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PopulationCount.java
630 lines (502 loc) · 22.8 KB
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PopulationCount.java
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/*
* Copyright (c) 2018, 2021, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
package org.openjdk.bench.jdk.incubator.vector.operation;
import jdk.incubator.vector.*;
import org.openjdk.jmh.annotations.*;
import java.util.concurrent.TimeUnit;
/**
* Population count algorithms from "Faster Population Counts Using AVX2 Instructions", 2018 by Mula, Kurz, Lemire
*/
@BenchmarkMode(Mode.Throughput)
@Warmup(iterations = 3, time = 1)
@Measurement(iterations = 5, time = 1)
@OutputTimeUnit(TimeUnit.MILLISECONDS)
@State(Scope.Benchmark)
@Fork(value = 1, jvmArgsPrepend = {"--add-modules=jdk.incubator.vector"})
public class PopulationCount extends AbstractVectorBenchmark {
@Param({"64", "1024", "65536"})
int size;
private long[] data;
@Setup
public void init() {
data = fillLong(size, i -> RANDOM.nextLong());
// data = fillLong(size, i -> 0L);
// data = fillLong(size, i -> -1L);
checkConsistency();
}
@TearDown
public void tearDown() {
checkConsistency();
}
void checkConsistency() {
long popCount = longBitCount();
assert popCount == treeOfAdders();
assert popCount == WilkesWheelerGill();
assert popCount == Wegner();
assert popCount == Lauradoux();
assert popCount == HarleySeal();
assert popCount == Mula128();
assert popCount == Mula256();
assert popCount == HarleySeal256();
}
long tail(int upper) {
long acc = 0;
for (int i = upper; i < data.length; i++) {
acc += Long.bitCount(data[i]);
}
return acc;
}
@Benchmark
public long longBitCount() {
long acc = 0;
for (int i = 0; i < data.length; i++) {
acc += Long.bitCount(data[i]);
}
return acc;
}
/* ============================================================================================================== */
// FIGURE 4. The Wegner function in C
long popcntWegner(long x) {
int v = 0;
while (x != 0) {
x &= x - 1;
v++;
}
return v;
}
@Benchmark
public long Wegner() {
long acc = 0;
for (int i = 0; i < data.length; i++) {
acc += popcntWegner(data[i]);
}
return acc;
}
/* ============================================================================================================== */
// FIGURE 2. A naive tree-of-adders function in C
static long popcntTree(long x) {
long c1 = 0x5555555555555555L;
long c2 = 0x3333333333333333L;
long c4 = 0x0F0F0F0F0F0F0F0FL;
long c8 = 0x00FF00FF00FF00FFL;
long c16 = 0x0000FFFF0000FFFFL;
long c32 = 0x00000000FFFFFFFFL;
x = (x & c1) + ((x >>> 1) & c1);
x = (x & c2) + ((x >>> 2) & c2);
x = (x & c4) + ((x >>> 4) & c4);
x = (x & c8) + ((x >>> 8) & c8);
x = (x & c16) + ((x >>> 16) & c16);
x = (x & c32) + ((x >>> 32) & c32);
return x;
}
@Benchmark
public long treeOfAdders() {
long acc = 0;
for (int i = 0; i < data.length; i++) {
acc += popcntTree(data[i]);
}
return acc;
}
/* ============================================================================================================== */
// FIGURE 3. The Wilkes-Wheeler-Gill function in C
static long popcntWWG(long x) {
long c1 = 0x5555555555555555L;
long c2 = 0x3333333333333333L;
long c4 = 0x0F0F0F0F0F0F0F0FL;
x -= (x >>> 1) & c1;
x = (( x >>> 2) & c2) + (x & c2) ;
x = ( x + (x >>> 4) ) & c4;
x *= 0x0101010101010101L;
x = x >>> 56;
return x;
}
@Benchmark
public long WilkesWheelerGill() {
long acc = 0;
for (int i = 0; i < data.length; i++) {
acc += popcntWWG(data[i]);
}
return acc;
}
/* ============================================================================================================== */
// FIGURE 5. The Lauradoux population count in C for sets of 12 words.
static long parallelPopcnt(long count1, long count2, long count3) {
long m1 = 0x5555555555555555L;
long m2 = 0x3333333333333333L;
long m4 = 0x0F0F0F0F0F0F0F0FL;
long half1 = (count3 ) & m1;
long half2 = (count3 >>> 1) & m1;
count1 -= (count1 >>> 1) & m1;
count2 -= (count2 >>> 1) & m1;
count1 += half1;
count2 += half2;
count1 = (count1 & m2) + (( count1 >>> 2) & m2);
count1 += (count2 & m2) + (( count2 >>> 2) & m2);
return (count1 & m4) + (( count1 >>> 4) & m4);
}
static long reduce(long acc) {
long m8 = 0x00FF00FF00FF00FFL;
long m16 = 0x0000FFFF0000FFFFL;
long m32 = 0x00000000FFFFFFFFL;
acc = (acc & m8) + (( acc >>> 8) & m8);
acc = (acc + (acc >>> 16) ) & m16;
acc = (acc & m32) + (acc >>> 32);
return acc;
}
static long popcntLauradoux(long[] xs, int off) {
long acc = 0;
for (int j = off; j < off+12; j += 3) {
acc += parallelPopcnt(xs[j+0], xs[j+1], xs[j+2]);
}
return reduce(acc);
}
@Benchmark
public long Lauradoux() {
long acc = 0;
int upper = data.length - (data.length % 12);
for (int i = 0; i < upper; i += 12) {
acc += popcntLauradoux(data, i);
}
return acc + tail(upper);
}
/* ============================================================================================================== */
// FIGURE 6. A C function implementing a bitwise parallel carry-save adder (CSA). Given three input words a, b, c, it
// generates two new words h, l in which each bit represents the high and low bits in the bitwise sum of the bits from a,
// b, and c.
static long csaLow(long a, long b, long c) {
long u = a ^ b;
long lo = u ^ c;
return lo;
}
static long csaHigh(long a, long b, long c) {
long u = a ^ b;
long hi = (a & b) | (u & c) ;
return hi;
}
// FIGURE 8. A C function implementing the Harley-Seal
// population count over an array of 64-bit words. The count
// function could be the Wilkes-Wheeler-Gill function.
@Benchmark
public long HarleySeal() {
long total = 0, ones = 0, twos = 0, fours = 0, eights = 0, sixteens = 0;
long twosA = 0, twosB = 0;
long foursA = 0, foursB = 0;
long eightsA = 0, eightsB = 0;
int step = 16;
int upper = data.length - (data.length % step);
for (int i = 0; i < upper; i += step) {
// CSA(&twosA, &ones, ones, d[i+0], d[i +1]);
twosA = csaHigh(ones, data[i+0], data[i+1]);
ones = csaLow(ones, data[i+0], data[i+1]);
// CSA(&twosB, &ones, ones, d[i+2], d[i+3]);
twosB = csaHigh(ones, data[i+2], data[i+3]);
ones = csaLow(ones, data[i+2], data[i+3]);
// CSA(&foursA, &twos, twos, twosA, twosB);
foursA = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+4], d[i+5]);
twosA = csaHigh(ones, data[i+4], data[i+5]);
ones = csaLow(ones, data[i+4], data[i+5]);
// CSA(&twosB, &ones, ones, d[i+6], d[i+7]);
twosB = csaHigh(ones, data[i+6], data[i+7]);
ones = csaLow(ones, data[i+6], data[i+7]);
// CSA(&foursB, &twos, twos, twosA, twosB);
foursB = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&eightsA, &fours, fours, foursA, foursB);
eightsA = csaHigh(fours, foursA, foursB);
fours = csaLow(fours, foursA, foursB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+8], d[i+9]);
twosA = csaHigh(ones, data[i+8], data[i+9]);
ones = csaLow(ones, data[i+8], data[i+9]);
// CSA(&twosB, &ones, ones, d[i+10],d[i+11]);
twosB = csaHigh(ones, data[i+10], data[i+11]);
ones = csaLow(ones, data[i+10], data[i+11]);
// CSA(&foursA, &twos, twos, twosA, twosB);
foursA = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+12], d[i +13]);
twosA = csaHigh(ones, data[i+12], data[i+13]);
ones = csaLow(ones, data[i+12], data[i+13]);
// CSA(&twosB, &ones, ones, d[i+14], d[i +15]);
twosB = csaHigh(ones, data[i+14], data[i+15]);
ones = csaLow(ones, data[i+14], data[i+15]);
// ====================================
// CSA(&foursB, &twos, twos, twosA, twosB);
foursB = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// CSA(&eightsB, &fours, fours, foursA, foursB);
eightsB = csaHigh(fours, foursA, foursB);
fours = csaLow(fours, foursA, foursB);
// ====================================
// CSA(&sixteens, &eights, eights, eightsA, eightsB);
sixteens = csaHigh(eights, eightsA, eightsB);
eights = csaLow(eights, eightsA, eightsB);
total += Long.bitCount(sixteens);
}
total = 16 * total
+ 8 * Long.bitCount(eights)
+ 4 * Long.bitCount(fours)
+ 2 * Long.bitCount(twos)
+ 1 * Long.bitCount(ones);
return total + tail(upper);
}
/* ============================================================================================================== */
// FIGURE 9. A C function using SSE intrinsics implementing Mula's algorithm to compute sixteen population counts,
// corresponding to sixteen input bytes.
static final ByteVector MULA128_LOOKUP = IntVector.fromArray(I128,
new int[]{
0x02_01_01_00, // 0, 1, 1, 2,
0x03_02_02_01, // 1, 2, 2, 3,
0x03_02_02_01, // 1, 2, 2, 3,
0x04_03_03_02 // 2, 3, 3, 4
},
0
).reinterpretAsBytes();
ByteVector popcntB128(ByteVector v) {
var low_mask = ByteVector.broadcast(B128, (byte)0x0f);
var lo = v .and(low_mask);
var hi = v.lanewise(VectorOperators.LSHR, 4).and(low_mask);
var cnt1 = MULA128_LOOKUP.rearrange(lo.toShuffle());
var cnt2 = MULA128_LOOKUP.rearrange(hi.toShuffle());
return cnt1.add(cnt2);
}
@Benchmark
public long Mula128() {
var acc = LongVector.zero(L128); // IntVector
int step = 32; // % B128.length() == 0!
int upper = data.length - (data.length % step);
for (int i = 0; i < upper; i += step) {
var bacc = ByteVector.zero(B128);
for (int j = 0; j < step; j += L128.length()) {
var v1 = LongVector.fromArray(L128, data, i + j);
var v2 = v1.reinterpretAsBytes();
var v3 = popcntB128(v2);
bacc = bacc.add(v3);
}
acc = acc.add(sumUnsignedBytes(bacc));
}
var r = acc.reduceLanes(VectorOperators.ADD) + tail(upper);
return r;
}
/* ============================================================================================================== */
// FIGURE 10. A C function using AVX2 intrinsics implementing Mula's algorithm to compute the four population counts
// of the four 64-bit words in a 256-bit vector. The 32 B output vector should be interpreted as four separate
// 64-bit counts that need to be summed to obtain the final population count.
static final ByteVector MULA256_LOOKUP =
join(I128, I256, MULA128_LOOKUP.reinterpretAsInts(), MULA128_LOOKUP.reinterpretAsInts()).reinterpretAsBytes();
ByteVector popcntB256(ByteVector v) {
var low_mask = ByteVector.broadcast(B256, (byte)0x0F);
var lo = v .and(low_mask);
var hi = v.lanewise(VectorOperators.LSHR, 4).and(low_mask);
var cnt1 = MULA256_LOOKUP.rearrange(lo.toShuffle());
var cnt2 = MULA256_LOOKUP.rearrange(hi.toShuffle());
var cnt = cnt1.add(cnt2);
return cnt;
}
// Horizontally sum each consecutive 8 differences to produce four unsigned 16-bit integers,
// and pack these unsigned 16-bit integers in the low 16 bits of 64-bit elements in dst:
// _mm256_sad_epu8(total, _mm256_setzero_si256())
LongVector sumUnsignedBytes(ByteVector vb) {
return sumUnsignedBytesShapes(vb);
// return sumUnsignedBytesShifts(vb);
}
LongVector sumUnsignedBytesShapes(ByteVector vb) {
VectorSpecies<Short> shortSpecies = VectorSpecies.of(short.class, vb.shape());
VectorSpecies<Integer> intSpecies = VectorSpecies.of(int.class, vb.shape());
VectorSpecies<Long> longSpecies = VectorSpecies.of(long.class, vb.shape());
var low_short_mask = ShortVector.broadcast(shortSpecies, (short) 0xFF);
var low_int_mask = IntVector.broadcast(intSpecies, 0xFFFF);
var low_long_mask = LongVector.broadcast(longSpecies, 0xFFFFFFFFL);
var vs = vb.reinterpretAsShorts(); // 16-bit
var vs0 = vs.and(low_short_mask);
var vs1 = vs.lanewise(VectorOperators.LSHR, 8).and(low_short_mask);
var vs01 = vs0.add(vs1);
var vi = vs01.reinterpretAsInts(); // 32-bit
var vi0 = vi.and(low_int_mask);
var vi1 = vi.lanewise(VectorOperators.LSHR, 16).and(low_int_mask);
var vi01 = vi0.add(vi1);
var vl = vi01.reinterpretAsLongs(); // 64-bit
var vl0 = vl.and(low_long_mask);
var vl1 = vl.lanewise(VectorOperators.LSHR, 32).and(low_long_mask);
var vl01 = vl0.add(vl1);
return vl01;
}
LongVector sumUnsignedBytesShifts(ByteVector vb) {
VectorSpecies<Long> to = VectorSpecies.of(long.class, vb.shape());
var low_mask = LongVector.broadcast(to, 0xFF);
var vl = vb.reinterpretAsLongs();
var v0 = vl .and(low_mask); // 8-bit
var v1 = vl.lanewise(VectorOperators.LSHR, 8).and(low_mask); // 8-bit
var v2 = vl.lanewise(VectorOperators.LSHR, 16).and(low_mask); // 8-bit
var v3 = vl.lanewise(VectorOperators.LSHR, 24).and(low_mask); // 8-bit
var v4 = vl.lanewise(VectorOperators.LSHR, 32).and(low_mask); // 8-bit
var v5 = vl.lanewise(VectorOperators.LSHR, 40).and(low_mask); // 8-bit
var v6 = vl.lanewise(VectorOperators.LSHR, 48).and(low_mask); // 8-bit
var v7 = vl.lanewise(VectorOperators.LSHR, 56).and(low_mask); // 8-bit
var v01 = v0.add(v1);
var v23 = v2.add(v3);
var v45 = v4.add(v5);
var v67 = v6.add(v7);
var v03 = v01.add(v23);
var v47 = v45.add(v67);
var sum = v03.add(v47); // 64-bit
return sum;
}
@Benchmark
public long Mula256() {
var acc = LongVector.zero(L256);
int step = 32; // % B256.length() == 0!
int upper = data.length - (data.length % step);
for (int i = 0; i < upper; i += step) {
var bacc = ByteVector.zero(B256);
for (int j = 0; j < step; j += L256.length()) {
var v1 = LongVector.fromArray(L256, data, i + j);
var v2 = popcntB256(v1.reinterpretAsBytes());
bacc = bacc.add(v2);
}
acc = acc.add(sumUnsignedBytes(bacc));
}
return acc.reduceLanes(VectorOperators.ADD) + tail(upper);
}
/* ============================================================================================================== */
// FIGURE 11. A C function using AVX2 intrinsics implementing a bitwise parallel carry-save adder (CSA).
LongVector csaLow(LongVector a, LongVector b, LongVector c) {
var u = a.lanewise(VectorOperators.XOR, b);
var r = u.lanewise(VectorOperators.XOR, c);
return r;
}
LongVector csaHigh(LongVector a, LongVector b, LongVector c) {
var u = a.lanewise(VectorOperators.XOR, b);
var ab = a.and(b);
var uc = u.and(c);
var r = ab.or(uc); // (a & b) | ((a ^ b) & c)
return r;
}
LongVector popcntL256(LongVector v) {
var vb1 = v.reinterpretAsBytes();
var vb2 = popcntB256(vb1);
return sumUnsignedBytes(vb2);
}
// FIGURE 12. A C function using AVX2 intrinsics implementing Harley-Seal's algorithm. It assumes, for
// simplicity, that the input size in 256-bit vectors is divisible by 16. See Fig. 10 for the count function.
@Benchmark
public long HarleySeal256() {
LongVector ones, twos, fours, eights, sixteens, vtotal, twosA, twosB, foursA, foursB, eightsA, eightsB;
ones = twos = fours = eights = sixteens = twosA = twosB = foursA = foursB = eightsA = eights = vtotal = LongVector.broadcast(L256, 0);
var vlen = L256.length();
int step = 16 * vlen;
int upper = data.length - (data.length % step);
for (int i = 0; i < upper; i += step) {
// CSA(&twosA, &ones, ones, d[i+0], d[i +1]);
var d0 = LongVector.fromArray(L256, data, i + 0 * vlen);
var d1 = LongVector.fromArray(L256, data, i + 1 * vlen);
twosA = csaHigh(ones, d0, d1);
ones = csaLow(ones, d0, d1);
// CSA(&twosB, &ones, ones, d[i+2], d[i+3]);
var d2 = LongVector.fromArray(L256, data, i + 2 * vlen);
var d3 = LongVector.fromArray(L256, data, i + 3 * vlen);
twosB = csaHigh(ones, d2, d3);
ones = csaLow(ones, d2, d3);
// CSA(&foursA, &twos, twos, twosA, twosB);
foursA = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+4], d[i+5]);
var d4 = LongVector.fromArray(L256, data, i + 4 * vlen);
var d5 = LongVector.fromArray(L256, data, i + 5 * vlen);
twosA = csaHigh(ones, d4, d5);
ones = csaLow(ones, d4, d5);
// CSA(&twosB, &ones, ones, d[i+6], d[i+7]);
var d6 = LongVector.fromArray(L256, data, i + 6 * vlen);
var d7 = LongVector.fromArray(L256, data, i + 7 * vlen);
twosB = csaHigh(ones, d6, d7);
ones = csaLow(ones, d6, d7);
// CSA(&foursB, &twos, twos, twosA, twosB);
foursB = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&eightsA, &fours, fours, foursA, foursB);
eightsA = csaHigh(fours, foursA, foursB);
fours = csaLow(fours, foursA, foursB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+8], d[i+9]);
var d8 = LongVector.fromArray(L256, data, i + 8 * vlen);
var d9 = LongVector.fromArray(L256, data, i + 9 * vlen);
twosA = csaHigh(ones, d8, d9);
ones = csaLow(ones, d8, d9);
// CSA(&twosB, &ones, ones, d[i+10],d[i+11]);
var d10 = LongVector.fromArray(L256, data, i + 10 * vlen);
var d11 = LongVector.fromArray(L256, data, i + 11 * vlen);
twosB = csaHigh(ones, d10, d11);
ones = csaLow(ones, d10, d11);
// CSA(&foursA, &twos, twos, twosA, twosB);
foursA = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// ====================================
// CSA(&twosA, &ones, ones, d[i+12], d[i +13]);
var d12 = LongVector.fromArray(L256, data, i + 12 * vlen);
var d13 = LongVector.fromArray(L256, data, i + 13 * vlen);
twosA = csaHigh(ones, d12, d13);
ones = csaLow(ones, d12, d13);
// CSA(&twosB, &ones, ones, d[i+14], d[i +15]);
var d14 = LongVector.fromArray(L256, data, i + 14 * vlen);
var d15 = LongVector.fromArray(L256, data, i + 15 * vlen);
twosB = csaHigh(ones, d14, d15);
ones = csaLow(ones, d14, d15);
// ====================================
// CSA(&foursB, &twos, twos, twosA, twosB);
foursB = csaHigh(twos, twosA, twosB);
twos = csaLow(twos, twosA, twosB);
// CSA(&eightsB, &fours, fours, foursA, foursB);
eightsB = csaHigh(fours, foursA, foursB);
fours = csaLow(fours, foursA, foursB);
// ====================================
// CSA(&sixteens, &eights, eights, eightsA, eightsB);
sixteens = csaHigh(eights, eightsA, eightsB);
eights = csaLow(eights, eightsA, eightsB);
vtotal = vtotal.add(popcntL256(sixteens));
}
vtotal = vtotal.mul(16); // << 4
vtotal = vtotal.add(popcntL256(eights).mul(8)); // << 3
vtotal = vtotal.add(popcntL256(fours).mul(4)); // << 2
vtotal = vtotal.add(popcntL256(twos).mul(2)); // << 1
vtotal = vtotal.add(popcntL256(ones)); // << 0
var total = vtotal.reduceLanes(VectorOperators.ADD);
return total + tail(upper);
}
/* ============================================================================================================== */
// ByteVector csaLow512(ByteVector a, ByteVector b, ByteVector c) {
// return _mm512_ternarylogic_epi32(c, b, a, 0x96); // vpternlogd
// }
//
// ByteVector csaLow512(ByteVector a, ByteVector b, ByteVector c) {
// return _mm512_ternarylogic_epi32(c, b, a, 0xe8); // vpternlogd
// }
}