these
              (BA & 0b11)      # CR_bit on the end
    else:
       # scalar constructs "00 spec[1:2] BA[0:4]"
       return (spec[1:2] << 5) | BA

Thus, for example, to access a given bit for a CR in SV mode, the v3.0B algorithm to determine CR_reg is modified to as follows:

    CR_index = (BA>>2)      # top 3 bits 
    if spec[0]:
        # vector mode, 0-124 increments of 4
        CR_index = (CR_index<<4) | (spec[1:2] << 2)
    else:
        # scalar mode, 0-32 increments of 1
        CR_index = (spec[1:2]<<3) | CR_index
    # same as for v3.0/v3.1 from this point onwards
    bit_index = (BA & 0b11) # low 2 bits
    CR_reg = CR{CR_index}     # get the CR
    # finally get the bit from the CR.
    CR_bit = (CR_reg & (1<<bit_index)) != 0

Note here that the decoding pattern to determine CR_bit does not change.

Note: high-performance implementations may read/write Vectors of CRs in batches of aligned 32-bit chunks (CR0-7, CR7-15). This is to greatly simplify internal design. If instructions are issued where CR Vectors do not start on a 32-bit aligned boundary, performance may be affected.

CR fields as inputs/outputs of vector operations

CRs (or, the arithmetic operations associated with them) may be marked as Vectorized or Scalar. When Rc=1 in arithmetic operations that have no explicit EXTRA to cover the CR, the CR is Vectorized if the destination is Vectorized. Likewise if the destination is scalar then so is the CR.

When vectorized, the CR inputs/outputs are sequentially read/written to 4-bit CR fields. Vectorized Integer results, when Rc=1, will begin writing to CR8 (TBD evaluate) and increase sequentially from there. This is so that:

  • implementations may rely on the Vector CRs being aligned to 8. This means that CRs may be read or written in aligned batches of 32 bits (8 CRs per batch), for high performance implementations.
  • scalar Rc=1 operation (CR0, CR1) and callee-saved CRs (CR2-4) are not overwritten by vector Rc=1 operations except for very large VL
  • CR-based predication, from CR32, is also not interfered with (except by large VL).

However when the SV result (destination) is marked as a scalar by the EXTRA field the standard v3.0B behaviour applies: the accompanying CR when Rc=1 is written to. This is CR0 for integer operations and CR1 for FP operations.

Note that yes, the CR Fields are genuinely Vectorized. Unlike in SIMD VSX which has a single CR (CR6) for a given SIMD result, SV Vectorized OpenPOWER v3.0B scalar operations produce a tuple of element results: the result of the operation as one part of that element and a corresponding CR element. Greatly simplified pseudocode:

    for i in range(VL):
         # calculate the vector result of an add
         iregs[RT+i] = iregs[RA+i] + iregs[RB+i]
         # now calculate CR bits
         CRs{8+i}.eq = iregs[RT+i] == 0
         CRs{8+i}.gt = iregs[RT+i] > 0
         ... etc

If a "cumulated" CR based analysis of results is desired (a la VSX CR6) then a followup instruction must be performed, setting "reduce" mode on the Vector of CRs, using cr ops (crand, crnor) to do so. This provides far more flexibility in analysing vectors than standard Vector ISAs. Normal Vector ISAs are typically restricted to "were all results nonzero" and "were some results nonzero". The application of mapreduce to Vectorized cr operations allows far more sophisticated analysis, particularly in conjunction with the new crweird operations see cr int predication.

Note in particular that the use of a separate instruction in this way ensures that high performance multi-issue OoO inplementations do not have the computation of the cumulative analysis CR as a bottleneck and hindrance, regardless of the length of VL.

Additionally, SVP64 branches may be used, even when the branch itself is to the following instruction. The combined side-effects of CTR reduction and VL truncation provide several benefits.

(see discussion. some alternative schemes are described there)

Rc=1 when SUBVL!=1

sub-vectors are effectively a form of Packed SIMD (length 2 to 4). Only 1 bit of predicate is allocated per subvector; likewise only one CR is allocated per subvector.

This leaves a conundrum as to how to apply CR computation per subvector, when normally Rc=1 is exclusively applied to scalar elements. A solution is to perform a bitwise OR or AND of the subvector tests. Given that OE is ignored in SVP64, this field may (when available) be used to select OR or AND behavior.

Table of CR fields

CRn is the notation used by the OpenPower spec to refer to CR field #i, so FP instructions with Rc=1 write to CR1 (n=1).

CRs are not stored in SPRs: they are registers in their own right. Therefore context-switching the full set of CRs involves a Vectorized mfcr or mtcr, using VL=8 to do so. This is exactly as how scalar OpenPOWER context-switches CRs: it is just that there are now more of them.

The 64 SV CRs are arranged similarly to the way the 128 integer registers are arranged. TODO a python program that auto-generates a CSV file which can be included in a table, which is in a new page (so as not to overwhelm this one). cr names

Register Profiles

Instructions are broken down by Register Profiles as listed in the following auto-generated page: opcode regs deduped. These tables, despite being auto-generated, are part of the Specification.

SV pseudocode illustration

Single-predicated Instruction

illustration of normal mode add operation: zeroing not included, elwidth overrides not included. if there is no predicate, it is set to all 1s

    function op_add(rd, rs1, rs2) # add not VADD!
      int i, id=0, irs1=0, irs2=0;
      predval = get_pred_val(FALSE, rd);
      for (i = 0; i < VL; i++)
        STATE.srcoffs = i # save context
        if (predval & 1<<i) # predication uses intregs
           ireg[rd+id] <= ireg[rs1+irs1] + ireg[rs2+irs2];
        if (!int_vec[rd].isvec) break;
        if (rd.isvec)  { id += 1; }
        if (rs1.isvec) { irs1 += 1; }
        if (rs2.isvec) { irs2 += 1; }
        if (id == VL or irs1 == VL or irs2 == VL) {
          # end VL hardware loop
          STATE.srcoffs = 0; # reset
          return;
        }

This has several modes:

  • RT.v = RA.v RB.v
  • RT.v = RA.v RB.s (and RA.s RB.v)
  • RT.v = RA.s RB.s
  • RT.s = RA.v RB.v
  • RT.s = RA.v RB.s (and RA.s RB.v)
  • RT.s = RA.s RB.s

All of these may be predicated. Vector-Vector is straightfoward. When one of source is a Vector and the other a Scalar, it is clear that each element of the Vector source should be added to the Scalar source, each result placed into the Vector (or, if the destination is a scalar, only the first nonpredicated result).

The one that is not obvious is RT=vector but both RA/RB=scalar. Here this acts as a "splat scalar result", copying the same result into all nonpredicated result elements. If a fixed destination scalar was intended, then an all-Scalar operation should be used.

See https://bugs.libre-soc.org/show_bug.cgi?id=552

Assembly Annotation

Assembly code annotation is required for SV to be able to successfully mark instructions as "prefixed".

A reasonable (prototype) starting point:

    svp64 [field=value]*

Fields:

  • ew=8/16/32 - element width
  • sew=8/16/32 - source element width
  • vec=2/3/4 - SUBVL
  • mode=mr/satu/sats/crpred
  • pred=1\<\<3/r3/~r3/r10/~r10/r30/~r30/lt/gt/le/ge/eq/ne

similar to x86 "rex" prefix.

For actual assembler:

    sv.asmcode/mode.vec{N}.ew=8,sw=16,m={pred},sm={pred} reg.v, src.s

Qualifiers:

  • m={pred}: predicate mask mode
  • sm={pred}: source-predicate mask mode (only allowed in Twin-predication)
  • vec{N}: vec2 OR vec3 OR vec4 - sets SUBVL=2/3/4
  • ew={N}: ew=8/16/32 - sets elwidth override
  • sw={N}: sw=8/16/32 - sets source elwidth override
  • ff={xx}: see fail-first mode
  • sat{x}: satu / sats - see saturation mode
  • mr: see map-reduce mode
  • mrr: map-reduce, reverse-gear (VL-1 downto 0)
  • mr.svm see map-reduce with sub-vector mode
  • crm: see map-reduce CR mode
  • crm.svm see map-reduce CR with sub-vector mode
  • sz: predication with source-zeroing
  • dz: predication with dest-zeroing

For modes:

  • fail-first
    • ff=lt/gt/le/ge/eq/ne/so/ns
    • RC1 mode
  • saturation:
    • sats
    • satu
  • map-reduce:
    • mr OR crm: "normal" map-reduce mode or CR-mode.
    • mr.svm OR crm.svm: when vec2/3/4 set, sub-vector mapreduce is enabled

Parallel-reduction algorithm

The principle of SVP64 is that SVP64 is a fully-independent Abstraction of hardware-looping in between issue and execute phases that has no relation to the operation it issues. Additional state cannot be saved on context-switching beyond that of SVSTATE, making things slightly tricky.

Executable demo pseudocode, full version here


def preduce_yield(vl, vec, pred):
    step = 1
    ix = list(range(vl))
    while step < vl:
        step *= 2
        for i in range(0, vl, step):
            other = i + step // 2
            ci = ix[i]
            oi = ix[other] if other < vl else None
            other_pred = other < vl and pred[oi]
            if pred[ci] and other_pred:
                yield ci, oi
            elif other_pred:
                ix[i] = oi

def preduce_y(vl, vec, pred):
   for i, other in preduce_yield(vl, vec, pred):
       vec[i] += vec[other]

This algorithm works by noting when data remains in-place rather than being reduced, and referring to that alternative position on subsequent layers of reduction. It is re-entrant. If however interrupted and restored, some implementations may take longer to re-establish the context.

Its application by default is that:

  • RA, FRA or BFA is the first register as the first operand (ci index offset in the above pseudocode)
  • RB, FRB or BFB is the second (co index offset)
  • RT (result) also uses ci if RA==RT

For more complex applications a REMAP Schedule must be used

Programmers's note: if passed a predicate mask with only one bit set, this algorithm takes no action, similar to when a predicate mask is all zero.

Implementor's Note: many SIMD-based Parallel Reduction Algorithms are implemented in hardware with MVs that ensure lane-crossing is minimised. The mistake which would be catastrophic to SVP64 to make is to then limit the Reduction Sequence for all implementors based solely and exclusively on what one specific internal microarchitecture does. In SIMD ISAs the internal SIMD Architectural design is exposed and imposed on the programmer. Cray-style Vector ISAs on the other hand provide convenient, compact and efficient encodings of abstract concepts. It is the Implementor's responsibility to produce a design that complies with the above algorithm, utilising internal Micro-coding and other techniques to transparently insert micro-architectural lane-crossing Move operations if necessary or desired, to give the level of efficiency or performance required.

Element-width overrides

Element-width overrides are best illustrated with a packed structure union in the c programming language. The following should be taken literally, and assume always a little-endian layout:

    #pragma pack
    typedef union {
        uint8_t  b[];
        uint16_t s[];
        uint32_t i[];
        uint64_t l[];
        uint8_t actual_bytes[8];
    } el_reg_t;

    elreg_t int_regfile[128];

Accessing (get and set) of registers given a value, register (in elreg_t form), and that all arithmetic, numbering and pseudo-Memory format is LE-endian and LSB0-numbered below:

    elreg_t& get_polymorphed_reg(elreg_t const& reg, bitwidth, offset):
        el_reg_t res; // result
        res.l = 0; // TODO: going to need sign-extending / zero-extending
        if !reg.isvec: // scalar access has no element offset
            offset = 0
        if bitwidth == 8:
            reg.b = int_regfile[reg].b[offset]
        elif bitwidth == 16:
            reg.s = int_regfile[reg].s[offset]
        elif bitwidth == 32:
            reg.i = int_regfile[reg].i[offset]
        elif bitwidth == 64:
            reg.l = int_regfile[reg].l[offset]
        return reg

    set_polymorphed_reg(elreg_t& reg, bitwidth, offset, val):
        if (!reg.isvec):
            # for safety mask out hi bits
            bytemask = (8 << bitwidth) - 1
            val &= bytemask
            # not a vector: first element only, overwrites high bits.
            # and with the *Architectural* definition being LE,
            # storing in the first DWORD works perfectly.
            int_regfile[reg].l[0] = val
        elif bitwidth == 8:
            int_regfile[reg].b[offset] = val
        elif bitwidth == 16:
            int_regfile[reg].s[offset] = val
        elif bitwidth == 32:
            int_regfile[reg].i[offset] = val
        elif bitwidth == 64:
            int_regfile[reg].l[offset] = val

In effect the GPR registers r0 to r127 (and corresponding FPRs fp0 to fp127) are reinterpreted to be "starting points" in a byte-addressable memory. Vectors - which become just a virtual naming construct - effectively overlap.

It is extremely important for implementors to note that the only circumstance where upper portions of an underlying 64-bit register are zero'd out is when the destination is a scalar. The ideal register file has byte-level write-enable lines, just like most SRAMs, in order to avoid READ-MODIFY-WRITE.

An example ADD operation with predication and element width overrides:

      for (i = 0; i < VL; i++)
        if (predval & 1<<i) # predication
           src1 = get_polymorphed_reg(RA, srcwid, irs1)
           src2 = get_polymorphed_reg(RB, srcwid, irs2)
           result = src1 + src2 # actual add here
           set_polymorphed_reg(RT, destwid, ird, result)
           if (!RT.isvec) break
        if (RT.isvec)  { id += 1; }
        if (RA.isvec)  { irs1 += 1; }
        if (RB.isvec)  { irs2 += 1; }

Thus it can be clearly seen that elements are packed by their element width, and the packing starts from the source (or destination) specified by the instruction.

Twin (implicit) result operations

Some operations in the Power ISA already target two 64-bit scalar registers: lq for example, and LD with update. Some mathematical algorithms are more efficient when there are two outputs rather than one, providing feedback loops between elements (the most well-known being add with carry). 64-bit multiply for example actually internally produces a 128 bit result, which clearly cannot be stored in a single 64 bit register. Some ISAs recommend "macro op fusion": the practice of setting a convention whereby if two commonly used instructions (mullo, mulhi) use the same ALU but one selects the low part of an identical operation and the other selects the high part, then optimised micro-architectures may "fuse" those two instructions together, using Micro-coding techniques, internally.

The practice and convention of macro-op fusion however is not compatible with SVP64 Horizontal-First, because Horizontal Mode may only be applied to a single instruction at a time, and SVP64 is based on the principle of strict Program Order even at the element level. Thus it becomes necessary to add explicit more complex single instructions with more operands than would normally be seen in the average RISC ISA (3-in, 2-out, in some cases). If it was not for Power ISA already having LD/ST with update as well as Condition Codes and lq this would be hard to justify.

With limited space in the EXTRA Field, and Power ISA opcodes being only 32 bit, 5 operands is quite an ask. lq however sets a precedent: RTp stands for "RT pair". In other words the result is stored in RT and RT+1. For Scalar operations, following this precedent is perfectly reasonable. In Scalar mode, maddedu therefore stores the two halves of the 128-bit multiply into RT and RT+1.

What, then, of sv.maddedu? If the destination is hard-coded to RT and RT+1 the instruction is not useful when Vectorized because the output will be overwritten on the next element. To solve this is easy: define the destination registers as RT and RT+MAXVL respectively. This makes it easy for compilers to statically allocate registers even when VL changes dynamically.

Bear in mind that both RT and RT+MAXVL are starting points for Vectors, and bear in mind that element-width overrides still have to be taken into consideration, the starting point for the implicit destination is best illustrated in pseudocode:

     # demo of maddedu
     for (i = 0; i < VL; i++)
        if (predval & 1<<i) # predication
           src1 = get_polymorphed_reg(RA, srcwid, irs1)
           src2 = get_polymorphed_reg(RB, srcwid, irs2)
           src2 = get_polymorphed_reg(RC, srcwid, irs3)
           result = src1*src2 + src2
           destmask = (2<<destwid)-1
           # store two halves of result, both start from RT.
           set_polymorphed_reg(RT, destwid, ird      , result&destmask)
           set_polymorphed_reg(RT, destwid, ird+MAXVL, result>>destwid)
           if (!RT.isvec) break
        if (RT.isvec)  { id += 1; }
        if (RA.isvec)  { irs1 += 1; }
        if (RB.isvec)  { irs2 += 1; }
        if (RC.isvec)  { irs3 += 1; }

The significant part here is that the second half is stored starting not from RT+MAXVL at all: it is the element index that is offset by MAXVL, both halves actually starting from RT. If VL is 3, MAXVL is 5, RT is 1, and dest elwidth is 32 then the elements RT0 to RT2 are stored:

     LSB0:  63:32     31:0
     MSB0:  0:31      32:63
     r0    unchanged unchanged
     r1    RT1.lo    RT0.lo
     r2    unchanged RT2.lo
     r3    RT0.hi    unchanged
     r4    RT2.hi    RT1.hi
     r5    unchanged unchanged

Note that all of the LO halves start from r1, but that the HI halves start from half-way into r3. The reason is that with MAXVL bring 5 and elwidth being 32, this is the 5th element offset (in 32 bit quantities) counting from r1.

Programmer's note: accessing registers that have been placed starting on a non-contiguous boundary (half-way along a scalar register) can be inconvenient: REMAP can provide an offset but it requires extra instructions to set up. A simple solution is to ensure that MAXVL is rounded up such that the Vector ends cleanly on a contiguous register boundary. MAXVL=6 in the above example would achieve that

Additional DRAFT Scalar instructions in 3-in 2-out form with an implicit 2nd destination:

\newpage{}