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.

Table of contents:

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).

ldst, cr ops and 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 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.
  • Pack/Unpack mode, only available when SUBVL is vec2/3/4, performs basic structure packing on sub-elements. Bits 4-5 (normally elwidth) are taken up as Pack/Unpack bits. Saturation may be simultaneously enabled.

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 ldst. For Condition Registers see cr ops. For Branch modes, see branches.

Rounding, clamp and saturate

See av opcodes for relevant opcodes and use-cases.

To help ensure 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 2elwidth-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.

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. 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 cr int predication

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 appendix

Reduce Mode should not be confused with Parallel Reduction remap. As explained in the ?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 remap deliberately issues a Tree-Schedule of operations that may be parallelised.

Fail-on-first

Data-dependent fail-on-first has two distinct variants: one for LD/ST, the other for arithmetic operations (actually, CR-driven). Note in each case the assumption is that 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 set.

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).

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 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 cr ops Mode format.

Programmer's note: VLi is only accessible in normal operations which in turn limits the CR field bit-testing to only EQ/NE. 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.

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. 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).the

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 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 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
    if Rc=1 or RC1:
        crregs[offs+i] = CRnew
    # now test CR, similar to branch
    if RC1 or CRnew[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.

Pack/Unpack Mode

TODO - move to sv.setvl setvl

Structured Pack/Unpack is similar to VSX vpack and vunpack except generalised not only to a Schedule to be applied to any operation but also extended to vec2/3/4.

Setting this mode changes the meaning of bits 4-5 in RM from being ELWIDTH to a pair of Pack/Unpack bits. Thus it is not possible to separately override source and destination elwidths at the same time as use Pack/Unpack: the SRC_ELWIDTH bits (6-7) must be used as both source and destination elwidth.

This was considered to be an acceptable compromise. If separate elwidths are required and Pack/Unpack needed without needing to perform a widening or narrowing register move then remap may be used: Matrix Mode may perform the same operation (but is more costly to set up). See appendix for details on how Pack/Unpack is implemented.