RISC-V "V" Vector Extension
Version 0.8-draft-20191117

Contributors include: Alon Amid, Krste Asanovic, Allen Baum, Alex Bradbury, Tony Brewer, Chris Celio, Aliaksei Chapyzhenka, Silviu Chiricescu, Ken Dockser, Bob Dreyer, Roger Espasa, Sean Halle, John Hauser, David Horner, Bruce Hoult, Bill Huffman, Constantine Korikov, Ben Korpan, Robin Kruppe, Yunsup Lee, Guy Lemieux, Filip Moc, Rich Newell, Albert Ou, David Patterson, Colin Schmidt, Alex Solomatnikov, Steve Wallach, Andrew Waterman, Jim Wilson.

Known issues with current version:

- encoding needs better formatting

- vector memory consistency model needs to be clarified

- interaction with privileged architectures

## 1. Introduction

This document describes the draft of the RISC-V base vector extension. The document describes all the individual features of the base vector extension.

Note | This is a draft of a stable proposal for the vector specification to be used for implementation and evaluation. Once the draft label is removed, version 0.7 is intended to be stable enough to begin developing toolchains, functional simulators, and initial implementations, though will continue to evolve with minor changes and updates.

The term base vector extension is used informally to describe the standard set of vector ISA components. This draft spec is intended to capture how a certain vector function will be implemented as vector instructions, but to not yet determine what set of vector instructions are mandatory for a given platform.

Note | Each actual platform profile will formally specify the mandatory components of any vector extension adopted by that platform. The base vector extension can expected to be close to that which will eventually be used in the standard Unix platform profile that supports vectors. Other platforms, including embedded platforms, may choose to implement subsets of these extensions. The exact set of mandatory supported instructions for an implementation to be compliant with a given profile is subject to change until each profile spec is ratified.

The base vector extension is designed to act as a base for additional vector extensions in various domains, including cryptography and machine learning.

## 2. Implementation-defined Constant Parameters

Each hart supporting the vector extension defines three parameters:

1. The maximum size of a single vector element in bits, ELEN, which must be a power of 2.

2. The number of bits in a vector register, VLEN ≥ ELEN, which must be a power of 2.

3. The striping distance in bits, SLEN, which must be VLEN ≥ SLEN ≥ 32, and which must be a power of 2.

Note | Platform profiles may set further constraints on these parameters, for example, requiring that ELEN ≥ max(XLEN,FLEN), or requiring a minimum VLEN value, or setting an SLEN value.

The ISA supports writing binary code that under certain constraints will execute portably on harts with different values for these parameters.

Note | Code can be written that will expose differences in implementation parameters.

Note | Thread contexts with active vector state cannot be migrated during execution between harts that have any difference in VLEN, ELEN, or SLEN parameters.

## 3. Vector Extension Programmer’s Model

The vector extension adds 32 vector registers, and six unprivileged CSRs (`vstart`, `vxsat`, `vxrm`, `vtype`, `vl`, `vlenb`) to a base scalar RISC-V ISA. If the base scalar ISA does not include floating-point, then a `fcsr` register is also added to hold mirrors of the `vxsat` and `vxrm` CSRs as explained below.

Table 1. New vector CSRs
Address | Privilege | Name | Description
--- | --- | --- | ---
0x008 | URW | vstart | Vector start position
0x009 | URW | vxsat | Fixed-Point Saturate Flag
0x00A | URW | vxrm | Fixed-Point Rounding Mode
0xC20 | URO | vl | Vector length
0xC21 | URO | vtype | Vector data type register
0xC22 | URO | vlenb | VLEN/8 (vector register length in bytes)

### 3.1. Vector Registers

The vector extension adds 32 architectural vector registers, `v0`-`v31` to the base scalar RISC-V ISA.

Each vector register has a fixed VLEN bits of state.

Note | Zfinx ("F in X") is a new ISA option under consideration where floating-point instructions take their arguments from the integer register file. The 0.7 vector extension is also compatible with this option.

### 3.2. Vector type register, `vtype`

The read-only XLEN-wide vector type CSR, `vtype` provides the default type used to interpret the contents of the vector register file, and can only be updated by `vsetvl{i}` instructions. The vector type also determines the organization of elements in each vector register, and how multiple vector registers are grouped.

Note | Earlier drafts allowed the `vtype` register to be written using regular CSR writes. Allowing updates only via the `vsetvl{i}` instructions simplifies maintenance of the `vtype` register state.

In the base vector extension, the `vtype` register has three fields, `vill`, `vsew[2:0]`, and `vlmul[1:0]`.

Table 2. `vtype` register layout
Bits | Name | Description
--- | --- | ---
XLEN-1 | vill | Illegal value if set
XLEN-2:7 |  | Reserved (write 0)
6:5 | vediv[1:0] | Used by EDIV extension
4:2 | vsew[2:0] | Standard element width (SEW) setting
1:0 | vlmul[1:0] | Vector register group multiplier (LMUL) setting

Note | The smallest base implementation requires storage for only four bits of storage in `vtype`, two bits for `vsew[1:0]` and two bits for `vlmul[1:0]`. The illegal value represented by `vill` can be encoded using the illegal 64-bit combination in `vsew[1:0]` without requiring an additional storage bit.

Note | The vediv[1:0] field is used by the EDIV extension described below.

Note | Further standard and custom extensions to the vector base will extend these fields to support a greater variety of data types.

Note | It is anticipated that an extended 64-bit instruction encoding would allow these fields to be specified statically in the instruction encoding.

#### 3.2.1. Vector standard element width `vsew`

The value in `vsew` sets the dynamic standard element width (SEW). By default, a vector register is viewed as being divided into VLEN / SEW standard-width elements. In the base vector extension, only SEW up to max(XLEN,FLEN) are required to be supported.

Table 3. vsew[2:0] (standard element width) encoding
vsew[2:0] | SEW
--- | ---
0 | 0 | 0 | 8
0 | 0 | 1 | 16
0 | 1 | 0 | 32
0 | 1 | 1 | 64
1 | 0 | 0 | 128
1 | 0 | 1 | 256
1 | 1 | 0 | 512
1 | 1 | 1 | 1024

Table 4. Example VLEN = 128 bits
SEW | Elements per vector register
--- | ---
64 | 2
32 | 4
16 | 8
8 | 16

#### 3.2.2. Vector Register Grouping (`vlmul`)

Multiple vector registers can be grouped together, so that a single vector instruction can operate on multiple vector registers. Vector register groups allow double-width or larger elements to be operated on with the same vector length as standard-width elements. Vector register groups also provide greater execution efficiency for longer application vectors.

The term vector register group is used herein to refer to one or more vector registers used as a single operand to a vector instruction. The number of vector registers in a group, LMUL, is an integer power of two set by the `vlmul` field in `vtype` (LMUL = 2`vlmul[1:0]`).

The derived value VLMAX = LMUL*VLEN/SEW represents the maximum number of elements that can be operated on with a single vector instruction given the current SEW and LMUL settings.

vlmul | LMUL | #groups | VLMAX | Grouped registers
--- | --- | --- | --- | ---
0 | 0 | 1 | 32 | VLEN/SEW | vn (single register in group)
0 | 1 | 2 | 16 | 2*VLEN/SEW | vn, vn+1
1 | 0 | 4 | 8 | 4*VLEN/SEW | vn, …​, vn+3
1 | 1 | 8 | 4 | 8*VLEN/SEW | vn, …​, vn+7

When `vlmul=01`, then vector operations on register `v` n also operate on vector register `v` n+1, giving twice the vector length in bits. Instructions specifying a vector operand with an odd-numbered vector register will raise an illegal instruction exception.

Similarly, when `vlmul=10`, vector instructions operate on four vector registers at a time, and instructions specifying vector operands using vector register numbers that are not multiples of four will raise an illegal instruction exception. When `vlmul=11`, operations operate on eight vector registers at a time, and instructions specifying vector operands using register numbers that are not multiples of eight will raise an illegal instruction exception.

Note | This grouping pattern (LMUL=8 has groups `v0`,`v8`,`v16`,`v24`) was adopted in 0.6 initially to avoid issues with the floating-point calling convention when floating-point values were overlaid on the vector registers, whereas earlier versions kept the vector register group names contiguous (LMUL=8 has groups `v0`, `v1`, `v2`, `v3`). In versions v0.7 onwards, the floating-point registers are separate again.

Mask register instructions always operate on a single vector register, regardless of LMUL setting.

#### 3.2.3. Vector Type Illegal `vill`

The `vill` bit is used to encode that a previous `vsetvl{i}` instruction attempted to write an unsupported value to `vtype`.

Note | The `vill` bit is held in bit XLEN-1 of the CSR to support checking for illegal values with a branch on the sign bit.

If the `vill` bit is set, then any attempt to execute a vector instruction (other than a vector configuration instruction) will raise an illegal instruction exception.

When the `vill` bit is set, the other XLEN-1 bits in `vtype` shall be zero.

### 3.3. Vector Length Register `vl`

The XLEN-bit-wide read-only `vl` CSR can only be updated by the `vsetvli` and `vsetvl` instructions, and the fault-only-first vector load instruction variants.

The `vl` register holds an unsigned integer specifying the number of elements to be updated by a vector instruction. Elements in any destination vector register group with indices ≥ `vl` are unmodified during execution of a vector instruction. When `vstart` ≥ `vl`, no elements are updated in any destination vector register group.

Note | As a consequence, when `vl`=0, no elements are updated in the destination vector register group, regardless of `vstart`.

Note | Instructions that write a scalar integer or floating-point register do so even when `vstart` ≥ `vl`.

Note | The number of bits implemented in `vl` depends on the implementation’s maximum vector length of the smallest supported type. The smallest vector implementation, RV32IV, would need at least six bits in `vl` to hold the values 0-32 (with VLEN=32, LMUL=8 and SEW=8 results in VLMAX of 32).

### 3.4. Vector Byte Length `vlenb`

The XLEN-bit-wide read-only CSR `vlenb` holds the value VLEN/8, i.e., the vector register length in bytes.

Note | The value in `vlenb` is a design-time constant in any implementation.

Note | Without this CSR, several instructions are needed to calculate VLEN in bytes. The code has to disturb current `vl` and `vtype` settings which require them to be saved and restored.

### 3.5. Vector Start Index CSR `vstart`

The `vstart` read-write CSR specifies the index of the first element to be executed by a vector instruction.

Normally, `vstart` is only written by hardware on a trap on a vector instruction, with the `vstart` value representing the element on which the trap was taken (either a synchronous exception or an asynchronous interrupt), and at which execution should resume after a resumable trap is handled.

All vector instructions are defined to begin execution with the element number given in the `vstart` CSR, leaving earlier elements in the destination vector undisturbed, and to reset the `vstart` CSR to zero at the end of execution.

Note | All vector instructions, including `vsetvl{i}`, reset the `vstart` CSR to zero.

`vstart` is not modified by vector instructions that raise illegal-instruction exceptions.

If the value in the `vstart` register is greater than or equal to the vector length `vl` then no element operations are performed. The `vstart` register is then reset to zero.

The `vstart` CSR is defined to have only enough writable bits to hold the largest element index (one less than the maximum VLMAX) or lg2(VLEN) bits. The upper bits of the `vstart` CSR are hardwired to zero (reads zero, writes ignored).

Note | The maximum vector length is obtained with the largest LMUL setting (8) and the smallest SEW setting (8), so VLMAX_max = 8*VLEN/8 = VLEN. For example, for VLEN=256, `vstart` would have 8 bits to represent indices from 0 through 255.

The `vstart` CSR is writable by unprivileged code, but non-zero `vstart` values may cause vector instructions to run substantially slower on some implementations, so `vstart` should not be used by application programmers. A few vector instructions cannot be executed with a non-zero `vstart` value and will raise an illegal instruction exception as defined below.

Implementations are permitted to raise illegal instruction exceptions when attempting to execute a vector instruction with a value of `vstart` that the implementation can never produce when executing that same instruction with the same `vtype` setting.

Note | For example, some implementations will never take interrupts during execution of a vector arithmetic instruction, instead waiting until the instruction completes to take the interrupt. Such implementations are permitted to raise an illegal instruction exception when attempting to execute a vector arithmetic instruction when `vstart` is nonzero.

### 3.6. Vector Fixed-Point Rounding Mode Register `vxrm`

The vector fixed-point rounding-mode register holds a two-bit read-write rounding-mode field. The vector fixed-point rounding-mode is given a separate CSR address to allow independent access, but is also reflected as a field in the upper bits of `fcsr`. Systems without floating-point must add `fcsr` when adding the vector extension.

The fixed-point rounding algorithm is specified as follows. Suppose the pre-rounding result is `v`, and `d` bits of that result are to be rounded off. Then the rounded result is `(v >> d) + r`, where `r` depends on the rounding mode as specified in the following table.

Table 5. vxrm encoding
Bits [1:0] | Abbreviation | Rounding Mode | Rounding increment, `r`
--- | --- | --- | ---
0 | 0 | rnu | round-to-nearest-up (add +0.5 LSB) | `v[d-1]`
0 | 1 | rne | round-to-nearest-even | `v[d-1] & (v[d-2:0]≠0 | v[d])`
1 | 0 | rdn | round-down (truncate) | `0`
1 | 1 | rod | round-to-odd (OR bits into LSB, aka "jam") | `!v[d] & v[d-1:0]≠0`

The rounding function:

    roundoff(v, d) = (v >> d) + r

is used to represent this operation in the instruction descriptions below.

Bits[XLEN-1:2] should be written as zeros.

Note | The rounding mode can be set with a single `csrwi` instruction.

### 3.7. Vector Fixed-Point Saturation Flag `vxsat`

The `vxsat` CSR holds a single read-write bit that indicates if a fixed-point instruction has had to saturate an output value to fit into a destination format.

The `vxsat` bit is mirrored in the upper bits of `fcsr`.

### 3.8. Vector Fixed-Point Fields in `fcsr`

The `vxrm` and `vxsat` separate CSRs can also be accessed via fields in the floating-point CSR, `fcsr`. The `fcsr` register must be added to systems without floating-point that add a vector extension.

Table 6. fcsr layout
Bits | Name | Description
--- | --- | ---
10:9 | vxrm | Fixed-point rounding mode
8 | vxsat | Fixed-point accrued saturation flag
7:5 | frm | Floating-point rounding mode
4:0 | fflags | Floating-point accrued exception flags

Note | The fields are packed into `fcsr` to make context-save/restore faster.

### 3.9. State of Vector Extension at Reset

The vector extension must have a consistent state at reset. In particular, `vtype` and `vl` must have values that can be read and then restored with a single `vsetvl` instruction.

Note | It is recommended that at reset, `vtype.vill` is set, the remaining bits in `vtype` are zero, and `vl` is set to zero.

The `vstart`, `vxrm`, `vxsat` CSRs can have arbitrary values at reset.

Note | Any use of the vector unit will require an initial `vsetvl{i}`, which will reset `vstart`. The `vxrm` and `vxsat` fields should be reset explicitly in software before use.

The vector registers can have arbitrary values at reset.

## 4. Mapping of Vector Elements to Vector Register State

The following diagrams illustrate how different width elements are packed into the bytes of a vector register depending on the current SEW and LMUL settings, as well as implementation ELEN and VLEN. Elements are packed into each vector register with the least-significant byte in the lowest-numbered bits.

Note | Previous RISC-V vector proposals (< 0.6) hid this mapping from software, whereas this proposal has a specific mapping for all configurations, which reduces implementation flexibility but removes need for zeroing on config changes. Making the mapping explicit also has the advantage of simplifying oblivious context save-restore code, as the code can save the configuration in `vl` and `vtype`, then reset `vtype` to a convenient value (e.g., four vector groups of LMUL=8, SEW=ELEN) before saving all vector register bits without needing to parse the configuration. The reverse process will restore the state.

### 4.1. Mapping with LMUL=1

When LMUL=1, elements are simply packed in order from the least-significant to most-significant bits of the vector register.

Note | To increase readability, vector register layouts are drawn with bytes ordered from right to left with increasing byte address. Bits within an element are numbered in a little-endian format with increasing bit index from right to left corresponding to increasing magnitude.

      The element index is given in hexadecimal and is shown placed at the least-significant byte of the stored element. ELEN <=128 and LMUL=1 throughout.

     VLEN=32b

     Byte         3 2 1 0

     SEW=8b       3 2 1 0
     SEW=16b        1   0
     SEW=32b            0

     VLEN=64b

     Byte        7 6 5 4 3 2 1 0

     SEW=8b      7 6 5 4 3 2 1 0
     SEW=16b       3   2   1   0
     SEW=32b           1       0
     SEW=64b                   0

     VLEN=128b

     Byte        F E D C B A 9 8 7 6 5 4 3 2 1 0

     SEW=8b      F E D C B A 9 8 7 6 5 4 3 2 1 0
     SEW=16b       7   6   5   4   3   2   1   0
     SEW=32b           3       2       1       0
     SEW=64b                   1               0
     SEW=128b                                  0

     VLEN=256b

     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0

     SEW=8b   1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     SEW=16b     F   E   D   C   B   A   9   8   7   6   5   4   3   2   1   0
     SEW=32b         7       6       5       4       3       2       1       0
     SEW=64b                 3               2               1               0
     SEW=128b                                1                               0

### 4.2. Mapping with LMUL > 1

When vector registers are grouped, the elements of the vector register group are striped across the constituent vector registers. The striping distance in bits, SLEN, sets how many bits are packed contiguously into one vector register before moving to the next in the group.

For example, when SLEN = 128, the striping pattern is repeated in multiples of 128 bits. The first 128/SEW elements are packed contiguously at the start of the first vector register in the group. The next 128/SEW elements are packed contiguously at the start of the next vector register in the group. After packing the first LMUL*128/SEW elements at the start of each of the LMUL vector registers in the group, the second LMUL*128/SEW group of elements are packed into the second 128b segment of each of the vector registers in the group, and so on.

     Example 1: VLEN=32b, SEW=16b, LMUL=2

     Byte         3 2 1 0
     v2*n           1   0
     v2*n+1         3   2

     Example 2: VLEN=64b, SEW=32b, LMUL=2

     Byte         7 6 5 4 3 2 1 0
     v2*n               1       0
     v2*n+1             3       2

     Example 3: VLEN=128b, SEW=32b, LMUL=2

     Byte        F E D C B A 9 8 7 6 5 4 3 2 1 0
     v2*n              3       2       1       0
     v2*n+1            7       6       5       4

     Example 4: VLEN=256b, SEW=32b, LMUL=2

     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     v2*n            B       A       9       8       3       2       1       0
     v2*n+1          F       E       D       C       7       6       5       4

If SEW > SLEN, the striping pattern places one element in each vector register in the group before moving to the next vector register in the group. So, when LMUL=2, the even-numbered vector register contains the even-numbered elements of the vector and the odd-numbered vector register contains the odd-numbered elements of the vector.

Note | In most implementations, the striping distance SLEN ≥ ELEN.

     Example: VLEN=256b, SEW=256b, LMUL=2

     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     v2*n                                                                    0
     v2*n+1                                                                  1

When LMUL = 4, four vector registers hold elements as shown:

     Example 1: VLEN=32b, SLEN=32b, SEW=16b, LMUL=4,

     Byte         3 2 1 0
     v4*n           1   0
     v4*n+1         3   2
     v4*n+2         5   4
     v4*n+3         7   6

     Example 2: VLEN=64b, SLEN=64b, SEW=32b, LMUL=4

     Byte         7 6 5 4 3 2 1 0
     v4*n               1       0
     v4*n+1             3       2
     v4*n+2             5       4
     v4*n+3             7       6

     Example 3: VLEN=128b, SLEN=64b, SEW=32b, LMUL=4

     Byte          F E D C B A 9 8 7 6 5 4 3 2 1 0
     v4*n                9       8       1       0   32b elements
     v4*n+1              B       A       3       2
     v4*n+2              D       C       5       4
     v4*n+3              F       E       7       6

     Example 4: VLEN=128b, SLEN=128b, SEW=32b, LMUL=4

     Byte          F E D C B A 9 8 7 6 5 4 3 2 1 0
     v4*n                3       2       1       0   32b elements
     v4*n+1              7       6       5       4
     v4*n+2              B       A       9       8
     v4*n+3              F       E       D       C

     Example 5: VLEN=256b, SLEN=128b, SEW=32b, LMUL=4

     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     v4*n           13      12      11      10       3       2       1       0
     v4*n+1         17      16      15      14       7       6       5       4
     v4*n+2         1B      1A      19      18       B       A       9       8
     v4*n+3         1F      1E      1D      1C       F       E       D       C

     Example 6: VLEN=256b, SLEN=128b, SEW=256b, LMUL=4

     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     v4*n                                                                    0
     v4*n+1                                                                  1
     v4*n+2                                                                  2
     v4*n+3                                                                  3

A similar pattern is followed for LMUL = 8.

     Example: VLEN=256b, SLEN=128b, SEW=32b, LMUL=8

     Byte   1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
     v8*n         23      22      21      20       3       2       1       0
     v8*n+1       27      26      25      24       7       6       5       4
     v8*n+2       2B      2A      29      28       B       A       9       8
     v8*n+3       2F      2E      2D      2C       F       E       D       C
     v8*n+4       33      32      31      30      13      12      11      10
     v8*n+5       37      36      35      34      17      16      15      14
     v8*n+6       3B      3A      39      38      1B      1A      19      18
     v8*n+7       3F      3E      3D      3C      1F      1E      1D      1C

Different striping patterns are architecturally visible, but software can be written that produces the same results regardless of striping pattern. The primary constraint is to not change the LMUL used to access values held in a vector register group (i.e., do not read values with a different LMUL than used to write values to the group).

Note | The striping length SLEN for an implementation is set to optimize the tradeoff between datapath wiring for mixed-width operations and buffering needed to corner-turn wide vector unit-stride memory accesses into parallel accesses for the vector register file.

Note | The previous explicit configuration design (version < 0.6) allowed these tradeoffs to be managed at the microarchitectural level and optimized for each configuration.

### 4.3. Mapping across Mixed-Width Operations

The pattern used to map elements within a vector register group is designed to reduce datapath wiring when supporting operations across multiple element widths. The recommended software strategy in this case is to modify `vtype` dynamically to keep SEW/LMUL constant (and hence VLMAX constant).

The following example shows four different packed element widths (8b, 16b, 32b, 64b) in a VLEN=256b/SLEN=128b implementation. The vector register grouping factor (LMUL) is increased by the relative element size such that each group can hold the same number of vector elements (32 in this example) to simplify stripmining code. Any operation between elements with the same index only touches operand bits located within the same 128b portion of the datapath.

     VLEN=256b, SLEN=128b
     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0

     SEW=8b, LMUL=1, VLMAX=32

     v1       1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0

     SEW=16b, LMUL=2, VLMAX=32

     v2*n       17  16  15  14  13  12  11  10   7   6   5   4   3   2   1   0
     v2*n+1     1F  1E  1D  1C  1B  1A  19  18   F   E   D   C   B   A   9   8

     SEW=32b, LMUL=4, VLMAX=32

     v4*n           13      12      11      10       3       2       1       0
     v4*n+1         17      16      15      14       7       6       5       4
     v4*n+2         1B      1A      19      18       B       A       9       8
     v4*n+3         1F      1E      1D      1C       F       E       D       C

     SEW=64b, LMUL=8, VLMAX=32

     v8*n                   11              10               1               0
     v8*n+1                 13              12               3               2
     v8*n+2                 15              14               5               4
     v8*n+3                 17              16               7               6
     v8*n+4                 19              18               9               8
     v8*n+5                 1B              1A               B               A
     v8*n+6                 1D              1C               D               C
     v8*n+7                 1F              1E               F               E

Larger LMUL settings can also used to simply increase vector length to reduce instruction fetch and dispatch overheads, in cases where fewer logical vector registers are required.

The following table shows each possible constant SEW/LMUL operating point for loops with mixed-width operations.

           Numbers in columns are LMUL values, and each column
           represents constant SEW/LMUL operating point

     SEW/LMUL    1   2   4   8  16  32  64 128 256 512 1024

          SEW
            8    8   4   2   1
           16        8   4   2   1
           32            8   4   2   1
           64                8   4   2   1
          128                    8   4   2   1
          256                        8   4   2   1
          512                            8   4   2   1
         1024                                8   4   2   1

Note | Larger LMUL values can cause lower datapath utilization for short vectors if SLEN is less than the spatial datapath width. In the example above with VLEN=256b, SLEN=128b, and LMUL=8, if the implementation is purely spatial with a 256b-wide vector datapath, then for an application vector length less than 17, only half of the datapath will be active. The `vsetvl` instructions below could have a facility added to dynamically select an appropriate LMUL according to the required application vector length (AVL) and range of element widths.

Note | Narrower machines will set SLEN to be at least as large as the datapath spatial width, so there is no need to reduce LMUL. Wider machines might set SLEN lower than the spatial datapath width to reduce wiring for mixed-width operations (e.g., width=1024, ELEN=32, SLEN=128), in which case optimizing LMUL will be important.

### 4.4. Mask Register Layout

A vector mask occupies only one vector register regardless of SEW and LMUL. The mask bits that are used for each vector operation depends on the current SEW and LMUL setting.

The maximum number of elements in a vector operand is:

                   VLMAX = LMUL * VLEN/SEW

A mask is allocated for each element by dividing the mask register into VLEN/VLMAX fields. The size of each mask element in bits, MLEN, is:

                    MLEN = VLEN/VLMAX
                         = VLEN/(LMUL * VLEN/SEW)
                         = SEW/LMUL

The size of MLEN varies from ELEN (SEW=ELEN, LMUL=1) down to 1 (SEW=8b,LMUL=8), and hence a single vector register can always hold the entire mask register.

The mask bits for element i are located in bits [MLEN*i+(MLEN-1) : MLEN*i] of the mask register. When a mask element is written by a compare instruction, the low bit in the mask element is written with the compare result and the upper bits of the mask element are zeroed. Destination mask elements past the end of the current vector length are unchanged. When a value is read as a mask, only the least-significant bit of the mask element is used to control masking and the upper bits are ignored.

The pattern is such that for constant SEW/LMUL values, the effective predicate bits are located in the same bit of the mask vector register, which simplifies use of masking in loops with mixed-width elements.

     VLEN=32b

              Byte    3   2   1   0
     LMUL=1,SEW=8b
                      3   2   1   0  Element
                    [24][16][08][00] Mask bit position in decimal

     LMUL=2,SEW=16b
                          1       0
                        [08]    [00]
                          3       2
                        [24]    [16]

     LMUL=4,SEW=32b               0
                                [00]
                                  1
                                [08]
                                  2
                                [16]
                                  3
                                [24]

     LMUL=2,SEW=8b
                      3   2   1   0
                    [12][08][04][00]
                      7   6   5   4
                    [28][24][20][16]

     LMUL=8,SEW=32b
                                  0
                                [00]
                                  1
                                [04]
                                  2
                                [08]
                                  3
                                [12]
                                  4
                                [16]
                                  5
                                [20]
                                  6
                                [24]
                                  7
                                [28]

     LMUL=8,SEW=8b
                      3   2   1   0
                    [03][02][01][00]
                      7   6   5   4
                    [07][06][05][04]
                      B   A   9   8
                    [11][10][09][08]
                      F   E   D   C
                    [15][14][13][12]
                     13  12  11  10
                    [19][18][17][16]
                     17  16  15  14
                    [23][22][21][20]
                     1B  1A  19  18
                    [27][26][25][24]
                     1F  1E  1D  1C
                    [31][30][29][28]

     VLEN=256b, SLEN=128b
     Byte     1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0

     SEW=8b, LMUL=1, VLMAX=32

     v1       1F1E1D1C1B1A19181716151413121110 F E D C B A 9 8 7 6 5 4 3 2 1 0
            [248]          ...            [128] ...[96] ...[64] ...[32] ... [0] Mask bit positions in decimal

     SEW=16b, LMUL=2, VLMAX=32

     v2*n       17  16  15  14  13  12  11  10   7   6   5   4   3   2   1   0
              [184]          ...          [128]    ...     [32]    ...      [0]
     v2*n+1     1F  1E  1D  1C  1B  1A  19  18   F   E   D   C   B   A   9   8
              [248]          ...          [196]    ...     [96]    ...     [64]

     SEW=32b, LMUL=4, VLMAX=32

     v4*n           13      12      11      10       3       2       1       0
                  [152]        ...        [128]    [24]        ...          [0]
     v4*n+1         17      16      15      14       7       6       5       4
                  [184]        ...        [160]    [56]        ...         [32]
     v4*n+2         1B      1A      19      18       B       A       9       8
                  [116]        ...        [192]    [88]        ...         [64]
     v4*n+3         1F      1E      1D      1C       F       E       D       C
                  [248]        ...        [224]   [120]        ...         [96]

     SEW=64b, LMUL=8, VLMAX=32

     v8*n                   11              10               1               0
                          [136]           [128]             [8]             [0]
     v8*n+1                 13              12               3               2
                          [152]           [144]            [24]            [16]
     v8*n+2                 15              14               5               4
                          [168]           [160]            [40]            [32]
     v8*n+3                 17              16               7               6
                          [184]           [176]            [56]            [48]
     v8*n+4                 19              18               9               8
                          [200]           [192]            [72]            [64]
     v8*n+5                 1B              1A               B               A
                          [216]           [208]            [88]            [80]
     v8*n+6                 1D              1C               D               C
                          [232]           [224]           [104]            [96]
     v8*n+7                 1F              1E               F               E
                          [248]           [240]           [120]           [112]

## 5. Vector Instruction Formats

The instructions in the vector extension fit under three existing major opcodes (LOAD-FP, STORE-FP, AMO) and one new major opcode (OP-V).

Vector loads and stores are encoding within the scalar floating-point load and store major opcodes (LOAD-FP/STORE-FP). The vector load and store encodings repurpose a portion of the standard scalar floating-point load/store 12-bit immediate field to provide further vector instruction encoding, with bit 25 holding the standard vector mask bit (see Mask Encoding).

    Format for Vector Load Instructions under LOAD-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | mop | vm |  lumop   |    rs1    | width |    vd   |0000111| VL*  unit-stride
     nf  | mop | vm |   rs2    |    rs1    | width |    vd   |0000111| VLS* strided
     nf  | mop | vm |   vs2    |    rs1    | width |    vd   |0000111| VLX* indexed
      3     3     1      5           5         3         5       7

    Format for Vector Store Instructions under STORE-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | mop | vm |  sumop   |    rs1    | width |   vs3   |0100111| VS*  unit-stride
     nf  | mop | vm |   rs2    |    rs1    | width |   vs3   |0100111| VSS* strided
     nf  | mop | vm |   vs2    |    rs1    | width |   vs3   |0100111| VSX* indexed
      3     3     1      5           5         3         5        7

    Format for Vector AMO Instructions under AMO major opcode
    31    27 26  25  24      20 19       15 14   12 11      7 6     0
     amoop  |wd| vm |   vs2    |    rs1    | width | vs3/vd  |0101111| VAMO*
       5      1   1      5           5         3        5        7

    Formats for Vector Arithmetic Instructions under OP-V major opcode

    31       26  25   24      20 19      15 14   12 11      7 6     0
      funct6   | vm  |   vs2    |    vs1   | 0 0 0 |    vd   |1010111| OP-V (OPIVV)
      funct6   | vm  |   vs2    |    vs1   | 0 0 1 |  vd/rd  |1010111| OP-V (OPFVV)
      funct6   | vm  |   vs2    |    vs1   | 0 1 0 |  vd/rd  |1010111| OP-V (OPMVV)
      funct6   | vm  |   vs2    |   simm5  | 0 1 1 |    vd   |1010111| OP-V (OPIVI)
      funct6   | vm  |   vs2    |    rs1   | 1 0 0 |    vd   |1010111| OP-V (OPIVX)
      funct6   | vm  |   vs2    |    rs1   | 1 0 1 |    vd   |1010111| OP-V (OPFVF)
      funct6   | vm  |   vs2    |    rs1   | 1 1 0 |  vd/rd  |1010111| OP-V (OPMVX)
         6        1        5          5        3        5        7

    Formats for Vector Configuration Instructions under OP-V major opcode

     31 30         25 24      20 19      15 14   12 11      7 6     0
     0 |        zimm[10:0]      |    rs1   | 1 1 1 |    rd   |1010111| vsetvli
     1 |   000000    |   rs2    |    rs1   | 1 1 1 |    rd   |1010111| vsetvl
     1        6            5          5        3        5        7

Vector instructions can have scalar or vector source operands and produce scalar or vector results, and most vector instructions can be performed either unconditionally or conditionally under a mask.

Vector loads and stores move bit patterns between vector register elements and memory. Vector arithmetic instructions operate on values held in vector register elements.

### 5.1. Scalar Operands

Scalar operands can be immediates, or taken from the `x` registers, the `f` registers, or element 0 of a vector register. Scalar results are written to an `x` or `f` register or to element 0 of a vector register. Any vector register can be used to hold a scalar regardless of the current LMUL setting.

Note | In a change from v0.6, the floating-point registers no longer overlay the vector registers and scalars can now come from the integer or floating-point registers. Not overlaying the `f` registers reduces vector register pressure, avoids interactions with the standard calling convention, simplifies high-performance scalar floating-point design, and provides compatibility with the Zfinx ISA option. Overlaying `f` with `v` would provide the advantage of lowering the number of state bits in some implementations, but complicates high-performance designs and would prevent compatibility with the Zfinx ISA option.

### 5.2. Vector Operands

Vector operands or results may occupy one or more vector registers depending on LMUL, but are always specified using the lowest-numbered vector register in the group. Using other than the lowest-numbered vector register to specify a vector register group will result in an illegal instruction exception.

Some vector instructions consume and produce wider-width elements and so operate on a larger vector register group than that specified in `vlmul`. The largest vector register group used by an instruction can not be greater than 8 vector registers, and if an vector instruction would require greater than 8 vector registers in a group, an illegal instruction exception is raised. For example, attempting a widening operation producing a widened vector register group result with LMUL=8 will raise an illegal instruction exception. Widened scalar values, e..g, results from widening reduction operations, are held in the first element of a vector register and are treated as if LMUL=1.

### 5.3. Vector Masking

Masking is supported on many vector instructions. Element operations that are masked off do not modify the destination vector register element and never generate exceptions.

In the base vector extension, the mask value used to control execution of a masked vector instruction is always supplied by vector register `v0`. Only the least-significant bit of each element of the mask vector is used to control execution.

Note | Future vector extensions may provide longer instruction encodings with space for a full mask register specifier.

The destination vector register group for a masked vector instruction can only overlap the source mask register (`v0`) when LMUL=1. Otherwise, an illegal instruction exception is raised.

Note | This constraint supports restart with a non-zero `vstart` value.

Other vector registers can be used to hold working mask values, and mask vector logical operations are provided to perform predicate calculations.

#### 5.3.1. Mask Encoding

Where available, masking is encoded in a single-bit `vm` field in the instruction (`inst[25]`).

vm | Description
--- | ---
0 | vector result, only where v0[i].LSB = 1
1 | unmasked

Note | In earlier proposals, `vm` was a two-bit field `vm[1:0]` that provided both true and complement masking using `v0` as well as encoding scalar operations.

Vector masking is represented in assembler code as another vector operand, with `.t` indicating if operation occurs when `v0[i].LSB` is `1`. If no masking operand is specified, unmasked vector execution (`vm=1`) is assumed.

        vop.v*    v1, v2, v3, v0.t  # enabled where v0[i].LSB=1, m=0
        vop.v*    v1, v2, v3        # unmasked vector operation, m=1

Note | Even though the base only supports one vector mask register `v0` and only the true form of predication, the assembly syntax writes it out in full to be compatible with future extensions that might add a mask register specifier and supporting both true and complement masking. The `.t` suffix on the masking operand also helps to visually encode the use of a mask.

### 5.4. Prestart, Active, Inactive, Body, and Tail Element Definitions

The elements operated on during a vector instruction’s execution can be divided into four disjoint subsets.

- The prestart elements are those whose element index is less than the initial value in the `vstart` register. The prestart elements do not raise exceptions and do not update the destination vector register.

- The active elements during a vector instruction’s execution are the elements within the current vector length setting and where the current mask is enabled at that element position. The active elements can raise exceptions and update the destination vector register group.

- The inactive elements are the elements within the current vector length setting but where the current mask is disabled at that element position. The inactive elements do not raise exceptions and do not update any destination vector register.

- The tail elements during a vector instruction’s execution are the elements past the current vector length setting. The tail elements do not raise exceptions, and do not update any destination vector register group.

- In addition, another term, body, is used for the set of elements that are either active or inactive, i.e., after prestart but before the tail.

        for element index x
        prestart    = (0 <= x < vstart)
        mask(x)     = unmasked || v0[x].LSB == 1
        active(x)   = (vstart <= x < vl) && mask(x)
        inactive(x) = (vstart <= x < vl) && !mask(x)
        body(x)     = active(x) || inactive(x)
        tail(x)     = (vl <= x < VLMAX)

Note | The inactive and tail update rules leave unchanged destination elements that are not participating in the vector operation. Previous versions (v0.7) of the specification zeros the tail elements to reduce the complexity of implementations that implement register renaming. In version 0.8, this was changed to leave the tail elements undisturbed, which reduces complexity for simpler implementations without register renaming and reduces software overhead for some common sequences. A rationale is provided in a separate document: https://github.com/riscv/riscv-v-spec/blob/master/v-undisturbed-versus-zeroing.adoc

## 6. Configuration-Setting Instructions

A set of instructions are provided to allow rapid configuration of the values in `vl` and `vtype` to match application needs.

### 6.1. `vsetvli`/`vsetvl` instructions

     vsetvli rd, rs1, vtypei # rd = new vl, rs1 = AVL, vtypei = new vtype setting
                             # if rs1 = x0, then use current vector length
     vsetvl  rd, rs1, rs2    # rd = new vl, rs1 = AVL, rs2 = new vtype value
                             # if rs1 = x0, then use current vector length

The `vsetvli` instruction sets the `vtype` and `vl` CSRs based on its arguments, and writes the new value of `vl` into `rd`.

The new `vtype` setting is encoded in the immediate fields of `vsetvli` and in the `rs2` register for `vsetvl`.

    Formats for Vector Configuration Instructions under OP-V major opcode

     31 30         25 24      20 19      15 14   12 11      7 6     0
     0 |        zimm[10:0]      |    rs1   | 1 1 1 |    rd   |1010111| vsetvli
     1 |   000000    |   rs2    |    rs1   | 1 1 1 |    rd   |1010111| vsetvl
     1        6            5          5        3        5        7

Table 7. `vtype` register layout
Bits | Name | Description
--- | --- | ---
XLEN-1 | vill | Illegal value if set
XLEN-2:7 |  | Reserved (write 0)
6:5 | vediv[1:0] | Used by EDIV extension
4:2 | vsew[2:0] | Standard element width (SEW) setting
1:0 | vlmul[1:0] | Vector register group multiplier (LMUL) setting

     Suggested assembler names used for vtypei setting

     e8    #   8b elements
     e16   #  16b elements
     e32   #  32b elements
     e64   #  64b elements
     e128  # 128b elements

     m1   # Vlmul x1, assumed if m setting absent
     m2   # Vlmul x2
     m4   # Vlmul x4
     m8   # Vlmul x8

     d1   # EDIV 1, assumed if d setting absent
     d2   # EDIV 2
     d4   # EDIV 4
     d8   # EDIV 8

    Examples:
        vsetvli t0, a0, e8          # SEW= 8, LMUL=1, EDIV=1
        vsetvli t0, a0, e8,m2       # SEW= 8, LMUL=2, EDIV=1
        vsetvli t0, a0, e32,m2,d4   # SEW=32, LMUL=2, EDIV=4

If the `vtype` setting is not supported by the implementation, then the `vill` bit is set in `vtype`, the remaining bits in `vtype` are set to zero, and the `vl` register is also set to zero.

The requested application vector length (AVL) is passed in `rs1` as an unsigned integer. Using `x0` as the `rs1` register specifier requests an AVL equal to the current `vl`.

Note | Executing `vsetvl{i}` with `rs1`=`x0` is guaranteed to keep the current `vl` intact if VLMAX is not reduced.

Note | The behavior of `vsetvl{i}` does not depend on whether `rd`=`x0`. Setting `rd`=`x0` can be useful when the application already knows what value `vl` will assume, e.g., when changing SEW and LMUL by the same factor while keeping `vl` constant by setting `rs1`=`x0`.

Note | Software can set `vl` to VLMAX by requesting an AVL of -1.

Note | Earlier drafts used `rs1`=`x0` to request an AVL of VLMAX. The current design supports efficient manipulation of SEW without knowing AVL or `vl`. Requesting a `vl` of VLMAX requires just one additional instruction.

Note | Earlier drafts required a trap when setting `vtype` to an illegal value. However, this would have added the first data-dependent trap on a CSR write to the ISA. The current scheme also supports light-weight runtime interrogation of the supported vector unit configurations by checking if `vill` is clear for a given setting.

### 6.2. Constraints on Setting `vl`

The `vsetvl{i}` instructions first set VLMAX according to the `vtype` argument, then set `vl` obeying the following constraints:

1. `vl = AVL` if `AVL ≤ VLMAX`

2. `ceil(AVL / 2) ≤ vl ≤ VLMAX` if `AVL < (2 * VLMAX)`

3. `vl = VLMAX` if `AVL ≥ (2 * VLMAX)`

4. Deterministic on any given implementation for same input AVL and VLMAX values

5. These specific properties follow from the prior rules:

   1. `vl = 0` if `AVL = 0`

   2. `vl > 0` if `AVL > 0`

   3. `vl ≤ VLMAX`

   4. `vl ≤ AVL`

   5. a value read from `vl` when used as the AVL argument to `vsetvl{i}` results in the same value in `vl`, provided the resultant VLMAX equals the value of VLMAX at the time that `vl` was read

Note | The `vl` setting rules are designed to be sufficiently strict to preserve `vl` behavior across register spills and context swaps for `AVL ≤ VLMAX`, yet flexible enough to enable implementations to improve vector lane utilization for `AVL > VLMAX`. For example, this permits an implementation to set `vl = ceil(AVL / 2)` for `VLMAX < AVL < 2*VLMAX` in order to evenly distribute work over the last two iterations of a stripmine loop. Requirement 2 ensures that the first stripmine iteration of reduction loops uses the largest vector length of all iterations, even in the case of `AVL < 2*VLMAX`. This allows software to avoid needing to explicitly calculate a running maximum of vector lengths observed during a stripmined loop.

### 6.3. `vsetvl` Instruction

The `vsetvl` variant operates similarly to `vsetvli` except that it takes a `vtype` value from `rs2` and can be used for context restore, and when the `vtypei` field is too small to hold the desired setting.

Note | Several active complex types can be held in different `x` registers and swapped in as needed using `vsetvl`.

### 6.4. Examples

The SEW and LMUL settings can be changed dynamically to provide high throughput on mixed-width operations in a single loop.

    # Example: Load 16-bit values, widen multiply to 32b, shift 32b result
    # right by 3, store 32b values.

    # Loop using only widest elements:

    loop:
        vsetvli a3, a0, e32,m8  # Use only 32-bit elements
        vlh.v v8, (a1)          # Sign-extend 16b load values to 32b elements
          sll t1, a3, 1         # Multiply length by two bytes/element
          add a1, a1, t1        # Bump pointer
        vmul.vx  v8, v8, x10    # 32b multiply result
        vsrl.vi  v8, v8, 3      # Shift elements
        vsw.v v8, (a2)          # Store vector of 32b results
          sll t1, a3, 2         # Multiply length by four bytes/element
          add a2, a2, t1        # Bump pointer
          sub a0, a0, a3        # Decrement count
          bnez a0, loop         # Any more?

    # Alternative loop that switches element widths.

    loop:
        vsetvli a3, a0, e16,m4  # vtype = 16-bit integer vectors
        vlh.v v4, (a1)          # Get 16b vector
          slli t1, a3, 1        # Multiply length by two bytes/element
          add a1, a1, t1        # Bump pointer
        vwmul.vx v8, v4, x10    # 32b in <v8--v15>

        vsetvli x0, a0, e32,m8  # Operate on 32b values
        vsrl.vi v8, v8, 3
        vsw.v v8, (a2)          # Store vector of 32b
          slli t1, a3, 2        # Multiply length by four bytes/element
          add a2, a2, t1        # Bump pointer
          sub a0, a0, a3        # Decrement count
          bnez a0, loop         # Any more?

The second loop is more complex but will have greater performance on machines where 16b widening multiplies are faster than 32b integer multiplies, and where 16b vector load can run faster due to the narrower writes to the vector regfile.

## 7. Vector Loads and Stores

Vector loads and stores move values between vector registers and memory. Vector loads and stores are masked and do not raise exceptions on inactive elements. Masked vector loads do not update inactive elements in the destination vector register group. Masked vector stores only update active memory elements.

### 7.1. Vector Load/Store Instruction Encoding

Vector loads and stores are encoded within the scalar floating-point load and store major opcodes (LOAD-FP/STORE-FP). The vector load and store encodings repurpose a portion of the standard scalar floating-point load/store 12-bit immediate field to provide further vector instruction encoding, with bit 25 holding the standard vector mask bit (see Mask Encoding).

    Format for Vector Load Instructions under LOAD-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | mop | vm |  lumop   |    rs1    | width |    vd   |0000111| VL*  unit-stride
     nf  | mop | vm |   rs2    |    rs1    | width |    vd   |0000111| VLS* strided
     nf  | mop | vm |   vs2    |    rs1    | width |    vd   |0000111| VLX* indexed
      3     3     1      5           5         3         5       7

    Format for Vector Store Instructions under STORE-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | mop | vm |  sumop   |    rs1    | width |   vs3   |0100111| VS*  unit-stride
     nf  | mop | vm |   rs2    |    rs1    | width |   vs3   |0100111| VSS* strided
     nf  | mop | vm |   vs2    |    rs1    | width |   vs3   |0100111| VSX* indexed
      3     3     1      5           5         3         5        7

Field | Description
--- | ---
rs1[4:0] | specifies x register holding base address
rs2[4:0] | specifies x register holding stride
vs2[4:0] | specifies v register holding address offsets
vs3[4:0] | specifies v register holding store data
vd[4:0] | specifies v register destination of load
vm | specifies vector mask
width[2:0] | specifies size of memory elements, and distinguishes from FP scalar
mop[2:0] | specifies memory addressing mode
nf[2:0] | specifies the number of fields in each segment, for segment load/stores
lumop[4:0]/sumop[4:0] | are additional fields encoding variants of unit-stride instructions

### 7.2. Vector Load/Store Addressing Modes

The base vector extension supports unit-stride, strided, and indexed (scatter/gather) addressing modes. Vector load/store base registers and strides are taken from the GPR `x` registers.

The base effective address for all vector accesses is given by the contents of the `x` register named in `rs1`.

Vector unit-stride operations access elements stored contiguously in memory starting from the base effective address.

Vector strided operations access the first memory element at the base effective address, and then access subsequent elements at address increments given by the byte offset contained in the `x` register specified by `rs2`.

Vector indexed operations add the contents of each element of the vector offset operand specified by `vs2` to the base effective address to give the effective address of each element. The vector offset operand is treated as a vector of byte offsets. If the vector offset elements are narrower than XLEN, they are zero-extended to XLEN before adding to the base effective address. If the vector offset elements are wider than XLEN, the least-significant XLEN bits are used in the address calculation.

Note | Current PoR for vector indexed instructions requires that vector byte offset (vs2) and vector read/write data (vs3/vd) are of same width. One question is whether and how to allow for two sizes of vector operand in a vector indexed instruction? For example, for scatter/gather of byte values in a 64-bit address space without requiring bytes use 64b of space in a vector register.

The vector addressing modes are encoded using the 3-bit `mop[2:0]` field.

Table 8. encoding for loads
mop [2:0] | Description | Opcodes
--- | --- | ---
0 | 0 | 0 | zero-extended unit-stride | VLxU,VLE
0 | 0 | 1 | reserved |
0 | 1 | 0 | zero-extended strided | VLSxU, VLSE
0 | 1 | 1 | zero-extended indexed | VLXxU, VLXE
1 | 0 | 0 | sign-extended unit-stride | VLx (x!=E)
1 | 0 | 1 | reserved |
1 | 1 | 0 | sign-extended strided | VLSx (x!=E)
1 | 1 | 1 | sign-extended indexed | VLXx (x!=E)

Table 9. encoding for stores
mop [2:0] | Description | Opcodes
--- | --- | ---
0 | 0 | 0 | unit-stride | VSx
0 | 0 | 1 | reserved |
0 | 1 | 0 | strided | VSSx
0 | 1 | 1 | indexed-ordered | VSXx
1 | 0 | 0 | reserved |
1 | 0 | 1 | reserved |
1 | 1 | 0 | reserved |
1 | 1 | 1 | indexed-unordered | VSUXx

The vector indexed memory operations have two forms, ordered and unordered. The indexed-unordered stores do not preserve element ordering on stores.

Note | The indexed-unordered variant is provided as a potential implementation optimization. Implementations are free to ignore the optimization and implement indexed-unordered identically to indexed-ordered.

Additional unit-stride vector addressing modes are encoded using the 5-bit `lumop` and `sumop` fields in the unit-stride load and store instruction encodings respectively.

Table 10. lumop
lumop[4:0] | Description
--- | ---
0 | 0 | 0 | 0 | 0 | unit-stride
0 | 0 | x | x | x | reserved, x !=0
0 | 1 | 0 | 0 | 0 | unit-stride, whole registers
0 | 1 | x | x | x | reserved, x !=0
1 | 0 | 0 | 0 | 0 | unit-stride fault-only-first
1 | x | x | x | x | reserved, x!=0

Table 11. sumop
sumop[4:0] | Description
--- | ---
0 | 0 | 0 | 0 | 0 | unit-stride
0 | 0 | x | x | x | reserved, x !=0
0 | 1 | 0 | 0 | 0 | unit-stride, whole registers
0 | 1 | x | x | x | reserved, x !=0
1 | x | x | x | x | reserved

The `nf[2:0]` field encodes the number of fields in each segment. For regular vector loads and stores, `nf`=0, indicating that a single value is moved between a vector register group and memory at each element position. Larger values in the `nf` field are used to access multiple contiguous fields within a segment as described below in Section Vector Load/Store Segment Instructions (`Zvlsseg`).

Note | The `nf` field for segment load/stores has replaced the use of the same bits for an address offset field. The offset can be replaced with a single scalar integer calculation, while segment load/stores add more powerful primitives to move items to and from memory.

The `nf[2:0]` field also encodes the number of whole vector registers to transfer for the whole vector register load/store instructions.

### 7.3. Vector Load/Store Width Encoding

The vector loads and stores are encoded using the width values that are not claimed by the standard scalar floating-point loads and stores. Three of the width types encode vector loads and stores that move fixed-size memory elements of 8 bits, 16 bits, or 32 bits, while the fourth encoding moves SEW-bit memory elements.

| Width [2:0] | Mem bits | Reg bits | Opcode
--- | --- | --- | --- | ---
Standard scalar FP | 0 | 0 | 1 | 16 | FLEN | FLH/FSH
Standard scalar FP | 0 | 1 | 0 | 32 | FLEN | FLW/FSW
Standard scalar FP | 0 | 1 | 1 | 64 | FLEN | FLD/FSD
Standard scalar FP | 1 | 0 | 0 | 128 | FLEN | FLQ/FSQ
Vector byte | 0 | 0 | 0 | vl*8 | vl*SEW | VxB
Vector halfword | 1 | 0 | 1 | vl*16 | vl*SEW | VxH
Vector word | 1 | 1 | 0 | vl*32 | vl*SEW | VxW
Vector element | 1 | 1 | 1 | vl*SEW | vl*SEW | VxE

Mem bits is the size of element accessed in memory

Reg bits is the size of element accessed in register

Fixed-sized vector loads can optionally sign or zero-extend their memory element into the destination register element if the register element is wider than the memory element. A fixed-size vector load raises an illegal instruction exception if the destination register element is narrower than the memory element. The variable-sized load is encoded as if a zero-extended load, with what would be the sign-extended encoding of a variable-sized load currently reserved.

Fixed-size vector stores take their operand from the least-significant bits of the register element if the register element if wider than the memory element. Fixed-sized vector stores raise an illegal instruction exception if the memory element is wider than the register element.

### 7.4. Vector Unit-Stride Instructions

        # Vector unit-stride loads and stores

        # vd destination, rs1 base address, vm is mask encoding (v0.t or <missing>)
        vlb.v  vd, (rs1), vm # 8b signed
        vlh.v  vd, (rs1), vm # 16b signed
        vlw.v  vd, (rs1), vm # 32b signed

        vlbu.v vd, (rs1), vm # 8b unsigned
        vlhu.v vd, (rs1), vm # 16b unsigned
        vlwu.v vd, (rs1), vm # 32b unsigned

        vle.v  vd, (rs1), vm # SEW

        # vs3 store data, rs1 base address, vm is mask encoding (v0.t or <missing>)
        vsb.v  vs3, (rs1), vm  # 8b store
        vsh.v  vs3, (rs1), vm  # 16b store
        vsw.v  vs3, (rs1), vm  # 32b store
        vse.v  vs3, (rs1), vm  # SEW store

### 7.5. Vector Strided Instructions

        # Vector strided loads and stores

        # vd destination, rs1 base address, rs2 byte stride
        vlsb.v  vd, (rs1), rs2, vm # 8b
        vlsh.v  vd, (rs1), rs2, vm # 16b
        vlsw.v  vd, (rs1), rs2, vm # 32b

        vlsbu.v vd, (rs1), rs2, vm # unsigned 8b
        vlshu.v vd, (rs1), rs2, vm # unsigned 16b
        vlswu.v vd, (rs1), rs2, vm # unsigned 32b

        vlse.v  vd, (rs1), rs2, vm  # SEW

        # vs3 store data, rs1 base address, rs2 byte stride
        vssb.v vs3, (rs1), rs2, vm  # 8b
        vssh.v vs3, (rs1), rs2, vm  # 16b
        vssw.v vs3, (rs1), rs2, vm  # 32b
        vsse.v vs3, (rs1), rs2, vm  # SEW

Note | Negative and zero strides are supported.

### 7.6. Vector Indexed Instructions

        # Vector indexed loads and stores

        # vd destination, rs1 base address, vs2 indices
        vlxb.v  vd, (rs1), vs2, vm  # 8b
        vlxh.v  vd, (rs1), vs2, vm  # 16b
        vlxw.v  vd, (rs1), vs2, vm  # 32b

        vlxbu.v vd, (rs1), vs2, vm  # 8b unsigned
        vlxhu.v vd, (rs1), vs2, vm  # 16b unsigned
        vlxwu.v vd, (rs1), vs2, vm  # 32b unsigned

        vlxe.v  vd, (rs1), vs2, vm  # SEW

        # Vector ordered-indexed store instructions
        # vs3 store data, rs1 base address, vs2 indices
        vsxb.v vs3, (rs1), vs2, vm  # 8b
        vsxh.v vs3, (rs1), vs2, vm  # 16b
        vsxw.v vs3, (rs1), vs2, vm  # 32b
        vsxe.v vs3, (rs1), vs2, vm  # SEW

        # Vector unordered-indexed store instructions
        vsuxb.v vs3, (rs1), vs2, vm  # 8b
        vsuxh.v vs3, (rs1), vs2, vm  # 16b
        vsuxw.v vs3, (rs1), vs2, vm  # 32b
        vsuxe.v vs3, (rs1), vs2, vm  # SEW

### 7.7. Unit-stride Fault-Only-First Loads

The unit-stride fault-only-first load instructions are used to vectorize loops with data-dependent exit conditions (while loops). These instructions execute as a regular load except that they will only take a trap on element 0. If an element > 0 raises an exception, that element and all following elements in the destination vector register are not modified, and the vector length `vl` is reduced to the number of elements processed without a trap.

        vlbff.v  vd, (rs1), vm # 8b
        vlhff.v  vd, (rs1), vm # 16b
        vlwff.v  vd, (rs1), vm # 32b

        vlbuff.v vd, (rs1), vm # unsigned 8b
        vlhuff.v vd, (rs1), vm # unsigned 16b
        vlwuff.v vd, (rs1), vm # unsigned 32b

        vleff.v  vd, (rs1), vm # SEW

    strlen example using unit-stride fault-only-first instruction

    # size_t strlen(const char *str)
    # a0 holds *str

    strlen:
        mv a3, a0             # Save start
        li t0, -1             # Infinite AVL
    loop:
        vsetvli a1, t0, e8  # Vector of bytes of maximum length
        vlbff.v v1, (a3)      # Load bytes
        csrr a1, vl           # Get bytes read
        vmseq.vi v0, v1, 0    # Set v0[i] where v1[i] = 0
        vfirst.m a2, v0       # Find first set bit
        add a3, a3, a1        # Bump pointer
        bltz a2, loop         # Not found?

        add a0, a0, a1        # Sum start + bump
        add a3, a3, a2        # Add index
        sub a0, a3, a0        # Subtract start address+bump

        ret

Note | Strided and scatter/gather fault-only-first instructions are not provided as they represent a large security hole, allowing software to check multiple random pages for accessibility without experiencing a trap. The unit-stride versions only allow probing a region immediately contiguous to a known region, and so do not appreciably impact security. It is possible that security mitigations can be implemented to allow fault-only-first variants of non-contiguous accesses in future vector extensions.

### 7.8. Vector Load/Store Segment Instructions (`Zvlsseg`)

Note | This is being written as an extension but will likely be mandated in most profiles, as the operation is too generally useful to omit.

The vector load/store segment instructions move multiple contiguous fields in memory to and from consecutively numbered vector registers.

Note | These operations support operations on "array-of-structures" datatypes by unpacking each field in a structure into separate vector registers.

As for regular vector loads and stores, the width encoding gives the size of the memory elements, which are homogeneous in size, while SEW encodes the size of the register elements.

The three-bit `nf` field in the vector instruction encoding is an unsigned integer that contains one less than the number of fields per segment, NFIELDS.

nf[2:0] | NFIELDS
--- | ---
0 | 0 | 0 | 1
0 | 0 | 1 | 2
0 | 1 | 0 | 3
0 | 1 | 1 | 4
1 | 0 | 0 | 5
1 | 0 | 1 | 6
1 | 1 | 0 | 7
1 | 1 | 1 | 8

The LMUL setting must be such that LMUL * NFIELDS ⇐ 8, otherwise an illegal instruction exception is raised.

Note | The product LMUL * NFIELDS represents the number of underlying vector registers that will be touched by a segmented load or store instruction. This constraint makes this total no larger than 1/4 of the architectural register file, and the same as for regular operations with LMUL=8. This constraint could be weakened in a future draft.

Each field will be held in successively numbered vector register groups. When LMUL>1, each field will occupy a vector register group held in multiple successively numbered vector registers, and the vector register group for each field must follow the usual vector register alignment constraints (e.g., when LMUL=2 and NFIELDS=4, each field’s vector register group must start at an even vector register, but does not have to start at a multiple of 8 vector register number).

Note | An earlier version imposed a vector register number constraint, but this decreased ability to make use of all registers when NFIELDS was not a power of 2.

If the vector register numbers accessed by the segment load or store would increment past 31, then an illegal instruction exception is raised.

Note | This constraint is to help provide forward-compatibility with a future longer instruction encoding that has more addressable vector registers.

The `vl` register gives the number of structures to move, which is equal to the number of elements transferred to each vector register group. Masking is also applied at the level of whole structures.

If a trap is taken, `vstart` is in units of structures.

#### 7.8.1. Vector Unit-Stride Segment Loads and Stores

The vector unit-stride load and store segment instructions move packed contiguous segments ("array-of-structures") into multiple destination vector register groups.

Note | For segments with heterogeneous-sized fields, software can later unpack fields using additional instructions after the segment load brings the values into the separate vector registers.

The assembler prefixes `vlseg`/`vsseg` are used for unit-stride segment loads and stores respectively.

        # Format
        vlseg<nf>{b,h,w}.v vd, (rs1),  vm    # Unit-stride signed segment load template
        vlseg<nf>e.v vd, (rs1), vm           # Unit-stride segment load template
        vlseg<nf>{b,h,w}u.v vd, (rs1), vm    # Unit-stride unsigned segment load template
        vsseg<nf>{b,h,w,e}.v vs3, (rs1), vm  # Unit-stride segment store template

        # Examples
        vlseg2b.v vd, (rs1), vm   # Load vector of signed 2*1-byte segments into vd, vd+1
        vlseg3bu.v vd, (rs1), vm  # Load vector of unsigned 3*1-byte segments into vd, vd+1, vd+2
        vlseg7w.v vd, (rs1), vm   # Load vector of 7*4-byte segments into vd, vd+1, ... vd+6
        vlseg8e.v vd, (rs1), vm   # Load vector of 8*SEW-byte segments into vd, vd+1, .. vd+7

        vsseg3b.v vs3, (rs1), vm  # Store packed vector of 3*1-byte segments from vs3,vs3+1,vs3+2 to memory

For loads, the `vd` register will hold the first field loaded from the segment. For stores, the `vs3` register is read to provide the first field to be stored in each segment.

        # Example 1
        # Memory structure holds packed RGB pixels (24-bit data structure, 8bpp)
        vlseg3bu.v v8, (a0), vm
        # v8 holds the red pixels
        # v9 holds the green pixels
        # v10 holds the blue pixels

        # Example 2
        # Memory structure holds complex values, 32b for real and 32b for imaginary
        vlseg2w.v v8, (a0), vm
        # v8 holds real
        # v9 holds imaginary

There are also fault-only-first versions of the unit-stride instructions.

        # Template for vector fault-only-first unit-stride segment loads and stores.
        vlseg<nf>{b,h,w}ff.v vd, (rs1),  vm    # Unit-stride signed fault-only-first segment loads
        vlseg<nf>eff.v vd, (rs1),  vm          # Unit-stride fault-only-first segment loads
        vlseg<nf>{b,h,w}uff.v vd, (rs1),   vm  # Unit-stride unsigned fault-only-first segment loads

#### 7.8.2. Vector Strided Segment Loads and Stores

Vector strided segment loads and stores move contiguous segments where each segment is separated by the byte stride offset given in the `rs2` GPR argument.

Note | Negative and zero strides are supported.

        # Format
        vlsseg<nf>{b,h,w}.v vd, (rs1), rs2, vm    # Strided signed segment loads
        vlsseg<nf>e.v vd, (rs1), rs2, vm          # Strided segment loads
        vlsseg<nf>{b,h,w}u.v vd, (rs1), rs2, vm   # Strided unsigned segment loads
        vssseg<nf>{b,h,w,e}.v vs3, (rs1), rs2, vm # Strided segment stores

        # Examples
        vlsseg3b.v v4, (x5), x6   # Load bytes at addresses x5+i*x6   into v4[i],
                                  #  and bytes at addresses x5+i*x6+1 into v5[i],
                                  #  and bytes at addresses x5+i*x6+2 into v6[i].

        # Examples
        vssseg2w.v v2, (x5), x6   # Store words from v2[i] to address x5+i*x6
                                  #   and words from v3[i] to address x5+i*x6+4

For strided segment stores where the byte stride is such that segments could overlap in memory, the segments must appear to be written in element order.

#### 7.8.3. Vector Indexed Segment Loads and Stores

Vector indexed segment loads and stores move contiguous segments where each segment is located at an address given by adding the scalar base address in the `rs1` field to byte offsets in vector register `vs2`.

        # Format
        vlxseg<nf>{b,h,w}.v vd, (rs1), vs2, vm    # Indexed signed segment loads
        vlxseg<nf>e.v vd, (rs1), vs2, vm          # Indexed segment loads
        vlxseg<nf>{b,h,w}u.v vd, (rs1), vs2, vm   # Indexed unsigned segment loads
        vsxseg<nf>{b,h,w,e}.v vs3, (rs1), vs2, vm # Indexed segment stores

        # Examples
        vlxseg3bu.v v4, (x5), v3   # Load bytes at addresses x5+v3[i]   into v4[i],
                                  #  and bytes at addresses x5+v3[i]+1 into v5[i],
                                  #  and bytes at addresses x5+v3[i]+2 into v6[i].

        # Examples
        vsxseg2w.v v2, (x5), v5   # Store words from v2[i] to address x5+v5[i]
                                  #   and words from v3[i] to address x5+v5[i]+4

For vector indexed segment loads, the destination vector register groups cannot overlap the source vector register group (specified by `vs2`), nor can they overlap the mask register if masked, else an illegal instruction exception is raised.

Note | This constraint supports restart of indexed segment loads that raise exceptions partway through loading a structure.

Only ordered indexed segment stores are provided. The segments must appear to be written in element order.

### 7.9. Vector Load/Store Whole Register Instructions

Note | These instructions are still under early consideration for inclusion.

These instructions load and store whole vector registers (i.e., VLEN bits), ignoring the settings in the `vl` and `vtype` registers.

Note | These instructions are intended to be used to save and restore vector registers when the type and length of the current contents of the vector register is not known, or where modifying `vl` and `vtype` would be costly. Examples include compiler register spills, vector function calls where values are passed in vector registers, interrupt handlers, and OS context switches.

    Format for Vector Load Whole Register Instructions under LOAD-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | 000 | 1 |   01000   |    rs1    |  111  |    vd   |0000111| VL<nf>R

    Format for Vector Store Whole Register Instructions under STORE-FP major opcode
    31 29 28 26  25  24      20 19       15 14   12 11      7 6     0
     nf  | 000 | 1 |   01000   |    rs1    |  111  |   vs3   |0100111| VS<nf>R

Note | The vector whole register load instructions are encoded similar to unmasked zero-extended unit-stride loads of elements, with the `nf` field encoding how many vector registers to load and store. The vector whole register store instructions are encoded similar to unmasked unit-stride store of elements.

The instructions operate similarly to unmasked unit-stride load and store instructions of elements, with the base address passed in the scalar `x` register specified by `rs1`. The base address must be naturally aligned to ELEN/8 bytes, else a misaligned load or store exception may be raised.

The instructions transfer one or more vector registers as indicated by the setting of the `nf` field in the instruction. The base vector register number is specified by `vd` for loads and `vs3` for stores. The `nf` field encodes the number of vector registers to transfer, numbered successively after the base. The base register plus the `nf` value cannot exceed 31, else an illegal instruction exception is raised.

When multiple registers are transferred, the vector register contents are mapped to contiguous bytes in memory, with the lowest-numbered vector register held in the lowest-numbered memory addresses.

       # Format
       vl<nf>r.v vd, (rs1)  # Vector load of nf vector registers
       vl1r.v v3, (a0)      # Load v3 with VLEN/8 bytes held at address in a0
       vl3r.v v3, (a0)      # Load v3,v4,v5 with 3*VLEN/8 bytes at address in a0

       vl<nf>r.v vd, (rs1)  # Vector store of nf vector registers
       vs3r.v v3, (a1)      # Store v3,v4,v5 (3*VLEN/8 bytes) to address in a1

## 8. Vector AMO Operations (`Zvamo`)

Note | Profiles will dictate whether vector AMO operations are supported. The expectation is that the Unix profile will require vector AMO operations.

If vector AMO instructions are supported, then the scalar Zaamo instructions (atomic operations from the standard A extension) must be present.

Vector AMO operations are encoded using the unused width encodings under the standard AMO major opcode. Each active element performs an atomic read-modify-write of a single memory location.

    Format for Vector AMO Instructions under AMO major opcode
    31    27 26  25  24      20 19       15 14   12 11      7 6     0
     amoop  |wd| vm |   vs2    |    rs1    | width | vs3/vd  |0101111| VAMO*
       5      1   1      5           5         3        5        7

    vs2[4:0] specifies v register holding address
    vs3/vd[4:0] specifies v register holding source operand and destination

    vm specifies vector mask
    width[2:0] specifies size of memory elements, and distinguishes from scalar AMO
    amoop[4:0] specifies the AMO operation
    wd specifies whether the original memory value is written to vd (1=yes, 0=no)

AMOs have the same addressing mode as indexed operations except with no immediate offset. A vector of byte offsets in register `vs2` are added to the scalar base register in `rs1` to give the addresses of the AMO operations.

The `vs2` vector register supplies the byte offset of each element, while the `vs3` vector register supplies the source data for the atomic memory operation.

If the `wd` bit is set, the `vd` register is written with the initial value of the memory element. If the `wd` bit is clear, the `vd` register is not written.

Note | When `wd` is clear, the memory system does not need to return the original memory value, and the original values in `vd` will be preserved.

Note | The AMOs were defined to overwrite source data partly to reduce total memory pipeline read port count for implementations with register renaming. Also, to support the same addressing mode as vector indexed operations, and because vector AMOs are less likely to need results given that the primary use is parallel in-memory reductions.

Vector AMOs operate as if `aq` and `rl` bits were zero on each element with regard to ordering relative to other instructions in the same hart.

Vector AMOs provide no ordering guarantee between element operations in the same vector AMO instruction.

Table 12. Vector AMO width encoding
| Width [2:0] | Mem bits | Reg bits | Opcode
--- | --- | --- | --- | ---
Standard scalar AMO | 0 | 1 | 0 | 32 | XLEN | AMO*.W
Standard scalar AMO | 0 | 1 | 1 | 64 | XLEN | AMO*.D
Standard scalar AMO | 1 | 0 | 0 | 128 | XLEN | AMO*.Q
Vector AMO | 1 | 1 | 0 | 32 | vl*SEW | VAMO*W.V
Vector AMO | 1 | 1 | 1 | SEW | vl*SEW | VAMO*E.V

Mem bits is the size of element accessed in memory

Reg bits is the size of element accessed in register

There are two widths of vector AMO, one for 32-bit words and one for SEW-bit words. For the 32-bit vector AMO operations, SEW must be at least 32 bits, otherwise an illegal instruction exception is raised. If SEW > 32 bits, the value returned from memory is sign-extended to fill SEW.

If SEW is less than XLEN, then addresses in the vector `vs2` are zero-extended to XLEN. If SEW is greater than XLEN, an illegal instruction exception is raised.

Note | Sign-extending addresses held in narrower SEW might match expectations on how narrow virtual addresses are usually handled, but requires slightly different hardware than for the zero-extension of offsets used in indexed load/stores. By far the most common use case for vector AMO instructions is expected to be for address elements that have SEW=XLEN, where there is no extension, so the decision was made to simplify the hardware. Software can always explicitly promote narrower addresses to sign-extended wider addresses if this is needed.

Vector AMO instructions are only supported for the memory element widths supported by AMOs in the implementation’s scalar architecture. Other widths raise an illegal instruction exception.

The vector `amoop[4:0]` field uses the same encoding as the scalar 5-bit AMO instruction field, except that LR and SC are not supported.

Table 13. amoop
amoop | opcode
--- | ---
0 | 0 | 0 | 0 | 1 | vamoswap
0 | 0 | 0 | 0 | 0 | vamoadd
0 | 0 | 1 | 0 | 0 | vamoxor
0 | 1 | 1 | 0 | 0 | vamoand
0 | 1 | 0 | 0 | 0 | vamoor
1 | 0 | 0 | 0 | 0 | vamomin
1 | 0 | 1 | 0 | 0 | vamomax
1 | 1 | 0 | 0 | 0 | vamominu
1 | 1 | 1 | 0 | 0 | vamomaxu

The assembly syntax uses `x0` in the destination register position to indicate the return value is not required (`wd=0`).

    # 32-bit vector AMOs
    vamoswapw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoswapw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoaddw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoaddw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoxorw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoxorw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoandw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoandw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoorw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoorw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamominw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamominw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamomaxw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamomaxw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamominuw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamominuw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamomaxuw.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamomaxuw.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    # SEW-bit vector AMOs
    vamoswape.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoswape.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoadde.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoadde.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoxore.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoxore.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoande.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoande.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamoore.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamoore.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamomine.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamomine.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamomaxe.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamomaxe.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamominue.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamominue.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

    vamomaxue.v vd, (rs1), v2, vd,  v0.t # Write original value to register, wd=1
    vamomaxue.v x0, (rs1), v2, vs3, v0.t # Do not write original value to register, wd=0

## 9. Vector Memory Alignment Constraints

If the elements accessed by a vector memory instruction are not naturally aligned to the memory element size, either an address misaligned exception is raised on that element or the element is transferred successfully.

Vector memory accesses follow the same rules for atomicity as scalar memory accesses.

## 10. Vector Memory Consistency Model

Vector memory instructions appear to execute in program order on the local hart. Vector memory instructions follow RVWMO at the instruction level, and element operations are ordered within the instruction as if performed by an element-ordered sequence of syntactically independent scalar instructions. Vector indexed-ordered stores write elements to memory in element order. Vector indexed-unordered stores do not preserve element order for writes within a single vector store instruction.

Note | Need to flesh out details.

## 11. Vector Arithmetic Instruction Formats

The vector arithmetic instructions use a new major opcode (OP-V = 10101112) which neighbors OP-FP. The three-bit `funct3` field is used to define sub-categories of vector instructions.

    Formats for Vector Arithmetic Instructions under OP-V major opcode

    31       26  25   24      20 19      15 14   12 11      7 6     0
      funct6   | vm  |   vs2    |    vs1   | 0 0 0 |    vd   |1010111| OP-V (OPIVV)
      funct6   | vm  |   vs2    |    vs1   | 0 0 1 |  vd/rd  |1010111| OP-V (OPFVV)
      funct6   | vm  |   vs2    |    vs1   | 0 1 0 |  vd/rd  |1010111| OP-V (OPMVV)
      funct6   | vm  |   vs2    |   simm5  | 0 1 1 |    vd   |1010111| OP-V (OPIVI)
      funct6   | vm  |   vs2    |    rs1   | 1 0 0 |    vd   |1010111| OP-V (OPIVX)
      funct6   | vm  |   vs2    |    rs1   | 1 0 1 |    vd   |1010111| OP-V (OPFVF)
      funct6   | vm  |   vs2    |    rs1   | 1 1 0 |  vd/rd  |1010111| OP-V (OPMVX)
         6        1        5          5        3        5        7

### 11.1. Vector Arithmetic Instruction encoding

The `funct3` field encodes the operand type and source locations.

Table 14. funct3
funct3[2:0] | Operands | Source of scalar(s) |
--- | --- | --- | ---
0 | 0 | 0 | OPIVV | vector-vector | -
0 | 0 | 1 | OPFVV | vector-vector | -
0 | 1 | 0 | OPMVV | vector-vector | -
0 | 1 | 1 | OPIVI | vector-immediate | imm[4:0]
1 | 0 | 0 | OPIVX | vector-scalar | GPR x register rs1
1 | 0 | 1 | OPFVF | vector-scalar | FP f register rs1
1 | 1 | 0 | OPMVX | vector-scalar | GPR x register rs1
1 | 1 | 1 | OPCFG | scalars-imms | GPR x register rs1 & rs2/imm

Integer operations are performed using unsigned or two’s-complement signed integer arithmetic depending on the opcode.

All standard vector floating-point arithmetic operations follow the IEEE-754/2008 standard. All vector floating-point operations use the dynamic rounding mode in the `frm` register.

Vector-vector operations take two vectors of operands from vector register groups specified by `vs2` and `vs1` respectively.

Vector-scalar operations can have three possible forms, but in all cases take one vector of operands from a vector register group specified by `vs2` and a second scalar source operand from one of three alternative sources.

1. For integer operations, the scalar can be a 5-bit immediate encoded in the `rs1` field. The value is sign- or zero-extended to SEW bits.

2. For integer operations, the scalar can be taken from the scalar `x` register specified by `rs1`. If XLEN>SEW, the least-significant bits of the `x` register are used. If XLEN<SEW, the value from the `x` register is sign-extended to SEW bits.

3. For floating-point operations, the scalar can be taken from a scalar `f` register. If FLEN>SEW, the value in the `f` registers is checked for a valid NaN-boxed value, in which case the least-significant bits of the `f`register are used, else the canonical NaN value is used. If FLEN<SEW, the value is NaN-boxed (one-extended) to SEW.

Note | The proposed Zfinx variants will take the floating-point scalar argument from the `x` registers.

Vector arithmetic instructions are masked under control of the `vm` field.

    # Assembly syntax pattern for vector binary arithmetic instructions

    # Operations returning vector results, masked by vm (v0.t, <nothing>)
    vop.vv  vd, vs2, vs1, vm  # integer vector-vector      vd[i] = vs2[i] op vs1[i]
    vop.vx  vd, vs2, rs1, vm  # integer vector-scalar      vd[i] = vs2[i] op x[rs1]
    vop.vi  vd, vs2, imm, vm  # integer vector-immediate   vd[i] = vs2[i] op imm

    vfop.vv  vd, vs2, vs1, vm # FP vector-vector operation vd[i] = vs2[i] fop vs1[i]
    vfop.vf  vd, vs2, rs1, vm # FP vector-scalar operation vd[i] = vs2[i] fop f[rs1]

Note | In the encoding, `vs2` is the first operand, while `rs1/simm5` is the second operand. This is the opposite to the standard scalar ordering. This arrangement retains the existing encoding conventions that instructions that read only one scalar register, read it from `rs1`, and that 5-bit immediates are sourced from the `rs1` field.

    # Assembly syntax pattern for vector ternary arithmetic instructions (multiply-add)

    # Integer operations overwriting sum input
    vop.vv vd, vs1, vs2, vm  # vd[i] = vs1[i] * vs2[i] + vd[i]
    vop.vx vd, rs1, vs2, vm  # vd[i] = x[rs1] * vs2[i] + vd[i]

    # Integer operations overwriting product input
    vop.vv vd, vs1, vs2, vm  # vd[i] = vs1[i] * vd[i] + vs2[i]
    vop.vx vd, rs1, vs2, vm  # vd[i] = x[rs1] * vd[i] + vs2[i]

    # Floating-point operations overwriting sum input
    vfop.vv vd, vs1, vs2, vm  # vd[i] = vs1[i] * vs2[i] + vd[i]
    vfop.vf vd, rs1, vs2, vm  # vd[i] = f[rs1] * vs2[i] + vd[i]

    # Floating-point operations overwriting product input
    vfop.vv vd, vs1, vs2, vm  # vd[i] = vs1[i] * vd[i] + vs2[i]
    vfop.vf vd, rs1, vs2, vm  # vd[i] = f[rs1] * vd[i] + vs2[i]

Note | For ternary multiply-add operations, the assembler syntax always places the destination vector register first, followed by either `rs1` or `vs1`, then `vs2`. This ordering provides a more natural reading of the assembler for these ternary operations, as the multiply operands are always next to each other.

### 11.2. Widening Vector Arithmetic Instructions

A few vector arithmetic instructions are defined to be widening operations where the destination elements are 2*SEW wide and are stored in a vector register group with twice the number of vector registers.

The first operand can be either single or double-width. These are generally written with a `vw*` prefix on the opcode or `vfw*` for vector floating-point operations.

    Assembly syntax pattern for vector widening arithmetic instructions

    # Double-width result, two single-width sources: 2*SEW = SEW op SEW
    vwop.vv  vd, vs2, vs1, vm  # integer vector-vector      vd[i] = vs2[i] op vs1[i]
    vwop.vx  vd, vs2, rs1, vm  # integer vector-scalar      vd[i] = vs2[i] op x[rs1]

    # Double-width result, first source double-width, second source single-width: 2*SEW = 2*SEW op SEW
    vwop.wv  vd, vs2, vs1, vm  # integer vector-vector      vd[i] = vs2[i] op vs1[i]
    vwop.wx  vd, vs2, rs1, vm  # integer vector-scalar      vd[i] = vs2[i] op x[rs1]

Note | Originally, a `w` suffix was used on opcode, but this could be confused with the use of a `w` suffix to mean word-sized operations in doubleword integers, so the `w` was moved to prefix.

Note | The floating-point widening operations were changed to `vfw*` from `vwf*` to be more consistent with any scalar widening floating-point operations that will be written as `fw*`.

Note | For integer multiply-add, another possible widening option increases the size of the accumulator to 4*SEW (i.e., 4*SEW += SEW*SEW). These would be distinguished by a `vw4*` prefix on the opcode. These are not included at this time, but are a possible addition to spec.

The destination vector register group results are arranged as if both SEW and LMUL were at twice their current settings (i.e., the destination element width is 2*SEW, and the destination vector register group LMUL is 2*LMUL).

For all widening instructions, the destination element width must be a supported element width and the destination LMUL value must also be a supported LMUL value (≤8, i.e., current LMUL must be ≤4), otherwise an illegal instruction exception is raised.

The destination vector register group must be specified using a vector register number that is valid for the destination’s LMUL value, otherwise an illegal instruction exception is raised.

The destination vector register group cannot overlap a source vector register group of a different element width (including the mask register if masked), otherwise an illegal instruction exception is raised.

Note | This constraint is necessary to support restart with non-zero `vstart`.

Note | For the `vw<op>.wv vd, vs2, vs1` format instructions, it is legal for vd to equal vs2.

### 11.3. Narrowing Vector Arithmetic Instructions

A few instructions are provided to convert double-width source vectors into single-width destination vectors. These instructions convert a vector register group organized as if LMUL and SEW were twice the current settings, and convert to a vector register group with the current LMUL/SEW vectors/elements.

If (2*LMUL > 8), or (2 * SEW) > ELEN, an illegal instruction exception is raised.

Note | An alternative design decision would have been to treat LMUL as defining the size of the source vector register group. The choice here is motivated by the belief the chosen approach will require fewer LMUL changes.

The source and destination vector register groups have to be specified with a vector register number that is legal for the source and destination LMUL value respectively, otherwise an illegal instruction exception is raised.

Where there is a second source vector register group (specified by `vs1`), this has the same (narrower) width as the result.

The destination vector register group cannot overlap the first source vector register group (specified by `vs2`). The destination vector register group cannot overlap the mask register if used, unless LMUL=1. If either constraint is violated, an illegal instruction exception is raised.

Note | It is safe to overwrite a second source vector register group with the same LMUL and element width as the result, or to overwrite a mask register when LMUL=1.

A `vn*` prefix on the opcode is used to distinguish these instructions in the assembler, or a `vfn*` prefix for narrowing floating-point opcodes. The double-width source vector register group is signified by a `w` in the source operand suffix (e.g., `vnsra.wv`)

Note | Comparison operations that set a mask register are also implicitly a narrowing operation.

## 12. Vector Integer Arithmetic Instructions

A set of vector integer arithmetic instructions are provided.

### 12.1. Vector Single-Width Integer Add and Subtract

Vector integer add and subtract are provided. Reverse-subtract instructions are also provided for the vector-scalar forms.

    # Integer adds.
    vadd.vv vd, vs2, vs1, vm   # Vector-vector
    vadd.vx vd, vs2, rs1, vm   # vector-scalar
    vadd.vi vd, vs2, imm, vm   # vector-immediate

    # Integer subtract
    vsub.vv vd, vs2, vs1, vm   # Vector-vector
    vsub.vx vd, vs2, rs1, vm   # vector-scalar

    # Integer reverse subtract
    vrsub.vx vd, vs2, rs1, vm   # vd[i] = rs1 - vs2[i]
    vrsub.vi vd, vs2, imm, vm   # vd[i] = imm - vs2[i]

### 12.2. Vector Widening Integer Add/Subtract

The widening add/subtract instructions are provided in both signed and unsigned variants, depending on whether the narrower source operands are first sign- or zero-extended before forming the double-width sum.

    # Widening unsigned integer add/subtract, 2*SEW = SEW +/- SEW
    vwaddu.vv  vd, vs2, vs1, vm  # vector-vector
    vwaddu.vx  vd, vs2, rs1, vm  # vector-scalar
    vwsubu.vv  vd, vs2, vs1, vm  # vector-vector
    vwsubu.vx  vd, vs2, rs1, vm  # vector-scalar

    # Widening signed integer add/subtract, 2*SEW = SEW +/- SEW
    vwadd.vv  vd, vs2, vs1, vm  # vector-vector
    vwadd.vx  vd, vs2, rs1, vm  # vector-scalar
    vwsub.vv  vd, vs2, vs1, vm  # vector-vector
    vwsub.vx  vd, vs2, rs1, vm  # vector-scalar

    # Widening unsigned integer add/subtract, 2*SEW = 2*SEW +/- SEW
    vwaddu.wv  vd, vs2, vs1, vm  # vector-vector
    vwaddu.wx  vd, vs2, rs1, vm  # vector-scalar
    vwsubu.wv  vd, vs2, vs1, vm  # vector-vector
    vwsubu.wx  vd, vs2, rs1, vm  # vector-scalar

    # Widening signed integer add/subtract, 2*SEW = 2*SEW +/- SEW
    vwadd.wv  vd, vs2, vs1, vm  # vector-vector
    vwadd.wx  vd, vs2, rs1, vm  # vector-scalar
    vwsub.wv  vd, vs2, vs1, vm  # vector-vector
    vwsub.wx  vd, vs2, rs1, vm  # vector-scalar

Note | An integer value can be doubled in width using the widening add instructions with a scalar operand of `x0`. Can define assembly pseudoinstructions `vwcvt.x.x.v vd,vs,vm = vwadd.vx vd,vs,x0,vm` and `vwcvtu.x.x.v vd,vs,vm = vwaddu.vx vd,vs,x0,vm`.

### 12.3. Vector Integer Add-with-Carry / Subtract-with-Borrow Instructions

To support multi-word integer arithmetic, instructions that operate on a carry bit are provided. For each operation (add or subtract), two instructions are provided: one to provide the result (SEW width), and the second to generate the carry output (single bit encoded as a mask boolean).

The carry inputs and outputs are represented using the mask register layout as described in Section Mask Register Layout. Due to encoding constraints, the carry input must come from the implicit `v0` register, but carry outputs can be written to any vector register that respects the source/destination overlap restrictions below.

`vadc` and `vsbc` add or subtract the source operands and the carry-in or borrow-in, and write the result to vector register `vd`. These instructions are encoded as masked instructions (`vm=0`), but they operate on and write back all body elements. Encodings corresponding to the unmasked versions (`vm=1`) are reserved.

`vmadc` and `vmsbc` add or subtract the source operands, optionally add the carry-in or subtract the borrow-in if masked (`vm=0`), and write the result back to mask register `vd`. If unmasked (`vm=1`), there is no carry-in or borrow-in. These instructions operate on and write back all body elements, even if masked.

     # Produce sum with carry.

     # vd[i] = vs2[i] + vs1[i] + v0[i].LSB
     vadc.vvm   vd, vs2, vs1, v0  # Vector-vector

     # vd[i] = vs2[i] + x[rs1] + v0[i].LSB
     vadc.vxm   vd, vs2, rs1, v0  # Vector-scalar

     # vd[i] = vs2[i] + imm + v0[i].LSB
     vadc.vim   vd, vs2, imm, v0  # Vector-immediate

     # Produce carry out in mask register format

     # vd[i] = carry_out(vs2[i] + vs1[i] + v0[i].LSB)
     vmadc.vvm   vd, vs2, vs1, v0  # Vector-vector

     # vd[i] = carry_out(vs2[i] + x[rs1] + v0[i].LSB)
     vmadc.vxm   vd, vs2, rs1, v0  # Vector-scalar

     # vd[i] = carry_out(vs2[i] + imm + v0[i].LSB)
     vmadc.vim   vd, vs2, imm, v0  # Vector-immediate

     # vd[i] = carry_out(vs2[i] + vs1[i])
     vmadc.vv    vd, vs2, vs1      # Vector-vector, no carry-in

     # vd[i] = carry_out(vs2[i] + x[rs1])
     vmadc.vx    vd, vs2, rs1      # Vector-scalar, no carry-in

     # vd[i] = carry_out(vs2[i] + imm)
     vmadc.vi    vd, vs2, imm      # Vector-immediate, no carry-in

Because implementing a carry propagation requires executing two instructions with unchanged inputs, destructive accumulations will require an additional move to obtain correct results.

      # Example multi-word arithmetic sequence, accumulating into v4
      vmadc.vvm v1, v4, v8, v0  # Get carry into temp register v1
      vadc.vvm v4, v4, v8, v0   # Calc new sum
      vmcpy.m v0, v1             # Move temp carry into v0 for next word

The subtract with borrow instruction `vsbc` performs the equivalent function to support long word arithmetic for subtraction. There are no subtract with immediate instructions.

     # Produce difference with borrow.

     # vd[i] = vs2[i] - vs1[i] - v0[i].LSB
     vsbc.vvm   vd, vs2, vs1, v0  # Vector-vector

     # vd[i] = vs2[i] - x[rs1] - v0[i].LSB
     vsbc.vxm   vd, vs2, rs1, v0  # Vector-scalar

     # Produce borrow out in mask register format

     # vd[i] = borrow_out(vs2[i] - vs1[i] - v0[i].LSB)
     vmsbc.vvm   vd, vs2, vs1, v0  # Vector-vector

     # vd[i] = borrow_out(vs2[i] - x[rs1] - v0[i].LSB)
     vmsbc.vxm   vd, vs2, rs1, v0  # Vector-scalar

     # vd[i] = borrow_out(vs2[i] - vs1[i])
     vmsbc.vv    vd, vs2, vs1      # Vector-vector, no borrow-in

     # vd[i] = borrow_out(vs2[i] - x[rs1])
     vmsbc.vx    vd, vs2, rs1      # Vector-scalar, no borrow-in

For `vmsbc`, the borrow is defined to be 1 iff the difference, prior to truncation, is negative.

For `vadc` and `vsbc`, an illegal instruction exception is raised if the destination vector register is `v0` and LMUL > 1.

Note | This constraint corresponds to the constraint on masked vector operations that overwrite the mask register.

For `vmadc` and `vmsbc`, an illegal instruction exception is raised if the destination vector register overlaps a source vector register group and LMUL > 1.

### 12.4. Vector Bitwise Logical Instructions

    # Bitwise logical operations.
    vand.vv vd, vs2, vs1, vm   # Vector-vector
    vand.vx vd, vs2, rs1, vm   # vector-scalar
    vand.vi vd, vs2, imm, vm   # vector-immediate

    vor.vv vd, vs2, vs1, vm    # Vector-vector
    vor.vx vd, vs2, rs1, vm    # vector-scalar
    vor.vi vd, vs2, imm, vm    # vector-immediate

    vxor.vv vd, vs2, vs1, vm    # Vector-vector
    vxor.vx vd, vs2, rs1, vm    # vector-scalar
    vxor.vi vd, vs2, imm, vm    # vector-immediate

Note | With an immediate of -1, scalar-immediate forms of the `vxor` instruction provide a bitwise NOT operation. This can be provided as an assembler pseudoinstruction `vnot.v`.

### 12.5. Vector Single-Width Bit Shift Instructions

A full complement of vector shift instructions are provided, including logical shift left, and logical (zero-extending) and arithmetic (sign-extending) shift right.

    # Bit shift operations
    vsll.vv vd, vs2, vs1, vm   # Vector-vector
    vsll.vx vd, vs2, rs1, vm   # vector-scalar
    vsll.vi vd, vs2, uimm, vm   # vector-immediate

    vsrl.vv vd, vs2, vs1, vm   # Vector-vector
    vsrl.vx vd, vs2, rs1, vm   # vector-scalar
    vsrl.vi vd, vs2, uimm, vm   # vector-immediate

    vsra.vv vd, vs2, vs1, vm   # Vector-vector
    vsra.vx vd, vs2, rs1, vm   # vector-scalar
    vsra.vi vd, vs2, uimm, vm   # vector-immediate

Only the low lg2(SEW) bits are read to obtain the shift amount from a register value.

The immediate is treated as an unsigned shift amount, with a maximum shift amount of 31.

### 12.6. Vector Narrowing Integer Right Shift Instructions

The narrowing right shifts extract a smaller field from a wider operand and have both zero-extending (`srl`) and sign-extending (`sra`) forms. The shift amount can come from a vector or a scalar `x` register or a 5-bit immediate. The low lg2(2*SEW) bits of the vector or scalar shift amount value are used (e.g., the low 6 bits for a SEW=64-bit to SEW=32-bit narrowing operation). The unsigned immediate form supports shift amounts up to 31 only.

     # Narrowing shift right logical, SEW = (2*SEW) >> SEW
     vnsrl.wv vd, vs2, vs1, vm   # vector-vector
     vnsrl.wx vd, vs2, rs1, vm   # vector-scalar
     vnsrl.wi vd, vs2, uimm, vm   # vector-immediate

     # Narrowing shift right arithmetic, SEW = (2*SEW) >> SEW
     vnsra.wv vd, vs2, vs1, vm   # vector-vector
     vnsra.wx vd, vs2, rs1, vm   # vector-scalar
     vnsra.wi vd, vs2, uimm, vm   # vector-immediate

Note | It could be useful to add support for `n4` variants, where the destination is 1/4 width of source.

### 12.7. Vector Integer Comparison Instructions

The following integer compare instructions write 1 to the destination mask register element if the comparison evaluates to true, and 0 otherwise. The destination mask vector is always held in a single vector register, with a layout of elements as described in Section Mask Register Layout.

    # Set if equal
    vmseq.vv vd, vs2, vs1, vm  # Vector-vector
    vmseq.vx vd, vs2, rs1, vm  # vector-scalar
    vmseq.vi vd, vs2, imm, vm  # vector-immediate

    # Set if not equal
    vmsne.vv vd, vs2, vs1, vm  # Vector-vector
    vmsne.vx vd, vs2, rs1, vm  # vector-scalar
    vmsne.vi vd, vs2, imm, vm  # vector-immediate

    # Set if less than, unsigned
    vmsltu.vv vd, vs2, vs1, vm  # Vector-vector
    vmsltu.vx vd, vs2, rs1, vm  # Vector-scalar

    # Set if less than, signed
    vmslt.vv vd, vs2, vs1, vm  # Vector-vector
    vmslt.vx vd, vs2, rs1, vm  # vector-scalar

    # Set if less than or equal, unsigned
    vmsleu.vv vd, vs2, vs1, vm   # Vector-vector
    vmsleu.vx vd, vs2, rs1, vm   # vector-scalar
    vmsleu.vi vd, vs2, imm, vm   # Vector-immediate

    # Set if less than or equal, signed
    vmsle.vv vd, vs2, vs1, vm  # Vector-vector
    vmsle.vx vd, vs2, rs1, vm  # vector-scalar
    vmsle.vi vd, vs2, imm, vm  # vector-immediate

    # Set if greater than, unsigned
    vmsgtu.vx vd, vs2, rs1, vm   # Vector-scalar
    vmsgtu.vi vd, vs2, imm, vm   # Vector-immediate

    # Set if greater than, signed
    vmsgt.vx vd, vs2, rs1, vm    # Vector-scalar
    vmsgt.vi vd, vs2, imm, vm    # Vector-immediate

    # Following two instructions are not provided directly
    # Set if greater than or equal, unsigned
    # vmsgeu.vx vd, vs2, rs1, vm    # Vector-scalar
    # Set if greater than or equal, signed
    # vmsge.vx vd, vs2, rs1, vm    # Vector-scalar

The following table indicates how all comparisons are implemented in native machine code.

    Comparison      Assembler Mapping             Assembler Pseudoinstruction

    va < vb         vmslt{u}.vv vd, va, vb, vm
    va <= vb        vmsle{u}.vv vd, va, vb, vm
    va > vb         vmslt{u}.vv vd, vb, va, vm    vmsgt{u}.vv vd, va, vb, vm
    va >= vb        vmsle{u}.vv vd, vb, va, vm    vmsge{u}.vv vd, va, vb, vm

    va < x          vmslt{u}.vx vd, va, x, vm
    va <= x         vmsle{u}.vx vd, va, x, vm
    va > x          vmsgt{u}.vx vd, va, x, vm
    va >= x         see below

    va < i          vmsle{u}.vi vd, va, i-1, vm    vmslt{u}.vi vd, va, i, vm
    va <= i         vmsle{u}.vi vd, va, i, vm
    va > i          vmsgt{u}.vi vd, va, i, vm
    va >= i         vmsgt{u}.vi vd, va, i-1, vm    vmsge{u}.vi vd, va, i, vm

    va, vb vector register groups
    x      scalar integer register
    i      immediate

Note | The immediate forms of `vmslt{u}.vi` are not provided as the immediate value can be decreased by 1 and the `vmsle{u}.vi` variants used instead. The `vmsle.vi` range is -16 to 15, resulting in an effective `vmslt.vi` range of -15 to 16. The `vmsleu.vi` range is 0 to 15 (and `(~0)-15` to `~0`), giving an effective `vmsltu.vi` range of 1 to 16 (Note, `vmsltu.vi` with immediate 0 is not useful as it is always false). Similarly, `vmsge{u}.vi` is not provided and the comparison is implemented using `vmsgt{u}.vi` with the immediate decremented by one. The resulting effective `vmsge.vi` range is -15 to 16, and the resulting effective `vmsgeu.vi` range is 1 to 16 (Note, `vmsgeu.vi` with immediate 0 is not useful as it is always true).

Note | The `vmsgt` forms for register scalar and immediates are provided to allow a single comparison instruction to provide the correct polarity of mask value without using additional mask logical instructions.

To reduce encoding space, the `vmsge{u}.vx` form is not directly provided, and so the `va ≥ x` case requires special treatment.

Note | The `vmsge{u}.vx` could potentially be encoded in a non-orthogonal way under the unused OPIVI variant of `vmslt{u}`. These would be the only instructions in OPIVI that use a scalar `x`register however. Alternatively, a further two funct6 encodings could be used, but these would have a different operand format (writes to mask register) than others in the same group of 8 funct6 encodings. The current PoR is to omit these instructions and to synthesize where needed as described below.

The `vmsge{u}.vx` operation can be synthesized by reducing the value of `x` by 1 and using the `vmsgt{u}.vx` instruction, when it is known that this will not underflow the representation in `x`.

    Sequences to synthesize `vmsge{u}.vx` instruction

    va >= x,  x > minimum

       addi t0, x, -1; vmsgt{u}.vx vd, va, t0, vm

The above sequence will usually be the most efficient implementation, but assembler pseudoinstructions can be provided for cases where the range of `x` is unknown.

    unmasked va >= x

      pseudoinstruction: vmsge{u}.vx vd, va, x
      expansion: vmslt{u}.vx vd, va, x; vmnand.mm vd, vd, vd

    masked va >= x, vd != v0

      pseudoinstruction: vmsge{u}.vx vd, va, x, v0.t
      expansion: vmslt{u}.vx vd, va, x, v0.t; vmxor.mm vd, vd, v0

    masked va >= x, any vd

      pseudoinstruction: vmsge{u}.vx vd, va, x, v0.t, vt
      expansion: vmslt{u}.vx vt, va, x;  vmandnot.mm vd, vd, vt

      The vt argument to the pseudoinstruction must name a temporary vector register that is
      not same as vd and which will be clobbered by the pseudoinstruction

Comparisons effectively AND in the mask, e.g,

        # (a < b) && (b < c) in two instructions
        vmslt.vv    v0, va, vb        # All body elements written
        vmslt.vv    v0, vb, vc, v0.t  # Only update at set mask

For all comparison instructions, an illegal instruction exception is raised if the destination vector register overlaps a source vector register group and LMUL > 1.

### 12.8. Vector Integer Min/Max Instructions

Signed and unsigned integer minimum and maximum instructions are supported.

    # Unsigned minimum
    vminu.vv vd, vs2, vs1, vm   # Vector-vector
    vminu.vx vd, vs2, rs1, vm   # vector-scalar

    # Signed minimum
    vmin.vv vd, vs2, vs1, vm   # Vector-vector
    vmin.vx vd, vs2, rs1, vm   # vector-scalar

    # Unsigned maximum
    vmaxu.vv vd, vs2, vs1, vm   # Vector-vector
    vmaxu.vx vd, vs2, rs1, vm   # vector-scalar

    # Signed maximum
    vmax.vv vd, vs2, vs1, vm   # Vector-vector
    vmax.vx vd, vs2, rs1, vm   # vector-scalar

### 12.9. Vector Single-Width Integer Multiply Instructions

The single-width multiply instructions perform a SEW-bit*SEW-bit multiply and return an SEW-bit-wide result. The `mulh` versions write the high word of the product to the destination register.

    # Signed multiply, returning low bits of product
    vmul.vv vd, vs2, vs1, vm   # Vector-vector
    vmul.vx vd, vs2, rs1, vm   # vector-scalar

    # Signed multiply, returning high bits of product
    vmulh.vv vd, vs2, vs1, vm   # Vector-vector
    vmulh.vx vd, vs2, rs1, vm   # vector-scalar

    # Unsigned multiply, returning high bits of product
    vmulhu.vv vd, vs2, vs1, vm   # Vector-vector
    vmulhu.vx vd, vs2, rs1, vm   # vector-scalar

    # Signed(vs2)-Unsigned multiply, returning high bits of product
    vmulhsu.vv vd, vs2, vs1, vm   # Vector-vector
    vmulhsu.vx vd, vs2, rs1, vm   # vector-scalar

Note | There is no `vmulhus` opcode to return high half of unsigned-vector * signed-scalar product.

Note | The current `vmulh*` opcodes perform simple fractional multiplies, but with no option to scale, round, and/or saturate the result. Can consider changing definition of `vmulh`, `vmulhu`, `vmulhsu` to use `vxrm` rounding mode when discarding low half of product. There is no possibility of overflow in this case.

### 12.10. Vector Integer Divide Instructions

The divide and remainder instructions are equivalent to the RISC-V standard scalar integer multiply/divides, with the same results for extreme inputs.

        # Unsigned divide.
        vdivu.vv vd, vs2, vs1, vm   # Vector-vector
        vdivu.vx vd, vs2, rs1, vm   # vector-scalar

        # Signed divide
        vdiv.vv vd, vs2, vs1, vm   # Vector-vector
        vdiv.vx vd, vs2, rs1, vm   # vector-scalar

        # Unsigned remainder
        vremu.vv vd, vs2, vs1, vm   # Vector-vector
        vremu.vx vd, vs2, rs1, vm   # vector-scalar

        # Signed remainder
        vrem.vv vd, vs2, vs1, vm   # Vector-vector
        vrem.vx vd, vs2, rs1, vm   # vector-scalar

Note | The decision to include integer divide and remainder was contentious. The argument in favor is that without a standard instruction, software would have to pick some algorithm to perform the operation, which would likely perform poorly on some microarchitectures versus others.

Note | There is no instruction to perform a "scalar divide by vector" operation.

### 12.11. Vector Widening Integer Multiply Instructions

The widening integer multiply instructions return the full 2*SEW-bit product from an SEW-bit*SEW-bit multiply.

    # Widening signed-integer multiply
    vwmul.vv  vd, vs2, vs1, vm# vector-vector
    vwmul.vx  vd, vs2, rs1, vm # vector-scalar

    # Widening unsigned-integer multiply
    vwmulu.vv vd, vs2, vs1, vm # vector-vector
    vwmulu.vx vd, vs2, rs1, vm # vector-scalar

    # Widening signed-unsigned integer multiply
    vwmulsu.vv vd, vs2, vs1, vm # vector-vector
    vwmulsu.vx vd, vs2, rs1, vm # vector-scalar

### 12.12. Vector Single-Width Integer Multiply-Add Instructions

The integer multiply-add instructions are destructive and are provided in two forms, one that overwrites the addend or minuend (`vmacc`, `vnmsac`) and one that overwrites the first multiplicand (`vmadd`, `vnmsub`).

The low half of the product is added or subtracted from the third operand.

Note | "sac" is intended to be read as "subtract from accumulator". The opcode is "vnmsac" to match the (unfortunately counterintuitive) floating-point `fnmsub` instruction definition. Similarly for the "vnmsub" opcode.

    # Integer multiply-add, overwrite addend
    vmacc.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vmacc.vx vd, rs1, vs2, vm    # vd[i] = +(x[rs1] * vs2[i]) + vd[i]

    # Integer multiply-sub, overwrite minuend
    vnmsac.vv vd, vs1, vs2, vm    # vd[i] = -(vs1[i] * vs2[i]) + vd[i]
    vnmsac.vx vd, rs1, vs2, vm    # vd[i] = -(x[rs1] * vs2[i]) + vd[i]

    # Integer multiply-add, overwrite multiplicand
    vmadd.vv vd, vs1, vs2, vm    # vd[i] = (vs1[i] * vd[i]) + vs2[i]
    vmadd.vx vd, rs1, vs2, vm    # vd[i] = (x[rs1] * vd[i]) + vs2[i]

    # Integer multiply-sub, overwrite multiplicand
    vnmsub.vv vd, vs1, vs2, vm    # vd[i] = -(vs1[i] * vd[i]) + vs2[i]
    vnmsub.vx vd, rs1, vs2, vm    # vd[i] = -(x[rs1] * vd[i]) + vs2[i]

### 12.13. Vector Widening Integer Multiply-Add Instructions

The widening integer multiply-add instructions add a SEW-bit*SEW-bit multiply result to (from) a 2*SEW-bit value and produce a 2*SEW-bit result. All combinations of signed and unsigned multiply operands are supported.

    # Widening unsigned-integer multiply-add, overwrite addend
    vwmaccu.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vwmaccu.vx vd, rs1, vs2, vm    # vd[i] = +(x[rs1] * vs2[i]) + vd[i]

    # Widening signed-integer multiply-add, overwrite addend
    vwmacc.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vwmacc.vx vd, rs1, vs2, vm    # vd[i] = +(x[rs1] * vs2[i]) + vd[i]

    # Widening signed-unsigned-integer multiply-add, overwrite addend
    vwmaccsu.vv vd, vs1, vs2, vm    # vd[i] = +(signed(vs1[i]) * unsigned(vs2[i])) + vd[i]
    vwmaccsu.vx vd, rs1, vs2, vm    # vd[i] = +(signed(x[rs1]) * unsigned(vs2[i])) + vd[i]

    # Widening unsigned-signed-integer multiply-add, overwrite addend
    vwmaccus.vx vd, rs1, vs2, vm    # vd[i] = +(unsigned(x[rs1]) * signed(vs2[i])) + vd[i]

### 12.14. Vector Quad-Widening Integer Multiply-Add Instructions

The quad-widening integer multiply-add instructions add a SEW-bit*SEW-bit multiply result to (from) a 4*SEW-bit value and produce a 4*SEW-bit result. All combinations of signed and unsigned multiply operands are supported.

Note | It is currently unclear if quad-widening will be part of standard base, or part of an extension. Quad-widening would add a new operand access pattern to the standard.

Note | On ELEN=32 machines, only 8b * 8b = 16b products accumulated in a 32b accumulator would be supported. Machines with ELEN=64 would also add 16b * 16b = 32b products accumulated in 64b.

    # Quad-widening unsigned-integer multiply-add, overwrite addend
    vqmaccu.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vqmaccu.vx vd, rs1, vs2, vm    # vd[i] = +(x[rs1] * vs2[i]) + vd[i]

    # Quad-widening signed-integer multiply-add, overwrite addend
    vqmacc.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vqmacc.vx vd, rs1, vs2, vm    # vd[i] = +(x[rs1] * vs2[i]) + vd[i]

    # Quad-widening signed-unsigned-integer multiply-add, overwrite addend
    vqmaccsu.vv vd, vs1, vs2, vm    # vd[i] = +(signed(vs1[i]) * unsigned(vs2[i])) + vd[i]
    vqmaccsu.vx vd, rs1, vs2, vm    # vd[i] = +(signed(x[rs1]) * unsigned(vs2[i])) + vd[i]

    # Quad-widening unsigned-signed-integer multiply-add, overwrite addend
    vqmaccus.vx vd, rs1, vs2, vm    # vd[i] = +(unsigned(x[rs1]) * signed(vs2[i])) + vd[i]

### 12.15. Vector Integer Merge Instructions

The vector integer merge instructions combine two source operands based on the mask field. Unlike regular arithmetic instructions, the merge operates on all body elements (i.e., the set of elements from `vstart` up to the current vector length in `vl`).

The `vmerge` instructions are always masked (`vm=0`). The instructions combine two sources as follows. At elements where the mask value is zero, the first operand is copied to the destination element, otherwise the second operand is copied to the destination element. The first operand is always a vector register group specified by `vs2`. The second operand is a vector register group specified by `vs1` or a scalar `x` register specified by `rs1` or a 5-bit sign-extended immediate.

    vmerge.vvm vd, vs2, vs1, v0  # vd[i] = v0[i].LSB ? vs1[i] : vs2[i]
    vmerge.vxm vd, vs2, rs1, v0  # vd[i] = v0[i].LSB ? x[rs1] : vs2[i]
    vmerge.vim vd, vs2, imm, v0  # vd[i] = v0[i].LSB ? imm    : vs2[i]

### 12.16. Vector Integer Move Instructions

The vector integer move instructions copy a source operand to a vector register group. These instructions are always unmasked (`vm=1`). The first operand specifier (`vs2`) must contain `v0`, and any other vector register number in `vs2` is reserved. This instruction copies the `vs1`, `rs1`, or immediate operand to the first `vl` locations of the destination vector register group.

    vmv.v.v vd, vs1 # vd[i] = vs1[i]
    vmv.v.x vd, rs1 # vd[i] = rs1
    vmv.v.i vd, imm # vd[i] = imm

Note | Mask values can be widened into SEW-width elements using a sequence `vmv.v.i vd, 0; vmerge.vim vd, vd, 1, v0`.

Note | The vector integer move instructions share the encoding with the vector merge instructions, but with `vm=1` and `vs2=v0`.

## 13. Vector Fixed-Point Arithmetic Instructions

A set of vector arithmetic instructions are provided to support fixed-point arithmetic.

An N-bit element can hold two’s-complement signed integers in the range -2N-1…​+2N-1-1, and unsigned integers in the range 0 …​ +2N-1. The fixed-point instructions help preserve precision in narrow operands by supporting scaling and rounding, and can handle overflow by saturating results into the destination format range.

Note | The widening integer operations described above can also be used to remove the possibility of overflow.

### 13.1. Vector Single-Width Saturating Add and Subtract

Saturating forms of integer add and subtract are provided, for both signed and unsigned integers. If the result would overflow the destination, the result is replaced with the closest representable value, and the `vxsat` bit is set.

    # Saturating adds of unsigned integers.
    vsaddu.vv vd, vs2, vs1, vm   # Vector-vector
    vsaddu.vx vd, vs2, rs1, vm   # vector-scalar
    vsaddu.vi vd, vs2, imm, vm   # vector-immediate

    # Saturating adds of signed integers.
    vsadd.vv vd, vs2, vs1, vm   # Vector-vector
    vsadd.vx vd, vs2, rs1, vm   # vector-scalar
    vsadd.vi vd, vs2, imm, vm   # vector-immediate

    # Saturating subtract of unsigned integers.
    vssubu.vv vd, vs2, vs1, vm   # Vector-vector
    vssubu.vx vd, vs2, rs1, vm   # vector-scalar

    # Saturating subtract of signed integers.
    vssub.vv vd, vs2, vs1, vm   # Vector-vector
    vssub.vx vd, vs2, rs1, vm   # vector-scalar

### 13.2. Vector Single-Width Averaging Add and Subtract

The averaging add and subtract instructions right shift the result by one bit and round off the result according to the setting in `vxrm`. Both unsigned and signed versions are provided. For `vaaddu`, `vaadd`, and `vasub`, there can be no overflow in the result. For `vasubu`, overflow is ignored.

    # Averaging add
    # result = roundoff(src1 + src2, 1)

    # Averaging adds of unsigned integers.
    vaaddu.vv vd, vs2, vs1, vm   # Vector-vector
    vaaddu.vx vd, vs2, rs1, vm   # vector-scalar

    # Averaging adds of signed integers.
    vaadd.vv vd, vs2, vs1, vm   # Vector-vector
    vaadd.vx vd, vs2, rs1, vm   # vector-scalar

    # Averaging subtract
    # result = roundoff(src1 - src2, 1)

    # Averaging subtract of unsigned integers.
    vasubu.vv vd, vs2, vs1, vm   # Vector-vector
    vasubu.vx vd, vs2, rs1, vm   # vector-scalar

    # Averaging subtract of signed integers.
    vasub.vv vd, vs2, vs1, vm   # Vector-vector
    vasub.vx vd, vs2, rs1, vm   # vector-scalar

### 13.3. Vector Single-Width Fractional Multiply with Rounding and Saturation

The signed fractional multiply instruction produces a 2*SEW product of the two SEW inputs, then shifts the result right by SEW-1 bits, rounding these bits according to `vxrm`, then saturates the result to fit into SEW bits. If the result causes saturation, the `vxsat` bit is set.

    # Signed saturating and rounding fractional multiply
    # See vxrm  description for rounding calculation
    vsmul.vv vd, vs2, vs1, vm  # vd[i] = clip(roundoff(vs2[i]*vs1[i], SEW-1))
    vsmul.vx vd, vs2, rs1, vm  # vd[i] = clip(roundoff(vs2[i]*x[rs1], SEW-1))

Note | When multiplying two N-bit signed numbers, the largest magnitude is obtained for -2N-1 * -2N-1 producing a result +22N-2, which has a single (zero) sign bit when held in 2N bits. All other products have two sign bits in 2N bits. To retain greater precision in N result bits, the product is shifted right by one bit less than N, saturating the largest magnitude result but increasing result precision by one bit for all other products.

### 13.4. Vector Single-Width Scaling Shift Instructions

These instructions shift the input value right, and round off the shifted out bits according to `vxrm`. The scaling right shifts have both zero-extending (`vssrl`) and sign-extending (`vssra`) forms. The low lg2(SEW) bits of the vector or scalar shift amount value are used. The immediate form supports shift amounts up to 31 only.

     # Scaling shift right logical
     vssrl.vv vd, vs2, vs1, vm   # vd[i] = roundoff(vs2[i], vs1[i])
     vssrl.vx vd, vs2, rs1, vm   # vd[i] = roundoff(vs2[i], x[rs1])
     vssrl.vi vd, vs2, uimm, vm   # vd[i] = roundoff(vs2[i], uimm)

     # Scaling shift right arithmetic
     vssra.vv vd, vs2, vs1, vm   # vd[i] = roundoff(vs2[i],vs1[i])
     vssra.vx vd, vs2, rs1, vm   # vd[i] = roundoff(vs2[i], x[rs1])
     vssra.vi vd, vs2, uimm, vm   # vd[i] = roundoff(vs2[i], uimm)

### 13.5. Vector Narrowing Fixed-Point Clip Instructions

The `vnclip` instructions are used to pack a fixed-point value into a narrower destination. The instructions support rounding, scaling, and saturation into the final destination format.

The second argument (vector element, scalar value, immediate value) gives the amount to right shift the source as in the narrowing shift instructions, which provides the scaling. The low lg2(2*SEW) bits of the vector or scalar shift amount value are used (e.g., the low 6 bits for a SEW=64-bit to SEW=32-bit narrowing operation). The immediate form supports shift amounts up to 31 only.

    # Narrowing unsigned clip,  vd[i] = clip(roundoff(vs2[i], vs1[i]) )
    #                            SEW                  2*SEW     SEW
     vnclipu.wv vd, vs2, vs1, vm   # vector-vector
     vnclipu.wx vd, vs2, rs1, vm   # vector-scalar
     vnclipu.wi vd, vs2, uimm, vm  # vector-immediate

    # Narrowing signed clip
     vnclip.wv vd, vs2, vs1, vm   # vector-vector
     vnclip.wx vd, vs2, rs1, vm   # vector-scalar
     vnclip.wi vd, vs2, uimm, vm  # vector-immediate

For `vnclipu`/`vnclip`, the rounding mode is specified in the `vxrm` CSR. Rounding occurs around the least-significant bit of the destination and before saturation.

For `vnclipu`, the shifted rounded source value is treated as an unsigned integer and saturates if the result would overflow the destination viewed as an unsigned integer.

For `vnclip`, the shifted rounded source value is treated as a signed integer and saturates if the result would overflow the destination viewed as a signed integer.

If any destination element is saturated, the `vxsat` bit is set in the `vxsat` register.

## 14. Vector Floating-Point Instructions

The standard vector floating-point instructions treat 16-bit, 32-bit, 64-bit, and 128-bit elements as IEEE-754/2008-compatible values. If the current SEW does not correspond to a supported IEEE floating-point type, an illegal instruction exception is raised.

Note | The floating-point element widths that are supported depend on the platform.

Note | Platforms supporting 16-bit half-precision floating-point values will also have to implement scalar half-precision floating-point support in the `f` registers.

The vector floating-point instructions have the same behavior as the scalar floating-point instructions with regard to NaNs.

Scalar values for vector-scalar operations can be sourced from the standard scalar `f` registers.

Note | Scalar floating-point values will be sourced from the integer `x` registers in the proposed Zfinx variant.

### 14.1. Vector Floating-Point Exception Flags

A vector floating-point exception at any active floating-point element sets the standard FP exception flags in the `fflags` register. Inactive elements do not set FP exception flags.

### 14.2. Vector Single-Width Floating-Point Add/Subtract Instructions

        # Floating-point add
        vfadd.vv vd, vs2, vs1, vm   # Vector-vector
        vfadd.vf vd, vs2, rs1, vm   # vector-scalar

        # Floating-point subtract
        vfsub.vv vd, vs2, vs1, vm   # Vector-vector
        vfsub.vf vd, vs2, rs1, vm   # Vector-scalar vd[i] = vs2[i] - f[rs1]
        vfrsub.vf vd, vs2, rs1, vm  # Scalar-vector vd[i] = f[rs1] - vs2[i]

### 14.3. Vector Widening Floating-Point Add/Subtract Instructions

    # Widening FP add/subtract, 2*SEW = SEW +/- SEW
    vfwadd.vv vd, vs2, vs1, vm  # vector-vector
    vfwadd.vf vd, vs2, rs1, vm  # vector-scalar
    vfwsub.vv vd, vs2, vs1, vm  # vector-vector
    vfwsub.vf vd, vs2, rs1, vm  # vector-scalar

    # Widening FP add/subtract, 2*SEW = 2*SEW +/- SEW
    vfwadd.wv  vd, vs2, vs1, vm  # vector-vector
    vfwadd.wf  vd, vs2, rs1, vm  # vector-scalar
    vfwsub.wv  vd, vs2, vs1, vm  # vector-vector
    vfwsub.wf  vd, vs2, rs1, vm  # vector-scalar

### 14.4. Vector Single-Width Floating-Point Multiply/Divide Instructions

        # Floating-point multiply
        vfmul.vv vd, vs2, vs1, vm   # Vector-vector
        vfmul.vf vd, vs2, rs1, vm   # vector-scalar

        # Floating-point divide
        vfdiv.vv vd, vs2, vs1, vm   # Vector-vector
        vfdiv.vf vd, vs2, rs1, vm   # vector-scalar

        # Reverse floating-point divide vector = scalar / vector
        vfrdiv.vf vd, vs2, rs1, vm  # scalar-vector, vd[i] = f[rs1]/vs2[i]

### 14.5. Vector Widening Floating-Point Multiply

    # Widening floating-point multiply
    vfwmul.vv    vd, vs2, vs1, vm # vector-vector
    vfwmul.vf    vd, vs2, rs1, vm # vector-scalar

### 14.6. Vector Single-Width Floating-Point Fused Multiply-Add Instructions

All four varieties of fused multiply-add are provided, and in two destructive forms that overwrite one of the operands, either the addend or the first multiplicand.

    # FP multiply-accumulate, overwrites addend
    vfmacc.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vfmacc.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vs2[i]) + vd[i]

    # FP negate-(multiply-accumulate), overwrites subtrahend
    vfnmacc.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vs2[i]) - vd[i]
    vfnmacc.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vs2[i]) - vd[i]

    # FP multiply-subtract-accumulator, overwrites subtrahend
    vfmsac.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) - vd[i]
    vfmsac.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vs2[i]) - vd[i]

    # FP negate-(multiply-subtract-accumulator), overwrites minuend
    vfnmsac.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vs2[i]) + vd[i]
    vfnmsac.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vs2[i]) + vd[i]

    # FP multiply-add, overwrites multiplicand
    vfmadd.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vd[i]) + vs2[i]
    vfmadd.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vd[i]) + vs2[i]

    # FP negate-(multiply-add), overwrites multiplicand
    vfnmadd.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vd[i]) - vs2[i]
    vfnmadd.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vd[i]) - vs2[i]

    # FP multiply-sub, overwrites multiplicand
    vfmsub.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vd[i]) - vs2[i]
    vfmsub.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vd[i]) - vs2[i]

    # FP negate-(multiply-sub), overwrites multiplicand
    vfnmsub.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vd[i]) + vs2[i]
    vfnmsub.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vd[i]) + vs2[i]

Note | It would be possible to use the two unused rounding modes in the scalar FP FMA encoding to provide a few non-destructive FMAs. However, this would be the only maskable operation with three inputs and separate output.

### 14.7. Vector Widening Floating-Point Fused Multiply-Add Instructions

The widening floating-point fused multiply-add instructions all overwrite the wide addend with the result. The multiplier inputs are all SEW wide, while the addend and destination is 2*SEW bits wide.

    # FP widening multiply-accumulate, overwrites addend
    vfwmacc.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) + vd[i]
    vfwmacc.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vs2[i]) + vd[i]

    # FP widening negate-(multiply-accumulate), overwrites addend
    vfwnmacc.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vs2[i]) - vd[i]
    vfwnmacc.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vs2[i]) - vd[i]

    # FP widening multiply-subtract-accumulator, overwrites addend
    vfwmsac.vv vd, vs1, vs2, vm    # vd[i] = +(vs1[i] * vs2[i]) - vd[i]
    vfwmsac.vf vd, rs1, vs2, vm    # vd[i] = +(f[rs1] * vs2[i]) - vd[i]

    # FP widening negate-(multiply-subtract-accumulator), overwrites addend
    vfwnmsac.vv vd, vs1, vs2, vm   # vd[i] = -(vs1[i] * vs2[i]) + vd[i]
    vfwnmsac.vf vd, rs1, vs2, vm   # vd[i] = -(f[rs1] * vs2[i]) + vd[i]

### 14.8. Vector Floating-Point Square-Root Instruction

This is a unary vector-vector instruction.

        # Floating-point square root
        vfsqrt.v vd, vs2, vm   # Vector-vector square root

### 14.9. Vector Floating-Point MIN/MAX Instructions

The vector floating-point `vfmin` and `vfmax` instructions have the same behavior as the corresponding scalar floating-point instructions in version 2.2 of the RISC-V F/D/Q extension.

        # Floating-point minimum
        vfmin.vv vd, vs2, vs1, vm   # Vector-vector
        vfmin.vf vd, vs2, rs1, vm   # vector-scalar

        # Floating-point maximum
        vfmax.vv vd, vs2, vs1, vm   # Vector-vector
        vfmax.vf vd, vs2, rs1, vm   # vector-scalar

### 14.10. Vector Floating-Point Sign-Injection Instructions

Vector versions of the scalar sign-injection instructions. The result takes all bits except the sign bit from the vector `vs2` operands.

        vfsgnj.vv vd, vs2, vs1, vm   # Vector-vector
        vfsgnj.vf vd, vs2, rs1, vm   # vector-scalar

        vfsgnjn.vv vd, vs2, vs1, vm   # Vector-vector
        vfsgnjn.vf vd, vs2, rs1, vm   # vector-scalar

        vfsgnjx.vv vd, vs2, vs1, vm   # Vector-vector
        vfsgnjx.vf vd, vs2, rs1, vm   # vector-scalar

### 14.11. Vector Floating-Point Compare Instructions

These vector FP compare instructions compare two source operands and write the comparison result to a mask register. The destination mask vector is always held in a single vector register, with a layout of elements as described in Section Mask Register Layout.

The compare instructions follow the semantics of the scalar floating-point compare instructions. `vmfeq` and `vmfne` raise the invalid operation exception only on signaling NaN inputs. `vmflt`, `vmfle`, `vmfgt`, and `vmfge` raise the invalid operation exception on both signaling and quiet NaN inputs.

For all comparison instructions, an illegal instruction exception is raised if the destination vector register overlaps a source vector register group and LMUL > 1.

        # Compare equal
        vmfeq.vv vd, vs2, vs1, vm  # Vector-vector
        vmfeq.vf vd, vs2, rs1, vm  # vector-scalar

        # Compare not equal
        vmfne.vv vd, vs2, vs1, vm  # Vector-vector
        vmfne.vf vd, vs2, rs1, vm  # vector-scalar

        # Compare less than
        vmflt.vv vd, vs2, vs1, vm  # Vector-vector
        vmflt.vf vd, vs2, rs1, vm  # vector-scalar

        # Compare less than or equal
        vmfle.vv vd, vs2, vs1, vm  # Vector-vector
        vmfle.vf vd, vs2, rs1, vm  # vector-scalar

        # Compare greater than
        vmfgt.vf vd, vs2, rs1, vm  # vector-scalar

        # Compare greater than or equal
        vmfge.vf vd, vs2, rs1, vm  # vector-scalar

    Comparison      Assembler Mapping             Assembler pseudoinstruction

    va < vb         vmflt.vv vd, va, vb, vm
    va <= vb        vmfle.vv vd, va, vb, vm
    va > vb         vmflt.vv vd, vb, va, vm    vmfgt.vv vd, va, vb, vm
    va >= vb        vmfle.vv vd, vb, va, vm    vmfge.vv vd, va, vb, vm

    va < f          vmflt.vf vd, va, f, vm
    va <= f         vmfle.vf vd, va, f, vm
    va > f          vmfgt.vf vd, va, f, vm
    va >= f         vmfge.vf vd, va, f, vm

    va, vb vector register groups
    f      scalar floating-point register

Note | Providing all forms is necessary to correctly handle unordered comparisons for NaNs.

Note | C99 floating-point quiet comparisons can be implemented by masking the signaling comparisons when either input is NaN, as follows. When the comparand is a non-NaN constant, the middle two instructions can be omitted.

        # Example of implementing isgreater()
        vmfeq.vv v0, va, va        # Only set where A is not NaN.
        vmfeq.vv v1, vb, vb        # Only set where B is not NaN.
        vmand.mm v0, v0, v1        # Only set where A and B are ordered,
        vmfgt.vv v0, va, vb, v0.t  #  so only set flags on ordered values.

Note | In the above sequence, it is tempting to mask the second `vmfeq` instruction and remove the `vmand` instruction, but this more efficient sequence incorrectly fails to raise the invalid exception when an element of `va` contains a quiet NaN and the corresponding element in `vb` contains a signaling NaN.

### 14.12. Vector Floating-Point Classify Instruction

This is a unary vector-vector instruction that operates in the same way as the scalar classify instruction.

        vfclass.v vd, vs2, vm   # Vector-vector

The 10-bit mask produced by this instruction is placed in the least-significant bits of the result elements. The instruction is only defined for SEW=16b and above, so the result will always fit in the destination elements.

### 14.13. Vector Floating-Point Merge Instruction

A vector-scalar floating-point merge instruction is provided, which operates on all body elements, from `vstart` up to the current vector length in `vl` regardless of mask value.

The `vfmerge.vfm` instruction is always masked (`vm=0`). At elements where the mask value is zero, the first vector operand is copied to the destination element, otherwise a scalar floating-point register value is copied to the destination element.

    vfmerge.vfm vd, vs2, rs1, v0  # vd[i] = v0[i].LSB ? f[rs1] : vs2[i]

Note | In Zfinx systems, the instruction is identical to `vmerge.vxm`.

### 14.14. Vector Floating-Point Move Instruction

The vector floating-point move instruction splats a floating-point scalar operand to a vector register group. The instruction copies a scalar `f` register value to all active elements of a vector register group. This instruction is always unmasked (`vm=1`). The instruction must have the `vs2` field set to `v0`, with all other values for `vs2` reserved.

    vfmv.v.f vd, rs1  # vd[i] = f[rs1]

Note | In Zfinx systems, the instruction is identical to `vmv.v.x`.

Note | The `vfmv.v.f` instruction shares the encoding with the `vfmerge.vfm` instruction, but with `vm=1` and `vs2=v0`.

### 14.15. Single-Width Floating-Point/Integer Type-Convert Instructions

Conversion operations are provided to convert to and from floating-point values and unsigned and signed integers, where both source and destination are SEW wide.

    vfcvt.xu.f.v vd, vs2, vm   # Convert float to unsigned integer.
    vfcvt.x.f.v  vd, vs2, vm   # Convert float to signed integer.

    vfcvt.f.xu.v vd, vs2, vm   # Convert unsigned integer to float.
    vfcvt.f.x.v  vd, vs2, vm   # Convert signed integer to float.

The conversions follow the same rules on exceptional conditions as the scalar conversion instructions. The conversions always use the dynamic rounding mode in `frm`.

### 14.16. Widening Floating-Point/Integer Type-Convert Instructions

A set of conversion instructions are provided to convert between narrower integer and floating-point datatypes to a type of twice the width.

    vfwcvt.xu.f.v vd, vs2, vm   # Convert float to double-width unsigned integer.
    vfwcvt.x.f.v  vd, vs2, vm   # Convert float to double-width signed integer.

    vfwcvt.f.xu.v vd, vs2, vm   # Convert unsigned integer to double-width float.
    vfwcvt.f.x.v  vd, vs2, vm   # Convert signed integer to double-width float.

    vfwcvt.f.f.v vd, vs2, vm   # Convert single-width float to double-width float.

These instructions have the same constraints on vector register overlap as other widening instructions (see Widening Vector Arithmetic Instructions).

Note | A double-width IEEE floating-point value can always represent a single-width integer exactly.

Note | A double-width IEEE floating-point value can always represent a single-width IEEE floating-point value exactly.

Note | A full set of floating-point widening conversions are not supported as single instructions, but any widening conversion can be implemented as several doubling steps with equivalent results and no additional exception flags raised.

### 14.17. Narrowing Floating-Point/Integer Type-Convert Instructions

A set of conversion instructions are provided to convert wider integer and floating-point datatypes to a type of half the width.

    vfncvt.xu.f.w vd, vs2, vm   # Convert double-width float to unsigned integer.
    vfncvt.x.f.w  vd, vs2, vm   # Convert double-width float to signed integer.

    vfncvt.f.xu.w vd, vs2, vm   # Convert double-width unsigned integer to float.
    vfncvt.f.x.w  vd, vs2, vm   # Convert double-width signed integer to float.

    vfncvt.f.f.w vd, vs2, vm    # Convert double-width float to single-width float.
    vfncvt.rod.f.f.w vd, vs2, vm  # Convert double-width float to single-width float,
                                  #  rounding towards odd.

These instructions have the same constraints on vector register overlap as other narrowing instructions (see Narrowing Vector Arithmetic Instructions).

Note | A full set of floating-point widening conversions are not supported as single instructions. Conversions can be implemented in a sequence of halving steps. Results are equivalently rounded and the same exception flags are raised if all but the last halving step use round-towards-odd (`vfncvt.rod.f.f.w`). Only the final step should use the desired rounding mode.

Note | An integer value can be halved in width using the narrowing integer shift instructions with a shift amount of 0.

## 15. Vector Reduction Operations

Vector reduction operations take a vector register group of elements and a scalar held in element 0 of a vector register, and perform a reduction using some binary operator, to produce a scalar result in element 0 of a vector register. The scalar input and output operands are held in element 0 of a single vector register, not a vector register group, so any vector register can be the scalar source or destination of a vector reduction regardless of LMUL setting.

Note | Reductions read and write the scalar operand and result into element 0 of a vector register to avoid a loss of decoupling with the scalar processor, and to support future polymorphic use with future types not supported in the scalar unit.

Inactive elements from the source vector register group are excluded from the reduction, but the scalar operand is always included regardless of mask.

The other elements in the destination vector register ( 0 < index < VLEN/SEW) are left unchanged.

If `vl`=0, no operation is performed and the destination register is not updated.

Traps on vector reduction instructions are always reported with a `vstart` of 0. Vector reduction operations raise an illegal instruction exception if `vstart` is non-zero.

The assembler syntax for a reduction operation is `vredop.vs`, where the `.vs` suffix denotes the first operand is a vector register group and the second operand is a scalar stored in element 0 of a vector register.

### 15.1. Vector Single-Width Integer Reduction Instructions

All operands and results of single-width reduction instructions have the same SEW width. Overflows wrap around on arithmetic sums.

        # Simple reductions, where [*] denotes all active elements:
        vredsum.vs  vd, vs2, vs1, vm   # vd[0] =  sum( vs1[0] , vs2[*] )
        vredmaxu.vs vd, vs2, vs1, vm   # vd[0] = maxu( vs1[0] , vs2[*] )
        vredmax.vs  vd, vs2, vs1, vm   # vd[0] =  max( vs1[0] , vs2[*] )
        vredminu.vs vd, vs2, vs1, vm   # vd[0] = minu( vs1[0] , vs2[*] )
        vredmin.vs  vd, vs2, vs1, vm   # vd[0] =  min( vs1[0] , vs2[*] )
        vredand.vs  vd, vs2, vs1, vm   # vd[0] =  and( vs1[0] , vs2[*] )
        vredor.vs   vd, vs2, vs1, vm   # vd[0] =   or( vs1[0] , vs2[*] )
        vredxor.vs  vd, vs2, vs1, vm   # vd[0] =  xor( vs1[0] , vs2[*] )

### 15.2. Vector Widening Integer Reduction Instructions

The unsigned `vwredsumu.vs` instruction zero-extends the SEW-wide vector elements before summing them, then adds the 2*SEW-width scalar element, and stores the result in a 2*SEW-width scalar element.

The `vwredsum.vs` instruction sign-extends the SEW-wide vector elements before summing them.

        # Unsigned sum reduction into double-width accumulator
        vwredsumu.vs vd, vs2, vs1, vm   # 2*SEW = 2*SEW + sum(zero-extend(SEW))

        # Signed sum reduction into double-width accumulator
        vwredsum.vs  vd, vs2, vs1, vm   # 2*SEW = 2*SEW + sum(sign-extend(SEW))

### 15.3. Vector Single-Width Floating-Point Reduction Instructions

        # Simple reductions.
        vfredosum.vs vd, vs2, vs1, vm # Ordered sum
        vfredsum.vs  vd, vs2, vs1, vm # Unordered sum
        vfredmax.vs  vd, vs2, vs1, vm # Maximum value
        vfredmin.vs  vd, vs2, vs1, vm # Minimum value

#### 15.3.1. Vector Ordered Single-Width Floating-Point Sum Reduction

The `vfredosum` instruction must sum the floating-point values in element order, starting with the scalar in `vs1[0]`--that is, it performs the computation: `(((vs1[0] + vs2[0]) + vs2[1]) + …​)
vs2[vl-1]`, where each addition operates identically to the scalar floating-point instructions in terms of raising exception flags and generating or propagating special values.

Note | The ordered reduction supports compiler autovectorization, while the unordered FP sum allows for faster implementations.

When the operation is masked (`vm=0`), the masked-off elements do not affect the result or the exception flags.

Note | If no elements are active, no additions are performed, so the scalar in `vs1[0]` is simply copied to the destination register, without canonicalizing NaN values and without setting any exception flags. This behavior preserves the handling of NaNs, exceptions, and rounding when autovectorizing a scalar summation loop.

#### 15.3.2. Vector Unordered Single-Width Floating-Point Sum Reduction

The unordered sum reduction instruction, `vfredsum`, provides an implementation more freedom in performing the reduction.

The implementation can produce a result equivalent to a reduction tree composed of binary operator nodes, with the inputs being elements from the source vector register group (`vs2`) and the source scalar value (`vs1[0]`). Each operator in the tree accepts two inputs and produces one result. Each operator can either perform an exact addition, or a floating-point addition according to the RISC-V IEEE scalar floating-point specification and with the currently active floating-point dynamic rounding mode. A node where one input is derived only from elements masked-off or beyond the active vector length may either treat that input as IEEE +0.0 of the appropriate SEW or simply copy the other input to its output. The root node in the tree must produce an IEEE result of the appropriate SEW. An implementation is allowed to add an additional IEEE +0.0 to the final result.

The reduction tree structure must be deterministic for a given value in `vtype` and `vl`.

Note | As a consequence of this definition, implementations need not propagate NaN payloads through the reduction tree when no elements are active. In particular, if no elements are active and the scalar input is NaN, implementations are permitted to canonicalize the NaN and, if the NaN is signaling, set the invalid exception flag. Implementations are alternatively permitted to pass through the original NaN and set no exception flags, as with `vfredosum`.

Note | The `vfredosum` instruction is a valid implementation of the `vfredsum` instruction.

#### 15.3.3. Vector Single-Width Floating Max and Min Reductions

Note | Floating-point max and min reductions should return the same final value and raise the same exception flags regardless of operation order.

### 15.4. Vector Widening Floating-Point Reduction Instructions

Widening forms of the sum reductions are provided that read and write a double-width reduction result.

     # Simple reductions.
     vfwredosum.vs vd, vs2, vs1, vm # Ordered sum
     vfwredsum.vs vd, vs2, vs1, vm  # Unordered sum

The reduction of the SEW-width elements is performed as in the single-width reduction case, with the elements in `vs2` promoted to 2*SEW bits before adding to the 2*SEW-bit accumulator.

## 16. Vector Mask Instructions

Several instructions are provided to help operate on mask values held in a vector register.

### 16.1. Vector Mask-Register Logical Instructions

Vector mask-register logical operations operate on mask registers. The size of one element in a mask register is SEW/LMUL, so these instructions all operate on single vector registers regardless of the setting of the `vlmul` field in `vtype`. They do not change the value of `vlmul`.

As with other vector instructions, the elements with indices less than `vstart` are unchanged, and `vstart` is reset to zero after execution. Vector mask logical instructions are always unmasked so there are no inactive elements. Mask elements past `vl`, the tail elements, are unchanged.

Within a mask element, these instructions perform their operations using only the least-significant bit of each operand and zero-extend the single-bit result to fill the destination mask element.

        vmand.mm vd, vs2, vs1     # vd[i] =   vs2[i].LSB &&  vs1[i].LSB
        vmnand.mm vd, vs2, vs1    # vd[i] = !(vs2[i].LSB &&  vs1[i].LSB)
        vmandnot.mm vd, vs2, vs1  # vd[i] =   vs2[i].LSB && !vs1[i].LSB
        vmxor.mm  vd, vs2, vs1    # vd[i] =   vs2[i].LSB ^^  vs1[i].LSB
        vmor.mm  vd, vs2, vs1     # vd[i] =   vs2[i].LSB ||  vs1[i].LSB
        vmnor.mm  vd, vs2, vs1    # vd[i] = !(vs2[i[.LSB ||  vs1[i].LSB)
        vmornot.mm  vd, vs2, vs1  # vd[i] =   vs2[i].LSB || !vs1[i].LSB
        vmxnor.mm vd, vs2, vs1    # vd[i] = !(vs2[i].LSB ^^  vs1[i].LSB)

Several assembler pseudoinstructions are defined as shorthand for common uses of mask logical operations:

        vmcpy.m vd, vs  => vmand.mm vd, vs, vs  # Copy mask register
        vmclr.m vd     => vmxor.mm vd, vd, vd   # Clear mask register
        vmset.m vd     => vmxnor.mm vd, vd, vd  # Set mask register
        vmnot.m vd, vs => vmnand.mm vd, vs, vs  # Invert bits

Note | The vmcpy.m instruction is not called vmmv as elsewhere in the architecture mv implies a bitwise copy without interpreting the bits. The vmcpy.m instruction will clear upper bits of the destination mask register to zero regardless of source values in these bits.

The set of eight mask logical instructions can generate any of the 16 possibly binary logical functions of the two input masks:

inputs |
--- | ---
0 | 0 | 1 | 1 | src1
0 | 1 | 0 | 1 | src2

output | instruction | pseudoinstruction
--- | --- | ---
0 | 0 | 0 | 0 | vmxor.mm vd, vd, vd | vmclr.m vd
1 | 0 | 0 | 0 | vmnor.mm vd, src1, src2 |
0 | 1 | 0 | 0 | vmandnot.mm vd, src2, src1 |
1 | 1 | 0 | 0 | vmnand.mm vd, src1, src1 | vmnot.m vd, src1
0 | 0 | 1 | 0 | vmandnot.mm vd, src1, src2 |
1 | 0 | 1 | 0 | vmnand.mm vd, src2, src2 | vmnot.m vd, src2
0 | 1 | 1 | 0 | vmxor.mm vd, src1, src2 |
1 | 1 | 1 | 0 | vmnand.mm vd, src1, src2 |
0 | 0 | 0 | 1 | vmand.mm vd, src1, src2 |
1 | 0 | 0 | 1 | vmxnor.mm vd, src1, src2 |
0 | 1 | 0 | 1 | vmand.mm vd, src2, src2 | vmcpy.m vd, src2
1 | 1 | 0 | 1 | vmornot.mm vd, src2, src1 |
0 | 0 | 1 | 1 | vmand.mm vd, src1, src1 | vmcpy.m vd, src1
1 | 0 | 1 | 1 | vmornot.mm vd, src1, src2 |
1 | 1 | 1 | 1 | vmxnor.mm vd, vd, vd | vmset.m vd

Note | The vector mask logical instructions are designed to be easily fused with a following masked vector operation to effectively expand the number of predicate registers by moving values into `v0` before use.

### 16.2. Vector mask population count `vpopc`

        vpopc.m rd, vs2, vm

The source operand is a single vector register holding mask register values as described in Section Mask Register Layout.

The `vpopc.m` instruction counts the number of mask elements of the active elements of the vector source mask register that have their least-significant bit set, and writes the result to a scalar `x` register.

The operation can be performed under a mask, in which case only the masked elements are counted.

     vpopc.m rd, vs2, v0.t # x[rd] = sum_i ( vs2[i].LSB && v0[i].LSB )

Traps on `vpopc.m` are always reported with a `vstart` of 0. The `vpopc` instruction will raise an illegal instruction exception if `vstart` is non-zero.

### 16.3. `vfirst` find-first-set mask bit

        vfirst.m rd, vs2, vm

The `vfirst` instruction finds the lowest-numbered active element of the source mask vector that has its LSB set and writes that element’s index to a GPR. If no element has an LSB set, -1 is written to the GPR.

Note | Software can assume that any negative value (highest bit set) corresponds to no element found, as vector lengths will never exceed 2(XLEN-1) on any implementation.

Traps on `vfirst` are always reported with a `vstart` of 0. The `vfirst` instruction will raise an illegal instruction exception if `vstart` is non-zero.

### 16.4. `vmsbf.m` set-before-first mask bit

        vmsbf.m vd, vs2, vm

     # Example

         7 6 5 4 3 2 1 0   Element number

         1 0 0 1 0 1 0 0   v3 contents
                           vmsbf.m v2, v3
         0 0 0 0 0 0 1 1   v2 contents

         1 0 0 1 0 1 0 1   v3 contents
                           vmsbf.m v2, v3
         0 0 0 0 0 0 0 0   v2

         0 0 0 0 0 0 0 0   v3 contents
                           vmsbf.m v2, v3
         1 1 1 1 1 1 1 1   v2

         1 1 0 0 0 0 1 1   v0 vcontents
         1 0 0 1 0 1 0 0   v3 contents
                           vmsbf.m v2, v3, v0.t
         0 1 x x x x 1 1   v2 contents

The `vmsbf.m` instruction takes a mask register as input and writes results to a mask register. The instruction writes a 1 to all active mask elements before the first source element that has a set LSB, then writes a zero to that element and all following active elements. If there is no set bit in the source vector, then all active elements in the destination are written with a 1.

The tail elements in the destination mask register are unchanged.

Traps on `vmsbf.m` are always reported with a `vstart` of 0. The `vmsbf` instruction will raise an illegal instruction exception if `vstart` is non-zero.

### 16.5. `vmsif.m` set-including-first mask bit

The vector mask set-including-first instruction is similar to set-before-first, except it also includes the element with a set bit.

        vmsif.m vd, vs2, vm

     # Example

         7 6 5 4 3 2 1 0   Element number

         1 0 0 1 0 1 0 0   v3 contents
                           vmsif.m v2, v3
         0 0 0 0 0 1 1 1   v2 contents

         1 0 0 1 0 1 0 1   v3 contents
                           vmsif.m v2, v3
         0 0 0 0 0 0 0 1   v2

         1 1 0 0 0 0 1 1   v0 vcontents
         1 0 0 1 0 1 0 0   v3 contents
                           vmsif.m v2, v3, v0.t
         1 1 x x x x 1 1   v2 contents

The tail elements in the destination mask register are unchanged.

Traps on `vmsif.m` are always reported with a `vstart` of 0. The `vmsif` instruction will raise an illegal instruction exception if `vstart` is non-zero.

### 16.6. `vmsof.m` set-only-first mask bit

The vector mask set-only-first instruction is similar to set-before-first, except it only sets the first element with a bit set, if any.

        vmsof.m vd, vs2, vm

     # Example

         7 6 5 4 3 2 1 0   Element number

         1 0 0 1 0 1 0 0   v3 contents
                           vmsof.m v2, v3
         0 0 0 0 0 1 0 0   v2 contents

         1 0 0 1 0 1 0 1   v3 contents
                           vmsof.m v2, v3
         0 0 0 0 0 0 0 1   v2

         1 1 0 0 0 0 1 1   v0 vcontents
         1 1 0 1 0 1 0 0   v3 contents
                           vmsof.m v2, v3, v0.t
         0 1 x x x x 0 0   v2 contents

The tail elements in the destination mask register are unchanged.

Traps on `vmsof.m` are always reported with a `vstart` of 0. The `vmsof` instruction will raise an illegal instruction exception if `vstart` is non-zero.

### 16.7. Example using vector mask instructions

The following is an example of vectorizing a data-dependent exit loop.

      # char* strcpy(char *dst, const char* src)
    strcpy:
          mv a2, a0             # Copy dst
          li t0, -1             # Infinite AVL
    loop:
        vsetvli x0, t0, e8      # Max length vectors of bytes
        vlbuff.v v1, (a1)       # Get src bytes
          csrr t1, vl           # Get number of bytes fetched
        vmseq.vi v0, v1, 0      # Flag zero bytes
        vfirst.m a3, v0         # Zero found?
          add a1, a1, t1        # Bump pointer
        vmsif.m v0, v0          # Set mask up to and including zero byte.
        vsb.v v1, (a2), v0.t    # Write out bytes
          add a2, a2, t1        # Bump pointer
          bltz a3, loop         # Zero byte not found, so loop

          ret

      # char* strncpy(char *dst, const char* src, size_t n)
    strncpy:
          mv a3, a0             # Copy dst
    loop:
        vsetvli x0, a2, e8   # Vectors of bytes.
        vlbuff.v v1, (a1)       # Get src bytes
        vmseq.vi v0, v1, 0      # Flag zero bytes
        vfirst.m a4, v0         # Zero found?
        vmsif.m v0, v0          # Set mask up to and including zero byte.
        vsb.v v1, (a3), v0.t    # Write out bytes
          csrr t1, vl           # Get number of bytes fetched
          sub a2, a2, t1        # Decrement count.
          bgez a4, zero_tail    # Zero remaining bytes.
          add a1, a1, t1        # Bump pointer
          add a3, a3, t1        # Bump pointer
          bnez a2, loop         # Anymore?

          ret

    zero_tail:
        vsetvli x0, a2, e8,m8   # Vectors of bytes.
        vmv.v.i v0, 0           # Splat zero.

    zero_loop:
        vsetvli t1, a2, e8,m8   # Vectors of bytes.
        vsb.v v0, (a3)          # Store zero.
          sub a2, a2, t1        # Decrement count.
          add a3, a3, t1        # Bump pointer
          bnez a2, zero_loop    # Anymore?

          ret

### 16.8. Vector Iota Instruction

The `viota.m` instruction reads a source vector mask register and writes to each element of the destination vector register group the sum of all the least-significant bits of elements in the mask register whose index is less than the element, e.g., a parallel prefix sum of the mask values.

This instruction can be masked, in which case only the enabled elements contribute to the sum and only the enabled elements are written.

     viota.m vd, vs2, vm

     # Example

         7 6 5 4 3 2 1 0   Element number

         1 0 0 1 0 0 0 1   v2 contents
                           viota.m v4, v2 # Unmasked
         2 2 2 1 1 1 1 0   v4 result

         1 1 1 0 1 0 1 1   v0 contents
         1 0 0 1 0 0 0 1   v2 contents
         2 3 4 5 6 7 8 9   v4 contents
                           viota.m v4, v2, v0.t # Masked
         1 1 1 5 1 7 1 0   v4 results

The result value is zero-extended to fill the destination element if SEW is wider than the result. If the result value would overflow the destination SEW, the least-significant SEW bits are retained.

Traps on `viota.m` are always reported with a `vstart` of 0, and execution is always restarted from the beginning when resuming after a trap handler. An illegal instruction exception is raised if `vstart` is non-zero.

An illegal instruction exception is raised if the destination vector register group overlaps the source vector mask register. If the instruction is masked, an illegal instruction exception is issued if the destination vector register group overlaps `v0`.

Note | These constraints exist for two reasons. First, to simplify avoidance of WAR hazards in implementations with temporally long vector registers and no vector register renaming. Second, to enable resuming execution after a trap simpler.

The `viota.m` instruction can be combined with memory scatter instructions (indexed stores) to perform vector compress functions.

        # Compact non-zero elements from input memory array to output memory array
        #
        # size_t compact_non_zero(size_t n, const int* in, int* out)
        # {
        #   size_t i;
        #   size_t count = 0;
        #   int *p = out;
        #
        #   for (i=0; i<n; i++)
        #   {
        #       const int v = *in++;
        #       if (v != 0)
        #           *p++ = v;
        #   }
        #
        #   return (size_t) (p - out);
        # }
        #
        # a0 = n
        # a1 = &in
        # a2 = &out

    compact_non_zero:
        li a6, 0                      # Clear count of non-zero elements
    loop:
        vsetvli a5, a0, e32,m8  # 32-bit integers
        vlw.v v8, (a1)                # Load input vector
          sub a0, a0, a5              # Decrement number done
          slli a5, a5, 2              # Multiply by four bytes
        vmsne.vi v0, v8, 0            # Locate non-zero values
          add a1, a1, a5              # Bump input pointer
        vpopc.m a5, v0                # Count number of elements set in v0
        viota.m v16, v0               # Get destination offsets of active elements
          add a6, a6, a5              # Accumulate number of elements
        vsll.vi v16, v16, 2, v0.t     # Multiply offsets by four bytes
          slli a5, a5, 2              # Multiply number of non-zero elements by four bytes
        vsuxw.v v8, (a2), v16, v0.t   # Scatter using scaled viota results under mask
          add a2, a2, a5              # Bump output pointer
          bnez a0, loop               # Any more?

          mv a0, a6                   # Return count
          ret

### 16.9. Vector Element Index Instruction

The `vid.v` instruction writes each element’s index to the destination vector register group, from 0 to `vl`-1.

        vid.v vd, vm  # Write element ID to destination.

The instruction can be masked.

The `vs2` field of the instruction must be set to `v0`, otherwise the encoding is reserved.

The result value is zero-extended to fill the destination element if SEW is wider than the result. If the result value would overflow the destination SEW, the least-significant SEW bits are retained.

Note | This constraint is to avoid WAR hazards in long vector implementations without register renaming, and to support restart.

Note | Microarchitectures can implement `vid.v` instruction using the same datapath as `viota.m` but with an implicit set mask source.

## 17. Vector Permutation Instructions

A range of permutation instructions are provided to move elements around within the vector registers.

### 17.1. Integer Scalar Move Instructions

The integer scalar read/write instructions transfer a single value between a scalar `x` register and element 0 of a vector register. The instructions ignore LMUL and vector register groups.

    vmv.x.s rd, vs2  # x[rd] = vs2[0] (rs1=0)
    vmv.s.x vd, rs1  # vd[0] = x[rs1] (vs2=0)

The `vmv.x.s` instruction copies a single SEW-wide element from index 0 of the source vector register to a destination integer register. If SEW > XLEN, the least-significant XLEN bits are transferred and the upper SEW-XLEN bits are ignored. If SEW < XLEN, the value is sign-extended to XLEN bits.

The `vmv.s.x` instruction copies the scalar integer register to element 0 of the destination vector register. If SEW < XLEN, the least-significant bits are copied and the upper XLEN-SEW bits are ignored. If SEW > XLEN, the value is sign-extended to SEW bits. The other elements in the destination vector register ( 0 < index < VLEN/SEW) are unchanged. If `vstart` ≥ `vl`, no operation is performed and the destination register is not updated.

Note | As a consequence, when `vl`=0, no elements are updated in the destination vector register group, regardless of `vstart`.

The encodings corresponding to the masked versions (`vm=0`) of `vmv.x.s` and `vmv.s.x` are reserved.

### 17.2. Floating-Point Scalar Move Instructions

The floating-point scalar read/write instructions transfer a single value between a scalar `f` register and element 0 of a vector register. The instructions ignore LMUL and vector register groups.

    vfmv.f.s rd, vs2  # f[rd] = vs2[0] (rs1=0)
    vfmv.s.f vd, rs1  # vd[0] = f[rs1] (vs2=0)

The `vfmv.f.s` instruction copies a single SEW-wide element from index 0 of the source vector register to a destination scalar floating-point register. If SEW > FLEN, the least-significant FLEN bits are transferred and the upper SEW-FLEN bits are ignored. If SEW < FLEN, the value is NaN-boxed (1-extended) to FLEN bits.

The `vfmv.s.f` instruction copies the scalar floating-point register to element 0 of the destination vector register. If SEW < FLEN, the least-significant bits are copied and the upper FLEN-SEW bits are ignored. If SEW > FLEN, the value is NaN-boxed (1-extended) to SEW bits. The other elements in the destination vector register ( 0 < index < VLEN/SEW) are unchanged. If `vstart` ≥ `vl`, no operation is performed and the destination register is not updated.

Note | As a consequence, when `vl`=0, no elements are updated in the destination vector register group, regardless of `vstart`.

The encodings corresponding to the masked versions (`vm=0`) of `vfmv.f.s` and `vfmv.s.f` are reserved.

### 17.3. Vector Slide Instructions

The slide instructions move elements up and down a vector register group.

Note | The slide operations can be implemented much more efficiently than using the arbitrary register gather instruction. Implementations may optimize certain OFFSET values for `vslideup` and `vslidedown`. In particular, power-of-2 offsets may operate substantially faster than other offsets.

For all of the `vslideup`, `vslidedown`, `vslide1up`, and `vslide1down` instructions, if `vstart` ≥ `vl`, the instruction performs no operation and leaves the destination vector register unchanged.

Note | As a consequence, when `vl`=0, no elements are updated in the destination vector register group, regardless of `vstart`.

The slide instructions may be masked, with mask element i controlling whether destination element i is written.

#### 17.3.1. Vector Slideup Instructions

     vslideup.vx vd, vs2, rs1, vm        # vd[i+rs1] = vs2[i]
     vslideup.vi vd, vs2, uimm[4:0], vm  # vd[i+uimm] = vs2[i]

For `vslideup`, the value in `vl` specifies the maximum number of destination elements that are written. The start index (OFFSET) for the destination can be either specified using an unsigned integer in the `x` register specified by `rs1`, or a 5-bit immediate treated as an unsigned 5-bit quantity. Destination elements OFFSET through `vl`-1 are written if unmasked and if OFFSET < `vl`.

       vslideup behavior for destination elements

       OFFSET is amount to slideup, either from x register or a 5-bit immediate

                        0 <  i < max(vstart, OFFSET)  Unchanged
      max(vstart, OFFSET) <= i < vl                   vd[i] = vs2[i-OFFSET] if mask enabled,
                                                       unchanged if not
                       vl <= i < VLMAX                Tail elements, unchanged

The destination vector register group for `vslideup` cannot overlap the vector register group of the source, otherwise an illegal instruction exception is raised.

Note | The non-overlap constraint avoids WAR hazards on the input vectors during execution, and enables restart with non-zero `vstart`.

#### 17.3.2. Vector Slidedown Instructions

     vslidedown.vx vd, vs2, rs1, vm       # vd[i] = vs2[i+rs1]
     vslidedown.vi vd, vs2, uimm[4:0], vm # vd[i] = vs2[i+uimm]

For `vslidedown`, the value in `vl` specifies the number of destination elements that are written.

The start index (OFFSET) for the source can be either specified using an unsigned integer in the `x` register specified by `rs1`, or a 5-bit immediate treated as an unsigned 5-bit quantity.

        vslidedown behavior for source elements for element i in slide
                         0 <= i+OFFSET < VLMAX   Read vs2[i+OFFSET]
                     VLMAX <= i+OFFSET           Read as 0

        vslidedown behavior for destination element i in slide
                         0 <  i < vstart         Unchanged
                    vstart <= i < vl             Updated if mask enabled, unchanged if not
                        vl <= i < VLMAX          Unchanged

#### 17.3.3. Vector Slide1up

Variants of slide are provided that only move by one element but which also allow a scalar integer value to be inserted at the vacated element position.

     vslide1up.vx vd, vs2, rs1, vm        # vd[0]=x[rs1], vd[i+1] = vs2[i]

The `vslide1up` instruction places the `x` register argument at location 0 of the destination vector register group, provided that element 0 is active, otherwise the destination element is unchanged. If XLEN < SEW, the value is sign-extended to SEW bits. If XLEN > SEW, the least-significant bits are copied over and the high SEW-XLEN bits are ignored.

The remaining active `vl`-1 elements are copied over from index i in the source vector register group to index i+1 in the destination vector register group.

The `vl` register specifies how many of the destination vector register elements are written with source values, and all tail elements are unchanged.

       vslide1up behavior

                        i < vstart  unchanged
                    0 = i = vstart  vd[i] = x[rs1] if mask enabled, unchanged if not
      max(vstart, 1) <= i < vl      vd[i] = vs2[i-1] if mask enabled, unchanged if not
                  vl <= i < VLMAX   unchanged

The `vslide1up` instruction requires that the destination vector register group does not overlap the source vector register group. Otherwise, an illegal instruction exception is raised.

#### 17.3.4. Vector Slide1down Instruction

The `vslide1down` instruction copies the first `vl`-1 active elements values from index i+1 in the source vector register group to index i in the destination vector register group.

The `vl` register specifies how many of the destination vector register elements are written with source values, and all tail elements are unchanged.

     vslide1down.vx vd, vs2, rs1, vm      # vd[i] = vs2[i+1], vd[vl-1]=x[rs1]

The `vslide1down` instruction places the `x` register argument at location `vl`-1 in the destination vector register, provided that element `vl-1` is active, otherwise the destination element is unchanged. If XLEN < SEW, the value is sign-extended to SEW bits. If XLEN > SEW, the least-significant bits are copied over and the high SEW-XLEN bits are ignored.

       vslide1down behavior

                           i < vstart  unchanged
                 vstart <= i < vl-1    vd[i] = vs2[i+1] if mask enabled, unchanged if not
                 vstart <= i = vl-1    vd[vl-1] = x[rs1] if mask enabled, unchanged if not
                     vl <= i < VLMAX   unchanged

Note | The `vslide1down` instruction can be used to load values into a vector register without using memory and without disturbing other vector registers. This provides a path for debuggers to modify the contents of a vector register, albeit slowly, with multiple repeated `vslide1down` invocations.

### 17.4. Vector Register Gather Instruction

The vector register gather instruction reads elements from a first source vector register group at locations given by a second source vector register group. The index values in the second vector are treated as unsigned integers. The source vector can be read at any index < VLMAX regardless of `vl`. The number of elements to write to the destination register is given by `vl`, and elements past `vl` in the destination are unchanged. The operation can be masked.

    vrgather.vv vd, vs2, vs1, vm # vd[i] = (vs1[i] >= VLMAX) ? 0 : vs2[vs1[i]];

If the element indices are out of range ( `vs1[i]` ≥ VLMAX ) then zero is returned for the element value.

Vector-scalar and vector-immediate forms of the register gather are also provided. These read one element from the source vector at the given index, and write this value to the `vl` elements at the start of the destination vector register. The index value in the scalar register and the immediate are treated as unsigned integers.

Note | These forms allow any vector element to be "splatted" to an entire vector.

    vrgather.vx vd, vs2, rs1, vm # vd[i] = (x[rs1] >= VLMAX) ? 0 : vs2[x[rs1]]
    vrgather.vi vd, vs2, uimm, vm # vd[i] = (uimm >= VLMAX) ? 0 : vs2[uimm]

For any `vrgather` instruction, the destination vector register group cannot overlap with the source vector register groups, including the mask register if the operation is masked, otherwise an illegal instruction exception is raised.

Note | When SEW=8, only vector elements 0-255 can be referenced.

### 17.5. Vector Compress Instruction

The vector compress instruction allows elements selected by a vector mask register from a source vector register group to be packed into contiguous elements at the start of the destination vector register group.

      vcompress.vm vd, vs2, vs1  # Compress into vd elements of vs2 where vs1 is enabled

The vector mask register specified by `vs1` indicates which of the first `vl` elements of vector register group `vs2` should be extracted and packed into contiguous elements at the beginning of vector register `vd`. Any remaining elements of `vd` are unchanged.

        Example use of vcompress instruction

            1 1 0 1 0 0 1 0 1   v0
            8 7 6 5 4 3 2 1 0   v1
            1 2 3 4 5 6 7 8 9   v2

                                    vcompress.vm v2, v1, v0
            1 2 3 4 8 7 5 2 0   v2

`vcompress` is encoded as an unmasked instruction (`vm=1`). The equivalent masked instruction (`vm=0`) is reserved.

The destination vector register group cannot overlap the source vector register group or the source vector mask register, otherwise an illegal instruction exception is raised.

A trap on a `vcompress` instruction is always reported with a `vstart` of 0. Executing a `vcompress` instruction with a non-zero `vstart` raises an illegal instruction exception.

Note | Although possible, `vcompress` is one of the more difficult instructions to restart with a non-zero `vstart`, so assumption is implementations will choose not do that but will instead restart from element 0. This does mean elements in destination register after `vstart` will already have been updated.

### 17.6. Whole Vector Register Move

The `vmv<nf>r.v` instructions copy whole vector registers (i.e., all VLEN bits) ignoring the current settings of the `vl` and `vtype` register.

Note | These instructions are intended to aid compilers to shuffle vector registers without needing to know or change `vl` or `vtype`.

The instruction is encoded as an OPIVI instruction. The number of vector registers to copy is encoded in the low three bits of the `simm` field using the same encoding as the `nf` field for memory instructions. The upper two bits of `simm` field must be zero.

Note | The instruction uses the same funct6 encoding as the `vsmul` instruction but with an immediate operand, and only the unmasked version (`vm=1`). This encoding is chosen as it is close to the related `vmerge` encoding, and it is unlikely the `vsmul` instruction would benefit from an immediate form.

        vmv<nf>r.v vd, vs2  # General form

        vmv1r.v v1, v2   #  Copy v1=v2
        vmv3r.v v5, v9   #  Copy v5=v9; v6=v10; v7=v11

The source and destination vector register groups cannot overlap if the register number in `vd` is greater than `vs2`, otherwise an illegal instruction exception will be raised.

Note | If `vd` is equal to `vs2` the instruction is a NOP.

The sum of `vd` and `nf` and the sum of `vs2` and `nf` must both be less than 32 (i.e., no wraparound of register addressing), else an illegal instruction exception is raised.

## 18. Exception Handling

On a trap during a vector instruction (caused by either a synchronous exception or an asynchronous interrupt), the existing `*epc` CSR is written with a pointer to the errant vector instruction, while the `vstart` CSR contains the element index that caused the trap to be taken.

Note | We chose to add a `vstart` CSR to allow resumption of a partially executed vector instruction to reduce interrupt latencies and to simplify forward-progress guarantees. This is similar to the scheme in the IBM 3090 vector facility. To ensure forward progress without the `vstart` CSR, implementations would have to guarantee an entire vector instruction can always complete atomically without generating a trap. This is particularly difficult to ensure in the presence of strided or scatter/gather operations and demand-paged virtual memory.

### 18.1. Precise vector traps

Precise vector traps require that:

1. all instructions older than the trapping vector instruction have committed their results

2. no instructions newer than the trapping vector instruction have altered architectural state

3. any operations within the trapping vector instruction affecting result elements preceding the index in the `vstart` CSR have committed their results

4. no operations within the trapping vector instruction affecting elements at or following the `vstart` CSR have altered architectural state except if restarting and completing the affected vector instruction will recover the correct state.

We relax the last requirement to allow elements following `vstart` to have been updated at the time the trap is reported, provided that re-executing the instruction from the given `vstart` will correctly overwrite those elements.

Note | We assume most supervisor-mode environments will require precise vector traps.

Except where noted above, vector instructions are allowed to overwrite their inputs, and so in most cases, the vector instruction restart must be from the `vstart` location. However, there are a number of cases where this overwrite is prohibited to enable execution of the the vector instructions to be idempotent and hence restartable from any location.

### 18.2. Imprecise vector traps

Imprecise vector traps are traps that are not precise. In particular, instructions newer than `*epc` may have committed results, and instructions older than `*epc` may have not completed execution. Imprecise traps are primarily intended to be used in situations where reporting an error and terminating execution is the appropriate response.

Note | A platform might specify that interrupts are precise while other traps are imprecise. We assume many embedded platforms will only generate imprecise traps for vector instructions on fatal errors, so do not require resumable traps.

### 18.3. Selectable precise/imprecise traps

Some platforms may choose to provide a privileged mode bit to select between precise and imprecise vector traps. Imprecise mode would run at high-performance but possibly make it difficult to discern error causes, while precise mode would run more slowly, but support debugging of errors albeit with a possibility of not experiencing the same errors as in imprecise mode.

### 18.4. Swappable traps

Another trap mode can support swappable state in the vector unit, where on a trap, special instructions can save and restore the vector unit microarchitectural state, to allow execution to continue correctly around imprecise traps.

This mechanism is not defined in the base vector ISA.

## 19. Divided Element Extension ('Zvediv')

Note | EDIV is the mostly likely part of the spec to change substantially.

The divided element extension allows each element to be treated as a packed sub-vector of narrower elements. This provides efficient support for some forms of narrow-width and mixed-width arithmetic, and also to allow outer-loop vectorization of short vector and matrix operations. In addition to modifying the behavior of some existing instructions, a few new instructions are provided to operate on vectors when EDIV > 1.

Note | This is written as an extension for now, but could become part of mandatory base in Unix vector profile.

The divided element extension adds a two-bit field, `vediv[1:0]` to the `vtype` register.

Table 15. `vtype` register layout
Bits | Name | Description
--- | --- | ---
XLEN-1 | vill | Illegal value if set
XLEN-2:7 |  | Reserved (write 0)
6:5 | vediv[1:0] | Used by EDIV extension
4:2 | vsew[2:0] | Standard element width (SEW) setting
1:0 | vlmul[1:0] | Vector register group multiplier (LMUL) setting

The `vediv` field encodes the number of ways, EDIV, into which each SEW-bit element is subdivided into equal sub-elements. A vector register group is now considered to hold a vector of sub-vectors.

vediv [1:0] | Division EDIV
--- | ---
0 | 0 | 1 | (undivided, as in base)
0 | 1 | 2 | two equal sub-elements
1 | 0 | 4 | four equal sub-elements
1 | 1 | 8 | eight equal sub-elements

SEW | EDIV | Sub-element | Integer accumulator | FP sum/dot accumulator
sum | dot | FLEN=32 | FLEN=64 | FLEN=128
8b | 2 | 4b | 8b | 8b | - | - | -
8b | 4 | 2b | 8b | 8b | - | - | -
8b | 8 | 1b | 8b | 8b | - | - | -
16b | 2 | 8b | 16b | 16b | - | - | -
16b | 4 | 4b | 8b | 16b | - | - | -
16b | 8 | 2b | 8b | 8b | - | - | -
32b | 2 | 16b | 32b | 32b | 32b | 32b | 32b
32b | 4 | 8b | 16b | 32b | - | - | -
32b | 8 | 4b | 8b | 16b | - | - | -
64b | 2 | 32b | 64b | 64b | 32b | 64b | 64b
64b | 4 | 16b | 32b | 64b | 32b | 32b | 32b
64b | 8 | 8b | 16b | 32b | - | - | -
128b | 2 | 64b | 128b | 128b | 32b | 64b | 128b
128b | 4 | 32b | 64b | 128b | 32b | 64b | 64b
128b | 8 | 16b | 32b | 64b | 32b | 32b | 32b
256b | 2 | 128b | 256b | 256b | 32b | 64b | 128b
256b | 4 | 64b | 128b | 256b | 32b | 64b | 128b
256b | 8 | 32b | 64b | 128b | 32b | 64b | 64b

Each implementation defines a minimum size for a sub-element, SELEN, which must be at most 8 bits.

Note | While SELEN is a fourth implementation-specific parameter, values smaller than 8 would be considered an additional extension.

### 19.1. Instructions not affected by EDIV

The vector start register `vstart` and exception reporting continue to work as before.

The vector length `vl` control and vector masking continue to operate at the element level.

Vector masking continues to operate at the element level, so sub-elements cannot be individually masked.

Note | SEW can be changed dynamically to enabled per-element masking for sub-elements of 8 bits and greater.

Vector load/store and AMO instructions are unaffected by EDIV, and continue to move whole elements.

Vector mask logical operations are unchanged by EDIV setting, and continue to operate on vector registers containing element masks.

Vector mask population count (`vpopc`), find-first and related instructions (`vfirst`, `vmsbf`, `vmsif`, `vmsof`), iota (`viota`), and element index (`vid`) instructions are unaffected by EDIV.

Vector integer bit insert/extract, and integer and floating-point scalar move instruction are unaffected by EDIV.

Vector slide-up/slide-down are unaffected by EDIV.

Vector compress instructions are unaffected by EDIV.

### 19.2. Instructions Affected by EDIV

#### 19.2.1. Regular Vector Arithmetic Instructions under EDIV

Most vector arithmetic operations are modified to operate on the individual sub-elements, so effective SEW is SEW/EDIV and effective vector length is `vl` * EDIV. For example, a vector add of 32-bit elements with a `vl` of 5 and EDIV of 4, operates identically to a vector add of 8-bit elements with a vector length of 20.

    vsetvli t0, a0, e32,m1,d4  # Vectors of 32-bit elements, divided into byte sub-elements
    vadd.vv v1,v2,v3                     # Performs a vector of 4*vl 8-bit additions.
    vsll.vx v1,v2,x1                     # Performs a vector of 4*vl 8-bit shifts.

#### 19.2.2. Vector Add with Carry/Subtract with Borrow Reserved under EDIV>1

For EDIV > 1, `vadc`, `vmadc`, `vsbc`, `vmsbc` are reserved.

#### 19.2.3. Vector Reduction Instructions under EDIV

Vector single-width integer sum reduction instructions are reserved under EDIV>1. Other vector single-width reductions and vector widening integer sum reduction instructions now operate independently on all elements in a vector, reducing sub-element values within an element to an element-wide result.

The scalar input is taken from the least-significant bits of the second operand, with the number of bits equal to the number of significant result bits (i.e., for sum and dot reductions, the number of bits are given in table above, for non-sum and non-dot reductions, equal to the element size).

    # Sum each sub-vector of four bytes into a 16-bit result.
    vsetvli t0, a0, e32,d4  # Vectors of 32-bit elements, divided into byte sub-elements
    vwredsum.vs v1, v2, v3 # v1[i][15:0] = v2[i][31:24] + v2[i][23:16]
                           #              + v2[i][15:8] + v2[i][7:0] + v3[i][15:0]

    # Find maximum among sub-elements
    vredmax.vs v5, v6, v7 # v5[i][7:0] = max(v6[i][31:24], v6[i][23:16],
                          #                    v6[i][15:8], v6[i][7:0], v7[i][7:0])

Integer sub-element non-sum reductions produce a final result that is max(8,SEW/EDIV) bits wide, sign- or zero-extended to full SEW if necessary.

Integer sub-element widening sum reductions produce a final result that is max(8,min(SEW,2*SEW/EDIV)) bits wide, sign- or zero-extended to full SEW if necessary.

Single-width floating-point reductions produce a final result that is SEW/EDIV bits wide.

Widening floating-point sum reductions produce a final result that is min(2*SEW/EDIV,FLEN) bits wide, NaN-boxed to the full SEW width if necessary.

#### 19.2.4. Vector Register Gather Instructions under EDIV

Vector register gather instructions under non-zero EDIV only gather sub-elements within the element. The source and index values are interpreted as relative to the enclosing element only. Index values ≥ EDIV write a zero value into the result sub-element.

           |       |       |  SEW = 32b, EDIV=4
            7 6 5 4 3 2 1 0  bytes
            d e a d b e e f  v1
            0 1 9 2 0 2 3 2  v2
                                vrgather.vv v3, v1, v2
            d a 0 e f e b e  v3
                                vrgather.vi v4, v1, 1
            a a a a e e e e  v4

Note | Vector register gathers with scalar or immediate arguments can "splat" values across sub-elements within an element.

Note | Implementations can provide fast implementations of register gathers constrained within a single element width.

### 19.3. Vector Integer Dot-Product Instruction

The integer dot-product reduction `vdot.vv` performs an element-wise multiplication between the source sub-elements then accumulates the results into the destination vector element. Note the assembler syntax uses a `.vv` suffix since both inputs are vectors of elements.

Sub-element integer dot reductions produce a final result that is max(8,min(SEW,4*SEW/EDIV)) bits wide, sign- or zero-extended to full SEW if necessary.

    # Unsigned dot-product
    vdotu.vv vd, vs2, vs1, vm  # Vector-vector

    # Signed dot-product
    vdot.vv vd, vs2, vs1, vm   # Vector-vector

      # Dot product, SEW=32, EDIV=1
      vdot.vv  vd, vs2, vs1, vm   # vd[i][31:0] += vs2[i][31:0] * vs1[i][31:0]

      # Dot product, SEW=32, EDIV=2
      vdot.vv vd, vs2, vs1, vm # vd[i][31:0] += vs2[i][31:16] * vs1[i][31:16]
                                                + vs2[i][15:0] * vs1[i][15:0]

      # Dot product, SEW=32, EDIV=4
      vdot.vv vd, vs2, vs1, vm # vd[i][31:0] += vs2[i][31:24] * vs1[i][31:24]
                                                + vs2[i][23:16] * vs1[i][23:16]
                                                + vs2[i][15:8] * vs1[i][15:8]
                                                + vs2[i][7:0] * vs1[i][7:0]

### 19.4. Vector Floating-Point Dot Product Instruction

The floating-point dot-product reduction `vfdot.vv` performs an element-wise multiplication between the source sub-elements then accumulates the results into the destination vector element. Note the assembler syntax uses a `.vv` suffix since both inputs are vectors of elements.

    # Signed dot-product
    vfdot.vv vd, vs2, vs1, vm   # Vector-vector

    # Dot product. SEW=32, EDIV=2
    vfdot.vv  vd, vs2, vs1, vm # vd[i][31:0] += vs2[i][31:16] * vs1[i][31:16]
                                               + vs2[i][15:0] * vs1[i][15:0]

    # Floating-point sub-vectors of two half-precision floats packed into 32-bit elements.
    vsetvli t0, a0, e32,m1,d2  # Vectors of 32-bit elements, divided into 16b sub-elements
    vfdot.vv v1, v2, v3   # v1[i][31:0] +=  v2[i][31:16]*v3[i][31:16] + v2[i][16:0]*v3[i][16:0]

    # Floating-point sub-vectors of four half-precision floats packed into 64-bit elements.
    vsetvli t0, a0, e64,m1,d4  # Vectors of 64-bit elements, divided into 16b sub-elements
    vfdot.vv v1, v2, v3
                     # v1[i][31:0] +=  v2[i][31:16]*v3[i][31:16] + v2[i][16:0]*v3[i][16:0] +
                     #                 v2[i][63:48]*v3[i][63:48] + v2[i][47:32]*v3[i][47:32];
                     # v1[i][63:32] = ~0 (NaN boxing)

## 20. Vector Instruction Listing

Integer | Integer | FP
--- | --- | ---
funct3 |  |  |  |  | funct3 |  |  |  | funct3 |  |  |
OPIVV | V |  |  |  | OPMVV | V |  |  | OPFVV | V |  |
OPIVX |  | X |  |  | OPMVX |  | X |  | OPFVF |  | F |
OPIVI |  |  | I |  |  |  |  |  |  |  |  |

funct6 | funct6 | funct6
--- | --- | ---
000000 | V | X | I | vadd | 000000 | V |  | vredsum | 000000 | V | F | vfadd
000001 |  |  |  |  | 000001 | V |  | vredand | 000001 | V |  | vfredsum
000010 | V | X |  | vsub | 000010 | V |  | vredor | 000010 | V | F | vfsub
000011 |  | X | I | vrsub | 000011 | V |  | vredxor | 000011 | V |  | vfredosum
000100 | V | X |  | vminu | 000100 | V |  | vredminu | 000100 | V | F | vfmin
000101 | V | X |  | vmin | 000101 | V |  | vredmin | 000101 | V |  | vfredmin
000110 | V | X |  | vmaxu | 000110 | V |  | vredmaxu | 000110 | V | F | vfmax
000111 | V | X |  | vmax | 000111 | V |  | vredmax | 000111 | V |  | vfredmax
001000 |  |  |  |  | 001000 | V | X | vaaddu | 001000 | V | F | vfsgnj
001001 | V | X | I | vand | 001001 | V | X | vaadd | 001001 | V | F | vfsgnjn
001010 | V | X | I | vor | 001010 | V | X | vasubu | 001010 | V | F | vfsgnjx
001011 | V | X | I | vxor | 001011 | V | X | vasub | 001011 |  |  |
001100 | V | X | I | vrgather | 001100 |  |  |  | 001100 |  |  |
001101 |  |  |  |  | 001101 |  |  |  | 001101 |  |  |
001110 |  | X | I | vslideup | 001110 |  | X | vslide1up | 001110 |  |  |
001111 |  | X | I | vslidedown | 001111 |  | X | vslide1down | 001111 |  |  |

funct6 | funct6 | funct6
--- | --- | ---
010000 | V | X | I | vadc | 010000 | V |  | VWXUNARY0 | 010000 | V |  | VWFUNARY0
|  |  |  |  | 010000 |  | X | VRXUNARY0 | 010000 |  | F | VRFUNARY0
010001 | V | X | I | vmadc | 010001 |  |  |  | 010001 |  |  |
010010 | V | X |  | vsbc | 010010 |  |  |  | 010010 |  |  |
010011 | V | X |  | vmsbc | 010011 |  |  |  | 010011 |  |  |
010100 |  |  |  |  | 010100 | V |  | VMUNARY0 | 010100 |  |  |
010101 |  |  |  |  | 010101 |  |  |  | 010101 |  |  |
010110 |  |  |  |  | 010110 |  |  |  | 010110 |  |  |
010111 | V | X | I | vmerge/vmv | 010111 | V |  | vcompress | 010111 |  | F | vfmerge.vf/vfmv
011000 | V | X | I | vmseq | 011000 | V |  | vmandnot | 011000 | V | F | vmfeq
011001 | V | X | I | vmsne | 011001 | V |  | vmand | 011001 | V | F | vmfle
011010 | V | X |  | vmsltu | 011010 | V |  | vmor | 011010 |  |  |
011011 | V | X |  | vmslt | 011011 | V |  | vmxor | 011011 | V | F | vmflt
011100 | V | X | I | vmsleu | 011100 | V |  | vmornot | 011100 | V | F | vmfne
011101 | V | X | I | vmsle | 011101 | V |  | vmnand | 011101 |  | F | vmfgt
011110 |  | X | I | vmsgtu | 011110 | V |  | vmnor | 011110 |  |  |
011111 |  | X | I | vmsgt | 011111 | V |  | vmxnor | 011111 |  | F | vmfge

funct6 | funct6 | funct6
--- | --- | ---
100000 | V | X | I | vsaddu | 100000 | V | X | vdivu | 100000 | V | F | vfdiv
100001 | V | X | I | vsadd | 100001 | V | X | vdiv | 100001 |  | F | vfrdiv
100010 | V | X |  | vssubu | 100010 | V | X | vremu | 100010 | V |  | VFUNARY0
100011 | V | X |  | vssub | 100011 | V | X | vrem | 100011 | V |  | VFUNARY1
100100 |  |  |  |  | 100100 | V | X | vmulhu | 100100 | V | F | vfmul
100101 | V | X | I | vsll | 100101 | V | X | vmul | 100101 |  |  |
100110 |  |  |  |  | 100110 | V | X | vmulhsu | 100110 |  |  |
100111 | V | X |  | vsmul | 100111 | V | X | vmulh | 100111 |  | F | vfrsub
|  |  | I | vmv<nf>r |  |  |  |  |  |  |  |
101000 | V | X | I | vsrl | 101000 |  |  |  | 101000 | V | F | vfmadd
101001 | V | X | I | vsra | 101001 | V | X | vmadd | 101001 | V | F | vfnmadd
101010 | V | X | I | vssrl | 101010 |  |  |  | 101010 | V | F | vfmsub
101011 | V | X | I | vssra | 101011 | V | X | vnmsub | 101011 | V | F | vfnmsub
101100 | V | X | I | vnsrl | 101100 |  |  |  | 101100 | V | F | vfmacc
101101 | V | X | I | vnsra | 101101 | V | X | vmacc | 101101 | V | F | vfnmacc
101110 | V | X | I | vnclipu | 101110 |  |  |  | 101110 | V | F | vfmsac
101111 | V | X | I | vnclip | 101111 | V | X | vnmsac | 101111 | V | F | vfnmsac

funct6 | funct6 | funct6
--- | --- | ---
110000 | V |  |  | vwredsumu | 110000 | V | X | vwaddu | 110000 | V | F | vfwadd
110001 | V |  |  | vwredsum | 110001 | V | X | vwadd | 110001 | V |  | vfwredsum
110010 |  |  |  |  | 110010 | V | X | vwsubu | 110010 | V | F | vfwsub
110011 |  |  |  |  | 110011 | V | X | vwsub | 110011 | V |  | vfwredosum
110100 |  |  |  |  | 110100 | V | X | vwaddu.w | 110100 | V | F | vfwadd.w
110101 |  |  |  |  | 110101 | V | X | vwadd.w | 110101 |  |  |
110110 |  |  |  |  | 110110 | V | X | vwsubu.w | 110110 | V | F | vfwsub.w
110111 |  |  |  |  | 110111 | V | X | vwsub.w | 110111 |  |  |
111000 | V |  |  | vdotu | 111000 | V | X | vwmulu | 111000 | V | F | vfwmul
111001 | V |  |  | vdot | 111001 |  |  |  | 111001 | V |  | vfdot
111010 |  |  |  |  | 111010 | V | X | vwmulsu | 111010 |  |  |
111011 |  |  |  |  | 111011 | V | X | vwmul | 111011 |  |  |
111100 | V | X |  | vqmaccu | 111100 | V | X | vwmaccu | 111100 | V | F | vfwmacc
111101 | V | X |  | vqmacc | 111101 | V | X | vwmacc | 111101 | V | F | vfwnmacc
111110 |  | X |  | vqmaccus | 111110 |  | X | vwmaccus | 111110 | V | F | vfwmsac
111111 | V | X |  | vqmaccsu | 111111 | V | X | vwmaccsu | 111111 | V | F | vfwnmsac

Table 16. VRXUNARY0 encoding space
vs2 |
--- | ---
00000 | vmv.s.x

Table 17. VWXUNARY0 encoding space
vs1 |
--- | ---
00000 | vmv.x.s
10000 | vpopc
10001 | vfirst

Table 18. VRFUNARY0 encoding space
vs2 |
--- | ---
00000 | vfmv.s.f

Table 19. VWFUNARY0 encoding space
vs1 |
--- | ---
00000 | vfmv.f.s

Table 20. VFUNARY0 encoding space
vs1 | name
--- | ---
single-width converts
00000 | vfcvt.xu.f.v
00001 | vfcvt.x.f.v
00010 | vfcvt.f.xu.v
00011 | vfcvt.f.x.v
widening converts
01000 | vfwcvt.xu.f.v
01001 | vfwcvt.x.f.v
01010 | vfwcvt.f.xu.v
01011 | vfwcvt.f.x.v
01100 | vfwcvt.f.f.v
narrowing converts
10000 | vfncvt.xu.f.w
10001 | vfncvt.x.f.w
10010 | vfncvt.f.xu.w
10011 | vfncvt.f.x.w
10100 | vfncvt.f.f.w
10101 | vfncvt.rod.f.f.w

Table 21. VFUNARY1 encoding space
vs1 | name
--- | ---
00000 | vfsqrt.v
10000 | vfclass.v

Table 22. VMUNARY0 encoding space
vs1 |
--- | ---
00001 | vmsbf
00010 | vmsof
00011 | vmsif
10000 | viota
10001 | vid

## Appendix A: Vector Assembly Code Examples

The following are provided as non-normative text to help explain the vector ISA.

### A.1. Vector-vector add example

        # vector-vector add routine of 32-bit integers
        # void vvaddint32(size_t n, const int*x, const int*y, int*z)
        # { for (size_t i=0; i<n; i++) { z[i]=x[i]+y[i]; } }
        #
        # a0 = n, a1 = x, a2 = y, a3 = z
        # Non-vector instructions are indented
    vvaddint32:
        vsetvli t0, a0, e32 # Set vector length based on 32-bit vectors
        vlw.v v0, (a1)           # Get first vector
          sub a0, a0, t0         # Decrement number done
          slli t0, t0, 2         # Multiply number done by 4 bytes
          add a1, a1, t0         # Bump pointer
        vlw.v v1, (a2)           # Get second vector
          add a2, a2, t0         # Bump pointer
        vadd.vv v2, v0, v1        # Sum vectors
        vsw.v v2, (a3)           # Store result
          add a3, a3, t0         # Bump pointer
          bnez a0, vvaddint32    # Loop back
          ret                    # Finished

### A.2. Example with mixed-width mask and compute.

    # Code using one width for predicate and different width for masked
    # compute.
    #   int8_t a[]; int32_t b[], c[];
    #   for (i=0;  i<n; i++) { b[i] =  (a[i] < 5) ? c[i] : 1; }
    #
    # Mixed-width code that keeps SEW/LMUL=8
      loop:
        vsetvli a4, a0, e8,m1  # Byte vector for predicate calc
        vlb.v v1, (a1)                # Load a[i]
          add a1, a1, a4              # Bump pointer.
        vmslt.vi v0, v1, 5            # a[i] < 5?

        vsetvli x0, a0, e32,m4 # Vector of 32-bit values.
          sub a0, a0, a4              # Decrement count
        vmv.v.i v4, 1                 # Splat immediate to destination
        vlw.v v4, (a3), v0.t          # Load requested elements of C.
          sll t1, a4, 2
          add a3, a3, t1              # Bump pointer.
        vsw.v v4, (a2)                # Store b[i].
          add a2, a2, t1              # Bump pointer.
          bnez a0, loop               # Any more?

### A.3. Memcpy example

        # void *memcpy(void* dest, const void* src, size_t n)
        # a0=dest, a1=src, a2=n
        #
      memcpy:
          mv a3, a0 # Copy destination
      loop:
        vsetvli t0, a2, e8,m8  # Vectors of 8b
        vlb.v v0, (a1)                # Load bytes
          add a1, a1, t0              # Bump pointer
          sub a2, a2, t0              # Decrement count
        vsb.v v0, (a3)                # Store bytes
          add a3, a3, t0              # Bump pointer
          bnez a2, loop               # Any more?
          ret                         # Return

### A.4. Conditional example

    # (int16) z[i] = ((int8) x[i] < 5) ? (int16) a[i] : (int16) b[i];
    #
    # Fixed 16b SEW:

    loop:
        vsetvli t0, a0, e16  # Use 16b elements.
        vlb.v v0, (a1)          # Get x[i], sign-extended to 16b
          sub a0, a0, t0        # Decrement element count
          add a1, a1, t0        # x[i] Bump pointer
        vmslt.vi v0, v0, 5      # Set mask in v0
          slli t0, t0, 1        # Multiply by 2 bytes
        vlh.v v1, (a2), v0.t    # z[i] = a[i] case
        vmnot.m v0, v0          # Invert v0
          add a2, a2, t0        # a[i] bump pointer
        vlh.v v1, (a3), v0.t    # z[i] = b[i] case
          add a3, a3, t0        # b[i] bump pointer
        vsh.v v1, (a4)          # Store z
          add a4, a4, t0        # b[i] bump pointer
          bnez a0, loop

### A.5. SAXPY example

    # void
    # saxpy(size_t n, const float a, const float *x, float *y)
    # {
    #   size_t i;
    #   for (i=0; i<n; i++)
    #     y[i] = a * x[i] + y[i];
    # }
    #
    # register arguments:
    #     a0      n
    #     fa0     a
    #     a1      x
    #     a2      y

    saxpy:
        vsetvli a4, a0, e32, m8
        vlw.v v0, (a1)
        sub a0, a0, a4
        slli a4, a4, 2
        add a1, a1, a4
        vlw.v v8, (a2)
        vfmacc.vf v8, fa0, v0
        vsw.v v8, (a2)
        add a2, a2, a4
        bnez a0, saxpy
        ret

### A.6. SGEMM example

    # RV64IDV system
    #
    # void
    # sgemm_nn(size_t n,
    #          size_t m,
    #          size_t k,
    #          const float*a,   // m * k matrix
    #          size_t lda,
    #          const float*b,   // k * n matrix
    #          size_t ldb,
    #          float*c,         // m * n matrix
    #          size_t ldc)
    #
    #  c += a*b (alpha=1, no transpose on input matrices)
    #  matrices stored in C row-major order

    #define n a0
    #define m a1
    #define k a2
    #define ap a3
    #define astride a4
    #define bp a5
    #define bstride a6
    #define cp a7
    #define cstride t0
    #define kt t1
    #define nt t2
    #define bnp t3
    #define cnp t4
    #define akp t5
    #define bkp s0
    #define nvl s1
    #define ccp s2
    #define amp s3

    # Use args as additional temporaries
    #define ft12 fa0
    #define ft13 fa1
    #define ft14 fa2
    #define ft15 fa3

    # This version holds a 16*VLMAX block of C matrix in vector registers
    # in inner loop, but otherwise does not cache or TLB tiling.

    sgemm_nn:
        addi sp, sp, -FRAMESIZE
        sd s0, OFFSET(sp)
        sd s1, OFFSET(sp)
        sd s2, OFFSET(sp)

        # Check for zero size matrices
        beqz n, exit
        beqz m, exit
        beqz k, exit

        # Convert elements strides to byte strides.
        ld cstride, OFFSET(sp)   # Get arg from stack frame
        slli astride, astride, 2
        slli bstride, bstride, 2
        slli cstride, cstride, 2

        slti t6, m, 16
        bnez t6, end_rows

    c_row_loop: # Loop across rows of C blocks

        mv nt, n  # Initialize n counter for next row of C blocks

        mv bnp, bp # Initialize B n-loop pointer to start
        mv cnp, cp # Initialize C n-loop pointer

    c_col_loop: # Loop across one row of C blocks
        vsetvli nvl, nt, e32  # 32-bit vectors, LMUL=1

        mv akp, ap   # reset pointer into A to beginning
        mv bkp, bnp # step to next column in B matrix

        # Initalize current C submatrix block from memory.
        vlw.v  v0, (cnp); add ccp, cnp, cstride;
        vlw.v  v1, (ccp); add ccp, ccp, cstride;
        vlw.v  v2, (ccp); add ccp, ccp, cstride;
        vlw.v  v3, (ccp); add ccp, ccp, cstride;
        vlw.v  v4, (ccp); add ccp, ccp, cstride;
        vlw.v  v5, (ccp); add ccp, ccp, cstride;
        vlw.v  v6, (ccp); add ccp, ccp, cstride;
        vlw.v  v7, (ccp); add ccp, ccp, cstride;
        vlw.v  v8, (ccp); add ccp, ccp, cstride;
        vlw.v  v9, (ccp); add ccp, ccp, cstride;
        vlw.v v10, (ccp); add ccp, ccp, cstride;
        vlw.v v11, (ccp); add ccp, ccp, cstride;
        vlw.v v12, (ccp); add ccp, ccp, cstride;
        vlw.v v13, (ccp); add ccp, ccp, cstride;
        vlw.v v14, (ccp); add ccp, ccp, cstride;
        vlw.v v15, (ccp)

        mv kt, k # Initialize inner loop counter

        # Inner loop scheduled assuming 4-clock occupancy of vfmacc instruction and single-issue pipeline
        # Software pipeline loads
        flw ft0, (akp); add amp, akp, astride;
        flw ft1, (amp); add amp, amp, astride;
        flw ft2, (amp); add amp, amp, astride;
        flw ft3, (amp); add amp, amp, astride;
        # Get vector from B matrix
        vlw.v v16, (bkp)

        # Loop on inner dimension for current C block
     k_loop:
        vfmacc.vf v0, ft0, v16
        add bkp, bkp, bstride
        flw ft4, (amp)
        add amp, amp, astride
        vfmacc.vf v1, ft1, v16
        addi kt, kt, -1    # Decrement k counter
        flw ft5, (amp)
        add amp, amp, astride
        vfmacc.vf v2, ft2, v16
        flw ft6, (amp)
        add amp, amp, astride
        flw ft7, (amp)
        vfmacc.vf v3, ft3, v16
        add amp, amp, astride
        flw ft8, (amp)
        add amp, amp, astride
        vfmacc.vf v4, ft4, v16
        flw ft9, (amp)
        add amp, amp, astride
        vfmacc.vf v5, ft5, v16
        flw ft10, (amp)
        add amp, amp, astride
        vfmacc.vf v6, ft6, v16
        flw ft11, (amp)
        add amp, amp, astride
        vfmacc.vf v7, ft7, v16
        flw ft12, (amp)
        add amp, amp, astride
        vfmacc.vf v8, ft8, v16
        flw ft13, (amp)
        add amp, amp, astride
        vfmacc.vf v9, ft9, v16
        flw ft14, (amp)
        add amp, amp, astride
        vfmacc.vf v10, ft10, v16
        flw ft15, (amp)
        add amp, amp, astride
        addi akp, akp, 4            # Move to next column of a
        vfmacc.vf v11, ft11, v16
        beqz kt, 1f                 # Don't load past end of matrix
        flw ft0, (akp)
        add amp, akp, astride
    1:  vfmacc.vf v12, ft12, v16
        beqz kt, 1f
        flw ft1, (amp)
        add amp, amp, astride
    1:  vfmacc.vf v13, ft13, v16
        beqz kt, 1f
        flw ft2, (amp)
        add amp, amp, astride
    1:  vfmacc.vf v14, ft14, v16
        beqz kt, 1f                 # Exit out of loop
        flw ft3, (amp)
        add amp, amp, astride
        vfmacc.vf v15, ft15, v16
        vlw.v v16, (bkp)            # Get next vector from B matrix, overlap loads with jump stalls
        j k_loop

    1:  vfmacc.vf v15, ft15, v16

        # Save C matrix block back to memory
        vsw.v  v0, (cnp); add ccp, cnp, cstride;
        vsw.v  v1, (ccp); add ccp, ccp, cstride;
        vsw.v  v2, (ccp); add ccp, ccp, cstride;
        vsw.v  v3, (ccp); add ccp, ccp, cstride;
        vsw.v  v4, (ccp); add ccp, ccp, cstride;
        vsw.v  v5, (ccp); add ccp, ccp, cstride;
        vsw.v  v6, (ccp); add ccp, ccp, cstride;
        vsw.v  v7, (ccp); add ccp, ccp, cstride;
        vsw.v  v8, (ccp); add ccp, ccp, cstride;
        vsw.v  v9, (ccp); add ccp, ccp, cstride;
        vsw.v v10, (ccp); add ccp, ccp, cstride;
        vsw.v v11, (ccp); add ccp, ccp, cstride;
        vsw.v v12, (ccp); add ccp, ccp, cstride;
        vsw.v v13, (ccp); add ccp, ccp, cstride;
        vsw.v v14, (ccp); add ccp, ccp, cstride;
        vsw.v v15, (ccp)

        # Following tail instructions should be scheduled earlier in free slots during C block save.
        # Leaving here for clarity.

        # Bump pointers for loop across blocks in one row
        slli t6, nvl, 2
        add cnp, cnp, t6                         # Move C block pointer over
        add bnp, bnp, t6                         # Move B block pointer over
        sub nt, nt, nvl                          # Decrement element count in n dimension
        bnez nt, c_col_loop                      # Any more to do?

        # Move to next set of rows
        addi m, m, -16  # Did 16 rows above
        slli t6, astride, 4  # Multiply astride by 16
        add ap, ap, t6         # Move A matrix pointer down 16 rows
        slli t6, cstride, 4  # Multiply cstride by 16
        add cp, cp, t6         # Move C matrix pointer down 16 rows

        slti t6, m, 16
        beqz t6, c_row_loop

        # Handle end of matrix with fewer than 16 rows.
        # Can use smaller versions of above decreasing in powers-of-2 depending on code-size concerns.
    end_rows:
        # Not done.

    exit:
        ld s0, OFFSET(sp)
        ld s1, OFFSET(sp)
        ld s2, OFFSET(sp)
        addi sp, sp, FRAMESIZE
        ret

## Appendix B: Calling Convention

In the RISC-V psABI, the vector registers `v0`-`v31` are all caller-saved. The `vstart`, `vl`, and `vtype` CSRs are also caller-saved.

The `vxrm` and `vxsat` fields have thread storage duration, like the other fields of the `fcsr`.

Executing a system call causes `v0`-`v31` to become unspecified.

Note | This scheme allows system calls that cause context switches to avoid saving and later restoring the vector registers.

Note | The values that `v0`-`v31` assume after a system call cannot expose information from other processes, so typically the registers will either remain intact or will be zeroed.