While porting the H264 standard encoder x264 to RISC-V, we've identified several operations that are challenging to implement efficiently with existing RVV instructions. In some cases, implementations require too many instructions and or transfer to / from memory, potentially impacting encoder performance.

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1. Vector transpose

2. Absolute difference

3. Zero-extended vmv.x.s

4. Rounded Shift Right Narrow

5. Signed saturate and Narrow to Unsigned

1. Vector transpose instructions

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Using RISC-V RVV, we have discovered two methods to perform matrix transposition(thanks camel-cdr for the assistance provided):

• Using segmented load or store

• Using vrgather

• Using vnsrl

Here, we use the example of transposing a 4x8 (2x4x4) matrix (transposing the left 4x4 and the right 4x4 separately) to illustrate these two methods.

Segmented load or store

In this way, we can use the `vssseg4e16.v` instruction to store each row of the original matrix into memory by columns, and then read them back by rows. Since we are transposing a 4x8 matrix, we also need to use `vslide` to combine the contents of the two registers together.

// Using extra loads and stores, and use vslide to combine them
.macro TRANSPOSE4x8_16 buf, bstride, v0, v1, v2, v3, t0, t1, t2, t3
    vssseg4e16.v \v0, (\buf), \bstride
    vsetivli zero, 4, e16, mf2, ta, ma
    vle16.v \v0, (\buf)
    add \buf, \buf, \bstride
    vle16.v \v1, (\buf)
    add \buf, \buf, \bstride
    vle16.v \v2, (\buf)
    add \buf, \buf, \bstride
    vle16.v \v3, (\buf)
    add \buf, \buf, \bstride
    vle16.v \t0, (\buf)
    add \buf, \buf, \bstride
    vle16.v \t1, (\buf)
    add \buf, \buf, \bstride
    vle16.v \t2, (\buf)
    add \buf, \buf, \bstride
    vle16.v \t3, (\buf)
    add \buf, \buf, \bstride
    vsetivli zero, 2, e64, m1, tu, ma
    vslideup.vi \v0, \t0, 1
    vslideup.vi \v1, \t1, 1
    vslideup.vi \v2, \t2, 1
    vslideup.vi \v3, \t3, 1
.endm

// under VLEN=128
function transpose4x8_16_one
    vsetivli zero, 8, e16, m1, ta, ma
    mv          t0, a0
    vl4re16.v   v0, (a0)
    li          t1, 8
    TRANSPOSE4x8_16 t0, t1, v0, v1, v2, v3, v8, v9, v10, v11
    vs4r.v   v0, (a0)
    ret
endfunc

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For creating index by hand, the idea is to set the index for gathering vector N to (i&3)*vl+(i&~3u)+N, where i is the element index obtained by vid.v.

// Using vrgather with index created by hand
.macro TRANSPOSE4x8_16_vrgather v0, v1, v2, v3, t0, t1, t2, t3, t4, t5, t6, t7, s0
    vsetivli    zero, 8, e16, m1, ta, ma
    vid.v       \t0
    li          \s0, 8
    vand.vi     \t1, \t0, 3
    vmul.vx     \t1, \t1, \s0
    vand.vi     \t0, \t0, -4

    vadd.vv     \t4, \t1, \t0
    vadd.vi     \t5, \t4, 1
    vadd.vi     \t6, \t4, 2
    vadd.vi     \t7, \t4, 3
    
    li          \s0, 32
    vsetvli    zero, \s0, e16, m4, ta, ma
    vrgatherei16.vv \t0, \v0, \t4
    vmv.v.v     \v0, \t0
.endm

// under VLEN=128
function transpose4x8_16_two
    vl4re16.v   v0, (a0)
    TRANSPOSE4x8_16_vrgather v0, v1, v2, v3, v8, v9, v10, v11, v12, v13, v14, v15, t0
    vs4r.v   v0, (a0)
    ret
endfunc

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This is also one of the main reasons why we want to add instructions similar to `trn1` and `trn2` in RVV.

Vnsrl

Olaf pointed out a new method to achieve matrix transposition, using the vnsrl instruction in RVV along with vslide instructions to achieve the effect of zip1 and zip2 in AArch64. Olaf provided detailed information for this method, and we are very grateful for his work. Below is an approach that works with VLEN=128:

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1. SABD / UABD - signed / unsigned absolute difference

2. SABDL / UABDL - signed / unsigned absolute difference (double-width result)

3. SABA / UABA - signed / unsigned absolute difference and add

4. SABAL/ UABAL - signed / unsigned absolute difference(double-width result) and add

x86

Compute sum of absolute difference: psadbw

Implementation in RISCV64

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• Vector Single-Width Signed/Unsigned Integer Absolute Difference

• Vector Widening Signed/Unsigned Integer Absolute Difference

• Vector Widening Signed/Unsigned Integer Absolute Difference and Accumulate

# Unsigned Absolute Difference.
vabdu.vv   vd, vs2, vs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(vs1[i]))
vabdu.vx   vd, vs2, rs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(x[rs1]))
vabdu.vi   vd, vs2, imm, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(imm))

# Widening Unsigned Absolute Difference.
vwabdu.vv  vd, vs2, vs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(vs1[i]))
vwabdu.vx  vd, vs2, rs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(x[rs1]))

# Widening Unsigned Absolute Difference Accumulate.
vwabdau.vv vd, vs2, vs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(vs1[i])) + unsigned(vd[i])
vwabdau.vx vd, vs2, rs1, vm   # vd[i] = abs(unsigned(vs2[i]) - unsigned(x[rs1])) + unsigned(vd[i])

Performance of SAD functions

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//uint16_t with zbb extension
vsetivli zero, 1, e16, m1, ta, ma
vmv.x.s a1, v1
zext.h a1, a1

4. Rounded Shift Right Narrow

Introduction

RVV 1.0 has instructions to -

• shift + scaling:  rssra

• shift + narrow:  vnsrl

• clip + narrow: vnclip

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// AArch64 implementation
rshrn v20.8b, v20.8h, #3
rshrn2 v20.16b, v21.8h, #3


// RISCV64 implementation
vsetivli zero, 8, e16, m1, ta, ma
vssrl.vi v20, v20, 3
vssrl.vi v21, v21, 3
vsetivli zero, 8, e8, mf2, ta, ma
vncvt.x.x.w v20, v20
vncvt.x.x.w v21, v21
vsetivli zero, 16, e8, m1, ta, ma
vslideup.vi v20, v21, 8

5. Signed saturate and Narrow to Unsigned

Introduction

Implementation in RISCV64

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