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# Simple-V (Parallelism Extension Proposal) Appendix

* Copyright (C) 2017, 2018, 2019 Luke Kenneth Casson Leighton
* Status: DRAFTv0.6
* Last edited: 28 jun 2019
* main spec [[specification]]

[[!toc ]]

# Fail-on-first modes

Fail-on-first data dependency has different behaviour for traps than
for conditional testing.  "Conditional" is taken to mean "anything
that is zero", however with traps, the first element has to
be given the opportunity to throw the exact same trap that would
be thrown if this were a scalar operation (when VL=1).

Note that implementors are required to mutually exclusively choose one or
the other modes: an instruction is **not** permitted to fail on a trap
*and* fail a conditional test.  This advice to custom opcode writers as
well as future extension writers.

## Fail-on-first traps

Except for the first element, ffirst stops sequential element processing
when a trap occurs.  The first element is treated normally (as if ffirst
is clear).  Should any subsequent element instruction require a trap,
instead it and subsequent indexed elements are ignored (or cancelled in
out-of-order designs), and VL is set to the *last* in-sequence instruction
that did not take the trap.

Note that predicated-out elements (where the predicate mask bit is
zero) are clearly excluded (i.e. the trap will not occur).  However,
note that the loop still had to test the predicate bit: thus on return,
VL is set to include elements that did not take the trap *and* includes
the elements that were predicated (masked) out (not tested up to the
point where the trap occurred).

If SUBVL is being used (SUBVL!=1), the first *sub-group* of elements
will cause a trap as normal (as if ffirst is not set); subsequently, the
trap must not occur in the *sub-group* of elements.  SUBVL will **NOT**
be modified.  Traps must analyse (x)eSTATE (subvl offset indices) to
determine the element that caused the trap.

Given that predication bits apply to SUBVL groups, the same rules apply
to predicated-out (masked-out) sub-groups in calculating the value that
VL is set to.

## Fail-on-first conditional tests

ffirst stops sequential (or sequentially-appearing in the case of
out-of-order designs) element conditional testing on the first element
result being zero (or other "fail" condition).  VL is set to the number
of elements that were (sequentially) processed before the fail-condition
was encountered.

Note that just as with traps, if SUBVL!=1, the first trap in the
*sub-group* will cause the processing to end, and, even if there were
elements within the *sub-group* that passed the test, that sub-group is
still (entirely) excluded from the count (from setting VL).  i.e. VL is
set to the total number of *sub-groups* that had no fail-condition up
until execution was stopped.  However, again: SUBVL must not be modified:
traps must analyse (x)eSTATE (subvl offset indices) to determine the
element that caused the trap.

Note again that, just as with traps, predicated-out (masked-out) elements
are included in the (sequential) count leading up to the fail-condition,
even though they were not tested.

# Instructions <a name="instructions" />

Despite being a 98% complete and accurate topological remap of RVV
concepts and functionality, no new instructions are needed.
Compared to RVV: *All* RVV instructions can be re-mapped, however xBitManip
becomes a critical dependency for efficient manipulation of predication
masks (as a bit-field).  Despite the removal of all operations,
with the exception of CLIP and VSELECT.X
*all instructions from RVV Base are topologically re-mapped and retain their
complete functionality, intact*.  Note that if RV64G ever had
a MV.X added as well as FCLIP, the full functionality of RVV-Base would
be obtained in SV.

Three instructions, VSELECT, VCLIP and VCLIPI, do not have RV Standard
equivalents, so are left out of Simple-V.  VSELECT could be included if
there existed a MV.X instruction in RV (MV.X is a hypothetical
non-immediate variant of MV that would allow another register to
specify which register was to be copied).  Note that if any of these three
instructions are added to any given RV extension, their functionality
will be inherently parallelised.

With some exceptions, where it does not make sense or is simply too
challenging, all RV-Base instructions are parallelised:

* CSR instructions, whilst a case could be made for fast-polling of
  a CSR into multiple registers, or for being able to copy multiple
  contiguously addressed CSRs into contiguous registers, and so on,
  are the fundamental core basis of SV.  If parallelised, extreme
  care would need to be taken.  Additionally, CSR reads are done
  using x0, and it is *really* inadviseable to tag x0.
* LUI, C.J, C.JR, WFI, AUIPC are not suitable for parallelising so are
  left as scalar.
* LR/SC could hypothetically be parallelised however their purpose is
  single (complex) atomic memory operations where the LR must be followed
  up by a matching SC.  A sequence of parallel LR instructions followed
  by a sequence of parallel SC instructions therefore is guaranteed to
  not be useful. Not least: the guarantees of a Multi-LR/SC
  would be impossible to provide if emulated in a trap.
* EBREAK, NOP, FENCE and others do not use registers so are not inherently
  paralleliseable anyway.

All other operations using registers are automatically parallelised.
This includes AMOMAX, AMOSWAP and so on, where particular care and
attention must be paid.

Example pseudo-code for an integer ADD operation (including scalar
operations).  Floating-point uses the FP Register Table.

[[!inline raw="yes" pages="simple_v_extension/simple_add_example" ]]

Note that for simplicity there is quite a lot missing from the above
pseudo-code: PCVBLK, element widths, zeroing on predication, dimensional
reshaping and offsets and so on.  However it demonstrates the basic
principle.  Augmentations that produce the full pseudo-code are covered in
other sections.

## SUBVL Pseudocode <a name="subvl-pseudocode"></a>

Adding in support for SUBVL is a matter of adding in an extra inner
for-loop, where register src and dest are still incremented inside the
inner part. Note that the predication is still taken from the VL index.

So whilst elements are indexed by "(i * SUBVL + s)", predicate bits are
indexed by "(i)"

    function op_add(rd, rs1, rs2) # add not VADD!
      int i, id=0, irs1=0, irs2=0;
      predval = get_pred_val(FALSE, rd);
      rd  = int_vec[rd ].isvector ? int_vec[rd ].regidx : rd;
      rs1 = int_vec[rs1].isvector ? int_vec[rs1].regidx : rs1;
      rs2 = int_vec[rs2].isvector ? int_vec[rs2].regidx : rs2;
      for (i = 0; i < VL; i++)
       xSTATE.srcoffs = i # save context
       for (s = 0; s < SUBVL; s++)
        xSTATE.ssvoffs = s # save context
        if (predval & 1<<i) # predication uses intregs
           # actual add is here (at last)
           ireg[rd+id] <= ireg[rs1+irs1] + ireg[rs2+irs2];
           if (!int_vec[rd ].isvector) break;
        if (int_vec[rd ].isvector)  { id += 1; }
        if (int_vec[rs1].isvector)  { irs1 += 1; }
        if (int_vec[rs2].isvector)  { irs2 += 1; }
        if (id == VL or irs1 == VL or irs2 == VL) {
          # end VL hardware loop
          xSTATE.srcoffs = 0; # reset
          xSTATE.ssvoffs = 0; # reset
          return;
        }


NOTE: pseudocode simplified greatly: zeroing, proper predicate handling,
elwidth handling etc. all left out.

## Instruction Format

It is critical to appreciate that there are
**no operations added to SV, at all**.

Instead, by using CSRs to tag registers as an indication of "changed
behaviour", SV *overloads* pre-existing branch operations into predicated
variants, and implicitly overloads arithmetic operations, MV, FCVT, and
LOAD/STORE depending on CSR configurations for bitwidth and predication.
**Everything** becomes parallelised.  *This includes Compressed
instructions* as well as any future instructions and Custom Extensions.

Note: CSR tags to change behaviour of instructions is nothing new, including
in RISC-V.  UXL, SXL and MXL change the behaviour so that XLEN=32/64/128.
FRM changes the behaviour of the floating-point unit, to alter the rounding
mode.  Other architectures change the LOAD/STORE byte-order from big-endian
to little-endian on a per-instruction basis.  SV is just a little more...
comprehensive in its effect on instructions.

## Branch Instructions

Branch operations are augmented slightly to be a little more like FP
Compares (FEQ, FNE etc.), by permitting the cumulation (and storage)
of multiple comparisons into a register (taken indirectly from the predicate
table).  As such, "ffirst" - fail-on-first - condition mode can be enabled.
See ffirst mode in the Predication Table section.

### Standard Branch <a name="standard_branch"></a>

Branch operations use standard RV opcodes that are reinterpreted to
be "predicate variants" in the instance where either of the two src
registers are marked as vectors (active=1, vector=1).

Note that the predication register to use (if one is enabled) is taken from
the *first* src register, and that this is used, just as with predicated
arithmetic operations, to mask whether the comparison operations take
place or not.  The target (destination) predication register
to use (if one is enabled) is taken from the *second* src register.

If either of src1 or src2 are scalars (whether by there being no
CSR register entry or whether by the CSR entry specifically marking
the register as "scalar") the comparison goes ahead as vector-scalar
or scalar-vector.

In instances where no vectorisation is detected on either src registers
the operation is treated as an absolutely standard scalar branch operation.
Where vectorisation is present on either or both src registers, the
branch may stil go ahead if any only if *all* tests succeed (i.e. excluding
those tests that are predicated out).

Note that when zero-predication is enabled (from source rs1),
a cleared bit in the predicate indicates that the result
of the compare is set to "false", i.e. that the corresponding
destination bit (or result)) be set to zero.  Contrast this with
when zeroing is not set: bits in the destination predicate are
only *set*; they are **not** cleared.  This is important to appreciate,
as there may be an expectation that, going into the hardware-loop,
the destination predicate is always expected to be set to zero:
this is **not** the case.  The destination predicate is only set
to zero if **zeroing** is enabled.

Note that just as with the standard (scalar, non-predicated) branch
operations, BLE, BGT, BLEU and BTGU may be synthesised by inverting
src1 and src2.

In Hwacha EECS-2015-262 Section 6.7.2 the following pseudocode is given
for predicated compare operations of function "cmp":

    for (int i=0; i<vl; ++i)
      if ([!]preg[p][i])
         preg[pd][i] = cmp(s1 ? vreg[rs1][i] : sreg[rs1],
                           s2 ? vreg[rs2][i] : sreg[rs2]);

With associated predication, vector-length adjustments and so on,
and temporarily ignoring bitwidth (which makes the comparisons more
complex), this becomes:

    s1 = reg_is_vectorised(src1);
    s2 = reg_is_vectorised(src2);

    if not s1 && not s2
        if cmp(rs1, rs2) # scalar compare
            goto branch
        return

    preg = int_pred_reg[rd]
    reg = int_regfile

    ps = get_pred_val(I/F==INT, rs1);
    rd = get_pred_val(I/F==INT, rs2); # this may not exist

    if not exists(rd) or zeroing:
        result = 0
    else
        result = preg[rd]

    for (int i = 0; i < VL; ++i)
      if (zeroing)
        if not (ps & (1<<i))
           result &= ~(1<<i);
      else if (ps & (1<<i))
          if (cmp(s1 ? reg[src1+i]:reg[src1],
                               s2 ? reg[src2+i]:reg[src2])
              result |= 1<<i;
          else
              result &= ~(1<<i);

     if not exists(rd)
        if result == ps
            goto branch
     else
        preg[rd] = result # store in destination
        if preg[rd] == ps
            goto branch

Notes:

* Predicated SIMD comparisons would break src1 and src2 further down
  into bitwidth-sized chunks (see Appendix "Bitwidth Virtual Register
  Reordering") setting Vector-Length times (number of SIMD elements) bits
  in Predicate Register rd, as opposed to just Vector-Length bits.
* The execution of "parallelised" instructions **must** be implemented
  as "re-entrant" (to use a term from software).  If an exception (trap)
  occurs during the middle of a vectorised
  Branch (now a SV predicated compare) operation, the partial results
  of any comparisons must be written out to the destination
  register before the trap is permitted to begin.  If however there
  is no predicate, the **entire** set of comparisons must be **restarted**,
  with the offset loop indices set back to zero.  This is because
  there is no place to store the temporary result during the handling
  of traps.

TODO: predication now taken from src2.  also branch goes ahead
if all compares are successful.

Note also that where normally, predication requires that there must
also be a CSR register entry for the register being used in order
for the **predication** CSR register entry to also be active,
for branches this is **not** the case.  src2 does **not** have
to have its CSR register entry marked as active in order for
predication on src2 to be active.

Also note: SV Branch operations are **not** twin-predicated
(see Twin Predication section).  This would require three
element offsets: one to track src1, one to track src2 and a third
to track where to store the accumulation of the results.  Given
that the element offsets need to be exposed via CSRs so that
the parallel hardware looping may be made re-entrant on traps
and exceptions, the decision was made not to make SV Branches
twin-predicated.

### Floating-point Comparisons

There does not exist floating-point branch operations, only compare.
Interestingly no change is needed to the instruction format because
FP Compare already stores a 1 or a zero in its "rd" integer register
target, i.e. it's not actually a Branch at all: it's a compare.

In RV (scalar) Base, a branch on a floating-point compare is
done via the sequence "FEQ x1, f0, f5; BEQ x1, x0, #jumploc".
This does extend to SV, as long as x1 (in the example sequence given)
is vectorised.  When that is the case, x1..x(1+VL-1) will also be
set to 0 or 1 depending on whether f0==f5, f1==f6, f2==f7 and so on.
The BEQ that follows will *also* compare x1==x0, x2==x0, x3==x0 and
so on.  Consequently, unlike integer-branch, FP Compare needs no
modification in its behaviour.

In addition, it is noted that an entry "FNE" (the opposite of FEQ) is
missing, and whilst in ordinary branch code this is fine because the
standard RVF compare can always be followed up with an integer BEQ or
a BNE (or a compressed comparison to zero or non-zero), in predication
terms that becomes more of an impact.  To deal with this, SV's predication
has had "invert" added to it.

Also: note that FP Compare may be predicated, using the destination
integer register (rd) to determine the predicate.  FP Compare is **not**
a twin-predication operation, as, again, just as with SV Branches,
there are three registers involved: FP src1, FP src2 and INT rd.

Also: note that ffirst (fail first mode) applies directly to this operation.

### Compressed Branch Instruction

Compressed Branch instructions are, just like standard Branch instructions,
reinterpreted to be vectorised and predicated based on the source register
(rs1s) CSR entries.  As however there is only the one source register,
given that c.beqz a10 is equivalent to beqz a10,x0, the optional target
to store the results of the comparisions is taken from CSR predication
table entries for **x0**.

The specific required use of x0 is, with a little thought, quite obvious,
but is counterintuitive.  Clearly it is **not** recommended to redirect
x0 with a CSR register entry, however as a means to opaquely obtain
a predication target it is the only sensible option that does not involve
additional special CSRs (or, worse, additional special opcodes).

Note also that, just as with standard branches, the 2nd source
(in this case x0 rather than src2) does **not** have to have its CSR
register table marked as "active" in order for predication to work.

## Vectorised Dual-operand instructions

There is a series of 2-operand instructions involving copying (and
sometimes alteration):

* C.MV
* FMV, FNEG, FABS, FCVT, FSGNJ, FSGNJN and FSGNJX
* C.LWSP, C.SWSP, C.LDSP, C.FLWSP etc.
* LOAD(-FP) and STORE(-FP)

All of these operations follow the same two-operand pattern, so it is
*both* the source *and* destination predication masks that are taken into
account.  This is different from
the three-operand arithmetic instructions, where the predication mask
is taken from the *destination* register, and applied uniformly to the
elements of the source register(s), element-for-element.

The pseudo-code pattern for twin-predicated operations is as
follows:

    function op(rd, rs):
      rd = int_csr[rd].active ? int_csr[rd].regidx : rd;
      rs = int_csr[rs].active ? int_csr[rs].regidx : rs;
      ps = get_pred_val(FALSE, rs); # predication on src
      pd = get_pred_val(FALSE, rd); # ... AND on dest
      for (int i = 0, int j = 0; i < VL && j < VL;):
        if (int_csr[rs].isvec) while (!(ps & 1<<i)) i++;
        if (int_csr[rd].isvec) while (!(pd & 1<<j)) j++;
        xSTATE.srcoffs = i # save context
        xSTATE.destoffs = j # save context
        reg[rd+j] = SCALAR_OPERATION_ON(reg[rs+i])
        if (int_csr[rs].isvec) i++;
        if (int_csr[rd].isvec) j++; else break

This pattern covers scalar-scalar, scalar-vector, vector-scalar
and vector-vector, and predicated variants of all of those.
Zeroing is not presently included (TODO).  As such, when compared
to RVV, the twin-predicated variants of C.MV and FMV cover
**all** standard vector operations: VINSERT, VSPLAT, VREDUCE,
VEXTRACT, VSCATTER, VGATHER, VCOPY, and more.

Note that:

* elwidth (SIMD) is not covered in the pseudo-code above
* ending the loop early in scalar cases (VINSERT, VEXTRACT) is also
  not covered
* zero predication is also not shown (TODO).

### C.MV Instruction <a name="c_mv"></a>

There is no MV instruction in RV however there is a C.MV instruction.
It is used for copying integer-to-integer registers (vectorised FMV
is used for copying floating-point).

If either the source or the destination register are marked as vectors
C.MV is reinterpreted to be a vectorised (multi-register) predicated
move operation.  The actual instruction's format does not change:

[[!table  data="""
15  12 | 11   7 | 6  2 | 1  0 |
funct4 | rd     | rs   | op   |
4      | 5      | 5    | 2    |
C.MV   | dest   | src  | C0   |
"""]]

A simplified version of the pseudocode for this operation is as follows:

    function op_mv(rd, rs) # MV not VMV!
      rd = int_csr[rd].active ? int_csr[rd].regidx : rd;
      rs = int_csr[rs].active ? int_csr[rs].regidx : rs;
      ps = get_pred_val(FALSE, rs); # predication on src
      pd = get_pred_val(FALSE, rd); # ... AND on dest
      for (int i = 0, int j = 0; i < VL && j < VL;):
        if (int_csr[rs].isvec) while (!(ps & 1<<i)) i++;
        if (int_csr[rd].isvec) while (!(pd & 1<<j)) j++;
        xSTATE.srcoffs = i # save context
        xSTATE.destoffs = j # save context
        ireg[rd+j] <= ireg[rs+i];
        if (int_csr[rs].isvec) i++;
        if (int_csr[rd].isvec) j++; else break

There are several different instructions from RVV that are covered by
this one opcode:

[[!table  data="""
src    | dest    | predication   | op             |
scalar | vector  | none          | VSPLAT         |
scalar | vector  | destination   | sparse VSPLAT  |
scalar | vector  | 1-bit dest    | VINSERT        |
vector | scalar  | 1-bit? src    | VEXTRACT       |
vector | vector  | none          | VCOPY          |
vector | vector  | src           | Vector Gather  |
vector | vector  | dest          | Vector Scatter |
vector | vector  | src & dest    | Gather/Scatter |
vector | vector  | src == dest   | sparse VCOPY   |
"""]]

Also, VMERGE may be implemented as back-to-back (macro-op fused) C.MV
operations with zeroing off, and inversion on the src and dest predication
for one of the two C.MV operations.  The non-inverted C.MV will place
one set of registers into the destination, and the inverted one the other
set.  With predicate-inversion, copying and inversion of the predicate mask
need not be done as a separate (scalar) instruction.

Note that in the instance where the Compressed Extension is not implemented,
MV may be used, but that is a pseudo-operation mapping to addi rd, x0, rs.
Note that the behaviour is **different** from C.MV because with addi the
predication mask to use is taken **only** from rd and is applied against
all elements: rs[i] = rd[i].

### FMV, FNEG and FABS Instructions

These are identical in form to C.MV, except covering floating-point
register copying.  The same double-predication rules also apply.
However when elwidth is not set to default the instruction is implicitly
and automatic converted to a (vectorised) floating-point type conversion
operation of the appropriate size covering the source and destination
register bitwidths.

(Note that FMV, FNEG and FABS are all actually pseudo-instructions)

### FVCT Instructions

These are again identical in form to C.MV, except that they cover
floating-point to integer and integer to floating-point.  When element
width in each vector is set to default, the instructions behave exactly
as they are defined for standard RV (scalar) operations, except vectorised
in exactly the same fashion as outlined in C.MV.

However when the source or destination element width is not set to default,
the opcode's explicit element widths are *over-ridden* to new definitions,
and the opcode's element width is taken as indicative of the SIMD width
(if applicable i.e. if packed SIMD is requested) instead.

For example FCVT.S.L would normally be used to convert a 64-bit
integer in register rs1 to a 64-bit floating-point number in rd.
If however the source rs1 is set to be a vector, where elwidth is set to
default/2 and "packed SIMD" is enabled, then the first 32 bits of
rs1 are converted to a floating-point number to be stored in rd's
first element and the higher 32-bits *also* converted to floating-point
and stored in the second.  The 32 bit size comes from the fact that
FCVT.S.L's integer width is 64 bit, and with elwidth on rs1 set to
divide that by two it means that rs1 element width is to be taken as 32.

Similar rules apply to the destination register.

## LOAD / STORE Instructions and LOAD-FP/STORE-FP <a name="load_store"></a>

An earlier draft of SV modified the behaviour of LOAD/STORE (modified
the interpretation of the instruction fields).  This
actually undermined the fundamental principle of SV, namely that there
be no modifications to the scalar behaviour (except where absolutely
necessary), in order to simplify an implementor's task if considering
converting a pre-existing scalar design to support parallelism.

So the original RISC-V scalar LOAD/STORE and LOAD-FP/STORE-FP functionality
do not change in SV, however just as with C.MV it is important to note
that dual-predication is possible.

In vectorised architectures there are usually at least two different modes
for LOAD/STORE:

* Read (or write for STORE) from sequential locations, where one
  register specifies the address, and the one address is incremented
  by a fixed amount.  This is usually known as "Unit Stride" mode.
* Read (or write) from multiple indirected addresses, where the
  vector elements each specify separate and distinct addresses.

To support these different addressing modes, the CSR Register "isvector"
bit is used.  So, for a LOAD, when the src register is set to
scalar, the LOADs are sequentially incremented by the src register
element width, and when the src register is set to "vector", the
elements are treated as indirection addresses.  Simplified
pseudo-code would look like this:

    function op_ld(rd, rs) # LD not VLD!
      rdv = int_csr[rd].active ? int_csr[rd].regidx : rd;
      rsv = int_csr[rs].active ? int_csr[rs].regidx : rs;
      ps = get_pred_val(FALSE, rs); # predication on src
      pd = get_pred_val(FALSE, rd); # ... AND on dest
      for (int i = 0, int j = 0; i < VL && j < VL;):
        if (int_csr[rs].isvec) while (!(ps & 1<<i)) i++;
        if (int_csr[rd].isvec) while (!(pd & 1<<j)) j++;
        if (int_csr[rd].isvec)
          # indirect mode (multi mode)
          srcbase = ireg[rsv+i];
        else
          # unit stride mode
          srcbase = ireg[rsv] + i * XLEN/8; # offset in bytes
        ireg[rdv+j] <= mem[srcbase + imm_offs];
        if (!int_csr[rs].isvec &&
            !int_csr[rd].isvec) break # scalar-scalar LD
        if (int_csr[rs].isvec) i++;
        if (int_csr[rd].isvec) j++;

Notes:

* For simplicity, zeroing and elwidth is not included in the above:
  the key focus here is the decision-making for srcbase; vectorised
  rs means use sequentially-numbered registers as the indirection
  address, and scalar rs is "offset" mode.
* The test towards the end for whether both source and destination are
  scalar is what makes the above pseudo-code provide the "standard" RV
  Base behaviour for LD operations.
* The offset in bytes (XLEN/8) changes depending on whether the
  operation is a LB (1 byte), LH (2 byes), LW (4 bytes) or LD
  (8 bytes), and also whether the element width is over-ridden
  (see special element width section).

## Compressed Stack LOAD / STORE Instructions <a name="c_ld_st"></a>

C.LWSP / C.SWSP and floating-point etc. are also source-dest twin-predicated,
where it is implicit in C.LWSP/FLWSP etc. that x2 is the source register.
It is therefore possible to use predicated C.LWSP to efficiently
pop registers off the stack (by predicating x2 as the source), cherry-picking
which registers to store to (by predicating the destination).  Likewise
for C.SWSP.  In this way, LOAD/STORE-Multiple is efficiently achieved.

The two modes ("unit stride" and multi-indirection) are still supported,
as with standard LD/ST.  Essentially, the only difference is that the
use of x2 is hard-coded into the instruction.

**Note**: it is still possible to redirect x2 to an alternative target
register.  With care, this allows C.LWSP / C.SWSP (and C.FLWSP) to be used as
general-purpose LOAD/STORE operations.

## Compressed LOAD / STORE Instructions

Compressed LOAD and STORE are again exactly the same as scalar LOAD/STORE,
where the same rules apply and the same pseudo-code apply as for
non-compressed LOAD/STORE.  Again: setting scalar or vector mode
on the src for LOAD and dest for STORE switches mode from "Unit Stride"
to "Multi-indirection", respectively.

# Element bitwidth polymorphism <a name="elwidth"></a>

Element bitwidth is best covered as its own special section, as it
is quite involved and applies uniformly across-the-board.  SV restricts
bitwidth polymorphism to default, 8-bit, 16-bit and 32-bit.

The effect of setting an element bitwidth is to re-cast each entry
in the register table, and for all memory operations involving
load/stores of certain specific sizes, to a completely different width.
Thus In c-style terms, on an RV64 architecture, effectively each register
now looks like this:

    typedef union {
        uint8_t  b[8];
        uint16_t s[4];
        uint32_t i[2];
        uint64_t l[1];
    } reg_t;

    // integer table: assume maximum SV 7-bit regfile size
    reg_t int_regfile[128];

where the CSR Register table entry (not the instruction alone) determines
which of those union entries is to be used on each operation, and the
VL element offset in the hardware-loop specifies the index into each array.

However a naive interpretation of the data structure above masks the
fact that setting VL greater than 8, for example, when the bitwidth is 8,
accessing one specific register "spills over" to the following parts of
the register file in a sequential fashion.  So a much more accurate way
to reflect this would be:

    typedef union {
        uint8_t  actual_bytes[8]; // 8 for RV64, 4 for RV32, 16 for RV128
        uint8_t  b[0]; // array of type uint8_t
        uint16_t s[0];
        uint32_t i[0];
        uint64_t l[0];
        uint128_t d[0];
    } reg_t;

    reg_t int_regfile[128];

where when accessing any individual regfile[n].b entry it is permitted
(in c) to arbitrarily over-run the *declared* length of the array (zero),
and thus "overspill" to consecutive register file entries in a fashion
that is completely transparent to a greatly-simplified software / pseudo-code
representation.
It is however critical to note that it is clearly the responsibility of
the implementor to ensure that, towards the end of the register file,
an exception is thrown if attempts to access beyond the "real" register
bytes is ever attempted.

Now we may modify pseudo-code an operation where all element bitwidths have
been set to the same size, where this pseudo-code is otherwise identical
to its "non" polymorphic versions (above):

    function op_add(rd, rs1, rs2) # add not VADD!
      ...
      ...
      for (i = 0; i < VL; i++)
           ...
           ...
           // TODO, calculate if over-run occurs, for each elwidth
           if (elwidth == 8) {
               int_regfile[rd].b[id] <= int_regfile[rs1].i[irs1] +
                                        int_regfile[rs2].i[irs2];
            } else if elwidth == 16 {
               int_regfile[rd].s[id] <= int_regfile[rs1].s[irs1] +
                                        int_regfile[rs2].s[irs2];
            } else if elwidth == 32 {
               int_regfile[rd].i[id] <= int_regfile[rs1].i[irs1] +
                                        int_regfile[rs2].i[irs2];
            } else { // elwidth == 64
               int_regfile[rd].l[id] <= int_regfile[rs1].l[irs1] +
                                        int_regfile[rs2].l[irs2];
            }
           ...
           ...

So here we can see clearly: for 8-bit entries rd, rs1 and rs2 (and registers
following sequentially on respectively from the same) are "type-cast"
to 8-bit; for 16-bit entries likewise and so on.

However that only covers the case where the element widths are the same.
Where the element widths are different, the following algorithm applies:

* Analyse the bitwidth of all source operands and work out the
  maximum.  Record this as "maxsrcbitwidth"
* If any given source operand requires sign-extension or zero-extension
  (ldb, div, rem, mul, sll, srl, sra etc.), instead of mandatory 32-bit
  sign-extension / zero-extension or whatever is specified in the standard
  RV specification, **change** that to sign-extending from the respective
  individual source operand's bitwidth from the CSR table out to
  "maxsrcbitwidth" (previously calculated), instead.
* Following separate and distinct (optional) sign/zero-extension of all
  source operands as specifically required for that operation, carry out the
  operation at "maxsrcbitwidth".  (Note that in the case of LOAD/STORE or MV
  this may be a "null" (copy) operation, and that with FCVT, the changes
  to the source and destination bitwidths may also turn FVCT effectively
  into a copy).
* If the destination operand requires sign-extension or zero-extension,
  instead of a mandatory fixed size (typically 32-bit for arithmetic,
  for subw for example, and otherwise various: 8-bit for sb, 16-bit for sw
  etc.), overload the RV specification with the bitwidth from the
  destination register's elwidth entry.
* Finally, store the (optionally) sign/zero-extended value into its
  destination: memory for sb/sw etc., or an offset section of the register
  file for an arithmetic operation.

In this way, polymorphic bitwidths are achieved without requiring a
massive 64-way permutation of calculations **per opcode**, for example
(4 possible rs1 bitwidths times 4 possible rs2 bitwidths times 4 possible
rd bitwidths).  The pseudo-code is therefore as follows:

    typedef union {
        uint8_t  b;
        uint16_t s;
        uint32_t i;
        uint64_t l;
    } el_reg_t;

    bw(elwidth):
        if elwidth == 0: return xlen
        if elwidth == 1: return 8
        if elwidth == 2: return 16
        // elwidth == 3:
        return 32

    get_max_elwidth(rs1, rs2):
        return max(bw(int_csr[rs1].elwidth), # default (XLEN) if not set
                   bw(int_csr[rs2].elwidth)) # again XLEN if no entry

    get_polymorphed_reg(reg, bitwidth, offset):
        el_reg_t res;
        res.l = 0; // TODO: going to need sign-extending / zero-extending
        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 res

    set_polymorphed_reg(reg, bitwidth, offset, val):
        if (!int_csr[reg].isvec):
            # sign/zero-extend depending on opcode requirements, from
            # the reg's bitwidth out to the full bitwidth of the regfile
            val = sign_or_zero_extend(val, bitwidth, xlen)
            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

      maxsrcwid =  get_max_elwidth(rs1, rs2) # source element width(s)
      destwid = int_csr[rs1].elwidth         # destination element width
      for (i = 0; i < VL; i++)
        if (predval & 1<<i) # predication uses intregs
           // TODO, calculate if over-run occurs, for each elwidth
           src1 = get_polymorphed_reg(rs1, maxsrcwid, irs1)
           // TODO, sign/zero-extend src1 and src2 as operation requires
           if (op_requires_sign_extend_src1)
              src1 = sign_extend(src1, maxsrcwid)
           src2 = get_polymorphed_reg(rs2, maxsrcwid, irs2)
           result = src1 + src2 # actual add here
           // TODO, sign/zero-extend result, as operation requires
           if (op_requires_sign_extend_dest)
              result = sign_extend(result, maxsrcwid)
           set_polymorphed_reg(rd, destwid, ird, result)
           if (!int_vec[rd].isvector) break
        if (int_vec[rd ].isvector)  { id += 1; }
        if (int_vec[rs1].isvector)  { irs1 += 1; }
        if (int_vec[rs2].isvector)  { irs2 += 1; }

Whilst specific sign-extension and zero-extension pseudocode call
details are left out, due to each operation being different, the above
should be clear that;

* the source operands are extended out to the maximum bitwidth of all
  source operands
* the operation takes place at that maximum source bitwidth (the
  destination bitwidth is not involved at this point, at all)
* the result is extended (or potentially even, truncated) before being
  stored in the destination.  i.e. truncation (if required) to the
  destination width occurs **after** the operation **not** before.
* when the destination is not marked as "vectorised", the **full**
  (standard, scalar) register file entry is taken up, i.e. the
  element is either sign-extended or zero-extended to cover the
  full register bitwidth (XLEN) if it is not already XLEN bits long.

Implementors are entirely free to optimise the above, particularly
if it is specifically known that any given operation will complete
accurately in less bits, as long as the results produced are
directly equivalent and equal, for all inputs and all outputs,
to those produced by the above algorithm.

## Polymorphic floating-point operation exceptions and error-handling

For floating-point operations, conversion takes place without raising any
kind of exception.  Exactly as specified in the standard RV specification,
NAN (or appropriate) is stored if the result is beyond the range of the
destination, and, again, exactly as with the standard RV specification
just as with scalar operations, the floating-point flag is raised
(FCSR).  And, again, just as with scalar operations, it is software's
responsibility to check this flag.  Given that the FCSR flags are
"accrued", the fact that multiple element operations could have occurred
is not a problem.

Note that it is perfectly legitimate for floating-point bitwidths of
only 8 to be specified.  However whilst it is possible to apply IEEE 754
principles, no actual standard yet exists.  Implementors wishing to
provide hardware-level 8-bit support rather than throw a trap to emulate
in software should contact the author of this specification before
proceeding.

## Polymorphic shift operators

A special note is needed for changing the element width of left and
right shift operators, particularly right-shift.  Even for standard RV
base, in order for correct results to be returned, the second operand
RS2 must be truncated to be within the range of RS1's bitwidth.
spike's implementation of sll for example is as follows:

    WRITE_RD(sext_xlen(zext_xlen(RS1) << (RS2 & (xlen-1))));

which means: where XLEN is 32 (for RV32), restrict RS2 to cover the
range 0..31 so that RS1 will only be left-shifted by the amount that
is possible to fit into a 32-bit register.  Whilst this appears not
to matter for hardware, it matters greatly in software implementations,
and it also matters where an RV64 system is set to "RV32" mode, such
that the underlying registers RS1 and RS2 comprise 64 hardware bits
each.

For SV, where each operand's element bitwidth may be over-ridden, the
rule about determining the operation's bitwidth *still applies*, being
defined as the maximum bitwidth of RS1 and RS2.  *However*, this rule
**also applies to the truncation of RS2**.  In other words, *after*
determining the maximum bitwidth, RS2's range must **also be truncated**
to ensure a correct answer.  Example:

* RS1 is over-ridden to a 16-bit width
* RS2 is over-ridden to an 8-bit width
* RD is over-ridden to a 64-bit width
* the maximum bitwidth is thus determined to be 16-bit - max(8,16)
* RS2 is **truncated to a range of values from 0 to 15**: RS2 & (16-1)

Pseudocode (in spike) for this example would therefore be:

    WRITE_RD(sext_xlen(zext_16bit(RS1) << (RS2 & (16-1))));

This example illustrates that considerable care therefore needs to be
taken to ensure that left and right shift operations are implemented
correctly.  The key is that

* The operation bitwidth is determined by the maximum bitwidth
  of the *source registers*, **not** the destination register bitwidth
* The result is then sign-extend (or truncated) as appropriate.

## Polymorphic MULH/MULHU/MULHSU

MULH is designed to take the top half MSBs of a multiply that
does not fit within the range of the source operands, such that
smaller width operations may produce a full double-width multiply
in two cycles.  The issue is: SV allows the source operands to
have variable bitwidth.

Here again special attention has to be paid to the rules regarding
bitwidth, which, again, are that the operation is performed at
the maximum bitwidth of the **source** registers.  Therefore:

* An 8-bit x 8-bit multiply will create a 16-bit result that must
  be shifted down by 8 bits
* A 16-bit x 8-bit multiply will create a 24-bit result that must
  be shifted down by 16 bits (top 8 bits being zero)
* A 16-bit x 16-bit multiply will create a 32-bit result that must
  be shifted down by 16 bits
* A 32-bit x 16-bit multiply will create a 48-bit result that must
  be shifted down by 32 bits
* A 32-bit x 8-bit multiply will create a 40-bit result that must
  be shifted down by 32 bits

So again, just as with shift-left and shift-right, the result
is shifted down by the maximum of the two source register bitwidths.
And, exactly again, truncation or sign-extension is performed on the
result.  If sign-extension is to be carried out, it is performed
from the same maximum of the two source register bitwidths out
to the result element's bitwidth.

If truncation occurs, i.e. the top MSBs of the result are lost,
this is "Officially Not Our Problem", i.e. it is assumed that the
programmer actually desires the result to be truncated.  i.e. if the
programmer wanted all of the bits, they would have set the destination
elwidth to accommodate them.

## Polymorphic elwidth on LOAD/STORE <a name="elwidth_loadstore"></a>

Polymorphic element widths in vectorised form means that the data
being loaded (or stored) across multiple registers needs to be treated
(reinterpreted) as a contiguous stream of elwidth-wide items, where
the source register's element width is **independent** from the destination's.

This makes for a slightly more complex algorithm when using indirection
on the "addressed" register (source for LOAD and destination for STORE),
particularly given that the LOAD/STORE instruction provides important
information about the width of the data to be reinterpreted.

Let's illustrate the "load" part, where the pseudo-code for elwidth=default
was as follows, and i is the loop from 0 to VL-1:

    srcbase = ireg[rs+i];
    return mem[srcbase + imm]; // returns XLEN bits

Instead, when elwidth != default, for a LW (32-bit LOAD), elwidth-wide
chunks are taken from the source memory location addressed by the current
indexed source address register, and only when a full 32-bits-worth
are taken will the index be moved on to the next contiguous source
address register:

    bitwidth = bw(elwidth);             // source elwidth from CSR reg entry
    elsperblock = 32 / bitwidth         // 1 if bw=32, 2 if bw=16, 4 if bw=8
    srcbase = ireg[rs+i/(elsperblock)]; // integer divide
    offs = i % elsperblock;             // modulo
    return &mem[srcbase + imm + offs];  // re-cast to uint8_t*, uint16_t* etc.

Note that the constant "32" above is replaced by 8 for LB, 16 for LH, 64 for LD
and 128 for LQ.

The principle is basically exactly the same as if the srcbase were pointing
at the memory of the *register* file: memory is re-interpreted as containing
groups of elwidth-wide discrete elements.

When storing the result from a load, it's important to respect the fact
that the destination register has its *own separate element width*.  Thus,
when each element is loaded (at the source element width), any sign-extension
or zero-extension (or truncation) needs to be done to the *destination*
bitwidth.  Also, the storing has the exact same analogous algorithm as
above, where in fact it is just the set\_polymorphed\_reg pseudocode
(completely unchanged) used above.

One issue remains: when the source element width is **greater** than
the width of the operation, it is obvious that a single LB for example
cannot possibly obtain 16-bit-wide data.  This condition may be detected
where, when using integer divide, elsperblock (the width of the LOAD
divided by the bitwidth of the element) is zero.

The issue is "fixed" by ensuring that elsperblock is a minimum of 1:

    elsperblock = min(1, LD_OP_BITWIDTH / element_bitwidth)

The elements, if the element bitwidth is larger than the LD operation's
size, will then be sign/zero-extended to the full LD operation size, as
specified by the LOAD (LDU instead of LD, LBU instead of LB), before
being passed on to the second phase.

As LOAD/STORE may be twin-predicated, it is important to note that
the rules on twin predication still apply, except where in previous
pseudo-code (elwidth=default for both source and target) it was
the *registers* that the predication was applied to, it is now the
**elements** that the predication is applied to.

Thus the full pseudocode for all LD operations may be written out
as follows:

    function LBU(rd, rs):
        load_elwidthed(rd, rs, 8, true)
    function LB(rd, rs):
        load_elwidthed(rd, rs, 8, false)
    function LH(rd, rs):
        load_elwidthed(rd, rs, 16, false)
    ...
    ...
    function LQ(rd, rs):
        load_elwidthed(rd, rs, 128, false)

    # returns 1 byte of data when opwidth=8, 2 bytes when opwidth=16..
    function load_memory(rs, imm, i, opwidth):
        elwidth = int_csr[rs].elwidth
        bitwidth = bw(elwidth);
        elsperblock = min(1, opwidth / bitwidth)
        srcbase = ireg[rs+i/(elsperblock)];
        offs = i % elsperblock;
        return mem[srcbase + imm + offs]; # 1/2/4/8/16 bytes

    function load_elwidthed(rd, rs, opwidth, unsigned):
      destwid = int_csr[rd].elwidth # destination element width
      rd = int_csr[rd].active ? int_csr[rd].regidx : rd;
      rs = int_csr[rs].active ? int_csr[rs].regidx : rs;
      ps = get_pred_val(FALSE, rs); # predication on src
      pd = get_pred_val(FALSE, rd); # ... AND on dest
      for (int i = 0, int j = 0; i < VL && j < VL;):
        if (int_csr[rs].isvec) while (!(ps & 1<<i)) i++;
        if (int_csr[rd].isvec) while (!(pd & 1<<j)) j++;
        val = load_memory(rs, imm, i, opwidth)
        if unsigned:
            val = zero_extend(val, min(opwidth, bitwidth))
        else:
            val = sign_extend(val, min(opwidth, bitwidth))
        set_polymorphed_reg(rd, bitwidth, j, val)
        if (int_csr[rs].isvec) i++;
        if (int_csr[rd].isvec) j++; else break;

Note:

* when comparing against for example the twin-predicated c.mv
  pseudo-code, the pattern of independent incrementing of rd and rs
  is preserved unchanged.
* just as with the c.mv pseudocode, zeroing is not included and must be
  taken into account (TODO).
* that due to the use of a twin-predication algorithm, LOAD/STORE also
  take on the same VSPLAT, VINSERT, VREDUCE, VEXTRACT, VGATHER and
  VSCATTER characteristics.
* that due to the use of the same set\_polymorphed\_reg pseudocode,
  a destination that is not vectorised (marked as scalar) will
  result in the element being fully sign-extended or zero-extended
  out to the full register file bitwidth (XLEN).  When the source
  is also marked as scalar, this is how the compatibility with
  standard RV LOAD/STORE is preserved by this algorithm.

### Example Tables showing LOAD elements

This section contains examples of vectorised LOAD operations, showing
how the two stage process works (three if zero/sign-extension is included).


#### Example: LD x8, x5(0), x8 CSR-elwidth=32, x5 CSR-elwidth=16, VL=7

This is:

* a 64-bit load, with an offset of zero
* with a source-address elwidth of 16-bit
* into a destination-register with an elwidth of 32-bit
* where VL=7
* from register x5 (actually x5-x6) to x8 (actually x8 to half of x11)
* RV64, where XLEN=64 is assumed.

First, the memory table, which, due to the element width being 16 and the
operation being LD (64), the 64-bits loaded from memory are subdivided
into groups of **four** elements.  And, with VL being 7 (deliberately
to illustrate that this is reasonable and possible), the first four are
sourced from the offset addresses pointed to by x5, and the next three
from the ofset addresses pointed to by the next contiguous register, x6:

[[!table  data="""
addr | byte 0 | byte 1 | byte 2 | byte 3 | byte 4 | byte 5 | byte 6 | byte 7 |
@x5  | elem 0         || elem 1         || elem 2         || elem 3         ||
@x6  | elem 4         || elem 5         || elem 6         || not loaded     ||
"""]]

Next, the elements are zero-extended from 16-bit to 32-bit, as whilst
the elwidth CSR entry for x5 is 16-bit, the destination elwidth on x8 is 32.

[[!table  data="""
byte 3 | byte 2 | byte 1 | byte 0 |
0x0    | 0x0    | elem0          ||
0x0    | 0x0    | elem1          ||
0x0    | 0x0    | elem2          ||
0x0    | 0x0    | elem3          ||
0x0    | 0x0    | elem4          ||
0x0    | 0x0    | elem5          ||
0x0    | 0x0    | elem6          ||
0x0    | 0x0    | elem7          ||
"""]]

Lastly, the elements are stored in contiguous blocks, as if x8 was also
byte-addressable "memory".  That "memory" happens to cover registers
x8, x9, x10 and x11, with the last 32 "bits" of x11 being **UNMODIFIED**:

[[!table  data="""
reg# | byte 7 | byte 6 | byte 5 | byte 4 | byte 3 | byte 2 | byte 1 | byte 0 |
x8   | 0x0    | 0x0    | elem 1         || 0x0    | 0x0    | elem 0         ||
x9   | 0x0    | 0x0    | elem 3         || 0x0    | 0x0    | elem 2         ||
x10  | 0x0    | 0x0    | elem 5         || 0x0    | 0x0    | elem 4         ||
x11  | **UNMODIFIED**                 |||| 0x0    | 0x0    | elem 6         ||
"""]]

Thus we have data that is loaded from the **addresses** pointed to by
x5 and x6, zero-extended from 16-bit to 32-bit, stored in the **registers**
x8 through to half of x11.
The end result is that elements 0 and 1 end up in x8, with element 8 being
shifted up 32 bits, and so on, until finally element 6 is in the
LSBs of x11.

Note that whilst the memory addressing table is shown left-to-right byte order,
the registers are shown in right-to-left (MSB) order.  This does **not**
imply that bit or byte-reversal is carried out: it's just easier to visualise
memory as being contiguous bytes, and emphasises that registers are not
really actually "memory" as such.

## Why SV bitwidth specification is restricted to 4 entries

The four entries for SV element bitwidths only allows three over-rides:

* 8 bit
* 16 hit
* 32 bit

This would seem inadequate, surely it would be better to have 3 bits or
more and allow 64, 128 and some other options besides.  The answer here
is, it gets too complex, no RV128 implementation yet exists, and so RV64's
default is 64 bit, so the 4 major element widths are covered anyway.

There is an absolutely crucial aspect oF SV here that explicitly
needs spelling out, and it's whether the "vectorised" bit is set in
the Register's CSR entry.

If "vectorised" is clear (not set), this indicates that the operation
is "scalar".  Under these circumstances, when set on a destination (RD),
then sign-extension and zero-extension, whilst changed to match the
override bitwidth (if set), will erase the **full** register entry
(64-bit if RV64).

When vectorised is *set*, this indicates that the operation now treats
**elements** as if they were independent registers, so regardless of
the length, any parts of a given actual register that are not involved
in the operation are **NOT** modified, but are **PRESERVED**.

For example:

* when the vector bit is clear and elwidth set to 16 on the destination
  register, operations are truncated to 16 bit and then sign or zero
  extended to the *FULL* XLEN register width.
* when the vector bit is set, elwidth is 16 and VL=1 (or other value where
  groups of elwidth sized elements do not fill an entire XLEN register),
  the "top" bits of the destination register do *NOT* get modified, zero'd
  or otherwise overwritten.

SIMD micro-architectures may implement this by using predication on
any elements in a given actual register that are beyond the end of
multi-element operation.

Other microarchitectures may choose to provide byte-level write-enable
lines on the register file, such that each 64 bit register in an RV64
system requires 8 WE lines.  Scalar RV64 operations would require
activation of all 8 lines, where SV elwidth based operations would
activate the required subset of those byte-level write lines.

Example:

* rs1, rs2 and rd are all set to 8-bit
* VL is set to 3
* RV64 architecture is set (UXL=64)
* add operation is carried out
* bits 0-23 of RD are modified to be rs1[23..16] + rs2[23..16]
  concatenated with similar add operations on bits 15..8 and 7..0
* bits 24 through 63 **remain as they originally were**.

Example SIMD micro-architectural implementation:

* SIMD architecture works out the nearest round number of elements
  that would fit into a full RV64 register (in this case: 8)
* SIMD architecture creates a hidden predicate, binary 0b00000111
  i.e. the bottom 3 bits set (VL=3) and the top 5 bits clear
* SIMD architecture goes ahead with the add operation as if it
  was a full 8-wide batch of 8 adds
* SIMD architecture passes top 5 elements through the adders
  (which are "disabled" due to zero-bit predication)
* SIMD architecture gets the 5 unmodified top 8-bits back unmodified
  and stores them in rd.

This requires a read on rd, however this is required anyway in order
to support non-zeroing mode.

## Polymorphic floating-point

Standard scalar RV integer operations base the register width on XLEN,
which may be changed (UXL in USTATUS, and the corresponding MXL and
SXL in MSTATUS and SSTATUS respectively).  Integer LOAD, STORE and
arithmetic operations are therefore restricted to an active XLEN bits,
with sign or zero extension to pad out the upper bits when XLEN has
been dynamically set to less than the actual register size.

For scalar floating-point, the active (used / changed) bits are
specified exclusively by the operation: ADD.S specifies an active
32-bits, with the upper bits of the source registers needing to
be all 1s ("NaN-boxed"), and the destination upper bits being
*set* to all 1s (including on LOAD/STOREs).

Where elwidth is set to default (on any source or the destination)
it is obvious that this NaN-boxing behaviour can and should be
preserved.  When elwidth is non-default things are less obvious,
so need to be thought through.  Here is a normal (scalar) sequence,
assuming an RV64 which supports Quad (128-bit) FLEN:

* FLD loads 64-bit wide from memory.  Top 64 MSBs are set to all 1s
* ADD.D performs a 64-bit-wide add.  Top 64 MSBs of destination set to 1s.
* FSD stores lowest 64-bits from the 128-bit-wide register to memory:
  top 64 MSBs ignored.

Therefore it makes sense to mirror this behaviour when, for example,
elwidth is set to 32.  Assume elwidth set to 32 on all source and
destination registers:

* FLD loads 64-bit wide from memory as **two** 32-bit single-precision
  floating-point numbers.
* ADD.D performs **two** 32-bit-wide adds, storing one of the adds
  in bits 0-31 and the second in bits 32-63.
* FSD stores lowest 64-bits from the 128-bit-wide register to memory

Here's the thing: it does not make sense to overwrite the top 64 MSBs
of the registers either during the FLD **or** the ADD.D.  The reason
is that, effectively, the top 64 MSBs actually represent a completely
independent 64-bit register, so overwriting it is not only gratuitous
but may actually be harmful for a future extension to SV which may
have a way to directly access those top 64 bits.

The decision is therefore **not** to touch the upper parts of floating-point
registers whereever elwidth is set to non-default values, including
when "isvec" is false in a given register's CSR entry.  Only when the
elwidth is set to default **and** isvec is false will the standard
RV behaviour be followed, namely that the upper bits be modified.

Ultimately if elwidth is default and isvec false on *all* source
and destination registers, a SimpleV instruction defaults completely
to standard RV scalar behaviour (this holds true for **all** operations,
right across the board).

The nice thing here is that ADD.S, ADD.D and ADD.Q when elwidth are
non-default values are effectively all the same: they all still perform
multiple ADD operations, just at different widths.  A future extension
to SimpleV may actually allow ADD.S to access the upper bits of the
register, effectively breaking down a 128-bit register into a bank
of 4 independently-accesible 32-bit registers.

In the meantime, although when e.g. setting VL to 8 it would technically
make no difference to the ALU whether ADD.S, ADD.D or ADD.Q is used,
using ADD.Q may be an easy way to signal to the microarchitecture that
it is to receive a higher VL value.  On a superscalar OoO architecture
there may be absolutely no difference, however on simpler SIMD-style
microarchitectures they may not necessarily have the infrastructure in
place to know the difference, such that when VL=8 and an ADD.D instruction
is issued, it completes in 2 cycles (or more) rather than one, where
if an ADD.Q had been issued instead on such simpler microarchitectures
it would complete in one.

## Specific instruction walk-throughs

This section covers walk-throughs of the above-outlined procedure
for converting standard RISC-V scalar arithmetic operations to
polymorphic widths, to ensure that it is correct.

### add

Standard Scalar RV32/RV64 (xlen):

* RS1 @ xlen bits
* RS2 @ xlen bits
* add @ xlen bits
* RD @ xlen bits

Polymorphic variant:

* RS1 @ rs1 bits, zero-extended to max(rs1, rs2) bits
* RS2 @ rs2 bits, zero-extended to max(rs1, rs2) bits
* add @ max(rs1, rs2) bits
* RD @ rd bits.  zero-extend to rd if rd > max(rs1, rs2) otherwise truncate

Note here that polymorphic add zero-extends its source operands,
where addw sign-extends.

### addw

The RV Specification specifically states that "W" variants of arithmetic
operations always produce 32-bit signed values.  In a polymorphic
environment it is reasonable to assume that the signed aspect is
preserved, where it is the length of the operands and the result
that may be changed.

Standard Scalar RV64 (xlen):

* RS1 @ xlen bits
* RS2 @ xlen bits
* add @ xlen bits
* RD @ xlen bits, truncate add to 32-bit and sign-extend to xlen.

Polymorphic variant:

* RS1 @ rs1 bits, sign-extended to max(rs1, rs2) bits
* RS2 @ rs2 bits, sign-extended to max(rs1, rs2) bits
* add @ max(rs1, rs2) bits
* RD @ rd bits. sign-extend to rd if rd > max(rs1, rs2) otherwise truncate

Note here that polymorphic addw sign-extends its source operands,
where add zero-extends.

This requires a little more in-depth analysis.  Where the bitwidth of
rs1 equals the bitwidth of rs2, no sign-extending will occur.  It is
only where the bitwidth of either rs1 or rs2 are different, will the
lesser-width operand be sign-extended.

Effectively however, both rs1 and rs2 are being sign-extended (or
truncated), where for add they are both zero-extended.  This holds true
for all arithmetic operations ending with "W".

### addiw

Standard Scalar RV64I:

* RS1 @ xlen bits, truncated to 32-bit
* immed @ 12 bits, sign-extended to 32-bit
* add @ 32 bits
* RD @ rd bits.  sign-extend to rd if rd > 32, otherwise truncate.

Polymorphic variant:

* RS1 @ rs1 bits
* immed @ 12 bits, sign-extend to max(rs1, 12) bits
* add @ max(rs1, 12) bits
* RD @ rd bits. sign-extend to rd if rd > max(rs1, 12) otherwise truncate

# Predication Element Zeroing

The introduction of zeroing on traditional vector predication is usually
intended as an optimisation for lane-based microarchitectures with register
renaming to be able to save power by avoiding a register read on elements
that are passed through en-masse through the ALU.  Simpler microarchitectures
do not have this issue: they simply do not pass the element through to
the ALU at all, and therefore do not store it back in the destination.
More complex non-lane-based micro-architectures can, when zeroing is
not set, use the predication bits to simply avoid sending element-based
operations to the ALUs, entirely: thus, over the long term, potentially
keeping all ALUs 100% occupied even when elements are predicated out.

SimpleV's design principle is not based on or influenced by
microarchitectural design factors: it is a hardware-level API.
Therefore, looking purely at whether zeroing is *useful* or not,
(whether less instructions are needed for certain scenarios),
given that a case can be made for zeroing *and* non-zeroing, the
decision was taken to add support for both.

## Single-predication (based on destination register)

Zeroing on predication for arithmetic operations is taken from
the destination register's predicate.  i.e. the predication *and*
zeroing settings to be applied to the whole operation come from the
CSR Predication table entry for the destination register.
Thus when zeroing is set on predication of a destination element,
if the predication bit is clear, then the destination element is *set*
to zero (twin-predication is slightly different, and will be covered
next).

Thus the pseudo-code loop for a predicated arithmetic operation
is modified to as follows:

      for (i = 0; i < VL; i++)
        if not zeroing: # an optimisation
           while (!(predval & 1<<i) && i < VL)
             if (int_vec[rd ].isvector)  { id += 1; }
             if (int_vec[rs1].isvector)  { irs1 += 1; }
             if (int_vec[rs2].isvector)  { irs2 += 1; }
           if i == VL:
             return
        if (predval & 1<<i)
           src1 = ....
           src2 = ...
           else:
               result = src1 + src2 # actual add (or other op) here
           set_polymorphed_reg(rd, destwid, ird, result)
           if int_vec[rd].ffirst and result == 0:
              VL = i # result was zero, end loop early, return VL
              return
           if (!int_vec[rd].isvector) return
        else if zeroing:
           result = 0
           set_polymorphed_reg(rd, destwid, ird, result)
        if (int_vec[rd ].isvector)  { id += 1; }
        else if (predval & 1<<i) return
        if (int_vec[rs1].isvector)  { irs1 += 1; }
        if (int_vec[rs2].isvector)  { irs2 += 1; }
        if (rd == VL or rs1 == VL or rs2 == VL): return

The optimisation to skip elements entirely is only possible for certain
micro-architectures when zeroing is not set.  However for lane-based
micro-architectures this optimisation may not be practical, as it
implies that elements end up in different "lanes".  Under these
circumstances it is perfectly fine to simply have the lanes
"inactive" for predicated elements, even though it results in
less than 100% ALU utilisation.

## Twin-predication (based on source and destination register)

Twin-predication is not that much different, except that that
the source is independently zero-predicated from the destination.
This means that the source may be zero-predicated *or* the
destination zero-predicated *or both*, or neither.

When with twin-predication, zeroing is set on the source and not
the destination, if a predicate bit is set it indicates that a zero
data element is passed through the operation (the exception being:
if the source data element is to be treated as an address - a LOAD -
then the data returned *from* the LOAD is zero, rather than looking up an
*address* of zero.

When zeroing is set on the destination and not the source, then just
as with single-predicated operations, a zero is stored into the destination
element (or target memory address for a STORE).

Zeroing on both source and destination effectively result in a bitwise
NOR operation of the source and destination predicate: the result is that
where either source predicate OR destination predicate is set to 0,
a zero element will ultimately end up in the destination register.

However: this may not necessarily be the case for all operations;
implementors, particularly of custom instructions, clearly need to
think through the implications in each and every case.

Here is pseudo-code for a twin zero-predicated operation:

    function op_mv(rd, rs) # MV not VMV!
      rd = int_csr[rd].active ? int_csr[rd].regidx : rd;
      rs = int_csr[rs].active ? int_csr[rs].regidx : rs;
      ps, zerosrc = get_pred_val(FALSE, rs); # predication on src
      pd, zerodst = get_pred_val(FALSE, rd); # ... AND on dest
      for (int i = 0, int j = 0; i < VL && j < VL):
        if (int_csr[rs].isvec && !zerosrc) while (!(ps & 1<<i)) i++;
        if (int_csr[rd].isvec && !zerodst) while (!(pd & 1<<j)) j++;
        if ((pd & 1<<j))
            if ((pd & 1<<j))
                sourcedata = ireg[rs+i];
            else
                sourcedata = 0
            ireg[rd+j] <= sourcedata
        else if (zerodst)
            ireg[rd+j] <= 0
        if (int_csr[rs].isvec)
            i++;
        if (int_csr[rd].isvec)
            j++;
        else
            if ((pd & 1<<j))
                break;

Note that in the instance where the destination is a scalar, the hardware
loop is ended the moment a value *or a zero* is placed into the destination
register/element.  Also note that, for clarity, variable element widths
have been left out of the above.

# Subsets of RV functionality

This section describes the differences when SV is implemented on top of
different subsets of RV.

## Common options

It is permitted to only implement SVprefix and not the VBLOCK instruction
format option, and vice-versa.  UNIX Platforms **MUST** raise illegal
instruction on seeing an unsupported VBLOCK or SVprefix opcode, so that
traps may emulate the format.

It is permitted in SVprefix to either not implement VL or not implement
SUBVL (see [[sv_prefix_proposal]] for full details. Again, UNIX Platforms
*MUST* raise illegal instruction on implementations that do not support
VL or SUBVL.

It is permitted to limit the size of either (or both) the register files
down to the original size of the standard RV architecture.  However, below
the mandatory limits set in the RV standard will result in non-compliance
with the SV Specification.

## RV32 / RV32F

When RV32 or RV32F is implemented, XLEN is set to 32, and thus the
maximum limit for predication is also restricted to 32 bits.  Whilst not
actually specifically an "option" it is worth noting.

## RV32G

Normally in standard RV32 it does not make much sense to have
RV32G, The critical instructions that are missing in standard RV32
are those for moving data to and from the double-width floating-point
registers into the integer ones, as well as the FCVT routines.

In an earlier draft of SV, it was possible to specify an elwidth
of double the standard register size: this had to be dropped,
and may be reintroduced in future revisions.

## RV32 (not RV32F / RV32G) and RV64 (not RV64F / RV64G)

When floating-point is not implemented, the size of the User Register and
Predication CSR tables may be halved, to only 4 2x16-bit CSRs (8 entries
per table).

## RV32E

In embedded scenarios the User Register and Predication CSRs may be
dropped entirely, or optionally limited to 1 CSR, such that the combined
number of entries from the M-Mode CSR Register table plus U-Mode
CSR Register table is either 4 16-bit entries or (if the U-Mode is
zero) only 2 16-bit entries (M-Mode CSR table only).  Likewise for
the Predication CSR tables.

RV32E is the most likely candidate for simply detecting that registers
are marked as "vectorised", and generating an appropriate exception
for the VL loop to be implemented in software.

## RV128

RV128 has not been especially considered, here, however it has some
extremely large possibilities: double the element width implies
256-bit operands, spanning 2 128-bit registers each, and predication
of total length 128 bit given that XLEN is now 128.

# Example usage

TODO evaluate strncpy and strlen
<https://groups.google.com/forum/m/#!msg/comp.arch/bGBeaNjAKvc/_vbqyxTUAQAJ>

## strncpy

RVV version: <a name="strncpy"></>

    strncpy: 
        mv a3, a0               # Copy dst 
    loop: 
        setvli x0, a2, vint8    # Vectors of bytes. 
        vlbff.v v1, (a1)        # Get src bytes 
        vseq.vi v0, v1, 0       # Flag zero bytes 
        vmfirst a4, v0          # Zero found? 
        vmsif.v v0, v0          # Set mask up to and including zero byte.
        vsb.v v1, (a3), v0.t    # Write out bytes 
        bgez a4, exit           # Done 
        csrr t1, vl             # Get number of bytes fetched 
        add a1, a1, t1          # Bump src pointer 
        sub a2, a2, t1          # Decrement count. 
        add a3, a3, t1          # Bump dst pointer 
        bnez a2, loop           # Anymore? 

    exit: 
        ret 

SV version (WIP):

    strncpy:
        mv a3, a0
        SETMVLI 8 # set max vector to 8
        RegCSR[a3] = 8bit, a3, scalar
        RegCSR[a1] = 8bit, a1, scalar
        RegCSR[t0] = 8bit, t0, vector
        PredTb[t0] = ffirst, x0, inv
    loop:
        SETVLI a2, t4 # t4 and VL now 1..8
        ldb t0, (a1) # t0 fail first mode
        bne t0, x0, allnonzero # still ff
        # VL points to last nonzero
        GETVL t4       # from bne tests
        addi t4, t4, 1 # include zero
        SETVL t4       # set exactly to t4
        stb t0, (a3)   # store incl zero
        ret            # end subroutine
    allnonzero:
        stb t0, (a3)    # VL legal range
        GETVL t4        # from bne tests
        add a1, a1, t4  # Bump src pointer 
        sub a2, a2, t4  # Decrement count. 
        add a3, a3, t4  # Bump dst pointer 
        bnez a2, loop   # Anymore? 
    exit:
        ret

Notes:

* Setting MVL to 8 is just an example. If enough registers are spare it
  may be set to XLEN which will require a bank of 8 scalar registers for
  a1, a3 and t0.
* obviously if that is done, t0 is not separated by 8 full registers, and
  would overwrite t1 thru t7. x80 would work well, as an example, instead.
* with the exception of the GETVL (a pseudo code alias for csrr), every
  single instruction above may use RVC.
* RVC C.BNEZ can be used because rs1' may be extended to the full 128
  registers through redirection
* RVC C.LW and C.SW may be used because the W format may be overridden by
  the 8 bit format. All of t0, a3 and a1 are overridden to make that work.
* with the exception of the GETVL, all Vector Context may be done in
  VBLOCK form.
* setting predication to x0 (zero) and invert on t0 is a trick to enable
  just ffirst on t0
* ldb and bne are both using t0, both in ffirst mode
* t0 vectorised, a1 scalar, both elwidth 8 bit: ldb enters "unit stride,
  vectorised, no (un)sign-extension or truncation" mode.
* ldb will end on illegal mem, reduce VL, but copied all sorts of stuff
  into t0 (could contain zeros).
* bne t0 x0 tests up to the NEW VL for nonzero, vector t0 against
  scalar x0
* however as t0 is in ffirst mode, the first fail wil ALSO stop the
  compares, and reduce VL as well
* the branch only goes to allnonzero if all tests succeed
* if it did not, we can safely increment VL by 1 (using a4) to include
  the zero.
* SETVL sets *exactly* the requested amount into VL.
* the SETVL just after allnonzero label is needed in case the ldb ffirst
  activates but the bne allzeros does not.
* this would cause the stb to copy up to the end of the legal memory
* of course, on the next loop the ldb would throw a trap, as a1 now
  points to the first illegal mem location.

## strcpy

RVV version:

        mv a3, a0             # Save start 
    loop: 
        setvli a1, x0, vint8  # byte vec, x0 (Zero reg) => use max hardware len
        vldbff.v v1, (a3)     # Get bytes
        csrr a1, vl           # Get bytes actually read e.g. if fault
        vseq.vi v0, v1, 0     # Set v0[i] where v1[i] = 0 
        add a3, a3, a1        # Bump pointer
        vmfirst a2, v0        # Find first set bit in mask, returns -1 if none
        bltz a2, loop         # Not found?
        add a0, a0, a1        # Sum start + bump
        add a3, a3, a2        # Add index of zero byte
        sub a0, a3, a0        # Subtract start address+bump
        ret 

## DAXPY

[[!inline raw="yes" pages="simple_v_extension/daxpy_example" ]]