Incidental Similarity

I recently saw an interesting class, BitVector, in Apache Arrow, which represents a column of bits, providing minimal or zero copy distribution. The implementation is similar to a bitset but backed by a byte[] rather than a long[]. Given the coincidental similarity in implementation, it’s tempting to look at this, extend its interface and try to use it as a general purpose, distributed bitset. Could this work? Why not just implement some extra methods? Fork it on Github!

This post details the caveats of trying to adapt an abstraction beyond its intended purpose; in a scenario where generic bitset capabilities are added to BitVector without due consideration, examined through the lens of performance. This runs into the observable effect of word widening on throughput, given the constraints imposed by JLS 15.22. In the end, the only remedy is to use a long[], sacrificing the original zero copy design goal. I hope this is a fairly self-contained example of how uncontrolled adaptation can be hostile to the original design goals: having the source code isn’t enough reason to modify it.

Checking bits

How fast is it to check if the bit at index i is set or not? BitVector implements this functionality, and was designed for it. This can be measured by JMH by generating a random long[] and creating a byte[] 8x longer with identical bits. The throughput of checking the value of the bit at random indices can be measured. It turns out that if all you want to do is access bits, byte[] isn’t such a bad choice, and if those bytes are coming directly from the network, it could even be a great choice. I ran the benchmark below and saw that the two operations are similar (within measurement error).


@OutputTimeUnit(TimeUnit.MICROSECONDS)
@State(Scope.Thread)
public class BitSet {

    @Param({"1024", "2048", "4096", "8192"})
    int size;

    private long[] leftLongs;
    private long[] rightLongs;
    private long[] differenceLongs;
    private byte[] leftBytes;
    private byte[] rightBytes;
    private byte[] differenceBytes;

    @Setup(Level.Trial)
    public void init() {
        this.leftLongs = createLongArray(size);
        this.rightLongs = createLongArray(size);
        this.differenceLongs = new long[size];
        this.leftBytes = makeBytesFromLongs(leftLongs);
        this.rightBytes = makeBytesFromLongs(rightLongs);
        this.differenceBytes = new byte[size * 8];
    }

    @Benchmark
    public boolean CheckBit_LongArray() {
        int index = index();
        return (leftLongs[index >>> 6] & (1L << index)) != 0;
    }

    @Benchmark
    public boolean CheckBit_ByteArray() {
        int index = index();
        return ((leftBytes[index >>> 3] & 0xFF) & (1 << (index & 7))) != 0;
    }

    private int index() {
        return ThreadLocalRandom.current().nextInt(size * 64);
    }

    private static byte[] makeBytesFromLongs(long[] array) {
        byte[] bytes = new byte[8 * array.length];
        for (int i = 0; i < array.length; ++i) {
            long word = array[i];
            bytes[8 * i + 7] = (byte) word;
            bytes[8 * i + 6] = (byte) (word >>> 8);
            bytes[8 * i + 5] = (byte) (word >>> 16);
            bytes[8 * i + 4] = (byte) (word >>> 24);
            bytes[8 * i + 3] = (byte) (word >>> 32);
            bytes[8 * i + 2] = (byte) (word >>> 40);
            bytes[8 * i + 1] = (byte) (word >>> 48);
            bytes[8 * i]     = (byte) (word >>> 56);
        }
        return bytes;
    }
}

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit Param: size
CheckBit_ByteArray thrpt 1 10 174.421170 1.583275 ops/us 1024
CheckBit_ByteArray thrpt 1 10 173.938408 1.445796 ops/us 2048
CheckBit_ByteArray thrpt 1 10 172.522190 0.815596 ops/us 4096
CheckBit_ByteArray thrpt 1 10 167.550530 1.677091 ops/us 8192
CheckBit_LongArray thrpt 1 10 171.639695 0.934494 ops/us 1024
CheckBit_LongArray thrpt 1 10 169.703960 2.427244 ops/us 2048
CheckBit_LongArray thrpt 1 10 169.333360 1.649654 ops/us 4096
CheckBit_LongArray thrpt 1 10 166.518375 0.815433 ops/us 8192

To support this functionality, there’s no reason to choose either way, and it must be very appealing to use bytes as they are delivered from the network, avoiding copying costs. Given that for a database column, this is the only operation needed, and Apache Arrow has a stated aim to copy data as little as possible, this seems like quite a good decision.

Logical Conjugations

But what happens if you try to add a logical operation to BitVector, such as an XOR? We need to handle the fact that bytes are signed and their sign bit must be preserved in promotion, according to the JLS. This would break the bitset, so extra operations are required to keep the 8th bit in its right place. With the widening and its associated workarounds, suddenly the byte[] is a much poorer choice than a long[], and it shows in benchmarks.


    @Benchmark
    public void Difference_ByteArray(Blackhole bh) {
        for (int i = 0; i < leftBytes.length && i < rightBytes.length; ++i) {
            differenceBytes[i] = (byte)((leftBytes[i] & 0xFF) ^ (rightBytes[i] & 0xFF));
        }
        bh.consume(differenceBytes);
    }

    @Benchmark
    public void Difference_LongArray(Blackhole bh) {
        for (int i = 0; i < leftLongs.length && i < rightLongs.length; ++i) {
            differenceLongs[i] = leftLongs[i] ^ rightLongs[i];
        }
        bh.consume(differenceLongs);
    }

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit Param: size
Difference_ByteArray thrpt 1 10 0.805872 0.038644 ops/us 1024
Difference_ByteArray thrpt 1 10 0.391705 0.017453 ops/us 2048
Difference_ByteArray thrpt 1 10 0.190102 0.008580 ops/us 4096
Difference_ByteArray thrpt 1 10 0.169104 0.015086 ops/us 8192
Difference_LongArray thrpt 1 10 2.450659 0.094590 ops/us 1024
Difference_LongArray thrpt 1 10 1.047330 0.016898 ops/us 2048
Difference_LongArray thrpt 1 10 0.546286 0.014211 ops/us 4096
Difference_LongArray thrpt 1 10 0.277378 0.015663 ops/us 8192

This is a fairly crazy slow down. Why? You need to look at the assembly generated in each case. For long[] it’s demonstrable that logical operations do vectorise. The JLS, specifically section 15.22, doesn’t really give the byte[] implementation a chance. It states that for logical operations, sub dword primitive types must be promoted or widened before the operation. This means that if one were to try to implement this operation with, say AVX2, using 256 bit ymmwords each consisting of 16 bytes, then each ymmword would have to be inflated by a factor of four: it gets complicated quickly, given this constraint. Despite that complexity, I was surprised to see that C2 does use 128 bit xmmwords, but it’s not as fast as using the full 256 bit registers available. This can be seen by printing out the emitted assembly like normal.

movsxd  r10,ebx     

vmovq   xmm2,mmword ptr [rsi+r10+10h]

vpxor   xmm2,xmm2,xmmword ptr [r8+r10+10h]

vmovq   mmword ptr [rax+r10+10h],xmm2

Posted on

Vectorised Logical Operations in Java 9

This is a short post for my own reference, since I feel I have already done the topic of does Java 9 use AVX for this? to death. Cutting to the chase, Java 9 autovectorises loops to compute logical ANDs, XORs, ORs and ANDNOTs between arrays, making use of the instructions VPXOR, VPOR and VPAND. You can replicate this by running the code at github.

XOR


    @Benchmark
    public long[] xor(LongData state) {
        long[] result = new long[state.data1.length];
        long[] data1 = state.data1;
        long[] data2 = state.data2;
        for (int i = 0; i < data1.length && i < data2.length; ++i) {
            result[i] = data1[i] ^ data2[i];
        }
        return result;
    }

vmovdqu ymm0,ymmword ptr [r10+r13*8+10h]

vpxor   ymm0,ymm0,ymmword ptr [rbx+r13*8+10h]

vmovdqu ymmword ptr [rax+r13*8+10h],ymm0

OR


    @Benchmark
    public long[] or(LongData state) {
        long[] result = new long[state.data1.length];
        long[] data1 = state.data1;
        long[] data2 = state.data2;
        for (int i = 0; i < data1.length && i < data2.length; ++i) {
            result[i] = data1[i] | data2[i];
        }
        return result;
    }

vmovdqu ymm0,ymmword ptr [r10+rsi*8+30h]
 
vpor    ymm0,ymm0,ymmword ptr [rbx+rsi*8+30h]

vmovdqu ymmword ptr [rax+rsi*8+30h],ymm0

AND


    @Benchmark
    public long[] and(LongData state) {
        long[] result = new long[state.data1.length];
        long[] data1 = state.data1;
        long[] data2 = state.data2;
        for (int i = 0; i < data1.length && i < data2.length; ++i) {
            result[i] = data1[i] & data2[i];
        }
        return result;
    }

vmovdqu ymm0,ymmword ptr [r10+r13*8+10h]

vpand   ymm0,ymm0,ymmword ptr [rbx+r13*8+10h]

vmovdqu ymmword ptr [rax+r13*8+10h],ymm0

ANDNOT


    @Benchmark
    public long[] andNot(LongData state) {
        long[] result = new long[state.data1.length];
        long[] data1 = state.data1;
        long[] data2 = state.data2;
        for (int i = 0; i < data1.length && i < data2.length; ++i) {
            result[i] = data1[i] & ~data2[i];
        }
        return result;
    }

vpunpcklqdq xmm0,xmm0,xmm0

vinserti128 ymm0,ymm0,xmm0,1h

vmovdqu ymm1,ymmword ptr [rbx+r13*8+10h]

vpxor   ymm1,ymm1,ymm0

vpand   ymm1,ymm1,ymmword ptr [r10+r13*8+10h]

vmovdqu ymmword ptr [rax+r13*8+10h],ymm1

Posted on

How much Algebra does C2 Know? Part 2: Distributivity

In part one of this series of posts, I looked at how important associativity and independence are for fast loops. C2 seems to utilise these properties to generate unrolled and pipelined machine code for loops, achieving higher throughput even in cases where the kernel of the loop is 3x slower according to vendor advertised instruction throughputs. C2 has a weird and wonderful relationship with distributivity, and hints from the programmer can both and help hinder the generation of good quality machine code.

Viability and Correctness

Distributivity is the simple notion of factoring out brackets. Is this, in general, a viable loop rewrite strategy? This can be utilised to transform the method Scale into FactoredScale, both of which perform floating point arithmetic:


    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public double Scale(DoubleData state) {
        double value = 0D;
        double[] data = state.data1;
        for (int i = 0; i < data.length; ++i) {
            value += 3.14159 * data[i];
        }
        return value;
    }

    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public double FactoredScale(DoubleData state) {
        double value = 0D;
        double[] data = state.data1;
        for (int i = 0; i < data.length; ++i) {
            value += data[i];
        }
        return 3.14159 * value;
    }

Running the project at github with the argument --include .*scale.*, there may be a performance gain to be had from this rewrite, but it isn’t clear cut:

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit Param: size
FactoredScale thrpt 1 10 7.011606 0.274742 ops/ms 100000
FactoredScale thrpt 1 10 0.621515 0.026853 ops/ms 1000000
Scale thrpt 1 10 6.962434 0.240180 ops/ms 100000
Scale thrpt 1 10 0.671042 0.011686 ops/ms 1000000

With the real numbers it would be completely valid, but floating point arithmetic is not associative. Joseph Darcy explains why in this deep dive on floating point semantics. Broken associativity of addition entails broken distributivity of any operation over it, so the two loops are not equivalent, and they give different outputs (e.g. 15662.513298516365 vs 15662.51329851632 for one sample input). The rewrite isn’t correct even for floating point data, so it isn’t an optimisation that could be applied in good faith, except in a very small number of cases. You have to rewrite the loop yourself and figure out if the small but inevitable differences are acceptable.

Counterintuitive Performance

Integer multiplication is distributive over addition, and we can check if C2 does this rewrite by running the same code with 32 bit integer values, for now fixing a scale factor of 10 (which seems like an innocuous value, no?)


    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public int Scale_Int(IntData state) {
        int value = 0;
        int[] data = state.data1;
        for (int i = 0; i < data.length; ++i) {
            value += 10 * data[i];
        }
        return value;
    }

    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public int FactoredScale_Int(IntData state) {
        int value = 0;
        int[] data = state.data1;
        for (int i = 0; i < data.length; ++i) {
            value += data[i];
        }
        return 10 * value;
    }

The results are fascinating:

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit Param: size
FactoredScale_Int thrpt 1 10 28.339699 0.608075 ops/ms 100000
FactoredScale_Int thrpt 1 10 2.392579 0.506413 ops/ms 1000000
Scale_Int thrpt 1 10 33.335721 0.295334 ops/ms 100000
Scale_Int thrpt 1 10 2.838242 0.448213 ops/ms 1000000

The code is doing thousands more multiplications in less time when the multiplication is not factored out of the loop. So what the devil is going on? Inspecting the assembly for the faster loop is revealing

com/openkappa/simd/scale/Scale.Scale_Int(Lcom/openkappa/simd/state/IntData;)I  [0x000001c89e499320, 0x000001c89e4996f8]  984 bytes
Argument 0 is unknown.RIP: 0x1c89e499320 Code size: 0x000003d8
[Entry Point]
[Verified Entry Point]
[Constants]
  # {method} {0x000001c8b3701b10} 'Scale_Int' '(Lcom/openkappa/simd/state/IntData;)I' in 'com/openkappa/simd/scale/Scale'
  0x000001c89e499320: int3                      ;...cc

  0x000001c89e499321: nop     word ptr [rax+rax+0h]  ;...66
                                                ;...66
                                                ;...66
                                                ;...0f
                                                ;...1f
                                                ;...84
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e49932c: nop                       ;...66
                                                ;...66
                                                ;...66
                                                ;...90

  0x000001c89e499330: mov     dword ptr [rsp+0ffffffffffff9000h],eax
                                                ;...89
                                                ;...84
                                                ;...24
                                                ;...00
                                                ;...90
                                                ;...ff
                                                ;...ff

  0x000001c89e499337: push    rbp               ;...55

  0x000001c89e499338: sub     rsp,40h           ;...48
                                                ;...83
                                                ;...ec
                                                ;...40

  0x000001c89e49933c: mov     rbp,qword ptr [rdx+8h]  ;...48
                                                ;...8b
                                                ;...6a
                                                ;...08

  0x000001c89e499340: mov     ebx,dword ptr [rdx+10h]  ;...8b
                                                ;...5a
                                                ;...10

  0x000001c89e499343: mov     r13d,dword ptr [rdx]  ;...44
                                                ;...8b
                                                ;...2a

  0x000001c89e499346: mov     rcx,rdx           ;...48
                                                ;...8b
                                                ;...ca

  0x000001c89e499349: vzeroupper                ;...c5
                                                ;...f8
                                                ;...77

  0x000001c89e49934c: mov     r10,51da8d20h     ;...49
                                                ;...ba
                                                ;...20
                                                ;...8d
                                                ;...da
                                                ;...51
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e499356: call indirect r10         ;...41
                                                ;...ff
                                                ;...d2

  0x000001c89e499359: mov     r11d,dword ptr [rbp+8h]  ;...44
                                                ;...8b
                                                ;...5d
                                                ;...08
                                                ; implicit exception: dispatches to 0x000001c89e4996c1
  0x000001c89e49935d: cmp     r11d,0f800016dh   ;...41
                                                ;...81
                                                ;...fb
                                                ;...6d
                                                ;...01
                                                ;...00
                                                ;...f8
                                                ;   {metadata({type array int})}
  0x000001c89e499364: jne     1c89e4996a9h      ;...0f
                                                ;...85
                                                ;...3f
                                                ;...03
                                                ;...00
                                                ;...00
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@10 (line 41)

  0x000001c89e49936a: mov     edi,dword ptr [rbp+0ch]  ;...8b
                                                ;...7d
                                                ;...0c
                                                ;*arraylength {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@13 (line 41)

  0x000001c89e49936d: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e499370: jnl     1c89e49967ah      ;...0f
                                                ;...8d
                                                ;...04
                                                ;...03
                                                ;...00
                                                ;...00
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@14 (line 41)

  0x000001c89e499376: mov     r10d,ebp          ;...44
                                                ;...8b
                                                ;...d5

  0x000001c89e499379: mov     r8d,r13d          ;...45
                                                ;...8b
                                                ;...c5

  0x000001c89e49937c: inc     r8d               ;...41
                                                ;...ff
                                                ;...c0

  0x000001c89e49937f: shr     r10d,2h           ;...41
                                                ;...c1
                                                ;...ea
                                                ;...02

  0x000001c89e499383: and     r10d,7h           ;...41
                                                ;...83
                                                ;...e2
                                                ;...07

  0x000001c89e499387: xor     r9d,r9d           ;...45
                                                ;...33
                                                ;...c9

  0x000001c89e49938a: cmp     r8d,r9d           ;...45
                                                ;...3b
                                                ;...c1

  0x000001c89e49938d: cmovl   r8d,r9d           ;...45
                                                ;...0f
                                                ;...4c
                                                ;...c1

  0x000001c89e499391: cmp     r8d,edi           ;...44
                                                ;...3b
                                                ;...c7

  0x000001c89e499394: cmovnle r8d,edi           ;...44
                                                ;...0f
                                                ;...4f
                                                ;...c7

  0x000001c89e499398: add     r10d,r8d          ;...45
                                                ;...03
                                                ;...d0

  0x000001c89e49939b: mov     r11d,4h           ;...41
                                                ;...bb
                                                ;...04
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e4993a1: sub     r11d,r10d         ;...45
                                                ;...2b
                                                ;...da

  0x000001c89e4993a4: and     r11d,7h           ;...41
                                                ;...83
                                                ;...e3
                                                ;...07

  0x000001c89e4993a8: add     r11d,r8d          ;...45
                                                ;...03
                                                ;...d8

  0x000001c89e4993ab: cmp     r11d,edi          ;...44
                                                ;...3b
                                                ;...df

  0x000001c89e4993ae: cmovnle r11d,edi          ;...44
                                                ;...0f
                                                ;...4f
                                                ;...df

  0x000001c89e4993b2: nop                       ;...66
                                                ;...90

  0x000001c89e4993b4: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e4993b7: jnb     1c89e49968bh      ;...0f
                                                ;...83
                                                ;...ce
                                                ;...02
                                                ;...00
                                                ;...00

  0x000001c89e4993bd: mov     r10d,dword ptr [rbp+r13*4+10h]
                                                ;...46
                                                ;...8b
                                                ;...54
                                                ;...ad
                                                ;...10
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@23 (line 42)

  0x000001c89e4993c2: mov     r9d,r10d          ;...45
                                                ;...8b
                                                ;...ca

  0x000001c89e4993c5: shl     r9d,3h            ;...41
                                                ;...c1
                                                ;...e1
                                                ;...03

  0x000001c89e4993c9: shl     r10d,1h           ;...41
                                                ;...d1
                                                ;...e2

  0x000001c89e4993cc: add     r9d,r10d          ;...45
                                                ;...03
                                                ;...ca

  0x000001c89e4993cf: add     ebx,r9d           ;...41
                                                ;...03
                                                ;...d9
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@25 (line 42)

  0x000001c89e4993d2: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@27 (line 41)

  0x000001c89e4993d5: cmp     r13d,r11d         ;...45
                                                ;...3b
                                                ;...eb

  0x000001c89e4993d8: jl      1c89e4993b4h      ;...7c
                                                ;...da
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@14 (line 41)

  0x000001c89e4993da: mov     r8d,edi           ;...44
                                                ;...8b
                                                ;...c7

  0x000001c89e4993dd: add     r8d,0ffffffc1h    ;...41
                                                ;...83
                                                ;...c0
                                                ;...c1

  0x000001c89e4993e1: mov     ecx,80000000h     ;...b9
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...80

  0x000001c89e4993e6: cmp     edi,r8d           ;...41
                                                ;...3b
                                                ;...f8

  0x000001c89e4993e9: cmovl   r8d,ecx           ;...44
                                                ;...0f
                                                ;...4c
                                                ;...c1

  0x000001c89e4993ed: cmp     r13d,r8d          ;...45
                                                ;...3b
                                                ;...e8

  0x000001c89e4993f0: jnl     1c89e499651h      ;...0f
                                                ;...8d
                                                ;...5b
                                                ;...02
                                                ;...00
                                                ;...00

  0x000001c89e4993f6: nop     word ptr [rax+rax+0h]  ;...66
                                                ;...66
                                                ;...0f
                                                ;...1f
                                                ;...84
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e499400: vmovdqu ymm8,ymmword ptr [rbp+r13*4+10h]
                                                ;...c4
                                                ;...21
                                                ;...7e
                                                ;...6f
                                                ;...44
                                                ;...ad
                                                ;...10

  0x000001c89e499407: movsxd  r10,r13d          ;...4d
                                                ;...63
                                                ;...d5

  0x000001c89e49940a: vmovdqu ymm9,ymmword ptr [rbp+r10*4+30h]
                                                ;...c4
                                                ;...21
                                                ;...7e
                                                ;...6f
                                                ;...4c
                                                ;...95
                                                ;...30

  0x000001c89e499411: vmovdqu ymm13,ymmword ptr [rbp+r10*4+0f0h]
                                                ;...c4
                                                ;...21
                                                ;...7e
                                                ;...6f
                                                ;...ac
                                                ;...95
                                                ;...f0
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e49941b: vmovdqu ymm12,ymmword ptr [rbp+r10*4+50h]
                                                ;...c4
                                                ;...21
                                                ;...7e
                                                ;...6f
                                                ;...64
                                                ;...95
                                                ;...50

  0x000001c89e499422: vmovdqu ymm4,ymmword ptr [rbp+r10*4+70h]
                                                ;...c4
                                                ;...a1
                                                ;...7e
                                                ;...6f
                                                ;...64
                                                ;...95
                                                ;...70

  0x000001c89e499429: vmovdqu ymm3,ymmword ptr [rbp+r10*4+90h]
                                                ;...c4
                                                ;...a1
                                                ;...7e
                                                ;...6f
                                                ;...9c
                                                ;...95
                                                ;...90
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e499433: vmovdqu ymm2,ymmword ptr [rbp+r10*4+0b0h]
                                                ;...c4
                                                ;...a1
                                                ;...7e
                                                ;...6f
                                                ;...94
                                                ;...95
                                                ;...b0
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001c89e49943d: vmovdqu ymm0,ymmword ptr [rbp+r10*4+0d0h]
                                                ;...c4
                                                ;...a1
                                                ;...7e
                                                ;...6f
                                                ;...84
                                                ;...95
                                                ;...d0
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@23 (line 42)

  0x000001c89e499447: vpslld  ymm11,ymm8,1h     ;...c4
                                                ;...c1
                                                ;...25
                                                ;...72
                                                ;...f0
                                                ;...01

  0x000001c89e49944d: vpslld  ymm1,ymm0,1h      ;...c5
                                                ;...f5
                                                ;...72
                                                ;...f0
                                                ;...01

  0x000001c89e499452: vpslld  ymm0,ymm0,3h      ;...c5
                                                ;...fd
                                                ;...72
                                                ;...f0
                                                ;...03

  0x000001c89e499457: vpaddd  ymm5,ymm0,ymm1    ;...c5
                                                ;...fd
                                                ;...fe
                                                ;...e9

  0x000001c89e49945b: vpslld  ymm0,ymm2,3h      ;...c5
                                                ;...fd
                                                ;...72
                                                ;...f2
                                                ;...03

  0x000001c89e499460: vpslld  ymm7,ymm3,3h      ;...c5
                                                ;...c5
                                                ;...72
                                                ;...f3
                                                ;...03

  0x000001c89e499465: vpslld  ymm10,ymm4,3h     ;...c5
                                                ;...ad
                                                ;...72
                                                ;...f4
                                                ;...03

  0x000001c89e49946a: vpslld  ymm15,ymm12,3h    ;...c4
                                                ;...c1
                                                ;...05
                                                ;...72
                                                ;...f4
                                                ;...03

  0x000001c89e499470: vpslld  ymm14,ymm13,3h    ;...c4
                                                ;...c1
                                                ;...0d
                                                ;...72
                                                ;...f5
                                                ;...03

  0x000001c89e499476: vpslld  ymm1,ymm9,3h      ;...c4
                                                ;...c1
                                                ;...75
                                                ;...72
                                                ;...f1
                                                ;...03

  0x000001c89e49947c: vpslld  ymm2,ymm2,1h      ;...c5
                                                ;...ed
                                                ;...72
                                                ;...f2
                                                ;...01

  0x000001c89e499481: vpaddd  ymm6,ymm0,ymm2    ;...c5
                                                ;...fd
                                                ;...fe
                                                ;...f2

  0x000001c89e499485: vpslld  ymm0,ymm3,1h      ;...c5
                                                ;...fd
                                                ;...72
                                                ;...f3
                                                ;...01

  0x000001c89e49948a: vpaddd  ymm7,ymm7,ymm0    ;...c5
                                                ;...c5
                                                ;...fe
                                                ;...f8

  0x000001c89e49948e: vpslld  ymm0,ymm4,1h      ;...c5
                                                ;...fd
                                                ;...72
                                                ;...f4
                                                ;...01

  0x000001c89e499493: vpaddd  ymm10,ymm10,ymm0  ;...c5
                                                ;...2d
                                                ;...fe
                                                ;...d0

  0x000001c89e499497: vpslld  ymm0,ymm12,1h     ;...c4
                                                ;...c1
                                                ;...7d
                                                ;...72
                                                ;...f4
                                                ;...01

  0x000001c89e49949d: vpaddd  ymm12,ymm15,ymm0  ;...c5
                                                ;...05
                                                ;...fe
                                                ;...e0

  0x000001c89e4994a1: vpslld  ymm0,ymm13,1h     ;...c4
                                                ;...c1
                                                ;...7d
                                                ;...72
                                                ;...f5
                                                ;...01

  0x000001c89e4994a7: vpaddd  ymm4,ymm14,ymm0   ;...c5
                                                ;...8d
                                                ;...fe
                                                ;...e0

  0x000001c89e4994ab: vpslld  ymm0,ymm9,1h      ;...c4
                                                ;...c1
                                                ;...7d
                                                ;...72
                                                ;...f1
                                                ;...01

  0x000001c89e4994b1: vpaddd  ymm2,ymm1,ymm0    ;...c5
                                                ;...f5
                                                ;...fe
                                                ;...d0

  0x000001c89e4994b5: vpslld  ymm0,ymm8,3h      ;...c4
                                                ;...c1
                                                ;...7d
                                                ;...72
                                                ;...f0
                                                ;...03

  0x000001c89e4994bb: vpaddd  ymm8,ymm0,ymm11   ;...c4
                                                ;...41
                                                ;...7d
                                                ;...fe
                                                ;...c3

  0x000001c89e4994c0: vphaddd ymm0,ymm8,ymm8    ;...c4
                                                ;...c2
                                                ;...3d
                                                ;...02
                                                ;...c0

  0x000001c89e4994c5: vphaddd ymm0,ymm0,ymm3    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c3

  0x000001c89e4994ca: vextracti128 xmm3,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c3
                                                ;...01

  0x000001c89e4994d0: vpaddd  xmm0,xmm0,xmm3    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c3

  0x000001c89e4994d4: vmovd   xmm3,ebx          ;...c5
                                                ;...f9
                                                ;...6e
                                                ;...db

  0x000001c89e4994d8: vpaddd  xmm3,xmm3,xmm0    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d8

  0x000001c89e4994dc: vmovd   r10d,xmm3         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...da

  0x000001c89e4994e1: vphaddd ymm0,ymm2,ymm2    ;...c4
                                                ;...e2
                                                ;...6d
                                                ;...02
                                                ;...c2

  0x000001c89e4994e6: vphaddd ymm0,ymm0,ymm3    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c3

  0x000001c89e4994eb: vextracti128 xmm3,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c3
                                                ;...01

  0x000001c89e4994f1: vpaddd  xmm0,xmm0,xmm3    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c3

  0x000001c89e4994f5: vmovd   xmm3,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...da

  0x000001c89e4994fa: vpaddd  xmm3,xmm3,xmm0    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d8

  0x000001c89e4994fe: vmovd   r11d,xmm3         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...db

  0x000001c89e499503: vphaddd ymm2,ymm12,ymm12  ;...c4
                                                ;...c2
                                                ;...1d
                                                ;...02
                                                ;...d4

  0x000001c89e499508: vphaddd ymm2,ymm2,ymm0    ;...c4
                                                ;...e2
                                                ;...6d
                                                ;...02
                                                ;...d0

  0x000001c89e49950d: vextracti128 xmm0,ymm2,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d0
                                                ;...01

  0x000001c89e499513: vpaddd  xmm2,xmm2,xmm0    ;...c5
                                                ;...e9
                                                ;...fe
                                                ;...d0

  0x000001c89e499517: vmovd   xmm0,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c3

  0x000001c89e49951c: vpaddd  xmm0,xmm0,xmm2    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c2

  0x000001c89e499520: vmovd   r10d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c2

  0x000001c89e499525: vphaddd ymm0,ymm10,ymm10  ;...c4
                                                ;...c2
                                                ;...2d
                                                ;...02
                                                ;...c2

  0x000001c89e49952a: vphaddd ymm0,ymm0,ymm3    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c3

  0x000001c89e49952f: vextracti128 xmm3,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c3
                                                ;...01

  0x000001c89e499535: vpaddd  xmm0,xmm0,xmm3    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c3

  0x000001c89e499539: vmovd   xmm3,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...da

  0x000001c89e49953e: vpaddd  xmm3,xmm3,xmm0    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d8

  0x000001c89e499542: vmovd   r11d,xmm3         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...db

  0x000001c89e499547: vphaddd ymm2,ymm7,ymm7    ;...c4
                                                ;...e2
                                                ;...45
                                                ;...02
                                                ;...d7

  0x000001c89e49954c: vphaddd ymm2,ymm2,ymm0    ;...c4
                                                ;...e2
                                                ;...6d
                                                ;...02
                                                ;...d0

  0x000001c89e499551: vextracti128 xmm0,ymm2,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d0
                                                ;...01

  0x000001c89e499557: vpaddd  xmm2,xmm2,xmm0    ;...c5
                                                ;...e9
                                                ;...fe
                                                ;...d0

  0x000001c89e49955b: vmovd   xmm0,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c3

  0x000001c89e499560: vpaddd  xmm0,xmm0,xmm2    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c2

  0x000001c89e499564: vmovd   r10d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c2

  0x000001c89e499569: vphaddd ymm0,ymm6,ymm6    ;...c4
                                                ;...e2
                                                ;...4d
                                                ;...02
                                                ;...c6

  0x000001c89e49956e: vphaddd ymm0,ymm0,ymm3    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c3

  0x000001c89e499573: vextracti128 xmm3,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c3
                                                ;...01

  0x000001c89e499579: vpaddd  xmm0,xmm0,xmm3    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c3

  0x000001c89e49957d: vmovd   xmm3,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...da

  0x000001c89e499582: vpaddd  xmm3,xmm3,xmm0    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d8

  0x000001c89e499586: vmovd   r11d,xmm3         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...db

  0x000001c89e49958b: vphaddd ymm2,ymm5,ymm5    ;...c4
                                                ;...e2
                                                ;...55
                                                ;...02
                                                ;...d5

  0x000001c89e499590: vphaddd ymm2,ymm2,ymm0    ;...c4
                                                ;...e2
                                                ;...6d
                                                ;...02
                                                ;...d0

  0x000001c89e499595: vextracti128 xmm0,ymm2,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d0
                                                ;...01

  0x000001c89e49959b: vpaddd  xmm2,xmm2,xmm0    ;...c5
                                                ;...e9
                                                ;...fe
                                                ;...d0

  0x000001c89e49959f: vmovd   xmm0,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c3

  0x000001c89e4995a4: vpaddd  xmm0,xmm0,xmm2    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c2

  0x000001c89e4995a8: vmovd   r10d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c2

  0x000001c89e4995ad: vphaddd ymm2,ymm4,ymm4    ;...c4
                                                ;...e2
                                                ;...5d
                                                ;...02
                                                ;...d4

  0x000001c89e4995b2: vphaddd ymm2,ymm2,ymm1    ;...c4
                                                ;...e2
                                                ;...6d
                                                ;...02
                                                ;...d1

  0x000001c89e4995b7: vextracti128 xmm1,ymm2,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d1
                                                ;...01

  0x000001c89e4995bd: vpaddd  xmm2,xmm2,xmm1    ;...c5
                                                ;...e9
                                                ;...fe
                                                ;...d1

  0x000001c89e4995c1: vmovd   xmm1,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...ca

  0x000001c89e4995c6: vpaddd  xmm1,xmm1,xmm2    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...ca

  0x000001c89e4995ca: vmovd   ebx,xmm1          ;...c5
                                                ;...f9
                                                ;...7e
                                                ;...cb
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@25 (line 42)

  0x000001c89e4995ce: add     r13d,40h          ;...41
                                                ;...83
                                                ;...c5
                                                ;...40
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@27 (line 41)

  0x000001c89e4995d2: cmp     r13d,r8d          ;...45
                                                ;...3b
                                                ;...e8

  0x000001c89e4995d5: jl      1c89e499400h      ;...0f
                                                ;...8c
                                                ;...25
                                                ;...fe
                                                ;...ff
                                                ;...ff
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@14 (line 41)

  0x000001c89e4995db: mov     r10d,edi          ;...44
                                                ;...8b
                                                ;...d7

  0x000001c89e4995de: add     r10d,0fffffff9h   ;...41
                                                ;...83
                                                ;...c2
                                                ;...f9

  0x000001c89e4995e2: cmp     edi,r10d          ;...41
                                                ;...3b
                                                ;...fa

  0x000001c89e4995e5: cmovl   r10d,ecx          ;...44
                                                ;...0f
                                                ;...4c
                                                ;...d1

  0x000001c89e4995e9: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000001c89e4995ec: jnl     1c89e49962eh      ;...7d
                                                ;...40

  0x000001c89e4995ee: nop                       ;...66
                                                ;...90

  0x000001c89e4995f0: vmovdqu ymm0,ymmword ptr [rbp+r13*4+10h]
                                                ;...c4
                                                ;...a1
                                                ;...7e
                                                ;...6f
                                                ;...44
                                                ;...ad
                                                ;...10
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@23 (line 42)

  0x000001c89e4995f7: vpslld  ymm1,ymm0,3h      ;...c5
                                                ;...f5
                                                ;...72
                                                ;...f0
                                                ;...03

  0x000001c89e4995fc: vpslld  ymm0,ymm0,1h      ;...c5
                                                ;...fd
                                                ;...72
                                                ;...f0
                                                ;...01

  0x000001c89e499601: vpaddd  ymm0,ymm1,ymm0    ;...c5
                                                ;...f5
                                                ;...fe
                                                ;...c0

  0x000001c89e499605: vphaddd ymm3,ymm0,ymm0    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...d8

  0x000001c89e49960a: vphaddd ymm3,ymm3,ymm1    ;...c4
                                                ;...e2
                                                ;...65
                                                ;...02
                                                ;...d9

  0x000001c89e49960f: vextracti128 xmm1,ymm3,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d9
                                                ;...01

  0x000001c89e499615: vpaddd  xmm3,xmm3,xmm1    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d9

  0x000001c89e499619: vmovd   xmm1,ebx          ;...c5
                                                ;...f9
                                                ;...6e
                                                ;...cb

  0x000001c89e49961d: vpaddd  xmm1,xmm1,xmm3    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...cb

  0x000001c89e499621: vmovd   ebx,xmm1          ;...c5
                                                ;...f9
                                                ;...7e
                                                ;...cb
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@25 (line 42)

  0x000001c89e499625: add     r13d,8h           ;...41
                                                ;...83
                                                ;...c5
                                                ;...08
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@27 (line 41)

  0x000001c89e499629: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000001c89e49962c: jl      1c89e4995f0h      ;...7c
                                                ;...c2
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@14 (line 41)

  0x000001c89e49962e: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e499631: jnl     1c89e499651h      ;...7d
                                                ;...1e

  0x000001c89e499633: nop                       ;...90

  0x000001c89e499634: mov     r11d,dword ptr [rbp+r13*4+10h]
                                                ;...46
                                                ;...8b
                                                ;...5c
                                                ;...ad
                                                ;...10
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@23 (line 42)

  0x000001c89e499639: mov     r10d,r11d         ;...45
                                                ;...8b
                                                ;...d3

  0x000001c89e49963c: shl     r10d,3h           ;...41
                                                ;...c1
                                                ;...e2
                                                ;...03

  0x000001c89e499640: shl     r11d,1h           ;...41
                                                ;...d1
                                                ;...e3

  0x000001c89e499643: add     r10d,r11d         ;...45
                                                ;...03
                                                ;...d3

  0x000001c89e499646: add     ebx,r10d          ;...41
                                                ;...03
                                                ;...da
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@25 (line 42)

  0x000001c89e499649: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@27 (line 41)

  0x000001c89e49964c: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e49964f: jl      1c89e499634h      ;...7c
                                                ;...e3
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@14 (line 41)

  0x000001c89e499651: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e499654: jnl     1c89e49967ah      ;...7d
                                                ;...24

  0x000001c89e499656: nop                       ;...66
                                                ;...90

  0x000001c89e499658: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e49965b: jnb     1c89e499691h      ;...73
                                                ;...34

  0x000001c89e49965d: mov     r11d,dword ptr [rbp+r13*4+10h]
                                                ;...46
                                                ;...8b
                                                ;...5c
                                                ;...ad
                                                ;...10
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@23 (line 42)

  0x000001c89e499662: mov     r10d,r11d         ;...45
                                                ;...8b
                                                ;...d3

  0x000001c89e499665: shl     r10d,3h           ;...41
                                                ;...c1
                                                ;...e2
                                                ;...03

  0x000001c89e499669: shl     r11d,1h           ;...41
                                                ;...d1
                                                ;...e3

  0x000001c89e49966c: add     r10d,r11d         ;...45
                                                ;...03
                                                ;...d3

  0x000001c89e49966f: add     ebx,r10d          ;...41
                                                ;...03
                                                ;...da
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@25 (line 42)

  0x000001c89e499672: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@27 (line 41)

  0x000001c89e499675: cmp     r13d,edi          ;...44
                                                ;...3b
                                                ;...ef

  0x000001c89e499678: jl      1c89e499658h      ;...7c
                                                ;...de
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int@10 (line 41)

  0x000001c89e49967a: mov     eax,ebx           ;...8b
                                                ;...c3

  0x000001c89e49967c: vzeroupper                ;...c5
                                                ;...f8
                                                ;...77

  0x000001c89e49967f: add     rsp,40h           ;...48
                                                ;...83
                                                ;...c4
                                                ;...40

  0x000001c89e499683: pop     rbp               ;...5d

  0x000001c89e499684: test    dword ptr [1c88a9e0000h],eax
                                                ;...85
                                                ;...05
                                                ;...76
                                                ;...69
                                                ;...54
                                                ;...ec
                                                ;   {poll_return}
  0x000001c89e49968a: ret 

The loop is aggressively unrolled, pipelined, and vectorised. Moreover, the multiplication by ten results not in a multiplication but two left shifts (see VPSLLD) and an addition. Note that x << 1 + x << 3 = x * 10 and C2 seems to know it; this rewrite can be applied because it can be proven statically that the factor is always 10. The “optimised” loop doesn’t vectorise at all (and I have no idea why not – isn’t this a bug? Yes it is.)

com/openkappa/simd/scale/Scale.FactoredScale_Int(Lcom/openkappa/simd/state/IntData;)I  [0x000002bbebeda320, 0x000002bbebeda4b8]  408 bytes
Argument 0 is unknown.RIP: 0x2bbebeda320 Code size: 0x00000198
[Entry Point]
[Verified Entry Point]
[Constants]
  # {method} {0x000002bb81241148} 'FactoredScale_Int' '(Lcom/openkappa/simd/state/IntData;)I' in 'com/openkappa/simd/scale/Scale'
  0x000002bbebeda320: int3                      ;...cc

  0x000002bbebeda321: nop     word ptr [rax+rax+0h]  ;...66
                                                ;...66
                                                ;...66
                                                ;...0f
                                                ;...1f
                                                ;...84
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002bbebeda32c: nop                       ;...66
                                                ;...66
                                                ;...66
                                                ;...90

  0x000002bbebeda330: mov     dword ptr [rsp+0ffffffffffff9000h],eax
                                                ;...89
                                                ;...84
                                                ;...24
                                                ;...00
                                                ;...90
                                                ;...ff
                                                ;...ff

  0x000002bbebeda337: push    rbp               ;...55

  0x000002bbebeda338: sub     rsp,40h           ;...48
                                                ;...83
                                                ;...ec
                                                ;...40

  0x000002bbebeda33c: mov     rbp,qword ptr [rdx+8h]  ;...48
                                                ;...8b
                                                ;...6a
                                                ;...08

  0x000002bbebeda340: mov     ebx,dword ptr [rdx+10h]  ;...8b
                                                ;...5a
                                                ;...10

  0x000002bbebeda343: mov     r13d,dword ptr [rdx]  ;...44
                                                ;...8b
                                                ;...2a

  0x000002bbebeda346: mov     rcx,rdx           ;...48
                                                ;...8b
                                                ;...ca

  0x000002bbebeda349: mov     r10,51da8d20h     ;...49
                                                ;...ba
                                                ;...20
                                                ;...8d
                                                ;...da
                                                ;...51
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002bbebeda353: call indirect r10         ;...41
                                                ;...ff
                                                ;...d2

  0x000002bbebeda356: mov     r10d,dword ptr [rbp+8h]  ;...44
                                                ;...8b
                                                ;...55
                                                ;...08
                                                ; implicit exception: dispatches to 0x000002bbebeda46d
  0x000002bbebeda35a: cmp     r10d,0f800016dh   ;...41
                                                ;...81
                                                ;...fa
                                                ;...6d
                                                ;...01
                                                ;...00
                                                ;...f8
                                                ;   {metadata({type array int})}
  0x000002bbebeda361: jne     2bbebeda459h      ;...0f
                                                ;...85
                                                ;...f2
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@10 (line 52)

  0x000002bbebeda367: mov     r10d,dword ptr [rbp+0ch]
                                                ;...44
                                                ;...8b
                                                ;...55
                                                ;...0c
                                                ;*arraylength {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@13 (line 52)

  0x000002bbebeda36b: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda36e: jnl     2bbebeda422h      ;...0f
                                                ;...8d
                                                ;...ae
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@14 (line 52)

  0x000002bbebeda374: mov     r11d,r13d         ;...45
                                                ;...8b
                                                ;...dd

  0x000002bbebeda377: inc     r11d              ;...41
                                                ;...ff
                                                ;...c3

  0x000002bbebeda37a: xor     r8d,r8d           ;...45
                                                ;...33
                                                ;...c0

  0x000002bbebeda37d: cmp     r11d,r8d          ;...45
                                                ;...3b
                                                ;...d8

  0x000002bbebeda380: cmovl   r11d,r8d          ;...45
                                                ;...0f
                                                ;...4c
                                                ;...d8

  0x000002bbebeda384: cmp     r11d,r10d         ;...45
                                                ;...3b
                                                ;...da

  0x000002bbebeda387: cmovnle r11d,r10d         ;...45
                                                ;...0f
                                                ;...4f
                                                ;...da

  0x000002bbebeda38b: nop                       ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@21 (line 53)

  0x000002bbebeda38c: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda38f: jnb     2bbebeda43ch      ;...0f
                                                ;...83
                                                ;...a7
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002bbebeda395: add     ebx,dword ptr [rbp+r13*4+10h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...ad
                                                ;...10
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@22 (line 53)

  0x000002bbebeda39a: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@24 (line 52)

  0x000002bbebeda39d: cmp     r13d,r11d         ;...45
                                                ;...3b
                                                ;...eb

  0x000002bbebeda3a0: jl      2bbebeda38ch      ;...7c
                                                ;...ea
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@14 (line 52)

  0x000002bbebeda3a2: mov     r11d,r10d         ;...45
                                                ;...8b
                                                ;...da

  0x000002bbebeda3a5: add     r11d,0fffffff9h   ;...41
                                                ;...83
                                                ;...c3
                                                ;...f9

  0x000002bbebeda3a9: mov     r8d,80000000h     ;...41
                                                ;...b8
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...80

  0x000002bbebeda3af: cmp     r10d,r11d         ;...45
                                                ;...3b
                                                ;...d3

  0x000002bbebeda3b2: cmovl   r11d,r8d          ;...45
                                                ;...0f
                                                ;...4c
                                                ;...d8

  0x000002bbebeda3b6: cmp     r13d,r11d         ;...45
                                                ;...3b
                                                ;...eb

  0x000002bbebeda3b9: jnl     2bbebeda409h      ;...7d
                                                ;...4e

  0x000002bbebeda3bb: nop     dword ptr [rax+rax+0h]  ;...0f
                                                ;...1f
                                                ;...44
                                                ;...00
                                                ;...00
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@21 (line 53)

  0x000002bbebeda3c0: add     ebx,dword ptr [rbp+r13*4+10h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...ad
                                                ;...10

  0x000002bbebeda3c5: movsxd  r8,r13d           ;...4d
                                                ;...63
                                                ;...c5

  0x000002bbebeda3c8: add     ebx,dword ptr [rbp+r8*4+14h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...14

  0x000002bbebeda3cd: add     ebx,dword ptr [rbp+r8*4+18h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...18

  0x000002bbebeda3d2: add     ebx,dword ptr [rbp+r8*4+1ch]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...1c

  0x000002bbebeda3d7: add     ebx,dword ptr [rbp+r8*4+20h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...20

  0x000002bbebeda3dc: add     ebx,dword ptr [rbp+r8*4+24h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...24

  0x000002bbebeda3e1: add     ebx,dword ptr [rbp+r8*4+28h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...28

  0x000002bbebeda3e6: add     ebx,dword ptr [rbp+r8*4+2ch]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...85
                                                ;...2c
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@22 (line 53)

  0x000002bbebeda3eb: add     r13d,8h           ;...41
                                                ;...83
                                                ;...c5
                                                ;...08
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@24 (line 52)

  0x000002bbebeda3ef: cmp     r13d,r11d         ;...45
                                                ;...3b
                                                ;...eb

  0x000002bbebeda3f2: jl      2bbebeda3c0h      ;...7c
                                                ;...cc
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@14 (line 52)

  0x000002bbebeda3f4: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda3f7: jnl     2bbebeda409h      ;...7d
                                                ;...10

  0x000002bbebeda3f9: nop                       ;...66
                                                ;...66
                                                ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@21 (line 53)

  0x000002bbebeda3fc: add     ebx,dword ptr [rbp+r13*4+10h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...ad
                                                ;...10
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@22 (line 53)

  0x000002bbebeda401: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@24 (line 52)

  0x000002bbebeda404: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda407: jl      2bbebeda3fch      ;...7c
                                                ;...f3
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@14 (line 52)

  0x000002bbebeda409: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda40c: jnl     2bbebeda422h      ;...7d
                                                ;...14

  0x000002bbebeda40e: nop                       ;...66
                                                ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@21 (line 53)

  0x000002bbebeda410: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda413: jnb     2bbebeda442h      ;...73
                                                ;...2d

  0x000002bbebeda415: add     ebx,dword ptr [rbp+r13*4+10h]
                                                ;...42
                                                ;...03
                                                ;...5c
                                                ;...ad
                                                ;...10
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@22 (line 53)

  0x000002bbebeda41a: inc     r13d              ;...41
                                                ;...ff
                                                ;...c5
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@24 (line 52)

  0x000002bbebeda41d: cmp     r13d,r10d         ;...45
                                                ;...3b
                                                ;...ea

  0x000002bbebeda420: jl      2bbebeda410h      ;...7c
                                                ;...ee
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@10 (line 52)

  0x000002bbebeda422: mov     r11d,ebx          ;...44
                                                ;...8b
                                                ;...db

  0x000002bbebeda425: shl     r11d,3h           ;...41
                                                ;...c1
                                                ;...e3
                                                ;...03

  0x000002bbebeda429: shl     ebx,1h            ;...d1
                                                ;...e3

  0x000002bbebeda42b: add     ebx,r11d          ;...41
                                                ;...03
                                                ;...db
                                                ;*imul {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::FactoredScale_Int@33 (line 55)

  0x000002bbebeda42e: mov     eax,ebx           ;...8b
                                                ;...c3

  0x000002bbebeda430: add     rsp,40h           ;...48
                                                ;...83
                                                ;...c4
                                                ;...40

  0x000002bbebeda434: pop     rbp               ;...5d

  0x000002bbebeda435: test    dword ptr [2bbd8590000h],eax
                                                ;...85
                                                ;...05
                                                ;...c5
                                                ;...5b
                                                ;...6b
                                                ;...ec
                                                ;   {poll_return}
  0x000002bbebeda43b: ret                       ;...c3

This is a special case: data is usually dynamic and variable, so the loop cannot always be proven to be equivalent to a linear combination of bit shifts. The routine is compiled for all possible parameters, not just statically contrived cases like the one above, so you may never see this assembly in the wild. However, even with random factors, the slow looking loop is aggressively optimised in a way the hand “optimised” code is not:


    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public int Scale_Int_Dynamic(ScaleState state) {
        int value = 0;
        int[] data = state.data;
        int factor = state.randomFactor();
        for (int i = 0; i < data.length; ++i) {
            value += factor * data[i];
        }
        return value;
    }

    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    @Benchmark
    public int FactoredScale_Int_Dynamic(ScaleState state) {
        int value = 0;
        int[] data = state.data;
        int factor = state.randomFactor();
        for (int i = 0; i < data.length; ++i) {
            value += data[i];
        }
        return factor * value;
    }

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit Param: size
FactoredScale_Int_Dynamic thrpt 1 10 26.100439 0.340069 ops/ms 100000
FactoredScale_Int_Dynamic thrpt 1 10 1.918011 0.297925 ops/ms 1000000
Scale_Int_Dynamic thrpt 1 10 30.219809 2.977389 ops/ms 100000
Scale_Int_Dynamic thrpt 1 10 2.314159 0.378442 ops/ms 1000000

Far from seeking to exploit distributivity to reduce the number of multiplication instructions, it seems to almost embrace the extraneous operations as metadata to drive optimisations. The assembly for Scale_Int_Dynamic confirms this (it shows vectorised multiplication, not shifts, within the loop):

com/openkappa/simd/scale/Scale.Scale_Int_Dynamic(Lcom/openkappa/simd/scale/ScaleState;)I  [0x000001f5ca2fa120, 0x000001f5ca2fa498]  888 bytes
Argument 0 is unknown.RIP: 0x1f5ca2fa120 Code size: 0x00000378
[Entry Point]
[Verified Entry Point]
[Constants]
  # {method} {0x000001f5df561a20} 'Scale_Int_Dynamic' '(Lcom/openkappa/simd/scale/ScaleState;)I' in 'com/openkappa/simd/scale/Scale'
  0x000001f5ca2fa120: int3                      ;...cc

  0x000001f5ca2fa121: nop     word ptr [rax+rax+0h]  ;...66
                                                ;...66
                                                ;...66
                                                ;...0f
                                                ;...1f
                                                ;...84
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa12c: nop                       ;...66
                                                ;...66
                                                ;...66
                                                ;...90

  0x000001f5ca2fa130: mov     dword ptr [rsp+0ffffffffffff9000h],eax
                                                ;...89
                                                ;...84
                                                ;...24
                                                ;...00
                                                ;...90
                                                ;...ff
                                                ;...ff

  0x000001f5ca2fa137: push    rbp               ;...55

  0x000001f5ca2fa138: sub     rsp,50h           ;...48
                                                ;...83
                                                ;...ec
                                                ;...50

  0x000001f5ca2fa13c: mov     r13,qword ptr [rdx+10h]  ;...4c
                                                ;...8b
                                                ;...6a
                                                ;...10

  0x000001f5ca2fa140: mov     ebx,dword ptr [rdx+18h]  ;...8b
                                                ;...5a
                                                ;...18

  0x000001f5ca2fa143: mov     ebp,dword ptr [rdx+8h]  ;...8b
                                                ;...6a
                                                ;...08

  0x000001f5ca2fa146: mov     r14d,dword ptr [rdx]  ;...44
                                                ;...8b
                                                ;...32

  0x000001f5ca2fa149: mov     rcx,rdx           ;...48
                                                ;...8b
                                                ;...ca

  0x000001f5ca2fa14c: vzeroupper                ;...c5
                                                ;...f8
                                                ;...77

  0x000001f5ca2fa14f: mov     r10,51da8d20h     ;...49
                                                ;...ba
                                                ;...20
                                                ;...8d
                                                ;...da
                                                ;...51
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa159: call indirect r10         ;...41
                                                ;...ff
                                                ;...d2

  0x000001f5ca2fa15c: mov     r10d,dword ptr [r13+8h]  ;...45
                                                ;...8b
                                                ;...55
                                                ;...08
                                                ; implicit exception: dispatches to 0x000001f5ca2fa461
  0x000001f5ca2fa160: cmp     r10d,0f800016dh   ;...41
                                                ;...81
                                                ;...fa
                                                ;...6d
                                                ;...01
                                                ;...00
                                                ;...f8
                                                ;   {metadata({type array int})}
  0x000001f5ca2fa167: jne     1f5ca2fa445h      ;...0f
                                                ;...85
                                                ;...d8
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@16 (line 64)

  0x000001f5ca2fa16d: mov     edi,dword ptr [r13+0ch]  ;...41
                                                ;...8b
                                                ;...7d
                                                ;...0c
                                                ;*arraylength {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@19 (line 64)

  0x000001f5ca2fa171: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa174: jnl     1f5ca2fa411h      ;...0f
                                                ;...8d
                                                ;...97
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@20 (line 64)

  0x000001f5ca2fa17a: mov     r11d,r13d         ;...45
                                                ;...8b
                                                ;...dd

  0x000001f5ca2fa17d: mov     r10d,r14d         ;...45
                                                ;...8b
                                                ;...d6

  0x000001f5ca2fa180: inc     r10d              ;...41
                                                ;...ff
                                                ;...c2

  0x000001f5ca2fa183: shr     r11d,2h           ;...41
                                                ;...c1
                                                ;...eb
                                                ;...02

  0x000001f5ca2fa187: and     r11d,7h           ;...41
                                                ;...83
                                                ;...e3
                                                ;...07

  0x000001f5ca2fa18b: xor     r8d,r8d           ;...45
                                                ;...33
                                                ;...c0

  0x000001f5ca2fa18e: cmp     r10d,r8d          ;...45
                                                ;...3b
                                                ;...d0

  0x000001f5ca2fa191: cmovl   r10d,r8d          ;...45
                                                ;...0f
                                                ;...4c
                                                ;...d0

  0x000001f5ca2fa195: cmp     r10d,edi          ;...44
                                                ;...3b
                                                ;...d7

  0x000001f5ca2fa198: cmovnle r10d,edi          ;...44
                                                ;...0f
                                                ;...4f
                                                ;...d7

  0x000001f5ca2fa19c: add     r11d,r10d         ;...45
                                                ;...03
                                                ;...da

  0x000001f5ca2fa19f: mov     r9d,4h            ;...41
                                                ;...b9
                                                ;...04
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa1a5: sub     r9d,r11d          ;...45
                                                ;...2b
                                                ;...cb

  0x000001f5ca2fa1a8: and     r9d,7h            ;...41
                                                ;...83
                                                ;...e1
                                                ;...07

  0x000001f5ca2fa1ac: add     r9d,r10d          ;...45
                                                ;...03
                                                ;...ca

  0x000001f5ca2fa1af: cmp     r9d,edi           ;...44
                                                ;...3b
                                                ;...cf

  0x000001f5ca2fa1b2: cmovnle r9d,edi           ;...44
                                                ;...0f
                                                ;...4f
                                                ;...cf
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@29 (line 65)

  0x000001f5ca2fa1b6: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa1b9: jnb     1f5ca2fa422h      ;...0f
                                                ;...83
                                                ;...63
                                                ;...02
                                                ;...00
                                                ;...00

  0x000001f5ca2fa1bf: mov     r11d,ebp          ;...44
                                                ;...8b
                                                ;...dd

  0x000001f5ca2fa1c2: imul    r11d,dword ptr [r13+r14*4+10h]
                                                ;...47
                                                ;...0f
                                                ;...af
                                                ;...5c
                                                ;...b5
                                                ;...10

  0x000001f5ca2fa1c8: add     ebx,r11d          ;...41
                                                ;...03
                                                ;...db
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@31 (line 65)

  0x000001f5ca2fa1cb: inc     r14d              ;...41
                                                ;...ff
                                                ;...c6
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@33 (line 64)

  0x000001f5ca2fa1ce: cmp     r14d,r9d          ;...45
                                                ;...3b
                                                ;...f1

  0x000001f5ca2fa1d1: jl      1f5ca2fa1b6h      ;...7c
                                                ;...e3
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@20 (line 64)

  0x000001f5ca2fa1d3: mov     r9d,edi           ;...44
                                                ;...8b
                                                ;...cf

  0x000001f5ca2fa1d6: add     r9d,0ffffffc1h    ;...41
                                                ;...83
                                                ;...c1
                                                ;...c1

  0x000001f5ca2fa1da: mov     r8d,80000000h     ;...41
                                                ;...b8
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...80

  0x000001f5ca2fa1e0: cmp     edi,r9d           ;...41
                                                ;...3b
                                                ;...f9

  0x000001f5ca2fa1e3: cmovl   r9d,r8d           ;...45
                                                ;...0f
                                                ;...4c
                                                ;...c8

  0x000001f5ca2fa1e7: cmp     r14d,r9d          ;...45
                                                ;...3b
                                                ;...f1

  0x000001f5ca2fa1ea: jnl     1f5ca2fa3f0h      ;...0f
                                                ;...8d
                                                ;...00
                                                ;...02
                                                ;...00
                                                ;...00

  0x000001f5ca2fa1f0: vmovd   xmm2,ebp          ;...c5
                                                ;...f9
                                                ;...6e
                                                ;...d5

  0x000001f5ca2fa1f4: vpshufd xmm2,xmm2,0h      ;...c5
                                                ;...f9
                                                ;...70
                                                ;...d2
                                                ;...00

  0x000001f5ca2fa1f9: vinserti128 ymm2,ymm2,xmm2,1h  ;...c4
                                                ;...e3
                                                ;...6d
                                                ;...38
                                                ;...d2
                                                ;...01

  0x000001f5ca2fa1ff: nop                       ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@29 (line 65)

  0x000001f5ca2fa200: vmovdqu ymm0,ymmword ptr [r13+r14*4+10h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...44
                                                ;...b5
                                                ;...10

  0x000001f5ca2fa207: vpmulld ymm11,ymm0,ymm2   ;...c4
                                                ;...62
                                                ;...7d
                                                ;...40
                                                ;...da

  0x000001f5ca2fa20c: movsxd  r10,r14d          ;...4d
                                                ;...63
                                                ;...d6

  0x000001f5ca2fa20f: vmovdqu ymm0,ymmword ptr [r13+r10*4+30h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...44
                                                ;...95
                                                ;...30

  0x000001f5ca2fa216: vmovdqu ymm1,ymmword ptr [r13+r10*4+0f0h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...8c
                                                ;...95
                                                ;...f0
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa220: vmovdqu ymm3,ymmword ptr [r13+r10*4+50h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...5c
                                                ;...95
                                                ;...50

  0x000001f5ca2fa227: vmovdqu ymm7,ymmword ptr [r13+r10*4+70h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...7c
                                                ;...95
                                                ;...70

  0x000001f5ca2fa22e: vmovdqu ymm6,ymmword ptr [r13+r10*4+90h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...b4
                                                ;...95
                                                ;...90
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa238: vmovdqu ymm5,ymmword ptr [r13+r10*4+0b0h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...ac
                                                ;...95
                                                ;...b0
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa242: vmovdqu ymm4,ymmword ptr [r13+r10*4+0d0h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...a4
                                                ;...95
                                                ;...d0
                                                ;...00
                                                ;...00
                                                ;...00

  0x000001f5ca2fa24c: vpmulld ymm9,ymm0,ymm2    ;...c4
                                                ;...62
                                                ;...7d
                                                ;...40
                                                ;...ca

  0x000001f5ca2fa251: vpmulld ymm4,ymm4,ymm2    ;...c4
                                                ;...e2
                                                ;...5d
                                                ;...40
                                                ;...e2

  0x000001f5ca2fa256: vpmulld ymm5,ymm5,ymm2    ;...c4
                                                ;...e2
                                                ;...55
                                                ;...40
                                                ;...ea

  0x000001f5ca2fa25b: vpmulld ymm6,ymm6,ymm2    ;...c4
                                                ;...e2
                                                ;...4d
                                                ;...40
                                                ;...f2

  0x000001f5ca2fa260: vpmulld ymm8,ymm7,ymm2    ;...c4
                                                ;...62
                                                ;...45
                                                ;...40
                                                ;...c2

  0x000001f5ca2fa265: vpmulld ymm10,ymm3,ymm2   ;...c4
                                                ;...62
                                                ;...65
                                                ;...40
                                                ;...d2

  0x000001f5ca2fa26a: vpmulld ymm3,ymm1,ymm2    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...40
                                                ;...da

  0x000001f5ca2fa26f: vphaddd ymm1,ymm11,ymm11  ;...c4
                                                ;...c2
                                                ;...25
                                                ;...02
                                                ;...cb

  0x000001f5ca2fa274: vphaddd ymm1,ymm1,ymm0    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...c8

  0x000001f5ca2fa279: vextracti128 xmm0,ymm1,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c8
                                                ;...01

  0x000001f5ca2fa27f: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa283: vmovd   xmm0,ebx          ;...c5
                                                ;...f9
                                                ;...6e
                                                ;...c3

  0x000001f5ca2fa287: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa28b: vmovd   r10d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c2

  0x000001f5ca2fa290: vphaddd ymm1,ymm9,ymm9    ;...c4
                                                ;...c2
                                                ;...35
                                                ;...02
                                                ;...c9

  0x000001f5ca2fa295: vphaddd ymm1,ymm1,ymm0    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...c8

  0x000001f5ca2fa29a: vextracti128 xmm0,ymm1,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c8
                                                ;...01

  0x000001f5ca2fa2a0: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa2a4: vmovd   xmm0,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c2

  0x000001f5ca2fa2a9: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa2ad: vmovd   r11d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c3

  0x000001f5ca2fa2b2: vphaddd ymm0,ymm10,ymm10  ;...c4
                                                ;...c2
                                                ;...2d
                                                ;...02
                                                ;...c2

  0x000001f5ca2fa2b7: vphaddd ymm0,ymm0,ymm1    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c1

  0x000001f5ca2fa2bc: vextracti128 xmm1,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c1
                                                ;...01

  0x000001f5ca2fa2c2: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa2c6: vmovd   xmm1,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...cb

  0x000001f5ca2fa2cb: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa2cf: vmovd   r10d,xmm1         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...ca

  0x000001f5ca2fa2d4: vphaddd ymm1,ymm8,ymm8    ;...c4
                                                ;...c2
                                                ;...3d
                                                ;...02
                                                ;...c8

  0x000001f5ca2fa2d9: vphaddd ymm1,ymm1,ymm0    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...c8

  0x000001f5ca2fa2de: vextracti128 xmm0,ymm1,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c8
                                                ;...01

  0x000001f5ca2fa2e4: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa2e8: vmovd   xmm0,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c2

  0x000001f5ca2fa2ed: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa2f1: vmovd   r11d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c3

  0x000001f5ca2fa2f6: vphaddd ymm0,ymm6,ymm6    ;...c4
                                                ;...e2
                                                ;...4d
                                                ;...02
                                                ;...c6

  0x000001f5ca2fa2fb: vphaddd ymm0,ymm0,ymm1    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c1

  0x000001f5ca2fa300: vextracti128 xmm1,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c1
                                                ;...01

  0x000001f5ca2fa306: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa30a: vmovd   xmm1,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...cb

  0x000001f5ca2fa30f: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa313: vmovd   r10d,xmm1         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...ca

  0x000001f5ca2fa318: vphaddd ymm1,ymm5,ymm5    ;...c4
                                                ;...e2
                                                ;...55
                                                ;...02
                                                ;...cd

  0x000001f5ca2fa31d: vphaddd ymm1,ymm1,ymm0    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...c8

  0x000001f5ca2fa322: vextracti128 xmm0,ymm1,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c8
                                                ;...01

  0x000001f5ca2fa328: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa32c: vmovd   xmm0,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...c2

  0x000001f5ca2fa331: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa335: vmovd   r11d,xmm0         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...c3

  0x000001f5ca2fa33a: vphaddd ymm0,ymm4,ymm4    ;...c4
                                                ;...e2
                                                ;...5d
                                                ;...02
                                                ;...c4

  0x000001f5ca2fa33f: vphaddd ymm0,ymm0,ymm1    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...02
                                                ;...c1

  0x000001f5ca2fa344: vextracti128 xmm1,ymm0,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...c1
                                                ;...01

  0x000001f5ca2fa34a: vpaddd  xmm0,xmm0,xmm1    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c1

  0x000001f5ca2fa34e: vmovd   xmm1,r11d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...cb

  0x000001f5ca2fa353: vpaddd  xmm1,xmm1,xmm0    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...c8

  0x000001f5ca2fa357: vmovd   r10d,xmm1         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...7e
                                                ;...ca

  0x000001f5ca2fa35c: vphaddd ymm1,ymm3,ymm3    ;...c4
                                                ;...e2
                                                ;...65
                                                ;...02
                                                ;...cb

  0x000001f5ca2fa361: vphaddd ymm1,ymm1,ymm7    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...cf

  0x000001f5ca2fa366: vextracti128 xmm7,ymm1,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...cf
                                                ;...01

  0x000001f5ca2fa36c: vpaddd  xmm1,xmm1,xmm7    ;...c5
                                                ;...f1
                                                ;...fe
                                                ;...cf

  0x000001f5ca2fa370: vmovd   xmm7,r10d         ;...c4
                                                ;...c1
                                                ;...79
                                                ;...6e
                                                ;...fa

  0x000001f5ca2fa375: vpaddd  xmm7,xmm7,xmm1    ;...c5
                                                ;...c1
                                                ;...fe
                                                ;...f9

  0x000001f5ca2fa379: vmovd   ebx,xmm7          ;...c5
                                                ;...f9
                                                ;...7e
                                                ;...fb
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@31 (line 65)

  0x000001f5ca2fa37d: add     r14d,40h          ;...41
                                                ;...83
                                                ;...c6
                                                ;...40
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@33 (line 64)

  0x000001f5ca2fa381: cmp     r14d,r9d          ;...45
                                                ;...3b
                                                ;...f1

  0x000001f5ca2fa384: jl      1f5ca2fa200h      ;...0f
                                                ;...8c
                                                ;...76
                                                ;...fe
                                                ;...ff
                                                ;...ff
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@20 (line 64)

  0x000001f5ca2fa38a: mov     r11d,edi          ;...44
                                                ;...8b
                                                ;...df

  0x000001f5ca2fa38d: add     r11d,0fffffff9h   ;...41
                                                ;...83
                                                ;...c3
                                                ;...f9

  0x000001f5ca2fa391: cmp     edi,r11d          ;...41
                                                ;...3b
                                                ;...fb

  0x000001f5ca2fa394: cmovl   r11d,r8d          ;...45
                                                ;...0f
                                                ;...4c
                                                ;...d8

  0x000001f5ca2fa398: cmp     r14d,r11d         ;...45
                                                ;...3b
                                                ;...f3

  0x000001f5ca2fa39b: jnl     1f5ca2fa3d5h      ;...7d
                                                ;...38

  0x000001f5ca2fa39d: nop                       ;...66
                                                ;...66
                                                ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@29 (line 65)

  0x000001f5ca2fa3a0: vmovdqu ymm0,ymmword ptr [r13+r14*4+10h]
                                                ;...c4
                                                ;...81
                                                ;...7e
                                                ;...6f
                                                ;...44
                                                ;...b5
                                                ;...10

  0x000001f5ca2fa3a7: vpmulld ymm1,ymm0,ymm2    ;...c4
                                                ;...e2
                                                ;...7d
                                                ;...40
                                                ;...ca

  0x000001f5ca2fa3ac: vphaddd ymm3,ymm1,ymm1    ;...c4
                                                ;...e2
                                                ;...75
                                                ;...02
                                                ;...d9

  0x000001f5ca2fa3b1: vphaddd ymm3,ymm3,ymm0    ;...c4
                                                ;...e2
                                                ;...65
                                                ;...02
                                                ;...d8

  0x000001f5ca2fa3b6: vextracti128 xmm0,ymm3,1h  ;...c4
                                                ;...e3
                                                ;...7d
                                                ;...39
                                                ;...d8
                                                ;...01

  0x000001f5ca2fa3bc: vpaddd  xmm3,xmm3,xmm0    ;...c5
                                                ;...e1
                                                ;...fe
                                                ;...d8

  0x000001f5ca2fa3c0: vmovd   xmm0,ebx          ;...c5
                                                ;...f9
                                                ;...6e
                                                ;...c3

  0x000001f5ca2fa3c4: vpaddd  xmm0,xmm0,xmm3    ;...c5
                                                ;...f9
                                                ;...fe
                                                ;...c3

  0x000001f5ca2fa3c8: vmovd   ebx,xmm0          ;...c5
                                                ;...f9
                                                ;...7e
                                                ;...c3
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@31 (line 65)

  0x000001f5ca2fa3cc: add     r14d,8h           ;...41
                                                ;...83
                                                ;...c6
                                                ;...08
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@33 (line 64)

  0x000001f5ca2fa3d0: cmp     r14d,r11d         ;...45
                                                ;...3b
                                                ;...f3

  0x000001f5ca2fa3d3: jl      1f5ca2fa3a0h      ;...7c
                                                ;...cb
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@20 (line 64)

  0x000001f5ca2fa3d5: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa3d8: jnl     1f5ca2fa3f0h      ;...7d
                                                ;...16

  0x000001f5ca2fa3da: nop                       ;...66
                                                ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@29 (line 65)

  0x000001f5ca2fa3dc: mov     r10d,ebp          ;...44
                                                ;...8b
                                                ;...d5

  0x000001f5ca2fa3df: imul    r10d,dword ptr [r13+r14*4+10h]
                                                ;...47
                                                ;...0f
                                                ;...af
                                                ;...54
                                                ;...b5
                                                ;...10

  0x000001f5ca2fa3e5: add     ebx,r10d          ;...41
                                                ;...03
                                                ;...da
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@31 (line 65)

  0x000001f5ca2fa3e8: inc     r14d              ;...41
                                                ;...ff
                                                ;...c6
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@33 (line 64)

  0x000001f5ca2fa3eb: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa3ee: jl      1f5ca2fa3dch      ;...7c
                                                ;...ec
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@20 (line 64)

  0x000001f5ca2fa3f0: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa3f3: jnl     1f5ca2fa411h      ;...7d
                                                ;...1c

  0x000001f5ca2fa3f5: nop                       ;...66
                                                ;...66
                                                ;...90
                                                ;*iaload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@29 (line 65)

  0x000001f5ca2fa3f8: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa3fb: jnb     1f5ca2fa428h      ;...73
                                                ;...2b

  0x000001f5ca2fa3fd: mov     r11d,ebp          ;...44
                                                ;...8b
                                                ;...dd

  0x000001f5ca2fa400: imul    r11d,dword ptr [r13+r14*4+10h]
                                                ;...47
                                                ;...0f
                                                ;...af
                                                ;...5c
                                                ;...b5
                                                ;...10

  0x000001f5ca2fa406: add     ebx,r11d          ;...41
                                                ;...03
                                                ;...db
                                                ;*iadd {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@31 (line 65)

  0x000001f5ca2fa409: inc     r14d              ;...41
                                                ;...ff
                                                ;...c6
                                                ;*iinc {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@33 (line 64)

  0x000001f5ca2fa40c: cmp     r14d,edi          ;...44
                                                ;...3b
                                                ;...f7

  0x000001f5ca2fa40f: jl      1f5ca2fa3f8h      ;...7c
                                                ;...e7
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.scale.Scale::Scale_Int_Dynamic@16 (line 64)

  0x000001f5ca2fa411: mov     eax,ebx           ;...8b
                                                ;...c3

  0x000001f5ca2fa413: vzeroupper                ;...c5
                                                ;...f8
                                                ;...77

  0x000001f5ca2fa416: add     rsp,50h           ;...48
                                                ;...83
                                                ;...c4
                                                ;...50

  0x000001f5ca2fa41a: pop     rbp               ;...5d

  0x000001f5ca2fa41b: test    dword ptr [1f5b68c0000h],eax
                                                ;...85
                                                ;...05
                                                ;...df
                                                ;...5b
                                                ;...5c
                                                ;...ec
                                                ;   {poll_return}
  0x000001f5ca2fa421: ret                       ;...c3

There are two lessons to be learnt here. The first is that what you see is not what you get. The second is about the correctness of asymptotic analysis. If hierarchical cache renders asymptotic analysis bullshit (linear time but cache friendly algorithms can, and do, outperform logarithmic algorithms with cache misses), optimising compilers render the field practically irrelevant.

Posted on

Zeroing Negative Values in Arrays Efficiently

Replacing negatives with zeroes in large arrays of values is a primitive function of several complex financial risk measures, including potential future exposure (PFE) and the liquidity coverage ratio (LCR). While this is not an interesting operation by any stretch of the imagination, it is useful and there is significant benefit in its performance. This is an operation that can be computed very efficiently using the instruction VMAXPD. For Intel Xeon processors, this instruction requires half a cycle to calculate and has a latency (how long before another instruction can use its result) of four cycles. There is currently no way to trick Java into using this instruction for this simple operation, though there is a placeholder implementation on the current DoubleVector prototype in Project Panama which may do so.

C++ Intel Intrinsics

It’s possible to target instructions from different processor vendors, in my case Intel, by using intrinsic functions which expose instructions as high level functions. The code looks incredibly ugly but it works. Here is a C++ function for 256 bit ymm registers:


void zero_negatives(const double* source, double* target, const size_t length) {
  for (size_t i = 0; i + 3 < length; i += 4) {
    __m256d vector = _mm256_load_pd(source + i);
    __m256d zeroed = _mm256_max_pd(vector, _mm256_setzero_pd());
    _mm256_storeu_pd(target + i, zeroed);
  }
}

The function loads doubles into 256 bit vectors, within each vector replaces the negative values with zero, and writes them back into an array. It generates the following assembly code (which, incidentally, is less of a shit show to access than in Java):


void zero_negatives(const double* source, double* target, const size_t length) {
00007FF746EE5110  mov         qword ptr [rsp+18h],r8  
00007FF746EE5115  mov         qword ptr [rsp+10h],rdx  
00007FF746EE511A  mov         qword ptr [rsp+8],rcx  
00007FF746EE511F  push        r13  
00007FF746EE5121  push        rbp  
00007FF746EE5122  push        rdi  
00007FF746EE5123  sub         rsp,250h  
00007FF746EE512A  mov         r13,rsp  
00007FF746EE512D  lea         rbp,[rsp+20h]  
00007FF746EE5132  and         rbp,0FFFFFFFFFFFFFFE0h  
00007FF746EE5136  mov         rdi,rsp  
00007FF746EE5139  mov         ecx,94h  
00007FF746EE513E  mov         eax,0CCCCCCCCh  
00007FF746EE5143  rep stos    dword ptr [rdi]  
00007FF746EE5145  mov         rcx,qword ptr [rsp+278h]  
  for (size_t i = 0; i + 3 < length; i += 4) {
00007FF746EE514D  mov         qword ptr [rbp+8],0  
00007FF746EE5155  jmp         zero_negatives+53h (07FF746EE5163h)  
00007FF746EE5157  mov         rax,qword ptr [rbp+8]  
00007FF746EE515B  add         rax,4  
00007FF746EE515F  mov         qword ptr [rbp+8],rax  
00007FF746EE5163  mov         rax,qword ptr [rbp+8]  
00007FF746EE5167  add         rax,3  
00007FF746EE516B  cmp         rax,qword ptr [length]  
00007FF746EE5172  jae         zero_negatives+0DDh (07FF746EE51EDh)  
    __m256d vector = _mm256_load_pd(source + i);
00007FF746EE5174  mov         rax,qword ptr [source]  
00007FF746EE517B  mov         rcx,qword ptr [rbp+8]  
00007FF746EE517F  lea         rax,[rax+rcx*8]  
00007FF746EE5183  vmovupd     ymm0,ymmword ptr [rax]  
00007FF746EE5187  vmovupd     ymmword ptr [rbp+180h],ymm0  
00007FF746EE518F  vmovupd     ymm0,ymmword ptr [rbp+180h]  
00007FF746EE5197  vmovupd     ymmword ptr [rbp+40h],ymm0  
    __m256d zeroed = _mm256_max_pd(vector, _mm256_setzero_pd());
00007FF746EE519C  vxorpd      xmm0,xmm0,xmm0  
00007FF746EE51A0  vmovupd     ymmword ptr [rbp+200h],ymm0  
00007FF746EE51A8  vmovupd     ymm0,ymmword ptr [rbp+40h]  
00007FF746EE51AD  vmaxpd      ymm0,ymm0,ymmword ptr [rbp+200h]  
00007FF746EE51B5  vmovupd     ymmword ptr [rbp+1C0h],ymm0  
00007FF746EE51BD  vmovupd     ymm0,ymmword ptr [rbp+1C0h]  
00007FF746EE51C5  vmovupd     ymmword ptr [rbp+80h],ymm0  
    _mm256_storeu_pd(target + i, zeroed);
00007FF746EE51CD  mov         rax,qword ptr [target]  
00007FF746EE51D4  mov         rcx,qword ptr [rbp+8]  
00007FF746EE51D8  lea         rax,[rax+rcx*8]  
00007FF746EE51DC  vmovupd     ymm0,ymmword ptr [rbp+80h]  
00007FF746EE51E4  vmovupd     ymmword ptr [rax],ymm0  
  }
00007FF746EE51E8  jmp         zero_negatives+47h (07FF746EE5157h)  
}
00007FF746EE51ED  lea         rsp,[r13+250h]  
00007FF746EE51F4  pop         rdi  
00007FF746EE51F5  pop         rbp  
00007FF746EE51F6  pop         r13  
00007FF746EE51F8  ret    

This code is noticeably fast. I measured the throughput averaged over 1000 iterations, with an array of 10 million doubles (800MB) uniformly distributed between +/- 1E7, to quantify the throughput in GB/s and iterations/s. This code does between 4.5 and 5 iterations per second, which translates to processing approximately 4GB/s. This seems high, and since I am unaware of best practices in C++, if the measurement is flawed, I would gratefully be educated in the comments.


void benchmark() {
  const size_t length = 1E8;
  double* values = new double[length];
  fill_array(values, length);
  double* zeroed = new double[length];
  auto start = std::chrono::high_resolution_clock::now();
  int iterations = 1000;
  for (int i = 0; i < iterations; ++i) {
    zero_negatives(values, zeroed, length);
  }
  auto end = std::chrono::high_resolution_clock::now();
  auto nanos = std::chrono::duration_cast<std::chrono::nanoseconds>(end - start).count();
  double thrpt_s = (iterations * 1E9) / nanos;
  double thrpt_gbps = (thrpt_s * sizeof(double) * length) / 1E9;
  std::cout << thrpt_s << "/s" << std::endl;
  std::cout << thrpt_gbps << "GB/s" << std::endl;
  delete[] values;
  delete[] zeroed;
}

While I am sure there are various ways an expert could tweak this for performance, this code can’t get much faster unless there are 512 bit zmm registers available, in which case it would be wasteful. While the code looks virtually the same for AVX512 (just replace “256” with “512”), portability and efficiency are at odds. Handling the mess of detecting the best instruction set for the deployed architecture is the main reason for using Java in performance sensitive (but not critical) applications. But this is not the code the JVM generates.

Java Auto-Vectorisation (Play Your Cards Right)

There is currently no abstraction modelling vectorisation in Java. The only access available is if the compiler engineers implement an intrinsic, or auto-vectorisation, which will try, and sometimes succeed admirably, to translate your code to a good vector implementation. There is currently a prototype project for explicit vectorisation in Project Panama. There are a few ways to skin this cat, and it’s worth looking at the code they generate and the throughput available from each approach.

There is a choice between copying the array and zeroing out the negatives, and allocating a new array and only writing the non-negative values. There is another choice between an if statement and branchless code using Math.max. This results in the following four implementations which I measure on comparable data to the C++ benchmark (10 million doubles, normally distributed with mean zero). To be fair to the Java code, as in the C++ benchmarks, the cost of allocation is isolated by writing into an array pre-allocated once per benchmark. This penalises the approaches where the array is copied first and then zeroed wherever the value is negative. The code is online at github.


    @Benchmark
    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    public double[] BranchyCopyAndMask(ArrayWithNegatives state) {
        double[] data = state.data;
        double[] result = state.target;
        System.arraycopy(data, 0, result, 0, data.length);
        for (int i = 0; i < result.length; ++i) {
            if (result[i] < 0D) {
                result[i] = 0D;
            }
        }
        return result;
    }

    @Benchmark
    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    public double[] BranchyNewArray(ArrayWithNegatives state) {
        double[] data = state.data;
        double[] result = state.target;
        for (int i = 0; i < result.length; ++i) {
            result[i] = data[i] < 0D ? 0D : data[i];
        }
        return result;
    }

    @Benchmark
    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    public double[] NewArray(ArrayWithNegatives state) {
        double[] data = state.data;
        double[] result = state.target;
        for (int i = 0; i < result.length; ++i) {
            result[i] = Math.max(data[i], 0D);
        }
        return result;
    }

    @Benchmark
    @CompilerControl(CompilerControl.Mode.DONT_INLINE)
    public double[] CopyAndMask(ArrayWithNegatives state) {
        double[] data = state.data;
        double[] result = state.target;
        System.arraycopy(data, 0, result, 0, data.length);
        for (int i = 0; i < result.length; ++i) {
            result[i] = Math.max(result[i], 0D);
        }
        return result;
    }

None of these implementations comes close to the native code above. The best implementation performs 1.8 iterations per second which equates to processing approximately 1.4GB/s, vastly inferior to the 4GB/s achieved with Intel intrinsics. The results are below:

Benchmark Mode Threads Samples Score Score Error (99.9%) Unit
BranchyCopyAndMask thrpt 1 10 1.314845 0.061662 ops/s
BranchyNewArray thrpt 1 10 1.802673 0.061835 ops/s
CopyAndMask thrpt 1 10 1.146630 0.018903 ops/s
NewArray thrpt 1 10 1.357020 0.116481 ops/s

As an aside, there is a very interesting observation to make, worthy of its own post: if the array consists only of positive values, the “branchy” implementations run very well, at speeds comparable to the zero_negatives (when it ran with 50% negatives). The ratio of branch hits to misses is an orthogonal explanatory variable, and the input data, while I often don’t think about it enough, is very important.

I only looked at the assembly emitted for the fastest version (BranchyNewArray) and it doesn’t look anything like zero_negatives, though it does use some vectorisation – as pointed out by Daniel Lemire in the comments, this code has probably not been vectorised and is probably using SSE2 (indeed only quad words are loaded into 128 bit registers):

com/openkappa/simd/positive/PositiveValues.BranchyNewArray(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D  [0x000002ae309c3ce0, 0x000002ae309c3ff8]  792 bytes
Argument 0 is unknown.RIP: 0x2ae309c3ce0 Code size: 0x00000318
[Entry Point]
[Constants]
  # {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues'
  0x000002ae309c3ce0: mov     r10d,dword ptr [rdx+8h]  ;...44
                                                ;...8b
                                                ;...52
                                                ;...08

  0x000002ae309c3ce4: shl     r10,3h            ;...49
                                                ;...c1
                                                ;...e2
                                                ;...03

  0x000002ae309c3ce8: cmp     r10,rax           ;...4c
                                                ;...3b
                                                ;...d0

  0x000002ae309c3ceb: jne     2ae3042c200h      ;...0f
                                                ;...85
                                                ;...0f
                                                ;...85
                                                ;...a6
                                                ;...ff
                                                ;   {runtime_call ic_miss_stub}
  0x000002ae309c3cf1: nop     word ptr [rax+rax+0h]  ;...66
                                                ;...66
                                                ;...66
                                                ;...0f
                                                ;...1f
                                                ;...84
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3cfc: nop                       ;...66
                                                ;...66
                                                ;...66
                                                ;...90

[Verified Entry Point]
  0x000002ae309c3d00: mov     dword ptr [rsp+0ffffffffffff9000h],eax
                                                ;...89
                                                ;...84
                                                ;...24
                                                ;...00
                                                ;...90
                                                ;...ff
                                                ;...ff

  0x000002ae309c3d07: push    rbp               ;...55

  0x000002ae309c3d08: sub     rsp,60h           ;...48
                                                ;...83
                                                ;...ec
                                                ;...60

  0x000002ae309c3d0c: mov     rcx,2ae4d163880h  ;...48
                                                ;...b9
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3d16: mov     esi,dword ptr [rcx+0fch]
                                                ;...8b
                                                ;...b1
                                                ;...fc
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d1c: add     esi,8h            ;...83
                                                ;...c6
                                                ;...08

  0x000002ae309c3d1f: mov     dword ptr [rcx+0fch],esi
                                                ;...89
                                                ;...b1
                                                ;...fc
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d25: and     esi,1ff8h         ;...81
                                                ;...e6
                                                ;...f8
                                                ;...1f
                                                ;...00
                                                ;...00

  0x000002ae309c3d2b: cmp     esi,0h            ;...83
                                                ;...fe
                                                ;...00

  0x000002ae309c3d2e: je      2ae309c3ec1h      ;...0f
                                                ;...84
                                                ;...8d
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;*aload_1 {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@0 (line 29)

  0x000002ae309c3d34: mov     edx,dword ptr [r8+0ch]  ;...41
                                                ;...8b
                                                ;...50
                                                ;...0c
                                                ; implicit exception: dispatches to 0x000002ae309c3ee2
  0x000002ae309c3d38: shl     rdx,3h            ;...48
                                                ;...c1
                                                ;...e2
                                                ;...03
                                                ;*getfield data {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@1 (line 29)

  0x000002ae309c3d3c: mov     ecx,dword ptr [r8+10h]  ;...41
                                                ;...8b
                                                ;...48
                                                ;...10

  0x000002ae309c3d40: shl     rcx,3h            ;...48
                                                ;...c1
                                                ;...e1
                                                ;...03
                                                ;*getfield target {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@6 (line 30)

  0x000002ae309c3d44: mov     esi,0h            ;...be
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d49: jmp     2ae309c3e27h      ;...e9
                                                ;...d9
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;*iload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@13 (line 31)

  0x000002ae309c3d4e: nop                       ;...66
                                                ;...90

  0x000002ae309c3d50: movsxd  rax,esi           ;...48
                                                ;...63
                                                ;...c6

  0x000002ae309c3d53: cmp     esi,dword ptr [rdx+0ch]  ;...3b
                                                ;...72
                                                ;...0c
                                                ; implicit exception: dispatches to 0x000002ae309c3ee7
  0x000002ae309c3d56: jnb     2ae309c3ef1h      ;...0f
                                                ;...83
                                                ;...95
                                                ;...01
                                                ;...00
                                                ;...00

  0x000002ae309c3d5c: vmovsd  xmm0,qword ptr [rdx+rax*8+10h]
                                                ;...c5
                                                ;...fb
                                                ;...10
                                                ;...44
                                                ;...c2
                                                ;...10
                                                ;*daload {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@26 (line 32)

  0x000002ae309c3d62: vxorpd  xmm1,xmm1,xmm1    ;...c5
                                                ;...f1
                                                ;...57
                                                ;...c9

  0x000002ae309c3d66: vucomisd xmm0,xmm1        ;...c5
                                                ;...f9
                                                ;...2e
                                                ;...c1

  0x000002ae309c3d6a: mov     eax,1h            ;...b8
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d6f: jp      2ae309c3d88h      ;...0f
                                                ;...8a
                                                ;...13
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d75: jnbe    2ae309c3d88h      ;...0f
                                                ;...87
                                                ;...0d
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d7b: mov     eax,0h            ;...b8
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d80: je      2ae309c3d88h      ;...0f
                                                ;...84
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d86: dec     eax               ;...ff
                                                ;...c8
                                                ;*dcmpg {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@28 (line 32)

  0x000002ae309c3d88: cmp     eax,0h            ;...83
                                                ;...f8
                                                ;...00

  0x000002ae309c3d8b: mov     rax,2ae4d163880h  ;...48
                                                ;...b8
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3d95: mov     rdi,158h          ;...48
                                                ;...bf
                                                ;...58
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3d9f: jnl     2ae309c3dafh      ;...0f
                                                ;...8d
                                                ;...0a
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3da5: mov     rdi,168h          ;...48
                                                ;...bf
                                                ;...68
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3daf: mov     rbx,qword ptr [rax+rdi]  ;...48
                                                ;...8b
                                                ;...1c
                                                ;...38

  0x000002ae309c3db3: lea     rbx,[rbx+1h]      ;...48
                                                ;...8d
                                                ;...5b
                                                ;...01

  0x000002ae309c3db7: mov     qword ptr [rax+rdi],rbx  ;...48
                                                ;...89
                                                ;...1c
                                                ;...38

  0x000002ae309c3dbb: jnl     2ae309c3dd5h      ;...0f
                                                ;...8d
                                                ;...14
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;*ifge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@29 (line 32)

  0x000002ae309c3dc1: mov     rax,2ae4d163880h  ;...48
                                                ;...b8
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3dcb: inc     dword ptr [rax+178h]  ;...ff
                                                ;...80
                                                ;...78
                                                ;...01
                                                ;...00
                                                ;...00

  0x000002ae309c3dd1: vxorpd  xmm0,xmm0,xmm0    ;...c5
                                                ;...f9
                                                ;...57
                                                ;...c0
                                                ;*goto {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@33 (line 32)

  0x000002ae309c3dd5: movsxd  rax,esi           ;...48
                                                ;...63
                                                ;...c6

  0x000002ae309c3dd8: cmp     esi,dword ptr [rcx+0ch]  ;...3b
                                                ;...71
                                                ;...0c

  0x000002ae309c3ddb: jnb     2ae309c3efah      ;...0f
                                                ;...83
                                                ;...19
                                                ;...01
                                                ;...00
                                                ;...00

  0x000002ae309c3de1: vmovsd  qword ptr [rcx+rax*8+10h],xmm0
                                                ;...c5
                                                ;...fb
                                                ;...11
                                                ;...44
                                                ;...c1
                                                ;...10
                                                ;*dastore {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@40 (line 32)

  0x000002ae309c3de7: inc     esi               ;...ff
                                                ;...c6

  0x000002ae309c3de9: mov     rax,2ae4d163880h  ;...48
                                                ;...b8
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3df3: mov     edi,dword ptr [rax+100h]
                                                ;...8b
                                                ;...b8
                                                ;...00
                                                ;...01
                                                ;...00
                                                ;...00

  0x000002ae309c3df9: add     edi,8h            ;...83
                                                ;...c7
                                                ;...08

  0x000002ae309c3dfc: mov     dword ptr [rax+100h],edi
                                                ;...89
                                                ;...b8
                                                ;...00
                                                ;...01
                                                ;...00
                                                ;...00

  0x000002ae309c3e02: and     edi,0fff8h        ;...81
                                                ;...e7
                                                ;...f8
                                                ;...ff
                                                ;...00
                                                ;...00

  0x000002ae309c3e08: cmp     edi,0h            ;...83
                                                ;...ff
                                                ;...00

  0x000002ae309c3e0b: je      2ae309c3f03h      ;...0f
                                                ;...84
                                                ;...f2
                                                ;...00
                                                ;...00
                                                ;...00
                                                ; ImmutableOopMap{rcx=Oop rdx=Oop }
                                                ;*goto {reexecute=1 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@44 (line 31)

  0x000002ae309c3e11: test    dword ptr [2ae24520000h],eax
                                                ;...85
                                                ;...05
                                                ;...e9
                                                ;...c1
                                                ;...b5
                                                ;...f3
                                                ;   {poll}
  0x000002ae309c3e17: mov     rax,2ae4d163880h  ;...48
                                                ;...b8
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3e21: inc     dword ptr [rax+190h]  ;...ff
                                                ;...80
                                                ;...90
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;*goto {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@44 (line 31)

  0x000002ae309c3e27: mov     eax,dword ptr [rcx+0ch]  ;...8b
                                                ;...41
                                                ;...0c
                                                ;*arraylength {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@16 (line 31)
                                                ; implicit exception: dispatches to 0x000002ae309c3f24
  0x000002ae309c3e2a: cmp     esi,eax           ;...3b
                                                ;...f0

  0x000002ae309c3e2c: mov     rax,2ae4d163880h  ;...48
                                                ;...b8
                                                ;...80
                                                ;...38
                                                ;...16
                                                ;...4d
                                                ;...ae
                                                ;...02
                                                ;...00
                                                ;...00
                                                ;   {metadata(method data for {method} {0x000002ae4d13ec70} 'BranchyNewArray' '(Lcom/openkappa/simd/positive/ArrayWithNegatives;)[D' in 'com/openkappa/simd/positive/PositiveValues')}
  0x000002ae309c3e36: mov     rdi,148h          ;...48
                                                ;...bf
                                                ;...48
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3e40: jl      2ae309c3e50h      ;...0f
                                                ;...8c
                                                ;...0a
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3e46: mov     rdi,138h          ;...48
                                                ;...bf
                                                ;...38
                                                ;...01
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00
                                                ;...00

  0x000002ae309c3e50: mov     rbx,qword ptr [rax+rdi]  ;...48
                                                ;...8b
                                                ;...1c
                                                ;...38

  0x000002ae309c3e54: lea     rbx,[rbx+1h]      ;...48
                                                ;...8d
                                                ;...5b
                                                ;...01

  0x000002ae309c3e58: mov     qword ptr [rax+rdi],rbx  ;...48
                                                ;...89
                                                ;...1c
                                                ;...38

  0x000002ae309c3e5c: jl      2ae309c3d50h      ;...0f
                                                ;...8c
                                                ;...ee
                                                ;...fe
                                                ;...ff
                                                ;...ff
                                                ;*if_icmpge {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@17 (line 31)

  0x000002ae309c3e62: mov     rax,rcx           ;...48
                                                ;...8b
                                                ;...c1

  0x000002ae309c3e65: add     rsp,60h           ;...48
                                                ;...83
                                                ;...c4
                                                ;...60

  0x000002ae309c3e69: pop     rbp               ;...5d

  0x000002ae309c3e6a: test    dword ptr [2ae24520000h],eax
                                                ;...85
                                                ;...05
                                                ;...90
                                                ;...c1
                                                ;...b5
                                                ;...f3
                                                ;   {poll_return}
  0x000002ae309c3e70: ret                       ;...c3
                                                ;*areturn {reexecute=0 rethrow=0 return_oop=0}
                                                ; - com.openkappa.simd.positive.PositiveValues::BranchyNewArray@48 (line 34)

I don’t really understand, and haven’t thought about, the intent of the emitted code, but it makes extensive use of the instruction VUCOMISD for comparisons with zero, which has a lower latency but lower throughput than VMAXPD. It would certainly be interesting to see how Project Panama does this. Perhaps this should just be made available as a fail-safe intrinsic like Arrays.mismatch?

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Project Panama and Population Count

Project Panama introduces a new interface Vector, where the specialisation for long looks like a promising substrate for an explicitly vectorised bit set. Bit sets are useful for representing composable predicates over data sets. One obvious omission on this interface, required for an adequate implementation of a bit set, is a bit count, otherwise known as population count. Perhaps this is because the vector API aims to generalise across primitive types, whereas population count is only meaningful for integral types. Even so, if Vector can be interpreted as a wider integer, then it would be consistent to add this to the interface. If the method existed, what possible implementation could it have?

In x86, the population count of a 64 bit register is computed by the POPCNT instruction, which is exposed in Java as an intrinsic in Long.bitCount. There is no SIMD equivalent in any extension set until VPOPCNTD/VPOPCNTQ in AVX-512. Very few processors (at the time of writing) support AVX-512, and only the Knights Mill processor supports this extension; there are not even Intel intrinsics exposing these instructions yet.

The algorithm for vectorised population count adopted by the clang compiler is outlined in this paper, which develops on an algorithm designed for 128 bit registers and SSE instructions, presented by Wojciech Muła on his blog in 2008. This approach is shown in the paper to outperform scalar code using POPCNT and 64 bit registers, almost doubling throughput when 256 bit ymm registers are available. The core algorithm (taken from figure 10 in the paper) returns a vector of four 64 bit counts, which can then be added together in a variety of ways to form a population count, proceeds as follows:


// The Muła Function
__m256i count(__m256i v) {
    __m256i lookup = _mm256_setr_epi8(
                 0, 1, 1, 2, 1, 2, 2, 3, 
                 1, 2, 2, 3, 2, 3, 3, 4,
                 0, 1, 1, 2, 1, 2, 2, 3,
                 1, 2, 2, 3, 2, 3, 3, 4);
    __m256i low_mask = _mm256_set1_epi8(0x0f);
    __m256i lo = _mm256_and_si256(v, low_mask);
    __m256i hi = _mm256_and_si256(_mm256_srli_epi32(v, 4), low_mask);
    __m256i popcnt1 = _mm256_shuffle_epi8(lookup, lo);
    __m256i popcnt2 = _mm256_shuffle_epi8(lookup, hi);
    __m256i total = _mm256_add_epi8(popcnt1, popcnt2);
    return _mm256_sad_epu8(total, _mm256_setzero_si256());
}

If you are struggling to read the code above, you are not alone. I haven’t programmed in C++ for several years – it’s amazing how nice the names in civilised languages like Java and python (and even bash) are compared to the black magic above. There is some logic to the naming though: read page 5 of the manual. You can also read an accessible description of some of the functions used in this blog post.

The basic idea starts from storing the population counts for each possible byte value in a lookup table, which can be looked up using bit level parallelism and ultimately added up. For efficiency’s sake, instead of bytes, 4 bit nibbles are used, which is why you only see numbers 0-4 in the lookup table. Various, occasionally obscure, optimisations are applied resulting in the magic numbers at the the top of the function. A large chunk of the paper is devoted to their derivation: if you are interested, go and read the paper – I could not understand the intent of the code at all until reading the paper twice, especially section 2.

The points I find interesting are:

  • This algorithm exists
  • It uses instructions all modern commodity processors have
  • It is fast
  • It is in use

Could this be implemented in the JVM as an intrinsic and exposed on Vector?

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