鐃緒申鐃緒申鐃初し鐃緒申鐃緒申

2009-07-04 - 鐃緒申鐃緒申C#鐃緒申.NET鐃淑居申録
鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申呂鐃緒申鐃緒申泙任砲鐃緒申董鐃緒申鐃緒申鐃緒申匹両匆鐃叔わ申鐃緒申Hacker's delight 鐃塾ワ申鐃緒申鐃宿わ申鐃�4鐃緒申5鐃緒申速鐃緒申鐃緒申鐃緒申鐃緒申鐃銃￥申鐃緒申鐃淳フ加醐申鐃緒申半端鐃緒申鐃緒申覆鐃緒申鐃緒申鐃緒申鐃緒申弔鐃� 64bit 鐃粛以駕申鐃塾わ申鐃駿てわ申鐃粛わ申鐃出縁申鐃叔わ申鐃殉わ申鐃緒申

鐃叔も、鐃渋際にどれく鐃初い鐃緒申鐃熟わ申鐃緒申鐃暑か鐃庶し鐃銃みわ申鐃緒申鐃獣わ申鐃塾わ申C鐃祝移随申鐃緒申鐃銃みわ申鐃緒申鐃春鰹申鐃淑件申未鐃緒申个討鐃緒申鐃殉わ申鐃緒申

0x03F566ED27179461ULL

鐃殉わ申鐃熟刻申鐃緒申僉鐃緒申鐃緒申鐃緒申鐃術っぽわ申鐃緒申鐃銃みまわ申鐃緒申鐃緒申

typedef unsigned long long U64;

#define HASH 0x03F566ED27179461ULL
static int ntzhash[64];

void init_ntzhash(){
    U64 h = HASH;
    int i;
    for (i = 0; i < 64; i++, h <<= 1) ntzhash[ h >> 58 ] = i;
}

int ntz_hash(U64 n){
    return n ? ntzhash[ (int)( ( ( n & -n ) * HASH ) >> 58) ] : 64;
}

鐃緒申鐃緒申鐃春ワ申

鐃叔わ申淵鐃緒申鐃緒申屬兵鐃緒申鐃緒申任鐃緒申諭鐃�O(n)

int ntz_shift(U64 n){
    int i;
    for (i = 0; i < 64; i++) if ( (n >> i) & 1 ) return i;
    return 64;
}

鐃緒申分探鐃緒申

Hacker's delight P. 85鐃祝出てわ申鐃殉わ申鐃緒申O(log n)鐃緒申64bit鐃塾常申鐃叔刻申8鐃緒申両鐃緒申分鐃緒申鐃夙わ申鐃緒申鐃緒申鐃夙になわ申泙鐃緒申鐃緒申鐃緒申鐃初算鐃述わ申箸辰鐃緒申鐃緒申鐃緒申鐃緒申笋刻申鐃緒申里任鐃緒申鐃緒申鐃緒申泙鐃緒申鐃緒申鐃�

int ntz_bsrch( U64 n ) {
    n &= -n;
    return n == 0 ? 64
    : n == 0x80000000ULL ? 31
    : (n <  0x80000000ULL ? n == 0x8000ULL ? 15
    /* 60鐃峻ほわ申鐃緒申略 */
               : (n <  0x4000000000000000ULL ? 61
              : 63))))));
}

鐃緒申鐃緒申覆劼鐃緒申鐃緒申匹鐃緒申鐃緒申鐃緒申鐃塾は種申能颪い討鐃緒申鐃緒申覆鐃緒申里如鐃緒申焚鐃緒申鐃�Perl Script鐃祝種申動鐃緒申鐃緒申鐃緒申鐃銃わ申蕕わ申泙鐃緒申鐃�(鐃緒申use64bitint)鐃緒申

sub foo{
    my ($head, $tail) = @_;
    my $mid = int(($head + $tail) / 2);
    return $mid if $head >= $tail;
    my $ret = sprintf "n == 0x%xULL ? %d\n", 2**$mid, $mid;
    $ret .= 
        sprintf ": (n <  0x%xULL ? %s\n: %s)", 2**$mid,
        foo($head, $mid-1),    foo($mid+1, $tail);
    $ret =~ s/\n+/\n/g;
    $ret;
}

print foo(0,63)

frexp

n & -n鐃叔￥申鐃緒申鐃緒申魅咼奪箸鐃緒申鐃塾�鐃銃わ申鐃緒申箸鐃緒申鐃緒申鐃緒申箸蓮鐃緒申鐃塾ベワ申鐃緒申砲鐃緒申任砲覆辰討鐃緒申鐃緒け鐃叔わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申匹鐃緒申鐃獣てビット随申鐃祝マップわ申鐃暑か鐃緒申鐃緒申鐃緒申鐃緒申僂里鐃緒申鐃緒申鐃緒申箸鐃緒申鐃緒申覆里任鐃緒申鐃緒申鐃緒申發�鐃緒申鐃緒申鐃緒申鐃緒申鐃淳のなわ申鐃緒申鐃緒申鐃緒申箸鐃緒申董鐃�frexp()鐃緒申箸鐃緒申箸鐃緒申鐃緒申鐃緒申鐃緒申鐃盾あ鐃緒申泙鐃緒申鐃�

#include <math.h>

int ntz_frexp(U64 n){
    int z;
    if ( n == 0 ) return 64;
    frexp( (double)( n & -n ), &z);
    return z - 1;
}

x86鐃緒申bsf命鐃緒申

鐃叔￥申x86鐃緒申bsf命鐃緒申鐃夙わ申鐃緒申鐃緒申鐃緒申任鐃緒申鐃緒申匹鐃�x86鐃叔わ申動鐃緒申鐃処う鐃緒申鐃緒申鐃緒申鐃叔わ申32bit鐃淑常申覆里鐃緒申櫃鐃緒申脳鐃緒申分鐃緒申鐃緒申鐃緒申鐃銃わ申鐃殉わ申鐃緒申

int ntz_bsf(U64 n){
    if (n == 0) return 64;
    unsigned int lo = n & 0xffffffff;
    int z;
    if (lo){
        __asm__("bsf %1, %0;" :"=r"(z) :"r"(lo));
    return z;
    }else{
        n >>= 32;
        __asm__("bsf %1, %0;" :"=r"(z) :"r"(n));
        return z + 32;
    }
}

鐃殉とわ申謄戰鐃緒申鐃殉￥申鐃緒申

鐃叔￥申鐃緒申鐃塾ｏ申鐃縦わ申泙箸鐃銃ベワ申鐃緒申沺鐃緒申鐃緒申鐃緒申討澆泙鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申坊鐃緒申鐃緒申屬鐃緒申鐃緒申鐃緒申鐃緒申蠅刻申鐃夙ベワ申鐃緒申沺鐃緒申鐃緒申鐃緒申鐃緒申鐃淑わ申鐃緒申丱謄鐃緒申箸砲覆鐃殉わ申鐃緒申Codepad鐃叔わ申動鐃緒申鐃殉わ申鐃緒申鐃緒申

http://codepad.org/9UXR2cOu 
#include <sys/time.h>

double time_hires(){
    struct timeval now;
    gettimeofday(&now, NULL);
    return now.tv_sec + now.tv_usec/1e6;
}

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>

#define D63 ((U64)1 << 63)

typedef struct { char *name; int (*func)(U64); } nfpair;

static nfpair ntz[] = {
    {"ntz_shift", ntz_shift },
    {"ntz_bsrch", ntz_bsrch },
    {"ntz_frexp", ntz_frexp },
    {"ntz_hash",  ntz_hash  },
    {"ntz_bsf",   ntz_bsf   }
};

int main (int argc, char **argv){
    U64 n;
    int i, j, count = 0;
    double timer;
    if (ntzhash[63] != 6) init_ntzhash();
    if (argc > 1){ /* benchmark */
        count = (int)strtod(argv[1], NULL);
        for (j = 0; j < 5; j++){
            timer = time_hires();
            for (i = 0; i < count; i++){
                assert(ntz[j].func(D63) == 63);
            }
            printf("%9s: %gs\n", ntz[j].name, time_hires() - timer);
        }
    }else{ /* test */
	printf("%d\n", ntz_bsrch(D63));
        for (j = 0; j < 5; j++){
            for (i = 0, n = 1 ; i <= 64; i++, n += n){
                assert(ntz[j].func(n) == i);
                printf("ok %d # %s(0x%016llx) = %d\n", 
                       ++count, ntz[j].name, n, ntz[j].func(n));
            }
        }
        printf("1..%d\n", count);
    }
    return 0;
}

鐃叔￥申鐃淑駕申鐃緒申鐃緒申未任鐃緒申鐃�

Core 2 Duo 2.4GHz, Mac OS X v10.5.7 
% gcc -W -Wall -O6 ntz.c && ./a.out 1e8
ntz_shift: 16.1367s
ntz_bsrch: 1.8118s
ntz_frexp: 2.79462s
 ntz_hash: 1.18244s
  ntz_bsf: 0.475164s
Dual Xeon 2.66GHz, FreeBSD 7.2 
% gcc -W -Wall -O6 ntz.c && ./a.out 1e8
ntz_shift: 25.2944s
ntz_bsrch: 1.65888s
ntz_frexp: 7.1559s
 ntz_hash: 1.50684s
  ntz_bsf: 0.905658s

鐃駿ワ申鐃緒申沺鐃緒申鐃緒申濃箸辰討鐃緒申鐃緒申鐃粛は￥申O(c)鐃叔なわ申鐃緒申鐃暑ゴ鐃所ズ鐃緒申悩念鐃緒申砲覆鐃処う鐃緒申1<<63鐃祝わ申鐃銃わ申鐃緒申泙鐃緒申鐃緒申鐃緒申討鐃緒申未蝓�鐃緒申分探鐃緒申鐃夙刻申鐃緒申僂虜鐃緒申鐃緒申奮鐃緒申判个討泙鐃緒申鐃�64bit鐃塾乗算鐃塾ワ申鐃緒申鐃夙わ申鐃淑わ申....

鐃緒申鐃殉わ申

Perl鐃塾逸申鐃緒申鐃熟削申鐃緒申箸鐃緒申鐃淑でわ申鐃順う鐃緒申鐃緒申0鐃塾常申鐃緒申鐃出縁申鐃緒申鐃銃わ申鐃殉わ申鐃緒申鐃緒申鐃緒申鐃熟削申粒鐃祝わ申鐃緒申直鐃緒申鐃緒申鐃緒申....

sub ntz{ length(sprintf("%064b", shift) =~ /(0+)$/ && $1) }

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