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convert_lyndon.c
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convert_lyndon.c
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#include"bch.h"
#include <stdio.h>
#include <assert.h>
#ifdef _OPENMP
#include <omp.h>
#endif
#ifdef __GNUC__
#define SIMD_VECTORIZED 1
// #define USE_SIMD_INTRINSICS 1
#endif
#include"khash.h"
KHASH_MAP_INIT_INT64(P_Dict, uint32_t) // instantiate structs and methods
typedef khash_t(P_Dict) PH;
typedef struct P_line_t {
uint32_t a11;
uint32_t a12;
uint32_t a21;
uint32_t a22;
} P_line_t;
typedef struct P_t {
P_line_t *L;
uint32_t len;
uint32_t maxlen;
uint8_t n;
uint8_t K;
void *H;
} P_t;
static P_t *P_init(uint8_t K, uint8_t n, uint32_t len) {
P_t *P = malloc(sizeof(P_t));
P->H = kh_init(P_Dict); // allocate hash table
P->n = n;
P->K = K;
if (len<K*n) {
len = K*n;
}
P->L = malloc(sizeof(P_line_t)*len);
P->maxlen = len;
khint_t k;
int l=0;
for (int i=0; i<K; i++) {
for (int j=0; j<n; j++) {
P->L[l].a11 = 0;
P->L[l].a12 = 0;
P->L[l].a21 = 0;
P->L[l].a22 = 0;
uint64_t key = (((uint64_t) i)<< 8) | j;
int absent;
k = kh_put(P_Dict, (PH*) P->H, key, &absent); // insert a key to the hash table
kh_val((PH*) P->H, k) = l;
l++;
}
}
P->len = l;
return P;
}
static void P_free(P_t *P) {
free(P->L);
kh_destroy(P_Dict, (PH*) P->H); // deallocate hash table
free(P);
}
static uint32_t P_append(P_t *P, uint32_t i, uint8_t l, uint32_t *p1, uint32_t *p2, uint8_t* nn) {
uint64_t key = (((uint64_t) i)<< 8) | l;
khint_t k = kh_get(P_Dict, (PH*) P->H, key); // query the hash table
if (k == kh_end((PH*) P->H)) { // test if the key is missing
if (nn[i]>1) {
uint32_t a11 = P_append(P, p1[i], l, p1, p2, nn);
uint32_t a12 = P_append(P, p1[i], l+nn[p2[i]], p1, p2, nn);
uint32_t a21 = P_append(P, p2[i], l, p1, p2, nn);
uint32_t a22 = P_append(P, p2[i], l+nn[p1[i]], p1, p2, nn);
if (P->len>=P->maxlen) {
P->maxlen *= 2;
P->L = realloc(P->L, sizeof(P_line_t)*P->maxlen);
}
P->L[P->len].a11 = a11;
P->L[P->len].a12 = a12;
P->L[P->len].a21 = a21;
P->L[P->len].a22 = a22;
}
int absent;
k = kh_put(P_Dict, (PH*) P->H, key, &absent); // insert a key to the hash table
kh_val((PH*) P->H, k) = P->len;
P->len++;
return (P->len-1);
}
else {
return kh_val((PH*) P->H, k);
}
}
#ifndef SIMD_VECTORIZED
static void P_run(int32_t *X, P_t *P, uint8_t w[], uint32_t stop) {
if (stop>=P->len) {
stop = P->len-1;
}
P_line_t *L = P->L;
for (int k=0; k<P->K; k++) {
for (int i=0; i<P->n; i++) {
X[k*P->n+i] = w[i]==k ? 1 : 0;
}
}
for (int p=P->K*P->n; p<=stop; p++) {
X[p] = X[L[p].a11]*X[L[p].a22] - X[L[p].a12]*X[L[p].a21];
}
}
#endif
#ifdef SIMD_VECTORIZED
#ifdef USE_SIMD_INTRINSICS
#include <smmintrin.h>
#endif
typedef int32_t v4int32_t __attribute__ ((vector_size(16), aligned(16)));
static void P_run_4(v4int32_t* X0, P_t *P, uint8_t w0[], uint8_t w1[], uint8_t w2[], uint8_t w3[], uint32_t stop) {
v4int32_t *X = __builtin_assume_aligned (X0, 16);
if (stop>=P->len) {
stop = P->len-1;
}
P_line_t *L = P->L;
for (int k=0; k<P->K; k++) {
for (int i=0; i<P->n; i++) {
X[k*P->n+i][0] = w0[i]==k ? 1 : 0;
X[k*P->n+i][1] = w1[i]==k ? 1 : 0;
X[k*P->n+i][2] = w2[i]==k ? 1 : 0;
X[k*P->n+i][3] = w3[i]==k ? 1 : 0;
}
}
#ifndef USE_SIMD_INTRINSICS
for (int p=P->K*P->n; p<=stop; p++) {
X[p] = X[L[p].a11]*X[L[p].a22] - X[L[p].a12]*X[L[p].a21];
}
#else
for (int p=P->K*P->n; p<=stop; p++) {
__m128i x11 = _mm_load_si128( (__m128i*) X + L[p].a11 );
__m128i x12 = _mm_load_si128( (__m128i*) X + L[p].a12 );
__m128i x21 = _mm_load_si128( (__m128i*) X + L[p].a21 );
__m128i x22 = _mm_load_si128( (__m128i*) X + L[p].a22 );
__m128i x11x22 = _mm_mullo_epi32(x11, x22);
__m128i x12x21 = _mm_mullo_epi32(x12, x21);
__m128i y = _mm_sub_epi32(x11x22, x12x21);
_mm_store_si128( (__m128i*) X +p, y);
}
#endif
}
#endif
void convert_to_lie_series(lie_series_t *LS, int N) {
if (get_verbosity_level()>=2) {
#ifdef _OPENMP
printf("# degree #basis time thread\n");
#else
printf("# degree #basis time\n");
#endif
}
double t0 = tic();
size_t i1 = LS->ii[N-1];
size_t i2 = LS->ii[N]-1;
uint32_t *DI = multi_degree_indices( LS->K, LS->dim, LS->W, LS->nn);
size_t h1 = DI[i1];
size_t h2 = DI[i2];
double h_time[h2-h1+1];
double h_time1[h2-h1+1];
double h_time2[h2-h1+1];
int h_n[h2-h1+1];
#ifdef _OPENMP
int h_thread[h2-h1+1];
#endif
#pragma omp parallel
{
int *jj = calloc(LS->dim, sizeof(int)); // LS->dim far too large upper bound
size_t JW[N];
size_t JB[N];
/* Note: We choose schedule(dynamic, 1) because each
* iteration of the loop is associated with a specific
* multi degree index, and the work to be done varies widely
* for different multi degree indices.
*/
#pragma omp for schedule(dynamic,1)
for (int h=h1; h<=h2; h++) { /* over all multi-degrees */
int k = h-h1;
h_time[k] = tic();
h_n[k] = 0;
#ifdef _OPENMP
h_thread[k] = omp_get_thread_num();
#endif
int jj_max = 0;
for (int i=i1; i<=i2; i++) {
if (DI[i]==h) {
jj[jj_max] = i;
jj_max++;
}
}
P_t *P = P_init(LS->K, N, 2*jj_max);
uint32_t *r = malloc(jj_max*sizeof(uint32_t));
for (int y=0; y<jj_max; y++) {
int j = jj[y];
size_t kB = get_right_factors(j, JB, N, LS->p1, LS->p2);
r[y] = P_append(P, JB[kB], kB, LS->p1, LS->p2, LS->nn);
}
#ifdef SIMD_VECTORIZED
h_time1[k] = tic();
v4int32_t *X = aligned_alloc(16, (P->len)*sizeof(v4int32_t));
h_time1[k] = toc(h_time1[k]);
h_time2[k] = tic();
int stop = 0;
for (int x=0; x<jj_max; x+=4) {
int i[4];
for (int s=0; s<4; s++) {
i[s] = x+s<jj_max ? jj[x+s] : jj[jj_max-1];
stop = (x+s < jj_max) && (r[x+s] > stop) ? r[x+s] : stop;
}
h_n[k]++; // TODO: adapt this to vectorized version
P_run_4(X, P, LS->W[i[0]], LS->W[i[1]], LS->W[i[2]], LS->W[i[3]], stop);
for (int s=0; s<4 && x+s<jj_max; s++) {
size_t kW = get_right_factors(i[s], JW, N, LS->p1, LS->p2);
int lA = 0; for (;LS->W[i[s]][lA]==0; lA++);
for (int y=0; y<=x+s-1; y++) {
int j = jj[y];
size_t kB = get_right_factors(j, JB, N, LS->p1, LS->p2);
if (lA>=kB) {
int d = X[r[y]][s];
if (d!=0) {
for (int k=0; k<=kB && k<=kW; k++) {
LS->c[JW[k]] -= d*LS->c[JB[k]];
}
}
}
}
}
}
h_time2[k] = toc(h_time2[k]);
#else
h_time1[k] = tic();
int32_t *X = malloc((P->len)*sizeof(int32_t));
h_time1[k] = toc(h_time1[k]);
h_time2[k] = tic();
int stop = 0;
for (int x=0; x<jj_max; x++) {
int i = jj[x];
stop = r[x] > stop ? r[x] : stop;
h_n[k]++;
size_t kW = get_right_factors(i, JW, N, LS->p1, LS->p2);
uint8_t *w = LS->W[i];
P_run(X, P, w, stop);
int lA = 0;
for (;w[lA]==0; lA++) ;
for (int y=0; y<=x-1; y++) {
int j = jj[y];
size_t kB = get_right_factors(j, JB, N, LS->p1, LS->p2);
if (lA>=kB) {
int d = X[r[y]];
if (d!=0) {
for (int k=0; k<=kB && k<=kW; k++) {
LS->c[JW[k]] -= d*LS->c[JB[k]];
}
}
}
}
}
h_time2[k] = toc(h_time2[k]);
#endif
free(r);
int len = P->len;
P_free(P);
free(X);
LS->R = 0;
h_time[k] = toc(h_time[k]);
if (get_verbosity_level()>=2) {
#ifdef _OPENMP
printf("#%7i %10i %11.2f %11.2f %11.2f %10i %4i\n", k+1, h_n[k], h_time1[k], h_time2[k], h_time[k], len, h_thread[k]);
#else
printf("#%7i %10i %11.2f\n", k+1, h_n[k], h_time[k]);
#endif
fflush(stdout);
}
}
free(jj);
}
free(DI);
if (get_verbosity_level()>=1) {
double t1 = toc(t0);
printf("#convert to Lie series: time=%g sec\n", t1);
if (get_verbosity_level()>=2) {
fflush(stdout);
}
}
}
/* tables beta_num[] and beta_den[]: numerators and denominators of
the coefficients of the power series of the function f(x)=tanh(x/2),
i.e., beta[] = { 1/2,
-1/24,
1/240,
-17/40320,
31/725760,
-691/159667200,
5461/12454041600,
-929569/20922789888000,
3202291/711374856192000,
-221930581/486580401635328000,
4722116521/102181884343418880000,
-56963745931/12165654935945871360000,
14717667114151/31022420086661971968000000,
-2093660879252671/43555477801673408643072000000,
86125672563201181/17683523987479403909087232000000,
-129848163681107301953/263130836933693530167218012160000000}
This data was computed with the following Julia code:
n=16
A = zeros(Rational{BigInt}, 2*n+1)
B = similar(A)
for k = 0:2*n
A[k+1] = 1//(k+1)
for j = k:-1:1
A[j] = j*(A[j] - A[j+1])
end
B[k+1] = A[1]
end
beta = [2*(2^(2*k)-1)*B[2*k+1]/factorial(BigInt(2*k)) for k=1:n]
*/
static const INTEGER H = 1000000000000000000;
/* beta_num, beta_den not static because also needed in convert_rightnormed.c */
INTEGER beta_num[16] = {1, -1, 1, -17, 31, -691, 5461, -929569, 3202291, -221930581, 4722116521,
-56963745931, 14717667114151, -2093660879252671, 86125672563201181, -129*H-848163681107301953};
INTEGER beta_den[16] = {2, 24, 240, 40320, 725760, 159667200, 12454041600, 20922789888000,
711374856192000, 486580401635328000, 102*H+181884343418880000, 12165*H+654935945871360000,
31022420*H+86661971968000000, 43555477801*H+673408643072000000, 17683523987479*H+403909087232000000,
263130836933693530*H+167218012160000000};
void compute_BCH_terms_of_even_degree_N(lie_series_t *LS) {
double t0 = tic();
assert(!(LS->N&1));
#pragma omp parallel for schedule(dynamic,256)
for (int i=LS->ii[LS->N-1]; i<=LS->ii[LS->N]-1; i++) {
LS->c[i] = 0;
int k = 0;
int l = 0;
int q = i;
while (LS->p1[q]==0) {
k += 1;
q = LS->p2[q];
if (k&1) {
INTEGER d = LS->c[q]/beta_den[l];
if (d*beta_den[l]!=LS->c[q]) {
fprintf(stderr, "PANIC: divisibility check failed in compute_BCH_terms_of_degree_N");
abort();
}
LS->c[i] += beta_num[l]*d;
l += 1;
}
}
}
if (get_verbosity_level()>=1) {
double t1 = toc(t0);
printf("#compute terms of degree %i: time=%g sec\n", LS->N, t1);
if (get_verbosity_level()>=2) {
fflush(stdout);
}
}
}