589 lines
16 KiB
C++
589 lines
16 KiB
C++
// Equihash solver
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// Copyright (c) 2013-2016 John Tromp
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// Fix N, K, such that n = N/(k+1) is integer
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// Fix M = 2^{n+1} hashes each of length N bits,
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// H_0, ... , H_{M-1}, generated fom (n+1)-bit indices.
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// Problem: find binary tree on 2^K distinct indices,
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// for which the exclusive-or of leaf hashes is all 0s.
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// Additionally, it should satisfy the Wagner conditions:
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// for each height i subtree, the exclusive-or
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// of its 2^i corresponding hashes starts with i*n 0 bits,
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// and for i>0 the leftmost leaf of its left subtree
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// is less than the leftmost leaf of its right subtree
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// The algorithm below solves this by maintaining the trees
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// in a graph of K layers, each split into buckets
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// with buckets indexed by the first n-RESTBITS bits following
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// the i*n 0s, each bucket having 4 * 2^RESTBITS slots,
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// twice the number of subtrees expected to land there.
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#include "equi.h"
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#include <stdio.h>
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#include <stdlib.h>
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#include <pthread.h>
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#include <assert.h>
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typedef uint64_t u64;
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#ifdef ATOMIC
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#include <atomic>
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typedef std::atomic<u32> au32;
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#else
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typedef u32 au32;
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#endif
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#ifndef RESTBITS
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#define RESTBITS 4
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#endif
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// 2_log of number of buckets
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#define BUCKBITS (DIGITBITS-RESTBITS)
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// number of buckets
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static const u32 NBUCKETS = 1<<BUCKBITS;
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// 2_log of number of slots per bucket
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static const u32 SLOTBITS = RESTBITS+1+1;
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// number of slots per bucket
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static const u32 NSLOTS = 1<<SLOTBITS;
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// number of per-xhash slots
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static const u32 XFULL = NSLOTS/4;
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// SLOTBITS mask
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static const u32 SLOTMASK = NSLOTS-1;
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// number of possible values of xhash (rest of n) bits
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static const u32 NRESTS = 1<<RESTBITS;
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// number of blocks of hashes extracted from single 512 bit blake2b output
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static const u32 NBLOCKS = (NHASHES+HASHESPERBLAKE-1)/HASHESPERBLAKE;
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// nothing larger found in 100000 runs
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static const u32 MAXSOLS = 8;
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// scaling factor for showing bucketsize histogra as sparkline
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#ifndef SPARKSCALE
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#define SPARKSCALE (40 << (BUCKBITS-12))
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#endif
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// tree node identifying its children as two different slots in
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// a bucket on previous layer with the same rest bits (x-tra hash)
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struct tree {
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unsigned bucketid : BUCKBITS;
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unsigned slotid0 : SLOTBITS;
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unsigned slotid1 : SLOTBITS;
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#ifndef XWITHASH
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unsigned xhash : RESTBITS;
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#endif
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// layer 0 has no children bit needs to encode index
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u32 getindex() const {
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return (bucketid << SLOTBITS) | slotid0;
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}
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void setindex(const u32 idx) {
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slotid0 = idx & SLOTMASK;
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bucketid = idx >> SLOTBITS;
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}
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};
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union htunit {
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tree attr;
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u32 hash;
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uchar bytes[sizeof(u32)];
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};
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// a bucket is NSLOTS treenodes
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typedef htunit bucket[NSLOTS];
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// the N-bit hash consists of K+1 n-bit "digits"
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// each of which corresponds to a layer of NBUCKETS buckets
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// size (in bytes) of hash in round 0 <= r < WK
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u32 hashsize(const u32 r) {
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#ifdef XWITHASH
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const u32 hashbits = WN - (r+1) * DIGITBITS + RESTBITS;
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#else
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const u32 hashbits = WN - (r+1) * DIGITBITS;
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#endif
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return (hashbits + 7) / 8;
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}
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u32 htunits(u32 bytes) {
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return (bytes + sizeof(htunit) - 1) / sizeof(htunit);
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}
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#ifdef JOINHT
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u32 slotsize(const u32 r) {
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return 1 + htunits(hashsize(r));
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}
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// size (in htunits) of bucket in round 0 <= r < WK
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u32 bucketsize(const u32 r) {
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return NSLOTS * slotsize(r);
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}
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#else
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u32 slotsize(const u32 r) {
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return 1;
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}
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#endif
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// manages hash and tree data
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struct htalloc {
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#ifdef JOINHT
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htunit *trees[WK];
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#else
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bucket *trees[WK];
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htunit *hashes[WK];
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#endif
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u64 alloced;
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htalloc() {
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alloced = 0;
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}
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void alloctrees() {
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#ifdef JOINHT
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for (int r=0; r<WK; r++)
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trees[r] = (htunit *)alloc(NBUCKETS * NSLOTS * (1 + htunits(hashsize(r))), sizeof(htunit));
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#endif
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}
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void dealloctrees() {
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#ifdef JOINHT
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for (int r=0; r<WK; r++)
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dealloc(trees[r], NBUCKETS * NSLOTS * (1 + htunits(hashsize(r))), sizeof(htunit));
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#else
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for (int r=0; r<WK; r++)
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dealloc(trees[r], NBUCKETS, sizeof(bucket));
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#endif
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}
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void alloc_ht(u32 r) {
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#ifndef JOINHT
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hashes[r] = (htunit *)alloc(NBUCKETS * NSLOTS * htunits(hashsize(r)), sizeof(htunit));
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trees[r] = (bucket *)alloc(NBUCKETS, sizeof(bucket));
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#endif
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}
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void dealloc_ht(u32 r) {
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#ifndef JOINHT
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dealloc(hashes[r], NBUCKETS * NSLOTS * htunits(hashsize(r)), sizeof(htunit));
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#endif
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}
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htunit *getbucket(u32 r, u32 bid) const {
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#ifdef JOINHT
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return &trees[r][bid * bucketsize(r)];
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#else
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return trees[r][bid];
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#endif
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}
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void *alloc(const u32 n, const u32 sz) {
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void *mem = calloc(n, sz);
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assert(mem);
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alloced += (u64)n * sz;
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return mem;
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}
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void dealloc(void *mem, const u32 n, const u32 sz) {
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free(mem);
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alloced -= (u64)n * sz;
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}
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};
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typedef au32 bsizes[NBUCKETS];
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u32 min(const u32 a, const u32 b) {
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return a < b ? a : b;
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}
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struct equi {
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blake2b_state blake_ctx;
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htalloc hta;
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bsizes *nslots;
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proof *sols;
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au32 nsols;
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u32 nthreads;
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u32 xfull;
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u32 hfull;
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u32 bfull;
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pthread_barrier_t barry;
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equi(const u32 n_threads) {
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nthreads = n_threads;
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const int err = pthread_barrier_init(&barry, NULL, nthreads);
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assert(!err);
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hta.alloctrees();
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nslots = (bsizes *)hta.alloc(2 * NBUCKETS, sizeof(au32));
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sols = (proof *)hta.alloc(MAXSOLS, sizeof(proof));
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}
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~equi() {
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free(nslots);
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free(sols);
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}
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void setnonce(const char *header, u32 nonce) {
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setheader(&blake_ctx, header, nonce);
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memset(nslots, 0, NBUCKETS * sizeof(au32)); // only nslots[0] needs zeroing
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nsols = 0;
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}
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u32 findslot(const u32 r, const u32 bucketi) {
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#ifdef ATOMIC
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return std::atomic_fetch_add_explicit(&nslots[r&1][bucketi], 1U, std::memory_order_relaxed);
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#else
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return nslots[r&1][bucketi]++;
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#endif
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}
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u32 getnslots(const u32 r, const u32 bid) {
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au32 &nslot = nslots[r&1][bid];
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const u32 n = min(nslot, NSLOTS);
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nslot = 0;
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return n;
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}
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void listindices(u32 r, const tree t, u32 *indices) {
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if (r == 0) {
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*indices = t.getindex();
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return;
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}
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const htunit *bt = hta.getbucket(--r,t.bucketid);
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const u32 size = 1 << r;
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u32 *indices1 = indices + size;
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listindices(r, bt[t.slotid0 * slotsize(r)].attr, indices);
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listindices(r, bt[t.slotid1 * slotsize(r)].attr, indices1);
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if (*indices > *indices1) {
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for (u32 i=0; i < size; i++) {
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const u32 tmp = indices[i];
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indices[i] = indices1[i];
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indices1[i] = tmp;
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}
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}
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}
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void candidate(const tree t) {
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proof prf;
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listindices(WK, t, prf);
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qsort(prf, PROOFSIZE, sizeof(u32), &compu32);
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for (u32 i=1; i<PROOFSIZE; i++)
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if (prf[i] <= prf[i-1])
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return;
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#ifdef ATOMIC
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u32 soli = std::atomic_fetch_add_explicit(&nsols, 1U, std::memory_order_relaxed);
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#else
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u32 soli = nsols++;
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#endif
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if (soli < MAXSOLS)
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listindices(WK, t, sols[soli]);
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}
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void showbsizes(u32 r) {
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#if defined(HIST) || defined(SPARK)
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u32 bsizes[NSLOTS+1];
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memset(bsizes, 0, (NSLOTS+1) * sizeof(u32));
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for (u32 bucketid = 0; bucketid < NBUCKETS; bucketid++) {
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u32 bsize = nslots[r&1][bucketid];
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if (bsize < NSLOTS)
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bsizes[bsize]++;
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else
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bsizes[NSLOTS]++;
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}
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for (u32 i=0; i<=NSLOTS; i++) {
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#ifdef HIST
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printf(" %d:%d", i, bsizes[i]);
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#else
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printf("\342\226%c", '\201'+bsizes[i]/SPARKSCALE);
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#endif
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}
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printf(" %ld MB\n", hta.alloced >> 20);
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#endif
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}
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struct htlayout {
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htalloc hta;
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u32 prevhtunits;
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u32 nexthtunits;
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u32 dunits;
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u32 prevbo;
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u32 nextbo;
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htunit *buck;
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htunit *hashbase;
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htlayout(equi *eq, u32 r): hta(eq->hta), prevhtunits(0), dunits(0) {
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u32 nexthashbytes = hashsize(r);
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nexthtunits = htunits(nexthashbytes);
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prevbo = 0;
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nextbo = nexthtunits * sizeof(htunit) - nexthashbytes; // 0-3
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if (r) {
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u32 prevhashbytes = hashsize(r-1);
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prevhtunits = htunits(prevhashbytes);
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prevbo = prevhtunits * sizeof(htunit) - prevhashbytes; // 0-3
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dunits = prevhtunits - nexthtunits;
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}
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#ifdef JOINHT
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nexthtunits++;
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prevhtunits++;
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#endif
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}
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void setbucket(u32 r, u32 bid) {
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buck = hta.getbucket(r, bid);
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#ifdef JOINHT
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hashbase = buck + 1;
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#else
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hashbase = hta.hashes[r] + (bid * NSLOTS) * prevhtunits;
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#endif
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}
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u32 getxhash(const u32 slot, const htunit *hash) const {
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#ifdef XWITHASH
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return hash->bytes[prevbo] & 0xf;
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#elif defined JOINHT
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return buck[slot * prevhtunits].attr.xhash;
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#else
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return buck[slot].attr.xhash;
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#endif
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}
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u32 prevhashunits() const {
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#ifdef JOINHT
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return prevhtunits - 1;
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#else
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return prevhtunits;
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#endif
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}
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bool equal(const htunit *hash0, const htunit *hash1) const {
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return hash0[prevhashunits()-1].hash == hash1[prevhashunits()-1].hash;
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}
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htunit *addtree(u32 r, tree t, u32 bid, u32 slot) {
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htunit *buck = hta.getbucket(r,bid);
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#ifdef JOINHT
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htunit *slotree = buck + slot * nexthtunits;
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slotree->attr = t;
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return slotree + 1;
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#else
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buck[slot].attr = t;
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return hta.hashes[r] + (bid * NSLOTS + slot) * nexthtunits;
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#endif
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}
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};
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struct collisiondata {
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#ifdef XBITMAP
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u64 xhashmap[NRESTS];
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u64 xmap;
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#else
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typedef uchar xslot;
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xslot nxhashslots[NRESTS];
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xslot xhashslots[NRESTS][XFULL];
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xslot *xx;
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u32 n0;
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u32 n1;
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#endif
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u32 s0;
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void clear() {
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#ifdef XBITMAP
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memset(xhashmap, 0, NRESTS * sizeof(u64));
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#else
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memset(nxhashslots, 0, NRESTS * sizeof(xslot));
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#endif
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}
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bool addslot(u32 s1, u32 xh) {
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#ifdef XBITMAP
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xmap = xhashmap[xh];
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xhashmap[xh] |= (u64)1 << s1;
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s0 = -1;
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return true;
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#else
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n1 = (u32)nxhashslots[xh]++;
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if (n1 >= XFULL)
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return false;
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xx = xhashslots[xh];
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xx[n1] = s1;
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n0 = 0;
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return true;
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#endif
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}
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bool nextcollision() const {
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#ifdef XBITMAP
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return xmap != 0;
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#else
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return n0 < n1;
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#endif
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}
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u32 slot() {
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#ifdef XBITMAP
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const u32 ffs = __builtin_ffsll(xmap);
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s0 += ffs; xmap >>= ffs;
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return s0;
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#else
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return (u32)xx[n0++];
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#endif
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}
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};
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void digit0(const u32 id) {
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uchar hash[HASHOUT];
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blake2b_state state;
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htlayout htl(this, 0);
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const u32 hashbytes = hashsize(0);
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for (u32 block = id; block < NBLOCKS; block += nthreads) {
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state = blake_ctx;
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const u32 leb = htole32(block);
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blake2b_update(&state, (uchar *)&leb, sizeof(u32));
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blake2b_final(&state, hash, HASHOUT);
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for (u32 i = 0; i<HASHESPERBLAKE; i++) {
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const uchar *ph = hash + i * WN/8;
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#if BUCKBITS == 16 && RESTBITS == 4
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const u32 bucketid = ((u32)ph[0] << 8) | ph[1];
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const u32 xhash = ph[2] >> 4;
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#elif BUCKBITS == 20 && RESTBITS == 4
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const u32 bucketid = ((((u32)ph[0] << 8) | ph[1]) << 4) | ph[2] >> 4;
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#ifndef XWITHASH
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const u32 xhash = ph[2] & 0xf;
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#endif
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#elif BUCKBITS == 12 && RESTBITS == 4
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const u32 bucketid = ((u32)ph[0] << 4) | ph[1] >> 4;
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const u32 xhash = ph[1] & 0xf;
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#else
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#error not implemented
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#endif
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const u32 slot = findslot(0, bucketid);
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if (slot >= NSLOTS) {
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bfull++;
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continue;
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}
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tree leaf;
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leaf.setindex(block*HASHESPERBLAKE+i);
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#ifndef XWITHASH
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leaf.xhash = xhash;
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#endif
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htunit *dest = htl.addtree(0, leaf, bucketid, slot);
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memcpy(dest->bytes+htl.nextbo, ph+WN/8-hashbytes, hashbytes);
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}
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}
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}
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void digitr(const u32 r, const u32 id) {
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htlayout htl(this, r);
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collisiondata cd;
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for (u32 bucketid=id; bucketid < NBUCKETS; bucketid += nthreads) {
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cd.clear();
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htl.setbucket(r-1, bucketid);
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u32 bsize = getnslots(r-1, bucketid);
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for (u32 s1 = 0; s1 < bsize; s1++) {
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const htunit *hash1 = htl.hashbase + s1 * htl.prevhtunits;
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if (!cd.addslot(s1, htl.getxhash(s1, hash1))) {
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xfull++;
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continue;
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}
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for (; cd.nextcollision(); ) {
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const u32 s0 = cd.slot();
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const htunit *hash0 = htl.hashbase + s0 * htl.prevhtunits;
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if (htl.equal(hash0, hash1)) {
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hfull++;
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continue;
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}
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u32 xorbucketid;
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u32 xhash;
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#if BUCKBITS == 16 && RESTBITS == 4
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xorbucketid = ((u32)(hash0->bytes[htl.prevbo]^hash1->bytes[htl.prevbo]) << 8)
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| (hash0->bytes[htl.prevbo+1]^hash1->bytes[htl.prevbo+1]);
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xhash = hash0->bytes[htl.prevbo+2] ^ hash1->bytes[htl.prevbo+2];
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if (r&1) {
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xorbucketid = ((xorbucketid & 0xfff) << 4) | (xhash >> 4);
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xhash &= 0xf;
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} else xhash >>= 4;
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#elif BUCKBITS == 20 && RESTBITS == 4 && defined XWITHASH
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xhash = hash0->bytes[htl.prevbo+3] ^ hash1->bytes[htl.prevbo+3];
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xorbucketid = ((((u32)(hash0->bytes[htl.prevbo+1]^hash1->bytes[htl.prevbo+1]) << 8) | (hash0->bytes[htl.prevbo+2]^hash1->bytes[htl.prevbo+2])) << 4) | xhash >> 4;
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xhash &= 0xf;
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#elif BUCKBITS == 12 && RESTBITS == 4
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xhash = hash0->bytes[htl.prevbo+1] ^ hash1->bytes[htl.prevbo+1];
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xorbucketid = ((u32)(hash0->bytes[htl.prevbo]^hash1->bytes[htl.prevbo]) << 4) | xhash >> 4;
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xhash &= 0xf;
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#else
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#error not implemented
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#endif
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const u32 xorslot = findslot(r, xorbucketid);
|
|
if (xorslot >= NSLOTS) {
|
|
bfull++;
|
|
continue;
|
|
}
|
|
tree xort; xort.bucketid = bucketid;
|
|
xort.slotid0 = s0; xort.slotid1 = s1;
|
|
#ifndef XWITHASH
|
|
xort.xhash = xhash;
|
|
#endif
|
|
htunit *xorhash = htl.addtree(r, xort, xorbucketid, xorslot);
|
|
for (u32 i=htl.dunits; i < htl.prevhashunits(); i++)
|
|
xorhash[i-htl.dunits].hash = hash0[i].hash ^ hash1[i].hash;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void digitK(const u32 id) {
|
|
collisiondata cd;
|
|
htlayout htl(this, WK);
|
|
for (u32 bucketid = id; bucketid < NBUCKETS; bucketid += nthreads) {
|
|
cd.clear();
|
|
htl.setbucket(WK-1, bucketid);
|
|
u32 bsize = getnslots(WK-1, bucketid);
|
|
for (u32 s1 = 0; s1 < bsize; s1++) {
|
|
const htunit *hash1 = htl.hashbase + s1 * htl.prevhtunits;
|
|
if (!cd.addslot(s1, htl.getxhash(s1, hash1)))
|
|
continue;
|
|
for (; cd.nextcollision(); ) {
|
|
const u32 s0 = cd.slot();
|
|
const htunit *hash0 = htl.hashbase + s0 * htl.prevhtunits;
|
|
if (htl.equal(hash0, hash1)) {
|
|
tree xort; xort.bucketid = bucketid;
|
|
xort.slotid0 = s0; xort.slotid1 = s1;
|
|
candidate(xort);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
};
|
|
|
|
typedef struct {
|
|
u32 id;
|
|
pthread_t thread;
|
|
equi *eq;
|
|
} thread_ctx;
|
|
|
|
void barrier(pthread_barrier_t *barry) {
|
|
const int rc = pthread_barrier_wait(barry);
|
|
if (rc != 0 && rc != PTHREAD_BARRIER_SERIAL_THREAD) {
|
|
printf("Could not wait on barrier\n");
|
|
pthread_exit(NULL);
|
|
}
|
|
}
|
|
|
|
|
|
void *worker(void *vp) {
|
|
thread_ctx *tp = (thread_ctx *)vp;
|
|
equi *eq = tp->eq;
|
|
|
|
if (tp->id == 0) {
|
|
printf("Digit 0\n");
|
|
eq->hta.alloc_ht(0);
|
|
}
|
|
barrier(&eq->barry);
|
|
eq->digit0(tp->id);
|
|
barrier(&eq->barry);
|
|
if (tp->id == 0) {
|
|
eq->xfull = eq->bfull = eq->hfull = 0;
|
|
eq->showbsizes(0);
|
|
}
|
|
barrier(&eq->barry);
|
|
for (u32 r = 1; r < WK; r++) {
|
|
if (tp->id == 0) {
|
|
printf("Digit %d", r);
|
|
eq->hta.alloc_ht(r);
|
|
}
|
|
barrier(&eq->barry);
|
|
eq->digitr(r, tp->id);
|
|
barrier(&eq->barry);
|
|
if (tp->id == 0) {
|
|
printf(" x%d b%d h%d\n", eq->xfull, eq->bfull, eq->hfull);
|
|
eq->xfull = eq->bfull = eq->hfull = 0;
|
|
eq->showbsizes(r);
|
|
eq->hta.dealloc_ht(r-1);
|
|
}
|
|
barrier(&eq->barry);
|
|
}
|
|
if (tp->id == 0)
|
|
printf("Digit %d\n", WK);
|
|
eq->digitK(tp->id);
|
|
barrier(&eq->barry);
|
|
if (tp->id == 0) {
|
|
eq->hta.dealloc_ht(WK-1);
|
|
eq->hta.dealloctrees();
|
|
}
|
|
pthread_exit(NULL);
|
|
return 0;
|
|
}
|